
(FPCore (x y) :precision binary64 (- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0))))
double code(double x, double y) {
return 1.0 - (((1.0 - x) * y) / (y + 1.0));
}
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
public static double code(double x, double y) {
return 1.0 - (((1.0 - x) * y) / (y + 1.0));
}
def code(x, y): return 1.0 - (((1.0 - x) * y) / (y + 1.0))
function code(x, y) return Float64(1.0 - Float64(Float64(Float64(1.0 - x) * y) / Float64(y + 1.0))) end
function tmp = code(x, y) tmp = 1.0 - (((1.0 - x) * y) / (y + 1.0)); end
code[x_, y_] := N[(1.0 - N[(N[(N[(1.0 - x), $MachinePrecision] * y), $MachinePrecision] / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
1 - \frac{\left(1 - x\right) \cdot y}{y + 1}
\end{array}
Sampling outcomes in binary64 precision:
Herbie found 14 alternatives:
| Alternative | Accuracy | Speedup |
|---|
(FPCore (x y) :precision binary64 (- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0))))
double code(double x, double y) {
return 1.0 - (((1.0 - x) * y) / (y + 1.0));
}
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
public static double code(double x, double y) {
return 1.0 - (((1.0 - x) * y) / (y + 1.0));
}
def code(x, y): return 1.0 - (((1.0 - x) * y) / (y + 1.0))
function code(x, y) return Float64(1.0 - Float64(Float64(Float64(1.0 - x) * y) / Float64(y + 1.0))) end
function tmp = code(x, y) tmp = 1.0 - (((1.0 - x) * y) / (y + 1.0)); end
code[x_, y_] := N[(1.0 - N[(N[(N[(1.0 - x), $MachinePrecision] * y), $MachinePrecision] / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
1 - \frac{\left(1 - x\right) \cdot y}{y + 1}
\end{array}
(FPCore (x y)
:precision binary64
(let* ((t_0 (/ (+ x -1.0) (pow y 2.0))))
(if (<= y -19000.0)
(+ x (- t_0 (+ (/ (+ x -1.0) y) (/ (+ x -1.0) (pow y 3.0)))))
(if (<= y 380000.0)
(fma (/ (+ x -1.0) (+ y 1.0)) y 1.0)
(+ t_0 (+ x (/ (- 1.0 x) y)))))))
double code(double x, double y) {
double t_0 = (x + -1.0) / pow(y, 2.0);
double tmp;
if (y <= -19000.0) {
tmp = x + (t_0 - (((x + -1.0) / y) + ((x + -1.0) / pow(y, 3.0))));
} else if (y <= 380000.0) {
tmp = fma(((x + -1.0) / (y + 1.0)), y, 1.0);
} else {
tmp = t_0 + (x + ((1.0 - x) / y));
}
return tmp;
}
function code(x, y) t_0 = Float64(Float64(x + -1.0) / (y ^ 2.0)) tmp = 0.0 if (y <= -19000.0) tmp = Float64(x + Float64(t_0 - Float64(Float64(Float64(x + -1.0) / y) + Float64(Float64(x + -1.0) / (y ^ 3.0))))); elseif (y <= 380000.0) tmp = fma(Float64(Float64(x + -1.0) / Float64(y + 1.0)), y, 1.0); else tmp = Float64(t_0 + Float64(x + Float64(Float64(1.0 - x) / y))); end return tmp end
code[x_, y_] := Block[{t$95$0 = N[(N[(x + -1.0), $MachinePrecision] / N[Power[y, 2.0], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -19000.0], N[(x + N[(t$95$0 - N[(N[(N[(x + -1.0), $MachinePrecision] / y), $MachinePrecision] + N[(N[(x + -1.0), $MachinePrecision] / N[Power[y, 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 380000.0], N[(N[(N[(x + -1.0), $MachinePrecision] / N[(y + 1.0), $MachinePrecision]), $MachinePrecision] * y + 1.0), $MachinePrecision], N[(t$95$0 + N[(x + N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]
\begin{array}{l}
\\
\begin{array}{l}
t_0 := \frac{x + -1}{{y}^{2}}\\
\mathbf{if}\;y \leq -19000:\\
\;\;\;\;x + \left(t_0 - \left(\frac{x + -1}{y} + \frac{x + -1}{{y}^{3}}\right)\right)\\
\mathbf{elif}\;y \leq 380000:\\
\;\;\;\;\mathsf{fma}\left(\frac{x + -1}{y + 1}, y, 1\right)\\
\mathbf{else}:\\
\;\;\;\;t_0 + \left(x + \frac{1 - x}{y}\right)\\
\end{array}
\end{array}
(FPCore (x y) :precision binary64 (if (or (<= y -720000.0) (not (<= y 380000.0))) (+ (/ (+ x -1.0) (pow y 2.0)) (+ x (/ (- 1.0 x) y))) (fma (/ (+ x -1.0) (+ y 1.0)) y 1.0)))
