
(FPCore (x y) :precision binary64 (+ x (* (- 1.0 x) (- 1.0 y))))
double code(double x, double y) {
return x + ((1.0 - x) * (1.0 - y));
}
real(8) function code(x, y)
real(8), intent (in) :: x
real(8), intent (in) :: y
code = x + ((1.0d0 - x) * (1.0d0 - y))
end function
public static double code(double x, double y) {
return x + ((1.0 - x) * (1.0 - y));
}
def code(x, y): return x + ((1.0 - x) * (1.0 - y))
function code(x, y) return Float64(x + Float64(Float64(1.0 - x) * Float64(1.0 - y))) end
function tmp = code(x, y) tmp = x + ((1.0 - x) * (1.0 - y)); end
code[x_, y_] := N[(x + N[(N[(1.0 - x), $MachinePrecision] * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
x + \left(1 - x\right) \cdot \left(1 - y\right)
\end{array}
Sampling outcomes in binary64 precision:
Herbie found 6 alternatives:
| Alternative | Accuracy | Speedup |
|---|
(FPCore (x y) :precision binary64 (+ x (* (- 1.0 x) (- 1.0 y))))
double code(double x, double y) {
return x + ((1.0 - x) * (1.0 - y));
}
real(8) function code(x, y)
real(8), intent (in) :: x
real(8), intent (in) :: y
code = x + ((1.0d0 - x) * (1.0d0 - y))
end function
public static double code(double x, double y) {
return x + ((1.0 - x) * (1.0 - y));
}
def code(x, y): return x + ((1.0 - x) * (1.0 - y))
function code(x, y) return Float64(x + Float64(Float64(1.0 - x) * Float64(1.0 - y))) end
function tmp = code(x, y) tmp = x + ((1.0 - x) * (1.0 - y)); end
code[x_, y_] := N[(x + N[(N[(1.0 - x), $MachinePrecision] * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
x + \left(1 - x\right) \cdot \left(1 - y\right)
\end{array}
(FPCore (x y) :precision binary64 (fma (- x 1.0) y 1.0))
double code(double x, double y) {
return fma((x - 1.0), y, 1.0);
}
function code(x, y) return fma(Float64(x - 1.0), y, 1.0) end
code[x_, y_] := N[(N[(x - 1.0), $MachinePrecision] * y + 1.0), $MachinePrecision]
\begin{array}{l}
\\
\mathsf{fma}\left(x - 1, y, 1\right)
\end{array}
Initial program 76.8%
Taylor expanded in y around 0
+-commutativeN/A
*-commutativeN/A
associate-*r*N/A
lower-fma.f64N/A
mul-1-negN/A
sub-negN/A
+-commutativeN/A
distribute-neg-inN/A
remove-double-negN/A
sub-negN/A
lower--.f64100.0
Applied rewrites100.0%
(FPCore (x y) :precision binary64 (if (<= x -2.2e+48) (* y x) (if (<= x 9.5e+15) (- 1.0 y) (* (- x 1.0) y))))
double code(double x, double y) {
double tmp;
if (x <= -2.2e+48) {
tmp = y * x;
} else if (x <= 9.5e+15) {
tmp = 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 (x <= (-2.2d+48)) then
tmp = y * x
else if (x <= 9.5d+15) then
tmp = 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 (x <= -2.2e+48) {
tmp = y * x;
} else if (x <= 9.5e+15) {
tmp = 1.0 - y;
} else {
tmp = (x - 1.0) * y;
}
return tmp;
}
def code(x, y): tmp = 0 if x <= -2.2e+48: tmp = y * x elif x <= 9.5e+15: tmp = 1.0 - y else: tmp = (x - 1.0) * y return tmp
function code(x, y) tmp = 0.0 if (x <= -2.2e+48) tmp = Float64(y * x); elseif (x <= 9.5e+15) tmp = Float64(1.0 - y); else tmp = Float64(Float64(x - 1.0) * y); end return tmp end
function tmp_2 = code(x, y) tmp = 0.0; if (x <= -2.2e+48) tmp = y * x; elseif (x <= 9.5e+15) tmp = 1.0 - y; else tmp = (x - 1.0) * y; end tmp_2 = tmp; end
