Average Error: 31.0 → 31.1
Time: 13.3s
Precision: binary64
\[\left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\]
↓
\[\left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \sqrt[3]{{\cos \left(\frac{\pi}{\sqrt[3]{32400}} \cdot \frac{angle}{\sqrt[3]{180}}\right)}^{3}}\]
\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(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \sqrt[3]{{\cos \left(\frac{\pi}{\sqrt[3]{32400}} \cdot \frac{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 (- (pow b 2.0) (pow a 2.0))) (sin (* PI (/ angle 180.0))))
  (cbrt (pow (cos (* (/ PI (cbrt 32400.0)) (/ 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 * (pow(b, 2.0) - pow(a, 2.0))) * sin(((double) M_PI) * (angle / 180.0))) * cbrt(pow(cos((((double) M_PI) / cbrt(32400.0)) * (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 31.0

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

  3. Applied add-cube-cbrt_binary64_11331.1

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

  4. Applied *-un-lft-identity_binary64_7831.1

    \[\leadsto \left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{\color{blue}{1 \cdot angle}}{\left(\sqrt[3]{180} \cdot \sqrt[3]{180}\right) \cdot \sqrt[3]{180}}\right)\]

  5. Applied times-frac_binary64_8431.1

    \[\leadsto \left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \color{blue}{\left(\frac{1}{\sqrt[3]{180} \cdot \sqrt[3]{180}} \cdot \frac{angle}{\sqrt[3]{180}}\right)}\right)\]

  6. Applied associate-*r*_binary64_1831.1

    \[\leadsto \left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \color{blue}{\left(\left(\pi \cdot \frac{1}{\sqrt[3]{180} \cdot \sqrt[3]{180}}\right) \cdot \frac{angle}{\sqrt[3]{180}}\right)}\]

  7. Simplified31.1

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

  9. Applied add-cbrt-cube_binary64_11431.1

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

  10. Simplified31.1

    \[\leadsto \left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\frac{\pi}{\sqrt[3]{\color{blue}{32400}}} \cdot \frac{angle}{\sqrt[3]{180}}\right)\]
  11. Using strategy rm

  12. Applied add-cbrt-cube_binary64_11431.1

    \[\leadsto \left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \color{blue}{\sqrt[3]{\left(\cos \left(\frac{\pi}{\sqrt[3]{32400}} \cdot \frac{angle}{\sqrt[3]{180}}\right) \cdot \cos \left(\frac{\pi}{\sqrt[3]{32400}} \cdot \frac{angle}{\sqrt[3]{180}}\right)\right) \cdot \cos \left(\frac{\pi}{\sqrt[3]{32400}} \cdot \frac{angle}{\sqrt[3]{180}}\right)}}\]

  13. Simplified31.1

    \[\leadsto \left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \sqrt[3]{\color{blue}{{\cos \left(\frac{\pi}{\sqrt[3]{32400}} \cdot \frac{angle}{\sqrt[3]{180}}\right)}^{3}}}\]

  14. Final simplification31.1

    \[\leadsto \left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \sqrt[3]{{\cos \left(\frac{\pi}{\sqrt[3]{32400}} \cdot \frac{angle}{\sqrt[3]{180}}\right)}^{3}}\]

Reproduce

herbie shell --seed 2020353 
(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)))))