
(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 8 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 100.0%
+-commutative100.0%
fma-def100.0%
Applied egg-rr100.0%
Final simplification100.0%
(FPCore (x y z) :precision binary64 (fma x (+ z y) (* z 5.0)))
double code(double x, double y, double z) {
return fma(x, (z + y), (z * 5.0));
}
function code(x, y, z) return fma(x, Float64(z + y), Float64(z * 5.0)) end
code[x_, y_, z_] := N[(x * N[(z + y), $MachinePrecision] + N[(z * 5.0), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
\mathsf{fma}\left(x, z + y, z \cdot 5\right)
\end{array}
Initial program 100.0%
fma-def100.0%
Simplified100.0%
Final simplification100.0%
(FPCore (x y z) :precision binary64 (if (<= x -2.9e-7) (* x y) (if (<= x 45.0) (* z 5.0) (if (<= x 1.15e+142) (* z x) (* x y)))))
double code(double x, double y, double z) {
double tmp;
if (x <= -2.9e-7) {
tmp = x * y;
} else if (x <= 45.0) {
tmp = z * 5.0;
} else if (x <= 1.15e+142) {
tmp = z * 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 (x <= (-2.9d-7)) then
tmp = x * y
else if (x <= 45.0d0) then
tmp = z * 5.0d0
else if (x <= 1.15d+142) then
tmp = z * x
else
tmp = x * y
end if
code = tmp
end function
public static double code(double x, double y, double z) {
double tmp;
if (x <= -2.9e-7) {
tmp = x * y;
} else if (x <= 45.0) {
tmp = z * 5.0;
} else if (x <= 1.15e+142) {
tmp = z * x;
} else {
tmp = x * y;
}
return tmp;
}
def code(x, y, z): tmp = 0 if x <= -2.9e-7: tmp = x * y elif x <= 45.0: tmp = z * 5.0 elif x <= 1.15e+142: tmp = z * x else: tmp = x * y return tmp
function code(x, y, z) tmp = 0.0 if (x <= -2.9e-7) tmp = Float64(x * y); elseif (x <= 45.0) tmp = Float64(z * 5.0); elseif (x <= 1.15e+142) tmp = Float64(z * x); else tmp = Float64(x * y); end return tmp end
function tmp_2 = code(x, y, z) tmp = 0.0; if (x <= -2.9e-7) tmp = x * y; elseif (x <= 45.0) tmp = z * 5.0; elseif (x <= 1.15e+142) tmp = z * x; else tmp = x * y; end tmp_2 = tmp; end
code[x_, y_, z_] := If[LessEqual[x, -2.9e-7], N[(x * y), $MachinePrecision], If[LessEqual[x, 45.0], N[(z * 5.0), $MachinePrecision], If[LessEqual[x, 1.15e+142], N[(z * x), $MachinePrecision], N[(x * y), $MachinePrecision]]]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;x \leq -2.9 \cdot 10^{-7}:\\
\;\;\;\;x \cdot y\\
\mathbf{elif}\;x \leq 45:\\
\;\;\;\;z \cdot 5\\
\mathbf{elif}\;x \leq 1.15 \cdot 10^{+142}:\\
\;\;\;\;z \cdot x\\
\mathbf{else}:\\
\;\;\;\;x \cdot y\\
\end{array}
\end{array}
if x < -2.8999999999999998e-7 or 1.15000000000000001e142 < x Initial program 100.0%
Taylor expanded in y around inf 53.9%
if -2.8999999999999998e-7 < x < 45Initial program 99.9%
Taylor expanded in x around 0 76.2%
if 45 < x < 1.15000000000000001e142Initial program 99.9%
Taylor expanded in x around inf 94.6%
+-commutative94.6%
Simplified94.6%
Taylor expanded in z around inf 62.8%
Final simplification66.0%
(FPCore (x y z) :precision binary64 (if (or (<= x -1.15e-7) (not (<= x 0.0075))) (* x (+ z y)) (* z 5.0)))
double code(double x, double y, double z) {
double tmp;
if ((x <= -1.15e-7) || !(x <= 0.0075)) {
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 <= (-1.15d-7)) .or. (.not. (x <= 0.0075d0))) 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 <= -1.15e-7) || !(x <= 0.0075)) {
tmp = x * (z + y);
} else {
tmp = z * 5.0;
}
return tmp;
}
def code(x, y, z): tmp = 0 if (x <= -1.15e-7) or not (x <= 0.0075): tmp = x * (z + y) else: tmp = z * 5.0 return tmp
function code(x, y, z) tmp = 0.0 if ((x <= -1.15e-7) || !(x <= 0.0075)) 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 <= -1.15e-7) || ~((x <= 0.0075))) tmp = x * (z + y); else tmp = z * 5.0; end tmp_2 = tmp; end
