Average Error: 30.4 → 30.5
Time: 15.1s
Precision: binary64
\[\left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
↓
\[\begin{array}{l} t_0 := \pi \cdot \frac{angle}{180}\\ t_1 := \sqrt[3]{\cos t_0}\\ \left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin t_0\right) \cdot \sqrt[3]{{\left(t_1 \cdot \left(t_1 \cdot \sqrt[3]{\cos \left(0.005555555555555556 \cdot \left(\pi \cdot angle\right)\right)}\right)\right)}^{3}} \end{array} \]
\left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)
↓
\begin{array}{l}
t_0 := \pi \cdot \frac{angle}{180}\\
t_1 := \sqrt[3]{\cos t_0}\\
\left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin t_0\right) \cdot \sqrt[3]{{\left(t_1 \cdot \left(t_1 \cdot \sqrt[3]{\cos \left(0.005555555555555556 \cdot \left(\pi \cdot angle\right)\right)}\right)\right)}^{3}}
\end{array}

(FPCore (a b angle)
 :precision binary64
 (*
  (* (* 2.0 (- (pow b 2.0) (pow a 2.0))) (sin (* PI (/ angle 180.0))))
  (cos (* PI (/ angle 180.0)))))
↓
(FPCore (a b angle)
 :precision binary64
 (let* ((t_0 (* PI (/ angle 180.0))) (t_1 (cbrt (cos t_0))))
   (*
    (* (* 2.0 (- (pow b 2.0) (pow a 2.0))) (sin t_0))
    (cbrt
     (pow
      (* t_1 (* t_1 (cbrt (cos (* 0.005555555555555556 (* PI angle))))))
      3.0)))))
double code(double a, double b, double angle) {
	return ((2.0 * (pow(b, 2.0) - pow(a, 2.0))) * sin(((double) M_PI) * (angle / 180.0))) * cos(((double) M_PI) * (angle / 180.0));
}
↓
double code(double a, double b, double angle) {
	double t_0 = ((double) M_PI) * (angle / 180.0);
	double t_1 = cbrt(cos(t_0));
	return ((2.0 * (pow(b, 2.0) - pow(a, 2.0))) * sin(t_0)) * cbrt(pow((t_1 * (t_1 * cbrt(cos(0.005555555555555556 * (((double) M_PI) * angle))))), 3.0));
}

Error

Bits error versus a

Bits error versus b

Bits error versus angle

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 30.4

    \[\left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]

  2. Applied add-cbrt-cube_binary6430.4

    \[\leadsto \left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \color{blue}{\sqrt[3]{\left(\cos \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)}} \]

  3. Simplified30.4

    \[\leadsto \left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \sqrt[3]{\color{blue}{{\cos \left(\pi \cdot \frac{angle}{180}\right)}^{3}}} \]

  4. Applied add-cube-cbrt_binary6430.4

    \[\leadsto \left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \sqrt[3]{{\color{blue}{\left(\left(\sqrt[3]{\cos \left(\pi \cdot \frac{angle}{180}\right)} \cdot \sqrt[3]{\cos \left(\pi \cdot \frac{angle}{180}\right)}\right) \cdot \sqrt[3]{\cos \left(\pi \cdot \frac{angle}{180}\right)}\right)}}^{3}} \]

  5. Taylor expanded in angle around inf 30.5

    \[\leadsto \left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \sqrt[3]{{\left(\left(\sqrt[3]{\cos \left(\pi \cdot \frac{angle}{180}\right)} \cdot \sqrt[3]{\color{blue}{\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}}\right) \cdot \sqrt[3]{\cos \left(\pi \cdot \frac{angle}{180}\right)}\right)}^{3}} \]

  6. Final simplification30.5

    \[\leadsto \left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \sqrt[3]{{\left(\sqrt[3]{\cos \left(\pi \cdot \frac{angle}{180}\right)} \cdot \left(\sqrt[3]{\cos \left(\pi \cdot \frac{angle}{180}\right)} \cdot \sqrt[3]{\cos \left(0.005555555555555556 \cdot \left(\pi \cdot angle\right)\right)}\right)\right)}^{3}} \]

Reproduce

herbie shell --seed 2021313 
(FPCore (a b angle)
  :name "ab-angle->ABCF B"
  :precision binary64
  (* (* (* 2.0 (- (pow b 2.0) (pow a 2.0))) (sin (* PI (/ angle 180.0)))) (cos (* PI (/ angle 180.0)))))