Average Error: 0.0 → 0.0
Time: 11.5s
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 r288582 = x;
        double r288583 = y;
        double r288584 = log(r288583);
        double r288585 = r288583 * r288584;
        double r288586 = r288582 + r288585;
        double r288587 = z;
        double r288588 = r288586 - r288587;
        double r288589 = exp(r288588);
        return r288589;
}
↓
double f(double x, double y, double z) {
        double r288590 = y;
        double r288591 = log(r288590);
        double r288592 = x;
        double r288593 = fma(r288590, r288591, r288592);
        double r288594 = z;
        double r288595 = r288593 - r288594;
        double r288596 = exp(r288595);
        return r288596;
}

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 2020043 +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)))