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

Average Error: 0.2 → 0.2

Time: 3.2s

Precision: 64

Math

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

↓

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

C

double f(double x) {
        double r118568 = x;
        double r118569 = 1.0;
        double r118570 = r118568 + r118569;
        double r118571 = sqrt(r118570);
        double r118572 = r118569 + r118571;
        double r118573 = r118568 / r118572;
        return r118573;
}

↓

double f(double x) {
        double r118574 = x;
        double r118575 = 1.0;
        double r118576 = r118574 + r118575;
        double r118577 = sqrt(r118576);
        double r118578 = r118575 + r118577;
        double r118579 = r118574 / r118578;
        return r118579;
}

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 2020033 +o rules:numerics
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  :precision binary64
  (/ x (+ 1 (sqrt (+ x 1)))))