Average Error: 6.1 → 0.1
Time: 7.0s
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 r1024996 = x;
        double r1024997 = y;
        double r1024998 = r1024997 * r1024997;
        double r1024999 = z;
        double r1025000 = r1024998 / r1024999;
        double r1025001 = r1024996 + r1025000;
        return r1025001;
}
↓
double f(double x, double y, double z) {
        double r1025002 = y;
        double r1025003 = z;
        double r1025004 = r1025002 / r1025003;
        double r1025005 = x;
        double r1025006 = fma(r1025004, r1025002, r1025005);
        return r1025006;
}

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 2020045 +o rules:numerics
(FPCore (x y z)
  :name "Crypto.Random.Test:calculate from crypto-random-0.0.9"
  :precision binary64

  :herbie-target
  (+ x (* y (/ y z)))

  (+ x (/ (* y y) z)))