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

Average Error: 6.3 → 0.1

Time: 9.0s

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 r932382 = x;
        double r932383 = y;
        double r932384 = r932383 * r932383;
        double r932385 = z;
        double r932386 = r932384 / r932385;
        double r932387 = r932382 + r932386;
        return r932387;
}

↓

double f(double x, double y, double z) {
        double r932388 = y;
        double r932389 = z;
        double r932390 = r932388 / r932389;
        double r932391 = x;
        double r932392 = fma(r932390, r932388, r932391);
        return r932392;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original	6.3
Target	0.1
Herbie	0.1

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

Derivation

1. Initial program 6.3

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

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 2020046 +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)))