Average Error: 20.8 → 20.9
Time: 14.5s
Precision: binary64
\[{\left(a \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} \]
↓
\[\begin{array}{l} t_0 := \sqrt[3]{\frac{angle}{180}}\\ t_1 := \sqrt[3]{\cos \left(t_0 \cdot \left(\pi \cdot \left(t_0 \cdot \left(\sqrt[3]{t_0 \cdot t_0} \cdot \sqrt[3]{t_0}\right)\right)\right)\right)}\\ {\left(a \cdot \log \left(e^{t_1 \cdot \left(t_1 \cdot t_1\right)}\right)\right)}^{2} + {\left(b \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} \end{array} \]
{\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]{\frac{angle}{180}}\\
t_1 := \sqrt[3]{\cos \left(t_0 \cdot \left(\pi \cdot \left(t_0 \cdot \left(\sqrt[3]{t_0 \cdot t_0} \cdot \sqrt[3]{t_0}\right)\right)\right)\right)}\\
{\left(a \cdot \log \left(e^{t_1 \cdot \left(t_1 \cdot t_1\right)}\right)\right)}^{2} + {\left(b \cdot \sin \left(\frac{angle}{180} \cdot \pi\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 180.0)))
        (t_1
         (cbrt
          (cos (* t_0 (* PI (* t_0 (* (cbrt (* t_0 t_0)) (cbrt t_0)))))))))
   (+
    (pow (* a (log (exp (* t_1 (* t_1 t_1))))) 2.0)
    (pow (* b (sin (* (/ angle 180.0) PI))) 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 / 180.0);
	double t_1 = cbrt(cos(t_0 * (((double) M_PI) * (t_0 * (cbrt(t_0 * t_0) * cbrt(t_0))))));
	return pow((a * log(exp(t_1 * (t_1 * t_1)))), 2.0) + pow((b * sin((angle / 180.0) * ((double) M_PI))), 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 20.8

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

  2. Applied add-cube-cbrt_binary6420.8

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

  3. Applied associate-*r*_binary6420.8

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

  4. Applied add-cube-cbrt_binary6420.9

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

  5. Applied cbrt-prod_binary6420.8

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

  6. Applied add-log-exp_binary6420.8

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

  7. Applied add-cube-cbrt_binary6420.9

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

  8. Simplified20.9

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

  9. Simplified20.9

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

  10. Final simplification20.9

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

Reproduce

herbie shell --seed 2021224 
(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)))