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

Average Error: 0.2 → 0.2

Time: 1.8s

Precision: 64

Math

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

↓

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

C

double f(double x) {
        double r82374 = x;
        double r82375 = 1.0;
        double r82376 = r82374 + r82375;
        double r82377 = sqrt(r82376);
        double r82378 = r82375 + r82377;
        double r82379 = r82374 / r82378;
        return r82379;
}

↓

double f(double x) {
        double r82380 = x;
        double r82381 = 1.0;
        double r82382 = r82380 + r82381;
        double r82383 = sqrt(r82382);
        double r82384 = r82381 + r82383;
        double r82385 = r82380 / r82384;
        return r82385;
}

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 2020064 
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  :precision binary64
  (/ x (+ 1 (sqrt (+ x 1)))))