Average Error: 6.2 → 0.1
Time: 3.7s
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 r758044 = x;
        double r758045 = y;
        double r758046 = r758045 * r758045;
        double r758047 = z;
        double r758048 = r758046 / r758047;
        double r758049 = r758044 + r758048;
        return r758049;
}
↓
double f(double x, double y, double z) {
        double r758050 = y;
        double r758051 = z;
        double r758052 = r758050 / r758051;
        double r758053 = x;
        double r758054 = fma(r758052, r758050, r758053);
        return r758054;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original6.2
Target0.1
Herbie0.1
\[x + y \cdot \frac{y}{z}\]

Derivation

  1. Initial program 6.2

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

  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 2020034 +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)))