Average Error: 1.7 → 1.7
Time: 36.0s
Precision: binary64
\[x \cdot \tan \left(\frac{x}{2}\right) + \frac{\left(q1 + q2 \cdot \sqrt{3}\right) \cdot \sinh q1 + \left(q1 \cdot \sqrt{3} - q2\right) \cdot \sin q2}{\cosh q1 + \cos q2}\]
↓
\[x \cdot \tan \left(\frac{x}{2}\right) + \frac{\left(q1 + q2 \cdot \sqrt{3}\right) \cdot \sinh q1 + \left(q1 \cdot \sqrt{3} - q2\right) \cdot \sin q2}{\cosh q1 + \cos q2}\]
x \cdot \tan \left(\frac{x}{2}\right) + \frac{\left(q1 + q2 \cdot \sqrt{3}\right) \cdot \sinh q1 + \left(q1 \cdot \sqrt{3} - q2\right) \cdot \sin q2}{\cosh q1 + \cos q2}
↓
x \cdot \tan \left(\frac{x}{2}\right) + \frac{\left(q1 + q2 \cdot \sqrt{3}\right) \cdot \sinh q1 + \left(q1 \cdot \sqrt{3} - q2\right) \cdot \sin q2}{\cosh q1 + \cos q2}
double code(double x, double q1, double q2) {
	return ((double) (((double) (x * ((double) tan(((double) (x / 2.0)))))) + ((double) (((double) (((double) (((double) (q1 + ((double) (q2 * ((double) sqrt(3.0)))))) * ((double) sinh(q1)))) + ((double) (((double) (((double) (q1 * ((double) sqrt(3.0)))) - q2)) * ((double) sin(q2)))))) / ((double) (((double) cosh(q1)) + ((double) cos(q2))))))));
}
↓
double code(double x, double q1, double q2) {
	return ((double) (((double) (x * ((double) tan(((double) (x / 2.0)))))) + ((double) (((double) (((double) (((double) (q1 + ((double) (q2 * ((double) sqrt(3.0)))))) * ((double) sinh(q1)))) + ((double) (((double) (((double) (q1 * ((double) sqrt(3.0)))) - q2)) * ((double) sin(q2)))))) / ((double) (((double) cosh(q1)) + ((double) cos(q2))))))));
}

Error

Bits error versus x

Bits error versus q1

Bits error versus q2

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 1.7

    \[x \cdot \tan \left(\frac{x}{2}\right) + \frac{\left(q1 + q2 \cdot \sqrt{3}\right) \cdot \sinh q1 + \left(q1 \cdot \sqrt{3} - q2\right) \cdot \sin q2}{\cosh q1 + \cos q2}\]

  2. Final simplification1.7

    \[\leadsto x \cdot \tan \left(\frac{x}{2}\right) + \frac{\left(q1 + q2 \cdot \sqrt{3}\right) \cdot \sinh q1 + \left(q1 \cdot \sqrt{3} - q2\right) \cdot \sin q2}{\cosh q1 + \cos q2}\]

Reproduce

herbie shell --seed 2020153 
(FPCore (x q1 q2)
  :name "(+ (* x (tan (/ x 2))) (/ (+ (* (+ q1 (* q2 (sqrt 3))) (sinh q1)) (* (- (* q1 (sqrt 3)) q2) (sin q2))) (+ (cosh q1) (cos q2))))"
  :precision binary64
  (+ (* x (tan (/ x 2.0))) (/ (+ (* (+ q1 (* q2 (sqrt 3.0))) (sinh q1)) (* (- (* q1 (sqrt 3.0)) q2) (sin q2))) (+ (cosh q1) (cos q2)))))