Average Error: 6.3 → 0.1
Time: 15.6s
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 r39406447 = x;
        double r39406448 = y;
        double r39406449 = r39406448 * r39406448;
        double r39406450 = z;
        double r39406451 = r39406449 / r39406450;
        double r39406452 = r39406447 + r39406451;
        return r39406452;
}
↓
double f(double x, double y, double z) {
        double r39406453 = y;
        double r39406454 = z;
        double r39406455 = r39406453 / r39406454;
        double r39406456 = x;
        double r39406457 = fma(r39406455, r39406453, r39406456);
        return r39406457;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original6.3
Target0.1
Herbie0.1
\[x + y \cdot \frac{y}{z}\]

Derivation

  1. Initial program 6.3

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

  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 2019192 +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)))