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

Average Error: 0.2 → 0.2

Time: 9.5s

Precision: 64

Math

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

↓

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

C

double f(double x) {
        double r115230 = x;
        double r115231 = 1.0;
        double r115232 = r115230 + r115231;
        double r115233 = sqrt(r115232);
        double r115234 = r115231 + r115233;
        double r115235 = r115230 / r115234;
        return r115235;
}

↓

double f(double x) {
        double r115236 = x;
        double r115237 = 1.0;
        double r115238 = r115236 + r115237;
        double r115239 = sqrt(r115238);
        double r115240 = r115237 + r115239;
        double r115241 = r115236 / r115240;
        return r115241;
}

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 2019325 +o rules:numerics
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  :precision binary64
  (/ x (+ 1 (sqrt (+ x 1)))))