
(FPCore (x y z) :precision binary64 (+ (+ (+ (+ (+ x y) y) x) z) x))
double code(double x, double y, double z) {
return ((((x + y) + y) + x) + z) + x;
}
real(8) function code(x, y, z)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8), intent (in) :: z
code = ((((x + y) + y) + x) + z) + x
end function
public static double code(double x, double y, double z) {
return ((((x + y) + y) + x) + z) + x;
}
def code(x, y, z): return ((((x + y) + y) + x) + z) + x
function code(x, y, z) return Float64(Float64(Float64(Float64(Float64(x + y) + y) + x) + z) + x) end
function tmp = code(x, y, z) tmp = ((((x + y) + y) + x) + z) + x; end
code[x_, y_, z_] := N[(N[(N[(N[(N[(x + y), $MachinePrecision] + y), $MachinePrecision] + x), $MachinePrecision] + z), $MachinePrecision] + x), $MachinePrecision]
\begin{array}{l}
\\
\left(\left(\left(\left(x + y\right) + y\right) + x\right) + z\right) + x
\end{array}
Sampling outcomes in binary64 precision:
Herbie found 6 alternatives:
| Alternative | Accuracy | Speedup |
|---|
(FPCore (x y z) :precision binary64 (+ (+ (+ (+ (+ x y) y) x) z) x))
double code(double x, double y, double z) {
return ((((x + y) + y) + x) + z) + x;
}
real(8) function code(x, y, z)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8), intent (in) :: z
code = ((((x + y) + y) + x) + z) + x
end function
public static double code(double x, double y, double z) {
return ((((x + y) + y) + x) + z) + x;
}
def code(x, y, z): return ((((x + y) + y) + x) + z) + x
function code(x, y, z) return Float64(Float64(Float64(Float64(Float64(x + y) + y) + x) + z) + x) end
function tmp = code(x, y, z) tmp = ((((x + y) + y) + x) + z) + x; end
code[x_, y_, z_] := N[(N[(N[(N[(N[(x + y), $MachinePrecision] + y), $MachinePrecision] + x), $MachinePrecision] + z), $MachinePrecision] + x), $MachinePrecision]
\begin{array}{l}
\\
\left(\left(\left(\left(x + y\right) + y\right) + x\right) + z\right) + x
\end{array}
(FPCore (x y z) :precision binary64 (fma 3.0 x (fma 2.0 y z)))
double code(double x, double y, double z) {
return fma(3.0, x, fma(2.0, y, z));
}
function code(x, y, z) return fma(3.0, x, fma(2.0, y, z)) end
code[x_, y_, z_] := N[(3.0 * x + N[(2.0 * y + z), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
\mathsf{fma}\left(3, x, \mathsf{fma}\left(2, y, z\right)\right)
\end{array}
Initial program 99.9%
Taylor expanded in x around 0
associate-+r+N/A
+-commutativeN/A
lower-fma.f64N/A
+-commutativeN/A
lower-fma.f64100.0
Applied rewrites100.0%
(FPCore (x y z) :precision binary64 (if (or (<= x -1.35e-11) (not (<= x 2.7e+78))) (fma 3.0 x z) (fma 2.0 y z)))
double code(double x, double y, double z) {
double tmp;
if ((x <= -1.35e-11) || !(x <= 2.7e+78)) {
tmp = fma(3.0, x, z);
} else {
tmp = fma(2.0, y, z);
}
return tmp;
}
function code(x, y, z) tmp = 0.0 if ((x <= -1.35e-11) || !(x <= 2.7e+78)) tmp = fma(3.0, x, z); else tmp = fma(2.0, y, z); end return tmp end
code[x_, y_, z_] := If[Or[LessEqual[x, -1.35e-11], N[Not[LessEqual[x, 2.7e+78]], $MachinePrecision]], N[(3.0 * x + z), $MachinePrecision], N[(2.0 * y + z), $MachinePrecision]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;x \leq -1.35 \cdot 10^{-11} \lor \neg \left(x \leq 2.7 \cdot 10^{+78}\right):\\
