Average Error: 30.6 → 30.6
Time: 2.6s
Precision: binary64
\[\sqrt{1 - \cos x \cdot \cos x}\]
↓
\[\sqrt{1 - \cos x \cdot \cos x}\]
\sqrt{1 - \cos x \cdot \cos x}
↓
\sqrt{1 - \cos x \cdot \cos x}
double code(double x) {
	return ((double) sqrt(((double) (1.0 - ((double) (((double) cos(x)) * ((double) cos(x))))))));
}
↓
double code(double x) {
	return ((double) sqrt(((double) (1.0 - ((double) (((double) cos(x)) * ((double) cos(x))))))));
}

Error

Bits error versus x

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Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 30.6

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

  2. Final simplification30.6

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

Reproduce

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