Average Error: 6.4 → 0.1
Time: 3.6s
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 r900203 = x;
        double r900204 = y;
        double r900205 = r900204 * r900204;
        double r900206 = z;
        double r900207 = r900205 / r900206;
        double r900208 = r900203 + r900207;
        return r900208;
}
↓
double f(double x, double y, double z) {
        double r900209 = y;
        double r900210 = z;
        double r900211 = r900209 / r900210;
        double r900212 = x;
        double r900213 = fma(r900211, r900209, r900212);
        return r900213;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original6.4
Target0.1
Herbie0.1
\[x + y \cdot \frac{y}{z}\]

Derivation

  1. Initial program 6.4

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

  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 2020064 +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)))