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

Average Error: 0.2 → 0.2

Time: 6.6s

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 r139463 = x;
        double r139464 = 1.0;
        double r139465 = r139463 + r139464;
        double r139466 = sqrt(r139465);
        double r139467 = r139464 + r139466;
        double r139468 = r139463 / r139467;
        return r139468;
}

↓

double f(double x) {
        double r139469 = x;
        double r139470 = 1.0;
        double r139471 = r139469 + r139470;
        double r139472 = sqrt(r139471);
        double r139473 = r139472 + r139470;
        double r139474 = r139469 / r139473;
        return r139474;
}

Error

Bits error versus x

Derivation

1. Initial program 0.2

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

3. Applied pow1 0.2

   \[\leadsto \frac{x}{\color{blue}{{\left(1 + \sqrt{x + 1}\right)}^{1}}}\]

4. Final simplification 0.2

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

Reproduce

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