
(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 -2.8e+121)
(* z x)
(if (<= x -2.3e-9)
(* x y)
(if (<= x 8e-44) (* z 5.0) (if (<= x 2.7e+214) (* x y) (* z x))))))
double code(double x, double y, double z) {
double tmp;
if (x <= -2.8e+121) {
tmp = z * x;
} else if (x <= -2.3e-9) {
tmp = x * y;
} else if (x <= 8e-44) {
tmp = z * 5.0;
} else if (x <= 2.7e+214) {
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 <= (-2.8d+121)) then
tmp = z * x
else if (x <= (-2.3d-9)) then
tmp = x * y
else if (x <= 8d-44) then
tmp = z * 5.0d0
else if (x <= 2.7d+214) 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 <= -2.8e+121) {
tmp = z * x;
} else if (x <= -2.3e-9) {
tmp = x * y;
} else if (x <= 8e-44) {
tmp = z * 5.0;
} else if (x <= 2.7e+214) {
tmp = x * y;
} else {
tmp = z * x;
}
return tmp;
}
def code(x, y, z): tmp = 0 if x <= -2.8e+121: tmp = z * x elif x <= -2.3e-9: tmp = x * y elif x <= 8e-44: tmp = z * 5.0 elif x <= 2.7e+214: tmp = x * y else: tmp = z * x return tmp
function code(x, y, z) tmp = 0.0 if (x <= -2.8e+121) tmp = Float64(z * x); elseif (x <= -2.3e-9) tmp = Float64(x * y); elseif (x <= 8e-44) tmp = Float64(z * 5.0); elseif (x <= 2.7e+214) 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 <= -2.8e+121) tmp = z * x; elseif (x <= -2.3e-9) tmp = x * y; elseif (x <= 8e-44) tmp = z * 5.0; elseif (x <= 2.7e+214) tmp = x * y; else tmp = z * x; end tmp_2 = tmp; end
code[x_, y_, z_] := If[LessEqual[x, -2.8e+121], N[(z * x), $MachinePrecision], If[LessEqual[x, -2.3e-9], N[(x * y), $MachinePrecision], If[LessEqual[x, 8e-44], N[(z * 5.0), $MachinePrecision], If[LessEqual[x, 2.7e+214], N[(x * y), $MachinePrecision], N[(z * x), $MachinePrecision]]]]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;x \leq -2.8 \cdot 10^{+121}:\\
\;\;\;\;z \cdot x\\
\mathbf{elif}\;x \leq -2.3 \cdot 10^{-9}:\\
\;\;\;\;x \cdot y\\
\mathbf{elif}\;x \leq 8 \cdot 10^{-44}:\\
\;\;\;\;z \cdot 5\\
\mathbf{elif}\;x \leq 2.7 \cdot 10^{+214}:\\
\;\;\;\;x \cdot y\\
\mathbf{else}:\\
\;\;\;\;z \cdot x\\
\end{array}
\end{array}
if x < -2.80000000000000006e121 or 2.70000000000000009e214 < x Initial program 100.0%
Taylor expanded in x around inf 100.0%
+-commutative100.0%
Simplified100.0%
Taylor expanded in z around inf 73.2%
if -2.80000000000000006e121 < x < -2.2999999999999999e-9 or 7.99999999999999962e-44 < x < 2.70000000000000009e214Initial program 99.9%
Taylor expanded in y around inf 66.6%
if -2.2999999999999999e-9 < x < 7.99999999999999962e-44Initial program 99.9%
Taylor expanded in x around 0 76.6%
Final simplification72.5%
(FPCore (x y z) :precision binary64 (if (or (<= x -1.6e-10) (not (<= x 6.5e-46))) (* x (+ z y)) (* z 5.0)))
double code(double x, double y, double z) {
double tmp;
if ((x <= -1.6e-10) || !(x <= 6.5e-46)) {
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 <= (-1.6d-10)) .or. (.not. (x <= 6.5d-46))) 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 <= -1.6e-10) || !(x <= 6.5e-46)) {
tmp = x * (z + y);
} else {
tmp = z * 5.0;
}
return tmp;
}
def code(x, y, z): tmp = 0 if (x <= -1.6e-10) or not (x <= 6.5e-46): tmp = x * (z + y) else: tmp = z * 5.0 return tmp
function code(x, y, z) tmp = 0.0 if ((x <= -1.6e-10) || !(x <= 6.5e-46)) 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 <= -1.6e-10) || ~((x <= 6.5e-46))) tmp = x * (z + y); else tmp = z * 5.0; end tmp_2 = tmp; end
code[x_, y_, z_] := If[Or[LessEqual[x, -1.6e-10], N[Not[LessEqual[x, 6.5e-46]], $MachinePrecision]], N[(x * N[(z + y), $MachinePrecision]), $MachinePrecision], N[(z * 5.0), $MachinePrecision]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;x \leq -1.6 \cdot 10^{-10} \lor \neg \left(x \leq 6.5 \cdot 10^{-46}\right):\\
