\[\sqrt{\frac{1}{2} \cdot \left(1 + \frac{1}{\sqrt{1 + {\left(\frac{2 \cdot \ell}{Om}\right)}^{2} \cdot \left({\sin kx}^{2} + {\sin ky}^{2}\right)}}\right)}
\]
↓
\[\sqrt{0.5 + \frac{0.5}{\mathsf{hypot}\left(1, \frac{2 \cdot \ell}{Om} \cdot \mathsf{hypot}\left(\sin kx, \sin ky\right)\right)}}
\]
(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 (hypot 1.0 (* (/ (* 2.0 l) Om) (hypot (sin kx) (sin ky))))))))
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 / hypot(1.0, (((2.0 * l) / Om) * hypot(sin(kx), sin(ky)))))));
}
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.hypot(1.0, (((2.0 * l) / Om) * Math.hypot(Math.sin(kx), Math.sin(ky)))))));
}
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.hypot(1.0, (((2.0 * l) / Om) * math.hypot(math.sin(kx), math.sin(ky)))))))
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 / hypot(1.0, Float64(Float64(Float64(2.0 * l) / Om) * hypot(sin(kx), sin(ky)))))))
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 / hypot(1.0, (((2.0 * l) / Om) * hypot(sin(kx), sin(ky)))))));
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[Sqrt[1.0 ^ 2 + N[(N[(N[(2.0 * l), $MachinePrecision] / Om), $MachinePrecision] * N[Sqrt[N[Sin[kx], $MachinePrecision] ^ 2 + N[Sin[ky], $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision] ^ 2], $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 + \frac{0.5}{\mathsf{hypot}\left(1, \frac{2 \cdot \ell}{Om} \cdot \mathsf{hypot}\left(\sin kx, \sin ky\right)\right)}}
Alternatives
| Alternative 1 |
|---|
| Error | 0.8 |
|---|
| Cost | 39944 |
|---|
\[\begin{array}{l}
\mathbf{if}\;\sin kx \leq -5 \cdot 10^{-71}:\\
\;\;\;\;\sqrt{0.5 + \frac{0.5}{\mathsf{hypot}\left(1, \frac{2 \cdot \sin kx}{\frac{Om}{\ell}}\right)}}\\
\mathbf{elif}\;\sin kx \leq 4 \cdot 10^{-57}:\\
\;\;\;\;\sqrt{0.5 + \frac{0.5}{\mathsf{hypot}\left(1, \frac{2 \cdot \sin ky}{\frac{Om}{\ell}}\right)}}\\
\mathbf{else}:\\
\;\;\;\;\sqrt{0.5 \cdot \left(1 + \frac{1}{\sqrt{1 + 4 \cdot \left(\left(\frac{\ell}{Om} \cdot \frac{\ell}{Om}\right) \cdot {\sin kx}^{2}\right)}}\right)}\\
\end{array}
\]
| Alternative 2 |
|---|
| Error | 0.8 |
|---|
| Cost | 33032 |
|---|
\[\begin{array}{l}
t_0 := \sqrt{0.5 + \frac{0.5}{\mathsf{hypot}\left(1, \frac{2 \cdot \sin kx}{\frac{Om}{\ell}}\right)}}\\
\mathbf{if}\;\sin kx \leq -5 \cdot 10^{-71}:\\
\;\;\;\;t_0\\
\mathbf{elif}\;\sin kx \leq 4 \cdot 10^{-57}:\\
\;\;\;\;\sqrt{0.5 + \frac{0.5}{\mathsf{hypot}\left(1, \frac{2 \cdot \sin ky}{\frac{Om}{\ell}}\right)}}\\
\mathbf{else}:\\
\;\;\;\;t_0\\
\end{array}
\]
| Alternative 3 |
|---|
| Error | 4.0 |
|---|
| Cost | 19968 |
|---|
\[\sqrt{0.5 + \frac{0.5}{\mathsf{hypot}\left(1, \frac{2 \cdot \sin ky}{\frac{Om}{\ell}}\right)}}
\]
| Alternative 4 |
|---|
| Error | 9.2 |
|---|
| Cost | 13832 |
|---|
\[\begin{array}{l}
t_0 := \sqrt{0.5 + \frac{0.5}{\mathsf{hypot}\left(1, \frac{2 \cdot \ell}{\frac{Om}{ky}}\right)}}\\
\mathbf{if}\;\ell \leq -7.677161523649325 \cdot 10^{-279}:\\
\;\;\;\;t_0\\
\mathbf{elif}\;\ell \leq 1.7488046334496753 \cdot 10^{-119}:\\
\;\;\;\;1\\
\mathbf{else}:\\
\;\;\;\;t_0\\
\end{array}
\]
| Alternative 5 |
|---|
| Error | 13.7 |
|---|
| Cost | 8008 |
|---|
\[\begin{array}{l}
\mathbf{if}\;Om \leq -8.991552487015289 \cdot 10^{-65}:\\
\;\;\;\;1\\
\mathbf{elif}\;Om \leq 1.5830130101145458 \cdot 10^{-96}:\\
\;\;\;\;\sqrt{0.5 \cdot \left(1 + \frac{1}{2 \cdot \frac{\ell \cdot ky}{Om} + 0.25 \cdot \frac{Om}{\ell \cdot ky}}\right)}\\
\mathbf{else}:\\
\;\;\;\;1\\
\end{array}
\]
| Alternative 6 |
|---|
| Error | 13.6 |
|---|
| Cost | 6728 |
|---|
\[\begin{array}{l}
\mathbf{if}\;Om \leq -8.991552487015289 \cdot 10^{-65}:\\
\;\;\;\;1\\
\mathbf{elif}\;Om \leq 1.5830130101145458 \cdot 10^{-96}:\\
\;\;\;\;\sqrt{0.5}\\
\mathbf{else}:\\
\;\;\;\;1\\
\end{array}
\]
| Alternative 7 |
|---|
| Error | 23.9 |
|---|
| Cost | 64 |
|---|
\[1
\]