Average Error: 30.4 → 30.4
Time: 2.5s
Precision: binary64
\[\frac{\sqrt{x + 1}}{\sqrt{x + 1} - \sqrt{x}} - \frac{\sqrt{x}}{\sqrt{x + 1} - \sqrt{x}}\]
↓
\[\frac{\sqrt{x + 1}}{\sqrt{x + 1} - \sqrt{x}} - \frac{\sqrt{x}}{\sqrt{x + 1} - \sqrt{x}}\]
\frac{\sqrt{x + 1}}{\sqrt{x + 1} - \sqrt{x}} - \frac{\sqrt{x}}{\sqrt{x + 1} - \sqrt{x}}
↓
\frac{\sqrt{x + 1}}{\sqrt{x + 1} - \sqrt{x}} - \frac{\sqrt{x}}{\sqrt{x + 1} - \sqrt{x}}
double code(double x) {
	return ((double) (((double) (((double) sqrt(((double) (x + 1.0)))) / ((double) (((double) sqrt(((double) (x + 1.0)))) - ((double) sqrt(x)))))) - ((double) (((double) sqrt(x)) / ((double) (((double) sqrt(((double) (x + 1.0)))) - ((double) sqrt(x))))))));
}
↓
double code(double x) {
	return ((double) (((double) (((double) sqrt(((double) (x + 1.0)))) / ((double) (((double) sqrt(((double) (x + 1.0)))) - ((double) sqrt(x)))))) - ((double) (((double) sqrt(x)) / ((double) (((double) sqrt(((double) (x + 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 30.4

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

  2. Final simplification30.4

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

Reproduce

herbie shell --seed 2020153 
(FPCore (x)
  :name "(- (/ (sqrt (+ x 1)) (- (sqrt (+ x 1)) (sqrt x))) (/ (sqrt x) (- (sqrt (+ x 1)) (sqrt x))))"
  :precision binary64
  (- (/ (sqrt (+ x 1.0)) (- (sqrt (+ x 1.0)) (sqrt x))) (/ (sqrt x) (- (sqrt (+ x 1.0)) (sqrt x)))))