
(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 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 -2.55e+182)
(* x y)
(if (<= x -2.2e+89)
(* z x)
(if (<= x -1.95e+60)
(* x y)
(if (<= x -4500.0)
(* z x)
(if (<= x 1.7e-99)
(* z 5.0)
(if (or (<= x 8e+82) (not (<= x 4.1e+229))) (* x y) (* z x))))))))
double code(double x, double y, double z) {
double tmp;
if (x <= -2.55e+182) {
tmp = x * y;
} else if (x <= -2.2e+89) {
tmp = z * x;
} else if (x <= -1.95e+60) {
tmp = x * y;
} else if (x <= -4500.0) {
tmp = z * x;
} else if (x <= 1.7e-99) {
tmp = z * 5.0;
} else if ((x <= 8e+82) || !(x <= 4.1e+229)) {
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 <= (-2.55d+182)) then
tmp = x * y
else if (x <= (-2.2d+89)) then
tmp = z * x
else if (x <= (-1.95d+60)) then
tmp = x * y
else if (x <= (-4500.0d0)) then
tmp = z * x
else if (x <= 1.7d-99) then
tmp = z * 5.0d0
else if ((x <= 8d+82) .or. (.not. (x <= 4.1d+229))) 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 <= -2.55e+182) {
tmp = x * y;
} else if (x <= -2.2e+89) {
tmp = z * x;
} else if (x <= -1.95e+60) {
tmp = x * y;
} else if (x <= -4500.0) {
tmp = z * x;
} else if (x <= 1.7e-99) {
tmp = z * 5.0;
} else if ((x <= 8e+82) || !(x <= 4.1e+229)) {
tmp = x * y;
} else {
tmp = z * x;
}
return tmp;
}
def code(x, y, z): tmp = 0 if x <= -2.55e+182: tmp = x * y elif x <= -2.2e+89: tmp = z * x elif x <= -1.95e+60: tmp = x * y elif x <= -4500.0: tmp = z * x elif x <= 1.7e-99: tmp = z * 5.0 elif (x <= 8e+82) or not (x <= 4.1e+229): tmp = x * y else: tmp = z * x return tmp
function code(x, y, z) tmp = 0.0 if (x <= -2.55e+182) tmp = Float64(x * y); elseif (x <= -2.2e+89) tmp = Float64(z * x); elseif (x <= -1.95e+60) tmp = Float64(x * y); elseif (x <= -4500.0) tmp = Float64(z * x); elseif (x <= 1.7e-99) tmp = Float64(z * 5.0); elseif ((x <= 8e+82) || !(x <= 4.1e+229)) 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 <= -2.55e+182) tmp = x * y; elseif (x <= -2.2e+89) tmp = z * x; elseif (x <= -1.95e+60) tmp = x * y; elseif (x <= -4500.0) tmp = z * x; elseif (x <= 1.7e-99) tmp = z * 5.0; elseif ((x <= 8e+82) || ~((x <= 4.1e+229))) tmp = x * y; else tmp = z * x; end tmp_2 = tmp; end
code[x_, y_, z_] := If[LessEqual[x, -2.55e+182], N[(x * y), $MachinePrecision], If[LessEqual[x, -2.2e+89], N[(z * x), $MachinePrecision], If[LessEqual[x, -1.95e+60], N[(x * y), $MachinePrecision], If[LessEqual[x, -4500.0], N[(z * x), $MachinePrecision], If[LessEqual[x, 1.7e-99], N[(z * 5.0), $MachinePrecision], If[Or[LessEqual[x, 8e+82], N[Not[LessEqual[x, 4.1e+229]], $MachinePrecision]], N[(x * y), $MachinePrecision], N[(z * x), $MachinePrecision]]]]]]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;x \leq -2.55 \cdot 10^{+182}:\\
\;\;\;\;x \cdot y\\
\mathbf{elif}\;x \leq -2.2 \cdot 10^{+89}:\\
\;\;\;\;z \cdot x\\
\mathbf{elif}\;x \leq -1.95 \cdot 10^{+60}:\\
\;\;\;\;x \cdot y\\
\mathbf{elif}\;x \leq -4500:\\
\;\;\;\;z \cdot x\\
\mathbf{elif}\;x \leq 1.7 \cdot 10^{-99}:\\
\;\;\;\;z \cdot 5\\
\mathbf{elif}\;x \leq 8 \cdot 10^{+82} \lor \neg \left(x \leq 4.1 \cdot 10^{+229}\right):\\
\;\;\;\;x \cdot y\\
\mathbf{else}:\\
\;\;\;\;z \cdot x\\
\end{array}
\end{array}
if x < -2.55000000000000005e182 or -2.2e89 < x < -1.95000000000000015e60 or 1.70000000000000003e-99 < x < 7.9999999999999997e82 or 4.1000000000000001e229 < x Initial program 99.9%
Taylor expanded in y around inf 67.7%
if -2.55000000000000005e182 < x < -2.2e89 or -1.95000000000000015e60 < x < -4500 or 7.9999999999999997e82 < x < 4.1000000000000001e229Initial program 100.0%
