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

Average Error: 0.2 → 0.2

Time: 5.1s

Precision: 64

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

Math

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

↓

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

C

double f(double x) {
        double r113891 = x;
        double r113892 = 1.0;
        double r113893 = r113891 + r113892;
        double r113894 = sqrt(r113893);
        double r113895 = r113892 + r113894;
        double r113896 = r113891 / r113895;
        return r113896;
}

↓

double f(double x) {
        double r113897 = x;
        double r113898 = 1.0;
        double r113899 = r113897 + r113898;
        double r113900 = sqrt(r113899);
        double r113901 = r113898 + r113900;
        double r113902 = r113897 / r113901;
        return r113902;
}

Error

Bits error versus x

Derivation

1. Initial program 0.2

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

2. Final simplification 0.2

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

Reproduce

herbie shell --seed 2020042 +o rules:numerics
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  :precision binary64
  (/ x (+ 1 (sqrt (+ x 1)))))