?

Average Error: 31.78% → 31.8%
Time: 21.3s
Precision: binary64
Cost: 65088

?

\[{\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \cos \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} \]
↓
\[{\left(a \cdot \sin \left(\frac{angle}{\frac{180}{\pi}}\right)\right)}^{2} + {\left(b \cdot \cos \left(\sqrt[3]{\pi} \cdot \frac{angle}{\frac{180}{{\left(\sqrt[3]{\pi}\right)}^{2}}}\right)\right)}^{2} \]
(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 (* (cbrt PI) (/ angle (/ 180.0 (pow (cbrt PI) 2.0)))))) 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((cbrt(((double) M_PI)) * (angle / (180.0 / pow(cbrt(((double) M_PI)), 2.0)))))), 2.0);
}

public static double code(double a, double b, double angle) {
	return Math.pow((a * Math.sin(((angle / 180.0) * Math.PI))), 2.0) + Math.pow((b * Math.cos(((angle / 180.0) * Math.PI))), 2.0);
}
↓
public static double code(double a, double b, double angle) {
	return Math.pow((a * Math.sin((angle / (180.0 / Math.PI)))), 2.0) + Math.pow((b * Math.cos((Math.cbrt(Math.PI) * (angle / (180.0 / Math.pow(Math.cbrt(Math.PI), 2.0)))))), 2.0);
}

function code(a, b, angle)
	return Float64((Float64(a * sin(Float64(Float64(angle / 180.0) * pi))) ^ 2.0) + (Float64(b * cos(Float64(Float64(angle / 180.0) * pi))) ^ 2.0))
end
↓
function code(a, b, angle)
	return Float64((Float64(a * sin(Float64(angle / Float64(180.0 / pi)))) ^ 2.0) + (Float64(b * cos(Float64(cbrt(pi) * Float64(angle / Float64(180.0 / (cbrt(pi) ^ 2.0)))))) ^ 2.0))
end

code[a_, b_, angle_] := N[(N[Power[N[(a * N[Sin[N[(N[(angle / 180.0), $MachinePrecision] * Pi), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[N[(b * N[Cos[N[(N[(angle / 180.0), $MachinePrecision] * Pi), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]
↓
code[a_, b_, angle_] := N[(N[Power[N[(a * N[Sin[N[(angle / N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[N[(b * N[Cos[N[(N[Power[Pi, 1/3], $MachinePrecision] * N[(angle / N[(180.0 / N[Power[N[Power[Pi, 1/3], $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]

{\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}{\frac{180}{\pi}}\right)\right)}^{2} + {\left(b \cdot \cos \left(\sqrt[3]{\pi} \cdot \frac{angle}{\frac{180}{{\left(\sqrt[3]{\pi}\right)}^{2}}}\right)\right)}^{2}

Error?

Try it out?

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation?

  1. Initial program 31.78

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

  2. Simplified31.77

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

    [Start]31.78

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

    associate-/r/ [<=]31.78

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

    associate-/r/ [<=]31.77

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

  3. Applied egg-rr31.8

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

  4. Final simplification31.8

    \[\leadsto {\left(a \cdot \sin \left(\frac{angle}{\frac{180}{\pi}}\right)\right)}^{2} + {\left(b \cdot \cos \left(\sqrt[3]{\pi} \cdot \frac{angle}{\frac{180}{{\left(\sqrt[3]{\pi}\right)}^{2}}}\right)\right)}^{2} \]

