(FPCore (x y) :precision binary64 (- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0))))
(FPCore (x y)
:precision binary64
(if (<= y -3962435670.6258354)
(+ x (* (/ -1.0 y) (+ -1.0 (/ 1.0 y))))
(if (<= y 244.49319934554606)
(- 1.0 (/ (* y (- 1.0 x)) (+ y 1.0)))
(+ x (/ (+ (/ -1.0 y) 1.0) y)))))double code(double x, double y) {
return 1.0 - (((1.0 - x) * y) / (y + 1.0));
}
double code(double x, double y) {
double tmp;
if (y <= -3962435670.6258354) {
tmp = x + ((-1.0 / y) * (-1.0 + (1.0 / y)));
} else if (y <= 244.49319934554606) {
tmp = 1.0 - ((y * (1.0 - x)) / (y + 1.0));
} else {
tmp = x + (((-1.0 / y) + 1.0) / y);
}
return tmp;
}
real(8) function code(x, y)
real(8), intent (in) :: x
real(8), intent (in) :: y
code = 1.0d0 - (((1.0d0 - x) * y) / (y + 1.0d0))
end function
real(8) function code(x, y)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8) :: tmp
if (y <= (-3962435670.6258354d0)) then
tmp = x + (((-1.0d0) / y) * ((-1.0d0) + (1.0d0 / y)))
else if (y <= 244.49319934554606d0) then
tmp = 1.0d0 - ((y * (1.0d0 - x)) / (y + 1.0d0))
else
tmp = x + ((((-1.0d0) / y) + 1.0d0) / y)
end if
code = tmp
end function
public static double code(double x, double y) {
return 1.0 - (((1.0 - x) * y) / (y + 1.0));
}
public static double code(double x, double y) {
double tmp;
if (y <= -3962435670.6258354) {
tmp = x + ((-1.0 / y) * (-1.0 + (1.0 / y)));
} else if (y <= 244.49319934554606) {
tmp = 1.0 - ((y * (1.0 - x)) / (y + 1.0));
} else {
tmp = x + (((-1.0 / y) + 1.0) / y);
}
return tmp;
}
def code(x, y): return 1.0 - (((1.0 - x) * y) / (y + 1.0))
def code(x, y): tmp = 0 if y <= -3962435670.6258354: tmp = x + ((-1.0 / y) * (-1.0 + (1.0 / y))) elif y <= 244.49319934554606: tmp = 1.0 - ((y * (1.0 - x)) / (y + 1.0)) else: tmp = x + (((-1.0 / y) + 1.0) / y) return tmp
function code(x, y) return Float64(1.0 - Float64(Float64(Float64(1.0 - x) * y) / Float64(y + 1.0))) end
function code(x, y) tmp = 0.0 if (y <= -3962435670.6258354) tmp = Float64(x + Float64(Float64(-1.0 / y) * Float64(-1.0 + Float64(1.0 / y)))); elseif (y <= 244.49319934554606) tmp = Float64(1.0 - Float64(Float64(y * Float64(1.0 - x)) / Float64(y + 1.0))); else tmp = Float64(x + Float64(Float64(Float64(-1.0 / y) + 1.0) / y)); end return tmp end
function tmp = code(x, y) tmp = 1.0 - (((1.0 - x) * y) / (y + 1.0)); end
function tmp_2 = code(x, y) tmp = 0.0; if (y <= -3962435670.6258354) tmp = x + ((-1.0 / y) * (-1.0 + (1.0 / y))); elseif (y <= 244.49319934554606) tmp = 1.0 - ((y * (1.0 - x)) / (y + 1.0)); else tmp = x + (((-1.0 / y) + 1.0) / y); end tmp_2 = tmp; end
code[x_, y_] := N[(1.0 - N[(N[(N[(1.0 - x), $MachinePrecision] * y), $MachinePrecision] / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
code[x_, y_] := If[LessEqual[y, -3962435670.6258354], N[(x + N[(N[(-1.0 / y), $MachinePrecision] * N[(-1.0 + N[(1.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 244.49319934554606], N[(1.0 - N[(N[(y * N[(1.0 - x), $MachinePrecision]), $MachinePrecision] / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(N[(-1.0 / y), $MachinePrecision] + 1.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]
1 - \frac{\left(1 - x\right) \cdot y}{y + 1}
\begin{array}{l}
\mathbf{if}\;y \leq -3962435670.6258354:\\
\;\;\;\;x + \frac{-1}{y} \cdot \left(-1 + \frac{1}{y}\right)\\
\mathbf{elif}\;y \leq 244.49319934554606:\\
\;\;\;\;1 - \frac{y \cdot \left(1 - x\right)}{y + 1}\\
\mathbf{else}:\\
\;\;\;\;x + \frac{\frac{-1}{y} + 1}{y}\\
\end{array}
Results
| Original | 22.4 |
|---|---|
| Target | 0.2 |
| Herbie | 0.2 |
if y < -3962435670.6258354Initial program 46.1
Taylor expanded in y around inf 0.0
Simplified0.0
Taylor expanded in x around 0 0.2
if -3962435670.6258354 < y < 244.49319934554606Initial program 0.1
if 244.49319934554606 < y Initial program 44.6
Taylor expanded in y around inf 0.2
Simplified0.2
Taylor expanded in x around 0 0.5
Taylor expanded in x around 0 0.5
Simplified0.5
Final simplification0.2
| Alternative 1 | |
|---|---|
| Error | 1.1 |
| Cost | 968 |
| Alternative 2 | |
|---|---|
| Error | 9.5 |
| Cost | 848 |
| Alternative 3 | |
|---|---|
| Error | 1.1 |
| Cost | 840 |
| Alternative 4 | |
|---|---|
| Error | 17.0 |
| Cost | 720 |
| Alternative 5 | |
|---|---|
| Error | 1.3 |
| Cost | 712 |
| Alternative 6 | |
|---|---|
| Error | 1.1 |
| Cost | 712 |
| Alternative 7 | |
|---|---|
| Error | 1.4 |
| Cost | 584 |
| Alternative 8 | |
|---|---|
| Error | 16.4 |
| Cost | 456 |
| Alternative 9 | |
|---|---|
| Error | 16.5 |
| Cost | 328 |
| Alternative 10 | |
|---|---|
| Error | 38.9 |
| Cost | 64 |
herbie shell --seed 2022310
(FPCore (x y)
:name "Diagrams.Trail:splitAtParam from diagrams-lib-1.3.0.3, D"
:precision binary64
:herbie-target
(if (< y -3693.8482788297247) (- (/ 1.0 y) (- (/ x y) x)) (if (< y 6799310503.41891) (- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0))) (- (/ 1.0 y) (- (/ x y) x))))
(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0))))