Average Error: 0.0 → 0.0
Time: 6.7s
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 r303720 = x;
        double r303721 = y;
        double r303722 = log(r303721);
        double r303723 = r303721 * r303722;
        double r303724 = r303720 + r303723;
        double r303725 = z;
        double r303726 = r303724 - r303725;
        double r303727 = exp(r303726);
        return r303727;
}
↓
double f(double x, double y, double z) {
        double r303728 = y;
        double r303729 = log(r303728);
        double r303730 = x;
        double r303731 = fma(r303728, r303729, r303730);
        double r303732 = z;
        double r303733 = r303731 - r303732;
        double r303734 = exp(r303733);
        return r303734;
}

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 2020047 +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)))