\[-1 \lt \varepsilon \land \varepsilon \lt 1\]

\[\frac{\varepsilon \cdot \left(e^{\left(a + b\right) \cdot \varepsilon} - 1\right)}{\left(e^{a \cdot \varepsilon} - 1\right) \cdot \left(e^{b \cdot \varepsilon} - 1\right)}\]

↓

\[\begin{array}{l} \mathbf{if}\;a \le -173005857.2304000556468963623046875 \lor \neg \left(a \le 100503816208437458162455618952188928196600\right):\\ \;\;\;\;\frac{\varepsilon \cdot \sqrt[3]{{\left({\left(e^{a + b}\right)}^{\varepsilon} - 1\right)}^{3}}}{\left({\left(e^{a}\right)}^{\varepsilon} - 1\right) \cdot \mathsf{fma}\left(b, \varepsilon, {b}^{2} \cdot \left(\frac{1}{2} \cdot {\varepsilon}^{2} + \left(\frac{1}{6} \cdot {\varepsilon}^{3}\right) \cdot b\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\varepsilon \cdot \left(e^{\left(a + b\right) \cdot \varepsilon} - 1\right)}{\mathsf{fma}\left(a, \varepsilon, {\varepsilon}^{2} \cdot \left(\frac{1}{2} \cdot {a}^{2} + \left(\frac{1}{6} \cdot {a}^{3}\right) \cdot \varepsilon\right)\right) \cdot \left(e^{b \cdot \varepsilon} - 1\right)}\\ \end{array}\]

\frac{\varepsilon \cdot \left(e^{\left(a + b\right) \cdot \varepsilon} - 1\right)}{\left(e^{a \cdot \varepsilon} - 1\right) \cdot \left(e^{b \cdot \varepsilon} - 1\right)}

↓

\begin{array}{l}
\mathbf{if}\;a \le -173005857.2304000556468963623046875 \lor \neg \left(a \le 100503816208437458162455618952188928196600\right):\\
\;\;\;\;\frac{\varepsilon \cdot \sqrt[3]{{\left({\left(e^{a + b}\right)}^{\varepsilon} - 1\right)}^{3}}}{\left({\left(e^{a}\right)}^{\varepsilon} - 1\right) \cdot \mathsf{fma}\left(b, \varepsilon, {b}^{2} \cdot \left(\frac{1}{2} \cdot {\varepsilon}^{2} + \left(\frac{1}{6} \cdot {\varepsilon}^{3}\right) \cdot b\right)\right)}\\

\mathbf{else}:\\
\;\;\;\;\frac{\varepsilon \cdot \left(e^{\left(a + b\right) \cdot \varepsilon} - 1\right)}{\mathsf{fma}\left(a, \varepsilon, {\varepsilon}^{2} \cdot \left(\frac{1}{2} \cdot {a}^{2} + \left(\frac{1}{6} \cdot {a}^{3}\right) \cdot \varepsilon\right)\right) \cdot \left(e^{b \cdot \varepsilon} - 1\right)}\\

\end{array}

double f(double a, double b, double eps) {
        double r145326 = eps;
        double r145327 = a;
        double r145328 = b;
        double r145329 = r145327 + r145328;
        double r145330 = r145329 * r145326;
        double r145331 = exp(r145330);
        double r145332 = 1.0;
        double r145333 = r145331 - r145332;
        double r145334 = r145326 * r145333;
        double r145335 = r145327 * r145326;
        double r145336 = exp(r145335);
        double r145337 = r145336 - r145332;
        double r145338 = r145328 * r145326;
        double r145339 = exp(r145338);
        double r145340 = r145339 - r145332;
        double r145341 = r145337 * r145340;
        double r145342 = r145334 / r145341;
        return r145342;
}

