Average Error: 30.1 → 30.1
Time: 1.4s
Precision: binary64
\[\sqrt{\sqrt{x + 1} - \sqrt{x}}\]
↓
\[\sqrt{\sqrt{x + 1} - \sqrt{x}}\]
\sqrt{\sqrt{x + 1} - \sqrt{x}}
↓
\sqrt{\sqrt{x + 1} - \sqrt{x}}
double code(double x) {
	return ((double) sqrt(((double) (((double) sqrt(((double) (x + 1.0)))) - ((double) sqrt(x))))));
}
↓
double code(double x) {
	return ((double) sqrt(((double) (((double) sqrt(((double) (x + 1.0)))) - ((double) sqrt(x))))));
}

Error

Bits error versus x

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Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 30.1

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

  2. Final simplification30.1

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

Reproduce

herbie shell --seed 2020152 
(FPCore (x)
  :name "(sqrt (- (sqrt (+ x 1)) (sqrt x)))"
  :precision binary64
  (sqrt (- (sqrt (+ x 1.0)) (sqrt x))))