Average Error: 20.6 → 20.6
Time: 11.9s
Precision: binary64
\[{\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \cos \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2}\]
↓
\[{\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \cos \left(\left(\sqrt[3]{\frac{angle}{180} \cdot \pi} \cdot \sqrt[3]{\frac{angle}{180} \cdot \pi}\right) \cdot \left(\sqrt[3]{\frac{angle}{180}} \cdot \left(\sqrt{\sqrt[3]{\pi}} \cdot \sqrt{\sqrt[3]{\pi}}\right)\right)\right)\right)}^{2}\]
{\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(\frac{angle}{180} \cdot \pi\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 \left(\sqrt[3]{\frac{angle}{180}} \cdot \left(\sqrt{\sqrt[3]{\pi}} \cdot \sqrt{\sqrt[3]{\pi}}\right)\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 180.0) PI))) 2.0)
  (pow
   (*
    b
    (cos
     (*
      (* (cbrt (* (/ angle 180.0) PI)) (cbrt (* (/ angle 180.0) PI)))
      (* (cbrt (/ angle 180.0)) (* (sqrt (cbrt PI)) (sqrt (cbrt PI)))))))
   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 / 180.0) * ((double) M_PI))), 2.0) + pow((b * cos((cbrt((angle / 180.0) * ((double) M_PI)) * cbrt((angle / 180.0) * ((double) M_PI))) * (cbrt(angle / 180.0) * (sqrt(cbrt((double) M_PI)) * sqrt(cbrt((double) M_PI)))))), 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 20.6

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

  3. Applied add-cube-cbrt_binary64_45420.6

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

  5. Applied cbrt-prod_binary64_45020.6

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

  7. Applied add-sqr-sqrt_binary64_44120.6

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

  8. Final simplification20.6

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

Reproduce

herbie shell --seed 2020346 
(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)))