
(FPCore (x y) :precision binary64 (- (+ x y) (* x y)))
double code(double x, double y) {
return (x + y) - (x * y);
}
real(8) function code(x, y)
real(8), intent (in) :: x
real(8), intent (in) :: y
code = (x + y) - (x * y)
end function
public static double code(double x, double y) {
return (x + y) - (x * y);
}
def code(x, y): return (x + y) - (x * y)
function code(x, y) return Float64(Float64(x + y) - Float64(x * y)) end
function tmp = code(x, y) tmp = (x + y) - (x * y); end
code[x_, y_] := N[(N[(x + y), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
\left(x + y\right) - x \cdot y
\end{array}
Sampling outcomes in binary64 precision:
Herbie found 8 alternatives:
| Alternative | Accuracy | Speedup |
|---|
(FPCore (x y) :precision binary64 (- (+ x y) (* x y)))
double code(double x, double y) {
return (x + y) - (x * y);
}
real(8) function code(x, y)
real(8), intent (in) :: x
real(8), intent (in) :: y
code = (x + y) - (x * y)
end function
public static double code(double x, double y) {
return (x + y) - (x * y);
}
def code(x, y): return (x + y) - (x * y)
function code(x, y) return Float64(Float64(x + y) - Float64(x * y)) end
function tmp = code(x, y) tmp = (x + y) - (x * y); end
code[x_, y_] := N[(N[(x + y), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
\left(x + y\right) - x \cdot y
\end{array}
NOTE: x and y should be sorted in increasing order before calling this function. (FPCore (x y) :precision binary64 (fma x (- 1.0 y) y))
assert(x < y);
double code(double x, double y) {
return fma(x, (1.0 - y), y);
}
x, y = sort([x, y]) function code(x, y) return fma(x, Float64(1.0 - y), y) end
NOTE: x and y should be sorted in increasing order before calling this function. code[x_, y_] := N[(x * N[(1.0 - y), $MachinePrecision] + y), $MachinePrecision]
\begin{array}{l}
[x, y] = \mathsf{sort}([x, y])\\
\\
\mathsf{fma}\left(x, 1 - y, y\right)
\end{array}
Initial program 100.0%
+-commutative100.0%
*-commutative100.0%
associate--l+100.0%
+-commutative100.0%
*-lft-identity100.0%
metadata-eval100.0%
distribute-rgt-out--100.0%
fma-define100.0%
metadata-eval100.0%
Simplified100.0%
NOTE: x and y should be sorted in increasing order before calling this function. (FPCore (x y) :precision binary64 (let* ((t_0 (* x (- y)))) (if (<= x -1.9e+207) t_0 (if (<= x -8e-102) x (if (<= x 1.0) y t_0)))))
assert(x < y);
double code(double x, double y) {
double t_0 = x * -y;
double tmp;
if (x <= -1.9e+207) {
tmp = t_0;
} else if (x <= -8e-102) {
tmp = x;
} else if (x <= 1.0) {
tmp = y;
} else {
tmp = t_0;
}
return tmp;
}
NOTE: x and y should be sorted in increasing order before calling this function.
