Average Error: 31.8 → 31.8
Time: 11.0s
Precision: binary64
\[\left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
↓
\[\begin{array}{l} t_0 := \pi \cdot \frac{angle}{180}\\ t_1 := \cos t_0\\ t_2 := \sqrt[3]{t_1}\\ \left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \mathsf{log1p}\left(\mathsf{expm1}\left(\sin t_0\right)\right)\right) \cdot \left(\left(\sqrt[3]{\sqrt[3]{t_1 \cdot \left(t_1 \cdot t_1\right)}} \cdot t_2\right) \cdot \sqrt[3]{t_2 \cdot \left(t_2 \cdot t_2\right)}\right) \end{array} \]
\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 := \cos t_0\\
t_2 := \sqrt[3]{t_1}\\
\left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \mathsf{log1p}\left(\mathsf{expm1}\left(\sin t_0\right)\right)\right) \cdot \left(\left(\sqrt[3]{\sqrt[3]{t_1 \cdot \left(t_1 \cdot t_1\right)}} \cdot t_2\right) \cdot \sqrt[3]{t_2 \cdot \left(t_2 \cdot t_2\right)}\right)
\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 (cos t_0)) (t_2 (cbrt t_1)))
   (*
    (* (* 2.0 (- (pow b 2.0) (pow a 2.0))) (log1p (expm1 (sin t_0))))
    (* (* (cbrt (cbrt (* t_1 (* t_1 t_1)))) t_2) (cbrt (* t_2 (* t_2 t_2)))))))
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 = cos(t_0);
	double t_2 = cbrt(t_1);
	return ((2.0 * (pow(b, 2.0) - pow(a, 2.0))) * log1p(expm1(sin(t_0)))) * ((cbrt(cbrt(t_1 * (t_1 * t_1))) * t_2) * cbrt(t_2 * (t_2 * t_2)));
}

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 31.8

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

  2. Applied add-cube-cbrt_binary6431.8

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

  3. Applied log1p-expm1-u_binary6431.8

    \[\leadsto \left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(\sin \left(\pi \cdot \frac{angle}{180}\right)\right)\right)}\right) \cdot \left(\left(\sqrt[3]{\cos \left(\pi \cdot \frac{angle}{180}\right)} \cdot \sqrt[3]{\cos \left(\pi \cdot \frac{angle}{180}\right)}\right) \cdot \sqrt[3]{\cos \left(\pi \cdot \frac{angle}{180}\right)}\right) \]

  4. Applied add-cube-cbrt_binary6431.8

    \[\leadsto \left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \mathsf{log1p}\left(\mathsf{expm1}\left(\sin \left(\pi \cdot \frac{angle}{180}\right)\right)\right)\right) \cdot \left(\left(\sqrt[3]{\cos \left(\pi \cdot \frac{angle}{180}\right)} \cdot \sqrt[3]{\cos \left(\pi \cdot \frac{angle}{180}\right)}\right) \cdot \sqrt[3]{\color{blue}{\left(\sqrt[3]{\cos \left(\pi \cdot \frac{angle}{180}\right)} \cdot \sqrt[3]{\cos \left(\pi \cdot \frac{angle}{180}\right)}\right) \cdot \sqrt[3]{\cos \left(\pi \cdot \frac{angle}{180}\right)}}}\right) \]

  5. Applied add-cbrt-cube_binary6431.8

    \[\leadsto \left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \mathsf{log1p}\left(\mathsf{expm1}\left(\sin \left(\pi \cdot \frac{angle}{180}\right)\right)\right)\right) \cdot \left(\left(\sqrt[3]{\color{blue}{\sqrt[3]{\left(\cos \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)}}} \cdot \sqrt[3]{\cos \left(\pi \cdot \frac{angle}{180}\right)}\right) \cdot \sqrt[3]{\left(\sqrt[3]{\cos \left(\pi \cdot \frac{angle}{180}\right)} \cdot \sqrt[3]{\cos \left(\pi \cdot \frac{angle}{180}\right)}\right) \cdot \sqrt[3]{\cos \left(\pi \cdot \frac{angle}{180}\right)}}\right) \]

  6. Final simplification31.8

    \[\leadsto \left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \mathsf{log1p}\left(\mathsf{expm1}\left(\sin \left(\pi \cdot \frac{angle}{180}\right)\right)\right)\right) \cdot \left(\left(\sqrt[3]{\sqrt[3]{\cos \left(\pi \cdot \frac{angle}{180}\right) \cdot \left(\cos \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right)}} \cdot \sqrt[3]{\cos \left(\pi \cdot \frac{angle}{180}\right)}\right) \cdot \sqrt[3]{\sqrt[3]{\cos \left(\pi \cdot \frac{angle}{180}\right)} \cdot \left(\sqrt[3]{\cos \left(\pi \cdot \frac{angle}{180}\right)} \cdot \sqrt[3]{\cos \left(\pi \cdot \frac{angle}{180}\right)}\right)}\right) \]

Reproduce

herbie shell --seed 2021224 
(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)))))