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<a class="dropdown-item" href="../../articles/prebuilt/2022_dmta_parent.html">Testing hierarchical parent degradation kinetics with residue data on dimethenamid and dimethenamid-P</a>
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<a class="dropdown-item" href="../../articles/web_only/dimethenamid_2018.html">Comparison of saemix and nlme evaluations of dimethenamid data from 2018</a>
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<img src="" class="logo" alt=""><h1>Benchmark timings for saem.mmkin</h1>
<h4 data-toc-skip class="author">Johannes
Ranke</h4>
<h4 data-toc-skip class="date">Last change 17 February 2023
(rebuilt 2023-11-16)</h4>
<small class="dont-index">Source: <a href="https://github.com/jranke/mkin/blob/HEAD/vignettes/web_only/saem_benchmarks.rmd" class="external-link"><code>vignettes/web_only/saem_benchmarks.rmd</code></a></small>
<div class="d-none name"><code>saem_benchmarks.rmd</code></div>
</div>
<p>Each system is characterized by operating system type, CPU type, mkin
version, saemix version and R version. A compiler was available, so if
no analytical solution was available, compiled ODE models are used.</p>
<p>Every fit is only performed once, so the accuracy of the benchmarks
is limited.</p>
<p>For the initial mmkin fits, we use all available cores.</p>
<div class="sourceCode" id="cb1"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="va">n_cores</span> <span class="op"><-</span> <span class="fu">parallel</span><span class="fu">::</span><span class="fu"><a href="https://rdrr.io/r/parallel/detectCores.html" class="external-link">detectCores</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div>
<div class="section level2">
<h2 id="test-data">Test data<a class="anchor" aria-label="anchor" href="#test-data"></a>
</h2>
<p>Please refer to the vignette <code>dimethenamid_2018</code> for an
explanation of the following preprocessing.</p>
<div class="sourceCode" id="cb2"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="va">dmta_ds</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/lapply.html" class="external-link">lapply</a></span><span class="op">(</span><span class="fl">1</span><span class="op">:</span><span class="fl">7</span>, <span class="kw">function</span><span class="op">(</span><span class="va">i</span><span class="op">)</span> <span class="op">{</span></span>
<span> <span class="va">ds_i</span> <span class="op"><-</span> <span class="va">dimethenamid_2018</span><span class="op">$</span><span class="va">ds</span><span class="op">[[</span><span class="va">i</span><span class="op">]</span><span class="op">]</span><span class="op">$</span><span class="va">data</span></span>
<span> <span class="va">ds_i</span><span class="op">[</span><span class="va">ds_i</span><span class="op">$</span><span class="va">name</span> <span class="op">==</span> <span class="st">"DMTAP"</span>, <span class="st">"name"</span><span class="op">]</span> <span class="op"><-</span> <span class="st">"DMTA"</span></span>
<span> <span class="va">ds_i</span><span class="op">$</span><span class="va">time</span> <span class="op"><-</span> <span class="va">ds_i</span><span class="op">$</span><span class="va">time</span> <span class="op">*</span> <span class="va">dimethenamid_2018</span><span class="op">$</span><span class="va">f_time_norm</span><span class="op">[</span><span class="va">i</span><span class="op">]</span></span>
<span> <span class="va">ds_i</span></span>
<span><span class="op">}</span><span class="op">)</span></span>
<span><span class="fu"><a href="https://rdrr.io/r/base/names.html" class="external-link">names</a></span><span class="op">(</span><span class="va">dmta_ds</span><span class="op">)</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/lapply.html" class="external-link">sapply</a></span><span class="op">(</span><span class="va">dimethenamid_2018</span><span class="op">$</span><span class="va">ds</span>, <span class="kw">function</span><span class="op">(</span><span class="va">ds</span><span class="op">)</span> <span class="va">ds</span><span class="op">$</span><span class="va">title</span><span class="op">)</span></span>
