
(FPCore (x y) :precision binary64 (+ x (/ (- x y) 2.0)))
double code(double x, double y) {
return x + ((x - y) / 2.0);
}
real(8) function code(x, y)
real(8), intent (in) :: x
real(8), intent (in) :: y
code = x + ((x - y) / 2.0d0)
end function
public static double code(double x, double y) {
return x + ((x - y) / 2.0);
}
def code(x, y): return x + ((x - y) / 2.0)
function code(x, y) return Float64(x + Float64(Float64(x - y) / 2.0)) end
function tmp = code(x, y) tmp = x + ((x - y) / 2.0); end
code[x_, y_] := N[(x + N[(N[(x - y), $MachinePrecision] / 2.0), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
x + \frac{x - y}{2}
\end{array}
Sampling outcomes in binary64 precision:
Herbie found 5 alternatives:
| Alternative | Accuracy | Speedup |
|---|
(FPCore (x y) :precision binary64 (+ x (/ (- x y) 2.0)))
double code(double x, double y) {
return x + ((x - y) / 2.0);
}
real(8) function code(x, y)
real(8), intent (in) :: x
real(8), intent (in) :: y
code = x + ((x - y) / 2.0d0)
end function
public static double code(double x, double y) {
return x + ((x - y) / 2.0);
}
def code(x, y): return x + ((x - y) / 2.0)
function code(x, y) return Float64(x + Float64(Float64(x - y) / 2.0)) end
function tmp = code(x, y) tmp = x + ((x - y) / 2.0); end
code[x_, y_] := N[(x + N[(N[(x - y), $MachinePrecision] / 2.0), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
x + \frac{x - y}{2}
\end{array}
(FPCore (x y) :precision binary64 (fma x 1.5 (* y -0.5)))
double code(double x, double y) {
return fma(x, 1.5, (y * -0.5));
}
function code(x, y) return fma(x, 1.5, Float64(y * -0.5)) end
code[x_, y_] := N[(x * 1.5 + N[(y * -0.5), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
\mathsf{fma}\left(x, 1.5, y \cdot -0.5\right)
\end{array}
Initial program 99.9%
lift-+.f64N/A
+-commutativeN/A
lift-/.f64N/A
lift--.f64N/A
div-subN/A
sub-negN/A
associate-+l+N/A
div-invN/A
lower-fma.f64N/A
metadata-evalN/A
div-invN/A
distribute-rgt-neg-inN/A
metadata-evalN/A
metadata-evalN/A
metadata-evalN/A
metadata-evalN/A
lower-fma.f64N/A
metadata-evalN/A
metadata-eval99.9
Applied rewrites99.9%
lift-fma.f64N/A
lift-fma.f64N/A
lift-*.f64N/A
+-commutativeN/A
associate-+r+N/A
*-commutativeN/A
distribute-lft1-inN/A
metadata-evalN/A
*-commutativeN/A
lower-fma.f64100.0
lift-*.f64N/A
*-commutativeN/A
lower-*.f64100.0
Applied rewrites100.0%
Final simplification100.0%
(FPCore (x y) :precision binary64 (if (<= x -0.105) (* 1.5 x) (if (<= x 2.3e+113) (+ (* y -0.5) x) (* 1.5 x))))
double code(double x, double y) {
double tmp;
if (x <= -0.105) {
tmp = 1.5 * x;
} else if (x <= 2.3e+113) {
tmp = (y * -0.5) + x;
} else {
tmp = 1.5 * x;
}
return tmp;
}
real(8) function code(x, y)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8) :: tmp
if (x <= (-0.105d0)) then
tmp = 1.5d0 * x
else if (x <= 2.3d+113) then
tmp = (y * (-0.5d0)) + x
else
tmp = 1.5d0 * x
end if
code = tmp
end function
public static double code(double x, double y) {
double tmp;
if (x <= -0.105) {
tmp = 1.5 * x;
} else if (x <= 2.3e+113) {
tmp = (y * -0.5) + x;
} else {
tmp = 1.5 * x;
}
return tmp;
}
def code(x, y): tmp = 0 if x <= -0.105: tmp = 1.5 * x elif x <= 2.3e+113: tmp = (y * -0.5) + x else: tmp = 1.5 * x return tmp
function code(x, y) tmp = 0.0 if (x <= -0.105) tmp = Float64(1.5 * x); elseif (x <= 2.3e+113) tmp = Float64(Float64(y * -0.5) + x); else tmp = Float64(1.5 * x); end return tmp end
function tmp_2 = code(x, y) tmp = 0.0; if (x <= -0.105) tmp = 1.5 * x; elseif (x <= 2.3e+113) tmp = (y * -0.5) + x; else tmp = 1.5 * x; end tmp_2 = tmp; end
code[x_, y_] := If[LessEqual[x, -0.105], N[(1.5 * x), $MachinePrecision], If[LessEqual[x, 2.3e+113], N[(N[(y * -0.5), $MachinePrecision] + x), $MachinePrecision], N[(1.5 * x), $MachinePrecision]]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;x \leq -0.105:\\
\;\;\;\;1.5 \cdot x\\
\mathbf{elif}\;x \leq 2.3 \cdot 10^{+113}:\\
\;\;\;\;y \cdot -0.5 + x\\
\mathbf{else}:\\
\;\;\;\;1.5 \cdot x\\
\end{array}
\end{array}
if x < -0.104999999999999996 or 2.29999999999999997e113 < x Initial program 99.8%
Taylor expanded in y around 0
distribute-rgt1-inN/A
metadata-evalN/A
lower-*.f6487.6
Applied rewrites87.6%
