Average Error: 0.0 → 0.0
Time: 12.0s
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 r328832 = x;
        double r328833 = y;
        double r328834 = log(r328833);
        double r328835 = r328833 * r328834;
        double r328836 = r328832 + r328835;
        double r328837 = z;
        double r328838 = r328836 - r328837;
        double r328839 = exp(r328838);
        return r328839;
}
↓
double f(double x, double y, double z) {
        double r328840 = y;
        double r328841 = log(r328840);
        double r328842 = x;
        double r328843 = fma(r328840, r328841, r328842);
        double r328844 = z;
        double r328845 = r328843 - r328844;
        double r328846 = exp(r328845);
        return r328846;
}

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 2019350 +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)))