Average Error: 0.0 → 0.0
Time: 7.6s
Precision: 64
\[e^{\left(x + y \cdot \log y\right) - z}\]
↓
\[e^{\mathsf{fma}\left(\log y, y, x - z\right)}\]
e^{\left(x + y \cdot \log y\right) - z}
↓
e^{\mathsf{fma}\left(\log y, y, x - z\right)}
double f(double x, double y, double z) {
        double r4689144 = x;
        double r4689145 = y;
        double r4689146 = log(r4689145);
        double r4689147 = r4689145 * r4689146;
        double r4689148 = r4689144 + r4689147;
        double r4689149 = z;
        double r4689150 = r4689148 - r4689149;
        double r4689151 = exp(r4689150);
        return r4689151;
}
↓
double f(double x, double y, double z) {
        double r4689152 = y;
        double r4689153 = log(r4689152);
        double r4689154 = x;
        double r4689155 = z;
        double r4689156 = r4689154 - r4689155;
        double r4689157 = fma(r4689153, r4689152, r4689156);
        double r4689158 = exp(r4689157);
        return r4689158;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019156 +o rules:numerics
(FPCore (x y z)
  :name "Statistics.Distribution.Poisson.Internal:probability from math-functions-0.1.5.2"

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

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