Average Error: 20.5 → 20.6
Time: 12.5s
Precision: binary64
\[{\left(a \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2}\]
↓
\[{\left(\cos \left(\frac{\frac{\pi \cdot angle}{{\left(\sqrt[3]{\sqrt[3]{180}}\right)}^{4}}}{{\left(\sqrt[3]{{\left(\sqrt[3]{\sqrt[3]{180}}\right)}^{2}} \cdot \sqrt[3]{\sqrt[3]{\sqrt[3]{180}}}\right)}^{5}}\right) \cdot a\right)}^{2} + {\left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot b\right)}^{2}\]
{\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}
↓
{\left(\cos \left(\frac{\frac{\pi \cdot angle}{{\left(\sqrt[3]{\sqrt[3]{180}}\right)}^{4}}}{{\left(\sqrt[3]{{\left(\sqrt[3]{\sqrt[3]{180}}\right)}^{2}} \cdot \sqrt[3]{\sqrt[3]{\sqrt[3]{180}}}\right)}^{5}}\right) \cdot a\right)}^{2} + {\left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot b\right)}^{2}
(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
 (+
  (pow
   (*
    (cos
     (/
      (/ (* PI angle) (pow (cbrt (cbrt 180.0)) 4.0))
      (pow
       (* (cbrt (pow (cbrt (cbrt 180.0)) 2.0)) (cbrt (cbrt (cbrt 180.0))))
       5.0)))
    a)
   2.0)
  (pow (* (sin (* PI (/ angle 180.0))) b) 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) {
	return pow((cos(((((double) M_PI) * angle) / pow(cbrt(cbrt(180.0)), 4.0)) / pow((cbrt(pow(cbrt(cbrt(180.0)), 2.0)) * cbrt(cbrt(cbrt(180.0)))), 5.0)) * a), 2.0) + pow((sin(((double) M_PI) * (angle / 180.0)) * b), 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 20.5

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

  3. Applied add-cube-cbrt_binary64_11320.5

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

  4. Applied add-cube-cbrt_binary64_11320.6

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

  5. Applied times-frac_binary64_8420.5

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

  6. Applied associate-*r*_binary64_1820.5

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

  8. Applied add-cube-cbrt_binary64_11320.6

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

  9. Applied associate-*r*_binary64_1820.6

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

  10. Simplified20.6

    \[\leadsto {\left(a \cdot \cos \left(\left(\pi \cdot \frac{\sqrt[3]{angle} \cdot \sqrt[3]{angle}}{\color{blue}{{\left(\sqrt[3]{\sqrt[3]{180}}\right)}^{5}} \cdot \sqrt[3]{\sqrt[3]{180}}}\right) \cdot \frac{\sqrt[3]{angle}}{\sqrt[3]{180}}\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2}\]
  11. Using strategy rm

  12. Applied add-cube-cbrt_binary64_11320.6

    \[\leadsto {\left(a \cdot \cos \left(\left(\pi \cdot \frac{\sqrt[3]{angle} \cdot \sqrt[3]{angle}}{{\left(\sqrt[3]{\color{blue}{\left(\sqrt[3]{\sqrt[3]{180}} \cdot \sqrt[3]{\sqrt[3]{180}}\right) \cdot \sqrt[3]{\sqrt[3]{180}}}}\right)}^{5} \cdot \sqrt[3]{\sqrt[3]{180}}}\right) \cdot \frac{\sqrt[3]{angle}}{\sqrt[3]{180}}\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2}\]

  13. Applied cbrt-prod_binary64_10920.6

    \[\leadsto {\left(a \cdot \cos \left(\left(\pi \cdot \frac{\sqrt[3]{angle} \cdot \sqrt[3]{angle}}{{\color{blue}{\left(\sqrt[3]{\sqrt[3]{\sqrt[3]{180}} \cdot \sqrt[3]{\sqrt[3]{180}}} \cdot \sqrt[3]{\sqrt[3]{\sqrt[3]{180}}}\right)}}^{5} \cdot \sqrt[3]{\sqrt[3]{180}}}\right) \cdot \frac{\sqrt[3]{angle}}{\sqrt[3]{180}}\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2}\]

  14. Simplified20.6

    \[\leadsto {\left(a \cdot \cos \left(\left(\pi \cdot \frac{\sqrt[3]{angle} \cdot \sqrt[3]{angle}}{{\left(\color{blue}{\sqrt[3]{{\left(\sqrt[3]{\sqrt[3]{180}}\right)}^{2}}} \cdot \sqrt[3]{\sqrt[3]{\sqrt[3]{180}}}\right)}^{5} \cdot \sqrt[3]{\sqrt[3]{180}}}\right) \cdot \frac{\sqrt[3]{angle}}{\sqrt[3]{180}}\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2}\]

  15. Simplified20.6

    \[\leadsto \color{blue}{{\left(\cos \left(\frac{\frac{\pi \cdot angle}{{\left(\sqrt[3]{\sqrt[3]{180}}\right)}^{4}}}{{\left(\sqrt[3]{{\left(\sqrt[3]{\sqrt[3]{180}}\right)}^{2}} \cdot \sqrt[3]{\sqrt[3]{\sqrt[3]{180}}}\right)}^{5}}\right) \cdot a\right)}^{2} + {\left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot b\right)}^{2}}\]

  16. Final simplification20.6

    \[\leadsto {\left(\cos \left(\frac{\frac{\pi \cdot angle}{{\left(\sqrt[3]{\sqrt[3]{180}}\right)}^{4}}}{{\left(\sqrt[3]{{\left(\sqrt[3]{\sqrt[3]{180}}\right)}^{2}} \cdot \sqrt[3]{\sqrt[3]{\sqrt[3]{180}}}\right)}^{5}}\right) \cdot a\right)}^{2} + {\left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot b\right)}^{2}\]

Reproduce

herbie shell --seed 2020354 
(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)))