code[x_, y_, z_] := If[Or[LessEqual[x, -1.15e-7], N[Not[LessEqual[x, 0.0075]], $MachinePrecision]], N[(x * N[(z + y), $MachinePrecision]), $MachinePrecision], N[(z * 5.0), $MachinePrecision]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;x \leq -1.15 \cdot 10^{-7} \lor \neg \left(x \leq 0.0075\right):\\
\;\;\;\;x \cdot \left(z + y\right)\\
\mathbf{else}:\\
\;\;\;\;z \cdot 5\\
\end{array}
\end{array}
if x < -1.14999999999999997e-7 or 0.0074999999999999997 < x Initial program 100.0%
Taylor expanded in x around inf 97.6%
+-commutative97.6%
Simplified97.6%
if -1.14999999999999997e-7 < x < 0.0074999999999999997Initial program 99.9%
Taylor expanded in x around 0 76.8%
Final simplification87.5%
(FPCore (x y z) :precision binary64 (if (or (<= x -34.0) (not (<= x 21000000000000.0))) (* x (+ z y)) (* z (+ 5.0 x))))
double code(double x, double y, double z) {
double tmp;
if ((x <= -34.0) || !(x <= 21000000000000.0)) {
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 <= (-34.0d0)) .or. (.not. (x <= 21000000000000.0d0))) 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 <= -34.0) || !(x <= 21000000000000.0)) {
tmp = x * (z + y);
} else {
tmp = z * (5.0 + x);
}
return tmp;
}
def code(x, y, z): tmp = 0 if (x <= -34.0) or not (x <= 21000000000000.0): tmp = x * (z + y) else: tmp = z * (5.0 + x) return tmp
function code(x, y, z) tmp = 0.0 if ((x <= -34.0) || !(x <= 21000000000000.0)) 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 <= -34.0) || ~((x <= 21000000000000.0))) tmp = x * (z + y); else tmp = z * (5.0 + x); end tmp_2 = tmp; end
code[x_, y_, z_] := If[Or[LessEqual[x, -34.0], N[Not[LessEqual[x, 21000000000000.0]], $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 -34 \lor \neg \left(x \leq 21000000000000\right):\\
\;\;\;\;x \cdot \left(z + y\right)\\
\mathbf{else}:\\
\;\;\;\;z \cdot \left(5 + x\right)\\
\end{array}
\end{array}
if x < -34 or 2.1e13 < x Initial program 100.0%
Taylor expanded in x around inf 99.5%
+-commutative99.5%
Simplified99.5%
if -34 < x < 2.1e13Initial program 99.9%
Taylor expanded in y around 0 77.9%
distribute-rgt-in78.0%
Simplified78.0%
Final simplification88.5%
(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 100.0%
Final simplification100.0%
(FPCore (x y z) :precision binary64 (if (or (<= x -1.7e-6) (not (<= x 0.0075))) (* x y) (* z 5.0)))
double code(double x, double y, double z) {
double tmp;
if ((x <= -1.7e-6) || !(x <= 0.0075)) {
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 <= (-1.7d-6)) .or. (.not. (x <= 0.0075d0))) 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 <= -1.7e-6) || !(x <= 0.0075)) {
tmp = x * y;
} else {
tmp = z * 5.0;
}
return tmp;
}
def code(x, y, z): tmp = 0 if (x <= -1.7e-6) or not (x <= 0.0075): tmp = x * y else: tmp = z * 5.0 return tmp
function code(x, y, z) tmp = 0.0 if ((x <= -1.7e-6) || !(x <= 0.0075)) 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 <= -1.7e-6) || ~((x <= 0.0075))) tmp = x * y; else tmp = z * 5.0; end tmp_2 = tmp; end
code[x_, y_, z_] := If[Or[LessEqual[x, -1.7e-6], N[Not[LessEqual[x, 0.0075]], $MachinePrecision]], N[(x * y), $MachinePrecision], N[(z * 5.0), $MachinePrecision]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;x \leq -1.7 \cdot 10^{-6} \lor \neg \left(x \leq 0.0075\right):\\
\;\;\;\;x \cdot y\\
\mathbf{else}:\\
\;\;\;\;z \cdot 5\\
\end{array}
\end{array}
if x < -1.70000000000000003e-6 or 0.0074999999999999997 < x Initial program 100.0%
Taylor expanded in y around inf 48.9%
if -1.70000000000000003e-6 < x < 0.0074999999999999997Initial program 99.9%
Taylor expanded in x around 0 76.8%
Final simplification62.5%
(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 100.0%
Taylor expanded in x around 0 39.1%
Final simplification39.1%
(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 2023301
(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)))