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

Average Error: 0.2 → 0.2

Time: 6.2s

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 r157898 = x;
        double r157899 = 1.0;
        double r157900 = r157898 + r157899;
        double r157901 = sqrt(r157900);
        double r157902 = r157899 + r157901;
        double r157903 = r157898 / r157902;
        return r157903;
}

↓

double f(double x) {
        double r157904 = x;
        double r157905 = 1.0;
        double r157906 = r157904 + r157905;
        double r157907 = sqrt(r157906);
        double r157908 = r157905 + r157907;
        double r157909 = r157904 / r157908;
        return r157909;
}

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