Average Error: 6.3 → 0.1
Time: 17.0s
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 r505586 = x;
        double r505587 = y;
        double r505588 = r505587 * r505587;
        double r505589 = z;
        double r505590 = r505588 / r505589;
        double r505591 = r505586 + r505590;
        return r505591;
}
↓
double f(double x, double y, double z) {
        double r505592 = y;
        double r505593 = z;
        double r505594 = r505592 / r505593;
        double r505595 = x;
        double r505596 = fma(r505594, r505592, r505595);
        return r505596;
}

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 2019325 +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)))