Average Error: 16.3 → 16.3
Time: 2.2s
Precision: binary64
\[\sqrt{1 + \frac{1}{{\left(\tan \left(\frac{x}{2}\right)\right)}^{2}}}\]
↓
\[\sqrt{1 + \frac{1}{{\left(\tan \left(\frac{x}{2}\right)\right)}^{2}}}\]
\sqrt{1 + \frac{1}{{\left(\tan \left(\frac{x}{2}\right)\right)}^{2}}}
↓
\sqrt{1 + \frac{1}{{\left(\tan \left(\frac{x}{2}\right)\right)}^{2}}}
double code(double x) {
	return ((double) sqrt(((double) (1.0 + ((double) (1.0 / ((double) pow(((double) tan(((double) (x / 2.0)))), 2.0))))))));
}
↓
double code(double x) {
	return ((double) sqrt(((double) (1.0 + ((double) (1.0 / ((double) pow(((double) tan(((double) (x / 2.0)))), 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 16.3

    \[\sqrt{1 + \frac{1}{{\left(\tan \left(\frac{x}{2}\right)\right)}^{2}}}\]

  2. Final simplification16.3

    \[\leadsto \sqrt{1 + \frac{1}{{\left(\tan \left(\frac{x}{2}\right)\right)}^{2}}}\]

Reproduce

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