Average Error: 0.0 → 0.0
Time: 4.7s
Precision: binary64
\[{\left(\sin \left(\sqrt{x + 1} - \sqrt{x}\right)\right)}^{2} + {\left(\cos \left(\sqrt{x + 1} - \sqrt{x}\right)\right)}^{2}\]
↓
\[{\left(\sin \left(\sqrt{x + 1} - \sqrt{x}\right)\right)}^{2} + {\left(\cos \left(\sqrt{x + 1} - \sqrt{x}\right)\right)}^{2}\]
{\left(\sin \left(\sqrt{x + 1} - \sqrt{x}\right)\right)}^{2} + {\left(\cos \left(\sqrt{x + 1} - \sqrt{x}\right)\right)}^{2}
↓
{\left(\sin \left(\sqrt{x + 1} - \sqrt{x}\right)\right)}^{2} + {\left(\cos \left(\sqrt{x + 1} - \sqrt{x}\right)\right)}^{2}
double code(double x) {
	return ((double) (((double) pow(((double) sin(((double) (((double) sqrt(((double) (x + 1.0)))) - ((double) sqrt(x)))))), 2.0)) + ((double) pow(((double) cos(((double) (((double) sqrt(((double) (x + 1.0)))) - ((double) sqrt(x)))))), 2.0))));
}
↓
double code(double x) {
	return ((double) (((double) pow(((double) sin(((double) (((double) sqrt(((double) (x + 1.0)))) - ((double) sqrt(x)))))), 2.0)) + ((double) pow(((double) cos(((double) (((double) sqrt(((double) (x + 1.0)))) - ((double) sqrt(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 0.0

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

  2. Final simplification0.0

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

Reproduce

herbie shell --seed 2020153 
(FPCore (x)
  :name "(+ (pow (sin (- (sqrt (+ x 1)) (sqrt x))) 2) (pow (cos (- (sqrt (+ x 1)) (sqrt x))) 2))"
  :precision binary64
  (+ (pow (sin (- (sqrt (+ x 1.0)) (sqrt x))) 2.0) (pow (cos (- (sqrt (+ x 1.0)) (sqrt x))) 2.0)))