Average Error: 5.7 → 0.1
Time: 6.1s
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 r9547839 = x;
        double r9547840 = y;
        double r9547841 = r9547840 * r9547840;
        double r9547842 = z;
        double r9547843 = r9547841 / r9547842;
        double r9547844 = r9547839 + r9547843;
        return r9547844;
}
↓
double f(double x, double y, double z) {
        double r9547845 = y;
        double r9547846 = z;
        double r9547847 = r9547845 / r9547846;
        double r9547848 = x;
        double r9547849 = fma(r9547847, r9547845, r9547848);
        return r9547849;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original5.7
Target0.1
Herbie0.1
\[x + y \cdot \frac{y}{z}\]

Derivation

  1. Initial program 5.7

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

  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 2019156 +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)))