double code(double x, double y) {
double tmp;
if ((y <= -720000.0) || !(y <= 380000.0)) {
tmp = ((x + -1.0) / pow(y, 2.0)) + (x + ((1.0 - x) / y));
} else {
tmp = fma(((x + -1.0) / (y + 1.0)), y, 1.0);
}
return tmp;
}
function code(x, y) tmp = 0.0 if ((y <= -720000.0) || !(y <= 380000.0)) tmp = Float64(Float64(Float64(x + -1.0) / (y ^ 2.0)) + Float64(x + Float64(Float64(1.0 - x) / y))); else tmp = fma(Float64(Float64(x + -1.0) / Float64(y + 1.0)), y, 1.0); end return tmp end
code[x_, y_] := If[Or[LessEqual[y, -720000.0], N[Not[LessEqual[y, 380000.0]], $MachinePrecision]], N[(N[(N[(x + -1.0), $MachinePrecision] / N[Power[y, 2.0], $MachinePrecision]), $MachinePrecision] + N[(x + N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x + -1.0), $MachinePrecision] / N[(y + 1.0), $MachinePrecision]), $MachinePrecision] * y + 1.0), $MachinePrecision]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;y \leq -720000 \lor \neg \left(y \leq 380000\right):\\
\;\;\;\;\frac{x + -1}{{y}^{2}} + \left(x + \frac{1 - x}{y}\right)\\
\mathbf{else}:\\
\;\;\;\;\mathsf{fma}\left(\frac{x + -1}{y + 1}, y, 1\right)\\
\end{array}
\end{array}
(FPCore (x y) :precision binary64 (if (or (<= y -18000000000.0) (not (<= y 960000000000.0))) (- x (/ -1.0 y)) (fma (/ (+ x -1.0) (+ y 1.0)) y 1.0)))
double code(double x, double y) {
double tmp;
if ((y <= -18000000000.0) || !(y <= 960000000000.0)) {
tmp = x - (-1.0 / y);
} else {
tmp = fma(((x + -1.0) / (y + 1.0)), y, 1.0);
}
return tmp;
}
function code(x, y) tmp = 0.0 if ((y <= -18000000000.0) || !(y <= 960000000000.0)) tmp = Float64(x - Float64(-1.0 / y)); else tmp = fma(Float64(Float64(x + -1.0) / Float64(y + 1.0)), y, 1.0); end return tmp end
code[x_, y_] := If[Or[LessEqual[y, -18000000000.0], N[Not[LessEqual[y, 960000000000.0]], $MachinePrecision]], N[(x - N[(-1.0 / y), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x + -1.0), $MachinePrecision] / N[(y + 1.0), $MachinePrecision]), $MachinePrecision] * y + 1.0), $MachinePrecision]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;y \leq -18000000000 \lor \neg \left(y \leq 960000000000\right):\\
\;\;\;\;x - \frac{-1}{y}\\
\mathbf{else}:\\
\;\;\;\;\mathsf{fma}\left(\frac{x + -1}{y + 1}, y, 1\right)\\
\end{array}
\end{array}
(FPCore (x y)
:precision binary64
(let* ((t_0 (- x (/ -1.0 y))))
(if (<= y -1.0)
t_0
(if (<= y -1.3e-116)
(- 1.0 y)
(if (<= y -1.15e-170)
(* y x)
(if (<= y 1.8e-58)
1.0
(if (<= y 2.45e-14) (* y x) (if (<= y 0.032) (- 1.0 y) t_0))))))))
double code(double x, double y) {
double t_0 = x - (-1.0 / y);
double tmp;
if (y <= -1.0) {
tmp = t_0;
} else if (y <= -1.3e-116) {
tmp = 1.0 - y;
} else if (y <= -1.15e-170) {
tmp = y * x;
} else if (y <= 1.8e-58) {
tmp = 1.0;
} else if (y <= 2.45e-14) {
tmp = y * x;
} else if (y <= 0.032) {
tmp = 1.0 - y;
} else {
tmp = t_0;
}
return tmp;
}
real(8) function code(x, y)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8) :: t_0
real(8) :: tmp
t_0 = x - ((-1.0d0) / y)
if (y <= (-1.0d0)) then
tmp = t_0
else if (y <= (-1.3d-116)) then
tmp = 1.0d0 - y
else if (y <= (-1.15d-170)) then
tmp = y * x
else if (y <= 1.8d-58) then
tmp = 1.0d0
else if (y <= 2.45d-14) then
tmp = y * x
else if (y <= 0.032d0) then
tmp = 1.0d0 - y
else
tmp = t_0
end if
code = tmp
end function
public static double code(double x, double y) {
double t_0 = x - (-1.0 / y);
double tmp;
if (y <= -1.0) {
tmp = t_0;
} else if (y <= -1.3e-116) {
tmp = 1.0 - y;
} else if (y <= -1.15e-170) {
tmp = y * x;
} else if (y <= 1.8e-58) {
tmp = 1.0;
} else if (y <= 2.45e-14) {
tmp = y * x;
} else if (y <= 0.032) {
tmp = 1.0 - y;
} else {
tmp = t_0;
}
return tmp;
}
