Average Error: 6.4 → 0.1
Time: 14.6s
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 r438748 = x;
        double r438749 = y;
        double r438750 = r438749 * r438749;
        double r438751 = z;
        double r438752 = r438750 / r438751;
        double r438753 = r438748 + r438752;
        return r438753;
}
↓
double f(double x, double y, double z) {
        double r438754 = y;
        double r438755 = z;
        double r438756 = r438754 / r438755;
        double r438757 = x;
        double r438758 = fma(r438756, r438754, r438757);
        return r438758;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original6.4
Target0.1
Herbie0.1
\[x + y \cdot \frac{y}{z}\]

Derivation

  1. Initial program 6.4

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

  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 2019326 +o rules:numerics
(FPCore (x y z)
  :name "Crypto.Random.Test:calculate from crypto-random-0.0.9"
  :precision binary64

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

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