Average Error: 31.1 → 31.1
Time: 14.7s
Precision: binary64
\[\left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\]
↓
\[\left(\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \left(2 \cdot \left(b \cdot b - a \cdot a\right)\right)\right) \cdot \sqrt[3]{{\left(\sqrt[3]{{\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{3}}\right)}^{3}}\]
\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(\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \left(2 \cdot \left(b \cdot b - a \cdot a\right)\right)\right) \cdot \sqrt[3]{{\left(\sqrt[3]{{\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{3}}\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
 (*
  (* (sin (* 0.005555555555555556 (* angle PI))) (* 2.0 (- (* b b) (* a a))))
  (cbrt
   (pow (cbrt (pow (cos (* 0.005555555555555556 (* angle PI))) 3.0)) 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 (sin(0.005555555555555556 * (angle * ((double) M_PI))) * (2.0 * ((b * b) - (a * a)))) * cbrt(pow(cbrt(pow(cos(0.005555555555555556 * (angle * ((double) M_PI))), 3.0)), 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 31.1

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

  3. Applied add-cbrt-cube_binary6431.1

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

  4. Simplified31.1

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

  6. Applied add-cbrt-cube_binary6431.1

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

  7. Simplified31.1

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

  8. Taylor expanded around 0 31.2

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

  9. Simplified31.2

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

  10. Taylor expanded around inf 31.1

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

  11. Final simplification31.1

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

Alternatives

Reproduce

herbie shell --seed 2021106 
(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)))))