Average Error: 31.7 → 21.5
Time: 15.3s
Precision: binary64
\[\left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\]
↓
\[\left(2 \cdot \left(\left(b + a\right) \cdot \left(\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \left(b - a\right)\right)\right)\right) \cdot \sqrt[3]{{\cos \left(\left(\pi \cdot \frac{\sqrt[3]{angle} \cdot \sqrt[3]{angle}}{\sqrt[3]{180} \cdot \sqrt[3]{180}}\right) \cdot \frac{\sqrt[3]{angle}}{\sqrt[3]{180}}\right)}^{3}}\]
\left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)
↓
\left(2 \cdot \left(\left(b + a\right) \cdot \left(\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \left(b - a\right)\right)\right)\right) \cdot \sqrt[3]{{\cos \left(\left(\pi \cdot \frac{\sqrt[3]{angle} \cdot \sqrt[3]{angle}}{\sqrt[3]{180} \cdot \sqrt[3]{180}}\right) \cdot \frac{\sqrt[3]{angle}}{\sqrt[3]{180}}\right)}^{3}}
(FPCore (a b angle)
 :precision binary64
 (*
  (* (* 2.0 (- (pow b 2.0) (pow a 2.0))) (sin (* PI (/ angle 180.0))))
  (cos (* PI (/ angle 180.0)))))
↓
(FPCore (a b angle)
 :precision binary64
 (*
  (* 2.0 (* (+ b a) (* (sin (* 0.005555555555555556 (* angle PI))) (- b a))))
  (cbrt
   (pow
    (cos
     (*
      (* PI (/ (* (cbrt angle) (cbrt angle)) (* (cbrt 180.0) (cbrt 180.0))))
      (/ (cbrt angle) (cbrt 180.0))))
    3.0))))
double code(double a, double b, double angle) {
	return ((2.0 * (pow(b, 2.0) - pow(a, 2.0))) * sin(((double) M_PI) * (angle / 180.0))) * cos(((double) M_PI) * (angle / 180.0));
}
↓
double code(double a, double b, double angle) {
	return (2.0 * ((b + a) * (sin(0.005555555555555556 * (angle * ((double) M_PI))) * (b - a)))) * cbrt(pow(cos((((double) M_PI) * ((cbrt(angle) * cbrt(angle)) / (cbrt(180.0) * cbrt(180.0)))) * (cbrt(angle) / cbrt(180.0))), 3.0));
}

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 31.7

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

  3. Applied add-cbrt-cube_binary6431.7

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

  4. Simplified31.7

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

  6. Applied add-sqr-sqrt_binary6448.1

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

  7. Applied unpow-prod-down_binary6448.1

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

  8. Applied add-sqr-sqrt_binary6456.1

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

  9. Applied unpow-prod-down_binary6456.1

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

  10. Applied difference-of-squares_binary6456.1

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

  11. Simplified56.1

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

  12. Simplified31.7

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

  13. Taylor expanded around 0 31.7

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

  14. Simplified21.5

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

  16. Applied add-cube-cbrt_binary6421.5

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

  17. Applied add-cube-cbrt_binary6421.5

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

  18. Applied times-frac_binary6421.5

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

  19. Applied associate-*r*_binary6421.5

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

  20. Final simplification21.5

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

Reproduce

herbie shell --seed 2021175 
(FPCore (a b angle)
  :name "ab-angle->ABCF B"
  :precision binary64
  (* (* (* 2.0 (- (pow b 2.0) (pow a 2.0))) (sin (* PI (/ angle 180.0)))) (cos (* PI (/ angle 180.0)))))