Average Error: 6.2 → 0.1
Time: 14.0s
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 r37035481 = x;
        double r37035482 = y;
        double r37035483 = r37035482 * r37035482;
        double r37035484 = z;
        double r37035485 = r37035483 / r37035484;
        double r37035486 = r37035481 + r37035485;
        return r37035486;
}
↓
double f(double x, double y, double z) {
        double r37035487 = y;
        double r37035488 = z;
        double r37035489 = r37035487 / r37035488;
        double r37035490 = x;
        double r37035491 = fma(r37035489, r37035487, r37035490);
        return r37035491;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original6.2
Target0.1
Herbie0.1
\[x + y \cdot \frac{y}{z}\]

Derivation

  1. Initial program 6.2

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

  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 2019170 +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)))