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

Average Error: 0.2 → 0.2

Time: 3.5s

Precision: 64

Math

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

↓

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

C

double f(double x) {
        double r104571 = x;
        double r104572 = 1.0;
        double r104573 = r104571 + r104572;
        double r104574 = sqrt(r104573);
        double r104575 = r104572 + r104574;
        double r104576 = r104571 / r104575;
        return r104576;
}

↓

double f(double x) {
        double r104577 = x;
        double r104578 = 1.0;
        double r104579 = r104577 + r104578;
        double r104580 = sqrt(r104579);
        double r104581 = r104578 + r104580;
        double r104582 = r104577 / r104581;
        return r104582;
}

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 2020018 +o rules:numerics
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  :precision binary64
  (/ x (+ 1 (sqrt (+ x 1)))))