
(FPCore (x y z) :precision binary64 (+ (* x (+ y z)) (* z 5.0)))
double code(double x, double y, double z) {
return (x * (y + z)) + (z * 5.0);
}
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 + z)) + (z * 5.0d0)
end function
public static double code(double x, double y, double z) {
return (x * (y + z)) + (z * 5.0);
}
def code(x, y, z): return (x * (y + z)) + (z * 5.0)
function code(x, y, z) return Float64(Float64(x * Float64(y + z)) + Float64(z * 5.0)) end
function tmp = code(x, y, z) tmp = (x * (y + z)) + (z * 5.0); end
code[x_, y_, z_] := N[(N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision] + N[(z * 5.0), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
x \cdot \left(y + z\right) + z \cdot 5
\end{array}
Sampling outcomes in binary64 precision:
Herbie found 7 alternatives:
| Alternative | Accuracy | Speedup |
|---|
(FPCore (x y z) :precision binary64 (+ (* x (+ y z)) (* z 5.0)))
double code(double x, double y, double z) {
return (x * (y + z)) + (z * 5.0);
}
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 + z)) + (z * 5.0d0)
end function
public static double code(double x, double y, double z) {
return (x * (y + z)) + (z * 5.0);
}
def code(x, y, z): return (x * (y + z)) + (z * 5.0)
function code(x, y, z) return Float64(Float64(x * Float64(y + z)) + Float64(z * 5.0)) end
function tmp = code(x, y, z) tmp = (x * (y + z)) + (z * 5.0); end
code[x_, y_, z_] := N[(N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision] + N[(z * 5.0), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
x \cdot \left(y + z\right) + z \cdot 5
\end{array}
(FPCore (x y z) :precision binary64 (fma z 5.0 (* x (+ z y))))
double code(double x, double y, double z) {
return fma(z, 5.0, (x * (z + y)));
}
function code(x, y, z) return fma(z, 5.0, Float64(x * Float64(z + y))) end
code[x_, y_, z_] := N[(z * 5.0 + N[(x * N[(z + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
\mathsf{fma}\left(z, 5, x \cdot \left(z + y\right)\right)
\end{array}
Initial program 99.9%
+-commutative99.9%
fma-def100.0%
Applied egg-rr100.0%
Final simplification100.0%
(FPCore (x y z)
:precision binary64
(if (<= x -3.5e-144)
(* x y)
(if (<= x 2.1e-7)
(* z 5.0)
(if (or (<= x 1.2e+249) (not (<= x 2.9e+280))) (* x y) (* z x)))))
double code(double x, double y, double z) {
double tmp;
if (x <= -3.5e-144) {
tmp = x * y;
} else if (x <= 2.1e-7) {
tmp = z * 5.0;
} else if ((x <= 1.2e+249) || !(x <= 2.9e+280)) {
tmp = x * y;
} else {
tmp = z * x;
}
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 <= (-3.5d-144)) then
tmp = x * y
else if (x <= 2.1d-7) then
tmp = z * 5.0d0
else if ((x <= 1.2d+249) .or. (.not. (x <= 2.9d+280))) then
tmp = x * y
else
tmp = z * x
end if
code = tmp
end function
public static double code(double x, double y, double z) {
double tmp;
if (x <= -3.5e-144) {
tmp = x * y;
} else if (x <= 2.1e-7) {
tmp = z * 5.0;
} else if ((x <= 1.2e+249) || !(x <= 2.9e+280)) {
tmp = x * y;
} else {
tmp = z * x;
}
return tmp;
}
def code(x, y, z): tmp = 0 if x <= -3.5e-144: tmp = x * y elif x <= 2.1e-7: tmp = z * 5.0 elif (x <= 1.2e+249) or not (x <= 2.9e+280): tmp = x * y else: tmp = z * x return tmp
