Average Error: 31.0 → 31.0
Time: 2.3s
Precision: binary64
\[\sqrt{\sqrt{{x}^{2} + 1}} - \sqrt{x}\]
↓
\[\sqrt{\sqrt{{x}^{2} + 1}} - \sqrt{x}\]
\sqrt{\sqrt{{x}^{2} + 1}} - \sqrt{x}
↓
\sqrt{\sqrt{{x}^{2} + 1}} - \sqrt{x}
double code(double x) {
	return ((double) (((double) sqrt(((double) sqrt(((double) (((double) pow(x, 2.0)) + 1.0)))))) - ((double) sqrt(x))));
}
↓
double code(double x) {
	return ((double) (((double) sqrt(((double) sqrt(((double) (((double) pow(x, 2.0)) + 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 31.0

    \[\sqrt{\sqrt{{x}^{2} + 1}} - \sqrt{x}\]

  2. Final simplification31.0

    \[\leadsto \sqrt{\sqrt{{x}^{2} + 1}} - \sqrt{x}\]

Reproduce

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