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

Average Error: 6.2 → 0.1

Time: 9.7s

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 r885894 = x;
        double r885895 = y;
        double r885896 = r885895 * r885895;
        double r885897 = z;
        double r885898 = r885896 / r885897;
        double r885899 = r885894 + r885898;
        return r885899;
}

↓

double f(double x, double y, double z) {
        double r885900 = y;
        double r885901 = z;
        double r885902 = r885900 / r885901;
        double r885903 = x;
        double r885904 = fma(r885902, r885900, r885903);
        return r885904;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original	6.2
Target	0.1
Herbie	0.1

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

Derivation

1. Initial program 6.2

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

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 2020043 +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)))