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

Average Error: 0.2 → 0.2

Time: 15.7s

Precision: 64

Math

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

↓

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

C

double f(double x) {
        double r108313 = x;
        double r108314 = 1.0;
        double r108315 = r108313 + r108314;
        double r108316 = sqrt(r108315);
        double r108317 = r108314 + r108316;
        double r108318 = r108313 / r108317;
        return r108318;
}

↓

double f(double x) {
        double r108319 = x;
        double r108320 = 1.0;
        double r108321 = r108319 + r108320;
        double r108322 = sqrt(r108321);
        double r108323 = r108320 + r108322;
        double r108324 = r108319 / r108323;
        return r108324;
}

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 2019323 +o rules:numerics
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  :precision binary64
  (/ x (+ 1 (sqrt (+ x 1)))))