def code(x, y): t_0 = x - (-1.0 / y) tmp = 0 if y <= -1.0: tmp = t_0 elif y <= -1.3e-116: tmp = 1.0 - y elif y <= -1.15e-170: tmp = y * x elif y <= 1.8e-58: tmp = 1.0 elif y <= 2.45e-14: tmp = y * x elif y <= 0.032: tmp = 1.0 - y else: tmp = t_0 return tmp
function code(x, y) t_0 = Float64(x - Float64(-1.0 / y)) tmp = 0.0 if (y <= -1.0) tmp = t_0; elseif (y <= -1.3e-116) tmp = Float64(1.0 - y); elseif (y <= -1.15e-170) tmp = Float64(y * x); elseif (y <= 1.8e-58) tmp = 1.0; elseif (y <= 2.45e-14) tmp = Float64(y * x); elseif (y <= 0.032) tmp = Float64(1.0 - y); else tmp = t_0; end return tmp end
function tmp_2 = code(x, y) t_0 = x - (-1.0 / y); tmp = 0.0; if (y <= -1.0) tmp = t_0; elseif (y <= -1.3e-116) tmp = 1.0 - y; elseif (y <= -1.15e-170) tmp = y * x; elseif (y <= 1.8e-58) tmp = 1.0; elseif (y <= 2.45e-14) tmp = y * x; elseif (y <= 0.032) tmp = 1.0 - y; else tmp = t_0; end tmp_2 = tmp; end
code[x_, y_] := Block[{t$95$0 = N[(x - N[(-1.0 / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.0], t$95$0, If[LessEqual[y, -1.3e-116], N[(1.0 - y), $MachinePrecision], If[LessEqual[y, -1.15e-170], N[(y * x), $MachinePrecision], If[LessEqual[y, 1.8e-58], 1.0, If[LessEqual[y, 2.45e-14], N[(y * x), $MachinePrecision], If[LessEqual[y, 0.032], N[(1.0 - y), $MachinePrecision], t$95$0]]]]]]]
\begin{array}{l}
\\
\begin{array}{l}
t_0 := x - \frac{-1}{y}\\
\mathbf{if}\;y \leq -1:\\
\;\;\;\;t_0\\
\mathbf{elif}\;y \leq -1.3 \cdot 10^{-116}:\\
\;\;\;\;1 - y\\
\mathbf{elif}\;y \leq -1.15 \cdot 10^{-170}:\\
\;\;\;\;y \cdot x\\
\mathbf{elif}\;y \leq 1.8 \cdot 10^{-58}:\\
\;\;\;\;1\\
\mathbf{elif}\;y \leq 2.45 \cdot 10^{-14}:\\
\;\;\;\;y \cdot x\\
\mathbf{elif}\;y \leq 0.032:\\
\;\;\;\;1 - y\\
\mathbf{else}:\\
\;\;\;\;t_0\\
\end{array}
\end{array}
(FPCore (x y)
:precision binary64
(if (<= y -1.0)
x
(if (<= y -8e-117)
(- 1.0 y)
(if (<= y -1.15e-170)
(* y x)
(if (<= y 1e-56)
1.0
(if (<= y 3.5e-14) (* y x) (if (<= y 0.42) (- 1.0 y) x)))))))
double code(double x, double y) {
double tmp;
if (y <= -1.0) {
tmp = x;
} else if (y <= -8e-117) {
tmp = 1.0 - y;
} else if (y <= -1.15e-170) {
tmp = y * x;
} else if (y <= 1e-56) {
tmp = 1.0;
} else if (y <= 3.5e-14) {
tmp = y * x;
} else if (y <= 0.42) {
tmp = 1.0 - y;
} else {
tmp = x;
}
return tmp;
}
real(8) function code(x, y)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8) :: tmp
if (y <= (-1.0d0)) then
tmp = x
else if (y <= (-8d-117)) then
tmp = 1.0d0 - y
else if (y <= (-1.15d-170)) then
tmp = y * x
else if (y <= 1d-56) then
tmp = 1.0d0
else if (y <= 3.5d-14) then
tmp = y * x
else if (y <= 0.42d0) then
tmp = 1.0d0 - y
else
tmp = x
end if
code = tmp
end function
public static double code(double x, double y) {
double tmp;
if (y <= -1.0) {
tmp = x;
} else if (y <= -8e-117) {
tmp = 1.0 - y;
} else if (y <= -1.15e-170) {
tmp = y * x;
} else if (y <= 1e-56) {
tmp = 1.0;
} else if (y <= 3.5e-14) {
tmp = y * x;
} else if (y <= 0.42) {
tmp = 1.0 - y;
} else {
tmp = x;
}
return tmp;
}
def code(x, y): tmp = 0 if y <= -1.0: tmp = x elif y <= -8e-117: tmp = 1.0 - y elif y <= -1.15e-170: tmp = y * x elif y <= 1e-56: tmp = 1.0 elif y <= 3.5e-14: tmp = y * x elif y <= 0.42: tmp = 1.0 - y else: tmp = x return tmp
function code(x, y) tmp = 0.0 if (y <= -1.0) tmp = x; elseif (y <= -8e-117) tmp = Float64(1.0 - y); elseif (y <= -1.15e-170) tmp = Float64(y * x); elseif (y <= 1e-56) tmp = 1.0; elseif (y <= 3.5e-14) tmp = Float64(y * x); elseif (y <= 0.42) tmp = Float64(1.0 - y); else tmp = x; end return tmp end
function tmp_2 = code(x, y) tmp = 0.0; if (y <= -1.0) tmp = x; elseif (y <= -8e-117) tmp = 1.0 - y; elseif (y <= -1.15e-170) tmp = y * x; elseif (y <= 1e-56) tmp = 1.0; elseif (y <= 3.5e-14) tmp = y * x; elseif (y <= 0.42) tmp = 1.0 - y; else tmp = x; end tmp_2 = tmp; end
