Average Error: 20.4 → 20.4
Time: 11.2s
Precision: binary64
\[{\left(a \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2}\]
↓
\[{\left(a \cdot \cos \left(\left(\pi \cdot \frac{\sqrt[3]{angle} \cdot \sqrt[3]{angle}}{\sqrt{180}}\right) \cdot \frac{\sqrt[3]{\sqrt[3]{angle}} \cdot \left(\sqrt[3]{\sqrt[3]{angle}} \cdot \sqrt[3]{\sqrt[3]{angle}}\right)}{\sqrt{180}}\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2}\]
{\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(\pi \cdot \frac{\sqrt[3]{angle} \cdot \sqrt[3]{angle}}{\sqrt{180}}\right) \cdot \frac{\sqrt[3]{\sqrt[3]{angle}} \cdot \left(\sqrt[3]{\sqrt[3]{angle}} \cdot \sqrt[3]{\sqrt[3]{angle}}\right)}{\sqrt{180}}\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
     (*
      (* PI (/ (* (cbrt angle) (cbrt angle)) (sqrt 180.0)))
      (/
       (* (cbrt (cbrt angle)) (* (cbrt (cbrt angle)) (cbrt (cbrt angle))))
       (sqrt 180.0)))))
   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((((double) M_PI) * ((cbrt(angle) * cbrt(angle)) / sqrt(180.0))) * ((cbrt(cbrt(angle)) * (cbrt(cbrt(angle)) * cbrt(cbrt(angle)))) / sqrt(180.0)))), 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_binary64_10020.4

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

  4. Applied add-cube-cbrt_binary64_11320.4

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

  5. Applied times-frac_binary64_8420.4

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

  6. Applied associate-*r*_binary64_1820.4

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

  8. Applied add-cube-cbrt_binary64_11320.4

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

  9. Final simplification20.4

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

Reproduce

herbie shell --seed 2020343 
(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)))