Average Error: 6.1 → 0.1
Time: 14.5s
Precision: 64
\[x + \frac{y \cdot y}{z}\]
↓
\[\mathsf{fma}\left(\frac{y}{z}, y, x\right)\]
x + \frac{y \cdot y}{z}
↓
\mathsf{fma}\left(\frac{y}{z}, y, x\right)
double f(double x, double y, double z) {
        double r607845 = x;
        double r607846 = y;
        double r607847 = r607846 * r607846;
        double r607848 = z;
        double r607849 = r607847 / r607848;
        double r607850 = r607845 + r607849;
        return r607850;
}
↓
double f(double x, double y, double z) {
        double r607851 = y;
        double r607852 = z;
        double r607853 = r607851 / r607852;
        double r607854 = x;
        double r607855 = fma(r607853, r607851, r607854);
        return r607855;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original6.1
Target0.1
Herbie0.1
\[x + y \cdot \frac{y}{z}\]

Derivation

  1. Initial program 6.1

    \[x + \frac{y \cdot y}{z}\]

  2. Simplified0.1

    \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{z}, y, x\right)}\]

  3. Final simplification0.1

    \[\leadsto \mathsf{fma}\left(\frac{y}{z}, y, x\right)\]

Reproduce

herbie shell --seed 2019174 +o rules:numerics
(FPCore (x y z)
  :name "Crypto.Random.Test:calculate from crypto-random-0.0.9"

  :herbie-target
  (+ x (* y (/ y z)))

  (+ x (/ (* y y) z)))