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

Average Error: 6.5 → 0.1

Time: 12.0s

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 r1144749 = x;
        double r1144750 = y;
        double r1144751 = r1144750 * r1144750;
        double r1144752 = z;
        double r1144753 = r1144751 / r1144752;
        double r1144754 = r1144749 + r1144753;
        return r1144754;
}

↓

double f(double x, double y, double z) {
        double r1144755 = y;
        double r1144756 = z;
        double r1144757 = r1144755 / r1144756;
        double r1144758 = x;
        double r1144759 = fma(r1144757, r1144755, r1144758);
        return r1144759;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original	6.5
Target	0.1
Herbie	0.1

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

Derivation

1. Initial program 6.5

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

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 2020042 +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)))