code[x_, y_] := If[LessEqual[y, -1.0], x, If[LessEqual[y, -8e-117], N[(1.0 - y), $MachinePrecision], If[LessEqual[y, -1.15e-170], N[(y * x), $MachinePrecision], If[LessEqual[y, 1e-56], 1.0, If[LessEqual[y, 3.5e-14], N[(y * x), $MachinePrecision], If[LessEqual[y, 0.42], N[(1.0 - y), $MachinePrecision], x]]]]]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;y \leq -1:\\
\;\;\;\;x\\
\mathbf{elif}\;y \leq -8 \cdot 10^{-117}:\\
\;\;\;\;1 - y\\
\mathbf{elif}\;y \leq -1.15 \cdot 10^{-170}:\\
\;\;\;\;y \cdot x\\
\mathbf{elif}\;y \leq 10^{-56}:\\
\;\;\;\;1\\
\mathbf{elif}\;y \leq 3.5 \cdot 10^{-14}:\\
\;\;\;\;y \cdot x\\
\mathbf{elif}\;y \leq 0.42:\\
\;\;\;\;1 - y\\
\mathbf{else}:\\
\;\;\;\;x\\
\end{array}
\end{array}
(FPCore (x y) :precision binary64 (if (or (<= y -17500000000.0) (not (<= y 175000000000.0))) (- x (/ -1.0 y)) (+ 1.0 (* (/ y (+ y 1.0)) (+ x -1.0)))))
double code(double x, double y) {
double tmp;
if ((y <= -17500000000.0) || !(y <= 175000000000.0)) {
tmp = x - (-1.0 / y);
} else {
tmp = 1.0 + ((y / (y + 1.0)) * (x + -1.0));
}
return tmp;
}
real(8) function code(x, y)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8) :: tmp
if ((y <= (-17500000000.0d0)) .or. (.not. (y <= 175000000000.0d0))) then
tmp = x - ((-1.0d0) / y)
else
tmp = 1.0d0 + ((y / (y + 1.0d0)) * (x + (-1.0d0)))
end if
code = tmp
end function
public static double code(double x, double y) {
double tmp;
if ((y <= -17500000000.0) || !(y <= 175000000000.0)) {
tmp = x - (-1.0 / y);
} else {
tmp = 1.0 + ((y / (y + 1.0)) * (x + -1.0));
}
return tmp;
}
def code(x, y): tmp = 0 if (y <= -17500000000.0) or not (y <= 175000000000.0): tmp = x - (-1.0 / y) else: tmp = 1.0 + ((y / (y + 1.0)) * (x + -1.0)) return tmp
function code(x, y) tmp = 0.0 if ((y <= -17500000000.0) || !(y <= 175000000000.0)) tmp = Float64(x - Float64(-1.0 / y)); else tmp = Float64(1.0 + Float64(Float64(y / Float64(y + 1.0)) * Float64(x + -1.0))); end return tmp end
function tmp_2 = code(x, y) tmp = 0.0; if ((y <= -17500000000.0) || ~((y <= 175000000000.0))) tmp = x - (-1.0 / y); else tmp = 1.0 + ((y / (y + 1.0)) * (x + -1.0)); end tmp_2 = tmp; end
code[x_, y_] := If[Or[LessEqual[y, -17500000000.0], N[Not[LessEqual[y, 175000000000.0]], $MachinePrecision]], N[(x - N[(-1.0 / y), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(N[(y / N[(y + 1.0), $MachinePrecision]), $MachinePrecision] * N[(x + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;y \leq -17500000000 \lor \neg \left(y \leq 175000000000\right):\\
\;\;\;\;x - \frac{-1}{y}\\
\mathbf{else}:\\
\;\;\;\;1 + \frac{y}{y + 1} \cdot \left(x + -1\right)\\
\end{array}
\end{array}
(FPCore (x y)
:precision binary64
(if (<= y -1.0)
x
(if (<= y -8.2e-117)
1.0
(if (<= y -1.15e-170)
(* y x)
(if (<= y 1.08e-57)
1.0
(if (<= y 3.8e-14) (* y x) (if (<= y 82000000000000.0) 1.0 x)))))))
double code(double x, double y) {
double tmp;
if (y <= -1.0) {
tmp = x;
} else if (y <= -8.2e-117) {
tmp = 1.0;
} else if (y <= -1.15e-170) {
tmp = y * x;
} else if (y <= 1.08e-57) {
tmp = 1.0;
} else if (y <= 3.8e-14) {
tmp = y * x;
} else if (y <= 82000000000000.0) {
tmp = 1.0;
} else {
tmp = x;
}
return tmp;
}
real(8) function code(x, y)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8) :: tmp
if (y <= (-1.0d0)) then
tmp = x
else if (y <= (-8.2d-117)) then
tmp = 1.0d0
else if (y <= (-1.15d-170)) then
tmp = y * x
else if (y <= 1.08d-57) then
tmp = 1.0d0
else if (y <= 3.8d-14) then
tmp = y * x
else if (y <= 82000000000000.0d0) then
tmp = 1.0d0
else
tmp = x
end if
code = tmp
end function
