Average Error: 0.0 → 0.0
Time: 16.6s
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 r166205 = x;
        double r166206 = y;
        double r166207 = log(r166206);
        double r166208 = r166206 * r166207;
        double r166209 = r166205 + r166208;
        double r166210 = z;
        double r166211 = r166209 - r166210;
        double r166212 = exp(r166211);
        return r166212;
}
↓
double f(double x, double y, double z) {
        double r166213 = y;
        double r166214 = log(r166213);
        double r166215 = x;
        double r166216 = fma(r166213, r166214, r166215);
        double r166217 = z;
        double r166218 = r166216 - r166217;
        double r166219 = exp(r166218);
        return r166219;
}

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 2019325 +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)))