Average Error: 6.3 → 0.1
Time: 2.2s
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 r432576 = x;
        double r432577 = y;
        double r432578 = r432577 * r432577;
        double r432579 = z;
        double r432580 = r432578 / r432579;
        double r432581 = r432576 + r432580;
        return r432581;
}
↓
double f(double x, double y, double z) {
        double r432582 = y;
        double r432583 = z;
        double r432584 = r432582 / r432583;
        double r432585 = x;
        double r432586 = fma(r432584, r432582, r432585);
        return r432586;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original6.3
Target0.1
Herbie0.1
\[x + y \cdot \frac{y}{z}\]

Derivation

  1. Initial program 6.3

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

  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 2019362 +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)))