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

↓

\[\begin{array}{l} \mathbf{if}\;z \le -6.105344974142014411594425737916935759131 \cdot 10^{-5}:\\ \;\;\;\;x - \frac{1}{\frac{t}{\log \left(\mathsf{fma}\left(e^{z}, y, 1 - y\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;x - \mathsf{fma}\left(y, \mathsf{fma}\left(0.5, {z}^{2}, 1 \cdot z\right), \log 1\right) \cdot \frac{1}{t}\\ \end{array}\]

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

↓

\begin{array}{l}
\mathbf{if}\;z \le -6.105344974142014411594425737916935759131 \cdot 10^{-5}:\\
\;\;\;\;x - \frac{1}{\frac{t}{\log \left(\mathsf{fma}\left(e^{z}, y, 1 - y\right)\right)}}\\

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

\end{array}

double f(double x, double y, double z, double t) {
        double r243058 = x;
        double r243059 = 1.0;
        double r243060 = y;
        double r243061 = r243059 - r243060;
        double r243062 = z;
        double r243063 = exp(r243062);
        double r243064 = r243060 * r243063;
        double r243065 = r243061 + r243064;
        double r243066 = log(r243065);
        double r243067 = t;
        double r243068 = r243066 / r243067;
        double r243069 = r243058 - r243068;
        return r243069;
}

↓

double f(double x, double y, double z, double t) {
        double r243070 = z;
        double r243071 = -6.105344974142014e-05;
        bool r243072 = r243070 <= r243071;
        double r243073 = x;
        double r243074 = 1.0;
        double r243075 = t;
        double r243076 = exp(r243070);
        double r243077 = y;
        double r243078 = 1.0;
        double r243079 = r243078 - r243077;
        double r243080 = fma(r243076, r243077, r243079);
        double r243081 = log(r243080);
        double r243082 = r243075 / r243081;
        double r243083 = r243074 / r243082;
        double r243084 = r243073 - r243083;
        double r243085 = 0.5;
        double r243086 = 2.0;
        double r243087 = pow(r243070, r243086);
        double r243088 = r243078 * r243070;
        double r243089 = fma(r243085, r243087, r243088);
        double r243090 = log(r243078);
        double r243091 = fma(r243077, r243089, r243090);
        double r243092 = r243074 / r243075;
        double r243093 = r243091 * r243092;
        double r243094 = r243073 - r243093;
        double r243095 = r243072 ? r243084 : r243094;
        return r243095;
}

Original	25.2
Target	16.1
Herbie	8.2

Derivation

Split input into 2 regimes
if z < -6.105344974142014e-05
1. Initial program 11.3
  \[x - \frac{\log \left(\left(1 - y\right) + y \cdot e^{z}\right)}{t}\]
2. Simplified11.3
  \[\leadsto \color{blue}{x - \frac{\log \left(\mathsf{fma}\left(e^{z}, y, 1 - y\right)\right)}{t}}\]
3. Using strategy rm
4. Applied clear-num11.4
  \[\leadsto x - \color{blue}{\frac{1}{\frac{t}{\log \left(\mathsf{fma}\left(e^{z}, y, 1 - y\right)\right)}}}\]
if -6.105344974142014e-05 < z
1. Initial program 31.1
  \[x - \frac{\log \left(\left(1 - y\right) + y \cdot e^{z}\right)}{t}\]
2. Simplified31.0
  \[\leadsto \color{blue}{x - \frac{\log \left(\mathsf{fma}\left(e^{z}, y, 1 - y\right)\right)}{t}}\]
3. Taylor expanded around 0 6.9
  \[\leadsto x - \frac{\color{blue}{0.5 \cdot \left({z}^{2} \cdot y\right) + \left(1 \cdot \left(z \cdot y\right) + \log 1\right)}}{t}\]
4. Simplified6.9
  \[\leadsto x - \frac{\color{blue}{\mathsf{fma}\left(y, \mathsf{fma}\left(0.5, {z}^{2}, 1 \cdot z\right), \log 1\right)}}{t}\]
5. Using strategy rm
6. Applied div-inv6.9
  \[\leadsto x - \color{blue}{\mathsf{fma}\left(y, \mathsf{fma}\left(0.5, {z}^{2}, 1 \cdot z\right), \log 1\right) \cdot \frac{1}{t}}\]
Recombined 2 regimes into one program.
Final simplification8.2
\[\leadsto \begin{array}{l} \mathbf{if}\;z \le -6.105344974142014411594425737916935759131 \cdot 10^{-5}:\\ \;\;\;\;x - \frac{1}{\frac{t}{\log \left(\mathsf{fma}\left(e^{z}, y, 1 - y\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;x - \mathsf{fma}\left(y, \mathsf{fma}\left(0.5, {z}^{2}, 1 \cdot z\right), \log 1\right) \cdot \frac{1}{t}\\ \end{array}\]

Reproduce

herbie shell --seed 2019209 +o rules:numerics
(FPCore (x y z t)
  :name "System.Random.MWC.Distributions:truncatedExp from mwc-random-0.13.3.2"
  :precision binary64

  :herbie-target
  (if (< z -2.88746230882079466e119) (- (- x (/ (/ (- 0.5) (* y t)) (* z z))) (* (/ (- 0.5) (* y t)) (/ (/ 2 z) (* z z)))) (- x (/ (log (+ 1 (* z y))) t)))

  (- x (/ (log (+ (- 1 y) (* y (exp z)))) t)))

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

Error

Target

Derivation

`if z < -6.105344974142014e-05`

`if -6.105344974142014e-05 < z`

Reproduce