<span><span class="va">dmta_ds</span><span class="op">[[</span><span class="st">"Elliot"</span><span class="op">]</span><span class="op">]</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/cbind.html" class="external-link">rbind</a></span><span class="op">(</span><span class="va">dmta_ds</span><span class="op">[[</span><span class="st">"Elliot 1"</span><span class="op">]</span><span class="op">]</span>, <span class="va">dmta_ds</span><span class="op">[[</span><span class="st">"Elliot 2"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></span>
<span><span class="va">dmta_ds</span><span class="op">[[</span><span class="st">"Elliot 1"</span><span class="op">]</span><span class="op">]</span> <span class="op"><-</span> <span class="cn">NULL</span></span>
<span><span class="va">dmta_ds</span><span class="op">[[</span><span class="st">"Elliot 2"</span><span class="op">]</span><span class="op">]</span> <span class="op"><-</span> <span class="cn">NULL</span></span></code></pre></div>
</div>
<div class="section level2">
<h2 id="test-cases">Test cases<a class="anchor" aria-label="anchor" href="#test-cases"></a>
</h2>
<div class="section level3">
<h3 id="parent-only">Parent only<a class="anchor" aria-label="anchor" href="#parent-only"></a>
</h3>
<div class="sourceCode" id="cb3"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="va">parent_mods</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"DFOP"</span>, <span class="st">"SFORB"</span>, <span class="st">"HS"</span><span class="op">)</span></span>
<span><span class="va">parent_sep_const</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mmkin.html">mmkin</a></span><span class="op">(</span><span class="va">parent_mods</span>, <span class="va">dmta_ds</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span>, cores <span class="op">=</span> <span class="va">n_cores</span><span class="op">)</span></span>
<span><span class="va">parent_sep_tc</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/stats/update.html" class="external-link">update</a></span><span class="op">(</span><span class="va">parent_sep_const</span>, error_model <span class="op">=</span> <span class="st">"tc"</span><span class="op">)</span></span>
<span></span>
<span><span class="va">t1</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.time.html" class="external-link">system.time</a></span><span class="op">(</span><span class="va">sfo_const</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/saem.html">saem</a></span><span class="op">(</span><span class="va">parent_sep_const</span><span class="op">[</span><span class="st">"SFO"</span>, <span class="op">]</span><span class="op">)</span><span class="op">)</span><span class="op">[[</span><span class="st">"elapsed"</span><span class="op">]</span><span class="op">]</span></span>
<span><span class="va">t2</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.time.html" class="external-link">system.time</a></span><span class="op">(</span><span class="va">dfop_const</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/saem.html">saem</a></span><span class="op">(</span><span class="va">parent_sep_const</span><span class="op">[</span><span class="st">"DFOP"</span>, <span class="op">]</span><span class="op">)</span><span class="op">)</span><span class="op">[[</span><span class="st">"elapsed"</span><span class="op">]</span><span class="op">]</span></span>
