Average Error: 6.4 → 0.1
Time: 21.1s
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 r678383 = x;
        double r678384 = y;
        double r678385 = r678384 * r678384;
        double r678386 = z;
        double r678387 = r678385 / r678386;
        double r678388 = r678383 + r678387;
        return r678388;
}
↓
double f(double x, double y, double z) {
        double r678389 = y;
        double r678390 = z;
        double r678391 = r678389 / r678390;
        double r678392 = x;
        double r678393 = fma(r678391, r678389, r678392);
        return r678393;
}

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 2019208 +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)))