Average Error: 31.9 → 31.9
Time: 2.9s
Precision: binary64
\[\frac{1 - {\left(\cos x\right)}^{2}}{{x}^{2}}\]
↓
\[\frac{1 - {\left(\cos x\right)}^{2}}{{x}^{2}}\]
\frac{1 - {\left(\cos x\right)}^{2}}{{x}^{2}}
↓
\frac{1 - {\left(\cos x\right)}^{2}}{{x}^{2}}
double code(double x) {
	return ((double) (((double) (1.0 - ((double) pow(((double) cos(x)), 2.0)))) / ((double) pow(x, 2.0))));
}
↓
double code(double x) {
	return ((double) (((double) (1.0 - ((double) pow(((double) cos(x)), 2.0)))) / ((double) pow(x, 2.0))));
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 31.9

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

  2. Final simplification31.9

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

Reproduce

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