
(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 -1.3e+221)
(* z x)
(if (<= x -7e-17)
(* x y)
(if (<= x 2.5e-30) (* z 5.0) (if (<= x 7e+156) (* x y) (* z x))))))
double code(double x, double y, double z) {
double tmp;
if (x <= -1.3e+221) {
tmp = z * x;
} else if (x <= -7e-17) {
tmp = x * y;
} else if (x <= 2.5e-30) {
tmp = z * 5.0;
} else if (x <= 7e+156) {
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 <= (-1.3d+221)) then
tmp = z * x
else if (x <= (-7d-17)) then
tmp = x * y
else if (x <= 2.5d-30) then
tmp = z * 5.0d0
else if (x <= 7d+156) 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 <= -1.3e+221) {
tmp = z * x;
} else if (x <= -7e-17) {
tmp = x * y;
} else if (x <= 2.5e-30) {
tmp = z * 5.0;
} else if (x <= 7e+156) {
tmp = x * y;
} else {
tmp = z * x;
}
return tmp;
}
def code(x, y, z): tmp = 0 if x <= -1.3e+221: tmp = z * x elif x <= -7e-17: tmp = x * y elif x <= 2.5e-30: tmp = z * 5.0 elif x <= 7e+156: tmp = x * y else: tmp = z * x return tmp
function code(x, y, z) tmp = 0.0 if (x <= -1.3e+221) tmp = Float64(z * x); elseif (x <= -7e-17) tmp = Float64(x * y); elseif (x <= 2.5e-30) tmp = Float64(z * 5.0); elseif (x <= 7e+156) 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 <= -1.3e+221) tmp = z * x; elseif (x <= -7e-17) tmp = x * y; elseif (x <= 2.5e-30) tmp = z * 5.0; elseif (x <= 7e+156) tmp = x * y; else tmp = z * x; end tmp_2 = tmp; end
code[x_, y_, z_] := If[LessEqual[x, -1.3e+221], N[(z * x), $MachinePrecision], If[LessEqual[x, -7e-17], N[(x * y), $MachinePrecision], If[LessEqual[x, 2.5e-30], N[(z * 5.0), $MachinePrecision], If[LessEqual[x, 7e+156], N[(x * y), $MachinePrecision], N[(z * x), $MachinePrecision]]]]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;x \leq -1.3 \cdot 10^{+221}:\\
\;\;\;\;z \cdot x\\
\mathbf{elif}\;x \leq -7 \cdot 10^{-17}:\\
\;\;\;\;x \cdot y\\
\mathbf{elif}\;x \leq 2.5 \cdot 10^{-30}:\\
\;\;\;\;z \cdot 5\\
\mathbf{elif}\;x \leq 7 \cdot 10^{+156}:\\
\;\;\;\;x \cdot y\\
\mathbf{else}:\\
\;\;\;\;z \cdot x\\
\end{array}
\end{array}
if x < -1.30000000000000002e221 or 7.0000000000000006e156 < x Initial program 100.0%
Taylor expanded in x around inf 100.0%
+-commutative100.0%
Simplified100.0%
Taylor expanded in z around inf 79.5%
if -1.30000000000000002e221 < x < -7.0000000000000003e-17 or 2.49999999999999986e-30 < x < 7.0000000000000006e156Initial program 100.0%
Taylor expanded in y around inf 64.5%
if -7.0000000000000003e-17 < x < 2.49999999999999986e-30Initial program 99.9%
Taylor expanded in x around 0 83.3%
Final simplification76.7%
(FPCore (x y z) :precision binary64 (if (or (<= x -4.6e-17) (not (<= x 3.2e-26))) (* x (+ z y)) (* z 5.0)))
double code(double x, double y, double z) {
double tmp;
if ((x <= -4.6e-17) || !(x <= 3.2e-26)) {
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 <= (-4.6d-17)) .or. (.not. (x <= 3.2d-26))) 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 <= -4.6e-17) || !(x <= 3.2e-26)) {
tmp = x * (z + y);
} else {
tmp = z * 5.0;
}
return tmp;
}
def code(x, y, z): tmp = 0 if (x <= -4.6e-17) or not (x <= 3.2e-26): tmp = x * (z + y) else: tmp = z * 5.0 return tmp
function code(x, y, z) tmp = 0.0 if ((x <= -4.6e-17) || !(x <= 3.2e-26)) 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 <= -4.6e-17) || ~((x <= 3.2e-26))) tmp = x * (z + y); else tmp = z * 5.0; end tmp_2 = tmp; end
