
(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 (or (<= x -14.0) (not (<= x 5.0))) (* x (+ z y)) (+ (* x y) (* z 5.0))))
double code(double x, double y, double z) {
double tmp;
if ((x <= -14.0) || !(x <= 5.0)) {
tmp = x * (z + y);
} else {
tmp = (x * y) + (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 <= (-14.0d0)) .or. (.not. (x <= 5.0d0))) then
tmp = x * (z + y)
else
tmp = (x * y) + (z * 5.0d0)
end if
code = tmp
end function
public static double code(double x, double y, double z) {
double tmp;
if ((x <= -14.0) || !(x <= 5.0)) {
tmp = x * (z + y);
} else {
tmp = (x * y) + (z * 5.0);
}
return tmp;
}
def code(x, y, z): tmp = 0 if (x <= -14.0) or not (x <= 5.0): tmp = x * (z + y) else: tmp = (x * y) + (z * 5.0) return tmp
function code(x, y, z) tmp = 0.0 if ((x <= -14.0) || !(x <= 5.0)) tmp = Float64(x * Float64(z + y)); else tmp = Float64(Float64(x * y) + Float64(z * 5.0)); end return tmp end
function tmp_2 = code(x, y, z) tmp = 0.0; if ((x <= -14.0) || ~((x <= 5.0))) tmp = x * (z + y); else tmp = (x * y) + (z * 5.0); end tmp_2 = tmp; end
code[x_, y_, z_] := If[Or[LessEqual[x, -14.0], N[Not[LessEqual[x, 5.0]], $MachinePrecision]], N[(x * N[(z + y), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] + N[(z * 5.0), $MachinePrecision]), $MachinePrecision]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;x \leq -14 \lor \neg \left(x \leq 5\right):\\
\;\;\;\;x \cdot \left(z + y\right)\\
\mathbf{else}:\\
\;\;\;\;x \cdot y + z \cdot 5\\
\end{array}
\end{array}
if x < -14 or 5 < x Initial program 100.0%
Taylor expanded in x around inf 99.1%
+-commutative99.1%
Simplified99.1%
if -14 < x < 5Initial program 99.8%
distribute-lft-in99.8%
associate-+r+99.8%
*-commutative99.8%
distribute-rgt-in99.8%
+-commutative99.8%
*-commutative99.8%
add-sqr-sqrt56.6%
associate-*r*56.6%
fma-def56.6%
Applied egg-rr56.6%
Taylor expanded in x around 0 55.8%
fma-udef55.8%
+-commutative55.8%
associate-*l*55.8%
add-sqr-sqrt98.2%
Applied egg-rr98.2%
Final simplification98.7%
(FPCore (x y z) :precision binary64 (if (or (<= x -0.0066) (not (<= x 5e-138))) (* x (+ z y)) (* z 5.0)))
double code(double x, double y, double z) {
double tmp;
if ((x <= -0.0066) || !(x <= 5e-138)) {
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 <= (-0.0066d0)) .or. (.not. (x <= 5d-138))) 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 <= -0.0066) || !(x <= 5e-138)) {
tmp = x * (z + y);
} else {
tmp = z * 5.0;
}
return tmp;
}
def code(x, y, z): tmp = 0 if (x <= -0.0066) or not (x <= 5e-138): tmp = x * (z + y) else: tmp = z * 5.0 return tmp
function code(x, y, z) tmp = 0.0 if ((x <= -0.0066) || !(x <= 5e-138)) 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 <= -0.0066) || ~((x <= 5e-138))) tmp = x * (z + y); else tmp = z * 5.0; end tmp_2 = tmp; end
code[x_, y_, z_] := If[Or[LessEqual[x, -0.0066], N[Not[LessEqual[x, 5e-138]], $MachinePrecision]], N[(x * N[(z + y), $MachinePrecision]), $MachinePrecision], N[(z * 5.0), $MachinePrecision]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;x \leq -0.0066 \lor \neg \left(x \leq 5 \cdot 10^{-138}\right):\\
\;\;\;\;x \cdot \left(z + y\right)\\
\mathbf{else}:\\
\;\;\;\;z \cdot 5\\
\end{array}
\end{array}
if x < -0.0066 or 4.99999999999999989e-138 < x Initial program 100.0%
Taylor expanded in x around inf 93.4%
+-commutative93.4%
