Average Error: 0.0 → 0.0
Time: 20.0s
Precision: 64
\[e^{\left(x + y \cdot \log y\right) - z}\]
↓
\[e^{\mathsf{fma}\left(y, \log y, x\right) - z}\]
e^{\left(x + y \cdot \log y\right) - z}
↓
e^{\mathsf{fma}\left(y, \log y, x\right) - z}
double f(double x, double y, double z) {
        double r175893 = x;
        double r175894 = y;
        double r175895 = log(r175894);
        double r175896 = r175894 * r175895;
        double r175897 = r175893 + r175896;
        double r175898 = z;
        double r175899 = r175897 - r175898;
        double r175900 = exp(r175899);
        return r175900;
}
↓
double f(double x, double y, double z) {
        double r175901 = y;
        double r175902 = log(r175901);
        double r175903 = x;
        double r175904 = fma(r175901, r175902, r175903);
        double r175905 = z;
        double r175906 = r175904 - r175905;
        double r175907 = exp(r175906);
        return r175907;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original0.0
Target0.0
Herbie0.0
\[e^{\left(x - z\right) + \log y \cdot y}\]

Derivation

  1. Initial program 0.0

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

  2. Simplified0.0

    \[\leadsto \color{blue}{e^{\mathsf{fma}\left(y, \log y, x\right) - z}}\]

  3. Final simplification0.0

    \[\leadsto e^{\mathsf{fma}\left(y, \log y, x\right) - z}\]

Reproduce

herbie shell --seed 2019306 +o rules:numerics
(FPCore (x y z)
  :name "Statistics.Distribution.Poisson.Internal:probability from math-functions-0.1.5.2"
  :precision binary64

  :herbie-target
  (exp (+ (- x z) (* (log y) y)))

  (exp (- (+ x (* y (log y))) z)))