<span><span class="va">t3</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.time.html" class="external-link">system.time</a></span><span class="op">(</span><span class="va">sforb_const</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/saem.html">saem</a></span><span class="op">(</span><span class="va">parent_sep_const</span><span class="op">[</span><span class="st">"SFORB"</span>, <span class="op">]</span><span class="op">)</span><span class="op">)</span><span class="op">[[</span><span class="st">"elapsed"</span><span class="op">]</span><span class="op">]</span></span>
<span><span class="va">t4</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.time.html" class="external-link">system.time</a></span><span class="op">(</span><span class="va">hs_const</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/saem.html">saem</a></span><span class="op">(</span><span class="va">parent_sep_const</span><span class="op">[</span><span class="st">"HS"</span>, <span class="op">]</span><span class="op">)</span><span class="op">)</span><span class="op">[[</span><span class="st">"elapsed"</span><span class="op">]</span><span class="op">]</span></span>
<span><span class="va">t5</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.time.html" class="external-link">system.time</a></span><span class="op">(</span><span class="va">sfo_tc</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/saem.html">saem</a></span><span class="op">(</span><span class="va">parent_sep_tc</span><span class="op">[</span><span class="st">"SFO"</span>, <span class="op">]</span><span class="op">)</span><span class="op">)</span><span class="op">[[</span><span class="st">"elapsed"</span><span class="op">]</span><span class="op">]</span></span>
<span><span class="va">t6</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.time.html" class="external-link">system.time</a></span><span class="op">(</span><span class="va">dfop_tc</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/saem.html">saem</a></span><span class="op">(</span><span class="va">parent_sep_tc</span><span class="op">[</span><span class="st">"DFOP"</span>, <span class="op">]</span><span class="op">)</span><span class="op">)</span><span class="op">[[</span><span class="st">"elapsed"</span><span class="op">]</span><span class="op">]</span></span>
<span><span class="va">t7</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.time.html" class="external-link">system.time</a></span><span class="op">(</span><span class="va">sforb_tc</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/saem.html">saem</a></span><span class="op">(</span><span class="va">parent_sep_tc</span><span class="op">[</span><span class="st">"SFORB"</span>, <span class="op">]</span><span class="op">)</span><span class="op">)</span><span class="op">[[</span><span class="st">"elapsed"</span><span class="op">]</span><span class="op">]</span></span>
<span><span class="va">t8</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.time.html" class="external-link">system.time</a></span><span class="op">(</span><span class="va">hs_tc</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/saem.html">saem</a></span><span class="op">(</span><span class="va">parent_sep_tc</span><span class="op">[</span><span class="st">"HS"</span>, <span class="op">]</span><span class="op">)</span><span class="op">)</span><span class="op">[[</span><span class="st">"elapsed"</span><span class="op">]</span><span class="op">]</span></span></code></pre></div>
<div class="sourceCode" id="cb4"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/stats/anova.html" class="external-link">anova</a></span><span class="op">(</span></span>
<span> <span class="va">sfo_const</span>, <span class="va">dfop_const</span>, <span class="va">sforb_const</span>, <span class="va">hs_const</span>,</span>
<span> <span class="va">sfo_tc</span>, <span class="va">dfop_tc</span>, <span class="va">sforb_tc</span>, <span class="va">hs_tc</span><span class="op">)</span> <span class="op">|></span> <span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span>, digits <span class="op">=</span> <span class="fl">1</span><span class="op">)</span></span></code></pre></div>
