Average Error: 20.4 → 20.4
Time: 11.6s
Precision: binary64
\[{\left(a \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2}\]
↓
\[{\left(a \cdot \cos \left(\left(\sqrt[3]{\sqrt[3]{{\pi}^{1.5}} \cdot \sqrt[3]{{\pi}^{1.5}}} \cdot \sqrt[3]{\sqrt[3]{{\pi}^{1.5}}}\right) \cdot \left(\frac{angle}{180} \cdot \sqrt{\pi}\right)\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2}\]
{\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(a \cdot \cos \left(\left(\sqrt[3]{\sqrt[3]{{\pi}^{1.5}} \cdot \sqrt[3]{{\pi}^{1.5}}} \cdot \sqrt[3]{\sqrt[3]{{\pi}^{1.5}}}\right) \cdot \left(\frac{angle}{180} \cdot \sqrt{\pi}\right)\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\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
   (*
    a
    (cos
     (*
      (*
       (cbrt (* (cbrt (pow PI 1.5)) (cbrt (pow PI 1.5))))
       (cbrt (cbrt (pow PI 1.5))))
      (* (/ angle 180.0) (sqrt PI)))))
   2.0)
  (pow (* b (sin (* PI (/ angle 180.0)))) 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((a * cos((cbrt(cbrt(pow(((double) M_PI), 1.5)) * cbrt(pow(((double) M_PI), 1.5))) * cbrt(cbrt(pow(((double) M_PI), 1.5)))) * ((angle / 180.0) * sqrt((double) M_PI)))), 2.0) + pow((b * sin(((double) M_PI) * (angle / 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 20.4

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

  3. Applied add-sqr-sqrt_binary6420.4

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

  4. Applied associate-*l*_binary6420.4

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

  5. Simplified20.4

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

  7. Applied add-cbrt-cube_binary6420.4

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

  8. Simplified20.4

    \[\leadsto {\left(a \cdot \cos \left(\sqrt[3]{\color{blue}{{\pi}^{1.5}}} \cdot \left(\frac{angle}{180} \cdot \sqrt{\pi}\right)\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2}\]
  9. Using strategy rm

  10. Applied add-cube-cbrt_binary6420.4

    \[\leadsto {\left(a \cdot \cos \left(\sqrt[3]{\color{blue}{\left(\sqrt[3]{{\pi}^{1.5}} \cdot \sqrt[3]{{\pi}^{1.5}}\right) \cdot \sqrt[3]{{\pi}^{1.5}}}} \cdot \left(\frac{angle}{180} \cdot \sqrt{\pi}\right)\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2}\]

  11. Applied cbrt-prod_binary6420.4

    \[\leadsto {\left(a \cdot \cos \left(\color{blue}{\left(\sqrt[3]{\sqrt[3]{{\pi}^{1.5}} \cdot \sqrt[3]{{\pi}^{1.5}}} \cdot \sqrt[3]{\sqrt[3]{{\pi}^{1.5}}}\right)} \cdot \left(\frac{angle}{180} \cdot \sqrt{\pi}\right)\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2}\]

  12. Final simplification20.4

    \[\leadsto {\left(a \cdot \cos \left(\left(\sqrt[3]{\sqrt[3]{{\pi}^{1.5}} \cdot \sqrt[3]{{\pi}^{1.5}}} \cdot \sqrt[3]{\sqrt[3]{{\pi}^{1.5}}}\right) \cdot \left(\frac{angle}{180} \cdot \sqrt{\pi}\right)\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2}\]

Alternatives

Reproduce

herbie shell --seed 2021110 
(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)))