
(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 74.6%
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 (let* ((t_0 (+ (* (- 1.0 x) (- 1.0 y)) x))) (if (<= t_0 -20000000000.0) (- y) (if (<= t_0 2.0) 1.0 (- y)))))
double code(double x, double y) {
double t_0 = ((1.0 - x) * (1.0 - y)) + x;
double tmp;
if (t_0 <= -20000000000.0) {
tmp = -y;
} else if (t_0 <= 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) :: t_0
real(8) :: tmp
t_0 = ((1.0d0 - x) * (1.0d0 - y)) + x
if (t_0 <= (-20000000000.0d0)) then
tmp = -y
else if (t_0 <= 2.0d0) then
tmp = 1.0d0
else
tmp = -y
end if
code = tmp
end function
public static double code(double x, double y) {
double t_0 = ((1.0 - x) * (1.0 - y)) + x;
double tmp;
if (t_0 <= -20000000000.0) {
tmp = -y;
} else if (t_0 <= 2.0) {
tmp = 1.0;
} else {
tmp = -y;
}
return tmp;
}
def code(x, y): t_0 = ((1.0 - x) * (1.0 - y)) + x tmp = 0 if t_0 <= -20000000000.0: tmp = -y elif t_0 <= 2.0: tmp = 1.0 else: tmp = -y return tmp
function code(x, y) t_0 = Float64(Float64(Float64(1.0 - x) * Float64(1.0 - y)) + x) tmp = 0.0 if (t_0 <= -20000000000.0) tmp = Float64(-y); elseif (t_0 <= 2.0) tmp = 1.0; else tmp = Float64(-y); end return tmp end
function tmp_2 = code(x, y) t_0 = ((1.0 - x) * (1.0 - y)) + x; tmp = 0.0; if (t_0 <= -20000000000.0) tmp = -y; elseif (t_0 <= 2.0) tmp = 1.0; else tmp = -y; end tmp_2 = tmp; end
code[x_, y_] := Block[{t$95$0 = N[(N[(N[(1.0 - x), $MachinePrecision] * N[(1.0 - y), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[t$95$0, -20000000000.0], (-y), If[LessEqual[t$95$0, 2.0], 1.0, (-y)]]]
\begin{array}{l}
\\
\begin{array}{l}
t_0 := \left(1 - x\right) \cdot \left(1 - y\right) + x\\
\mathbf{if}\;t\_0 \leq -20000000000:\\
\;\;\;\;-y\\
\mathbf{elif}\;t\_0 \leq 2:\\
\;\;\;\;1\\
\mathbf{else}:\\
\;\;\;\;-y\\
\end{array}
\end{array}
if (+.f64 x (*.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) y))) < -2e10 or 2 < (+.f64 x (*.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) y))) Initial program 99.3%
Taylor expanded in x around 0
lower--.f6447.5
Applied rewrites47.5%
Taylor expanded in y around inf
Applied rewrites47.3%
if -2e10 < (+.f64 x (*.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) y))) < 2Initial program 49.1%
Taylor expanded in y around 0
Applied rewrites75.8%
Final simplification61.3%
(FPCore (x y) :precision binary64 (let* ((t_0 (* y (- x 1.0)))) (if (<= y -0.85) t_0 (if (<= y 3e-113) (- 1.0 y) t_0))))
double code(double x, double y) {
double t_0 = y * (x - 1.0);
double tmp;
if (y <= -0.85) {
tmp = t_0;
} else if (y <= 3e-113) {
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 = y * (x - 1.0d0)
if (y <= (-0.85d0)) then
tmp = t_0
else if (y <= 3d-113) 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 = y * (x - 1.0);
double tmp;
if (y <= -0.85) {
tmp = t_0;
} else if (y <= 3e-113) {
tmp = 1.0 - y;
} else {
tmp = t_0;
}
return tmp;
}
def code(x, y): t_0 = y * (x - 1.0) tmp = 0 if y <= -0.85: tmp = t_0 elif y <= 3e-113: tmp = 1.0 - y else: tmp = t_0 return tmp