<table class="table">
<thead><tr class="header">
<th align="left"></th>
<th align="right">npar</th>
<th align="right">AIC</th>
<th align="right">BIC</th>
<th align="right">Lik</th>
</tr></thead>
<tbody>
<tr class="odd">
<td align="left">sfo_const</td>
<td align="right">5</td>
<td align="right">796.3</td>
<td align="right">795.3</td>
<td align="right">-393.2</td>
</tr>
<tr class="even">
<td align="left">sfo_tc</td>
<td align="right">6</td>
<td align="right">798.3</td>
<td align="right">797.1</td>
<td align="right">-393.2</td>
</tr>
<tr class="odd">
<td align="left">dfop_const</td>
<td align="right">9</td>
<td align="right">709.4</td>
<td align="right">707.5</td>
<td align="right">-345.7</td>
</tr>
<tr class="even">
<td align="left">sforb_const</td>
<td align="right">9</td>
<td align="right">710.0</td>
<td align="right">708.1</td>
<td align="right">-346.0</td>
</tr>
<tr class="odd">
<td align="left">hs_const</td>
<td align="right">9</td>
<td align="right">713.7</td>
<td align="right">711.8</td>
<td align="right">-347.8</td>
</tr>
<tr class="even">
<td align="left">dfop_tc</td>
<td align="right">10</td>
<td align="right">670.1</td>
<td align="right">668.0</td>
<td align="right">-325.0</td>
</tr>
<tr class="odd">
<td align="left">sforb_tc</td>
<td align="right">10</td>
<td align="right">662.9</td>
<td align="right">660.8</td>
<td align="right">-321.4</td>
</tr>
<tr class="even">
<td align="left">hs_tc</td>
<td align="right">10</td>
<td align="right">667.2</td>
<td align="right">665.1</td>
<td align="right">-323.6</td>
</tr>
</tbody>
</table>
<p>The above model comparison suggests to use the SFORB model with
two-component error. For comparison, we keep the DFOP model with
two-component error, as it competes with SFORB for biphasic curves.</p>
<div class="sourceCode" id="cb5"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="fu"><a href="../../reference/illparms.html">illparms</a></span><span class="op">(</span><span class="va">dfop_tc</span><span class="op">)</span></span></code></pre></div>
<pre><code><span><span class="co">## [1] "sd(log_k2)"</span></span></code></pre>
<div class="sourceCode" id="cb7"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="fu"><a href="../../reference/illparms.html">illparms</a></span><span class="op">(</span><span class="va">sforb_tc</span><span class="op">)</span></span></code></pre></div>
<pre><code><span><span class="co">## [1] "sd(log_k_DMTA_bound_free)"</span></span></code></pre>
<p>For these two models, random effects for the transformed parameters
<code>k2</code> and <code>k_DMTA_bound_free</code> could not be
quantified.</p>
</div>
<div class="section level3">
<h3 id="one-metabolite">One metabolite<a class="anchor" aria-label="anchor" href="#one-metabolite"></a>
</h3>
<p>We remove parameters that were found to be ill-defined in the parent
only fits.</p>
<div class="sourceCode" id="cb9"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="va">one_met_mods</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span></span>
<span> DFOP_SFO <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span></span>
<span> DMTA <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"DFOP"</span>, <span class="st">"M23"</span><span class="op">)</span>,</span>
<span> M23 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span><span class="op">)</span>,</span>
<span> SFORB_SFO <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span></span>
<span> DMTA <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFORB"</span>, <span class="st">"M23"</span><span class="op">)</span>,</span>
<span> M23 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span><span class="op">)</span><span class="op">)</span></span>
<span></span>
<span><span class="va">one_met_sep_const</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mmkin.html">mmkin</a></span><span class="op">(</span><span class="va">one_met_mods</span>, <span class="va">dmta_ds</span>, error_model <span class="op">=</span> <span class="st">"const"</span>,</span>
