Average Error: 20.2 → 20.2
Time: 17.5s
Precision: binary64
\[{\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \cos \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} \]
↓
\[\begin{array}{l} t_0 := \sqrt[3]{angle} \cdot \sqrt[3]{angle}\\ {\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \cos \left(t_0 \cdot \left(\pi \cdot \frac{\sqrt[3]{\sqrt[3]{angle} \cdot t_0}}{180}\right)\right)\right)}^{2} \end{array} \]
{\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \cos \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2}
↓
\begin{array}{l}
t_0 := \sqrt[3]{angle} \cdot \sqrt[3]{angle}\\
{\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \cos \left(t_0 \cdot \left(\pi \cdot \frac{\sqrt[3]{\sqrt[3]{angle} \cdot t_0}}{180}\right)\right)\right)}^{2}
\end{array}

(FPCore (a b angle)
 :precision binary64
 (+
  (pow (* a (sin (* (/ angle 180.0) PI))) 2.0)
  (pow (* b (cos (* (/ angle 180.0) PI))) 2.0)))
↓
(FPCore (a b angle)
 :precision binary64
 (let* ((t_0 (* (cbrt angle) (cbrt angle))))
   (+
    (pow (* a (sin (* (/ angle 180.0) PI))) 2.0)
    (pow
     (* b (cos (* t_0 (* PI (/ (cbrt (* (cbrt angle) t_0)) 180.0)))))
     2.0))))
double code(double a, double b, double angle) {
	return pow((a * sin((angle / 180.0) * ((double) M_PI))), 2.0) + pow((b * cos((angle / 180.0) * ((double) M_PI))), 2.0);
}
↓
double code(double a, double b, double angle) {
	double t_0 = cbrt(angle) * cbrt(angle);
	return pow((a * sin((angle / 180.0) * ((double) M_PI))), 2.0) + pow((b * cos(t_0 * (((double) M_PI) * (cbrt(cbrt(angle) * t_0) / 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 20.2

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

  2. Applied *-un-lft-identity_binary6420.2

    \[\leadsto {\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \cos \left(\frac{angle}{\color{blue}{1 \cdot 180}} \cdot \pi\right)\right)}^{2} \]

  3. Applied add-cube-cbrt_binary6420.3

    \[\leadsto {\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \cos \left(\frac{\color{blue}{\left(\sqrt[3]{angle} \cdot \sqrt[3]{angle}\right) \cdot \sqrt[3]{angle}}}{1 \cdot 180} \cdot \pi\right)\right)}^{2} \]

  4. Applied times-frac_binary6420.3

    \[\leadsto {\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \cos \left(\color{blue}{\left(\frac{\sqrt[3]{angle} \cdot \sqrt[3]{angle}}{1} \cdot \frac{\sqrt[3]{angle}}{180}\right)} \cdot \pi\right)\right)}^{2} \]

  5. Applied associate-*l*_binary6420.3

    \[\leadsto {\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \cos \color{blue}{\left(\frac{\sqrt[3]{angle} \cdot \sqrt[3]{angle}}{1} \cdot \left(\frac{\sqrt[3]{angle}}{180} \cdot \pi\right)\right)}\right)}^{2} \]

  6. Applied add-cbrt-cube_binary6420.2

    \[\leadsto {\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \cos \left(\frac{\sqrt[3]{angle} \cdot \sqrt[3]{angle}}{1} \cdot \left(\frac{\color{blue}{\sqrt[3]{\left(\sqrt[3]{angle} \cdot \sqrt[3]{angle}\right) \cdot \sqrt[3]{angle}}}}{180} \cdot \pi\right)\right)\right)}^{2} \]

  7. Final simplification20.2

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

Reproduce

herbie shell --seed 2022055 
(FPCore (a b angle)
  :name "ab-angle->ABCF A"
  :precision binary64
  (+ (pow (* a (sin (* (/ angle 180.0) PI))) 2.0) (pow (* b (cos (* (/ angle 180.0) PI))) 2.0)))