Average Error: 15.9 → 0.3
Time: 4.1s
Precision: binary64
\[\left(\left(\frac{1}{x} + \frac{x}{x \cdot \tan x}\right) - \frac{\sqrt{x}}{\sqrt{x \cdot \sqrt{x} + 1}}\right) - 2^{\sin x}\]
↓
\[\left(\frac{1}{x} - \left(\frac{\sqrt{x}}{\sqrt{x \cdot \sqrt{x} + 1}} + 2^{\sin x}\right)\right) - \frac{-1}{\tan x}\]
\left(\left(\frac{1}{x} + \frac{x}{x \cdot \tan x}\right) - \frac{\sqrt{x}}{\sqrt{x \cdot \sqrt{x} + 1}}\right) - 2^{\sin x}
↓
\left(\frac{1}{x} - \left(\frac{\sqrt{x}}{\sqrt{x \cdot \sqrt{x} + 1}} + 2^{\sin x}\right)\right) - \frac{-1}{\tan x}
double code(double x) {
	return ((double) (((double) (((double) (((double) (1.0 / x)) + ((double) (x / ((double) (x * ((double) tan(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) (((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)))))))) - ((double) (-1.0 / ((double) tan(x))))));
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 15.9

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

  2. Simplified0.3

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

  3. Final simplification0.3

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

Reproduce

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