<span> cores <span class="op">=</span> <span class="va">n_cores</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span>
<span><span class="va">one_met_sep_tc</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mmkin.html">mmkin</a></span><span class="op">(</span><span class="va">one_met_mods</span>, <span class="va">dmta_ds</span>, error_model <span class="op">=</span> <span class="st">"tc"</span>,</span>
<span> cores <span class="op">=</span> <span class="va">n_cores</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span>
<span></span>
<span><span class="va">t9</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.time.html" class="external-link">system.time</a></span><span class="op">(</span><span class="va">dfop_sfo_tc</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/saem.html">saem</a></span><span class="op">(</span><span class="va">one_met_sep_tc</span><span class="op">[</span><span class="st">"DFOP_SFO"</span>, <span class="op">]</span>,</span>
<span> no_random_effect <span class="op">=</span> <span class="st">"log_k2"</span><span class="op">)</span><span class="op">)</span><span class="op">[[</span><span class="st">"elapsed"</span><span class="op">]</span><span class="op">]</span></span>
<span><span class="va">t10</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.time.html" class="external-link">system.time</a></span><span class="op">(</span><span class="va">sforb_sfo_tc</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/saem.html">saem</a></span><span class="op">(</span><span class="va">one_met_sep_tc</span><span class="op">[</span><span class="st">"SFORB_SFO"</span>, <span class="op">]</span>,</span>
<span> no_random_effect <span class="op">=</span> <span class="st">"log_k_DMTA_bound_free"</span><span class="op">)</span><span class="op">)</span><span class="op">[[</span><span class="st">"elapsed"</span><span class="op">]</span><span class="op">]</span></span></code></pre></div>
</div>
<div class="section level3">
<h3 id="three-metabolites">Three metabolites<a class="anchor" aria-label="anchor" href="#three-metabolites"></a>
</h3>
<p>For the case of three metabolites, we only keep the SFORB model in
order to limit the time for compiling this vignette, and as fitting in
parallel may disturb the benchmark. Again, we do not include random
effects that were ill-defined in previous fits of subsets of the
degradation model.</p>
<div class="sourceCode" id="cb10"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="fu"><a href="../../reference/illparms.html">illparms</a></span><span class="op">(</span><span class="va">sforb_sfo_tc</span><span class="op">)</span></span></code></pre></div>
<div class="sourceCode" id="cb11"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="va">three_met_mods</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span></span>
<span> SFORB_SFO3_plus <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span></span>
<span> DMTA <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFORB"</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"M23"</span>, <span class="st">"M27"</span>, <span class="st">"M31"</span><span class="op">)</span><span class="op">)</span>,</span>
<span> M23 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span>,</span>
<span> M27 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span>,</span>
<span> M31 <span class="op">=</span> <span class="fu"><a href="../../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"M27"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span><span class="op">)</span><span class="op">)</span></span>
<span></span>
<span><span class="va">three_met_sep_tc</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/mmkin.html">mmkin</a></span><span class="op">(</span><span class="va">three_met_mods</span>, <span class="va">dmta_ds</span>, error_model <span class="op">=</span> <span class="st">"tc"</span>,</span>
