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

Average Error: 0.2 → 0.2

Time: 6.3s

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 r141333 = x;
        double r141334 = 1.0;
        double r141335 = r141333 + r141334;
        double r141336 = sqrt(r141335);
        double r141337 = r141334 + r141336;
        double r141338 = r141333 / r141337;
        return r141338;
}

↓

double f(double x) {
        double r141339 = x;
        double r141340 = 1.0;
        double r141341 = r141339 + r141340;
        double r141342 = sqrt(r141341);
        double r141343 = r141340 + r141342;
        double r141344 = r141339 / r141343;
        return r141344;
}

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 2020042 
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  :precision binary64
  (/ x (+ 1 (sqrt (+ x 1)))))