(FPCore (x eps) :precision binary64 (/ (- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))) 2.0))
(FPCore (x eps) :precision binary64 (let* ((t_0 (/ (+ x 1.0) (exp x)))) (/ (+ t_0 t_0) 2.0)))
double code(double x, double eps) {
return (((1.0 + (1.0 / eps)) * exp(-((1.0 - eps) * x))) - (((1.0 / eps) - 1.0) * exp(-((1.0 + eps) * x)))) / 2.0;
}
double code(double x, double eps) {
double t_0 = (x + 1.0) / exp(x);
return (t_0 + t_0) / 2.0;
}
real(8) function code(x, eps)
real(8), intent (in) :: x
real(8), intent (in) :: eps
code = (((1.0d0 + (1.0d0 / eps)) * exp(-((1.0d0 - eps) * x))) - (((1.0d0 / eps) - 1.0d0) * exp(-((1.0d0 + eps) * x)))) / 2.0d0
end function
real(8) function code(x, eps)
real(8), intent (in) :: x
real(8), intent (in) :: eps
real(8) :: t_0
t_0 = (x + 1.0d0) / exp(x)
code = (t_0 + t_0) / 2.0d0
end function
public static double code(double x, double eps) {
return (((1.0 + (1.0 / eps)) * Math.exp(-((1.0 - eps) * x))) - (((1.0 / eps) - 1.0) * Math.exp(-((1.0 + eps) * x)))) / 2.0;
}
public static double code(double x, double eps) {
double t_0 = (x + 1.0) / Math.exp(x);
return (t_0 + t_0) / 2.0;
}
def code(x, eps): return (((1.0 + (1.0 / eps)) * math.exp(-((1.0 - eps) * x))) - (((1.0 / eps) - 1.0) * math.exp(-((1.0 + eps) * x)))) / 2.0
def code(x, eps): t_0 = (x + 1.0) / math.exp(x) return (t_0 + t_0) / 2.0
function code(x, eps) return Float64(Float64(Float64(Float64(1.0 + Float64(1.0 / eps)) * exp(Float64(-Float64(Float64(1.0 - eps) * x)))) - Float64(Float64(Float64(1.0 / eps) - 1.0) * exp(Float64(-Float64(Float64(1.0 + eps) * x))))) / 2.0) end
function code(x, eps) t_0 = Float64(Float64(x + 1.0) / exp(x)) return Float64(Float64(t_0 + t_0) / 2.0) end
function tmp = code(x, eps) tmp = (((1.0 + (1.0 / eps)) * exp(-((1.0 - eps) * x))) - (((1.0 / eps) - 1.0) * exp(-((1.0 + eps) * x)))) / 2.0; end
function tmp = code(x, eps) t_0 = (x + 1.0) / exp(x); tmp = (t_0 + t_0) / 2.0; end
code[x_, eps_] := N[(N[(N[(N[(1.0 + N[(1.0 / eps), $MachinePrecision]), $MachinePrecision] * N[Exp[(-N[(N[(1.0 - eps), $MachinePrecision] * x), $MachinePrecision])], $MachinePrecision]), $MachinePrecision] - N[(N[(N[(1.0 / eps), $MachinePrecision] - 1.0), $MachinePrecision] * N[Exp[(-N[(N[(1.0 + eps), $MachinePrecision] * x), $MachinePrecision])], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / 2.0), $MachinePrecision]
code[x_, eps_] := Block[{t$95$0 = N[(N[(x + 1.0), $MachinePrecision] / N[Exp[x], $MachinePrecision]), $MachinePrecision]}, N[(N[(t$95$0 + t$95$0), $MachinePrecision] / 2.0), $MachinePrecision]]
\frac{\left(1 + \frac{1}{\varepsilon}\right) \cdot e^{-\left(1 - \varepsilon\right) \cdot x} - \left(\frac{1}{\varepsilon} - 1\right) \cdot e^{-\left(1 + \varepsilon\right) \cdot x}}{2}
\begin{array}{l}
t_0 := \frac{x + 1}{e^{x}}\\
\frac{t_0 + t_0}{2}
\end{array}
Results
Initial program 29.6
Simplified29.6
Taylor expanded in eps around 0 0.7
Simplified0.7
Applied egg-rr0.7
Applied egg-rr0.7
Final simplification0.7
| Alternative 1 | |
|---|---|
| Error | 1.1 |
| Cost | 13636 |
| Alternative 2 | |
|---|---|
| Error | 1.1 |
| Cost | 7556 |
| Alternative 3 | |
|---|---|
| Error | 1.1 |
| Cost | 7492 |
| Alternative 4 | |
|---|---|
| Error | 1.2 |
| Cost | 7108 |
| Alternative 5 | |
|---|---|
| Error | 1.2 |
| Cost | 836 |
| Alternative 6 | |
|---|---|
| Error | 1.2 |
| Cost | 196 |
| Alternative 7 | |
|---|---|
| Error | 46.5 |
| Cost | 64 |
herbie shell --seed 2022329
(FPCore (x eps)
:name "NMSE Section 6.1 mentioned, A"
:precision binary64
(/ (- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))) 2.0))