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

Average Error: 0.2 → 0.2

Time: 1.7s

Precision: 64

Math

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

↓

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

C

double f(double x) {
        double r110129 = x;
        double r110130 = 1.0;
        double r110131 = r110129 + r110130;
        double r110132 = sqrt(r110131);
        double r110133 = r110130 + r110132;
        double r110134 = r110129 / r110133;
        return r110134;
}

↓

double f(double x) {
        double r110135 = x;
        double r110136 = 1.0;
        double r110137 = r110135 + r110136;
        double r110138 = sqrt(r110137);
        double r110139 = r110136 + r110138;
        double r110140 = r110135 / r110139;
        return r110140;
}

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 2020064 +o rules:numerics
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  :precision binary64
  (/ x (+ 1 (sqrt (+ x 1)))))