\[\left(\alpha > -1 \land \beta > -1\right) \land i > 0\]
\[\frac{\frac{\frac{\left(\alpha + \beta\right) \cdot \left(\beta - \alpha\right)}{\left(\alpha + \beta\right) + 2 \cdot i}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) + 2} + 1}{2}
\]
↓
\[\begin{array}{l}
t_0 := \left(\alpha + \beta\right) + 2 \cdot i\\
\mathbf{if}\;\frac{\frac{\left(\alpha + \beta\right) \cdot \left(\beta - \alpha\right)}{t_0}}{2 + t_0} \leq -0.9999998:\\
\;\;\;\;\frac{\frac{\left(\beta - \beta\right) + \left(i \cdot 4 + \left(2 + \beta \cdot 2\right)\right)}{\alpha}}{2}\\
\mathbf{else}:\\
\;\;\;\;\frac{{\left({\left(\mathsf{fma}\left(\alpha + \beta, \frac{\frac{\beta - \alpha}{\mathsf{fma}\left(2, i, \alpha + \beta\right)}}{\beta + \left(\alpha + \mathsf{fma}\left(2, i, 2\right)\right)}, 1\right)\right)}^{3}\right)}^{0.3333333333333333}}{2}\\
\end{array}
\]
(FPCore (alpha beta i)
:precision binary64
(/
(+
(/
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))
(+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
1.0)
2.0))↓
(FPCore (alpha beta i)
:precision binary64
(let* ((t_0 (+ (+ alpha beta) (* 2.0 i))))
(if (<=
(/ (/ (* (+ alpha beta) (- beta alpha)) t_0) (+ 2.0 t_0))
-0.9999998)
(/ (/ (+ (- beta beta) (+ (* i 4.0) (+ 2.0 (* beta 2.0)))) alpha) 2.0)
(/
(pow
(pow
(fma
(+ alpha beta)
(/
(/ (- beta alpha) (fma 2.0 i (+ alpha beta)))
(+ beta (+ alpha (fma 2.0 i 2.0))))
1.0)
3.0)
0.3333333333333333)
2.0))))double code(double alpha, double beta, double i) {
return (((((alpha + beta) * (beta - alpha)) / ((alpha + beta) + (2.0 * i))) / (((alpha + beta) + (2.0 * i)) + 2.0)) + 1.0) / 2.0;
}
↓
double code(double alpha, double beta, double i) {
double t_0 = (alpha + beta) + (2.0 * i);
double tmp;
if (((((alpha + beta) * (beta - alpha)) / t_0) / (2.0 + t_0)) <= -0.9999998) {
tmp = (((beta - beta) + ((i * 4.0) + (2.0 + (beta * 2.0)))) / alpha) / 2.0;
} else {
tmp = pow(pow(fma((alpha + beta), (((beta - alpha) / fma(2.0, i, (alpha + beta))) / (beta + (alpha + fma(2.0, i, 2.0)))), 1.0), 3.0), 0.3333333333333333) / 2.0;
}
return tmp;
}
function code(alpha, beta, i)
return Float64(Float64(Float64(Float64(Float64(Float64(alpha + beta) * Float64(beta - alpha)) / Float64(Float64(alpha + beta) + Float64(2.0 * i))) / Float64(Float64(Float64(alpha + beta) + Float64(2.0 * i)) + 2.0)) + 1.0) / 2.0)
end
↓
function code(alpha, beta, i)
t_0 = Float64(Float64(alpha + beta) + Float64(2.0 * i))
tmp = 0.0
if (Float64(Float64(Float64(Float64(alpha + beta) * Float64(beta - alpha)) / t_0) / Float64(2.0 + t_0)) <= -0.9999998)
tmp = Float64(Float64(Float64(Float64(beta - beta) + Float64(Float64(i * 4.0) + Float64(2.0 + Float64(beta * 2.0)))) / alpha) / 2.0);
else
tmp = Float64(((fma(Float64(alpha + beta), Float64(Float64(Float64(beta - alpha) / fma(2.0, i, Float64(alpha + beta))) / Float64(beta + Float64(alpha + fma(2.0, i, 2.0)))), 1.0) ^ 3.0) ^ 0.3333333333333333) / 2.0);
end
return tmp
end
code[alpha_, beta_, i_] := N[(N[(N[(N[(N[(N[(alpha + beta), $MachinePrecision] * N[(beta - alpha), $MachinePrecision]), $MachinePrecision] / N[(N[(alpha + beta), $MachinePrecision] + N[(2.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(alpha + beta), $MachinePrecision] + N[(2.0 * i), $MachinePrecision]), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision] / 2.0), $MachinePrecision]
