Average Error: 19.9 → 19.9
Time: 13.3s
Precision: binary64
\[{\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \cos \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2}\]
↓
\[{\left(a \cdot \sin \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right)\right)}^{2} + {\left(b \cdot \sqrt[3]{{\cos \left(\sqrt{0.005555555555555556} \cdot \left(\sqrt{0.005555555555555556} \cdot \left(angle \cdot \pi\right)\right)\right)}^{3}}\right)}^{2}\]
{\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(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right)\right)}^{2} + {\left(b \cdot \sqrt[3]{{\cos \left(\sqrt{0.005555555555555556} \cdot \left(\sqrt{0.005555555555555556} \cdot \left(angle \cdot \pi\right)\right)\right)}^{3}}\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 (* 0.005555555555555556 PI)))) 2.0)
  (pow
   (*
    b
    (cbrt
     (pow
      (cos
       (*
        (sqrt 0.005555555555555556)
        (* (sqrt 0.005555555555555556) (* angle PI))))
      3.0)))
   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) {
	return pow((a * sin(angle * (0.005555555555555556 * ((double) M_PI)))), 2.0) + pow((b * cbrt(pow(cos(sqrt(0.005555555555555556) * (sqrt(0.005555555555555556) * (angle * ((double) M_PI)))), 3.0))), 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 19.9

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

  3. Applied div-inv_binary6419.9

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

  4. Applied associate-*l*_binary6419.9

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

  5. Simplified19.9

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

  7. Applied div-inv_binary6419.9

    \[\leadsto {\left(a \cdot \sin \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right)\right)}^{2} + {\left(b \cdot \cos \left(\color{blue}{\left(angle \cdot \frac{1}{180}\right)} \cdot \pi\right)\right)}^{2}\]

  8. Applied associate-*l*_binary6419.9

    \[\leadsto {\left(a \cdot \sin \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right)\right)}^{2} + {\left(b \cdot \cos \color{blue}{\left(angle \cdot \left(\frac{1}{180} \cdot \pi\right)\right)}\right)}^{2}\]

  9. Simplified19.9

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

  11. Applied add-cbrt-cube_binary6419.9

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

  12. Simplified19.9

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

  14. Applied add-sqr-sqrt_binary6419.9

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

  15. Applied associate-*l*_binary6419.9

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

  16. Simplified19.9

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

  17. Final simplification19.9

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

Alternatives

Reproduce

herbie shell --seed 2021118 
(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)))