Average Error: 5.7 → 0.1
Time: 13.9s
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 r44020249 = x;
        double r44020250 = y;
        double r44020251 = r44020250 * r44020250;
        double r44020252 = z;
        double r44020253 = r44020251 / r44020252;
        double r44020254 = r44020249 + r44020253;
        return r44020254;
}
↓
double f(double x, double y, double z) {
        double r44020255 = y;
        double r44020256 = z;
        double r44020257 = r44020255 / r44020256;
        double r44020258 = x;
        double r44020259 = fma(r44020257, r44020255, r44020258);
        return r44020259;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original5.7
Target0.1
Herbie0.1
\[x + y \cdot \frac{y}{z}\]

Derivation

  1. Initial program 5.7

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

  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 2019163 +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)))