function code(x, y, z) tmp = 0.0 if (x <= -3.5e-144) tmp = Float64(x * y); elseif (x <= 2.1e-7) tmp = Float64(z * 5.0); elseif ((x <= 1.2e+249) || !(x <= 2.9e+280)) tmp = Float64(x * y); else tmp = Float64(z * x); end return tmp end
function tmp_2 = code(x, y, z) tmp = 0.0; if (x <= -3.5e-144) tmp = x * y; elseif (x <= 2.1e-7) tmp = z * 5.0; elseif ((x <= 1.2e+249) || ~((x <= 2.9e+280))) tmp = x * y; else tmp = z * x; end tmp_2 = tmp; end
code[x_, y_, z_] := If[LessEqual[x, -3.5e-144], N[(x * y), $MachinePrecision], If[LessEqual[x, 2.1e-7], N[(z * 5.0), $MachinePrecision], If[Or[LessEqual[x, 1.2e+249], N[Not[LessEqual[x, 2.9e+280]], $MachinePrecision]], N[(x * y), $MachinePrecision], N[(z * x), $MachinePrecision]]]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;x \leq -3.5 \cdot 10^{-144}:\\
\;\;\;\;x \cdot y\\
\mathbf{elif}\;x \leq 2.1 \cdot 10^{-7}:\\
\;\;\;\;z \cdot 5\\
\mathbf{elif}\;x \leq 1.2 \cdot 10^{+249} \lor \neg \left(x \leq 2.9 \cdot 10^{+280}\right):\\
\;\;\;\;x \cdot y\\
\mathbf{else}:\\
\;\;\;\;z \cdot x\\
\end{array}
\end{array}
if x < -3.4999999999999998e-144 or 2.1e-7 < x < 1.2e249 or 2.89999999999999985e280 < x Initial program 99.9%
Taylor expanded in y around inf 61.0%
if -3.4999999999999998e-144 < x < 2.1e-7Initial program 99.9%
Taylor expanded in x around 0 85.2%
if 1.2e249 < x < 2.89999999999999985e280Initial program 100.0%
Taylor expanded in x around inf 100.0%
+-commutative100.0%
Simplified100.0%
Taylor expanded in z around inf 78.6%
Final simplification70.8%
(FPCore (x y z) :precision binary64 (if (or (<= x -3.5e-144) (not (<= x 1.85e-7))) (* x (+ z y)) (* z 5.0)))
double code(double x, double y, double z) {
double tmp;
if ((x <= -3.5e-144) || !(x <= 1.85e-7)) {
tmp = x * (z + y);
} else {
tmp = z * 5.0;
}
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 <= (-3.5d-144)) .or. (.not. (x <= 1.85d-7))) then
tmp = x * (z + y)
else
tmp = z * 5.0d0
end if
code = tmp
end function
public static double code(double x, double y, double z) {
double tmp;
if ((x <= -3.5e-144) || !(x <= 1.85e-7)) {
tmp = x * (z + y);
} else {
tmp = z * 5.0;
}
return tmp;
}
def code(x, y, z): tmp = 0 if (x <= -3.5e-144) or not (x <= 1.85e-7): tmp = x * (z + y) else: tmp = z * 5.0 return tmp
function code(x, y, z) tmp = 0.0 if ((x <= -3.5e-144) || !(x <= 1.85e-7)) tmp = Float64(x * Float64(z + y)); else tmp = Float64(z * 5.0); end return tmp end
function tmp_2 = code(x, y, z) tmp = 0.0; if ((x <= -3.5e-144) || ~((x <= 1.85e-7))) tmp = x * (z + y); else tmp = z * 5.0; end tmp_2 = tmp; end
code[x_, y_, z_] := If[Or[LessEqual[x, -3.5e-144], N[Not[LessEqual[x, 1.85e-7]], $MachinePrecision]], N[(x * N[(z + y), $MachinePrecision]), $MachinePrecision], N[(z * 5.0), $MachinePrecision]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;x \leq -3.5 \cdot 10^{-144} \lor \neg \left(x \leq 1.85 \cdot 10^{-7}\right):\\
\;\;\;\;x \cdot \left(z + y\right)\\
\mathbf{else}:\\
\;\;\;\;z \cdot 5\\
\end{array}
\end{array}
if x < -3.4999999999999998e-144 or 1.85000000000000002e-7 < x Initial program 100.0%
