Average Error: 16.1 → 16.1
Time: 848.0ms
Precision: binary64
\[\sqrt{{x}^{2} + 9.9999999999999989 \cdot 10^{-51}} - 9.9999999999999989 \cdot 10^{-51}\]
↓
\[\sqrt{{x}^{2} + 9.9999999999999989 \cdot 10^{-51}} - 9.9999999999999989 \cdot 10^{-51}\]
\sqrt{{x}^{2} + 9.9999999999999989 \cdot 10^{-51}} - 9.9999999999999989 \cdot 10^{-51}
↓
\sqrt{{x}^{2} + 9.9999999999999989 \cdot 10^{-51}} - 9.9999999999999989 \cdot 10^{-51}
double code(double x) {
	return ((double) (((double) sqrt(((double) (((double) pow(x, 2.0)) + 9.999999999999999e-51)))) - 9.999999999999999e-51));
}
↓
double code(double x) {
	return ((double) (((double) sqrt(((double) (((double) pow(x, 2.0)) + 9.999999999999999e-51)))) - 9.999999999999999e-51));
}

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

    \[\sqrt{{x}^{2} + 9.9999999999999989 \cdot 10^{-51}} - 9.9999999999999989 \cdot 10^{-51}\]

  2. Final simplification16.1

    \[\leadsto \sqrt{{x}^{2} + 9.9999999999999989 \cdot 10^{-51}} - 9.9999999999999989 \cdot 10^{-51}\]

Reproduce

herbie shell --seed 2020153 
(FPCore (x)
  :name "(- (sqrt (+ (pow x 2) 9.999999999999999e-51)) 9.999999999999999e-51)"
  :precision binary64
  (- (sqrt (+ (pow x 2.0) 9.999999999999999e-51)) 9.999999999999999e-51))