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

Average Error: 0.2 → 0.2

Time: 4.0s

Precision: 64

Math

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

↓

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

C

double f(double x) {
        double r108044 = x;
        double r108045 = 1.0;
        double r108046 = r108044 + r108045;
        double r108047 = sqrt(r108046);
        double r108048 = r108045 + r108047;
        double r108049 = r108044 / r108048;
        return r108049;
}

↓

double f(double x) {
        double r108050 = x;
        double r108051 = 1.0;
        double r108052 = r108050 + r108051;
        double r108053 = sqrt(r108052);
        double r108054 = r108051 + r108053;
        double r108055 = r108050 / r108054;
        return r108055;
}

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 2020025 +o rules:numerics
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  :precision binary64
  (/ x (+ 1 (sqrt (+ x 1)))))