Average Error: 30.0 → 30.0
Time: 5.1s
Precision: binary64
\[\sin \left(\sqrt{x + 1}\right) \cdot \cos \left(\sqrt{x}\right) - \sin \left(\sqrt{x}\right) \cdot \cos \left(\sqrt{x + 1}\right)\]
↓
\[\sin \left(\sqrt{x + 1}\right) \cdot \cos \left(\sqrt{x}\right) - \sin \left(\sqrt{x}\right) \cdot \cos \left(\sqrt{x + 1}\right)\]
\sin \left(\sqrt{x + 1}\right) \cdot \cos \left(\sqrt{x}\right) - \sin \left(\sqrt{x}\right) \cdot \cos \left(\sqrt{x + 1}\right)
↓
\sin \left(\sqrt{x + 1}\right) \cdot \cos \left(\sqrt{x}\right) - \sin \left(\sqrt{x}\right) \cdot \cos \left(\sqrt{x + 1}\right)
double code(double x) {
	return ((double) (((double) (((double) sin(((double) sqrt(((double) (x + 1.0)))))) * ((double) cos(((double) sqrt(x)))))) - ((double) (((double) sin(((double) sqrt(x)))) * ((double) cos(((double) sqrt(((double) (x + 1.0))))))))));
}
↓
double code(double x) {
	return ((double) (((double) (((double) sin(((double) sqrt(((double) (x + 1.0)))))) * ((double) cos(((double) sqrt(x)))))) - ((double) (((double) sin(((double) sqrt(x)))) * ((double) cos(((double) sqrt(((double) (x + 1.0))))))))));
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 30.0

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

  2. Final simplification30.0

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

Reproduce

herbie shell --seed 2020152 
(FPCore (x)
  :name "(- (* (sin (sqrt (+ x 1))) (cos (sqrt x))) (* (sin (sqrt x)) (cos (sqrt (+ x 1)))))"
  :precision binary64
  (- (* (sin (sqrt (+ x 1.0))) (cos (sqrt x))) (* (sin (sqrt x)) (cos (sqrt (+ x 1.0))))))