\[x - \frac{\log \left(\left(1.0 - y\right) + y \cdot e^{z}\right)}{t}\]

↓

\[\begin{array}{l} \mathbf{if}\;z \le -1.0731100139682523 \cdot 10^{-36}:\\ \;\;\;\;x - \frac{1}{t} \cdot \log \left(\mathsf{fma}\left(\mathsf{expm1}\left(z\right), y, 1.0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x - \mathsf{fma}\left(1.0, \frac{z}{t} \cdot y, \frac{\log 1.0}{t}\right)\\ \end{array}\]

x - \frac{\log \left(\left(1.0 - y\right) + y \cdot e^{z}\right)}{t}

↓

\begin{array}{l}
\mathbf{if}\;z \le -1.0731100139682523 \cdot 10^{-36}:\\
\;\;\;\;x - \frac{1}{t} \cdot \log \left(\mathsf{fma}\left(\mathsf{expm1}\left(z\right), y, 1.0\right)\right)\\

\mathbf{else}:\\
\;\;\;\;x - \mathsf{fma}\left(1.0, \frac{z}{t} \cdot y, \frac{\log 1.0}{t}\right)\\

\end{array}

double f(double x, double y, double z, double t) {
        double r12341682 = x;
        double r12341683 = 1.0;
        double r12341684 = y;
        double r12341685 = r12341683 - r12341684;
        double r12341686 = z;
        double r12341687 = exp(r12341686);
        double r12341688 = r12341684 * r12341687;
        double r12341689 = r12341685 + r12341688;
        double r12341690 = log(r12341689);
        double r12341691 = t;
        double r12341692 = r12341690 / r12341691;
        double r12341693 = r12341682 - r12341692;
        return r12341693;
}

↓

double f(double x, double y, double z, double t) {
        double r12341694 = z;
        double r12341695 = -1.0731100139682523e-36;
        bool r12341696 = r12341694 <= r12341695;
        double r12341697 = x;
        double r12341698 = 1.0;
        double r12341699 = t;
        double r12341700 = r12341698 / r12341699;
        double r12341701 = expm1(r12341694);
        double r12341702 = y;
        double r12341703 = 1.0;
        double r12341704 = fma(r12341701, r12341702, r12341703);
        double r12341705 = log(r12341704);
        double r12341706 = r12341700 * r12341705;
        double r12341707 = r12341697 - r12341706;
        double r12341708 = r12341694 / r12341699;
        double r12341709 = r12341708 * r12341702;
        double r12341710 = log(r12341703);
        double r12341711 = r12341710 / r12341699;
        double r12341712 = fma(r12341703, r12341709, r12341711);
        double r12341713 = r12341697 - r12341712;
        double r12341714 = r12341696 ? r12341707 : r12341713;
        return r12341714;
}

Original	25.5
Target	16.7
Herbie	8.0

Derivation

Split input into 2 regimes
if z < -1.0731100139682523e-36
1. Initial program 13.0
  \[x - \frac{\log \left(\left(1.0 - y\right) + y \cdot e^{z}\right)}{t}\]
2. Simplified11.9
  \[\leadsto \color{blue}{x - \frac{\log \left(\mathsf{fma}\left(\mathsf{expm1}\left(z\right), y, 1.0\right)\right)}{t}}\]
3. Using strategy rm
4. Applied div-inv11.9
  \[\leadsto x - \color{blue}{\log \left(\mathsf{fma}\left(\mathsf{expm1}\left(z\right), y, 1.0\right)\right) \cdot \frac{1}{t}}\]
if -1.0731100139682523e-36 < z
1. Initial program 31.8
  \[x - \frac{\log \left(\left(1.0 - y\right) + y \cdot e^{z}\right)}{t}\]
2. Simplified11.9
  \[\leadsto \color{blue}{x - \frac{\log \left(\mathsf{fma}\left(\mathsf{expm1}\left(z\right), y, 1.0\right)\right)}{t}}\]
3. Using strategy rm
4. Applied div-inv11.9
  \[\leadsto x - \color{blue}{\log \left(\mathsf{fma}\left(\mathsf{expm1}\left(z\right), y, 1.0\right)\right) \cdot \frac{1}{t}}\]
5. Taylor expanded around 0 7.0
  \[\leadsto \color{blue}{x - \left(1.0 \cdot \frac{z \cdot y}{t} + \frac{\log 1.0}{t}\right)}\]
6. Simplified6.0
  \[\leadsto \color{blue}{x - \mathsf{fma}\left(1.0, \frac{z}{t} \cdot y, \frac{\log 1.0}{t}\right)}\]
Recombined 2 regimes into one program.
Final simplification8.0
\[\leadsto \begin{array}{l} \mathbf{if}\;z \le -1.0731100139682523 \cdot 10^{-36}:\\ \;\;\;\;x - \frac{1}{t} \cdot \log \left(\mathsf{fma}\left(\mathsf{expm1}\left(z\right), y, 1.0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x - \mathsf{fma}\left(1.0, \frac{z}{t} \cdot y, \frac{\log 1.0}{t}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019165 +o rules:numerics
(FPCore (x y z t)
  :name "System.Random.MWC.Distributions:truncatedExp from mwc-random-0.13.3.2"

  :herbie-target
  (if (< z -2.8874623088207947e+119) (- (- x (/ (/ (- 0.5) (* y t)) (* z z))) (* (/ (- 0.5) (* y t)) (/ (/ 2.0 z) (* z z)))) (- x (/ (log (+ 1.0 (* z y))) t)))

  (- x (/ (log (+ (- 1.0 y) (* y (exp z)))) t)))

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

Error

Target

Derivation

`if z < -1.0731100139682523e-36`

`if -1.0731100139682523e-36 < z`

Reproduce