
(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 y x (- 1.0 y)))
double code(double x, double y) {
return fma(y, x, (1.0 - y));
}
function code(x, y) return fma(y, x, Float64(1.0 - y)) end
code[x_, y_] := N[(y * x + N[(1.0 - y), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
\mathsf{fma}\left(y, x, 1 - y\right)
\end{array}
Initial program 82.0%
Taylor expanded in x around 0
Applied rewrites100.0%
(FPCore (x y)
:precision binary64
(let* ((t_0 (+ x (* (- 1.0 x) (- 1.0 y)))))
(if (or (<= t_0 0.0) (not (<= t_0 10000000000000.0)))
(* (+ -1.0 x) y)
(- 1.0 y))))
double code(double x, double y) {
double t_0 = x + ((1.0 - x) * (1.0 - y));
double tmp;
if ((t_0 <= 0.0) || !(t_0 <= 10000000000000.0)) {
tmp = (-1.0 + x) * y;
} else {
tmp = 1.0 - 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 = x + ((1.0d0 - x) * (1.0d0 - y))
if ((t_0 <= 0.0d0) .or. (.not. (t_0 <= 10000000000000.0d0))) then
tmp = ((-1.0d0) + x) * y
else
tmp = 1.0d0 - y
end if
code = tmp
end function
public static double code(double x, double y) {
double t_0 = x + ((1.0 - x) * (1.0 - y));
double tmp;
if ((t_0 <= 0.0) || !(t_0 <= 10000000000000.0)) {
tmp = (-1.0 + x) * y;
} else {
tmp = 1.0 - y;
}
return tmp;
}
def code(x, y): t_0 = x + ((1.0 - x) * (1.0 - y)) tmp = 0 if (t_0 <= 0.0) or not (t_0 <= 10000000000000.0): tmp = (-1.0 + x) * y else: tmp = 1.0 - y return tmp
function code(x, y) t_0 = Float64(x + Float64(Float64(1.0 - x) * Float64(1.0 - y))) tmp = 0.0 if ((t_0 <= 0.0) || !(t_0 <= 10000000000000.0)) tmp = Float64(Float64(-1.0 + x) * y); else tmp = Float64(1.0 - y); end return tmp end
function tmp_2 = code(x, y) t_0 = x + ((1.0 - x) * (1.0 - y)); tmp = 0.0; if ((t_0 <= 0.0) || ~((t_0 <= 10000000000000.0))) tmp = (-1.0 + x) * y; else tmp = 1.0 - y; end tmp_2 = tmp; end
code[x_, y_] := Block[{t$95$0 = N[(x + N[(N[(1.0 - x), $MachinePrecision] * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$0, 0.0], N[Not[LessEqual[t$95$0, 10000000000000.0]], $MachinePrecision]], N[(N[(-1.0 + x), $MachinePrecision] * y), $MachinePrecision], N[(1.0 - y), $MachinePrecision]]]
\begin{array}{l}
\\
\begin{array}{l}
t_0 := x + \left(1 - x\right) \cdot \left(1 - y\right)\\
\mathbf{if}\;t\_0 \leq 0 \lor \neg \left(t\_0 \leq 10000000000000\right):\\
\;\;\;\;\left(-1 + x\right) \cdot y\\
\mathbf{else}:\\
\;\;\;\;1 - y\\
\end{array}
\end{array}
if (+.f64 x (*.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) y))) < 0.0 or 1e13 < (+.f64 x (*.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) y))) Initial program 73.4%
Taylor expanded in y around inf
*-commutativeN/A
associate-*r*N/A
lower-*.f64N/A
mul-1-negN/A
*-lft-identityN/A
metadata-evalN/A
fp-cancel-sign-sub-invN/A
distribute-neg-inN/A
metadata-evalN/A
mul-1-negN/A
remove-double-negN/A
lower-+.f6488.5
Applied rewrites88.5%
if 0.0 < (+.f64 x (*.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) y))) < 1e13Initial program 100.0%
Taylor expanded in x around 0
lower--.f6499.9
Applied rewrites99.9%
Final simplification92.2%
(FPCore (x y) :precision binary64 (if (or (<= x -1.5e+24) (not (<= x 480000.0))) (* y x) (- 1.0 y)))
double code(double x, double y) {
double tmp;
if ((x <= -1.5e+24) || !(x <= 480000.0)) {
tmp = y * x;
} else {
tmp = 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 <= (-1.5d+24)) .or. (.not. (x <= 480000.0d0))) then
tmp = y * x
else
tmp = 1.0d0 - y
end if
code = tmp
