\[x - \frac{\log \left(\left(1 - y\right) + y \cdot e^{z}\right)}{t}\]

↓

\[\begin{array}{l} \mathbf{if}\;z \le -0.3115017031960372051457852649036794900894:\\ \;\;\;\;x - \sqrt{\log \left(\mathsf{fma}\left(\mathsf{expm1}\left(z\right), y, 1\right)\right)} \cdot \frac{\sqrt{\log \left(\mathsf{fma}\left(\mathsf{expm1}\left(z\right), y, 1\right)\right)}}{t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{1}{\frac{t}{\mathsf{fma}\left(y, \mathsf{fma}\left(0.5, {z}^{2}, 1 \cdot z\right), \log 1\right)}}\\ \end{array}\]

x - \frac{\log \left(\left(1 - y\right) + y \cdot e^{z}\right)}{t}

↓

\begin{array}{l}
\mathbf{if}\;z \le -0.3115017031960372051457852649036794900894:\\
\;\;\;\;x - \sqrt{\log \left(\mathsf{fma}\left(\mathsf{expm1}\left(z\right), y, 1\right)\right)} \cdot \frac{\sqrt{\log \left(\mathsf{fma}\left(\mathsf{expm1}\left(z\right), y, 1\right)\right)}}{t}\\

\mathbf{else}:\\
\;\;\;\;x - \frac{1}{\frac{t}{\mathsf{fma}\left(y, \mathsf{fma}\left(0.5, {z}^{2}, 1 \cdot z\right), \log 1\right)}}\\

\end{array}

double f(double x, double y, double z, double t) {
        double r231967 = x;
        double r231968 = 1.0;
        double r231969 = y;
        double r231970 = r231968 - r231969;
        double r231971 = z;
        double r231972 = exp(r231971);
        double r231973 = r231969 * r231972;
        double r231974 = r231970 + r231973;
        double r231975 = log(r231974);
        double r231976 = t;
        double r231977 = r231975 / r231976;
        double r231978 = r231967 - r231977;
        return r231978;
}

↓

double f(double x, double y, double z, double t) {
        double r231979 = z;
        double r231980 = -0.3115017031960372;
        bool r231981 = r231979 <= r231980;
        double r231982 = x;
        double r231983 = expm1(r231979);
        double r231984 = y;
        double r231985 = 1.0;
        double r231986 = fma(r231983, r231984, r231985);
        double r231987 = log(r231986);
        double r231988 = sqrt(r231987);
        double r231989 = t;
        double r231990 = r231988 / r231989;
        double r231991 = r231988 * r231990;
        double r231992 = r231982 - r231991;
        double r231993 = 1.0;
        double r231994 = 0.5;
        double r231995 = 2.0;
        double r231996 = pow(r231979, r231995);
        double r231997 = r231985 * r231979;
        double r231998 = fma(r231994, r231996, r231997);
        double r231999 = log(r231985);
        double r232000 = fma(r231984, r231998, r231999);
        double r232001 = r231989 / r232000;
        double r232002 = r231993 / r232001;
        double r232003 = r231982 - r232002;
        double r232004 = r231981 ? r231992 : r232003;
        return r232004;
}

Original	25.4
Target	16.5
Herbie	8.8

Derivation

Split input into 2 regimes
if z < -0.3115017031960372
1. Initial program 10.9
  \[x - \frac{\log \left(\left(1 - y\right) + y \cdot e^{z}\right)}{t}\]
2. Simplified10.9
  \[\leadsto \color{blue}{x - \frac{\log \left(\mathsf{fma}\left(\mathsf{expm1}\left(z\right), y, 1\right)\right)}{t}}\]
3. Using strategy rm
4. Applied *-un-lft-identity10.9
  \[\leadsto x - \frac{\log \left(\mathsf{fma}\left(\mathsf{expm1}\left(z\right), y, 1\right)\right)}{\color{blue}{1 \cdot t}}\]
5. Applied add-sqr-sqrt11.8
  \[\leadsto x - \frac{\color{blue}{\sqrt{\log \left(\mathsf{fma}\left(\mathsf{expm1}\left(z\right), y, 1\right)\right)} \cdot \sqrt{\log \left(\mathsf{fma}\left(\mathsf{expm1}\left(z\right), y, 1\right)\right)}}}{1 \cdot t}\]
6. Applied times-frac11.8
  \[\leadsto x - \color{blue}{\frac{\sqrt{\log \left(\mathsf{fma}\left(\mathsf{expm1}\left(z\right), y, 1\right)\right)}}{1} \cdot \frac{\sqrt{\log \left(\mathsf{fma}\left(\mathsf{expm1}\left(z\right), y, 1\right)\right)}}{t}}\]
7. Simplified11.8
  \[\leadsto x - \color{blue}{\sqrt{\log \left(\mathsf{fma}\left(\mathsf{expm1}\left(z\right), y, 1\right)\right)}} \cdot \frac{\sqrt{\log \left(\mathsf{fma}\left(\mathsf{expm1}\left(z\right), y, 1\right)\right)}}{t}\]
if -0.3115017031960372 < z
1. Initial program 31.3
  \[x - \frac{\log \left(\left(1 - y\right) + y \cdot e^{z}\right)}{t}\]
2. Simplified11.9
  \[\leadsto \color{blue}{x - \frac{\log \left(\mathsf{fma}\left(\mathsf{expm1}\left(z\right), y, 1\right)\right)}{t}}\]
3. Using strategy rm
4. Applied clear-num11.9
  \[\leadsto x - \color{blue}{\frac{1}{\frac{t}{\log \left(\mathsf{fma}\left(\mathsf{expm1}\left(z\right), y, 1\right)\right)}}}\]
5. Taylor expanded around 0 7.6
  \[\leadsto x - \frac{1}{\frac{t}{\color{blue}{0.5 \cdot \left({z}^{2} \cdot y\right) + \left(1 \cdot \left(z \cdot y\right) + \log 1\right)}}}\]
6. Simplified7.6
  \[\leadsto x - \frac{1}{\frac{t}{\color{blue}{\mathsf{fma}\left(y, \mathsf{fma}\left(0.5, {z}^{2}, 1 \cdot z\right), \log 1\right)}}}\]
Recombined 2 regimes into one program.
Final simplification8.8
\[\leadsto \begin{array}{l} \mathbf{if}\;z \le -0.3115017031960372051457852649036794900894:\\ \;\;\;\;x - \sqrt{\log \left(\mathsf{fma}\left(\mathsf{expm1}\left(z\right), y, 1\right)\right)} \cdot \frac{\sqrt{\log \left(\mathsf{fma}\left(\mathsf{expm1}\left(z\right), y, 1\right)\right)}}{t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{1}{\frac{t}{\mathsf{fma}\left(y, \mathsf{fma}\left(0.5, {z}^{2}, 1 \cdot z\right), \log 1\right)}}\\ \end{array}\]

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

Error

Target

Derivation

`if z < -0.3115017031960372`

`if -0.3115017031960372 < z`

Reproduce