Average Error: 20.3 → 20.3
Time: 16.0s
Precision: binary64
\[{\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \cos \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} \]
↓
\[{\left(a \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)}^{2} + {\left(b \cdot \cos \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right)\right)}^{2} \]
{\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \cos \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2}
↓
{\left(a \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)}^{2} + {\left(b \cdot \cos \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right)\right)}^{2}

(FPCore (a b angle)
 :precision binary64
 (+
  (pow (* a (sin (* (/ angle 180.0) PI))) 2.0)
  (pow (* b (cos (* (/ angle 180.0) PI))) 2.0)))
↓
(FPCore (a b angle)
 :precision binary64
 (+
  (pow (* a (sin (* 0.005555555555555556 (* angle PI)))) 2.0)
  (pow (* b (cos (* angle (* 0.005555555555555556 PI)))) 2.0)))
double code(double a, double b, double angle) {
	return pow((a * sin((angle / 180.0) * ((double) M_PI))), 2.0) + pow((b * cos((angle / 180.0) * ((double) M_PI))), 2.0);
}
↓
double code(double a, double b, double angle) {
	return pow((a * sin(0.005555555555555556 * (angle * ((double) M_PI)))), 2.0) + pow((b * cos(angle * (0.005555555555555556 * ((double) M_PI)))), 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

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

  3. Applied pow1_binary6420.3

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

  4. Applied pow1_binary6420.3

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

  5. Applied pow-prod-down_binary6420.3

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

  6. Simplified20.3

    \[\leadsto {\left(a \cdot \sin \left({\color{blue}{\left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}}^{1}\right)\right)}^{2} + {\left(b \cdot \cos \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} \]
  7. Using strategy rm

  8. Applied div-inv_binary6420.3

    \[\leadsto {\left(a \cdot \sin \left({\left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{1}\right)\right)}^{2} + {\left(b \cdot \cos \left(\color{blue}{\left(angle \cdot \frac{1}{180}\right)} \cdot \pi\right)\right)}^{2} \]

  9. Applied associate-*l*_binary6420.3

    \[\leadsto {\left(a \cdot \sin \left({\left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{1}\right)\right)}^{2} + {\left(b \cdot \cos \color{blue}{\left(angle \cdot \left(\frac{1}{180} \cdot \pi\right)\right)}\right)}^{2} \]

  10. Simplified20.3

    \[\leadsto {\left(a \cdot \sin \left({\left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}^{1}\right)\right)}^{2} + {\left(b \cdot \cos \left(angle \cdot \color{blue}{\left(0.005555555555555556 \cdot \pi\right)}\right)\right)}^{2} \]

  11. Final simplification20.3

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

Reproduce

herbie shell --seed 2021205 
(FPCore (a b angle)
  :name "ab-angle->ABCF A"
  :precision binary64
  (+ (pow (* a (sin (* (/ angle 180.0) PI))) 2.0) (pow (* b (cos (* (/ angle 180.0) PI))) 2.0)))