Average Error: 20.7 → 20.7
Time: 12.0s
Precision: binary64
\[{\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \cos \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2}\]
↓
\[{\left(a \cdot \sin \left(\left(angle \cdot \pi\right) \cdot 0.005555555555555556\right)\right)}^{2} + {\left(b \cdot \cos \left(\sqrt[3]{\pi \cdot \frac{angle}{180}} \cdot \left(\sqrt[3]{\pi \cdot \frac{angle}{180}} \cdot \sqrt[3]{\pi \cdot \frac{angle}{180}}\right)\right)\right)}^{2}\]
{\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(\left(angle \cdot \pi\right) \cdot 0.005555555555555556\right)\right)}^{2} + {\left(b \cdot \cos \left(\sqrt[3]{\pi \cdot \frac{angle}{180}} \cdot \left(\sqrt[3]{\pi \cdot \frac{angle}{180}} \cdot \sqrt[3]{\pi \cdot \frac{angle}{180}}\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 PI) 0.005555555555555556))) 2.0)
  (pow
   (*
    b
    (cos
     (*
      (cbrt (* PI (/ angle 180.0)))
      (* (cbrt (* PI (/ angle 180.0))) (cbrt (* PI (/ angle 180.0)))))))
   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 * ((double) M_PI)) * 0.005555555555555556)), 2.0) + pow((b * cos(cbrt(((double) M_PI) * (angle / 180.0)) * (cbrt(((double) M_PI) * (angle / 180.0)) * cbrt(((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 20.7

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

  3. Applied add-cube-cbrt_binary64_45420.7

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

  4. Taylor expanded around inf 20.7

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

  5. Simplified20.7

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

  6. Final simplification20.7

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

Reproduce

herbie shell --seed 2020342 
(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)))