Taylor expanded in x around inf 92.0%
+-commutative92.0%
Simplified92.0%
if -3.4999999999999998e-144 < x < 1.85000000000000002e-7Initial program 99.9%
Taylor expanded in x around 0 85.2%
Final simplification89.4%
(FPCore (x y z) :precision binary64 (if (or (<= x -3.5e-144) (not (<= x 1.75))) (* x (+ z y)) (* z (+ 5.0 x))))
double code(double x, double y, double z) {
double tmp;
if ((x <= -3.5e-144) || !(x <= 1.75)) {
tmp = x * (z + y);
} else {
tmp = z * (5.0 + x);
}
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 <= (-3.5d-144)) .or. (.not. (x <= 1.75d0))) then
tmp = x * (z + y)
else
tmp = z * (5.0d0 + x)
end if
code = tmp
end function
public static double code(double x, double y, double z) {
double tmp;
if ((x <= -3.5e-144) || !(x <= 1.75)) {
tmp = x * (z + y);
} else {
tmp = z * (5.0 + x);
}
return tmp;
}
def code(x, y, z): tmp = 0 if (x <= -3.5e-144) or not (x <= 1.75): tmp = x * (z + y) else: tmp = z * (5.0 + x) return tmp
function code(x, y, z) tmp = 0.0 if ((x <= -3.5e-144) || !(x <= 1.75)) tmp = Float64(x * Float64(z + y)); else tmp = Float64(z * Float64(5.0 + x)); end return tmp end
function tmp_2 = code(x, y, z) tmp = 0.0; if ((x <= -3.5e-144) || ~((x <= 1.75))) tmp = x * (z + y); else tmp = z * (5.0 + x); end tmp_2 = tmp; end
code[x_, y_, z_] := If[Or[LessEqual[x, -3.5e-144], N[Not[LessEqual[x, 1.75]], $MachinePrecision]], N[(x * N[(z + y), $MachinePrecision]), $MachinePrecision], N[(z * N[(5.0 + x), $MachinePrecision]), $MachinePrecision]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;x \leq -3.5 \cdot 10^{-144} \lor \neg \left(x \leq 1.75\right):\\
\;\;\;\;x \cdot \left(z + y\right)\\
\mathbf{else}:\\
\;\;\;\;z \cdot \left(5 + x\right)\\
\end{array}
\end{array}
if x < -3.4999999999999998e-144 or 1.75 < x Initial program 100.0%
Taylor expanded in x around inf 92.0%
+-commutative92.0%
Simplified92.0%
if -3.4999999999999998e-144 < x < 1.75Initial program 99.9%
Taylor expanded in y around 0 86.0%
distribute-rgt-in86.0%
Simplified86.0%
Final simplification89.7%
(FPCore (x y z) :precision binary64 (if (or (<= x -3.5e-144) (not (<= x 1.85e-6))) (* x y) (* z 5.0)))
double code(double x, double y, double z) {
double tmp;
if ((x <= -3.5e-144) || !(x <= 1.85e-6)) {
tmp = x * y;
} else {
tmp = z * 5.0;
}
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 <= (-3.5d-144)) .or. (.not. (x <= 1.85d-6))) then
tmp = x * y
else
tmp = z * 5.0d0
end if
code = tmp
end function
public static double code(double x, double y, double z) {
double tmp;
if ((x <= -3.5e-144) || !(x <= 1.85e-6)) {
tmp = x * y;
} else {
tmp = z * 5.0;
}
return tmp;
}
def code(x, y, z): tmp = 0 if (x <= -3.5e-144) or not (x <= 1.85e-6): tmp = x * y else: tmp = z * 5.0 return tmp
function code(x, y, z) tmp = 0.0 if ((x <= -3.5e-144) || !(x <= 1.85e-6)) tmp = Float64(x * y); else tmp = Float64(z * 5.0); end return tmp end
function tmp_2 = code(x, y, z) tmp = 0.0; if ((x <= -3.5e-144) || ~((x <= 1.85e-6))) tmp = x * y; else tmp = z * 5.0; end tmp_2 = tmp; end