↓
code[alpha_, beta_, i_] := Block[{t$95$0 = N[(N[(alpha + beta), $MachinePrecision] + N[(2.0 * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(N[(N[(alpha + beta), $MachinePrecision] * N[(beta - alpha), $MachinePrecision]), $MachinePrecision] / t$95$0), $MachinePrecision] / N[(2.0 + t$95$0), $MachinePrecision]), $MachinePrecision], -0.9999998], N[(N[(N[(N[(beta - beta), $MachinePrecision] + N[(N[(i * 4.0), $MachinePrecision] + N[(2.0 + N[(beta * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / alpha), $MachinePrecision] / 2.0), $MachinePrecision], N[(N[Power[N[Power[N[(N[(alpha + beta), $MachinePrecision] * N[(N[(N[(beta - alpha), $MachinePrecision] / N[(2.0 * i + N[(alpha + beta), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(beta + N[(alpha + N[(2.0 * i + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision], 3.0], $MachinePrecision], 0.3333333333333333], $MachinePrecision] / 2.0), $MachinePrecision]]]
\frac{\frac{\frac{\left(\alpha + \beta\right) \cdot \left(\beta - \alpha\right)}{\left(\alpha + \beta\right) + 2 \cdot i}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) + 2} + 1}{2}
↓
\begin{array}{l}
t_0 := \left(\alpha + \beta\right) + 2 \cdot i\\
\mathbf{if}\;\frac{\frac{\left(\alpha + \beta\right) \cdot \left(\beta - \alpha\right)}{t_0}}{2 + t_0} \leq -0.9999998:\\
\;\;\;\;\frac{\frac{\left(\beta - \beta\right) + \left(i \cdot 4 + \left(2 + \beta \cdot 2\right)\right)}{\alpha}}{2}\\
\mathbf{else}:\\
\;\;\;\;\frac{{\left({\left(\mathsf{fma}\left(\alpha + \beta, \frac{\frac{\beta - \alpha}{\mathsf{fma}\left(2, i, \alpha + \beta\right)}}{\beta + \left(\alpha + \mathsf{fma}\left(2, i, 2\right)\right)}, 1\right)\right)}^{3}\right)}^{0.3333333333333333}}{2}\\
\end{array}
Alternatives
| Alternative 1 |
|---|
| Error | 1.3 |
|---|
| Cost | 22340 |
|---|
\[\begin{array}{l}
t_0 := \left(\alpha + \beta\right) + 2 \cdot i\\
\mathbf{if}\;\frac{\frac{\left(\alpha + \beta\right) \cdot \left(\beta - \alpha\right)}{t_0}}{2 + t_0} \leq -0.9999998:\\
\;\;\;\;\frac{\frac{\left(\beta - \beta\right) + \left(i \cdot 4 + \left(2 + \beta \cdot 2\right)\right)}{\alpha}}{2}\\
\mathbf{else}:\\
\;\;\;\;\frac{\mathsf{fma}\left(\alpha + \beta, \frac{\frac{\beta - \alpha}{\alpha + \mathsf{fma}\left(2, i, \beta\right)}}{\alpha + \mathsf{fma}\left(2, i, \beta + 2\right)}, 1\right)}{2}\\
\end{array}
\]
| Alternative 2 |
|---|
| Error | 1.3 |
|---|
| Cost | 16068 |
|---|
\[\begin{array}{l}
t_0 := \left(\alpha + \beta\right) + 2 \cdot i\\
\mathbf{if}\;\frac{\frac{\left(\alpha + \beta\right) \cdot \left(\beta - \alpha\right)}{t_0}}{2 + t_0} \leq -0.9999998:\\
\;\;\;\;\frac{\frac{\left(\beta - \beta\right) + \left(i \cdot 4 + \left(2 + \beta \cdot 2\right)\right)}{\alpha}}{2}\\
\mathbf{else}:\\
\;\;\;\;\frac{1 + \frac{\alpha + \beta}{\left(\alpha + \left(\beta + \mathsf{fma}\left(2, i, 2\right)\right)\right) \cdot \frac{\mathsf{fma}\left(2, i, \alpha + \beta\right)}{\beta - \alpha}}}{2}\\
\end{array}
\]
| Alternative 3 |
|---|
