Average Error: 5.9 → 0.1
Time: 18.4s
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 r611331 = x;
        double r611332 = y;
        double r611333 = r611332 * r611332;
        double r611334 = z;
        double r611335 = r611333 / r611334;
        double r611336 = r611331 + r611335;
        return r611336;
}
↓
double f(double x, double y, double z) {
        double r611337 = y;
        double r611338 = z;
        double r611339 = r611337 / r611338;
        double r611340 = x;
        double r611341 = fma(r611339, r611337, r611340);
        return r611341;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original5.9
Target0.1
Herbie0.1
\[x + y \cdot \frac{y}{z}\]

Derivation

  1. Initial program 5.9

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

  2. Simplified0.1

    \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{z}, y, x\right)}\]
  3. Using strategy rm

  4. Applied *-un-lft-identity0.1

    \[\leadsto \color{blue}{1 \cdot \mathsf{fma}\left(\frac{y}{z}, y, x\right)}\]

  5. Final simplification0.1

    \[\leadsto \mathsf{fma}\left(\frac{y}{z}, y, x\right)\]

Reproduce

herbie shell --seed 2019198 +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)))