\;\;\;\;\mathsf{fma}\left(3, x, z\right)\\
\mathbf{else}:\\
\;\;\;\;\mathsf{fma}\left(2, y, z\right)\\
\end{array}
\end{array}
if x < -1.35000000000000002e-11 or 2.70000000000000004e78 < x Initial program 99.9%
Taylor expanded in y around 0
+-commutativeN/A
associate-+r+N/A
distribute-rgt1-inN/A
metadata-evalN/A
lower-fma.f6486.8
Applied rewrites86.8%
if -1.35000000000000002e-11 < x < 2.70000000000000004e78Initial program 100.0%
Taylor expanded in x around 0
+-commutativeN/A
lower-fma.f6493.2
Applied rewrites93.2%
Final simplification90.9%
(FPCore (x y z) :precision binary64 (if (or (<= x -2e-11) (not (<= x 1.95e+143))) (* 3.0 x) (fma 2.0 y z)))
double code(double x, double y, double z) {
double tmp;
if ((x <= -2e-11) || !(x <= 1.95e+143)) {
tmp = 3.0 * x;
} else {
tmp = fma(2.0, y, z);
}
return tmp;
}
function code(x, y, z) tmp = 0.0 if ((x <= -2e-11) || !(x <= 1.95e+143)) tmp = Float64(3.0 * x); else tmp = fma(2.0, y, z); end return tmp end
code[x_, y_, z_] := If[Or[LessEqual[x, -2e-11], N[Not[LessEqual[x, 1.95e+143]], $MachinePrecision]], N[(3.0 * x), $MachinePrecision], N[(2.0 * y + z), $MachinePrecision]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;x \leq -2 \cdot 10^{-11} \lor \neg \left(x \leq 1.95 \cdot 10^{+143}\right):\\
\;\;\;\;3 \cdot x\\
\mathbf{else}:\\
\;\;\;\;\mathsf{fma}\left(2, y, z\right)\\
\end{array}
\end{array}
if x < -1.99999999999999988e-11 or 1.9499999999999999e143 < x Initial program 99.8%
Taylor expanded in x around inf
lower-*.f6469.8
Applied rewrites69.8%
if -1.99999999999999988e-11 < x < 1.9499999999999999e143Initial program 100.0%
Taylor expanded in x around 0
+-commutativeN/A
lower-fma.f6492.5
Applied rewrites92.5%
Final simplification85.2%
(FPCore (x y z) :precision binary64 (if (<= x -3.9e-22) (fma 3.0 x (+ y y)) (if (<= x 2.7e+78) (fma 2.0 y z) (fma 3.0 x z))))
double code(double x, double y, double z) {
double tmp;
if (x <= -3.9e-22) {
tmp = fma(3.0, x, (y + y));
} else if (x <= 2.7e+78) {
tmp = fma(2.0, y, z);
} else {
tmp = fma(3.0, x, z);
}
return tmp;
}
function code(x, y, z) tmp = 0.0 if (x <= -3.9e-22) tmp = fma(3.0, x, Float64(y + y)); elseif (x <= 2.7e+78) tmp = fma(2.0, y, z); else tmp = fma(3.0, x, z); end return tmp end
code[x_, y_, z_] := If[LessEqual[x, -3.9e-22], N[(3.0 * x + N[(y + y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.7e+78], N[(2.0 * y + z), $MachinePrecision], N[(3.0 * x + z), $MachinePrecision]]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;x \leq -3.9 \cdot 10^{-22}:\\
\;\;\;\;\mathsf{fma}\left(3, x, y + y\right)\\
\mathbf{elif}\;x \leq 2.7 \cdot 10^{+78}:\\
\;\;\;\;\mathsf{fma}\left(2, y, z\right)\\
\mathbf{else}:\\
\;\;\;\;\mathsf{fma}\left(3, x, z\right)\\
\end{array}
\end{array}
if x < -3.89999999999999998e-22Initial program 99.9%
Taylor expanded in z around 0
+-commutativeN/A
distribute-lft-outN/A
*-commutativeN/A
lower-fma.f64N/A
+-commutativeN/A
lower-+.f6484.5
Applied rewrites84.5%
Taylor expanded in x around 0
Applied rewrites84.6%
Applied rewrites84.6%
if -3.89999999999999998e-22 < x < 2.70000000000000004e78Initial program 100.0%
Taylor expanded in x around 0
