Average Error: 0.0 → 0.0
Time: 8.4s
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 r349662 = x;
        double r349663 = y;
        double r349664 = log(r349663);
        double r349665 = r349663 * r349664;
        double r349666 = r349662 + r349665;
        double r349667 = z;
        double r349668 = r349666 - r349667;
        double r349669 = exp(r349668);
        return r349669;
}
↓
double f(double x, double y, double z) {
        double r349670 = y;
        double r349671 = log(r349670);
        double r349672 = x;
        double r349673 = fma(r349670, r349671, r349672);
        double r349674 = z;
        double r349675 = r349673 - r349674;
        double r349676 = exp(r349675);
        return r349676;
}

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 2019351 +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)))