Average Error: 6.5 → 0.1
Time: 3.3s
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 r846760 = x;
        double r846761 = y;
        double r846762 = r846761 * r846761;
        double r846763 = z;
        double r846764 = r846762 / r846763;
        double r846765 = r846760 + r846764;
        return r846765;
}
↓
double f(double x, double y, double z) {
        double r846766 = y;
        double r846767 = z;
        double r846768 = r846766 / r846767;
        double r846769 = x;
        double r846770 = fma(r846768, r846766, r846769);
        return r846770;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original6.5
Target0.1
Herbie0.1
\[x + y \cdot \frac{y}{z}\]

Derivation

  1. Initial program 6.5

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

  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 2020089 +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)))