↓

double f(double a, double b, double eps) {
        double r145343 = a;
        double r145344 = -173005857.23040006;
        bool r145345 = r145343 <= r145344;
        double r145346 = 1.0050381620843746e+41;
        bool r145347 = r145343 <= r145346;
        double r145348 = !r145347;
        bool r145349 = r145345 || r145348;
        double r145350 = eps;
        double r145351 = b;
        double r145352 = r145343 + r145351;
        double r145353 = exp(r145352);
        double r145354 = pow(r145353, r145350);
        double r145355 = 1.0;
        double r145356 = r145354 - r145355;
        double r145357 = 3.0;
        double r145358 = pow(r145356, r145357);
        double r145359 = cbrt(r145358);
        double r145360 = r145350 * r145359;
        double r145361 = exp(r145343);
        double r145362 = pow(r145361, r145350);
        double r145363 = r145362 - r145355;
        double r145364 = 2.0;
        double r145365 = pow(r145351, r145364);
        double r145366 = 0.5;
        double r145367 = pow(r145350, r145364);
        double r145368 = r145366 * r145367;
        double r145369 = 0.16666666666666666;
        double r145370 = pow(r145350, r145357);
        double r145371 = r145369 * r145370;
        double r145372 = r145371 * r145351;
        double r145373 = r145368 + r145372;
        double r145374 = r145365 * r145373;
        double r145375 = fma(r145351, r145350, r145374);
        double r145376 = r145363 * r145375;
        double r145377 = r145360 / r145376;
        double r145378 = r145352 * r145350;
        double r145379 = exp(r145378);
        double r145380 = r145379 - r145355;
        double r145381 = r145350 * r145380;
        double r145382 = pow(r145343, r145364);
        double r145383 = r145366 * r145382;
        double r145384 = pow(r145343, r145357);
        double r145385 = r145369 * r145384;
        double r145386 = r145385 * r145350;
        double r145387 = r145383 + r145386;
        double r145388 = r145367 * r145387;
        double r145389 = fma(r145343, r145350, r145388);
        double r145390 = r145351 * r145350;
        double r145391 = exp(r145390);
        double r145392 = r145391 - r145355;
        double r145393 = r145389 * r145392;
        double r145394 = r145381 / r145393;
        double r145395 = r145349 ? r145377 : r145394;
        return r145395;
}

