Average Error: 6.2 → 0.1
Time: 40.2s
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 r39049316 = x;
        double r39049317 = y;
        double r39049318 = r39049317 * r39049317;
        double r39049319 = z;
        double r39049320 = r39049318 / r39049319;
        double r39049321 = r39049316 + r39049320;
        return r39049321;
}
↓
double f(double x, double y, double z) {
        double r39049322 = y;
        double r39049323 = z;
        double r39049324 = r39049322 / r39049323;
        double r39049325 = x;
        double r39049326 = fma(r39049324, r39049322, r39049325);
        return r39049326;
}

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 2019200 +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)))