Average Error: 38.9 → 38.9
Time: 6.8s
Precision: binary64
\[{\left(1 + x\right)}^{\left(\frac{1}{2}\right)} - 1\]
↓
\[{\left(1 + x\right)}^{\left(\frac{1}{2}\right)} - 1\]
{\left(1 + x\right)}^{\left(\frac{1}{2}\right)} - 1
↓
{\left(1 + x\right)}^{\left(\frac{1}{2}\right)} - 1
double code(double x) {
	return ((double) (((double) pow(((double) (1.0 + x)), ((double) (1.0 / 2.0)))) - 1.0));
}
↓
double code(double x) {
	return ((double) (((double) pow(((double) (1.0 + x)), ((double) (1.0 / 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 38.9

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

  2. Final simplification38.9

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

Reproduce

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