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

Average Error: 0.2 → 0.2

Time: 1.5s

Precision: 64

Math

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

↓

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

C

double f(double x) {
        double r65150 = x;
        double r65151 = 1.0;
        double r65152 = r65150 + r65151;
        double r65153 = sqrt(r65152);
        double r65154 = r65151 + r65153;
        double r65155 = r65150 / r65154;
        return r65155;
}

↓

double f(double x) {
        double r65156 = x;
        double r65157 = 1.0;
        double r65158 = r65156 + r65157;
        double r65159 = sqrt(r65158);
        double r65160 = r65157 + r65159;
        double r65161 = r65156 / r65160;
        return r65161;
}

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 2020056 
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  :precision binary64
  (/ x (+ 1 (sqrt (+ x 1)))))