Average Error: 20.2 → 20.2
Time: 13.8s
Precision: binary64
\[{\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \cos \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} \]
↓
\[{\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \cos \left(\frac{1}{\sqrt{180}} \cdot \left(\pi \cdot \frac{angle}{\sqrt{180}}\right)\right)\right)}^{2} \]
{\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(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \cos \left(\frac{1}{\sqrt{180}} \cdot \left(\pi \cdot \frac{angle}{\sqrt{180}}\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 (* (/ angle 180.0) PI))) 2.0)
  (pow
   (* b (cos (* (/ 1.0 (sqrt 180.0)) (* PI (/ angle (sqrt 180.0))))))
   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((angle / 180.0) * ((double) M_PI))), 2.0) + pow((b * cos((1.0 / sqrt(180.0)) * (((double) M_PI) * (angle / sqrt(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 20.2

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

  3. Applied add-sqr-sqrt_binary6420.2

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

  4. Applied *-un-lft-identity_binary6420.2

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

  5. Applied times-frac_binary6420.2

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

  6. Applied associate-*l*_binary6420.2

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

  7. Simplified20.2

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

  8. Final simplification20.2

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

Reproduce

herbie shell --seed 2021198 
(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)))