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

Average Error: 0.2 → 0.2

Time: 8.2s

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 r113461 = x;
        double r113462 = 1.0;
        double r113463 = r113461 + r113462;
        double r113464 = sqrt(r113463);
        double r113465 = r113462 + r113464;
        double r113466 = r113461 / r113465;
        return r113466;
}

↓

double f(double x) {
        double r113467 = x;
        double r113468 = 1.0;
        double r113469 = r113467 + r113468;
        double r113470 = sqrt(r113469);
        double r113471 = r113468 + r113470;
        double r113472 = r113467 / r113471;
        return r113472;
}

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)))))