Average Error: 20.3 → 20.3
Time: 14.6s
Precision: binary64
\[{\left(a \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2}\]
↓
\[{\left(a \cdot \cos \left(\sqrt{\pi} \cdot \left(\sqrt{\pi} \cdot \frac{angle}{180}\right)\right)\right)}^{2} + {\left(b \cdot \sin \left(0.005555555555555556 \cdot \left(\pi \cdot angle\right)\right)\right)}^{2}\]
{\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(\sqrt{\pi} \cdot \left(\sqrt{\pi} \cdot \frac{angle}{180}\right)\right)\right)}^{2} + {\left(b \cdot \sin \left(0.005555555555555556 \cdot \left(\pi \cdot angle\right)\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 (* (sqrt PI) (* (sqrt PI) (/ angle 180.0))))) 2.0)
  (pow (* b (sin (* 0.005555555555555556 (* PI angle)))) 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(sqrt((double) M_PI) * (sqrt((double) M_PI) * (angle / 180.0)))), 2.0) + pow((b * sin(0.005555555555555556 * (((double) M_PI) * angle))), 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 20.3

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

  2. Taylor expanded around inf 20.3

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

  4. Applied add-sqr-sqrt_binary64_10020.3

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

  5. Applied associate-*l*_binary64_1920.3

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

  6. Final simplification20.3

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

Reproduce

herbie shell --seed 2021015 
(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)))