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

Average Error: 0.2 → 0.2

Time: 7.8s

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 r146725 = x;
        double r146726 = 1.0;
        double r146727 = r146725 + r146726;
        double r146728 = sqrt(r146727);
        double r146729 = r146726 + r146728;
        double r146730 = r146725 / r146729;
        return r146730;
}

↓

double f(double x) {
        double r146731 = x;
        double r146732 = 1.0;
        double r146733 = r146731 + r146732;
        double r146734 = sqrt(r146733);
        double r146735 = r146732 + r146734;
        double r146736 = r146731 / r146735;
        return r146736;
}

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