Average Error: 30.6 → 30.6
Time: 3.2s
Precision: binary64
\[\sqrt{1 - {\left(\cos x\right)}^{2}}\]
↓
\[\sqrt{1 - {\left(\cos x\right)}^{2}}\]
\sqrt{1 - {\left(\cos x\right)}^{2}}
↓
\sqrt{1 - {\left(\cos x\right)}^{2}}
double code(double x) {
	return ((double) sqrt(((double) (1.0 - ((double) pow(((double) cos(x)), 2.0))))));
}
↓
double code(double x) {
	return ((double) sqrt(((double) (1.0 - ((double) pow(((double) cos(x)), 2.0))))));
}

Error

Bits error versus x

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Results

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Derivation

  1. Initial program 30.6

    \[\sqrt{1 - {\left(\cos x\right)}^{2}}\]

  2. Final simplification30.6

    \[\leadsto \sqrt{1 - {\left(\cos x\right)}^{2}}\]

Reproduce

herbie shell --seed 2020152 
(FPCore (x)
  :name "(sqrt (- 1 (pow (cos x) 2)))"
  :precision binary64
  (sqrt (- 1.0 (pow (cos x) 2.0))))