Average Error: 6.5 → 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 r895531 = x;
        double r895532 = y;
        double r895533 = r895532 * r895532;
        double r895534 = z;
        double r895535 = r895533 / r895534;
        double r895536 = r895531 + r895535;
        return r895536;
}
↓
double f(double x, double y, double z) {
        double r895537 = y;
        double r895538 = z;
        double r895539 = r895537 / r895538;
        double r895540 = x;
        double r895541 = fma(r895539, r895537, r895540);
        return r895541;
}

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 2020039 +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)))