Average Error: 31.5 → 0.0
Time: 9.9s
Precision: binary64
\[\frac{x - \sin x}{x - \tan x}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \leq -0.02787034415248285:\\ \;\;\;\;\frac{x - \sin x}{x - \tan x}\\ \mathbf{elif}\;x \leq 0.026051316717657508:\\ \;\;\;\;x \cdot \left(x \cdot 0.225\right) + \left(-0.5 + {x}^{4} \cdot -0.009642857142857142\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{x - \tan x}{x - \sin x}}\\ \end{array}\]
\frac{x - \sin x}{x - \tan x}
↓
\begin{array}{l}
\mathbf{if}\;x \leq -0.02787034415248285:\\
\;\;\;\;\frac{x - \sin x}{x - \tan x}\\

\mathbf{elif}\;x \leq 0.026051316717657508:\\
\;\;\;\;x \cdot \left(x \cdot 0.225\right) + \left(-0.5 + {x}^{4} \cdot -0.009642857142857142\right)\\

\mathbf{else}:\\
\;\;\;\;\frac{1}{\frac{x - \tan x}{x - \sin x}}\\

\end{array}
(FPCore (x) :precision binary64 (/ (- x (sin x)) (- x (tan x))))
↓
(FPCore (x)
 :precision binary64
 (if (<= x -0.02787034415248285)
   (/ (- x (sin x)) (- x (tan x)))
   (if (<= x 0.026051316717657508)
     (+ (* x (* x 0.225)) (+ -0.5 (* (pow x 4.0) -0.009642857142857142)))
     (/ 1.0 (/ (- x (tan x)) (- x (sin x)))))))
double code(double x) {
	return (((double) (x - ((double) sin(x)))) / ((double) (x - ((double) tan(x)))));
}
↓
double code(double x) {
	double tmp;
	if ((x <= -0.02787034415248285)) {
		tmp = (((double) (x - ((double) sin(x)))) / ((double) (x - ((double) tan(x)))));
	} else {
		double tmp_1;
		if ((x <= 0.026051316717657508)) {
			tmp_1 = ((double) (((double) (x * ((double) (x * 0.225)))) + ((double) (-0.5 + ((double) (((double) pow(x, 4.0)) * -0.009642857142857142))))));
		} else {
			tmp_1 = (1.0 / (((double) (x - ((double) tan(x)))) / ((double) (x - ((double) sin(x))))));
		}
		tmp = tmp_1;
	}
	return tmp;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 3 regimes

  2. if x < -0.027870344152482851

    1. Initial program Error: 0.1 bits

      \[\frac{x - \sin x}{x - \tan x}\]

    if -0.027870344152482851 < x < 0.026051316717657508

    1. Initial program Error: 63.1 bits

      \[\frac{x - \sin x}{x - \tan x}\]

    2. Taylor expanded around 0 Error: 0.0 bits

      \[\leadsto \color{blue}{0.225 \cdot {x}^{2} - \left(0.009642857142857142 \cdot {x}^{4} + 0.5\right)}\]

    3. SimplifiedError: 0.0 bits

      \[\leadsto \color{blue}{x \cdot \left(x \cdot 0.225\right) + \left(-0.5 + {x}^{4} \cdot -0.009642857142857142\right)}\]

    if 0.026051316717657508 < x

    1. Initial program Error: 0.0 bits

      \[\frac{x - \sin x}{x - \tan x}\]
    2. Using strategy rm

    3. Applied clear-numError: 0.0 bits

      \[\leadsto \color{blue}{\frac{1}{\frac{x - \tan x}{x - \sin x}}}\]
  3. Recombined 3 regimes into one program.

  4. Final simplificationError: 0.0 bits

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.02787034415248285:\\ \;\;\;\;\frac{x - \sin x}{x - \tan x}\\ \mathbf{elif}\;x \leq 0.026051316717657508:\\ \;\;\;\;x \cdot \left(x \cdot 0.225\right) + \left(-0.5 + {x}^{4} \cdot -0.009642857142857142\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{x - \tan x}{x - \sin x}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020203 
(FPCore (x)
  :name "sintan (problem 3.4.5)"
  :precision binary64
  (/ (- x (sin x)) (- x (tan x))))