Average Error: 6.5 → 0.1
Time: 13.9s
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 r37800449 = x;
        double r37800450 = y;
        double r37800451 = r37800450 * r37800450;
        double r37800452 = z;
        double r37800453 = r37800451 / r37800452;
        double r37800454 = r37800449 + r37800453;
        return r37800454;
}
↓
double f(double x, double y, double z) {
        double r37800455 = y;
        double r37800456 = z;
        double r37800457 = r37800455 / r37800456;
        double r37800458 = x;
        double r37800459 = fma(r37800457, r37800455, r37800458);
        return r37800459;
}

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)))