<span> cores <span class="op">=</span> <span class="va">n_cores</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span>
<span></span>
<span><span class="va">t11</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/system.time.html" class="external-link">system.time</a></span><span class="op">(</span><span class="va">sforb_sfo3_plus_const</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/saem.html">saem</a></span><span class="op">(</span><span class="va">three_met_sep_tc</span><span class="op">[</span><span class="st">"SFORB_SFO3_plus"</span>, <span class="op">]</span>,</span>
<span> no_random_effect <span class="op">=</span> <span class="st">"log_k_DMTA_bound_free"</span><span class="op">)</span><span class="op">)</span><span class="op">[[</span><span class="st">"elapsed"</span><span class="op">]</span><span class="op">]</span></span></code></pre></div>
</div>
</div>
<div class="section level2">
<h2 id="results">Results<a class="anchor" aria-label="anchor" href="#results"></a>
</h2>
<p>Benchmarks for all available error models are shown. They are
intended for improving mkin, not for comparing CPUs or operating
systems. All trademarks belong to their respective owners.</p>
<div class="section level3">
<h3 id="parent-only-1">Parent only<a class="anchor" aria-label="anchor" href="#parent-only-1"></a>
</h3>
<p>Constant variance for SFO, DFOP, SFORB and HS.</p>
<table style="width:100%;" class="table">
<colgroup>
<col width="48%">
<col width="7%">
<col width="7%">
<col width="8%">
<col width="7%">
<col width="7%">
<col width="7%">
<col width="7%">
</colgroup>
<thead><tr class="header">
<th align="left">CPU</th>
<th align="left">OS</th>
<th align="left">mkin</th>
<th align="left">saemix</th>
<th align="right">t1</th>
<th align="right">t2</th>
<th align="right">t3</th>
<th align="right">t4</th>
</tr></thead>
<tbody>
<tr class="odd">
<td align="left">Ryzen 7 1700</td>
<td align="left">Linux</td>
<td align="left">1.2.0</td>
<td align="left">3.2</td>
<td align="right">2.140</td>
<td align="right">4.626</td>
<td align="right">4.328</td>
<td align="right">4.998</td>
</tr>
<tr class="even">
<td align="left">Ryzen 7 1700</td>
<td align="left">Linux</td>
<td align="left">1.2.2</td>
<td align="left">3.2</td>
<td align="right">2.427</td>
<td align="right">4.550</td>
<td align="right">4.217</td>
<td align="right">4.851</td>
</tr>
<tr class="odd">
<td align="left">Ryzen 9 7950X</td>
<td align="left">Linux</td>
<td align="left">1.2.1</td>
<td align="left">3.2</td>
<td align="right">1.352</td>
<td align="right">2.813</td>
<td align="right">2.401</td>
<td align="right">2.074</td>
</tr>
<tr class="even">
<td align="left">Ryzen 9 7950X</td>
<td align="left">Linux</td>
<td align="left">1.2.2</td>
<td align="left">3.2</td>
<td align="right">1.328</td>
<td align="right">2.738</td>
<td align="right">2.336</td>
<td align="right">2.023</td>
</tr>
<tr class="odd">
<td align="left">Ryzen 9 7950X</td>
<td align="left">Linux</td>
<td align="left">1.2.3</td>
<td align="left">3.2</td>
<td align="right">1.118</td>
<td align="right">2.036</td>
<td align="right">2.010</td>
<td align="right">2.088</td>
</tr>
<tr class="even">
<td align="left">Ryzen 9 7950X</td>
<td align="left">Linux</td>
<td align="left">1.2.3</td>
<td align="left">3.2</td>
<td align="right">1.419</td>
<td align="right">2.374</td>
<td align="right">1.926</td>
<td align="right">2.398</td>
</tr>
<tr class="odd">
<td align="left">Ryzen 9 7950X</td>
<td align="left">Linux</td>
<td align="left">1.2.4</td>
<td align="left">3.2</td>
<td align="right">0.972</td>
<td align="right">2.550</td>
<td align="right">1.987</td>
<td align="right">2.055</td>
</tr>
<tr class="even">
<td align="left">Intel(R) Xeon(R) Gold 6134 CPU @ 3.20GHz</td>
<td align="left">Linux</td>
<td align="left">1.2.6</td>
<td align="left">3.2</td>
<td align="right">2.998</td>
<td align="right">6.523</td>
