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

Average Error: 0.2 → 0.2

Time: 13.8s

Precision: 64

Math

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

↓

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

C

double f(double x) {
        double r107490 = x;
        double r107491 = 1.0;
        double r107492 = r107490 + r107491;
        double r107493 = sqrt(r107492);
        double r107494 = r107491 + r107493;
        double r107495 = r107490 / r107494;
        return r107495;
}

↓

double f(double x) {
        double r107496 = x;
        double r107497 = 1.0;
        double r107498 = r107496 + r107497;
        double r107499 = sqrt(r107498);
        double r107500 = r107497 + r107499;
        double r107501 = r107496 / r107500;
        return r107501;
}

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 2019235 
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  :precision binary64
  (/ x (+ 1 (sqrt (+ x 1)))))