+-commutativeN/A
lower-fma.f6493.7
Applied rewrites93.7%
if 2.70000000000000004e78 < x Initial program 99.9%
Taylor expanded in y around 0
+-commutativeN/A
associate-+r+N/A
distribute-rgt1-inN/A
metadata-evalN/A
lower-fma.f6492.4
Applied rewrites92.4%
(FPCore (x y z) :precision binary64 (if (or (<= x -1.35e-11) (not (<= x 2.7e+78))) (* 3.0 x) (+ y y)))
double code(double x, double y, double z) {
double tmp;
if ((x <= -1.35e-11) || !(x <= 2.7e+78)) {
tmp = 3.0 * x;
} else {
tmp = y + y;
}
return tmp;
}
real(8) function code(x, y, z)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8), intent (in) :: z
real(8) :: tmp
if ((x <= (-1.35d-11)) .or. (.not. (x <= 2.7d+78))) then
tmp = 3.0d0 * x
else
tmp = y + y
end if
code = tmp
end function
public static double code(double x, double y, double z) {
double tmp;
if ((x <= -1.35e-11) || !(x <= 2.7e+78)) {
tmp = 3.0 * x;
} else {
tmp = y + y;
}
return tmp;
}
def code(x, y, z): tmp = 0 if (x <= -1.35e-11) or not (x <= 2.7e+78): tmp = 3.0 * x else: tmp = y + y return tmp
function code(x, y, z) tmp = 0.0 if ((x <= -1.35e-11) || !(x <= 2.7e+78)) tmp = Float64(3.0 * x); else tmp = Float64(y + y); end return tmp end
function tmp_2 = code(x, y, z) tmp = 0.0; if ((x <= -1.35e-11) || ~((x <= 2.7e+78))) tmp = 3.0 * x; else tmp = y + y; end tmp_2 = tmp; end
code[x_, y_, z_] := If[Or[LessEqual[x, -1.35e-11], N[Not[LessEqual[x, 2.7e+78]], $MachinePrecision]], N[(3.0 * x), $MachinePrecision], N[(y + y), $MachinePrecision]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;x \leq -1.35 \cdot 10^{-11} \lor \neg \left(x \leq 2.7 \cdot 10^{+78}\right):\\
\;\;\;\;3 \cdot x\\
\mathbf{else}:\\
\;\;\;\;y + y\\
\end{array}
\end{array}
if x < -1.35000000000000002e-11 or 2.70000000000000004e78 < x Initial program 99.9%
Taylor expanded in x around inf
lower-*.f6464.2
Applied rewrites64.2%
if -1.35000000000000002e-11 < x < 2.70000000000000004e78Initial program 100.0%
Taylor expanded in z around 0
+-commutativeN/A
distribute-lft-outN/A
*-commutativeN/A
lower-fma.f64N/A
+-commutativeN/A
lower-+.f6457.5
Applied rewrites57.5%
Taylor expanded in x around 0
Applied rewrites51.6%
Applied rewrites51.6%
Final simplification56.2%
(FPCore (x y z) :precision binary64 (+ y y))
double code(double x, double y, double z) {
return y + y;
}
real(8) function code(x, y, z)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8), intent (in) :: z
code = y + y
end function
public static double code(double x, double y, double z) {
return y + y;
}
def code(x, y, z): return y + y
function code(x, y, z) return Float64(y + y) end
function tmp = code(x, y, z) tmp = y + y; end
code[x_, y_, z_] := N[(y + y), $MachinePrecision]
\begin{array}{l}
\\
y + y
\end{array}
Initial program 99.9%
Taylor expanded in z around 0
+-commutativeN/A
distribute-lft-outN/A
*-commutativeN/A
lower-fma.f64N/A
+-commutativeN/A
lower-+.f6464.6
Applied rewrites64.6%
Taylor expanded in x around 0
Applied rewrites38.5%
Applied rewrites38.5%
herbie shell --seed 2024342
(FPCore (x y z)
:name "Graphics.Rendering.Plot.Render.Plot.Legend:renderLegendInside from plot-0.2.3.4"
:precision binary64
(+ (+ (+ (+ (+ x y) y) x) z) x))