Average Error: 0.0 → 0.0
Time: 10.2s
Precision: 64
\[e^{\left(x + y \cdot \log y\right) - z}\]
↓
\[e^{\mathsf{fma}\left(y, \log y, x - z\right)}\]
e^{\left(x + y \cdot \log y\right) - z}
↓
e^{\mathsf{fma}\left(y, \log y, x - z\right)}
double f(double x, double y, double z) {
        double r12130960 = x;
        double r12130961 = y;
        double r12130962 = log(r12130961);
        double r12130963 = r12130961 * r12130962;
        double r12130964 = r12130960 + r12130963;
        double r12130965 = z;
        double r12130966 = r12130964 - r12130965;
        double r12130967 = exp(r12130966);
        return r12130967;
}
↓
double f(double x, double y, double z) {
        double r12130968 = y;
        double r12130969 = log(r12130968);
        double r12130970 = x;
        double r12130971 = z;
        double r12130972 = r12130970 - r12130971;
        double r12130973 = fma(r12130968, r12130969, r12130972);
        double r12130974 = exp(r12130973);
        return r12130974;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019179 +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)))