Average Error: 30.1 → 30.1
Time: 1.5s
Precision: binary64
\[1 - \sqrt{1 - x \cdot x}\]
↓
\[1 - \sqrt{1 - x \cdot x}\]
1 - \sqrt{1 - x \cdot x}
↓
1 - \sqrt{1 - x \cdot x}
double code(double x) {
	return ((double) (1.0 - ((double) sqrt(((double) (1.0 - ((double) (x * x))))))));
}
↓
double code(double x) {
	return ((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 30.1

    \[1 - \sqrt{1 - x \cdot x}\]

  2. Final simplification30.1

    \[\leadsto 1 - \sqrt{1 - x \cdot x}\]

Reproduce

herbie shell --seed 2020153 
(FPCore (x)
  :name "(- 1 (sqrt (- 1 (* x x))))"
  :precision binary64
  (- 1.0 (sqrt (- 1.0 (* x x)))))