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

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

↓

\[\begin{array}{l} \mathbf{if}\;b \le 1.2596314720077241 \cdot 10^{+207}:\\ \;\;\;\;\frac{1}{a} + \frac{1}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\mathsf{expm1}\left(\left(\left(b + a\right) \cdot \varepsilon\right)\right) \cdot \varepsilon}{\mathsf{expm1}\left(\left(a \cdot \varepsilon\right)\right)}}{\mathsf{expm1}\left(\left(b \cdot \varepsilon\right)\right)}\\ \end{array}\]

\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}\;b \le 1.2596314720077241 \cdot 10^{+207}:\\
\;\;\;\;\frac{1}{a} + \frac{1}{b}\\

\mathbf{else}:\\
\;\;\;\;\frac{\frac{\mathsf{expm1}\left(\left(\left(b + a\right) \cdot \varepsilon\right)\right) \cdot \varepsilon}{\mathsf{expm1}\left(\left(a \cdot \varepsilon\right)\right)}}{\mathsf{expm1}\left(\left(b \cdot \varepsilon\right)\right)}\\

\end{array}

double f(double a, double b, double eps) {
        double r7100252 = eps;
        double r7100253 = a;
        double r7100254 = b;
        double r7100255 = r7100253 + r7100254;
        double r7100256 = r7100255 * r7100252;
        double r7100257 = exp(r7100256);
        double r7100258 = 1.0;
        double r7100259 = r7100257 - r7100258;
        double r7100260 = r7100252 * r7100259;
        double r7100261 = r7100253 * r7100252;
        double r7100262 = exp(r7100261);
        double r7100263 = r7100262 - r7100258;
        double r7100264 = r7100254 * r7100252;
        double r7100265 = exp(r7100264);
        double r7100266 = r7100265 - r7100258;
        double r7100267 = r7100263 * r7100266;
        double r7100268 = r7100260 / r7100267;
        return r7100268;
}

↓

double f(double a, double b, double eps) {
        double r7100269 = b;
        double r7100270 = 1.2596314720077241e+207;
        bool r7100271 = r7100269 <= r7100270;
        double r7100272 = 1.0;
        double r7100273 = a;
        double r7100274 = r7100272 / r7100273;
        double r7100275 = r7100272 / r7100269;
        double r7100276 = r7100274 + r7100275;
        double r7100277 = r7100269 + r7100273;
        double r7100278 = eps;
        double r7100279 = r7100277 * r7100278;
        double r7100280 = expm1(r7100279);
        double r7100281 = r7100280 * r7100278;
        double r7100282 = r7100273 * r7100278;
        double r7100283 = expm1(r7100282);
        double r7100284 = r7100281 / r7100283;
        double r7100285 = r7100269 * r7100278;
        double r7100286 = expm1(r7100285);
        double r7100287 = r7100284 / r7100286;
        double r7100288 = r7100271 ? r7100276 : r7100287;
        return r7100288;
}

Original	58.6
Target	13.7
Herbie	3.7

Derivation

Split input into 2 regimes
if b < 1.2596314720077241e+207
1. Initial program 59.2
  \[\frac{\varepsilon \cdot \left(e^{\left(a + b\right) \cdot \varepsilon} - 1\right)}{\left(e^{a \cdot \varepsilon} - 1\right) \cdot \left(e^{b \cdot \varepsilon} - 1\right)}\]
2. Simplified35.0
  \[\leadsto \color{blue}{\frac{\frac{\mathsf{expm1}\left(\left(\left(a + b\right) \cdot \varepsilon\right)\right) \cdot \varepsilon}{\mathsf{expm1}\left(\left(\varepsilon \cdot a\right)\right)}}{\mathsf{expm1}\left(\left(\varepsilon \cdot b\right)\right)}}\]
3. Taylor expanded around 0 2.7
  \[\leadsto \color{blue}{\frac{1}{a} + \frac{1}{b}}\]
if 1.2596314720077241e+207 < b
1. Initial program 49.1
  \[\frac{\varepsilon \cdot \left(e^{\left(a + b\right) \cdot \varepsilon} - 1\right)}{\left(e^{a \cdot \varepsilon} - 1\right) \cdot \left(e^{b \cdot \varepsilon} - 1\right)}\]
2. Simplified18.5
  \[\leadsto \color{blue}{\frac{\frac{\mathsf{expm1}\left(\left(\left(a + b\right) \cdot \varepsilon\right)\right) \cdot \varepsilon}{\mathsf{expm1}\left(\left(\varepsilon \cdot a\right)\right)}}{\mathsf{expm1}\left(\left(\varepsilon \cdot b\right)\right)}}\]
3. Taylor expanded around -inf 22.4
  \[\leadsto \frac{\frac{\color{blue}{\left(e^{\left(a + b\right) \cdot \varepsilon} - 1\right) \cdot \varepsilon}}{\mathsf{expm1}\left(\left(\varepsilon \cdot a\right)\right)}}{\mathsf{expm1}\left(\left(\varepsilon \cdot b\right)\right)}\]
4. Simplified18.5
  \[\leadsto \frac{\frac{\color{blue}{\varepsilon \cdot \mathsf{expm1}\left(\left(\left(b + a\right) \cdot \varepsilon\right)\right)}}{\mathsf{expm1}\left(\left(\varepsilon \cdot a\right)\right)}}{\mathsf{expm1}\left(\left(\varepsilon \cdot b\right)\right)}\]
Recombined 2 regimes into one program.
Final simplification3.7
\[\leadsto \begin{array}{l} \mathbf{if}\;b \le 1.2596314720077241 \cdot 10^{+207}:\\ \;\;\;\;\frac{1}{a} + \frac{1}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\mathsf{expm1}\left(\left(\left(b + a\right) \cdot \varepsilon\right)\right) \cdot \varepsilon}{\mathsf{expm1}\left(\left(a \cdot \varepsilon\right)\right)}}{\mathsf{expm1}\left(\left(b \cdot \varepsilon\right)\right)}\\ \end{array}\]

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

Error

Try it out

Target

Derivation

`if b < 1.2596314720077241e+207`

`if 1.2596314720077241e+207 < b`

Reproduce

In
Out