public static double code(double x, double y) {
double tmp;
if (y <= -1.0) {
tmp = x;
} else if (y <= -8.2e-117) {
tmp = 1.0;
} else if (y <= -1.15e-170) {
tmp = y * x;
} else if (y <= 1.08e-57) {
tmp = 1.0;
} else if (y <= 3.8e-14) {
tmp = y * x;
} else if (y <= 82000000000000.0) {
tmp = 1.0;
} else {
tmp = x;
}
return tmp;
}
def code(x, y): tmp = 0 if y <= -1.0: tmp = x elif y <= -8.2e-117: tmp = 1.0 elif y <= -1.15e-170: tmp = y * x elif y <= 1.08e-57: tmp = 1.0 elif y <= 3.8e-14: tmp = y * x elif y <= 82000000000000.0: tmp = 1.0 else: tmp = x return tmp
function code(x, y) tmp = 0.0 if (y <= -1.0) tmp = x; elseif (y <= -8.2e-117) tmp = 1.0; elseif (y <= -1.15e-170) tmp = Float64(y * x); elseif (y <= 1.08e-57) tmp = 1.0; elseif (y <= 3.8e-14) tmp = Float64(y * x); elseif (y <= 82000000000000.0) tmp = 1.0; else tmp = x; end return tmp end
function tmp_2 = code(x, y) tmp = 0.0; if (y <= -1.0) tmp = x; elseif (y <= -8.2e-117) tmp = 1.0; elseif (y <= -1.15e-170) tmp = y * x; elseif (y <= 1.08e-57) tmp = 1.0; elseif (y <= 3.8e-14) tmp = y * x; elseif (y <= 82000000000000.0) tmp = 1.0; else tmp = x; end tmp_2 = tmp; end
code[x_, y_] := If[LessEqual[y, -1.0], x, If[LessEqual[y, -8.2e-117], 1.0, If[LessEqual[y, -1.15e-170], N[(y * x), $MachinePrecision], If[LessEqual[y, 1.08e-57], 1.0, If[LessEqual[y, 3.8e-14], N[(y * x), $MachinePrecision], If[LessEqual[y, 82000000000000.0], 1.0, x]]]]]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;y \leq -1:\\
\;\;\;\;x\\
\mathbf{elif}\;y \leq -8.2 \cdot 10^{-117}:\\
\;\;\;\;1\\
\mathbf{elif}\;y \leq -1.15 \cdot 10^{-170}:\\
\;\;\;\;y \cdot x\\
\mathbf{elif}\;y \leq 1.08 \cdot 10^{-57}:\\
\;\;\;\;1\\
\mathbf{elif}\;y \leq 3.8 \cdot 10^{-14}:\\
\;\;\;\;y \cdot x\\
\mathbf{elif}\;y \leq 82000000000000:\\
\;\;\;\;1\\
\mathbf{else}:\\
\;\;\;\;x\\
\end{array}
\end{array}
(FPCore (x y) :precision binary64 (if (<= y -380000.0) (+ x (/ (- 1.0 x) y)) (if (<= y 660000.0) (- 1.0 (/ y (/ (- -1.0 y) x))) (- x (/ -1.0 y)))))
double code(double x, double y) {
double tmp;
if (y <= -380000.0) {
tmp = x + ((1.0 - x) / y);
} else if (y <= 660000.0) {
tmp = 1.0 - (y / ((-1.0 - y) / x));
} else {
tmp = x - (-1.0 / y);
}
return tmp;
}
real(8) function code(x, y)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8) :: tmp
if (y <= (-380000.0d0)) then
tmp = x + ((1.0d0 - x) / y)
else if (y <= 660000.0d0) then
tmp = 1.0d0 - (y / (((-1.0d0) - y) / x))
else
tmp = x - ((-1.0d0) / y)
end if
code = tmp
end function
public static double code(double x, double y) {
double tmp;
if (y <= -380000.0) {
tmp = x + ((1.0 - x) / y);
} else if (y <= 660000.0) {
tmp = 1.0 - (y / ((-1.0 - y) / x));
} else {
tmp = x - (-1.0 / y);
}
return tmp;
}
def code(x, y): tmp = 0 if y <= -380000.0: tmp = x + ((1.0 - x) / y) elif y <= 660000.0: tmp = 1.0 - (y / ((-1.0 - y) / x)) else: tmp = x - (-1.0 / y) return tmp
function code(x, y) tmp = 0.0 if (y <= -380000.0) tmp = Float64(x + Float64(Float64(1.0 - x) / y)); elseif (y <= 660000.0) tmp = Float64(1.0 - Float64(y / Float64(Float64(-1.0 - y) / x))); else tmp = Float64(x - Float64(-1.0 / y)); end return tmp end
function tmp_2 = code(x, y) tmp = 0.0; if (y <= -380000.0) tmp = x + ((1.0 - x) / y); elseif (y <= 660000.0) tmp = 1.0 - (y / ((-1.0 - y) / x)); else tmp = x - (-1.0 / y); end tmp_2 = tmp; end
code[x_, y_] := If[LessEqual[y, -380000.0], N[(x + N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 660000.0], N[(1.0 - N[(y / N[(N[(-1.0 - y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(-1.0 / y), $MachinePrecision]), $MachinePrecision]]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;y \leq -380000:\\
\;\;\;\;x + \frac{1 - x}{y}\\
