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

Average Error: 0.2 → 0.2

Time: 8.5s

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 r136048 = x;
        double r136049 = 1.0;
        double r136050 = r136048 + r136049;
        double r136051 = sqrt(r136050);
        double r136052 = r136049 + r136051;
        double r136053 = r136048 / r136052;
        return r136053;
}

↓

double f(double x) {
        double r136054 = x;
        double r136055 = 1.0;
        double r136056 = r136054 + r136055;
        double r136057 = sqrt(r136056);
        double r136058 = r136055 + r136057;
        double r136059 = r136054 / r136058;
        return r136059;
}

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 2020045 +o rules:numerics
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  :precision binary64
  (/ x (+ 1 (sqrt (+ x 1)))))