Average Error: 0.0 → 0.0
Time: 2.1s
Precision: binary64
\[\left(\left(\frac{1}{x} + \frac{x}{x} \cdot x\right) - \frac{\sqrt{x}}{\sqrt{x \cdot \sqrt{x} + 1}}\right) - 2^{\sin x}\]
↓
\[x + \left(\frac{1}{x} - \left(\frac{\sqrt{x}}{\sqrt{x \cdot \sqrt{x} + 1}} + 2^{\sin x}\right)\right)\]
\left(\left(\frac{1}{x} + \frac{x}{x} \cdot x\right) - \frac{\sqrt{x}}{\sqrt{x \cdot \sqrt{x} + 1}}\right) - 2^{\sin x}
↓
x + \left(\frac{1}{x} - \left(\frac{\sqrt{x}}{\sqrt{x \cdot \sqrt{x} + 1}} + 2^{\sin x}\right)\right)
double code(double x) {
	return ((double) (((double) (((double) (((double) (1.0 / x)) + ((double) (((double) (x / x)) * x)))) - ((double) (((double) sqrt(x)) / ((double) sqrt(((double) (((double) (x * ((double) sqrt(x)))) + 1.0)))))))) - ((double) exp2(((double) sin(x))))));
}
↓
double code(double x) {
	return ((double) (x + ((double) (((double) (1.0 / x)) - ((double) (((double) (((double) sqrt(x)) / ((double) sqrt(((double) (((double) (x * ((double) sqrt(x)))) + 1.0)))))) + ((double) exp2(((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 0.0

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

  2. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2020152 
(FPCore (x)
  :name "(- (- (+ (/ 1 x) (* (/ x x) x)) (/ (sqrt x) (sqrt (+ (* x (sqrt x)) 1)))) (exp2 (sin x)))"
  :precision binary64
  (- (- (+ (/ 1.0 x) (* (/ x x) x)) (/ (sqrt x) (sqrt (+ (* x (sqrt x)) 1.0)))) (exp2 (sin x))))