\[\sqrt{\frac{1}{2} \cdot \left(1 + \frac{1}{\sqrt{1 + {\left(\frac{2 \cdot \ell}{Om}\right)}^{2} \cdot \left({\sin kx}^{2} + {\sin ky}^{2}\right)}}\right)}
\]
↓
\[\sqrt{0.5 + 0.5 \cdot {\left(\sqrt{\mathsf{hypot}\left(1, \mathsf{hypot}\left(\sin ky, \sin kx\right) \cdot \left(2 \cdot \frac{\ell}{Om}\right)\right)}\right)}^{-2}}
\]
(FPCore (l Om kx ky)
:precision binary64
(sqrt
(*
(/ 1.0 2.0)
(+
1.0
(/
1.0
(sqrt
(+
1.0
(*
(pow (/ (* 2.0 l) Om) 2.0)
(+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))))))↓
(FPCore (l Om kx ky)
:precision binary64
(sqrt
(+
0.5
(*
0.5
(pow
(sqrt (hypot 1.0 (* (hypot (sin ky) (sin kx)) (* 2.0 (/ l Om)))))
-2.0)))))double code(double l, double Om, double kx, double ky) {
return sqrt(((1.0 / 2.0) * (1.0 + (1.0 / sqrt((1.0 + (pow(((2.0 * l) / Om), 2.0) * (pow(sin(kx), 2.0) + pow(sin(ky), 2.0)))))))));
}
↓
double code(double l, double Om, double kx, double ky) {
return sqrt((0.5 + (0.5 * pow(sqrt(hypot(1.0, (hypot(sin(ky), sin(kx)) * (2.0 * (l / Om))))), -2.0))));
}
public static double code(double l, double Om, double kx, double ky) {
return Math.sqrt(((1.0 / 2.0) * (1.0 + (1.0 / Math.sqrt((1.0 + (Math.pow(((2.0 * l) / Om), 2.0) * (Math.pow(Math.sin(kx), 2.0) + Math.pow(Math.sin(ky), 2.0)))))))));
}
↓
public static double code(double l, double Om, double kx, double ky) {
return Math.sqrt((0.5 + (0.5 * Math.pow(Math.sqrt(Math.hypot(1.0, (Math.hypot(Math.sin(ky), Math.sin(kx)) * (2.0 * (l / Om))))), -2.0))));
}
def code(l, Om, kx, ky):
return math.sqrt(((1.0 / 2.0) * (1.0 + (1.0 / math.sqrt((1.0 + (math.pow(((2.0 * l) / Om), 2.0) * (math.pow(math.sin(kx), 2.0) + math.pow(math.sin(ky), 2.0)))))))))
↓
def code(l, Om, kx, ky):
return math.sqrt((0.5 + (0.5 * math.pow(math.sqrt(math.hypot(1.0, (math.hypot(math.sin(ky), math.sin(kx)) * (2.0 * (l / Om))))), -2.0))))
function code(l, Om, kx, ky)
return sqrt(Float64(Float64(1.0 / 2.0) * Float64(1.0 + Float64(1.0 / sqrt(Float64(1.0 + Float64((Float64(Float64(2.0 * l) / Om) ^ 2.0) * Float64((sin(kx) ^ 2.0) + (sin(ky) ^ 2.0)))))))))
end
↓
function code(l, Om, kx, ky)
return sqrt(Float64(0.5 + Float64(0.5 * (sqrt(hypot(1.0, Float64(hypot(sin(ky), sin(kx)) * Float64(2.0 * Float64(l / Om))))) ^ -2.0))))
end
function tmp = code(l, Om, kx, ky)
tmp = sqrt(((1.0 / 2.0) * (1.0 + (1.0 / sqrt((1.0 + ((((2.0 * l) / Om) ^ 2.0) * ((sin(kx) ^ 2.0) + (sin(ky) ^ 2.0)))))))));
end
↓
function tmp = code(l, Om, kx, ky)
tmp = sqrt((0.5 + (0.5 * (sqrt(hypot(1.0, (hypot(sin(ky), sin(kx)) * (2.0 * (l / Om))))) ^ -2.0))));
end
code[l_, Om_, kx_, ky_] := N[Sqrt[N[(N[(1.0 / 2.0), $MachinePrecision] * N[(1.0 + N[(1.0 / N[Sqrt[N[(1.0 + N[(N[Power[N[(N[(2.0 * l), $MachinePrecision] / Om), $MachinePrecision], 2.0], $MachinePrecision] * N[(N[Power[N[Sin[kx], $MachinePrecision], 2.0], $MachinePrecision] + N[Power[N[Sin[ky], $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]
↓
code[l_, Om_, kx_, ky_] := N[Sqrt[N[(0.5 + N[(0.5 * N[Power[N[Sqrt[N[Sqrt[1.0 ^ 2 + N[(N[Sqrt[N[Sin[ky], $MachinePrecision] ^ 2 + N[Sin[kx], $MachinePrecision] ^ 2], $MachinePrecision] * N[(2.0 * N[(l / Om), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] ^ 2], $MachinePrecision]], $MachinePrecision], -2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]
\sqrt{\frac{1}{2} \cdot \left(1 + \frac{1}{\sqrt{1 + {\left(\frac{2 \cdot \ell}{Om}\right)}^{2} \cdot \left({\sin kx}^{2} + {\sin ky}^{2}\right)}}\right)}
