Average Error: 16.1 → 16.1
Time: 766.0ms
Precision: binary64
\[\sqrt{{x}^{2} + 1}\]
↓
\[\sqrt{{x}^{2} + 1}\]
\sqrt{{x}^{2} + 1}
↓
\sqrt{{x}^{2} + 1}
double code(double x) {
	return ((double) sqrt(((double) (((double) pow(x, 2.0)) + 1.0))));
}
↓
double code(double x) {
	return ((double) sqrt(((double) (((double) pow(x, 2.0)) + 1.0))));
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 16.1

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

  2. Final simplification16.1

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

Reproduce

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