Average Error: 40.7 → 40.7
Time: 2.8s
Precision: binary64
\[\frac{\sin \left(\sqrt{\left|x + y\right|}\right)}{\sqrt{\left|x + y\right|}} + \frac{\sin \left(\sqrt{\left|x - y\right|}\right)}{\sqrt{\left|x - y\right|}}\]
↓
\[\frac{\sin \left(\sqrt{\left|x + y\right|}\right)}{\sqrt{\left|x + y\right|}} + \frac{\sin \left(\sqrt{\left|x - y\right|}\right)}{\sqrt{\left|x - y\right|}}\]
\frac{\sin \left(\sqrt{\left|x + y\right|}\right)}{\sqrt{\left|x + y\right|}} + \frac{\sin \left(\sqrt{\left|x - y\right|}\right)}{\sqrt{\left|x - y\right|}}
↓
\frac{\sin \left(\sqrt{\left|x + y\right|}\right)}{\sqrt{\left|x + y\right|}} + \frac{\sin \left(\sqrt{\left|x - y\right|}\right)}{\sqrt{\left|x - y\right|}}
double code(double x, double y) {
	return ((double) (((double) (((double) sin(((double) sqrt(((double) fabs(((double) (x + y)))))))) / ((double) sqrt(((double) fabs(((double) (x + y)))))))) + ((double) (((double) sin(((double) sqrt(((double) fabs(((double) (x - y)))))))) / ((double) sqrt(((double) fabs(((double) (x - y))))))))));
}
↓
double code(double x, double y) {
	return ((double) (((double) (((double) sin(((double) sqrt(((double) fabs(((double) (x + y)))))))) / ((double) sqrt(((double) fabs(((double) (x + y)))))))) + ((double) (((double) sin(((double) sqrt(((double) fabs(((double) (x - y)))))))) / ((double) sqrt(((double) fabs(((double) (x - y))))))))));
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 40.7

    \[\frac{\sin \left(\sqrt{\left|x + y\right|}\right)}{\sqrt{\left|x + y\right|}} + \frac{\sin \left(\sqrt{\left|x - y\right|}\right)}{\sqrt{\left|x - y\right|}}\]

  2. Final simplification40.7

    \[\leadsto \frac{\sin \left(\sqrt{\left|x + y\right|}\right)}{\sqrt{\left|x + y\right|}} + \frac{\sin \left(\sqrt{\left|x - y\right|}\right)}{\sqrt{\left|x - y\right|}}\]

Reproduce

herbie shell --seed 2020153 
(FPCore (x y)
  :name "(+ (/ (sin (sqrt (fabs (+ x y)))) (sqrt (fabs (+ x y)))) (/ (sin (sqrt (fabs (- x y)))) (sqrt (fabs (- x y)))))"
  :precision binary64
  (+ (/ (sin (sqrt (fabs (+ x y)))) (sqrt (fabs (+ x y)))) (/ (sin (sqrt (fabs (- x y)))) (sqrt (fabs (- x y))))))