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

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

↓

\[\begin{array}{l} \mathbf{if}\;b \le -7.147724553383306 \cdot 10^{+163}:\\ \;\;\;\;\frac{\mathsf{expm1}\left(\left(\left(a + b\right) \cdot \varepsilon\right)\right) \cdot \frac{\varepsilon}{\mathsf{expm1}\left(\left(a \cdot \varepsilon\right)\right)}}{\mathsf{expm1}\left(\left(\varepsilon \cdot b\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{b} + \frac{1}{a}\\ \end{array}\]

\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}\;b \le -7.147724553383306 \cdot 10^{+163}:\\
\;\;\;\;\frac{\mathsf{expm1}\left(\left(\left(a + b\right) \cdot \varepsilon\right)\right) \cdot \frac{\varepsilon}{\mathsf{expm1}\left(\left(a \cdot \varepsilon\right)\right)}}{\mathsf{expm1}\left(\left(\varepsilon \cdot b\right)\right)}\\

\mathbf{else}:\\
\;\;\;\;\frac{1}{b} + \frac{1}{a}\\

\end{array}

double f(double a, double b, double eps) {
        double r4872480 = eps;
        double r4872481 = a;
        double r4872482 = b;
        double r4872483 = r4872481 + r4872482;
        double r4872484 = r4872483 * r4872480;
        double r4872485 = exp(r4872484);
        double r4872486 = 1.0;
        double r4872487 = r4872485 - r4872486;
        double r4872488 = r4872480 * r4872487;
        double r4872489 = r4872481 * r4872480;
        double r4872490 = exp(r4872489);
        double r4872491 = r4872490 - r4872486;
        double r4872492 = r4872482 * r4872480;
        double r4872493 = exp(r4872492);
        double r4872494 = r4872493 - r4872486;
        double r4872495 = r4872491 * r4872494;
        double r4872496 = r4872488 / r4872495;
        return r4872496;
}

↓

double f(double a, double b, double eps) {
        double r4872497 = b;
        double r4872498 = -7.147724553383306e+163;
        bool r4872499 = r4872497 <= r4872498;
        double r4872500 = a;
        double r4872501 = r4872500 + r4872497;
        double r4872502 = eps;
        double r4872503 = r4872501 * r4872502;
        double r4872504 = expm1(r4872503);
        double r4872505 = r4872500 * r4872502;
        double r4872506 = expm1(r4872505);
        double r4872507 = r4872502 / r4872506;
        double r4872508 = r4872504 * r4872507;
        double r4872509 = r4872502 * r4872497;
        double r4872510 = expm1(r4872509);
        double r4872511 = r4872508 / r4872510;
        double r4872512 = 1.0;
        double r4872513 = r4872512 / r4872497;
        double r4872514 = r4872512 / r4872500;
        double r4872515 = r4872513 + r4872514;
        double r4872516 = r4872499 ? r4872511 : r4872515;
        return r4872516;
}

Original	58.5
Target	14.2
Herbie	3.7

Derivation

Split input into 2 regimes
if b < -7.147724553383306e+163
1. Initial program 49.2
  \[\frac{\varepsilon \cdot \left(e^{\left(a + b\right) \cdot \varepsilon} - 1\right)}{\left(e^{a \cdot \varepsilon} - 1\right) \cdot \left(e^{b \cdot \varepsilon} - 1\right)}\]
2. Simplified20.7
  \[\leadsto \color{blue}{\frac{\frac{\mathsf{expm1}\left(\left(\left(a + b\right) \cdot \varepsilon\right)\right) \cdot \varepsilon}{\mathsf{expm1}\left(\left(\varepsilon \cdot a\right)\right)}}{\mathsf{expm1}\left(\left(\varepsilon \cdot b\right)\right)}}\]
3. Using strategy rm
4. Applied *-un-lft-identity20.7
  \[\leadsto \frac{\frac{\mathsf{expm1}\left(\left(\left(a + b\right) \cdot \varepsilon\right)\right) \cdot \varepsilon}{\color{blue}{1 \cdot \mathsf{expm1}\left(\left(\varepsilon \cdot a\right)\right)}}}{\mathsf{expm1}\left(\left(\varepsilon \cdot b\right)\right)}\]
5. Applied times-frac15.6
  \[\leadsto \frac{\color{blue}{\frac{\mathsf{expm1}\left(\left(\left(a + b\right) \cdot \varepsilon\right)\right)}{1} \cdot \frac{\varepsilon}{\mathsf{expm1}\left(\left(\varepsilon \cdot a\right)\right)}}}{\mathsf{expm1}\left(\left(\varepsilon \cdot b\right)\right)}\]
6. Simplified15.6
  \[\leadsto \frac{\color{blue}{\mathsf{expm1}\left(\left(\left(b + a\right) \cdot \varepsilon\right)\right)} \cdot \frac{\varepsilon}{\mathsf{expm1}\left(\left(\varepsilon \cdot a\right)\right)}}{\mathsf{expm1}\left(\left(\varepsilon \cdot b\right)\right)}\]
if -7.147724553383306e+163 < b
1. Initial program 59.5
  \[\frac{\varepsilon \cdot \left(e^{\left(a + b\right) \cdot \varepsilon} - 1\right)}{\left(e^{a \cdot \varepsilon} - 1\right) \cdot \left(e^{b \cdot \varepsilon} - 1\right)}\]
2. Simplified35.8
  \[\leadsto \color{blue}{\frac{\frac{\mathsf{expm1}\left(\left(\left(a + b\right) \cdot \varepsilon\right)\right) \cdot \varepsilon}{\mathsf{expm1}\left(\left(\varepsilon \cdot a\right)\right)}}{\mathsf{expm1}\left(\left(\varepsilon \cdot b\right)\right)}}\]
3. Taylor expanded around 0 2.5
  \[\leadsto \color{blue}{\frac{1}{a} + \frac{1}{b}}\]
Recombined 2 regimes into one program.
Final simplification3.7
\[\leadsto \begin{array}{l} \mathbf{if}\;b \le -7.147724553383306 \cdot 10^{+163}:\\ \;\;\;\;\frac{\mathsf{expm1}\left(\left(\left(a + b\right) \cdot \varepsilon\right)\right) \cdot \frac{\varepsilon}{\mathsf{expm1}\left(\left(a \cdot \varepsilon\right)\right)}}{\mathsf{expm1}\left(\left(\varepsilon \cdot b\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{b} + \frac{1}{a}\\ \end{array}\]

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

Error

Try it out

Target

Derivation

`if b < -7.147724553383306e+163`

`if -7.147724553383306e+163 < b`

Reproduce

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