| Alternative 1 | |
|---|---|
| Error | 0.3 |
| Cost | 26308 |
\[\begin{array}{l}
t_0 := \sqrt{1 + x} - \sqrt{x}\\
\mathbf{if}\;t_0 \leq 4 \cdot 10^{-5}:\\
\;\;\;\;0.5 \cdot {x}^{-0.5}\\
\mathbf{else}:\\
\;\;\;\;t_0\\
\end{array}
\]
(FPCore (x) :precision binary64 (- (sqrt (+ x 1.0)) (sqrt x)))
(FPCore (x) :precision binary64 (/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x))))
double code(double x) {
return sqrt((x + 1.0)) - sqrt(x);
}
double code(double x) {
return 1.0 / (sqrt((1.0 + x)) + sqrt(x));
}
real(8) function code(x)
real(8), intent (in) :: x
code = sqrt((x + 1.0d0)) - sqrt(x)
end function
real(8) function code(x)
real(8), intent (in) :: x
code = 1.0d0 / (sqrt((1.0d0 + x)) + sqrt(x))
end function
public static double code(double x) {
return Math.sqrt((x + 1.0)) - Math.sqrt(x);
}
public static double code(double x) {
return 1.0 / (Math.sqrt((1.0 + x)) + Math.sqrt(x));
}
def code(x): return math.sqrt((x + 1.0)) - math.sqrt(x)
def code(x): return 1.0 / (math.sqrt((1.0 + x)) + math.sqrt(x))
function code(x) return Float64(sqrt(Float64(x + 1.0)) - sqrt(x)) end
function code(x) return Float64(1.0 / Float64(sqrt(Float64(1.0 + x)) + sqrt(x))) end
function tmp = code(x) tmp = sqrt((x + 1.0)) - sqrt(x); end
function tmp = code(x) tmp = 1.0 / (sqrt((1.0 + x)) + sqrt(x)); end
code[x_] := N[(N[Sqrt[N[(x + 1.0), $MachinePrecision]], $MachinePrecision] - N[Sqrt[x], $MachinePrecision]), $MachinePrecision]
code[x_] := N[(1.0 / N[(N[Sqrt[N[(1.0 + x), $MachinePrecision]], $MachinePrecision] + N[Sqrt[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
\sqrt{x + 1} - \sqrt{x}
\frac{1}{\sqrt{1 + x} + \sqrt{x}}
Results
| Original | 29.9 |
|---|---|
| Target | 0.2 |
| Herbie | 0.2 |
Initial program 29.9
Applied egg-rr29.2
Simplified0.2
Final simplification0.2
| Alternative 1 | |
|---|---|
| Error | 0.3 |
| Cost | 26308 |
| Alternative 2 | |
|---|---|
| Error | 0.8 |
| Cost | 6980 |
| Alternative 3 | |
|---|---|
| Error | 1.9 |
| Cost | 6788 |
| Alternative 4 | |
|---|---|
| Error | 31.1 |
| Cost | 64 |
herbie shell --seed 2022329
(FPCore (x)
:name "Main:bigenough3 from C"
:precision binary64
:herbie-target
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
(- (sqrt (+ x 1.0)) (sqrt x)))