Average Error: 6.1 → 0.1
Time: 18.0s
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 r56463067 = x;
        double r56463068 = y;
        double r56463069 = r56463068 * r56463068;
        double r56463070 = z;
        double r56463071 = r56463069 / r56463070;
        double r56463072 = r56463067 + r56463071;
        return r56463072;
}
↓
double f(double x, double y, double z) {
        double r56463073 = y;
        double r56463074 = z;
        double r56463075 = r56463073 / r56463074;
        double r56463076 = x;
        double r56463077 = fma(r56463075, r56463073, r56463076);
        return r56463077;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

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

Derivation

  1. Initial program 6.1

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

  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 2019174 +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)))