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

Average Error: 0.2 → 0.2

Time: 5.8s

Precision: 64

Math

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

↓

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

C

double f(double x) {
        double r124730 = x;
        double r124731 = 1.0;
        double r124732 = r124730 + r124731;
        double r124733 = sqrt(r124732);
        double r124734 = r124731 + r124733;
        double r124735 = r124730 / r124734;
        return r124735;
}

↓

double f(double x) {
        double r124736 = x;
        double r124737 = 1.0;
        double r124738 = r124736 + r124737;
        double r124739 = sqrt(r124738);
        double r124740 = r124737 + r124739;
        double r124741 = r124736 / r124740;
        return r124741;
}

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 2020021 +o rules:numerics
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  :precision binary64
  (/ x (+ 1 (sqrt (+ x 1)))))