Taylor expanded in x around inf 100.0%
+-commutative100.0%
Simplified100.0%
Taylor expanded in z around inf 69.1%
if -4500 < x < 1.70000000000000003e-99Initial program 100.0%
Taylor expanded in x around 0 74.3%
Final simplification70.9%
(FPCore (x y z) :precision binary64 (if (or (<= x -1.25e-16) (not (<= x 2.3e-99))) (* x (+ z y)) (* z 5.0)))
double code(double x, double y, double z) {
double tmp;
if ((x <= -1.25e-16) || !(x <= 2.3e-99)) {
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 <= (-1.25d-16)) .or. (.not. (x <= 2.3d-99))) 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 <= -1.25e-16) || !(x <= 2.3e-99)) {
tmp = x * (z + y);
} else {
tmp = z * 5.0;
}
return tmp;
}
def code(x, y, z): tmp = 0 if (x <= -1.25e-16) or not (x <= 2.3e-99): tmp = x * (z + y) else: tmp = z * 5.0 return tmp
function code(x, y, z) tmp = 0.0 if ((x <= -1.25e-16) || !(x <= 2.3e-99)) 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 <= -1.25e-16) || ~((x <= 2.3e-99))) tmp = x * (z + y); else tmp = z * 5.0; end tmp_2 = tmp; end
code[x_, y_, z_] := If[Or[LessEqual[x, -1.25e-16], N[Not[LessEqual[x, 2.3e-99]], $MachinePrecision]], N[(x * N[(z + y), $MachinePrecision]), $MachinePrecision], N[(z * 5.0), $MachinePrecision]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;x \leq -1.25 \cdot 10^{-16} \lor \neg \left(x \leq 2.3 \cdot 10^{-99}\right):\\
\;\;\;\;x \cdot \left(z + y\right)\\
\mathbf{else}:\\
\;\;\;\;z \cdot 5\\
\end{array}
\end{array}
if x < -1.2500000000000001e-16 or 2.2999999999999998e-99 < x Initial program 100.0%
Taylor expanded in x around inf 91.8%
+-commutative91.8%
Simplified91.8%
if -1.2500000000000001e-16 < x < 2.2999999999999998e-99Initial program 100.0%
Taylor expanded in x around 0 76.0%
Final simplification85.0%
(FPCore (x y z) :precision binary64 (if (or (<= x -1.25e-18) (not (<= x 7.5e-100))) (* x y) (* z 5.0)))
double code(double x, double y, double z) {
double tmp;
if ((x <= -1.25e-18) || !(x <= 7.5e-100)) {
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 <= (-1.25d-18)) .or. (.not. (x <= 7.5d-100))) 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 <= -1.25e-18) || !(x <= 7.5e-100)) {
tmp = x * y;
} else {
tmp = z * 5.0;
}
return tmp;
}
def code(x, y, z): tmp = 0 if (x <= -1.25e-18) or not (x <= 7.5e-100): tmp = x * y else: tmp = z * 5.0 return tmp
function code(x, y, z) tmp = 0.0 if ((x <= -1.25e-18) || !(x <= 7.5e-100)) 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 <= -1.25e-18) || ~((x <= 7.5e-100))) tmp = x * y; else tmp = z * 5.0; end tmp_2 = tmp; end
code[x_, y_, z_] := If[Or[LessEqual[x, -1.25e-18], N[Not[LessEqual[x, 7.5e-100]], $MachinePrecision]], N[(x * y), $MachinePrecision], N[(z * 5.0), $MachinePrecision]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;x \leq -1.25 \cdot 10^{-18} \lor \neg \left(x \leq 7.5 \cdot 10^{-100}\right):\\
\;\;\;\;x \cdot y\\
\mathbf{else}:\\
\;\;\;\;z \cdot 5\\
\end{array}
\end{array}
if x < -1.25000000000000009e-18 or 7.50000000000000015e-100 < x Initial program 100.0%
Taylor expanded in y around inf 54.7%
if -1.25000000000000009e-18 < x < 7.50000000000000015e-100Initial program 100.0%
Taylor expanded in x around 0 76.0%
Final simplification63.9%
(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 100.0%
Final simplification100.0%
(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 37.6%
Final simplification37.6%
(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 2024031
(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)))