code[x_, y_] := If[LessEqual[x, -2.2e+48], N[(y * x), $MachinePrecision], If[LessEqual[x, 9.5e+15], N[(1.0 - y), $MachinePrecision], N[(N[(x - 1.0), $MachinePrecision] * y), $MachinePrecision]]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;x \leq -2.2 \cdot 10^{+48}:\\
\;\;\;\;y \cdot x\\
\mathbf{elif}\;x \leq 9.5 \cdot 10^{+15}:\\
\;\;\;\;1 - y\\
\mathbf{else}:\\
\;\;\;\;\left(x - 1\right) \cdot y\\
\end{array}
\end{array}
if x < -2.1999999999999999e48Initial program 51.4%
Taylor expanded in x around inf
mul-1-negN/A
unsub-negN/A
sub-negN/A
associate--r+N/A
metadata-evalN/A
neg-sub0N/A
remove-double-negN/A
lower-*.f6479.5
Applied rewrites79.5%
if -2.1999999999999999e48 < x < 9.5e15Initial program 96.9%
Taylor expanded in x around 0
lower--.f6497.4
Applied rewrites97.4%
if 9.5e15 < x Initial program 51.4%
Taylor expanded in y around inf
*-commutativeN/A
associate-*r*N/A
lower-*.f64N/A
mul-1-negN/A
sub-negN/A
+-commutativeN/A
distribute-neg-inN/A
remove-double-negN/A
sub-negN/A
lower--.f6481.1
Applied rewrites81.1%
Final simplification89.9%
(FPCore (x y) :precision binary64 (if (<= (- 1.0 y) -1e+17) (- y) (if (<= (- 1.0 y) 2.0) 1.0 (- y))))
double code(double x, double y) {
double tmp;
if ((1.0 - y) <= -1e+17) {
tmp = -y;
} else if ((1.0 - y) <= 2.0) {
tmp = 1.0;
} else {
tmp = -y;
}
return tmp;
}
real(8) function code(x, y)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8) :: tmp
if ((1.0d0 - y) <= (-1d+17)) then
tmp = -y
else if ((1.0d0 - y) <= 2.0d0) then
tmp = 1.0d0
else
tmp = -y
end if
code = tmp
end function
public static double code(double x, double y) {
double tmp;
if ((1.0 - y) <= -1e+17) {
tmp = -y;
} else if ((1.0 - y) <= 2.0) {
tmp = 1.0;
} else {
tmp = -y;
}
return tmp;
}
def code(x, y): tmp = 0 if (1.0 - y) <= -1e+17: tmp = -y elif (1.0 - y) <= 2.0: tmp = 1.0 else: tmp = -y return tmp
function code(x, y) tmp = 0.0 if (Float64(1.0 - y) <= -1e+17) tmp = Float64(-y); elseif (Float64(1.0 - y) <= 2.0) tmp = 1.0; else tmp = Float64(-y); end return tmp end
function tmp_2 = code(x, y) tmp = 0.0; if ((1.0 - y) <= -1e+17) tmp = -y; elseif ((1.0 - y) <= 2.0) tmp = 1.0; else tmp = -y; end tmp_2 = tmp; end
code[x_, y_] := If[LessEqual[N[(1.0 - y), $MachinePrecision], -1e+17], (-y), If[LessEqual[N[(1.0 - y), $MachinePrecision], 2.0], 1.0, (-y)]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;1 - y \leq -1 \cdot 10^{+17}:\\
\;\;\;\;-y\\
\mathbf{elif}\;1 - y \leq 2:\\
\;\;\;\;1\\
\mathbf{else}:\\
\;\;\;\;-y\\
\end{array}
\end{array}
if (-.f64 #s(literal 1 binary64) y) < -1e17 or 2 < (-.f64 #s(literal 1 binary64) y) Initial program 99.9%
Taylor expanded in x around 0
lower--.f6453.9
Applied rewrites53.9%
Taylor expanded in y around inf
Applied rewrites53.9%
if -1e17 < (-.f64 #s(literal 1 binary64) y) < 2Initial program 56.5%
Taylor expanded in y around 0
Applied rewrites72.1%
(FPCore (x y) :precision binary64 (if (<= x -2.2e+48) (* y x) (if (<= x 9.5e+15) (- 1.0 y) (* y x))))
double code(double x, double y) {
double tmp;
if (x <= -2.2e+48) {
tmp = y * x;
} else if (x <= 9.5e+15) {
tmp = 1.0 - y;
} else {
tmp = y * x;
}
return tmp;
}