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 * -y
if (x <= (-1.9d+207)) then
tmp = t_0
else if (x <= (-8d-102)) then
tmp = x
else if (x <= 1.0d0) then
tmp = y
else
tmp = t_0
end if
code = tmp
end function
assert x < y;
public static double code(double x, double y) {
double t_0 = x * -y;
double tmp;
if (x <= -1.9e+207) {
tmp = t_0;
} else if (x <= -8e-102) {
tmp = x;
} else if (x <= 1.0) {
tmp = y;
} else {
tmp = t_0;
}
return tmp;
}
[x, y] = sort([x, y]) def code(x, y): t_0 = x * -y tmp = 0 if x <= -1.9e+207: tmp = t_0 elif x <= -8e-102: tmp = x elif x <= 1.0: tmp = y else: tmp = t_0 return tmp
x, y = sort([x, y]) function code(x, y) t_0 = Float64(x * Float64(-y)) tmp = 0.0 if (x <= -1.9e+207) tmp = t_0; elseif (x <= -8e-102) tmp = x; elseif (x <= 1.0) tmp = y; else tmp = t_0; end return tmp end
x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y)
t_0 = x * -y;
tmp = 0.0;
if (x <= -1.9e+207)
tmp = t_0;
elseif (x <= -8e-102)
tmp = x;
elseif (x <= 1.0)
tmp = y;
else
tmp = t_0;
end
tmp_2 = tmp;
end
NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_] := Block[{t$95$0 = N[(x * (-y)), $MachinePrecision]}, If[LessEqual[x, -1.9e+207], t$95$0, If[LessEqual[x, -8e-102], x, If[LessEqual[x, 1.0], y, t$95$0]]]]
\begin{array}{l}
[x, y] = \mathsf{sort}([x, y])\\
\\
\begin{array}{l}
t_0 := x \cdot \left(-y\right)\\
\mathbf{if}\;x \leq -1.9 \cdot 10^{+207}:\\
\;\;\;\;t\_0\\
\mathbf{elif}\;x \leq -8 \cdot 10^{-102}:\\
\;\;\;\;x\\
\mathbf{elif}\;x \leq 1:\\
\;\;\;\;y\\
\mathbf{else}:\\
\;\;\;\;t\_0\\
\end{array}
\end{array}
if x < -1.89999999999999993e207 or 1 < x Initial program 100.0%
Taylor expanded in y around inf 49.2%
Taylor expanded in x around inf 48.6%
associate-*r*48.6%
neg-mul-148.6%
*-commutative48.6%
Simplified48.6%
if -1.89999999999999993e207 < x < -7.99999999999999946e-102Initial program 100.0%
Taylor expanded in x around inf 78.8%
Taylor expanded in y around 0 46.5%
if -7.99999999999999946e-102 < x < 1Initial program 100.0%
Taylor expanded in y around inf 68.2%
Taylor expanded in x around 0 67.7%
Final simplification56.8%
NOTE: x and y should be sorted in increasing order before calling this function. (FPCore (x y) :precision binary64 (if (<= y -1.0) (* x (- y)) (if (<= y 1.16e-132) x (* y (- 1.0 x)))))
assert(x < y);
double code(double x, double y) {
double tmp;
if (y <= -1.0) {
tmp = x * -y;
} else if (y <= 1.16e-132) {
tmp = x;
} else {
tmp = y * (1.0 - x);
}
return tmp;
}
NOTE: x and y should be sorted in increasing order before calling this function.
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 * -y
else if (y <= 1.16d-132) then
tmp = x
else
tmp = y * (1.0d0 - x)
end if
code = tmp
end function
assert x < y;
public static double code(double x, double y) {
double tmp;
if (y <= -1.0) {
tmp = x * -y;
} else if (y <= 1.16e-132) {
tmp = x;
} else {
tmp = y * (1.0 - x);
}
return tmp;
}
[x, y] = sort([x, y]) def code(x, y): tmp = 0 if y <= -1.0: tmp = x * -y elif y <= 1.16e-132: tmp = x else: tmp = y * (1.0 - x) return tmp
x, y = sort([x, y]) function code(x, y) tmp = 0.0 if (y <= -1.0) tmp = Float64(x * Float64(-y)); elseif (y <= 1.16e-132) tmp = x; else tmp = Float64(y * Float64(1.0 - x)); end return tmp end
x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y)
tmp = 0.0;
if (y <= -1.0)
tmp = x * -y;
elseif (y <= 1.16e-132)
tmp = x;
else
tmp = y * (1.0 - x);
end
tmp_2 = tmp;
end
NOTE: x and y should be sorted in increasing order before calling this function. code[x_, y_] := If[LessEqual[y, -1.0], N[(x * (-y)), $MachinePrecision], If[LessEqual[y, 1.16e-132], x, N[(y * N[(1.0 - x), $MachinePrecision]), $MachinePrecision]]]
\begin{array}{l}
[x, y] = \mathsf{sort}([x, y])\\
\\
\begin{array}{l}
\mathbf{if}\;y \leq -1:\\
\;\;\;\;x \cdot \left(-y\right)\\
\mathbf{elif}\;y \leq 1.16 \cdot 10^{-132}:\\
\;\;\;\;x\\
\mathbf{else}:\\
\;\;\;\;y \cdot \left(1 - x\right)\\
\end{array}
\end{array}
if y < -1Initial program 100.0%
Taylor expanded in y around inf 98.7%
Taylor expanded in x around inf 54.3%
associate-*r*54.3%
neg-mul-154.3%
*-commutative54.3%
Simplified54.3%
if -1 < y < 1.1599999999999999e-132Initial program 100.0%
Taylor expanded in x around inf 77.6%
Taylor expanded in y around 0 77.1%
if 1.1599999999999999e-132 < y Initial program 99.9%
Taylor expanded in y around inf 82.3%
Final simplification73.5%
NOTE: x and y should be sorted in increasing order before calling this function. (FPCore (x y) :precision binary64 (if (<= x -1.95e-117) (- x (* x y)) (* y (- 1.0 x))))
assert(x < y);
double code(double x, double y) {
double tmp;
if (x <= -1.95e-117) {
tmp = x - (x * y);
} else {
tmp = y * (1.0 - x);
}
return tmp;
}
NOTE: x and y should be sorted in increasing order before calling this function.
