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

Average Error: 0.2 → 0.2

Time: 5.8s

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 r112986 = x;
        double r112987 = 1.0;
        double r112988 = r112986 + r112987;
        double r112989 = sqrt(r112988);
        double r112990 = r112987 + r112989;
        double r112991 = r112986 / r112990;
        return r112991;
}

↓

double f(double x) {
        double r112992 = x;
        double r112993 = 1.0;
        double r112994 = r112992 + r112993;
        double r112995 = sqrt(r112994);
        double r112996 = r112995 + r112993;
        double r112997 = r112992 / r112996;
        return r112997;
}

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