Alternatives

Alternative 1
Error31.82%
Cost58752
\[{\left(a \cdot \sin \left(\frac{angle}{\frac{180}{\pi}}\right)\right)}^{2} + {\left(b \cdot \cos \left({\left(\sqrt[3]{angle}\right)}^{2} \cdot \left(\sqrt[3]{angle} \cdot \left(\pi \cdot 0.005555555555555556\right)\right)\right)\right)}^{2} \]
Alternative 2
Error31.83%
Cost39360
\[{\left(a \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)}^{2} + {\left(b \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} \]
Alternative 3
Error31.76%
Cost39360
\[\begin{array}{l} t_0 := angle \cdot \frac{\pi}{180}\\ {\left(a \cdot \sin t_0\right)}^{2} + {\left(b \cdot \cos t_0\right)}^{2} \end{array} \]
Alternative 4
Error31.78%
Cost39360
\[{\left(a \cdot \sin \left(\frac{angle}{\frac{180}{\pi}}\right)\right)}^{2} + {\left(b \cdot \cos \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}^{2} \]
Alternative 5
Error31.88%
Cost26240
\[{\left(a \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)}^{2} + {b}^{2} \]
Alternative 6
Error31.81%
Cost26240
\[{\left(a \cdot \sin \left(angle \cdot \frac{\pi}{180}\right)\right)}^{2} + {b}^{2} \]
Alternative 7
Error31.82%
Cost26240
\[{\left(a \cdot \sin \left(\frac{angle}{\frac{180}{\pi}}\right)\right)}^{2} + {b}^{2} \]
Alternative 8
Error31.94%
Cost20489
\[\begin{array}{l} \mathbf{if}\;angle \leq -4.5 \cdot 10^{-5} \lor \neg \left(angle \leq 0.00071\right):\\ \;\;\;\;{b}^{2} + \frac{a \cdot a}{2} \cdot \left(1 - \cos \left(angle \cdot \left(\pi \cdot 0.011111111111111112\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;{b}^{2} + 0.005555555555555556 \cdot \left(\left(angle \cdot \left(a \cdot \pi\right)\right) \cdot \left(angle \cdot \left(0.005555555555555556 \cdot \left(a \cdot \pi\right)\right)\right)\right)\\ \end{array} \]
Alternative 9
Error31.99%
Cost20425
\[\begin{array}{l} \mathbf{if}\;angle \leq -4.5 \cdot 10^{-5} \lor \neg \left(angle \leq 0.00071\right):\\ \;\;\;\;{b}^{2} + \frac{a}{\frac{2}{a}} \cdot \left(1 - \cos \left(\pi \cdot \left(angle \cdot 0.011111111111111112\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;{b}^{2} + \left({\pi}^{2} \cdot \left(\left(a \cdot angle\right) \cdot \left(a \cdot angle\right)\right)\right) \cdot 3.08641975308642 \cdot 10^{-5}\\ \end{array} \]
Alternative 10
Error32%
Cost20425
\[\begin{array}{l} \mathbf{if}\;angle \leq -4.5 \cdot 10^{-5} \lor \neg \left(angle \leq 0.00071\right):\\ \;\;\;\;{b}^{2} + \frac{a \cdot a}{2} \cdot \left(1 - \cos \left(angle \cdot \left(\pi \cdot 0.011111111111111112\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;{b}^{2} + \left({\pi}^{2} \cdot \left(\left(a \cdot angle\right) \cdot \left(a \cdot angle\right)\right)\right) \cdot 3.08641975308642 \cdot 10^{-5}\\ \end{array} \]
Alternative 11
Error36.95%
Cost20360
\[\begin{array}{l} \mathbf{if}\;a \leq -2 \cdot 10^{+154}:\\ \;\;\;\;{b}^{2} + {\left(a \cdot \left(angle \cdot \left(\pi \cdot 0.005555555555555556\right)\right)\right)}^{2}\\ \mathbf{elif}\;a \leq 3 \cdot 10^{+128}:\\ \;\;\;\;{b}^{2} + 3.08641975308642 \cdot 10^{-5} \cdot \left(angle \cdot \left(angle \cdot \left(\left(a \cdot a\right) \cdot {\pi}^{2}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;{b}^{2} + {\left(a \cdot \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)}^{2}\\ \end{array} \]
Alternative 12
Error37%
Cost20360
\[\begin{array}{l} \mathbf{if}\;a \leq -1.22 \cdot 10^{+153}:\\ \;\;\;\;{b}^{2} + {\left(a \cdot \left(angle \cdot \left(\pi \cdot 0.005555555555555556\right)\right)\right)}^{2}\\ \mathbf{elif}\;a \leq 6 \cdot 10^{+69}:\\ \;\;\;\;{b}^{2} + 3.08641975308642 \cdot 10^{-5} \cdot \left(angle \cdot \left(angle \cdot \left(\left(a \cdot a\right) \cdot {\pi}^{2}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;{b}^{2} + \left({\pi}^{2} \cdot \left(\left(a \cdot angle\right) \cdot \left(a \cdot angle\right)\right)\right) \cdot 3.08641975308642 \cdot 10^{-5}\\ \end{array} \]
Alternative 13
Error40.67%
Cost19840
\[{b}^{2} + 3.08641975308642 \cdot 10^{-5} \cdot {\left(angle \cdot \left(a \cdot \pi\right)\right)}^{2} \]

Error

Reproduce?

herbie shell --seed 2023102 
(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)))