\[ \begin{array}{c}[x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \end{array} \]
\[\left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right)
\]
↓
\[\left(\left(\frac{1 + \left(x - x\right)}{\sqrt{x} + \sqrt{1 + x}} + \frac{1}{\sqrt{1 + y} + \sqrt{y}}\right) + \left(\sqrt{1 + z} - \sqrt{z}\right)\right) + \left(\sqrt{1 + t} - \sqrt{t}\right)
\]
(FPCore (x y z t)
:precision binary64
(+
(+
(+ (- (sqrt (+ x 1.0)) (sqrt x)) (- (sqrt (+ y 1.0)) (sqrt y)))
(- (sqrt (+ z 1.0)) (sqrt z)))
(- (sqrt (+ t 1.0)) (sqrt t))))
↓
(FPCore (x y z t)
:precision binary64
(+
(+
(+
(/ (+ 1.0 (- x x)) (+ (sqrt x) (sqrt (+ 1.0 x))))
(/ 1.0 (+ (sqrt (+ 1.0 y)) (sqrt y))))
(- (sqrt (+ 1.0 z)) (sqrt z)))
(- (sqrt (+ 1.0 t)) (sqrt t))))double code(double x, double y, double z, double t) {
return (((sqrt((x + 1.0)) - sqrt(x)) + (sqrt((y + 1.0)) - sqrt(y))) + (sqrt((z + 1.0)) - sqrt(z))) + (sqrt((t + 1.0)) - sqrt(t));
}
↓
double code(double x, double y, double z, double t) {
return ((((1.0 + (x - x)) / (sqrt(x) + sqrt((1.0 + x)))) + (1.0 / (sqrt((1.0 + y)) + sqrt(y)))) + (sqrt((1.0 + z)) - sqrt(z))) + (sqrt((1.0 + t)) - sqrt(t));
}
real(8) function code(x, y, z, t)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8), intent (in) :: z
real(8), intent (in) :: t
code = (((sqrt((x + 1.0d0)) - sqrt(x)) + (sqrt((y + 1.0d0)) - sqrt(y))) + (sqrt((z + 1.0d0)) - sqrt(z))) + (sqrt((t + 1.0d0)) - sqrt(t))
end function
↓
real(8) function code(x, y, z, t)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8), intent (in) :: z
real(8), intent (in) :: t
code = ((((1.0d0 + (x - x)) / (sqrt(x) + sqrt((1.0d0 + x)))) + (1.0d0 / (sqrt((1.0d0 + y)) + sqrt(y)))) + (sqrt((1.0d0 + z)) - sqrt(z))) + (sqrt((1.0d0 + t)) - sqrt(t))
end function
public static double code(double x, double y, double z, double t) {
return (((Math.sqrt((x + 1.0)) - Math.sqrt(x)) + (Math.sqrt((y + 1.0)) - Math.sqrt(y))) + (Math.sqrt((z + 1.0)) - Math.sqrt(z))) + (Math.sqrt((t + 1.0)) - Math.sqrt(t));
}
↓
public static double code(double x, double y, double z, double t) {
return ((((1.0 + (x - x)) / (Math.sqrt(x) + Math.sqrt((1.0 + x)))) + (1.0 / (Math.sqrt((1.0 + y)) + Math.sqrt(y)))) + (Math.sqrt((1.0 + z)) - Math.sqrt(z))) + (Math.sqrt((1.0 + t)) - Math.sqrt(t));
}
def code(x, y, z, t):
return (((math.sqrt((x + 1.0)) - math.sqrt(x)) + (math.sqrt((y + 1.0)) - math.sqrt(y))) + (math.sqrt((z + 1.0)) - math.sqrt(z))) + (math.sqrt((t + 1.0)) - math.sqrt(t))
↓
def code(x, y, z, t):
return ((((1.0 + (x - x)) / (math.sqrt(x) + math.sqrt((1.0 + x)))) + (1.0 / (math.sqrt((1.0 + y)) + math.sqrt(y)))) + (math.sqrt((1.0 + z)) - math.sqrt(z))) + (math.sqrt((1.0 + t)) - math.sqrt(t))
function code(x, y, z, t)
return Float64(Float64(Float64(Float64(sqrt(Float64(x + 1.0)) - sqrt(x)) + Float64(sqrt(Float64(y + 1.0)) - sqrt(y))) + Float64(sqrt(Float64(z + 1.0)) - sqrt(z))) + Float64(sqrt(Float64(t + 1.0)) - sqrt(t)))
end
↓
function code(x, y, z, t)