\mathbf{elif}\;y \leq 660000:\\
\;\;\;\;1 - \frac{y}{\frac{-1 - y}{x}}\\
\mathbf{else}:\\
\;\;\;\;x - \frac{-1}{y}\\
\end{array}
\end{array}
(FPCore (x y) :precision binary64 (if (<= y -1650.0) (+ x (/ (- 1.0 x) y)) (if (<= y 21000000.0) (+ 1.0 (/ x (+ 1.0 (/ 1.0 y)))) (- x (/ -1.0 y)))))
double code(double x, double y) {
double tmp;
if (y <= -1650.0) {
tmp = x + ((1.0 - x) / y);
} else if (y <= 21000000.0) {
tmp = 1.0 + (x / (1.0 + (1.0 / y)));
} else {
tmp = x - (-1.0 / y);
}
return tmp;
}
real(8) function code(x, y)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8) :: tmp
if (y <= (-1650.0d0)) then
tmp = x + ((1.0d0 - x) / y)
else if (y <= 21000000.0d0) then
tmp = 1.0d0 + (x / (1.0d0 + (1.0d0 / y)))
else
tmp = x - ((-1.0d0) / y)
end if
code = tmp
end function
public static double code(double x, double y) {
double tmp;
if (y <= -1650.0) {
tmp = x + ((1.0 - x) / y);
} else if (y <= 21000000.0) {
tmp = 1.0 + (x / (1.0 + (1.0 / y)));
} else {
tmp = x - (-1.0 / y);
}
return tmp;
}
def code(x, y): tmp = 0 if y <= -1650.0: tmp = x + ((1.0 - x) / y) elif y <= 21000000.0: tmp = 1.0 + (x / (1.0 + (1.0 / y))) else: tmp = x - (-1.0 / y) return tmp
function code(x, y) tmp = 0.0 if (y <= -1650.0) tmp = Float64(x + Float64(Float64(1.0 - x) / y)); elseif (y <= 21000000.0) tmp = Float64(1.0 + Float64(x / Float64(1.0 + Float64(1.0 / y)))); else tmp = Float64(x - Float64(-1.0 / y)); end return tmp end
function tmp_2 = code(x, y) tmp = 0.0; if (y <= -1650.0) tmp = x + ((1.0 - x) / y); elseif (y <= 21000000.0) tmp = 1.0 + (x / (1.0 + (1.0 / y))); else tmp = x - (-1.0 / y); end tmp_2 = tmp; end
code[x_, y_] := If[LessEqual[y, -1650.0], N[(x + N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 21000000.0], N[(1.0 + N[(x / N[(1.0 + N[(1.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(-1.0 / y), $MachinePrecision]), $MachinePrecision]]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;y \leq -1650:\\
\;\;\;\;x + \frac{1 - x}{y}\\
\mathbf{elif}\;y \leq 21000000:\\
\;\;\;\;1 + \frac{x}{1 + \frac{1}{y}}\\
\mathbf{else}:\\
\;\;\;\;x - \frac{-1}{y}\\
\end{array}
\end{array}
(FPCore (x y) :precision binary64 (if (or (<= y -1.0) (not (<= y 0.8))) (- x (/ -1.0 y)) (- 1.0 (* y (- 1.0 x)))))
double code(double x, double y) {
double tmp;
if ((y <= -1.0) || !(y <= 0.8)) {
tmp = x - (-1.0 / y);
} else {
tmp = 1.0 - (y * (1.0 - x));
}
return tmp;
}
real(8) function code(x, y)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8) :: tmp
if ((y <= (-1.0d0)) .or. (.not. (y <= 0.8d0))) then
tmp = x - ((-1.0d0) / y)
else
tmp = 1.0d0 - (y * (1.0d0 - x))
end if
code = tmp
end function
public static double code(double x, double y) {
double tmp;
if ((y <= -1.0) || !(y <= 0.8)) {
tmp = x - (-1.0 / y);
} else {
tmp = 1.0 - (y * (1.0 - x));
}
return tmp;
}
def code(x, y): tmp = 0 if (y <= -1.0) or not (y <= 0.8): tmp = x - (-1.0 / y) else: tmp = 1.0 - (y * (1.0 - x)) return tmp
function code(x, y) tmp = 0.0 if ((y <= -1.0) || !(y <= 0.8)) tmp = Float64(x - Float64(-1.0 / y)); else tmp = Float64(1.0 - Float64(y * Float64(1.0 - x))); end return tmp end
function tmp_2 = code(x, y) tmp = 0.0; if ((y <= -1.0) || ~((y <= 0.8))) tmp = x - (-1.0 / y); else tmp = 1.0 - (y * (1.0 - x)); end tmp_2 = tmp; end
code[x_, y_] := If[Or[LessEqual[y, -1.0], N[Not[LessEqual[y, 0.8]], $MachinePrecision]], N[(x - N[(-1.0 / y), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(y * N[(1.0 - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 0.8\right):\\
\;\;\;\;x - \frac{-1}{y}\\
\mathbf{else}:\\
\;\;\;\;1 - y \cdot \left(1 - x\right)\\
\end{array}
\end{array}
(FPCore (x y) :precision binary64 (if (<= y -1.0) (+ x (/ (- 1.0 x) y)) (if (<= y 0.78) (- 1.0 (* y (- 1.0 x))) (- x (/ -1.0 y)))))
