Average Error: 0.8 → 0.8
Time: 1.1s
Precision: binary64
\[\left(\sqrt{x + 2} - \sqrt{x + 1}\right) + \sqrt{x}\]
↓
\[\left(\sqrt{x + 2} - \sqrt{x + 1}\right) + \sqrt{x}\]
\left(\sqrt{x + 2} - \sqrt{x + 1}\right) + \sqrt{x}
↓
\left(\sqrt{x + 2} - \sqrt{x + 1}\right) + \sqrt{x}
double code(double x) {
	return ((double) (((double) (((double) sqrt(((double) (x + 2.0)))) - ((double) sqrt(((double) (x + 1.0)))))) + ((double) sqrt(x))));
}
↓
double code(double x) {
	return ((double) (((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 0.8

    \[\left(\sqrt{x + 2} - \sqrt{x + 1}\right) + \sqrt{x}\]

  2. Final simplification0.8

    \[\leadsto \left(\sqrt{x + 2} - \sqrt{x + 1}\right) + \sqrt{x}\]

Reproduce

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