Simplified93.4%
if -0.0066 < x < 4.99999999999999989e-138Initial program 99.8%
Taylor expanded in x around 0 77.8%
Final simplification88.1%
(FPCore (x y z) :precision binary64 (if (or (<= x -0.0165) (not (<= x 4.4e-138))) (* x (+ z y)) (* z (+ 5.0 x))))
double code(double x, double y, double z) {
double tmp;
if ((x <= -0.0165) || !(x <= 4.4e-138)) {
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 <= (-0.0165d0)) .or. (.not. (x <= 4.4d-138))) 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 <= -0.0165) || !(x <= 4.4e-138)) {
tmp = x * (z + y);
} else {
tmp = z * (5.0 + x);
}
return tmp;
}
def code(x, y, z): tmp = 0 if (x <= -0.0165) or not (x <= 4.4e-138): tmp = x * (z + y) else: tmp = z * (5.0 + x) return tmp
function code(x, y, z) tmp = 0.0 if ((x <= -0.0165) || !(x <= 4.4e-138)) 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 <= -0.0165) || ~((x <= 4.4e-138))) tmp = x * (z + y); else tmp = z * (5.0 + x); end tmp_2 = tmp; end
code[x_, y_, z_] := If[Or[LessEqual[x, -0.0165], N[Not[LessEqual[x, 4.4e-138]], $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 -0.0165 \lor \neg \left(x \leq 4.4 \cdot 10^{-138}\right):\\
\;\;\;\;x \cdot \left(z + y\right)\\
\mathbf{else}:\\
\;\;\;\;z \cdot \left(5 + x\right)\\
\end{array}
\end{array}
if x < -0.016500000000000001 or 4.3999999999999998e-138 < x Initial program 100.0%
Taylor expanded in x around inf 93.4%
+-commutative93.4%
Simplified93.4%
if -0.016500000000000001 < x < 4.3999999999999998e-138Initial program 99.8%
Taylor expanded in y around 0 79.7%
distribute-rgt-in79.7%
Simplified79.7%
Final simplification88.8%
(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 -0.0066) (* x y) (if (<= x 4.9e-138) (* z 5.0) (* x y))))
double code(double x, double y, double z) {
double tmp;
if (x <= -0.0066) {
tmp = x * y;
} else if (x <= 4.9e-138) {
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 <= (-0.0066d0)) then
tmp = x * y
else if (x <= 4.9d-138) 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 <= -0.0066) {
tmp = x * y;
} else if (x <= 4.9e-138) {
tmp = z * 5.0;
} else {
tmp = x * y;
}
return tmp;
}
def code(x, y, z): tmp = 0 if x <= -0.0066: tmp = x * y elif x <= 4.9e-138: tmp = z * 5.0 else: tmp = x * y return tmp
function code(x, y, z) tmp = 0.0 if (x <= -0.0066) tmp = Float64(x * y); elseif (x <= 4.9e-138) 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 <= -0.0066) tmp = x * y; elseif (x <= 4.9e-138) tmp = z * 5.0; else tmp = x * y; end tmp_2 = tmp; end
code[x_, y_, z_] := If[LessEqual[x, -0.0066], N[(x * y), $MachinePrecision], If[LessEqual[x, 4.9e-138], N[(z * 5.0), $MachinePrecision], N[(x * y), $MachinePrecision]]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;x \leq -0.0066:\\
\;\;\;\;x \cdot y\\
\mathbf{elif}\;x \leq 4.9 \cdot 10^{-138}:\\
\;\;\;\;z \cdot 5\\
\mathbf{else}:\\
\;\;\;\;x \cdot y\\
\end{array}
\end{array}
if x < -0.0066 or 4.90000000000000016e-138 < x Initial program 100.0%
Taylor expanded in y around inf 54.4%
if -0.0066 < x < 4.90000000000000016e-138Initial program 99.8%
Taylor expanded in x around 0 77.8%
Final simplification62.4%
(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 32.1%
Final simplification32.1%
(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 2023297
(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)))