Average Error: 6.1 → 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 r39459626 = x;
        double r39459627 = y;
        double r39459628 = r39459627 * r39459627;
        double r39459629 = z;
        double r39459630 = r39459628 / r39459629;
        double r39459631 = r39459626 + r39459630;
        return r39459631;
}
↓
double f(double x, double y, double z) {
        double r39459632 = y;
        double r39459633 = z;
        double r39459634 = r39459632 / r39459633;
        double r39459635 = x;
        double r39459636 = fma(r39459634, r39459632, r39459635);
        return r39459636;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

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

Derivation

  1. Initial program 6.1

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

  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 2019162 +o rules:numerics
(FPCore (x y z)
  :name "Crypto.Random.Test:calculate from crypto-random-0.0.9"

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

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