Average Error: 20.5 → 20.6
Time: 11.1s
Precision: binary64
\[{\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \cos \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2}\]
↓
\[{\left(\sin \left(\frac{angle}{180} \cdot \pi\right) \cdot a\right)}^{2} + {\left(\cos \left({\left(\sqrt[3]{\pi}\right)}^{2} \cdot \left(\frac{angle}{180} \cdot {\left(\sqrt[3]{\sqrt{\pi}}\right)}^{2}\right)\right) \cdot b\right)}^{2}\]
{\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(\sin \left(\frac{angle}{180} \cdot \pi\right) \cdot a\right)}^{2} + {\left(\cos \left({\left(\sqrt[3]{\pi}\right)}^{2} \cdot \left(\frac{angle}{180} \cdot {\left(\sqrt[3]{\sqrt{\pi}}\right)}^{2}\right)\right) \cdot b\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 (* (sin (* (/ angle 180.0) PI)) a) 2.0)
  (pow
   (*
    (cos
     (* (pow (cbrt PI) 2.0) (* (/ angle 180.0) (pow (cbrt (sqrt PI)) 2.0))))
    b)
   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((sin((angle / 180.0) * ((double) M_PI)) * a), 2.0) + pow((cos(pow(cbrt((double) M_PI), 2.0) * ((angle / 180.0) * pow(cbrt(sqrt((double) M_PI)), 2.0))) * 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

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

  3. Applied add-cube-cbrt_binary64_45420.6

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

  4. Applied associate-*r*_binary64_35920.6

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

  6. Applied add-sqr-sqrt_binary64_44120.6

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

  7. Applied cbrt-prod_binary64_45020.6

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

  9. Applied add-log-exp_binary64_45820.6

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

  10. Simplified20.6

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

  11. Simplified20.6

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

  12. Final simplification20.6

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

Reproduce

herbie shell --seed 2020356 
(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)))