Average Error: 20.0 → 20.0
Time: 9.3s
Precision: binary64
\[\frac{1}{\sqrt{x + 1}} - \frac{1}{\sqrt{x}}\]
↓
\[\frac{1}{\sqrt{x + 1}} - \frac{1}{\sqrt{x}}\]
\frac{1}{\sqrt{x + 1}} - \frac{1}{\sqrt{x}}
↓
\frac{1}{\sqrt{x + 1}} - \frac{1}{\sqrt{x}}
double code(double x) {
	return ((double) (((double) (1.0 / ((double) sqrt(((double) (x + 1.0)))))) - ((double) (1.0 / ((double) sqrt(x))))));
}
↓
double code(double x) {
	return ((double) (((double) (1.0 / ((double) sqrt(((double) (x + 1.0)))))) - ((double) (1.0 / ((double) sqrt(x))))));
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 20.0

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

  2. Final simplification20.0

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

Reproduce

herbie shell --seed 2020153 
(FPCore (x)
  :name "(- (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt x)))"
  :precision binary64
  (- (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt x))))