Original	60.3
Target	15.0
Herbie	50.6

Derivation

Split input into 2 regimes
if a < -173005857.23040006 or 1.0050381620843746e+41 < a
1. Initial program 55.1
  \[\frac{\varepsilon \cdot \left(e^{\left(a + b\right) \cdot \varepsilon} - 1\right)}{\left(e^{a \cdot \varepsilon} - 1\right) \cdot \left(e^{b \cdot \varepsilon} - 1\right)}\]
2. Taylor expanded around 0 50.1
  \[\leadsto \frac{\varepsilon \cdot \left(e^{\left(a + b\right) \cdot \varepsilon} - 1\right)}{\left(e^{a \cdot \varepsilon} - 1\right) \cdot \color{blue}{\left(\frac{1}{6} \cdot \left({\varepsilon}^{3} \cdot {b}^{3}\right) + \left(\frac{1}{2} \cdot \left({\varepsilon}^{2} \cdot {b}^{2}\right) + \varepsilon \cdot b\right)\right)}}\]
3. Simplified47.7
  \[\leadsto \frac{\varepsilon \cdot \left(e^{\left(a + b\right) \cdot \varepsilon} - 1\right)}{\left(e^{a \cdot \varepsilon} - 1\right) \cdot \color{blue}{\mathsf{fma}\left(b, \varepsilon, {b}^{2} \cdot \left(\frac{1}{2} \cdot {\varepsilon}^{2} + \left(\frac{1}{6} \cdot {\varepsilon}^{3}\right) \cdot b\right)\right)}}\]
4. Taylor expanded around inf 47.7
  \[\leadsto \frac{\varepsilon \cdot \left(e^{\left(a + b\right) \cdot \varepsilon} - 1\right)}{\color{blue}{\left(e^{a \cdot \varepsilon} - 1\right)} \cdot \mathsf{fma}\left(b, \varepsilon, {b}^{2} \cdot \left(\frac{1}{2} \cdot {\varepsilon}^{2} + \left(\frac{1}{6} \cdot {\varepsilon}^{3}\right) \cdot b\right)\right)}\]
5. Simplified49.1
  \[\leadsto \frac{\varepsilon \cdot \left(e^{\left(a + b\right) \cdot \varepsilon} - 1\right)}{\color{blue}{\left({\left(e^{a}\right)}^{\varepsilon} - 1\right)} \cdot \mathsf{fma}\left(b, \varepsilon, {b}^{2} \cdot \left(\frac{1}{2} \cdot {\varepsilon}^{2} + \left(\frac{1}{6} \cdot {\varepsilon}^{3}\right) \cdot b\right)\right)}\]
6. Using strategy rm
7. Applied add-cbrt-cube49.1
  \[\leadsto \frac{\varepsilon \cdot \color{blue}{\sqrt[3]{\left(\left(e^{\left(a + b\right) \cdot \varepsilon} - 1\right) \cdot \left(e^{\left(a + b\right) \cdot \varepsilon} - 1\right)\right) \cdot \left(e^{\left(a + b\right) \cdot \varepsilon} - 1\right)}}}{\left({\left(e^{a}\right)}^{\varepsilon} - 1\right) \cdot \mathsf{fma}\left(b, \varepsilon, {b}^{2} \cdot \left(\frac{1}{2} \cdot {\varepsilon}^{2} + \left(\frac{1}{6} \cdot {\varepsilon}^{3}\right) \cdot b\right)\right)}\]
8. Simplified42.1
  \[\leadsto \frac{\varepsilon \cdot \sqrt[3]{\color{blue}{{\left({\left(e^{a + b}\right)}^{\varepsilon} - 1\right)}^{3}}}}{\left({\left(e^{a}\right)}^{\varepsilon} - 1\right) \cdot \mathsf{fma}\left(b, \varepsilon, {b}^{2} \cdot \left(\frac{1}{2} \cdot {\varepsilon}^{2} + \left(\frac{1}{6} \cdot {\varepsilon}^{3}\right) \cdot b\right)\right)}\]
if -173005857.23040006 < a < 1.0050381620843746e+41
1. Initial program 63.9
  \[\frac{\varepsilon \cdot \left(e^{\left(a + b\right) \cdot \varepsilon} - 1\right)}{\left(e^{a \cdot \varepsilon} - 1\right) \cdot \left(e^{b \cdot \varepsilon} - 1\right)}\]
2. Taylor expanded around 0 56.4
  \[\leadsto \frac{\varepsilon \cdot \left(e^{\left(a + b\right) \cdot \varepsilon} - 1\right)}{\color{blue}{\left(\frac{1}{6} \cdot \left({a}^{3} \cdot {\varepsilon}^{3}\right) + \left(\frac{1}{2} \cdot \left({a}^{2} \cdot {\varepsilon}^{2}\right) + a \cdot \varepsilon\right)\right)} \cdot \left(e^{b \cdot \varepsilon} - 1\right)}\]
3. Simplified56.4
  \[\leadsto \frac{\varepsilon \cdot \left(e^{\left(a + b\right) \cdot \varepsilon} - 1\right)}{\color{blue}{\mathsf{fma}\left(a, \varepsilon, {\varepsilon}^{2} \cdot \left(\frac{1}{2} \cdot {a}^{2} + \left(\frac{1}{6} \cdot {a}^{3}\right) \cdot \varepsilon\right)\right)} \cdot \left(e^{b \cdot \varepsilon} - 1\right)}\]
Recombined 2 regimes into one program.
Final simplification50.6
\[\leadsto \begin{array}{l} \mathbf{if}\;a \le -173005857.2304000556468963623046875 \lor \neg \left(a \le 100503816208437458162455618952188928196600\right):\\ \;\;\;\;\frac{\varepsilon \cdot \sqrt[3]{{\left({\left(e^{a + b}\right)}^{\varepsilon} - 1\right)}^{3}}}{\left({\left(e^{a}\right)}^{\varepsilon} - 1\right) \cdot \mathsf{fma}\left(b, \varepsilon, {b}^{2} \cdot \left(\frac{1}{2} \cdot {\varepsilon}^{2} + \left(\frac{1}{6} \cdot {\varepsilon}^{3}\right) \cdot b\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\varepsilon \cdot \left(e^{\left(a + b\right) \cdot \varepsilon} - 1\right)}{\mathsf{fma}\left(a, \varepsilon, {\varepsilon}^{2} \cdot \left(\frac{1}{2} \cdot {a}^{2} + \left(\frac{1}{6} \cdot {a}^{3}\right) \cdot \varepsilon\right)\right) \cdot \left(e^{b \cdot \varepsilon} - 1\right)}\\ \end{array}\]

could not determine a ground truth for program body (more)

Error

Target

Derivation

`if a < -173005857.23040006 or 1.0050381620843746e+41 < a`

`if -173005857.23040006 < a < 1.0050381620843746e+41`

Reproduce