?

Average Accuracy: 68.2% → 68.2%
Time: 21.7s
Precision: binary64
Cost: 58752

?

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

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

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

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

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

Error?

Try it out?

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation?

  1. Initial program 68.2%

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

  2. Applied egg-rr68.2%

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

    [Start]68.2

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

    *-commutative [=>]68.2

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

    add-cube-cbrt [=>]68.2

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

    associate-/l* [=>]68.2

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

    associate-*l/ [=>]68.2

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

    pow2 [=>]68.2

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

  3. Final simplification68.2%

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

Alternatives

Alternative 1
Accuracy68.2%
Cost58752
\[{\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} + {\left(a \cdot \cos \left(\sqrt[3]{angle} \cdot \frac{{\left(\sqrt[3]{angle}\right)}^{2}}{\frac{180}{\pi}}\right)\right)}^{2} \]
Alternative 2
Accuracy68.2%
Cost52160
\[{\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} + {\left(a \cdot \mathsf{expm1}\left(\mathsf{log1p}\left(\cos \left(\frac{\pi}{\frac{180}{angle}}\right)\right)\right)\right)}^{2} \]
Alternative 3
Accuracy68.2%
Cost52160
\[{\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} + {\left(a \cdot \mathsf{log1p}\left(\mathsf{expm1}\left(\cos \left(\frac{\pi}{\frac{180}{angle}}\right)\right)\right)\right)}^{2} \]
Alternative 4
Accuracy68.3%
Cost39488
\[{\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} + {\left(a \cdot \cos \left(\frac{1}{\frac{\frac{180}{angle}}{\pi}}\right)\right)}^{2} \]
Alternative 5
Accuracy68.2%
Cost39360
\[{\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} + {\left(a \cdot \cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)}^{2} \]
Alternative 6
Accuracy68.3%
Cost39360
\[{\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} + {\left(a \cdot \cos \left(angle \cdot \frac{\pi}{180}\right)\right)}^{2} \]
Alternative 7
Accuracy68.3%
Cost39360
\[{\left(a \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} + {\left(b \cdot \sin \left(angle \cdot \frac{\pi}{180}\right)\right)}^{2} \]
Alternative 8
Accuracy68.2%
Cost39360
\[\begin{array}{l} t_0 := \pi \cdot \frac{angle}{180}\\ {\left(b \cdot \sin t_0\right)}^{2} + {\left(a \cdot \cos t_0\right)}^{2} \end{array} \]
Alternative 9
Accuracy68.2%
Cost26240
\[{a}^{2} + {\left(b \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)}^{2} \]
Alternative 10
Accuracy68.2%
Cost26240
\[{\left(b \cdot \sin \left(angle \cdot \frac{\pi}{180}\right)\right)}^{2} + {a}^{2} \]
Alternative 11
Accuracy68.2%
Cost26240
\[{\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} + {a}^{2} \]
Alternative 12
Accuracy68.2%
Cost20425
\[\begin{array}{l} \mathbf{if}\;angle \leq -0.0146 \lor \neg \left(angle \leq 0.00305\right):\\ \;\;\;\;{a}^{2} + \left(1 - \cos \left(angle \cdot \left(\pi \cdot 0.011111111111111112\right)\right)\right) \cdot \frac{b}{\frac{2}{b}}\\ \mathbf{else}:\\ \;\;\;\;{a}^{2} + {\left(\left(\pi \cdot 0.005555555555555556\right) \cdot \left(angle \cdot b\right)\right)}^{2}\\ \end{array} \]
Alternative 13
Accuracy68.2%
Cost20424
\[\begin{array}{l} t_0 := 1 - \cos \left(angle \cdot \left(\pi \cdot 0.011111111111111112\right)\right)\\ \mathbf{if}\;angle \leq -0.0054:\\ \;\;\;\;{a}^{2} + \frac{b \cdot b}{2} \cdot t_0\\ \mathbf{elif}\;angle \leq 0.00305:\\ \;\;\;\;{a}^{2} + {\left(\left(\pi \cdot 0.005555555555555556\right) \cdot \left(angle \cdot b\right)\right)}^{2}\\ \mathbf{else}:\\ \;\;\;\;{a}^{2} + t_0 \cdot \frac{b}{\frac{2}{b}}\\ \end{array} \]
Alternative 14
Accuracy59.2%
Cost19840
\[{a}^{2} + 3.08641975308642 \cdot 10^{-5} \cdot {\left(angle \cdot \left(\pi \cdot b\right)\right)}^{2} \]
Alternative 15
Accuracy59.2%
Cost19840
\[{a}^{2} + {\left(b \cdot \left(angle \cdot \pi\right)\right)}^{2} \cdot 3.08641975308642 \cdot 10^{-5} \]
Alternative 16
Accuracy59.3%
Cost19840
\[{a}^{2} + {\left(0.005555555555555556 \cdot \left(b \cdot \left(angle \cdot \pi\right)\right)\right)}^{2} \]
Alternative 17
Accuracy59.3%
Cost19840
\[{a}^{2} + {\left(0.005555555555555556 \cdot \left(\pi \cdot \left(angle \cdot b\right)\right)\right)}^{2} \]
Alternative 18
Accuracy59.4%
Cost19840
\[{a}^{2} + {\left(\left(\pi \cdot 0.005555555555555556\right) \cdot \left(angle \cdot b\right)\right)}^{2} \]

Error

Reproduce?

herbie shell --seed 2023133 
(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)))