double code(double x, double y) {
double tmp;
if (y <= -1.0) {
tmp = x + ((1.0 - x) / y);
} else if (y <= 0.78) {
tmp = 1.0 - (y * (1.0 - x));
} else {
tmp = x - (-1.0 / y);
}
return tmp;
}
real(8) function code(x, y)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8) :: tmp
if (y <= (-1.0d0)) then
tmp = x + ((1.0d0 - x) / y)
else if (y <= 0.78d0) then
tmp = 1.0d0 - (y * (1.0d0 - x))
else
tmp = x - ((-1.0d0) / y)
end if
code = tmp
end function
public static double code(double x, double y) {
double tmp;
if (y <= -1.0) {
tmp = x + ((1.0 - x) / y);
} else if (y <= 0.78) {
tmp = 1.0 - (y * (1.0 - x));
} else {
tmp = x - (-1.0 / y);
}
return tmp;
}
def code(x, y): tmp = 0 if y <= -1.0: tmp = x + ((1.0 - x) / y) elif y <= 0.78: tmp = 1.0 - (y * (1.0 - x)) else: tmp = x - (-1.0 / y) return tmp
function code(x, y) tmp = 0.0 if (y <= -1.0) tmp = Float64(x + Float64(Float64(1.0 - x) / y)); elseif (y <= 0.78) tmp = Float64(1.0 - Float64(y * Float64(1.0 - x))); else tmp = Float64(x - Float64(-1.0 / y)); end return tmp end
function tmp_2 = code(x, y) tmp = 0.0; if (y <= -1.0) tmp = x + ((1.0 - x) / y); elseif (y <= 0.78) tmp = 1.0 - (y * (1.0 - x)); else tmp = x - (-1.0 / y); end tmp_2 = tmp; end
code[x_, y_] := If[LessEqual[y, -1.0], N[(x + N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 0.78], N[(1.0 - N[(y * N[(1.0 - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(-1.0 / y), $MachinePrecision]), $MachinePrecision]]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;y \leq -1:\\
\;\;\;\;x + \frac{1 - x}{y}\\
\mathbf{elif}\;y \leq 0.78:\\
\;\;\;\;1 - y \cdot \left(1 - x\right)\\
\mathbf{else}:\\
\;\;\;\;x - \frac{-1}{y}\\
\end{array}
\end{array}
(FPCore (x y) :precision binary64 (if (or (<= y -1.0) (not (<= y 1.0))) (- x (/ -1.0 y)) (+ 1.0 (* y x))))
double code(double x, double y) {
double tmp;
if ((y <= -1.0) || !(y <= 1.0)) {
tmp = x - (-1.0 / y);
} else {
tmp = 1.0 + (y * x);
}
return tmp;
}
real(8) function code(x, y)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8) :: tmp
if ((y <= (-1.0d0)) .or. (.not. (y <= 1.0d0))) then
tmp = x - ((-1.0d0) / y)
else
tmp = 1.0d0 + (y * x)
end if
code = tmp
end function
public static double code(double x, double y) {
double tmp;
if ((y <= -1.0) || !(y <= 1.0)) {
tmp = x - (-1.0 / y);
} else {
tmp = 1.0 + (y * x);
}
return tmp;
}
def code(x, y): tmp = 0 if (y <= -1.0) or not (y <= 1.0): tmp = x - (-1.0 / y) else: tmp = 1.0 + (y * x) return tmp
function code(x, y) tmp = 0.0 if ((y <= -1.0) || !(y <= 1.0)) tmp = Float64(x - Float64(-1.0 / y)); else tmp = Float64(1.0 + Float64(y * x)); end return tmp end
function tmp_2 = code(x, y) tmp = 0.0; if ((y <= -1.0) || ~((y <= 1.0))) tmp = x - (-1.0 / y); else tmp = 1.0 + (y * x); end tmp_2 = tmp; end
code[x_, y_] := If[Or[LessEqual[y, -1.0], N[Not[LessEqual[y, 1.0]], $MachinePrecision]], N[(x - N[(-1.0 / y), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(y * x), $MachinePrecision]), $MachinePrecision]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 1\right):\\
\;\;\;\;x - \frac{-1}{y}\\
\mathbf{else}:\\
\;\;\;\;1 + y \cdot x\\
\end{array}
\end{array}
(FPCore (x y) :precision binary64 (if (<= y -1.0) x (if (<= y 82000000000000.0) 1.0 x)))
double code(double x, double y) {
double tmp;
if (y <= -1.0) {
tmp = x;
} else if (y <= 82000000000000.0) {
tmp = 1.0;
} else {
tmp = x;
}
return tmp;
}
real(8) function code(x, y)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8) :: tmp
if (y <= (-1.0d0)) then
tmp = x
else if (y <= 82000000000000.0d0) then
tmp = 1.0d0
else
tmp = x
end if
code = tmp
end function
