Average Error: 0.0 → 0.0
Time: 16.4s
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 r210218 = x;
        double r210219 = y;
        double r210220 = log(r210219);
        double r210221 = r210219 * r210220;
        double r210222 = r210218 + r210221;
        double r210223 = z;
        double r210224 = r210222 - r210223;
        double r210225 = exp(r210224);
        return r210225;
}
↓
double f(double x, double y, double z) {
        double r210226 = y;
        double r210227 = log(r210226);
        double r210228 = x;
        double r210229 = fma(r210226, r210227, r210228);
        double r210230 = z;
        double r210231 = r210229 - r210230;
        double r210232 = exp(r210231);
        return r210232;
}

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 2019347 +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)))