Average Error: 6.6 → 0.1
Time: 2.5s
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 r906038 = x;
        double r906039 = y;
        double r906040 = r906039 * r906039;
        double r906041 = z;
        double r906042 = r906040 / r906041;
        double r906043 = r906038 + r906042;
        return r906043;
}
↓
double f(double x, double y, double z) {
        double r906044 = y;
        double r906045 = z;
        double r906046 = r906044 / r906045;
        double r906047 = x;
        double r906048 = fma(r906046, r906044, r906047);
        return r906048;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original6.6
Target0.1
Herbie0.1
\[x + y \cdot \frac{y}{z}\]

Derivation

  1. Initial program 6.6

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

  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 2020065 +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)))