
(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 -7e+83) (* z x) (if (<= x -1.4e-6) (* x y) (if (<= x 5.0) (* z 5.0) (* z x)))))
double code(double x, double y, double z) {
double tmp;
if (x <= -7e+83) {
tmp = z * x;
} else if (x <= -1.4e-6) {
tmp = x * y;
} else if (x <= 5.0) {
tmp = z * 5.0;
} 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 <= (-7d+83)) then
tmp = z * x
else if (x <= (-1.4d-6)) then
tmp = x * y
else if (x <= 5.0d0) then
tmp = z * 5.0d0
else
tmp = z * x
end if
code = tmp
end function
public static double code(double x, double y, double z) {
double tmp;
if (x <= -7e+83) {
tmp = z * x;
} else if (x <= -1.4e-6) {
tmp = x * y;
} else if (x <= 5.0) {
tmp = z * 5.0;
} else {
tmp = z * x;
}
return tmp;
}
def code(x, y, z): tmp = 0 if x <= -7e+83: tmp = z * x elif x <= -1.4e-6: tmp = x * y elif x <= 5.0: tmp = z * 5.0 else: tmp = z * x return tmp
function code(x, y, z) tmp = 0.0 if (x <= -7e+83) tmp = Float64(z * x); elseif (x <= -1.4e-6) tmp = Float64(x * y); elseif (x <= 5.0) tmp = Float64(z * 5.0); else tmp = Float64(z * x); end return tmp end
function tmp_2 = code(x, y, z) tmp = 0.0; if (x <= -7e+83) tmp = z * x; elseif (x <= -1.4e-6) tmp = x * y; elseif (x <= 5.0) tmp = z * 5.0; else tmp = z * x; end tmp_2 = tmp; end
code[x_, y_, z_] := If[LessEqual[x, -7e+83], N[(z * x), $MachinePrecision], If[LessEqual[x, -1.4e-6], N[(x * y), $MachinePrecision], If[LessEqual[x, 5.0], N[(z * 5.0), $MachinePrecision], N[(z * x), $MachinePrecision]]]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;x \leq -7 \cdot 10^{+83}:\\
\;\;\;\;z \cdot x\\
\mathbf{elif}\;x \leq -1.4 \cdot 10^{-6}:\\
\;\;\;\;x \cdot y\\
\mathbf{elif}\;x \leq 5:\\
\;\;\;\;z \cdot 5\\
\mathbf{else}:\\
\;\;\;\;z \cdot x\\
\end{array}
\end{array}
if x < -6.99999999999999954e83 or 5 < x Initial program 100.0%
Taylor expanded in y around 0 58.5%
+-commutative58.5%
*-commutative58.5%
distribute-rgt-in58.5%
Simplified58.5%
Taylor expanded in x around inf 58.5%
if -6.99999999999999954e83 < x < -1.39999999999999994e-6Initial program 99.9%
Taylor expanded in y around inf 62.7%
if -1.39999999999999994e-6 < x < 5Initial program 99.8%
Taylor expanded in x around 0 69.1%
Final simplification64.4%
(FPCore (x y z) :precision binary64 (if (or (<= x -8.5e-5) (not (<= x 2.2e-9))) (* x (+ z y)) (* z (+ 5.0 x))))
double code(double x, double y, double z) {
double tmp;
if ((x <= -8.5e-5) || !(x <= 2.2e-9)) {
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 <= (-8.5d-5)) .or. (.not. (x <= 2.2d-9))) 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 <= -8.5e-5) || !(x <= 2.2e-9)) {
tmp = x * (z + y);
} else {
tmp = z * (5.0 + x);
}
return tmp;
}
def code(x, y, z): tmp = 0 if (x <= -8.5e-5) or not (x <= 2.2e-9): tmp = x * (z + y) else: tmp = z * (5.0 + x) return tmp
function code(x, y, z) tmp = 0.0 if ((x <= -8.5e-5) || !(x <= 2.2e-9)) 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 <= -8.5e-5) || ~((x <= 2.2e-9))) tmp = x * (z + y); else tmp = z * (5.0 + x); end tmp_2 = tmp; end
code[x_, y_, z_] := If[Or[LessEqual[x, -8.5e-5], N[Not[LessEqual[x, 2.2e-9]], $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 -8.5 \cdot 10^{-5} \lor \neg \left(x \leq 2.2 \cdot 10^{-9}\right):\\
\;\;\;\;x \cdot \left(z + y\right)\\
\mathbf{else}:\\
\;\;\;\;z \cdot \left(5 + x\right)\\
\end{array}
\end{array}
if x < -8.500000000000001e-5 or 2.1999999999999998e-9 < x Initial program 100.0%
Taylor expanded in x around inf 98.3%
+-commutative98.3%
Simplified98.3%
if -8.500000000000001e-5 < x < 2.1999999999999998e-9Initial program 99.8%
Taylor expanded in y around 0 71.6%
+-commutative71.6%
*-commutative71.6%
distribute-rgt-in71.6%
Simplified71.6%
Final simplification84.6%
