Numeric.Log:$clog1p from log-domain-0.10.2.1, B

Average Error: 0.2 → 0.2

Time: 8.6s

Precision: 64

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

Math

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

↓

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

C

double f(double x) {
        double r138909 = x;
        double r138910 = 1.0;
        double r138911 = r138909 + r138910;
        double r138912 = sqrt(r138911);
        double r138913 = r138910 + r138912;
        double r138914 = r138909 / r138913;
        return r138914;
}

↓

double f(double x) {
        double r138915 = x;
        double r138916 = 1.0;
        double r138917 = r138915 + r138916;
        double r138918 = sqrt(r138917);
        double r138919 = r138918 + r138916;
        double r138920 = r138915 / r138919;
        return r138920;
}

Error

Bits error versus x

Derivation

1. Initial program 0.2

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

3. Applied +-commutative 0.2

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

4. Final simplification 0.2

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

Reproduce

herbie shell --seed 2020047 
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  :precision binary64
  (/ x (+ 1 (sqrt (+ x 1)))))