code[x_, y_, z_] := If[Or[LessEqual[x, -3.5e-144], N[Not[LessEqual[x, 1.85e-6]], $MachinePrecision]], N[(x * y), $MachinePrecision], N[(z * 5.0), $MachinePrecision]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;x \leq -3.5 \cdot 10^{-144} \lor \neg \left(x \leq 1.85 \cdot 10^{-6}\right):\\
\;\;\;\;x \cdot y\\
\mathbf{else}:\\
\;\;\;\;z \cdot 5\\
\end{array}
\end{array}
if x < -3.4999999999999998e-144 or 1.8500000000000001e-6 < x Initial program 100.0%
Taylor expanded in y around inf 58.9%
if -3.4999999999999998e-144 < x < 1.8500000000000001e-6Initial program 99.9%
Taylor expanded in x around 0 85.2%
Final simplification68.9%
(FPCore (x y z) :precision binary64 (+ (* x (+ z y)) (* z 5.0)))
double code(double x, double y, double z) {
return (x * (z + y)) + (z * 5.0);
}
real(8) function code(x, y, z)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8), intent (in) :: z
code = (x * (z + y)) + (z * 5.0d0)
end function
public static double code(double x, double y, double z) {
return (x * (z + y)) + (z * 5.0);
}
def code(x, y, z): return (x * (z + y)) + (z * 5.0)
function code(x, y, z) return Float64(Float64(x * Float64(z + y)) + Float64(z * 5.0)) end
function tmp = code(x, y, z) tmp = (x * (z + y)) + (z * 5.0); end
code[x_, y_, z_] := N[(N[(x * N[(z + y), $MachinePrecision]), $MachinePrecision] + N[(z * 5.0), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
x \cdot \left(z + y\right) + z \cdot 5
\end{array}
Initial program 99.9%
Final simplification99.9%
(FPCore (x y z) :precision binary64 (* z 5.0))
double code(double x, double y, double z) {
return z * 5.0;
}
real(8) function code(x, y, z)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8), intent (in) :: z
code = z * 5.0d0
end function
public static double code(double x, double y, double z) {
return z * 5.0;
}
def code(x, y, z): return z * 5.0
function code(x, y, z) return Float64(z * 5.0) end
function tmp = code(x, y, z) tmp = z * 5.0; end
code[x_, y_, z_] := N[(z * 5.0), $MachinePrecision]
\begin{array}{l}
\\
z \cdot 5
\end{array}
Initial program 99.9%
Taylor expanded in x around 0 38.5%
Final simplification38.5%
(FPCore (x y z) :precision binary64 (+ (* (+ x 5.0) z) (* x y)))
double code(double x, double y, double z) {
return ((x + 5.0) * z) + (x * y);
}
real(8) function code(x, y, z)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8), intent (in) :: z
code = ((x + 5.0d0) * z) + (x * y)
end function
public static double code(double x, double y, double z) {
return ((x + 5.0) * z) + (x * y);
}
def code(x, y, z): return ((x + 5.0) * z) + (x * y)
function code(x, y, z) return Float64(Float64(Float64(x + 5.0) * z) + Float64(x * y)) end
function tmp = code(x, y, z) tmp = ((x + 5.0) * z) + (x * y); end
code[x_, y_, z_] := N[(N[(N[(x + 5.0), $MachinePrecision] * z), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
\left(x + 5\right) \cdot z + x \cdot y
\end{array}
herbie shell --seed 2024036
(FPCore (x y z)
:name "Graphics.Rendering.Plot.Render.Plot.Legend:renderLegendOutside from plot-0.2.3.4, C"
:precision binary64
:herbie-target
(+ (* (+ x 5.0) z) (* x y))
(+ (* x (+ y z)) (* z 5.0)))