(FPCore (x y z) :precision binary64 (if (<= y -3.5e-32) (* x y) (if (<= y 8.4e+18) (* z (+ 5.0 x)) (* x y))))
double code(double x, double y, double z) {
double tmp;
if (y <= -3.5e-32) {
tmp = x * y;
} else if (y <= 8.4e+18) {
tmp = z * (5.0 + x);
} else {
tmp = x * 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 (y <= (-3.5d-32)) then
tmp = x * y
else if (y <= 8.4d+18) then
tmp = z * (5.0d0 + x)
else
tmp = x * y
end if
code = tmp
end function
public static double code(double x, double y, double z) {
double tmp;
if (y <= -3.5e-32) {
tmp = x * y;
} else if (y <= 8.4e+18) {
tmp = z * (5.0 + x);
} else {
tmp = x * y;
}
return tmp;
}
def code(x, y, z): tmp = 0 if y <= -3.5e-32: tmp = x * y elif y <= 8.4e+18: tmp = z * (5.0 + x) else: tmp = x * y return tmp
function code(x, y, z) tmp = 0.0 if (y <= -3.5e-32) tmp = Float64(x * y); elseif (y <= 8.4e+18) tmp = Float64(z * Float64(5.0 + x)); else tmp = Float64(x * y); end return tmp end
function tmp_2 = code(x, y, z) tmp = 0.0; if (y <= -3.5e-32) tmp = x * y; elseif (y <= 8.4e+18) tmp = z * (5.0 + x); else tmp = x * y; end tmp_2 = tmp; end
code[x_, y_, z_] := If[LessEqual[y, -3.5e-32], N[(x * y), $MachinePrecision], If[LessEqual[y, 8.4e+18], N[(z * N[(5.0 + x), $MachinePrecision]), $MachinePrecision], N[(x * y), $MachinePrecision]]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;y \leq -3.5 \cdot 10^{-32}:\\
\;\;\;\;x \cdot y\\
\mathbf{elif}\;y \leq 8.4 \cdot 10^{+18}:\\
\;\;\;\;z \cdot \left(5 + x\right)\\
\mathbf{else}:\\
\;\;\;\;x \cdot y\\
\end{array}
\end{array}
if y < -3.4999999999999999e-32 or 8.4e18 < y Initial program 99.9%
Taylor expanded in y around inf 70.6%
if -3.4999999999999999e-32 < y < 8.4e18Initial program 99.8%
Taylor expanded in y around 0 88.1%
+-commutative88.1%
*-commutative88.1%
distribute-rgt-in88.1%
Simplified88.1%
Final simplification79.7%
(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 (if (<= x -1.1e-5) (* x y) (if (<= x 6e-9) (* z 5.0) (* x y))))
double code(double x, double y, double z) {
double tmp;
if (x <= -1.1e-5) {
tmp = x * y;
} else if (x <= 6e-9) {
tmp = z * 5.0;
} else {
tmp = x * 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 <= (-1.1d-5)) then
tmp = x * y
else if (x <= 6d-9) then
tmp = z * 5.0d0
else
tmp = x * y
end if
code = tmp
end function
public static double code(double x, double y, double z) {
double tmp;
if (x <= -1.1e-5) {
tmp = x * y;
} else if (x <= 6e-9) {
tmp = z * 5.0;
} else {
tmp = x * y;
}
return tmp;
}
def code(x, y, z): tmp = 0 if x <= -1.1e-5: tmp = x * y elif x <= 6e-9: tmp = z * 5.0 else: tmp = x * y return tmp
function code(x, y, z) tmp = 0.0 if (x <= -1.1e-5) tmp = Float64(x * y); elseif (x <= 6e-9) tmp = Float64(z * 5.0); else tmp = Float64(x * y); end return tmp end
function tmp_2 = code(x, y, z) tmp = 0.0; if (x <= -1.1e-5) tmp = x * y; elseif (x <= 6e-9) tmp = z * 5.0; else tmp = x * y; end tmp_2 = tmp; end
code[x_, y_, z_] := If[LessEqual[x, -1.1e-5], N[(x * y), $MachinePrecision], If[LessEqual[x, 6e-9], N[(z * 5.0), $MachinePrecision], N[(x * y), $MachinePrecision]]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;x \leq -1.1 \cdot 10^{-5}:\\
\;\;\;\;x \cdot y\\
\mathbf{elif}\;x \leq 6 \cdot 10^{-9}:\\
\;\;\;\;z \cdot 5\\
\mathbf{else}:\\
\;\;\;\;x \cdot y\\
\end{array}
\end{array}
if x < -1.1e-5 or 5.99999999999999996e-9 < x Initial program 100.0%
Taylor expanded in y around inf 52.3%
if -1.1e-5 < x < 5.99999999999999996e-9Initial program 99.8%
Taylor expanded in x around 0 70.5%
Final simplification61.6%
(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 37.9%
Final simplification37.9%
(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 2023274
(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)))