Average Error: 6.3 → 0.1
Time: 17.4s
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 r500437 = x;
        double r500438 = y;
        double r500439 = r500438 * r500438;
        double r500440 = z;
        double r500441 = r500439 / r500440;
        double r500442 = r500437 + r500441;
        return r500442;
}
↓
double f(double x, double y, double z) {
        double r500443 = y;
        double r500444 = z;
        double r500445 = r500443 / r500444;
        double r500446 = x;
        double r500447 = fma(r500445, r500443, r500446);
        return r500447;
}

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)))