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

Average Error: 0.2 → 0.2

Time: 7.3s

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 r119680 = x;
        double r119681 = 1.0;
        double r119682 = r119680 + r119681;
        double r119683 = sqrt(r119682);
        double r119684 = r119681 + r119683;
        double r119685 = r119680 / r119684;
        return r119685;
}

↓

double f(double x) {
        double r119686 = x;
        double r119687 = 1.0;
        double r119688 = r119686 + r119687;
        double r119689 = sqrt(r119688);
        double r119690 = r119687 + r119689;
        double r119691 = r119686 / r119690;
        return r119691;
}

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)))))