real(8) function code(x, y)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8) :: tmp
if (x <= (-2.2d+48)) then
tmp = y * x
else if (x <= 9.5d+15) then
tmp = 1.0d0 - y
else
tmp = y * x
end if
code = tmp
end function
public static double code(double x, double y) {
double tmp;
if (x <= -2.2e+48) {
tmp = y * x;
} else if (x <= 9.5e+15) {
tmp = 1.0 - y;
} else {
tmp = y * x;
}
return tmp;
}
def code(x, y): tmp = 0 if x <= -2.2e+48: tmp = y * x elif x <= 9.5e+15: tmp = 1.0 - y else: tmp = y * x return tmp
function code(x, y) tmp = 0.0 if (x <= -2.2e+48) tmp = Float64(y * x); elseif (x <= 9.5e+15) tmp = Float64(1.0 - y); else tmp = Float64(y * x); end return tmp end
function tmp_2 = code(x, y) tmp = 0.0; if (x <= -2.2e+48) tmp = y * x; elseif (x <= 9.5e+15) tmp = 1.0 - y; else tmp = y * x; end tmp_2 = tmp; end
code[x_, y_] := If[LessEqual[x, -2.2e+48], N[(y * x), $MachinePrecision], If[LessEqual[x, 9.5e+15], N[(1.0 - y), $MachinePrecision], N[(y * x), $MachinePrecision]]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;x \leq -2.2 \cdot 10^{+48}:\\
\;\;\;\;y \cdot x\\
\mathbf{elif}\;x \leq 9.5 \cdot 10^{+15}:\\
\;\;\;\;1 - y\\
\mathbf{else}:\\
\;\;\;\;y \cdot x\\
\end{array}
\end{array}
if x < -2.1999999999999999e48 or 9.5e15 < x Initial program 51.4%
Taylor expanded in x around inf
mul-1-negN/A
unsub-negN/A
sub-negN/A
associate--r+N/A
metadata-evalN/A
neg-sub0N/A
remove-double-negN/A
lower-*.f6480.5
Applied rewrites80.5%
if -2.1999999999999999e48 < x < 9.5e15Initial program 96.9%
Taylor expanded in x around 0
lower--.f6497.4
Applied rewrites97.4%
Final simplification89.9%
(FPCore (x y) :precision binary64 (- 1.0 y))
double code(double x, double y) {
return 1.0 - y;
}
real(8) function code(x, y)
real(8), intent (in) :: x
real(8), intent (in) :: y
code = 1.0d0 - y
end function
public static double code(double x, double y) {
return 1.0 - y;
}
def code(x, y): return 1.0 - y
function code(x, y) return Float64(1.0 - y) end
function tmp = code(x, y) tmp = 1.0 - y; end
code[x_, y_] := N[(1.0 - y), $MachinePrecision]
\begin{array}{l}
\\
1 - y
\end{array}
Initial program 76.8%
Taylor expanded in x around 0
lower--.f6464.0
Applied rewrites64.0%
(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}
Initial program 76.8%
Taylor expanded in y around 0
Applied rewrites39.6%
(FPCore (x y) :precision binary64 (- (* y x) (- y 1.0)))
double code(double x, double y) {
return (y * x) - (y - 1.0);
}
real(8) function code(x, y)
real(8), intent (in) :: x
real(8), intent (in) :: y
code = (y * x) - (y - 1.0d0)
end function
public static double code(double x, double y) {
return (y * x) - (y - 1.0);
}
def code(x, y): return (y * x) - (y - 1.0)
function code(x, y) return Float64(Float64(y * x) - Float64(y - 1.0)) end
function tmp = code(x, y) tmp = (y * x) - (y - 1.0); end
code[x_, y_] := N[(N[(y * x), $MachinePrecision] - N[(y - 1.0), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
y \cdot x - \left(y - 1\right)
\end{array}
herbie shell --seed 2024249
(FPCore (x y)
:name "Graphics.Rendering.Chart.Plot.Vectors:renderPlotVectors from Chart-1.5.3"
:precision binary64
:alt
(! :herbie-platform default (- (* y x) (- y 1)))
(+ x (* (- 1.0 x) (- 1.0 y))))