end function
public static double code(double x, double y) {
double tmp;
if ((x <= -1.5e+24) || !(x <= 480000.0)) {
tmp = y * x;
} else {
tmp = 1.0 - y;
}
return tmp;
}
def code(x, y): tmp = 0 if (x <= -1.5e+24) or not (x <= 480000.0): tmp = y * x else: tmp = 1.0 - y return tmp
function code(x, y) tmp = 0.0 if ((x <= -1.5e+24) || !(x <= 480000.0)) tmp = Float64(y * x); else tmp = Float64(1.0 - y); end return tmp end
function tmp_2 = code(x, y) tmp = 0.0; if ((x <= -1.5e+24) || ~((x <= 480000.0))) tmp = y * x; else tmp = 1.0 - y; end tmp_2 = tmp; end
code[x_, y_] := If[Or[LessEqual[x, -1.5e+24], N[Not[LessEqual[x, 480000.0]], $MachinePrecision]], N[(y * x), $MachinePrecision], N[(1.0 - y), $MachinePrecision]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;x \leq -1.5 \cdot 10^{+24} \lor \neg \left(x \leq 480000\right):\\
\;\;\;\;y \cdot x\\
\mathbf{else}:\\
\;\;\;\;1 - y\\
\end{array}
\end{array}
if x < -1.49999999999999997e24 or 4.8e5 < x Initial program 57.5%
Taylor expanded in x around inf
fp-cancel-sign-sub-invN/A
metadata-evalN/A
*-lft-identityN/A
associate--r-N/A
metadata-evalN/A
+-lft-identityN/A
*-commutativeN/A
lower-*.f6482.0
Applied rewrites82.0%
if -1.49999999999999997e24 < x < 4.8e5Initial program 99.3%
Taylor expanded in x around 0
lower--.f6498.7
Applied rewrites98.7%
Final simplification91.8%
(FPCore (x y) :precision binary64 (if (or (<= y -1.0) (not (<= y 245000.0))) (- y) 1.0))
double code(double x, double y) {
double tmp;
if ((y <= -1.0) || !(y <= 245000.0)) {
tmp = -y;
} else {
tmp = 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 <= (-1.0d0)) .or. (.not. (y <= 245000.0d0))) then
tmp = -y
else
tmp = 1.0d0
end if
code = tmp
end function
public static double code(double x, double y) {
double tmp;
if ((y <= -1.0) || !(y <= 245000.0)) {
tmp = -y;
} else {
tmp = 1.0;
}
return tmp;
}
def code(x, y): tmp = 0 if (y <= -1.0) or not (y <= 245000.0): tmp = -y else: tmp = 1.0 return tmp
function code(x, y) tmp = 0.0 if ((y <= -1.0) || !(y <= 245000.0)) tmp = Float64(-y); else tmp = 1.0; end return tmp end
function tmp_2 = code(x, y) tmp = 0.0; if ((y <= -1.0) || ~((y <= 245000.0))) tmp = -y; else tmp = 1.0; end tmp_2 = tmp; end
code[x_, y_] := If[Or[LessEqual[y, -1.0], N[Not[LessEqual[y, 245000.0]], $MachinePrecision]], (-y), 1.0]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 245000\right):\\
\;\;\;\;-y\\
\mathbf{else}:\\
\;\;\;\;1\\
\end{array}
\end{array}
if y < -1 or 245000 < y Initial program 100.0%
Taylor expanded in y around inf
*-commutativeN/A
associate-*r*N/A
lower-*.f64N/A
mul-1-negN/A
*-lft-identityN/A
metadata-evalN/A
fp-cancel-sign-sub-invN/A
distribute-neg-inN/A
metadata-evalN/A
mul-1-negN/A
remove-double-negN/A
lower-+.f6499.8
Applied rewrites99.8%
Taylor expanded in x around 0
Applied rewrites53.6%
if -1 < y < 245000Initial program 64.9%
Taylor expanded in x around 0
Applied rewrites100.0%
Taylor expanded in y around 0
Applied rewrites75.0%
Final simplification64.5%
(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 82.0%
Taylor expanded in x around 0
lower--.f6466.1
Applied rewrites66.1%
(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 82.0%
Taylor expanded in x around 0
Applied rewrites100.0%
Taylor expanded in y around 0
Applied rewrites39.7%
(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 2024326
(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))))