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

Average Error: 0.2 → 0.2

Time: 5.7s

Precision: 64

• Falling back on racket egraph because egg-herbie package not installed

Math

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

↓

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

C

double f(double x) {
        double r129430 = x;
        double r129431 = 1.0;
        double r129432 = r129430 + r129431;
        double r129433 = sqrt(r129432);
        double r129434 = r129431 + r129433;
        double r129435 = r129430 / r129434;
        return r129435;
}

↓

double f(double x) {
        double r129436 = x;
        double r129437 = 1.0;
        double r129438 = r129436 + r129437;
        double r129439 = sqrt(r129438);
        double r129440 = r129439 + r129437;
        double r129441 = r129436 / r129440;
        return r129441;
}

Error

Bits error versus x

Derivation

1. Initial program 0.2

   \[\frac{x}{1 + \sqrt{x + 1}}\]
2. Using strategy rm

3. Applied +-commutative 0.2

   \[\leadsto \frac{x}{\color{blue}{\sqrt{x + 1} + 1}}\]

4. Final simplification 0.2

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

Reproduce

herbie shell --seed 2020047 
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  :precision binary64
  (/ x (+ 1 (sqrt (+ x 1)))))