Average Error: 6.5 → 0.1
Time: 20.5s
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 r716921 = x;
        double r716922 = y;
        double r716923 = r716922 * r716922;
        double r716924 = z;
        double r716925 = r716923 / r716924;
        double r716926 = r716921 + r716925;
        return r716926;
}
↓
double f(double x, double y, double z) {
        double r716927 = y;
        double r716928 = z;
        double r716929 = r716927 / r716928;
        double r716930 = x;
        double r716931 = fma(r716929, r716927, r716930);
        return r716931;
}

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 2019209 +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)))