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

Average Error: 6.3 → 0.1

Time: 9.5s

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 r1008998 = x;
        double r1008999 = y;
        double r1009000 = r1008999 * r1008999;
        double r1009001 = z;
        double r1009002 = r1009000 / r1009001;
        double r1009003 = r1008998 + r1009002;
        return r1009003;
}

↓

double f(double x, double y, double z) {
        double r1009004 = y;
        double r1009005 = z;
        double r1009006 = r1009004 / r1009005;
        double r1009007 = x;
        double r1009008 = fma(r1009006, r1009004, r1009007);
        return r1009008;
}

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)))