if -0.104999999999999996 < x < 2.29999999999999997e113Initial program 99.9%
Taylor expanded in y around inf
*-commutativeN/A
lower-*.f6478.3
Applied rewrites78.3%
Final simplification82.5%
(FPCore (x y) :precision binary64 (if (<= x -0.105) (* 1.5 x) (if (<= x 1.25e+98) (* y -0.5) (* 1.5 x))))
double code(double x, double y) {
double tmp;
if (x <= -0.105) {
tmp = 1.5 * x;
} else if (x <= 1.25e+98) {
tmp = y * -0.5;
} else {
tmp = 1.5 * x;
}
return tmp;
}
real(8) function code(x, y)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8) :: tmp
if (x <= (-0.105d0)) then
tmp = 1.5d0 * x
else if (x <= 1.25d+98) then
tmp = y * (-0.5d0)
else
tmp = 1.5d0 * x
end if
code = tmp
end function
public static double code(double x, double y) {
double tmp;
if (x <= -0.105) {
tmp = 1.5 * x;
} else if (x <= 1.25e+98) {
tmp = y * -0.5;
} else {
tmp = 1.5 * x;
}
return tmp;
}
def code(x, y): tmp = 0 if x <= -0.105: tmp = 1.5 * x elif x <= 1.25e+98: tmp = y * -0.5 else: tmp = 1.5 * x return tmp
function code(x, y) tmp = 0.0 if (x <= -0.105) tmp = Float64(1.5 * x); elseif (x <= 1.25e+98) tmp = Float64(y * -0.5); else tmp = Float64(1.5 * x); end return tmp end
function tmp_2 = code(x, y) tmp = 0.0; if (x <= -0.105) tmp = 1.5 * x; elseif (x <= 1.25e+98) tmp = y * -0.5; else tmp = 1.5 * x; end tmp_2 = tmp; end
code[x_, y_] := If[LessEqual[x, -0.105], N[(1.5 * x), $MachinePrecision], If[LessEqual[x, 1.25e+98], N[(y * -0.5), $MachinePrecision], N[(1.5 * x), $MachinePrecision]]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;x \leq -0.105:\\
\;\;\;\;1.5 \cdot x\\
\mathbf{elif}\;x \leq 1.25 \cdot 10^{+98}:\\
\;\;\;\;y \cdot -0.5\\
\mathbf{else}:\\
\;\;\;\;1.5 \cdot x\\
\end{array}
\end{array}
if x < -0.104999999999999996 or 1.25e98 < x Initial program 99.8%
Taylor expanded in y around 0
distribute-rgt1-inN/A
metadata-evalN/A
lower-*.f6487.0
Applied rewrites87.0%
if -0.104999999999999996 < x < 1.25e98Initial program 99.9%
Taylor expanded in y around inf
*-commutativeN/A
lower-*.f6474.8
Applied rewrites74.8%
(FPCore (x y) :precision binary64 (fma (- y x) -0.5 x))
double code(double x, double y) {
return fma((y - x), -0.5, x);
}
function code(x, y) return fma(Float64(y - x), -0.5, x) end
code[x_, y_] := N[(N[(y - x), $MachinePrecision] * -0.5 + x), $MachinePrecision]
\begin{array}{l}
\\
\mathsf{fma}\left(y - x, -0.5, x\right)
\end{array}
Initial program 99.9%
lift-+.f64N/A
+-commutativeN/A
lift-/.f64N/A
frac-2negN/A
div-invN/A
lower-fma.f64N/A
neg-sub0N/A
lift--.f64N/A
sub-negN/A
+-commutativeN/A
associate--r+N/A
neg-sub0N/A
remove-double-negN/A
lower--.f64N/A
metadata-evalN/A
metadata-eval99.9
Applied rewrites99.9%
(FPCore (x y) :precision binary64 (* 1.5 x))
double code(double x, double y) {
return 1.5 * x;
}
real(8) function code(x, y)
real(8), intent (in) :: x
real(8), intent (in) :: y
code = 1.5d0 * x
end function
public static double code(double x, double y) {
return 1.5 * x;
}
def code(x, y): return 1.5 * x
function code(x, y) return Float64(1.5 * x) end
function tmp = code(x, y) tmp = 1.5 * x; end
code[x_, y_] := N[(1.5 * x), $MachinePrecision]
\begin{array}{l}
\\
1.5 \cdot x
\end{array}
Initial program 99.9%
Taylor expanded in y around 0
distribute-rgt1-inN/A
metadata-evalN/A
lower-*.f6454.7
Applied rewrites54.7%
(FPCore (x y) :precision binary64 (- (* 1.5 x) (* 0.5 y)))
double code(double x, double y) {
return (1.5 * x) - (0.5 * y);
}
real(8) function code(x, y)
real(8), intent (in) :: x
real(8), intent (in) :: y
code = (1.5d0 * x) - (0.5d0 * y)
end function
public static double code(double x, double y) {
return (1.5 * x) - (0.5 * y);
}
def code(x, y): return (1.5 * x) - (0.5 * y)
function code(x, y) return Float64(Float64(1.5 * x) - Float64(0.5 * y)) end
function tmp = code(x, y) tmp = (1.5 * x) - (0.5 * y); end
code[x_, y_] := N[(N[(1.5 * x), $MachinePrecision] - N[(0.5 * y), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
1.5 \cdot x - 0.5 \cdot y
\end{array}
herbie shell --seed 2024235
(FPCore (x y)
:name "Graphics.Rendering.Chart.Axis.Types:hBufferRect from Chart-1.5.3"
:precision binary64
:alt
(! :herbie-platform default (- (* 3/2 x) (* 1/2 y)))
(+ x (/ (- x y) 2.0)))