real(8) function code(x, y)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8) :: tmp
if (x <= (-1.95d-117)) then
tmp = x - (x * y)
else
tmp = y * (1.0d0 - x)
end if
code = tmp
end function
assert x < y;
public static double code(double x, double y) {
double tmp;
if (x <= -1.95e-117) {
tmp = x - (x * y);
} else {
tmp = y * (1.0 - x);
}
return tmp;
}
[x, y] = sort([x, y]) def code(x, y): tmp = 0 if x <= -1.95e-117: tmp = x - (x * y) else: tmp = y * (1.0 - x) return tmp
x, y = sort([x, y]) function code(x, y) tmp = 0.0 if (x <= -1.95e-117) tmp = Float64(x - Float64(x * y)); else tmp = Float64(y * Float64(1.0 - x)); end return tmp end
x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y)
tmp = 0.0;
if (x <= -1.95e-117)
tmp = x - (x * y);
else
tmp = y * (1.0 - x);
end
tmp_2 = tmp;
end
NOTE: x and y should be sorted in increasing order before calling this function. code[x_, y_] := If[LessEqual[x, -1.95e-117], N[(x - N[(x * y), $MachinePrecision]), $MachinePrecision], N[(y * N[(1.0 - x), $MachinePrecision]), $MachinePrecision]]
\begin{array}{l}
[x, y] = \mathsf{sort}([x, y])\\
\\
\begin{array}{l}
\mathbf{if}\;x \leq -1.95 \cdot 10^{-117}:\\
\;\;\;\;x - x \cdot y\\
\mathbf{else}:\\
\;\;\;\;y \cdot \left(1 - x\right)\\
\end{array}
\end{array}
if x < -1.94999999999999996e-117Initial program 100.0%
Taylor expanded in x around inf 80.1%
if -1.94999999999999996e-117 < x Initial program 100.0%
Taylor expanded in y around inf 60.6%
NOTE: x and y should be sorted in increasing order before calling this function. (FPCore (x y) :precision binary64 (- (+ x y) (* x y)))
assert(x < y);
double code(double x, double y) {
return (x + y) - (x * y);
}
NOTE: x and y should be sorted in increasing order before calling this function.
real(8) function code(x, y)
real(8), intent (in) :: x
real(8), intent (in) :: y
code = (x + y) - (x * y)
end function
assert x < y;
public static double code(double x, double y) {
return (x + y) - (x * y);
}
[x, y] = sort([x, y]) def code(x, y): return (x + y) - (x * y)
x, y = sort([x, y]) function code(x, y) return Float64(Float64(x + y) - Float64(x * y)) end
x, y = num2cell(sort([x, y])){:}
function tmp = code(x, y)
tmp = (x + y) - (x * y);
end
NOTE: x and y should be sorted in increasing order before calling this function. code[x_, y_] := N[(N[(x + y), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
[x, y] = \mathsf{sort}([x, y])\\
\\
\left(x + y\right) - x \cdot y
\end{array}
Initial program 100.0%
NOTE: x and y should be sorted in increasing order before calling this function. (FPCore (x y) :precision binary64 (if (<= x -1e-101) x y))
assert(x < y);
double code(double x, double y) {
double tmp;
if (x <= -1e-101) {
tmp = x;
} else {
tmp = y;
}
return tmp;
}
NOTE: x and y should be sorted in increasing order before calling this function.
