Average Error: 0.5 → 0.5
Time: 1.2s
Precision: binary64
\[\frac{1}{\sqrt{x + 2} + \sqrt{x + 1}} + \sqrt{x}\]
↓
\[\frac{1}{\sqrt{x + 2} + \sqrt{x + 1}} + \sqrt{x}\]
\frac{1}{\sqrt{x + 2} + \sqrt{x + 1}} + \sqrt{x}
↓
\frac{1}{\sqrt{x + 2} + \sqrt{x + 1}} + \sqrt{x}
double code(double x) {
	return ((double) (((double) (1.0 / ((double) (((double) sqrt(((double) (x + 2.0)))) + ((double) sqrt(((double) (x + 1.0)))))))) + ((double) sqrt(x))));
}
↓
double code(double x) {
	return ((double) (((double) (1.0 / ((double) (((double) sqrt(((double) (x + 2.0)))) + ((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 0.5

    \[\frac{1}{\sqrt{x + 2} + \sqrt{x + 1}} + \sqrt{x}\]

  2. Final simplification0.5

    \[\leadsto \frac{1}{\sqrt{x + 2} + \sqrt{x + 1}} + \sqrt{x}\]

Reproduce

herbie shell --seed 2020153 
(FPCore (x)
  :name "(+ (/ 1 (+ (sqrt (+ x 2)) (sqrt (+ x 1)))) (sqrt x))"
  :precision binary64
  (+ (/ 1.0 (+ (sqrt (+ x 2.0)) (sqrt (+ x 1.0)))) (sqrt x)))