return Float64(Float64(Float64(Float64(Float64(1.0 + Float64(x - x)) / Float64(sqrt(x) + sqrt(Float64(1.0 + x)))) + Float64(1.0 / Float64(sqrt(Float64(1.0 + y)) + sqrt(y)))) + Float64(sqrt(Float64(1.0 + z)) - sqrt(z))) + Float64(sqrt(Float64(1.0 + t)) - sqrt(t)))
end
function tmp = code(x, y, z, t)
tmp = (((sqrt((x + 1.0)) - sqrt(x)) + (sqrt((y + 1.0)) - sqrt(y))) + (sqrt((z + 1.0)) - sqrt(z))) + (sqrt((t + 1.0)) - sqrt(t));
end
↓
function tmp = code(x, y, z, t)
tmp = ((((1.0 + (x - x)) / (sqrt(x) + sqrt((1.0 + x)))) + (1.0 / (sqrt((1.0 + y)) + sqrt(y)))) + (sqrt((1.0 + z)) - sqrt(z))) + (sqrt((1.0 + t)) - sqrt(t));
end
code[x_, y_, z_, t_] := N[(N[(N[(N[(N[Sqrt[N[(x + 1.0), $MachinePrecision]], $MachinePrecision] - N[Sqrt[x], $MachinePrecision]), $MachinePrecision] + N[(N[Sqrt[N[(y + 1.0), $MachinePrecision]], $MachinePrecision] - N[Sqrt[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[Sqrt[N[(z + 1.0), $MachinePrecision]], $MachinePrecision] - N[Sqrt[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[Sqrt[N[(t + 1.0), $MachinePrecision]], $MachinePrecision] - N[Sqrt[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
↓
code[x_, y_, z_, t_] := N[(N[(N[(N[(N[(1.0 + N[(x - x), $MachinePrecision]), $MachinePrecision] / N[(N[Sqrt[x], $MachinePrecision] + N[Sqrt[N[(1.0 + x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(1.0 / N[(N[Sqrt[N[(1.0 + y), $MachinePrecision]], $MachinePrecision] + N[Sqrt[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[Sqrt[N[(1.0 + z), $MachinePrecision]], $MachinePrecision] - N[Sqrt[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[Sqrt[N[(1.0 + t), $MachinePrecision]], $MachinePrecision] - N[Sqrt[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
\left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right)
↓
\left(\left(\frac{1 + \left(x - x\right)}{\sqrt{x} + \sqrt{1 + x}} + \frac{1}{\sqrt{1 + y} + \sqrt{y}}\right) + \left(\sqrt{1 + z} - \sqrt{z}\right)\right) + \left(\sqrt{1 + t} - \sqrt{t}\right)
Alternatives
| Alternative 1 |
|---|
| Error | 2.1 |
|---|
| Cost | 52932 |
|---|
\[\begin{array}{l}
t_1 := \sqrt{1 + x}\\
\mathbf{if}\;t_1 - \sqrt{x} \leq 0.999999999995:\\
\;\;\;\;\frac{1}{\sqrt{x} + t_1}\\
\mathbf{else}:\\
\;\;\;\;\left(\sqrt{1 + t} - \sqrt{t}\right) + \left(\left(\sqrt{1 + z} - \sqrt{z}\right) + \left(1 + \frac{1}{\sqrt{1 + y} + \sqrt{y}}\right)\right)\\
\end{array}
\]
| Alternative 2 |
|---|
| Error | 2.6 |
|---|
| Cost | 52800 |
|---|
\[\left(\sqrt{1 + t} - \sqrt{t}\right) + \left(\left(\sqrt{1 + z} - \sqrt{z}\right) + \left(\frac{1}{\sqrt{x} + \sqrt{1 + x}} + \left(\sqrt{1 + y} - \sqrt{y}\right)\right)\right)
\]
| Alternative 3 |
|---|
| Error | 5.1 |
|---|
| Cost | 39748 |
|---|
\[\begin{array}{l}
t_1 := \sqrt{1 + x}\\
\mathbf{if}\;x \leq 4.4 \cdot 10^{-10}:\\
\;\;\;\;t_1 + \left(\left(\sqrt{1 + y} - \sqrt{y}\right) + \left(\frac{1}{\sqrt{z} + \sqrt{1 + z}} - \sqrt{x}\right)\right)\\
\mathbf{else}:\\
\;\;\;\;\frac{1}{\sqrt{x} + t_1}\\
\end{array}
\]
| Alternative 4 |
|---|
| Error | 2.8 |
|---|
| Cost | 39748 |
