Crypto.Random.Test:calculate from crypto-random-0.0.9

Average Error: 6.1 → 0.1

Time: 12.6s

Precision: 64

• Falling back on racket egraph because egg-herbie package not installed

Math

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

↓

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

C

double f(double x, double y, double z) {
        double r848896 = x;
        double r848897 = y;
        double r848898 = r848897 * r848897;
        double r848899 = z;
        double r848900 = r848898 / r848899;
        double r848901 = r848896 + r848900;
        return r848901;
}

↓

double f(double x, double y, double z) {
        double r848902 = y;
        double r848903 = z;
        double r848904 = r848902 / r848903;
        double r848905 = x;
        double r848906 = fma(r848904, r848902, r848905);
        return r848906;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original	6.1
Target	0.1
Herbie	0.1

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

Derivation

1. Initial program 6.1

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

2. Simplified 0.1

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

3. Final simplification 0.1

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

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)))