<td align="right">6.126</td>
<td align="right">4.721</td>
</tr>
<tr class="odd">
<td align="left">Ryzen 9 7950X</td>
<td align="left">Linux</td>
<td align="left">1.2.6</td>
<td align="left">3.2</td>
<td align="right">1.135</td>
<td align="right">2.025</td>
<td align="right">2.406</td>
<td align="right">2.478</td>
</tr>
</tbody>
</table>
<p>Two-component error fits for SFO, DFOP, SFORB and HS.</p>
<table style="width:100%;" class="table">
<colgroup>
<col width="48%">
<col width="7%">
<col width="7%">
<col width="8%">
<col width="7%">
<col width="7%">
<col width="7%">
<col width="7%">
</colgroup>
<thead><tr class="header">
<th align="left">CPU</th>
<th align="left">OS</th>
<th align="left">mkin</th>
<th align="left">saemix</th>
<th align="right">t5</th>
<th align="right">t6</th>
<th align="right">t7</th>
<th align="right">t8</th>
</tr></thead>
<tbody>
<tr class="odd">
<td align="left">Ryzen 7 1700</td>
<td align="left">Linux</td>
<td align="left">1.2.0</td>
<td align="left">3.2</td>
<td align="right">5.678</td>
<td align="right">7.441</td>
<td align="right">8.000</td>
<td align="right">7.980</td>
</tr>
<tr class="even">
<td align="left">Ryzen 7 1700</td>
<td align="left">Linux</td>
<td align="left">1.2.2</td>
<td align="left">3.2</td>
<td align="right">5.352</td>
<td align="right">7.201</td>
<td align="right">8.174</td>
<td align="right">8.401</td>
</tr>
<tr class="odd">
<td align="left">Ryzen 9 7950X</td>
<td align="left">Linux</td>
<td align="left">1.2.1</td>
<td align="left">3.2</td>
<td align="right">2.388</td>
<td align="right">3.033</td>
<td align="right">3.532</td>
<td align="right">3.310</td>
</tr>
<tr class="even">
<td align="left">Ryzen 9 7950X</td>
<td align="left">Linux</td>
<td align="left">1.2.2</td>
<td align="left">3.2</td>
<td align="right">2.341</td>
<td align="right">2.968</td>
<td align="right">3.465</td>
<td align="right">3.341</td>
</tr>
<tr class="odd">
<td align="left">Ryzen 9 7950X</td>
<td align="left">Linux</td>
<td align="left">1.2.3</td>
<td align="left">3.2</td>
<td align="right">2.159</td>
<td align="right">3.584</td>
<td align="right">3.307</td>
<td align="right">3.460</td>
</tr>
<tr class="even">
<td align="left">Ryzen 9 7950X</td>
<td align="left">Linux</td>
<td align="left">1.2.3</td>
<td align="left">3.2</td>
<td align="right">2.348</td>
<td align="right">3.134</td>
<td align="right">3.253</td>
<td align="right">3.530</td>
</tr>
<tr class="odd">
<td align="left">Ryzen 9 7950X</td>
<td align="left">Linux</td>
<td align="left">1.2.4</td>
<td align="left">3.2</td>
<td align="right">2.127</td>
<td align="right">3.587</td>
<td align="right">3.433</td>
<td align="right">3.595</td>
</tr>
<tr class="even">
<td align="left">Intel(R) Xeon(R) Gold 6134 CPU @ 3.20GHz</td>
<td align="left">Linux</td>
<td align="left">1.2.6</td>
<td align="left">3.2</td>
<td align="right">5.070</td>
<td align="right">8.464</td>
<td align="right">8.525</td>
<td align="right">7.599</td>
</tr>
<tr class="odd">
<td align="left">Ryzen 9 7950X</td>
<td align="left">Linux</td>
<td align="left">1.2.6</td>
<td align="left">3.2</td>
<td align="right">2.161</td>
<td align="right">3.325</td>
<td align="right">3.669</td>
<td align="right">3.153</td>
</tr>
</tbody>
</table>
</div>
<div class="section level3">
<h3 id="one-metabolite-1">One metabolite<a class="anchor" aria-label="anchor" href="#one-metabolite-1"></a>
</h3>
<p>Two-component error for DFOP-SFO and SFORB-SFO.</p>
<table class="table">
<colgroup>
<col width="54%">
<col width="8%">
<col width="8%">
<col width="9%">
<col width="9%">
<col width="10%">
</colgroup>
<thead><tr class="header">
<th align="left">CPU</th>
<th align="left">OS</th>
<th align="left">mkin</th>
<th align="left">saemix</th>
<th align="right">t9</th>
<th align="right">t10</th>
</tr></thead>
<tbody>
<tr class="odd">
<td align="left">Ryzen 7 1700</td>
<td align="left">Linux</td>
<td align="left">1.2.0</td>
<td align="left">3.2</td>