public static double code(double x, double y) {
double tmp;
if (y <= -1.0) {
tmp = x;
} else if (y <= 82000000000000.0) {
tmp = 1.0;
} else {
tmp = x;
}
return tmp;
}
def code(x, y): tmp = 0 if y <= -1.0: tmp = x elif y <= 82000000000000.0: tmp = 1.0 else: tmp = x return tmp
function code(x, y) tmp = 0.0 if (y <= -1.0) tmp = x; elseif (y <= 82000000000000.0) tmp = 1.0; else tmp = x; end return tmp end
function tmp_2 = code(x, y) tmp = 0.0; if (y <= -1.0) tmp = x; elseif (y <= 82000000000000.0) tmp = 1.0; else tmp = x; end tmp_2 = tmp; end
code[x_, y_] := If[LessEqual[y, -1.0], x, If[LessEqual[y, 82000000000000.0], 1.0, x]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;y \leq -1:\\
\;\;\;\;x\\
\mathbf{elif}\;y \leq 82000000000000:\\
\;\;\;\;1\\
\mathbf{else}:\\
\;\;\;\;x\\
\end{array}
\end{array}
(FPCore (x y) :precision binary64 1.0)
double code(double x, double y) {
return 1.0;
}
real(8) function code(x, y)
real(8), intent (in) :: x
real(8), intent (in) :: y
code = 1.0d0
end function
public static double code(double x, double y) {
return 1.0;
}
def code(x, y): return 1.0
function code(x, y) return 1.0 end
function tmp = code(x, y) tmp = 1.0; end
code[x_, y_] := 1.0
\begin{array}{l}
\\
1
\end{array}
(FPCore (x y)
:precision binary64
(let* ((t_0 (- (/ 1.0 y) (- (/ x y) x))))
(if (< y -3693.8482788297247)
t_0
(if (< y 6799310503.41891) (- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0))) t_0))))
double code(double x, double y) {
double t_0 = (1.0 / y) - ((x / y) - x);
double tmp;
if (y < -3693.8482788297247) {
tmp = t_0;
} else if (y < 6799310503.41891) {
tmp = 1.0 - (((1.0 - x) * y) / (y + 1.0));
} else {
tmp = t_0;
}
return tmp;
}
real(8) function code(x, y)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8) :: t_0
real(8) :: tmp
t_0 = (1.0d0 / y) - ((x / y) - x)
if (y < (-3693.8482788297247d0)) then
tmp = t_0
else if (y < 6799310503.41891d0) then
tmp = 1.0d0 - (((1.0d0 - x) * y) / (y + 1.0d0))
else
tmp = t_0
end if
code = tmp
end function
public static double code(double x, double y) {
double t_0 = (1.0 / y) - ((x / y) - x);
double tmp;
if (y < -3693.8482788297247) {
tmp = t_0;
} else if (y < 6799310503.41891) {
tmp = 1.0 - (((1.0 - x) * y) / (y + 1.0));
} else {
tmp = t_0;
}
return tmp;
}
def code(x, y): t_0 = (1.0 / y) - ((x / y) - x) tmp = 0 if y < -3693.8482788297247: tmp = t_0 elif y < 6799310503.41891: tmp = 1.0 - (((1.0 - x) * y) / (y + 1.0)) else: tmp = t_0 return tmp
function code(x, y) t_0 = Float64(Float64(1.0 / y) - Float64(Float64(x / y) - x)) tmp = 0.0 if (y < -3693.8482788297247) tmp = t_0; elseif (y < 6799310503.41891) tmp = Float64(1.0 - Float64(Float64(Float64(1.0 - x) * y) / Float64(y + 1.0))); else tmp = t_0; end return tmp end
function tmp_2 = code(x, y) t_0 = (1.0 / y) - ((x / y) - x); tmp = 0.0; if (y < -3693.8482788297247) tmp = t_0; elseif (y < 6799310503.41891) tmp = 1.0 - (((1.0 - x) * y) / (y + 1.0)); else tmp = t_0; end tmp_2 = tmp; end
code[x_, y_] := Block[{t$95$0 = N[(N[(1.0 / y), $MachinePrecision] - N[(N[(x / y), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]}, If[Less[y, -3693.8482788297247], t$95$0, If[Less[y, 6799310503.41891], N[(1.0 - N[(N[(N[(1.0 - x), $MachinePrecision] * y), $MachinePrecision] / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]
\begin{array}{l}
\\
\begin{array}{l}
t_0 := \frac{1}{y} - \left(\frac{x}{y} - x\right)\\
\mathbf{if}\;y < -3693.8482788297247:\\
\;\;\;\;t_0\\
\mathbf{elif}\;y < 6799310503.41891:\\
\;\;\;\;1 - \frac{\left(1 - x\right) \cdot y}{y + 1}\\
\mathbf{else}:\\
\;\;\;\;t_0\\
\end{array}
\end{array}
herbie shell --seed 2023350
(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))))