| Error | 1.3 |
|---|
| Cost | 3524 |
|---|
\[\begin{array}{l}
t_0 := \left(\alpha + \beta\right) + 2 \cdot i\\
\mathbf{if}\;\frac{\frac{\left(\alpha + \beta\right) \cdot \left(\beta - \alpha\right)}{t_0}}{2 + t_0} \leq -0.9999998:\\
\;\;\;\;\frac{\frac{\left(\beta - \beta\right) + \left(i \cdot 4 + \left(2 + \beta \cdot 2\right)\right)}{\alpha}}{2}\\
\mathbf{else}:\\
\;\;\;\;\frac{1 + \frac{\frac{\alpha + \beta}{\frac{\alpha - \left(i \cdot -2 - \beta\right)}{\beta - \alpha}}}{\left(\alpha + \beta\right) + \left(2 + 2 \cdot i\right)}}{2}\\
\end{array}
\]
| Alternative 4 |
|---|
| Error | 1.8 |
|---|
| Cost | 3268 |
|---|
\[\begin{array}{l}
t_0 := \left(\alpha + \beta\right) + 2 \cdot i\\
\mathbf{if}\;\frac{\frac{\left(\alpha + \beta\right) \cdot \left(\beta - \alpha\right)}{t_0}}{2 + t_0} \leq -0.5:\\
\;\;\;\;\frac{\frac{\left(\beta - \beta\right) + \left(i \cdot 4 + \left(2 + \beta \cdot 2\right)\right)}{\alpha}}{2}\\
\mathbf{else}:\\
\;\;\;\;\frac{1 + \frac{\frac{\alpha + \beta}{\frac{\beta + 2 \cdot i}{\beta}}}{\left(\alpha + \beta\right) + \left(2 + 2 \cdot i\right)}}{2}\\
\end{array}
\]
| Alternative 5 |
|---|
| Error | 6.8 |
|---|
| Cost | 1220 |
|---|
\[\begin{array}{l}
\mathbf{if}\;\alpha \leq 4.5 \cdot 10^{+128}:\\
\;\;\;\;\frac{1 + \frac{\beta}{\beta + \left(2 - i \cdot -4\right)}}{2}\\
\mathbf{else}:\\
\;\;\;\;\frac{\frac{\left(\beta - \beta\right) + \left(i \cdot 4 + \left(2 + \beta \cdot 2\right)\right)}{\alpha}}{2}\\
\end{array}
\]
| Alternative 6 |
|---|
| Error | 12.9 |
|---|
| Cost | 968 |
|---|
\[\begin{array}{l}
\mathbf{if}\;\alpha \leq 2 \cdot 10^{-168}:\\
\;\;\;\;\frac{1 + \frac{\beta}{\beta + 2}}{2}\\
\mathbf{elif}\;\alpha \leq 9 \cdot 10^{+124}:\\
\;\;\;\;\frac{1 + \frac{\beta}{\beta + 2 \cdot i}}{2}\\
\mathbf{else}:\\
\;\;\;\;\frac{\frac{2 - i \cdot -4}{\alpha}}{2}\\
\end{array}
\]
| Alternative 7 |
|---|
| Error | 8.7 |
|---|
| Cost | 964 |
|---|
\[\begin{array}{l}
t_0 := 2 - i \cdot -4\\
\mathbf{if}\;\alpha \leq 5.5 \cdot 10^{+129}:\\
\;\;\;\;\frac{1 + \frac{\beta}{\beta + t_0}}{2}\\
\mathbf{else}:\\
\;\;\;\;\frac{\frac{t_0}{\alpha}}{2}\\
\end{array}
\]
| Alternative 8 |
|---|
| Error | 15.1 |
|---|
| Cost | 708 |
|---|
\[\begin{array}{l}
\mathbf{if}\;i \leq 3.2 \cdot 10^{+151}:\\
\;\;\;\;\frac{1 + \frac{\beta}{\beta + 2}}{2}\\
\mathbf{else}:\\
\;\;\;\;0.5\\
\end{array}
\]
| Alternative 9 |
|---|
| Error | 13.9 |
|---|
| Cost | 708 |
|---|
\[\begin{array}{l}
\mathbf{if}\;\alpha \leq 1.8 \cdot 10^{+126}:\\
\;\;\;\;\frac{1 + \frac{\beta}{\beta + 2}}{2}\\
\mathbf{else}:\\
\;\;\;\;\frac{\frac{2 + \beta \cdot 2}{\alpha}}{2}\\
\end{array}
\]
| Alternative 10 |
|---|
| Error | 12.6 |
|---|
| Cost | 708 |
|---|
\[\begin{array}{l}
\mathbf{if}\;\alpha \leq 1.5 \cdot 10^{+127}:\\
\;\;\;\;\frac{1 + \frac{\beta}{\beta + 2}}{2}\\
\mathbf{else}:\\
\;\;\;\;\frac{\frac{2 - i \cdot -4}{\alpha}}{2}\\
\end{array}
\]
| Alternative 11 |
|---|
| Error | 17.5 |
|---|
| Cost | 196 |
|---|
\[\begin{array}{l}
\mathbf{if}\;\beta \leq 1.85 \cdot 10^{+84}:\\
\;\;\;\;0.5\\
\mathbf{else}:\\
\;\;\;\;1\\
\end{array}
\]
| Alternative 12 |
|---|
| Error | 24.5 |
|---|
| Cost | 64 |
|---|
\[0.5
\]