Average Error: 6.5 → 0.1
Time: 15.1s
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 r36624018 = x;
        double r36624019 = y;
        double r36624020 = r36624019 * r36624019;
        double r36624021 = z;
        double r36624022 = r36624020 / r36624021;
        double r36624023 = r36624018 + r36624022;
        return r36624023;
}
↓
double f(double x, double y, double z) {
        double r36624024 = y;
        double r36624025 = z;
        double r36624026 = r36624024 / r36624025;
        double r36624027 = x;
        double r36624028 = fma(r36624026, r36624024, r36624027);
        return r36624028;
}

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 2019172 +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)))