Average Error: 6.5 → 0.1
Time: 26.1s
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 r37152911 = x;
        double r37152912 = y;
        double r37152913 = r37152912 * r37152912;
        double r37152914 = z;
        double r37152915 = r37152913 / r37152914;
        double r37152916 = r37152911 + r37152915;
        return r37152916;
}
↓
double f(double x, double y, double z) {
        double r37152917 = y;
        double r37152918 = z;
        double r37152919 = r37152917 / r37152918;
        double r37152920 = x;
        double r37152921 = fma(r37152919, r37152917, r37152920);
        return r37152921;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original6.5
Target0.1
Herbie0.1
\[x + y \cdot \frac{y}{z}\]

Derivation

  1. Initial program 6.5

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

  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 2019168 +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)))