↓
\sqrt{0.5 + 0.5 \cdot {\left(\sqrt{\mathsf{hypot}\left(1, \mathsf{hypot}\left(\sin ky, \sin kx\right) \cdot \left(2 \cdot \frac{\ell}{Om}\right)\right)}\right)}^{-2}}
Alternatives
| Alternative 1 |
|---|
| Error | 1.3 |
|---|
| Cost | 33160 |
|---|
\[\begin{array}{l}
t_0 := \frac{2 \cdot \ell}{Om}\\
t_1 := \sqrt{0.5 + 0.5 \cdot \frac{1}{\mathsf{hypot}\left(1, \sin kx \cdot t_0\right)}}\\
\mathbf{if}\;\sin kx \leq -1 \cdot 10^{-169}:\\
\;\;\;\;t_1\\
\mathbf{elif}\;\sin kx \leq 10^{-152}:\\
\;\;\;\;\sqrt{0.5 + 0.5 \cdot \frac{1}{\mathsf{hypot}\left(1, \sin ky \cdot t_0\right)}}\\
\mathbf{else}:\\
\;\;\;\;t_1\\
\end{array}
\]
| Alternative 2 |
|---|
| Error | 1.3 |
|---|
| Cost | 33160 |
|---|
\[\begin{array}{l}
t_0 := \frac{2 \cdot \ell}{Om}\\
\mathbf{if}\;\sin kx \leq -1 \cdot 10^{-169}:\\
\;\;\;\;\sqrt{0.5 + 0.5 \cdot \frac{1}{\sqrt{1 + {\left(2 \cdot \left(\sin kx \cdot \frac{\ell}{Om}\right)\right)}^{2}}}}\\
\mathbf{elif}\;\sin kx \leq 10^{-152}:\\
\;\;\;\;\sqrt{0.5 + 0.5 \cdot \frac{1}{\mathsf{hypot}\left(1, \sin ky \cdot t_0\right)}}\\
\mathbf{else}:\\
\;\;\;\;\sqrt{0.5 + 0.5 \cdot \frac{1}{\mathsf{hypot}\left(1, \sin kx \cdot t_0\right)}}\\
\end{array}
\]
| Alternative 3 |
|---|
| Error | 0.0 |
|---|
| Cost | 32960 |
|---|
\[\sqrt{0.5 + 0.5 \cdot \frac{1}{\mathsf{hypot}\left(1, \mathsf{hypot}\left(\sin ky, \sin kx\right) \cdot \left(2 \cdot \frac{\ell}{Om}\right)\right)}}
\]
| Alternative 4 |
|---|
| Error | 2.2 |
|---|
| Cost | 20872 |
|---|
\[\begin{array}{l}
t_0 := \frac{2 \cdot \ell}{Om}\\
\mathbf{if}\;t_0 \leq -5 \cdot 10^{+15}:\\
\;\;\;\;\sqrt{0.5}\\
\mathbf{elif}\;t_0 \leq 5 \cdot 10^{+69}:\\
\;\;\;\;\sqrt{0.5 + 0.5 \cdot \frac{1}{\mathsf{hypot}\left(1, \sin kx \cdot t_0\right)}}\\
\mathbf{else}:\\
\;\;\;\;\sqrt{0.5}\\
\end{array}
\]
| Alternative 5 |
|---|
| Error | 9.6 |
|---|
| Cost | 13832 |
|---|
\[\begin{array}{l}
t_0 := \sqrt{0.5 + \frac{0.5}{\mathsf{hypot}\left(1, 2 \cdot \frac{\ell}{\frac{Om}{kx}}\right)}}\\
\mathbf{if}\;Om \leq -1.5 \cdot 10^{-185}:\\
\;\;\;\;t_0\\
\mathbf{elif}\;Om \leq 10^{-187}:\\
\;\;\;\;\sqrt{0.5}\\
\mathbf{else}:\\
\;\;\;\;t_0\\
\end{array}
\]
| Alternative 6 |
|---|
| Error | 12.7 |
|---|
| Cost | 8008 |
|---|
\[\begin{array}{l}
\mathbf{if}\;Om \leq -5.5 \cdot 10^{+84}:\\
\;\;\;\;1\\
\mathbf{elif}\;Om \leq -1.42 \cdot 10^{-148}:\\
\;\;\;\;\sqrt{0.5 + 0.5 \cdot \frac{1}{1 + 2 \cdot \frac{\ell \cdot \ell}{\frac{Om \cdot Om}{kx \cdot kx}}}}\\
\mathbf{elif}\;Om \leq 5 \cdot 10^{-66}:\\
\;\;\;\;\sqrt{0.5}\\
\mathbf{else}:\\
\;\;\;\;1\\
\end{array}
\]
| Alternative 7 |
|---|
| Error | 12.5 |
|---|
| Cost | 8008 |
|---|
\[\begin{array}{l}
\mathbf{if}\;Om \leq -9.5 \cdot 10^{+82}:\\
\;\;\;\;1\\
\mathbf{elif}\;Om \leq -9 \cdot 10^{-151}:\\
\;\;\;\;\sqrt{0.5 + 0.5 \cdot \frac{1}{1 + 2 \cdot \frac{\left(kx \cdot kx\right) \cdot \left(\ell \cdot \ell\right)}{Om \cdot Om}}}\\
\mathbf{elif}\;Om \leq 4 \cdot 10^{-64}:\\
\;\;\;\;\sqrt{0.5}\\
\mathbf{else}:\\
\;\;\;\;1\\
\end{array}
\]
| Alternative 8 |
|---|
| Error | 13.4 |
|---|
| Cost | 6728 |
|---|
\[\begin{array}{l}
\mathbf{if}\;Om \leq -1.02 \cdot 10^{-34}:\\
\;\;\;\;1\\
\mathbf{elif}\;Om \leq 1.4 \cdot 10^{-63}:\\
\;\;\;\;\sqrt{0.5}\\
\mathbf{else}:\\
\;\;\;\;1\\
\end{array}
\]
| Alternative 9 |
|---|
| Error | 28.4 |
|---|
| Cost | 6464 |
|---|
\[\sqrt{0.5}
\]