Average Error: 0.1 → 0.1
Time: 3.0s
Precision: binary64
\[\sqrt{{\left(\sin x\right)}^{2} + {\left(\cos x\right)}^{2}}\]
↓
\[\sqrt{{\left(\sin x\right)}^{2} + {\left(\cos x\right)}^{2}}\]
\sqrt{{\left(\sin x\right)}^{2} + {\left(\cos x\right)}^{2}}
↓
\sqrt{{\left(\sin x\right)}^{2} + {\left(\cos x\right)}^{2}}
double code(double x) {
	return ((double) sqrt(((double) (((double) pow(((double) sin(x)), 2.0)) + ((double) pow(((double) cos(x)), 2.0))))));
}
↓
double code(double x) {
	return ((double) sqrt(((double) (((double) pow(((double) sin(x)), 2.0)) + ((double) pow(((double) cos(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 0.1

    \[\sqrt{{\left(\sin x\right)}^{2} + {\left(\cos x\right)}^{2}}\]

  2. Final simplification0.1

    \[\leadsto \sqrt{{\left(\sin x\right)}^{2} + {\left(\cos x\right)}^{2}}\]

Reproduce

herbie shell --seed 2020153 
(FPCore (x)
  :name "(sqrt (+ (pow (sin x) 2) (pow (cos x) 2)))"
  :precision binary64
  (sqrt (+ (pow (sin x) 2.0) (pow (cos x) 2.0))))