Average Error: 17.3 → 17.3
Time: 4.9s
Precision: binary64
\[\left(\left(\frac{1}{\sqrt{x + 1}} - \sqrt{x}\right) + \frac{\sin \left(x \cdot x\right)}{\cos \left(x + 125\right)}\right) - \frac{1}{\tan \left(\sin x\right)}\]
↓
\[\left(\left(\frac{1}{\sqrt{x + 1}} - \sqrt{x}\right) + \frac{\sin \left(x \cdot x\right)}{\cos \left(x + 125\right)}\right) - \frac{1}{\tan \left(\sin x\right)}\]
\left(\left(\frac{1}{\sqrt{x + 1}} - \sqrt{x}\right) + \frac{\sin \left(x \cdot x\right)}{\cos \left(x + 125\right)}\right) - \frac{1}{\tan \left(\sin x\right)}
↓
\left(\left(\frac{1}{\sqrt{x + 1}} - \sqrt{x}\right) + \frac{\sin \left(x \cdot x\right)}{\cos \left(x + 125\right)}\right) - \frac{1}{\tan \left(\sin x\right)}
double code(double x) {
	return ((double) (((double) (((double) (((double) (1.0 / ((double) sqrt(((double) (x + 1.0)))))) - ((double) sqrt(x)))) + ((double) (((double) sin(((double) (x * x)))) / ((double) cos(((double) (x + 125.0)))))))) - ((double) (1.0 / ((double) tan(((double) sin(x))))))));
}
↓
double code(double x) {
	return ((double) (((double) (((double) (((double) (1.0 / ((double) sqrt(((double) (x + 1.0)))))) - ((double) sqrt(x)))) + ((double) (((double) sin(((double) (x * x)))) / ((double) cos(((double) (x + 125.0)))))))) - ((double) (1.0 / ((double) tan(((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 17.3

    \[\left(\left(\frac{1}{\sqrt{x + 1}} - \sqrt{x}\right) + \frac{\sin \left(x \cdot x\right)}{\cos \left(x + 125\right)}\right) - \frac{1}{\tan \left(\sin x\right)}\]

  2. Final simplification17.3

    \[\leadsto \left(\left(\frac{1}{\sqrt{x + 1}} - \sqrt{x}\right) + \frac{\sin \left(x \cdot x\right)}{\cos \left(x + 125\right)}\right) - \frac{1}{\tan \left(\sin x\right)}\]

Reproduce

herbie shell --seed 2020152 
(FPCore (x)
  :name "(- (+ (- (/ 1 (sqrt (+ x 1))) (sqrt x)) (/ (sin (* x x)) (cos (+ x 125)))) (/ 1 (tan (sin x))))"
  :precision binary64
  (- (+ (- (/ 1.0 (sqrt (+ x 1.0))) (sqrt x)) (/ (sin (* x x)) (cos (+ x 125.0)))) (/ 1.0 (tan (sin x)))))