<td align="right">24.465</td>
<td align="right">800.266</td>
</tr>
<tr class="even">
<td align="left">Ryzen 7 1700</td>
<td align="left">Linux</td>
<td align="left">1.2.2</td>
<td align="left">3.2</td>
<td align="right">25.193</td>
<td align="right">798.580</td>
</tr>
<tr class="odd">
<td align="left">Ryzen 9 7950X</td>
<td align="left">Linux</td>
<td align="left">1.2.1</td>
<td align="left">3.2</td>
<td align="right">11.247</td>
<td align="right">285.216</td>
</tr>
<tr class="even">
<td align="left">Ryzen 9 7950X</td>
<td align="left">Linux</td>
<td align="left">1.2.2</td>
<td align="left">3.2</td>
<td align="right">11.242</td>
<td align="right">284.258</td>
</tr>
<tr class="odd">
<td align="left">Ryzen 9 7950X</td>
<td align="left">Linux</td>
<td align="left">1.2.3</td>
<td align="left">3.2</td>
<td align="right">11.796</td>
<td align="right">216.012</td>
</tr>
<tr class="even">
<td align="left">Ryzen 9 7950X</td>
<td align="left">Linux</td>
<td align="left">1.2.3</td>
<td align="left">3.2</td>
<td align="right">12.841</td>
<td align="right">292.688</td>
</tr>
<tr class="odd">
<td align="left">Ryzen 9 7950X</td>
<td align="left">Linux</td>
<td align="left">1.2.4</td>
<td align="left">3.2</td>
<td align="right">12.160</td>
<td align="right">265.934</td>
</tr>
<tr class="even">
<td align="left">Intel(R) Xeon(R) Gold 6134 CPU @ 3.20GHz</td>
<td align="left">Linux</td>
<td align="left">1.2.6</td>
<td align="left">3.2</td>
<td align="right">30.168</td>
<td align="right">748.675</td>
</tr>
<tr class="odd">
<td align="left">Ryzen 9 7950X</td>
<td align="left">Linux</td>
<td align="left">1.2.6</td>
<td align="left">3.2</td>
<td align="right">12.007</td>
<td align="right">286.757</td>
</tr>
</tbody>
</table>
</div>
<div class="section level3">
<h3 id="three-metabolites-1">Three metabolites<a class="anchor" aria-label="anchor" href="#three-metabolites-1"></a>
</h3>
<p>Two-component error for SFORB-SFO3-plus</p>
<table style="width:100%;" class="table">
<colgroup>
<col width="59%">
<col width="8%">
<col width="8%">
<col width="10%">
<col width="13%">
</colgroup>
<thead><tr class="header">
<th align="left">CPU</th>
<th align="left">OS</th>
<th align="left">mkin</th>
<th align="left">saemix</th>
<th align="right">t11</th>
</tr></thead>
<tbody>
<tr class="odd">
<td align="left">Ryzen 7 1700</td>
<td align="left">Linux</td>
<td align="left">1.2.0</td>
<td align="left">3.2</td>
<td align="right">1289.198</td>
</tr>
<tr class="even">
<td align="left">Ryzen 7 1700</td>
<td align="left">Linux</td>
<td align="left">1.2.2</td>
<td align="left">3.2</td>
<td align="right">1312.445</td>
</tr>
<tr class="odd">
<td align="left">Ryzen 9 7950X</td>
<td align="left">Linux</td>
<td align="left">1.2.1</td>
<td align="left">3.2</td>
<td align="right">489.939</td>
</tr>
<tr class="even">
<td align="left">Ryzen 9 7950X</td>
<td align="left">Linux</td>
<td align="left">1.2.2</td>
<td align="left">3.2</td>
<td align="right">482.970</td>
</tr>
<tr class="odd">
<td align="left">Ryzen 9 7950X</td>
<td align="left">Linux</td>
<td align="left">1.2.3</td>
<td align="left">3.2</td>
<td align="right">392.364</td>
</tr>
<tr class="even">
<td align="left">Ryzen 9 7950X</td>
<td align="left">Linux</td>
<td align="left">1.2.3</td>
<td align="left">3.2</td>
<td align="right">483.027</td>
</tr>
<tr class="odd">
<td align="left">Ryzen 9 7950X</td>
<td align="left">Linux</td>
<td align="left">1.2.4</td>
<td align="left">3.2</td>
<td align="right">456.252</td>
</tr>
<tr class="even">
<td align="left">Intel(R) Xeon(R) Gold 6134 CPU @ 3.20GHz</td>
<td align="left">Linux</td>
<td align="left">1.2.6</td>
<td align="left">3.2</td>
<td align="right">1235.028</td>
</tr>
<tr class="odd">
<td align="left">Ryzen 9 7950X</td>
<td align="left">Linux</td>
<td align="left">1.2.6</td>
<td align="left">3.2</td>
<td align="right">480.577</td>
</tr>
</tbody>
</table>
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