Average Error: 6.1 → 0.1
Time: 3.2s
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 r805890 = x;
        double r805891 = y;
        double r805892 = r805891 * r805891;
        double r805893 = z;
        double r805894 = r805892 / r805893;
        double r805895 = r805890 + r805894;
        return r805895;
}
↓
double f(double x, double y, double z) {
        double r805896 = y;
        double r805897 = z;
        double r805898 = r805896 / r805897;
        double r805899 = x;
        double r805900 = fma(r805898, r805896, r805899);
        return r805900;
}

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 2020001 +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)))