Average Error: 6.0 → 0.1
Time: 3.6s
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 r772642 = x;
        double r772643 = y;
        double r772644 = r772643 * r772643;
        double r772645 = z;
        double r772646 = r772644 / r772645;
        double r772647 = r772642 + r772646;
        return r772647;
}
↓
double f(double x, double y, double z) {
        double r772648 = y;
        double r772649 = z;
        double r772650 = r772648 / r772649;
        double r772651 = x;
        double r772652 = fma(r772650, r772648, r772651);
        return r772652;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original6.0
Target0.1
Herbie0.1
\[x + y \cdot \frac{y}{z}\]

Derivation

  1. Initial program 6.0

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

  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 2020033 +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)))