Average Error: 35.3 → 35.3
Time: 6.1s
Precision: binary64
\[\frac{\sin \left(\sqrt{{\left(x + y\right)}^{2}}\right)}{\sqrt{{\left(x + y\right)}^{2}}} + \frac{\sin \left(\sqrt{{\left(x - y\right)}^{2}}\right)}{\sqrt{{\left(x - y\right)}^{2}}}\]
↓
\[\frac{\sin \left(\sqrt{{\left(x + y\right)}^{2}}\right)}{\sqrt{{\left(x + y\right)}^{2}}} + \frac{\sin \left(\sqrt{{\left(x - y\right)}^{2}}\right)}{\sqrt{{\left(x - y\right)}^{2}}}\]
\frac{\sin \left(\sqrt{{\left(x + y\right)}^{2}}\right)}{\sqrt{{\left(x + y\right)}^{2}}} + \frac{\sin \left(\sqrt{{\left(x - y\right)}^{2}}\right)}{\sqrt{{\left(x - y\right)}^{2}}}
↓
\frac{\sin \left(\sqrt{{\left(x + y\right)}^{2}}\right)}{\sqrt{{\left(x + y\right)}^{2}}} + \frac{\sin \left(\sqrt{{\left(x - y\right)}^{2}}\right)}{\sqrt{{\left(x - y\right)}^{2}}}
double code(double x, double y) {
	return ((double) (((double) (((double) sin(((double) sqrt(((double) pow(((double) (x + y)), 2.0)))))) / ((double) sqrt(((double) pow(((double) (x + y)), 2.0)))))) + ((double) (((double) sin(((double) sqrt(((double) pow(((double) (x - y)), 2.0)))))) / ((double) sqrt(((double) pow(((double) (x - y)), 2.0))))))));
}
↓
double code(double x, double y) {
	return ((double) (((double) (((double) sin(((double) sqrt(((double) pow(((double) (x + y)), 2.0)))))) / ((double) sqrt(((double) pow(((double) (x + y)), 2.0)))))) + ((double) (((double) sin(((double) sqrt(((double) pow(((double) (x - y)), 2.0)))))) / ((double) sqrt(((double) pow(((double) (x - y)), 2.0))))))));
}

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 35.3

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

  2. Final simplification35.3

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

Reproduce

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