real(8) function code(x, y)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8) :: tmp
if (x <= (-1d-101)) then
tmp = x
else
tmp = y
end if
code = tmp
end function
assert x < y;
public static double code(double x, double y) {
double tmp;
if (x <= -1e-101) {
tmp = x;
} else {
tmp = y;
}
return tmp;
}
[x, y] = sort([x, y]) def code(x, y): tmp = 0 if x <= -1e-101: tmp = x else: tmp = y return tmp
x, y = sort([x, y]) function code(x, y) tmp = 0.0 if (x <= -1e-101) tmp = x; else tmp = y; end return tmp end
x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y)
tmp = 0.0;
if (x <= -1e-101)
tmp = x;
else
tmp = y;
end
tmp_2 = tmp;
end
NOTE: x and y should be sorted in increasing order before calling this function. code[x_, y_] := If[LessEqual[x, -1e-101], x, y]
\begin{array}{l}
[x, y] = \mathsf{sort}([x, y])\\
\\
\begin{array}{l}
\mathbf{if}\;x \leq -1 \cdot 10^{-101}:\\
\;\;\;\;x\\
\mathbf{else}:\\
\;\;\;\;y\\
\end{array}
\end{array}
if x < -1.00000000000000005e-101Initial program 100.0%
Taylor expanded in x around inf 83.5%
Taylor expanded in y around 0 46.1%
if -1.00000000000000005e-101 < x Initial program 100.0%
Taylor expanded in y around inf 61.2%
Taylor expanded in x around 0 46.0%
NOTE: x and y should be sorted in increasing order before calling this function. (FPCore (x y) :precision binary64 x)
assert(x < y);
double code(double x, double y) {
return x;
}
NOTE: x and y should be sorted in increasing order before calling this function.
real(8) function code(x, y)
real(8), intent (in) :: x
real(8), intent (in) :: y
code = x
end function
assert x < y;
public static double code(double x, double y) {
return x;
}
[x, y] = sort([x, y]) def code(x, y): return x
x, y = sort([x, y]) function code(x, y) return x end
x, y = num2cell(sort([x, y])){:}
function tmp = code(x, y)
tmp = x;
end
NOTE: x and y should be sorted in increasing order before calling this function. code[x_, y_] := x
\begin{array}{l}
[x, y] = \mathsf{sort}([x, y])\\
\\
x
\end{array}
Initial program 100.0%
Taylor expanded in x around inf 64.4%
Taylor expanded in y around 0 42.3%
NOTE: x and y should be sorted in increasing order before calling this function. (FPCore (x y) :precision binary64 0.0)
assert(x < y);
double code(double x, double y) {
return 0.0;
}
NOTE: x and y should be sorted in increasing order before calling this function.
real(8) function code(x, y)
real(8), intent (in) :: x
real(8), intent (in) :: y
code = 0.0d0
end function
assert x < y;
public static double code(double x, double y) {
return 0.0;
}
[x, y] = sort([x, y]) def code(x, y): return 0.0
x, y = sort([x, y]) function code(x, y) return 0.0 end
x, y = num2cell(sort([x, y])){:}
function tmp = code(x, y)
tmp = 0.0;
end
NOTE: x and y should be sorted in increasing order before calling this function. code[x_, y_] := 0.0
\begin{array}{l}
[x, y] = \mathsf{sort}([x, y])\\
\\
0
\end{array}
Initial program 100.0%
Taylor expanded in y around inf 59.5%
Taylor expanded in x around inf 24.9%
associate-*r*24.9%
neg-mul-124.9%
*-commutative24.9%
Simplified24.9%
add-log-exp15.9%
add-sqr-sqrt15.9%
sqrt-unprod15.9%
exp-prod15.9%
add-sqr-sqrt7.9%
sqrt-unprod8.2%
sqr-neg8.2%
sqrt-unprod2.1%
add-sqr-sqrt2.3%
pow-flip2.3%
exp-prod2.0%
rgt-mult-inverse2.8%
metadata-eval2.8%
metadata-eval2.8%
Applied egg-rr2.8%
herbie shell --seed 2024191
(FPCore (x y)
:name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, A"
:precision binary64
(- (+ x y) (* x y)))