Average Error: 16.2 → 16.2
Time: 3.9s
Precision: binary64
\[\sqrt{\left(1 + \sin x\right) + {\left(\sin x\right)}^{2}} - \sqrt{1 + \sin x}\]
↓
\[\sqrt{\left(1 + \sin x\right) + {\left(\sin x\right)}^{2}} - \sqrt{1 + \sin x}\]
\sqrt{\left(1 + \sin x\right) + {\left(\sin x\right)}^{2}} - \sqrt{1 + \sin x}
↓
\sqrt{\left(1 + \sin x\right) + {\left(\sin x\right)}^{2}} - \sqrt{1 + \sin x}
double code(double x) {
	return ((double) (((double) sqrt(((double) (((double) (1.0 + ((double) sin(x)))) + ((double) pow(((double) sin(x)), 2.0)))))) - ((double) sqrt(((double) (1.0 + ((double) sin(x))))))));
}
↓
double code(double x) {
	return ((double) (((double) sqrt(((double) (((double) (1.0 + ((double) sin(x)))) + ((double) pow(((double) sin(x)), 2.0)))))) - ((double) sqrt(((double) (1.0 + ((double) sin(x))))))));
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 16.2

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

  2. Final simplification16.2

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

Reproduce

herbie shell --seed 2020152 
(FPCore (x)
  :name "(- (sqrt (+ (+ 1.0 (sin x)) (pow (sin x) 2.0))) (sqrt (+ 1.0 (sin x))))"
  :precision binary64
  (- (sqrt (+ (+ 1.0 (sin x)) (pow (sin x) 2.0))) (sqrt (+ 1.0 (sin x)))))