Average Error: 20.5 → 20.6
Time: 21.0s
Precision: binary64
\[{\left(a \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2}\]
↓
\[{\left(a \cdot \left(\left(\sqrt[3]{\cos \left(\frac{\sqrt[3]{angle}}{\sqrt{180}} \cdot \left(\pi \cdot \left(\sqrt[3]{angle} \cdot \frac{\sqrt[3]{angle}}{\sqrt{180}}\right)\right)\right)} \cdot \sqrt[3]{\cos \left(\frac{\pi \cdot angle}{{\left(\sqrt{180}\right)}^{2}}\right)}\right) \cdot \sqrt[3]{\cos \left(\pi \cdot \frac{angle}{180}\right)}\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2}\]
{\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 \left(\left(\sqrt[3]{\cos \left(\frac{\sqrt[3]{angle}}{\sqrt{180}} \cdot \left(\pi \cdot \left(\sqrt[3]{angle} \cdot \frac{\sqrt[3]{angle}}{\sqrt{180}}\right)\right)\right)} \cdot \sqrt[3]{\cos \left(\frac{\pi \cdot angle}{{\left(\sqrt{180}\right)}^{2}}\right)}\right) \cdot \sqrt[3]{\cos \left(\pi \cdot \frac{angle}{180}\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
    (*
     (*
      (cbrt
       (cos
        (*
         (/ (cbrt angle) (sqrt 180.0))
         (* PI (* (cbrt angle) (/ (cbrt angle) (sqrt 180.0)))))))
      (cbrt (cos (/ (* PI angle) (pow (sqrt 180.0) 2.0)))))
     (cbrt (cos (* PI (/ angle 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 * ((cbrt(cos((cbrt(angle) / sqrt(180.0)) * (((double) M_PI) * (cbrt(angle) * (cbrt(angle) / sqrt(180.0)))))) * cbrt(cos((((double) M_PI) * angle) / pow(sqrt(180.0), 2.0)))) * cbrt(cos(((double) M_PI) * (angle / 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 20.5

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

  3. Applied add-sqr-sqrt_binary64_10020.6

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

  4. Applied add-cube-cbrt_binary64_11320.6

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

  5. Applied times-frac_binary64_8420.6

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

  6. Applied associate-*r*_binary64_1820.6

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

  7. Simplified20.6

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

  9. Applied add-cube-cbrt_binary64_11320.6

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

  10. Simplified20.6

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

  11. Taylor expanded around inf 20.6

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

  12. Final simplification20.6

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

Reproduce

herbie shell --seed 2021176 
(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)))