Average Error: 13.0 → 13.0
Time: 15.2s
Precision: binary64
\[{\left(a \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} \]
↓
\[\begin{array}{l} t_0 := \sqrt[3]{\sqrt[3]{angle}}\\ {\left(a \cdot \cos \left(\left(\pi \cdot \frac{\mathsf{expm1}\left(\mathsf{log1p}\left(\sqrt[3]{angle} \cdot \sqrt[3]{angle}\right)\right)}{\sqrt{180}}\right) \cdot \frac{t_0 \cdot \left(t_0 \cdot t_0\right)}{\sqrt{180}}\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} \end{array} \]
{\left(a \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2}
↓
\begin{array}{l}
t_0 := \sqrt[3]{\sqrt[3]{angle}}\\
{\left(a \cdot \cos \left(\left(\pi \cdot \frac{\mathsf{expm1}\left(\mathsf{log1p}\left(\sqrt[3]{angle} \cdot \sqrt[3]{angle}\right)\right)}{\sqrt{180}}\right) \cdot \frac{t_0 \cdot \left(t_0 \cdot t_0\right)}{\sqrt{180}}\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2}
\end{array}

(FPCore (a b angle)
 :precision binary64
 (+
  (pow (* a (cos (* PI (/ angle 180.0)))) 2.0)
  (pow (* b (sin (* PI (/ angle 180.0)))) 2.0)))
↓
(FPCore (a b angle)
 :precision binary64
 (let* ((t_0 (cbrt (cbrt angle))))
   (+
    (pow
     (*
      a
      (cos
       (*
        (* PI (/ (expm1 (log1p (* (cbrt angle) (cbrt angle)))) (sqrt 180.0)))
        (/ (* t_0 (* t_0 t_0)) (sqrt 180.0)))))
     2.0)
    (pow (* b (sin (* PI (/ angle 180.0)))) 2.0))))
double code(double a, double b, double angle) {
	return pow((a * cos(((double) M_PI) * (angle / 180.0))), 2.0) + pow((b * sin(((double) M_PI) * (angle / 180.0))), 2.0);
}
↓
double code(double a, double b, double angle) {
	double t_0 = cbrt(cbrt(angle));
	return pow((a * cos((((double) M_PI) * (expm1(log1p(cbrt(angle) * cbrt(angle))) / sqrt(180.0))) * ((t_0 * (t_0 * t_0)) / sqrt(180.0)))), 2.0) + pow((b * sin(((double) M_PI) * (angle / 180.0))), 2.0);
}

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 13.0

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

  2. Applied add-sqr-sqrt_binary6413.0

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

  3. Applied add-cube-cbrt_binary6413.0

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

  4. Applied times-frac_binary6413.0

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

  5. Applied associate-*r*_binary6413.0

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

  6. Applied expm1-log1p-u_binary6413.0

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

  7. Applied add-cube-cbrt_binary6413.0

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

  8. Final simplification13.0

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

Reproduce

herbie shell --seed 2022068 
(FPCore (a b angle)
  :name "ab-angle->ABCF C"
  :precision binary64
  (+ (pow (* a (cos (* PI (/ angle 180.0)))) 2.0) (pow (* b (sin (* PI (/ angle 180.0)))) 2.0)))