Average Error: 20.3 → 20.3
Time: 17.8s
Precision: binary64
\[{\left(a \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} \]
↓
\[\begin{array}{l} t_0 := \frac{\sqrt[3]{angle}}{\sqrt{180}}\\ t_1 := \sqrt[3]{angle} \cdot \sqrt[3]{angle}\\ t_2 := \cos \left(\left(\pi \cdot \frac{t_1}{\sqrt{180}}\right) \cdot t_0\right)\\ {\left(a \cdot \sqrt[3]{\left(t_2 \cdot t_2\right) \cdot \cos \left(t_0 \cdot \left(\pi \cdot \frac{\sqrt[3]{t_1} \cdot {\left(\sqrt[3]{\sqrt[3]{angle}}\right)}^{4}}{\sqrt{180}}\right)\right)}\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} \end{array} \]
{\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 := \frac{\sqrt[3]{angle}}{\sqrt{180}}\\
t_1 := \sqrt[3]{angle} \cdot \sqrt[3]{angle}\\
t_2 := \cos \left(\left(\pi \cdot \frac{t_1}{\sqrt{180}}\right) \cdot t_0\right)\\
{\left(a \cdot \sqrt[3]{\left(t_2 \cdot t_2\right) \cdot \cos \left(t_0 \cdot \left(\pi \cdot \frac{\sqrt[3]{t_1} \cdot {\left(\sqrt[3]{\sqrt[3]{angle}}\right)}^{4}}{\sqrt{180}}\right)\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 angle) (sqrt 180.0)))
        (t_1 (* (cbrt angle) (cbrt angle)))
        (t_2 (cos (* (* PI (/ t_1 (sqrt 180.0))) t_0))))
   (+
    (pow
     (*
      a
      (cbrt
       (*
        (* t_2 t_2)
        (cos
         (*
          t_0
          (*
           PI
           (/ (* (cbrt t_1) (pow (cbrt (cbrt angle)) 4.0)) (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(angle) / sqrt(180.0);
	double t_1 = cbrt(angle) * cbrt(angle);
	double t_2 = cos((((double) M_PI) * (t_1 / sqrt(180.0))) * t_0);
	return pow((a * cbrt((t_2 * t_2) * cos(t_0 * (((double) M_PI) * ((cbrt(t_1) * pow(cbrt(cbrt(angle)), 4.0)) / 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 20.3

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

  2. Applied add-sqr-sqrt_binary6420.3

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

  3. Applied add-cube-cbrt_binary6420.3

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

  4. Applied times-frac_binary6420.3

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

  5. Applied associate-*r*_binary6420.3

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

  6. Applied add-cbrt-cube_binary6420.3

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

  7. Applied add-cube-cbrt_binary6420.3

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

  8. Applied cbrt-prod_binary6420.3

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

  9. Applied associate-*l*_binary6420.3

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

  10. Simplified20.3

    \[\leadsto {\left(a \cdot \sqrt[3]{\left(\cos \left(\left(\pi \cdot \frac{\sqrt[3]{angle} \cdot \sqrt[3]{angle}}{\sqrt{180}}\right) \cdot \frac{\sqrt[3]{angle}}{\sqrt{180}}\right) \cdot \cos \left(\left(\pi \cdot \frac{\sqrt[3]{angle} \cdot \sqrt[3]{angle}}{\sqrt{180}}\right) \cdot \frac{\sqrt[3]{angle}}{\sqrt{180}}\right)\right) \cdot \cos \left(\left(\pi \cdot \frac{\sqrt[3]{\sqrt[3]{angle} \cdot \sqrt[3]{angle}} \cdot \color{blue}{{\left(\sqrt[3]{\sqrt[3]{angle}}\right)}^{4}}}{\sqrt{180}}\right) \cdot \frac{\sqrt[3]{angle}}{\sqrt{180}}\right)}\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} \]

  11. Final simplification20.3

    \[\leadsto {\left(a \cdot \sqrt[3]{\left(\cos \left(\left(\pi \cdot \frac{\sqrt[3]{angle} \cdot \sqrt[3]{angle}}{\sqrt{180}}\right) \cdot \frac{\sqrt[3]{angle}}{\sqrt{180}}\right) \cdot \cos \left(\left(\pi \cdot \frac{\sqrt[3]{angle} \cdot \sqrt[3]{angle}}{\sqrt{180}}\right) \cdot \frac{\sqrt[3]{angle}}{\sqrt{180}}\right)\right) \cdot \cos \left(\frac{\sqrt[3]{angle}}{\sqrt{180}} \cdot \left(\pi \cdot \frac{\sqrt[3]{\sqrt[3]{angle} \cdot \sqrt[3]{angle}} \cdot {\left(\sqrt[3]{\sqrt[3]{angle}}\right)}^{4}}{\sqrt{180}}\right)\right)}\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} \]

Reproduce

herbie shell --seed 2021307 
(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)))