Average Error: 15.0 → 15.0
Time: 616.0ms
Precision: binary64
\[\frac{1}{1 + \sqrt{1 + x \cdot x}}\]
↓
\[\frac{1}{1 + \sqrt{1 + x \cdot x}}\]
\frac{1}{1 + \sqrt{1 + x \cdot x}}
↓
\frac{1}{1 + \sqrt{1 + x \cdot x}}
double code(double x) {
	return ((double) (1.0 / ((double) (1.0 + ((double) sqrt(((double) (1.0 + ((double) (x * x))))))))));
}
↓
double code(double x) {
	return ((double) (1.0 / ((double) (1.0 + ((double) sqrt(((double) (1.0 + ((double) (x * x))))))))));
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 15.0

    \[\frac{1}{1 + \sqrt{1 + x \cdot x}}\]

  2. Final simplification15.0

    \[\leadsto \frac{1}{1 + \sqrt{1 + x \cdot x}}\]

Reproduce

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