Average Error: 0.0 → 0.0
Time: 20.9s
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 r168554 = x;
        double r168555 = y;
        double r168556 = log(r168555);
        double r168557 = r168555 * r168556;
        double r168558 = r168554 + r168557;
        double r168559 = z;
        double r168560 = r168558 - r168559;
        double r168561 = exp(r168560);
        return r168561;
}
↓
double f(double x, double y, double z) {
        double r168562 = y;
        double r168563 = log(r168562);
        double r168564 = x;
        double r168565 = fma(r168562, r168563, r168564);
        double r168566 = z;
        double r168567 = r168565 - r168566;
        double r168568 = exp(r168567);
        return r168568;
}

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 2019323 +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)))