Average Error: 20.3 → 20.3
Time: 1.3min
Precision: binary64
Cost: 39744
\[{\left(a \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2}\]
↓
\[{\left(a \cdot \cos \left(\left(\pi \cdot \frac{1}{\sqrt{180}}\right) \cdot \frac{angle}{\sqrt{180}}\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2}\]
{\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(\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}
(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 (/ 1.0 (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) * (1.0 / 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

Alternatives

Alternative 1
Error20.3
Cost39616
\[{\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} + {\left(a \cdot \cos \left(\frac{angle}{\sqrt{180}} \cdot \frac{\pi}{\sqrt{180}}\right)\right)}^{2}\]
Alternative 2
Error20.3
Cost26688
\[{\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} + {\left(a \cdot \cos \left(\frac{\pi \cdot angle}{180}\right)\right)}^{2}\]
Alternative 3
Error20.3
Cost26688
\[{\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} + {\left(a \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2}\]
Alternative 4
Error20.4
Cost19904
\[{\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} + {a}^{2}\]
Alternative 5
Error25.1
Cost7873
\[\begin{array}{l} \mathbf{if}\;angle \leq 6.4529624093927074 \cdot 10^{+66}:\\ \;\;\;\;{a}^{2} + \left(b \cdot \left(\left(\pi \cdot angle\right) \cdot 0.005555555555555556\right)\right) \cdot \left(b \cdot \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array}\]
Alternative 6
Error25.1
Cost7873
\[\begin{array}{l} \mathbf{if}\;angle \leq 1.1243485923516999 \cdot 10^{+64}:\\ \;\;\;\;{a}^{2} + \left(b \cdot \left(\left(\pi \cdot angle\right) \cdot 0.005555555555555556\right)\right) \cdot \left(b \cdot \left(\left(\pi \cdot angle\right) \cdot 0.005555555555555556\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array}\]
Alternative 7
Error52.9
Cost64
\[0\]
Alternative 8
Error60.7
Cost64
\[1\]

Error

Time

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. Using strategy rm

  3. Applied add-sqr-sqrt_binary64_10020.3

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

  4. Applied *-un-lft-identity_binary64_7820.3

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

  5. Applied times-frac_binary64_8420.3

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

  6. Applied associate-*r*_binary64_1820.3

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

  7. Simplified20.3

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

  9. Applied div-inv_binary64_7520.3

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

  11. Applied *-un-lft-identity_binary64_7820.3

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

  12. Simplified20.3

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

  13. Final simplification20.3

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

Reproduce

herbie shell --seed 2021040 
(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)))