Average Error: 0.0 → 0.0
Time: 22.2s
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 r166694 = x;
        double r166695 = y;
        double r166696 = log(r166695);
        double r166697 = r166695 * r166696;
        double r166698 = r166694 + r166697;
        double r166699 = z;
        double r166700 = r166698 - r166699;
        double r166701 = exp(r166700);
        return r166701;
}
↓
double f(double x, double y, double z) {
        double r166702 = y;
        double r166703 = log(r166702);
        double r166704 = x;
        double r166705 = fma(r166702, r166703, r166704);
        double r166706 = z;
        double r166707 = r166705 - r166706;
        double r166708 = exp(r166707);
        return r166708;
}

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)))