| Alternative 1 | |
|---|---|
| Error | 2.2 |
| Cost | 1600 |
\[\begin{array}{l}
t_0 := \alpha + \left(\beta + 2\right)\\
\frac{\beta + 1}{t_0 \cdot \left(\beta + \left(\alpha + 3\right)\right)} \cdot \frac{1 + \alpha}{t_0}
\end{array}
\]
(FPCore (alpha beta) :precision binary64 (/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
(FPCore (alpha beta) :precision binary64 (let* ((t_0 (+ beta (+ alpha 2.0)))) (/ (* (/ (+ beta 1.0) t_0) (/ (+ 1.0 alpha) t_0)) (+ beta (+ alpha 3.0)))))
double code(double alpha, double beta) {
return (((((alpha + beta) + (beta * alpha)) + 1.0) / ((alpha + beta) + (2.0 * 1.0))) / ((alpha + beta) + (2.0 * 1.0))) / (((alpha + beta) + (2.0 * 1.0)) + 1.0);
}
double code(double alpha, double beta) {
double t_0 = beta + (alpha + 2.0);
return (((beta + 1.0) / t_0) * ((1.0 + alpha) / t_0)) / (beta + (alpha + 3.0));
}
real(8) function code(alpha, beta)
real(8), intent (in) :: alpha
real(8), intent (in) :: beta
code = (((((alpha + beta) + (beta * alpha)) + 1.0d0) / ((alpha + beta) + (2.0d0 * 1.0d0))) / ((alpha + beta) + (2.0d0 * 1.0d0))) / (((alpha + beta) + (2.0d0 * 1.0d0)) + 1.0d0)
end function
real(8) function code(alpha, beta)
real(8), intent (in) :: alpha
real(8), intent (in) :: beta
real(8) :: t_0
t_0 = beta + (alpha + 2.0d0)
code = (((beta + 1.0d0) / t_0) * ((1.0d0 + alpha) / t_0)) / (beta + (alpha + 3.0d0))
end function
public static double code(double alpha, double beta) {
return (((((alpha + beta) + (beta * alpha)) + 1.0) / ((alpha + beta) + (2.0 * 1.0))) / ((alpha + beta) + (2.0 * 1.0))) / (((alpha + beta) + (2.0 * 1.0)) + 1.0);
}
public static double code(double alpha, double beta) {
double t_0 = beta + (alpha + 2.0);
return (((beta + 1.0) / t_0) * ((1.0 + alpha) / t_0)) / (beta + (alpha + 3.0));
}
def code(alpha, beta): return (((((alpha + beta) + (beta * alpha)) + 1.0) / ((alpha + beta) + (2.0 * 1.0))) / ((alpha + beta) + (2.0 * 1.0))) / (((alpha + beta) + (2.0 * 1.0)) + 1.0)
def code(alpha, beta): t_0 = beta + (alpha + 2.0) return (((beta + 1.0) / t_0) * ((1.0 + alpha) / t_0)) / (beta + (alpha + 3.0))
function code(alpha, beta) return Float64(Float64(Float64(Float64(Float64(Float64(alpha + beta) + Float64(beta * alpha)) + 1.0) / Float64(Float64(alpha + beta) + Float64(2.0 * 1.0))) / Float64(Float64(alpha + beta) + Float64(2.0 * 1.0))) / Float64(Float64(Float64(alpha + beta) + Float64(2.0 * 1.0)) + 1.0)) end
function code(alpha, beta) t_0 = Float64(beta + Float64(alpha + 2.0)) return Float64(Float64(Float64(Float64(beta + 1.0) / t_0) * Float64(Float64(1.0 + alpha) / t_0)) / Float64(beta + Float64(alpha + 3.0))) end
function tmp = code(alpha, beta) tmp = (((((alpha + beta) + (beta * alpha)) + 1.0) / ((alpha + beta) + (2.0 * 1.0))) / ((alpha + beta) + (2.0 * 1.0))) / (((alpha + beta) + (2.0 * 1.0)) + 1.0); end
function tmp = code(alpha, beta) t_0 = beta + (alpha + 2.0); tmp = (((beta + 1.0) / t_0) * ((1.0 + alpha) / t_0)) / (beta + (alpha + 3.0)); end
code[alpha_, beta_] := N[(N[(N[(N[(N[(N[(alpha + beta), $MachinePrecision] + N[(beta * alpha), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision] / N[(N[(alpha + beta), $MachinePrecision] + N[(2.0 * 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(alpha + beta), $MachinePrecision] + N[(2.0 * 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(alpha + beta), $MachinePrecision] + N[(2.0 * 1.0), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]
code[alpha_, beta_] := Block[{t$95$0 = N[(beta + N[(alpha + 2.0), $MachinePrecision]), $MachinePrecision]}, N[(N[(N[(N[(beta + 1.0), $MachinePrecision] / t$95$0), $MachinePrecision] * N[(N[(1.0 + alpha), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision] / N[(beta + N[(alpha + 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]
\frac{\frac{\frac{\left(\left(\alpha + \beta\right) + \beta \cdot \alpha\right) + 1}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) + 1}
\begin{array}{l}
t_0 := \beta + \left(\alpha + 2\right)\\
\frac{\frac{\beta + 1}{t_0} \cdot \frac{1 + \alpha}{t_0}}{\beta + \left(\alpha + 3\right)}
\end{array}
Results
Initial program 3.7
Simplified9.9
Applied egg-rr2.2
Applied egg-rr0.1
Final simplification0.1
| Alternative 1 | |
|---|---|
| Error | 2.2 |
| Cost | 1600 |
| Alternative 2 | |
|---|---|
| Error | 2.2 |
| Cost | 1600 |
| Alternative 3 | |
|---|---|
| Error | 0.1 |
| Cost | 1600 |
herbie shell --seed 2022334
(FPCore (alpha beta)
:name "Octave 3.8, jcobi/3"
:precision binary64
:pre (and (> alpha -1.0) (> beta -1.0))
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))