|---|
\[\begin{array}{l}
\mathbf{if}\;y \leq 6.7 \cdot 10^{+30}:\\
\;\;\;\;\left(\sqrt{1 + t} - \sqrt{t}\right) + \left(\left(\sqrt{1 + z} - \sqrt{z}\right) + \left(1 + \left(\sqrt{1 + y} - \sqrt{y}\right)\right)\right)\\
\mathbf{else}:\\
\;\;\;\;\frac{1}{\sqrt{x} + \sqrt{1 + x}}\\
\end{array}
\]
| Alternative 5 |
|---|
| Error | 5.8 |
|---|
| Cost | 26696 |
|---|
\[\begin{array}{l}
t_1 := \sqrt{1 + x}\\
t_2 := \sqrt{1 + y}\\
\mathbf{if}\;z \leq 1.18 \cdot 10^{-30}:\\
\;\;\;\;t_1 + \left(\left(\sqrt{1 + t} - \sqrt{t}\right) + 2\right)\\
\mathbf{elif}\;z \leq 1.35 \cdot 10^{+23}:\\
\;\;\;\;1 + \left(\sqrt{1 + z} + \left(t_2 - \left(\sqrt{y} + \sqrt{z}\right)\right)\right)\\
\mathbf{else}:\\
\;\;\;\;t_1 + \left(\left(t_2 - \sqrt{y}\right) - \sqrt{x}\right)\\
\end{array}
\]
| Alternative 6 |
|---|
| Error | 5.3 |
|---|
| Cost | 26692 |
|---|
\[\begin{array}{l}
\mathbf{if}\;y \leq 6.7 \cdot 10^{+30}:\\
\;\;\;\;1 + \left(\sqrt{1 + y} + \left(\frac{1}{\sqrt{z} + \sqrt{1 + z}} - \sqrt{y}\right)\right)\\
\mathbf{else}:\\
\;\;\;\;\frac{1}{\sqrt{x} + \sqrt{1 + x}}\\
\end{array}
\]
| Alternative 7 |
|---|
| Error | 5.3 |
|---|
| Cost | 26692 |
|---|
\[\begin{array}{l}
\mathbf{if}\;y \leq 6.7 \cdot 10^{+30}:\\
\;\;\;\;\left(1 + \sqrt{1 + y}\right) + \left(\frac{1}{\sqrt{z} + \sqrt{1 + z}} - \sqrt{y}\right)\\
\mathbf{else}:\\
\;\;\;\;\frac{1}{\sqrt{x} + \sqrt{1 + x}}\\
\end{array}
\]
| Alternative 8 |
|---|
| Error | 8.3 |
|---|
| Cost | 26436 |
|---|
\[\begin{array}{l}
t_1 := \sqrt{1 + x}\\
\mathbf{if}\;z \leq 0.68:\\
\;\;\;\;t_1 + \left(\left(\sqrt{1 + t} - \sqrt{t}\right) + 2\right)\\
\mathbf{else}:\\
\;\;\;\;t_1 + \left(\left(\sqrt{1 + y} - \sqrt{y}\right) - \sqrt{x}\right)\\
\end{array}
\]
| Alternative 9 |
|---|
| Error | 8.8 |
|---|
| Cost | 20164 |
|---|
\[\begin{array}{l}
\mathbf{if}\;z \leq 0.55:\\
\;\;\;\;\sqrt{1 + x} + \left(\left(\sqrt{1 + t} - \sqrt{t}\right) + 2\right)\\
\mathbf{else}:\\
\;\;\;\;\left(\left(\sqrt{1 + y} - \sqrt{y}\right) - \sqrt{x}\right) + \left(1 + x \cdot 0.5\right)\\
\end{array}
\]
| Alternative 10 |
|---|
| Error | 9.2 |
|---|
| Cost | 20036 |
|---|
\[\begin{array}{l}
\mathbf{if}\;z \leq 0.3:\\
\;\;\;\;\sqrt{1 + x} + \left(\left(\sqrt{1 + t} - \sqrt{t}\right) + 2\right)\\
\mathbf{else}:\\
\;\;\;\;1 + \left(\sqrt{1 + y} - \sqrt{y}\right)\\
\end{array}
\]
| Alternative 11 |
|---|
| Error | 12.3 |
|---|
| Cost | 13380 |
|---|
\[\begin{array}{l}
\mathbf{if}\;z \leq 0.26:\\
\;\;\;\;\sqrt{1 + x} + \left(2 - \sqrt{x}\right)\\
\mathbf{else}:\\
\;\;\;\;1 + \left(\sqrt{1 + y} - \sqrt{y}\right)\\
\end{array}
\]
| Alternative 12 |
|---|
| Error | 23.1 |
|---|
| Cost | 13248 |
|---|
\[1 + \left(\sqrt{1 + y} - \sqrt{y}\right)
\]
| Alternative 13 |
|---|
| Error | 41.0 |
|---|
| Cost | 13120 |
|---|
\[\sqrt{1 + x} - \sqrt{x}
\]
| Alternative 14 |
|---|
| Error | 41.4 |
|---|
| Cost | 6848 |
|---|
\[\left(1 + x \cdot 0.5\right) - \sqrt{x}
\]
| Alternative 15 |
|---|
| Error | 41.8 |
|---|
| Cost | 64 |
|---|
\[1
\]