\;\;\;\;x \cdot \left(z + y\right)\\
\mathbf{else}:\\
\;\;\;\;z \cdot 5\\
\end{array}
\end{array}
if x < -1.5999999999999999e-10 or 6.49999999999999966e-46 < x Initial program 100.0%
Taylor expanded in x around inf 98.9%
+-commutative98.9%
Simplified98.9%
if -1.5999999999999999e-10 < x < 6.49999999999999966e-46Initial program 99.9%
Taylor expanded in x around 0 76.6%
Final simplification89.3%
(FPCore (x y z) :precision binary64 (if (or (<= x -6.5e-10) (not (<= x 1.5e-47))) (* x (+ z y)) (* z (+ 5.0 x))))
double code(double x, double y, double z) {
double tmp;
if ((x <= -6.5e-10) || !(x <= 1.5e-47)) {
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 <= (-6.5d-10)) .or. (.not. (x <= 1.5d-47))) 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 <= -6.5e-10) || !(x <= 1.5e-47)) {
tmp = x * (z + y);
} else {
tmp = z * (5.0 + x);
}
return tmp;
}
def code(x, y, z): tmp = 0 if (x <= -6.5e-10) or not (x <= 1.5e-47): tmp = x * (z + y) else: tmp = z * (5.0 + x) return tmp
function code(x, y, z) tmp = 0.0 if ((x <= -6.5e-10) || !(x <= 1.5e-47)) 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 <= -6.5e-10) || ~((x <= 1.5e-47))) tmp = x * (z + y); else tmp = z * (5.0 + x); end tmp_2 = tmp; end
code[x_, y_, z_] := If[Or[LessEqual[x, -6.5e-10], N[Not[LessEqual[x, 1.5e-47]], $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 -6.5 \cdot 10^{-10} \lor \neg \left(x \leq 1.5 \cdot 10^{-47}\right):\\
\;\;\;\;x \cdot \left(z + y\right)\\
\mathbf{else}:\\
\;\;\;\;z \cdot \left(5 + x\right)\\
\end{array}
\end{array}
if x < -6.5000000000000003e-10 or 1.50000000000000008e-47 < x Initial program 100.0%
Taylor expanded in x around inf 98.9%
+-commutative98.9%
Simplified98.9%
if -6.5000000000000003e-10 < x < 1.50000000000000008e-47Initial program 99.9%
Taylor expanded in y around 0 77.1%
distribute-rgt-in77.1%
Simplified77.1%
Final simplification89.5%
(FPCore (x y z) :precision binary64 (if (or (<= x -1.35e-9) (not (<= x 1.5e-43))) (* x y) (* z 5.0)))
double code(double x, double y, double z) {
double tmp;
if ((x <= -1.35e-9) || !(x <= 1.5e-43)) {
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 <= (-1.35d-9)) .or. (.not. (x <= 1.5d-43))) 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 <= -1.35e-9) || !(x <= 1.5e-43)) {
tmp = x * y;
} else {
tmp = z * 5.0;
}
return tmp;
}
def code(x, y, z): tmp = 0 if (x <= -1.35e-9) or not (x <= 1.5e-43): tmp = x * y else: tmp = z * 5.0 return tmp
function code(x, y, z) tmp = 0.0 if ((x <= -1.35e-9) || !(x <= 1.5e-43)) 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 <= -1.35e-9) || ~((x <= 1.5e-43))) tmp = x * y; else tmp = z * 5.0; end tmp_2 = tmp; end
code[x_, y_, z_] := If[Or[LessEqual[x, -1.35e-9], N[Not[LessEqual[x, 1.5e-43]], $MachinePrecision]], N[(x * y), $MachinePrecision], N[(z * 5.0), $MachinePrecision]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;x \leq -1.35 \cdot 10^{-9} \lor \neg \left(x \leq 1.5 \cdot 10^{-43}\right):\\
\;\;\;\;x \cdot y\\
\mathbf{else}:\\
\;\;\;\;z \cdot 5\\
\end{array}
\end{array}
if x < -1.3500000000000001e-9 or 1.50000000000000002e-43 < x Initial program 100.0%
Taylor expanded in y around inf 53.5%
if -1.3500000000000001e-9 < x < 1.50000000000000002e-43Initial program 99.9%
Taylor expanded in x around 0 76.6%
Final simplification63.4%
(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 35.0%
Final simplification35.0%
(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 2024020
(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)))