Average Error: 0.0 → 0.0
Time: 22.3s
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 r167104 = x;
        double r167105 = y;
        double r167106 = log(r167105);
        double r167107 = r167105 * r167106;
        double r167108 = r167104 + r167107;
        double r167109 = z;
        double r167110 = r167108 - r167109;
        double r167111 = exp(r167110);
        return r167111;
}
↓
double f(double x, double y, double z) {
        double r167112 = y;
        double r167113 = log(r167112);
        double r167114 = x;
        double r167115 = fma(r167112, r167113, r167114);
        double r167116 = z;
        double r167117 = r167115 - r167116;
        double r167118 = exp(r167117);
        return r167118;
}

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)))