function code(x, y) t_0 = Float64(y * Float64(x - 1.0)) tmp = 0.0 if (y <= -0.85) tmp = t_0; elseif (y <= 3e-113) tmp = Float64(1.0 - y); else tmp = t_0; end return tmp end
function tmp_2 = code(x, y) t_0 = y * (x - 1.0); tmp = 0.0; if (y <= -0.85) tmp = t_0; elseif (y <= 3e-113) tmp = 1.0 - y; else tmp = t_0; end tmp_2 = tmp; end
code[x_, y_] := Block[{t$95$0 = N[(y * N[(x - 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -0.85], t$95$0, If[LessEqual[y, 3e-113], N[(1.0 - y), $MachinePrecision], t$95$0]]]
\begin{array}{l}
\\
\begin{array}{l}
t_0 := y \cdot \left(x - 1\right)\\
\mathbf{if}\;y \leq -0.85:\\
\;\;\;\;t\_0\\
\mathbf{elif}\;y \leq 3 \cdot 10^{-113}:\\
\;\;\;\;1 - y\\
\mathbf{else}:\\
\;\;\;\;t\_0\\
\end{array}
\end{array}
if y < -0.849999999999999978 or 3.0000000000000001e-113 < y Initial program 91.1%
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--.f6493.2
Applied rewrites93.2%
if -0.849999999999999978 < y < 3.0000000000000001e-113Initial program 50.6%
Taylor expanded in x around 0
lower--.f6483.9
Applied rewrites83.9%
Final simplification89.4%
(FPCore (x y) :precision binary64 (if (<= x -4.5e+27) (* y x) (if (<= x 2.6e+33) (- 1.0 y) (* y x))))
double code(double x, double y) {
double tmp;
if (x <= -4.5e+27) {
tmp = y * x;
} else if (x <= 2.6e+33) {
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 <= (-4.5d+27)) then
tmp = y * x
else if (x <= 2.6d+33) 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 <= -4.5e+27) {
tmp = y * x;
} else if (x <= 2.6e+33) {
tmp = 1.0 - y;
} else {
tmp = y * x;
}
return tmp;
}
def code(x, y): tmp = 0 if x <= -4.5e+27: tmp = y * x elif x <= 2.6e+33: tmp = 1.0 - y else: tmp = y * x return tmp
function code(x, y) tmp = 0.0 if (x <= -4.5e+27) tmp = Float64(y * x); elseif (x <= 2.6e+33) 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 <= -4.5e+27) tmp = y * x; elseif (x <= 2.6e+33) tmp = 1.0 - y; else tmp = y * x; end tmp_2 = tmp; end
code[x_, y_] := If[LessEqual[x, -4.5e+27], N[(y * x), $MachinePrecision], If[LessEqual[x, 2.6e+33], N[(1.0 - y), $MachinePrecision], N[(y * x), $MachinePrecision]]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;x \leq -4.5 \cdot 10^{+27}:\\
\;\;\;\;y \cdot x\\
\mathbf{elif}\;x \leq 2.6 \cdot 10^{+33}:\\
\;\;\;\;1 - y\\
\mathbf{else}:\\
\;\;\;\;y \cdot x\\
\end{array}
\end{array}
if x < -4.4999999999999999e27 or 2.5999999999999997e33 < x Initial program 53.3%
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-*.f6474.8
Applied rewrites74.8%
if -4.4999999999999999e27 < x < 2.5999999999999997e33Initial program 95.3%
Taylor expanded in x around 0
lower--.f6496.4
Applied rewrites96.4%
Final simplification85.8%
(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 74.6%
Taylor expanded in x around 0
lower--.f6462.3
Applied rewrites62.3%
(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 74.6%
Taylor expanded in y around 0
Applied rewrites38.6%
(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 2024277
(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))))