Average Error: 20.6 → 20.6
Time: 13.3s
Precision: binary64
\[{\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \cos \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2}\]
↓
\[{\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \cos \left(\left(\sqrt[3]{\frac{angle}{180}} \cdot \sqrt[3]{\sqrt[3]{\frac{angle}{180}} \cdot \left(\sqrt[3]{\frac{angle}{180}} \cdot \sqrt[3]{\frac{angle}{180}}\right)}\right) \cdot \left(\pi \cdot \sqrt[3]{angle \cdot 0.005555555555555556}\right)\right)\right)}^{2}\]
{\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}
↓
{\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \cos \left(\left(\sqrt[3]{\frac{angle}{180}} \cdot \sqrt[3]{\sqrt[3]{\frac{angle}{180}} \cdot \left(\sqrt[3]{\frac{angle}{180}} \cdot \sqrt[3]{\frac{angle}{180}}\right)}\right) \cdot \left(\pi \cdot \sqrt[3]{angle \cdot 0.005555555555555556}\right)\right)\right)}^{2}
(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
 (+
  (pow (* a (sin (* (/ angle 180.0) PI))) 2.0)
  (pow
   (*
    b
    (cos
     (*
      (*
       (cbrt (/ angle 180.0))
       (cbrt
        (*
         (cbrt (/ angle 180.0))
         (* (cbrt (/ angle 180.0)) (cbrt (/ angle 180.0))))))
      (* PI (cbrt (* angle 0.005555555555555556))))))
   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) {
	return pow((a * sin((angle / 180.0) * ((double) M_PI))), 2.0) + pow((b * cos((cbrt(angle / 180.0) * cbrt(cbrt(angle / 180.0) * (cbrt(angle / 180.0) * cbrt(angle / 180.0)))) * (((double) M_PI) * cbrt(angle * 0.005555555555555556)))), 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 20.6

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

  3. Applied add-cube-cbrt_binary6420.6

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

  4. Applied associate-*l*_binary6420.6

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

  5. Simplified20.6

    \[\leadsto {\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \cos \left(\left(\sqrt[3]{\frac{angle}{180}} \cdot \sqrt[3]{\frac{angle}{180}}\right) \cdot \color{blue}{\left(\pi \cdot \sqrt[3]{0.005555555555555556 \cdot angle}\right)}\right)\right)}^{2}\]
  6. Using strategy rm

  7. Applied add-cbrt-cube_binary6420.6

    \[\leadsto {\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \cos \left(\left(\color{blue}{\sqrt[3]{\left(\sqrt[3]{\frac{angle}{180}} \cdot \sqrt[3]{\frac{angle}{180}}\right) \cdot \sqrt[3]{\frac{angle}{180}}}} \cdot \sqrt[3]{\frac{angle}{180}}\right) \cdot \left(\pi \cdot \sqrt[3]{0.005555555555555556 \cdot angle}\right)\right)\right)}^{2}\]

  8. Final simplification20.6

    \[\leadsto {\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \cos \left(\left(\sqrt[3]{\frac{angle}{180}} \cdot \sqrt[3]{\sqrt[3]{\frac{angle}{180}} \cdot \left(\sqrt[3]{\frac{angle}{180}} \cdot \sqrt[3]{\frac{angle}{180}}\right)}\right) \cdot \left(\pi \cdot \sqrt[3]{angle \cdot 0.005555555555555556}\right)\right)\right)}^{2}\]

Alternatives

Reproduce

herbie shell --seed 2021106 
(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)))