Numeric.SpecFunctions:$slogFactorial from math-functions-0.1.5.2, A

Average Error: 0.6 → 0.2

Time: 8.8s

Precision: 64

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

Math

\[\frac{1}{x \cdot x}\]

↓

\[\frac{\frac{1}{x}}{x}\]

C

double f(double x) {
        double r1195593 = 1.0;
        double r1195594 = x;
        double r1195595 = r1195594 * r1195594;
        double r1195596 = r1195593 / r1195595;
        return r1195596;
}

↓

double f(double x) {
        double r1195597 = 1.0;
        double r1195598 = x;
        double r1195599 = r1195597 / r1195598;
        double r1195600 = r1195599 / r1195598;
        return r1195600;
}

Error

Bits error versus x

Target

Original	0.6
Target	0.2
Herbie	0.2

\[\frac{\frac{1}{x}}{x}\]

Derivation

1. Initial program 0.6

   \[\frac{1}{x \cdot x}\]
2. Using strategy rm

3. Applied associate-/r* 0.2

   \[\leadsto \color{blue}{\frac{\frac{1}{x}}{x}}\]

4. Final simplification 0.2

   \[\leadsto \frac{\frac{1}{x}}{x}\]

Reproduce

herbie shell --seed 2020047 
(FPCore (x)
  :name "Numeric.SpecFunctions:$slogFactorial from math-functions-0.1.5.2, A"
  :precision binary64

  :herbie-target
  (/ (/ 1 x) x)

  (/ 1 (* x x)))