?

Average Accuracy: 67.3% → 67.3%
Time: 21.5s
Precision: binary64
Cost: 65600

?

\[{\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \cos \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} \]
↓
\[\begin{array}{l} t_0 := \sqrt[3]{\frac{180}{angle}}\\ {\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \cos \left(\frac{\frac{\pi}{t_0 \cdot t_0}}{\sqrt[3]{180} \cdot \sqrt[3]{\frac{1}{angle}}}\right)\right)}^{2} \end{array} \]
(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
 (let* ((t_0 (cbrt (/ 180.0 angle))))
   (+
    (pow (* a (sin (* (/ angle 180.0) PI))) 2.0)
    (pow
     (* b (cos (/ (/ PI (* t_0 t_0)) (* (cbrt 180.0) (cbrt (/ 1.0 angle))))))
     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) {
	double t_0 = cbrt((180.0 / angle));
	return pow((a * sin(((angle / 180.0) * ((double) M_PI)))), 2.0) + pow((b * cos(((((double) M_PI) / (t_0 * t_0)) / (cbrt(180.0) * cbrt((1.0 / angle)))))), 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) {
	double t_0 = Math.cbrt((180.0 / angle));
	return Math.pow((a * Math.sin(((angle / 180.0) * Math.PI))), 2.0) + Math.pow((b * Math.cos(((Math.PI / (t_0 * t_0)) / (Math.cbrt(180.0) * Math.cbrt((1.0 / angle)))))), 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)
	t_0 = cbrt(Float64(180.0 / angle))
	return Float64((Float64(a * sin(Float64(Float64(angle / 180.0) * pi))) ^ 2.0) + (Float64(b * cos(Float64(Float64(pi / Float64(t_0 * t_0)) / Float64(cbrt(180.0) * cbrt(Float64(1.0 / angle)))))) ^ 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_] := Block[{t$95$0 = N[Power[N[(180.0 / angle), $MachinePrecision], 1/3], $MachinePrecision]}, 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[(Pi / N[(t$95$0 * t$95$0), $MachinePrecision]), $MachinePrecision] / N[(N[Power[180.0, 1/3], $MachinePrecision] * N[Power[N[(1.0 / angle), $MachinePrecision], 1/3], $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}
↓
\begin{array}{l}
t_0 := \sqrt[3]{\frac{180}{angle}}\\
{\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \cos \left(\frac{\frac{\pi}{t_0 \cdot t_0}}{\sqrt[3]{180} \cdot \sqrt[3]{\frac{1}{angle}}}\right)\right)}^{2}
\end{array}

Error?

Try it out?

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation?

  1. Initial program 67.3%

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

  2. Applied egg-rr67.3%

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

    [Start]67.3

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

    *-commutative [=>]67.3

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

    clear-num [=>]67.3

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

    un-div-inv [=>]67.3

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

    add-cube-cbrt [=>]67.3

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

    associate-/r* [=>]67.3

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

  3. Applied egg-rr67.3%

    \[\leadsto {\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \cos \left(\frac{\frac{\pi}{\sqrt[3]{\frac{180}{angle}} \cdot \sqrt[3]{\frac{180}{angle}}}}{\color{blue}{\sqrt[3]{180} \cdot \sqrt[3]{\frac{1}{angle}}}}\right)\right)}^{2} \]
    Proof

    [Start]67.3

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

    div-inv [=>]67.3

    \[ {\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \cos \left(\frac{\frac{\pi}{\sqrt[3]{\frac{180}{angle}} \cdot \sqrt[3]{\frac{180}{angle}}}}{\sqrt[3]{\color{blue}{180 \cdot \frac{1}{angle}}}}\right)\right)}^{2} \]

    cbrt-prod [=>]67.3

    \[ {\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \cos \left(\frac{\frac{\pi}{\sqrt[3]{\frac{180}{angle}} \cdot \sqrt[3]{\frac{180}{angle}}}}{\color{blue}{\sqrt[3]{180} \cdot \sqrt[3]{\frac{1}{angle}}}}\right)\right)}^{2} \]

  4. Final simplification67.3%

    \[\leadsto {\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \cos \left(\frac{\frac{\pi}{\sqrt[3]{\frac{180}{angle}} \cdot \sqrt[3]{\frac{180}{angle}}}}{\sqrt[3]{180} \cdot \sqrt[3]{\frac{1}{angle}}}\right)\right)}^{2} \]

Alternatives

Alternative 1
Accuracy67.4%
Cost39488
\[{\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \cos \left(\frac{\frac{\pi}{180}}{\frac{1}{angle}}\right)\right)}^{2} \]
Alternative 2
Accuracy67.4%
Cost39488
\[{\left(a \cdot \sin \left(\frac{\frac{\pi}{180}}{\frac{1}{angle}}\right)\right)}^{2} + {\left(b \cdot \cos \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} \]
Alternative 3
Accuracy67.4%
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
Accuracy67.3%
Cost39360
\[\begin{array}{l} t_0 := \frac{angle}{180} \cdot \pi\\ {\left(a \cdot \sin t_0\right)}^{2} + {\left(b \cdot \cos t_0\right)}^{2} \end{array} \]
Alternative 5
Accuracy66.5%
Cost26372
\[\begin{array}{l} \mathbf{if}\;angle \leq 9.5 \cdot 10^{-16}:\\ \;\;\;\;{b}^{2} + {\left(a \cdot \mathsf{expm1}\left(angle \cdot \left(\pi \cdot 0.005555555555555556\right)\right)\right)}^{2}\\ \mathbf{else}:\\ \;\;\;\;{b}^{2} + \frac{a}{\frac{2}{a}} \cdot \left(1 - \cos \left(\pi \cdot \left(angle \cdot 0.011111111111111112\right)\right)\right)\\ \end{array} \]
Alternative 6
Accuracy67.2%
Cost26368
\[{\left(a \cdot \sin \left(\frac{\frac{\pi}{180}}{\frac{1}{angle}}\right)\right)}^{2} + {b}^{2} \]
Alternative 7
Accuracy67.3%
Cost26240
\[{\left(a \cdot \sin \left(angle \cdot \frac{\pi}{180}\right)\right)}^{2} + {b}^{2} \]
Alternative 8
Accuracy66.8%
Cost20425
\[\begin{array}{l} \mathbf{if}\;angle \leq -0.0045 \lor \neg \left(angle \leq 9.5 \cdot 10^{-16}\right):\\ \;\;\;\;{b}^{2} + \frac{a}{\frac{2}{a}} \cdot \left(1 - \cos \left(\pi \cdot \left(angle \cdot 0.011111111111111112\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;{b}^{2} + \left({\pi}^{2} \cdot \left(\left(a \cdot angle\right) \cdot \left(a \cdot angle\right)\right)\right) \cdot 3.08641975308642 \cdot 10^{-5}\\ \end{array} \]
Alternative 9
Accuracy58.4%
Cost20096
\[{b}^{2} + \left({\pi}^{2} \cdot \left(\left(a \cdot angle\right) \cdot \left(a \cdot angle\right)\right)\right) \cdot 3.08641975308642 \cdot 10^{-5} \]
Alternative 10
Accuracy58.3%
Cost19840
\[{b}^{2} + 3.08641975308642 \cdot 10^{-5} \cdot {\left(angle \cdot \left(a \cdot \pi\right)\right)}^{2} \]
Alternative 11
Accuracy58.4%
Cost19840
\[{b}^{2} + 3.08641975308642 \cdot 10^{-5} \cdot {\left(\pi \cdot \left(a \cdot angle\right)\right)}^{2} \]

Error

Reproduce?

herbie shell --seed 2023131 
(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)))