Average Error: 30.9 → 29.8
Time: 4.9s
Precision: binary64
\[\frac{\sin x - x \cdot \cos x}{x \cdot \sin x}\]
↓
\[-1 \cdot \frac{\cos x}{\sin x} + \frac{1}{x}\]
\frac{\sin x - x \cdot \cos x}{x \cdot \sin x}
↓
-1 \cdot \frac{\cos x}{\sin x} + \frac{1}{x}
double code(double x) {
	return ((double) (((double) (((double) sin(x)) - ((double) (x * ((double) cos(x)))))) / ((double) (x * ((double) sin(x))))));
}
↓
double code(double x) {
	return ((double) (((double) (-1.0 * ((double) (((double) cos(x)) / ((double) sin(x)))))) + ((double) (1.0 / x))));
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 30.9

    \[\frac{\sin x - x \cdot \cos x}{x \cdot \sin x}\]

  2. Simplified29.8

    \[\leadsto \color{blue}{-1 \cdot \frac{\cos x}{\sin x} + \frac{1}{x}}\]

  3. Final simplification29.8

    \[\leadsto -1 \cdot \frac{\cos x}{\sin x} + \frac{1}{x}\]

Reproduce

herbie shell --seed 2020153 
(FPCore (x)
  :name "(/ (- (sin x) (* x (cos x))) (* x (sin x)))"
  :precision binary64
  (/ (- (sin x) (* x (cos x))) (* x (sin x))))