Average Error: 20.5 → 20.5
Time: 27.5s
Precision: binary64
\[{\left(a \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} \]
↓
\[{\left(a \cdot \cos \left(\frac{\pi}{\sqrt{180}} \cdot \frac{angle}{\sqrt{180}}\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} \]
{\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(\frac{\pi}{\sqrt{180}} \cdot \frac{angle}{\sqrt{180}}\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\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 (* (/ PI (sqrt 180.0)) (/ angle (sqrt 180.0))))) 2.0)
  (pow (* b (sin (* PI (/ angle 180.0)))) 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((((double) M_PI) / sqrt(180.0)) * (angle / sqrt(180.0)))), 2.0) + pow((b * sin(((double) M_PI) * (angle / 180.0))), 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 20.5

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

  2. Applied add-sqr-sqrt_binary6420.5

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

  3. Applied *-un-lft-identity_binary6420.5

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

  4. Applied times-frac_binary6420.5

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

  5. Applied associate-*r*_binary6420.5

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

  6. Simplified20.5

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

  7. Final simplification20.5

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

Reproduce

herbie shell --seed 2021280 
(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)))