Average Error: 0.0 → 0.0
Time: 8.0s
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 r285276 = x;
        double r285277 = y;
        double r285278 = log(r285277);
        double r285279 = r285277 * r285278;
        double r285280 = r285276 + r285279;
        double r285281 = z;
        double r285282 = r285280 - r285281;
        double r285283 = exp(r285282);
        return r285283;
}
↓
double f(double x, double y, double z) {
        double r285284 = y;
        double r285285 = log(r285284);
        double r285286 = x;
        double r285287 = fma(r285284, r285285, r285286);
        double r285288 = z;
        double r285289 = r285287 - r285288;
        double r285290 = exp(r285289);
        return r285290;
}

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 2020047 +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)))