code[x_, y_, z_] := If[Or[LessEqual[x, -4.6e-17], N[Not[LessEqual[x, 3.2e-26]], $MachinePrecision]], N[(x * N[(z + y), $MachinePrecision]), $MachinePrecision], N[(z * 5.0), $MachinePrecision]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;x \leq -4.6 \cdot 10^{-17} \lor \neg \left(x \leq 3.2 \cdot 10^{-26}\right):\\
\;\;\;\;x \cdot \left(z + y\right)\\
\mathbf{else}:\\
\;\;\;\;z \cdot 5\\
\end{array}
\end{array}
if x < -4.60000000000000018e-17 or 3.2000000000000001e-26 < x Initial program 100.0%
Taylor expanded in x around inf 98.6%
+-commutative98.6%
Simplified98.6%
if -4.60000000000000018e-17 < x < 3.2000000000000001e-26Initial program 99.9%
Taylor expanded in x around 0 83.3%
Final simplification91.5%
(FPCore (x y z) :precision binary64 (if (or (<= x -5.5e-15) (not (<= x 4.8e-31))) (* x (+ z y)) (* z (+ 5.0 x))))
double code(double x, double y, double z) {
double tmp;
if ((x <= -5.5e-15) || !(x <= 4.8e-31)) {
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 <= (-5.5d-15)) .or. (.not. (x <= 4.8d-31))) 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 <= -5.5e-15) || !(x <= 4.8e-31)) {
tmp = x * (z + y);
} else {
tmp = z * (5.0 + x);
}
return tmp;
}
def code(x, y, z): tmp = 0 if (x <= -5.5e-15) or not (x <= 4.8e-31): tmp = x * (z + y) else: tmp = z * (5.0 + x) return tmp
function code(x, y, z) tmp = 0.0 if ((x <= -5.5e-15) || !(x <= 4.8e-31)) 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 <= -5.5e-15) || ~((x <= 4.8e-31))) tmp = x * (z + y); else tmp = z * (5.0 + x); end tmp_2 = tmp; end
code[x_, y_, z_] := If[Or[LessEqual[x, -5.5e-15], N[Not[LessEqual[x, 4.8e-31]], $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 -5.5 \cdot 10^{-15} \lor \neg \left(x \leq 4.8 \cdot 10^{-31}\right):\\
\;\;\;\;x \cdot \left(z + y\right)\\
\mathbf{else}:\\
\;\;\;\;z \cdot \left(5 + x\right)\\
\end{array}
\end{array}
if x < -5.5000000000000002e-15 or 4.8e-31 < x Initial program 100.0%
Taylor expanded in x around inf 98.6%
+-commutative98.6%
Simplified98.6%
if -5.5000000000000002e-15 < x < 4.8e-31Initial program 99.9%
Taylor expanded in y around 0 83.3%
distribute-rgt-in83.3%
Simplified83.3%
Final simplification91.5%
(FPCore (x y z) :precision binary64 (if (or (<= x -1.4e-15) (not (<= x 3.7e-35))) (* x y) (* z 5.0)))
double code(double x, double y, double z) {
double tmp;
if ((x <= -1.4e-15) || !(x <= 3.7e-35)) {
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 <= (-1.4d-15)) .or. (.not. (x <= 3.7d-35))) 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 <= -1.4e-15) || !(x <= 3.7e-35)) {
tmp = x * y;
} else {
tmp = z * 5.0;
}
return tmp;
}
def code(x, y, z): tmp = 0 if (x <= -1.4e-15) or not (x <= 3.7e-35): tmp = x * y else: tmp = z * 5.0 return tmp
function code(x, y, z) tmp = 0.0 if ((x <= -1.4e-15) || !(x <= 3.7e-35)) 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 <= -1.4e-15) || ~((x <= 3.7e-35))) tmp = x * y; else tmp = z * 5.0; end tmp_2 = tmp; end
code[x_, y_, z_] := If[Or[LessEqual[x, -1.4e-15], N[Not[LessEqual[x, 3.7e-35]], $MachinePrecision]], N[(x * y), $MachinePrecision], N[(z * 5.0), $MachinePrecision]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;x \leq -1.4 \cdot 10^{-15} \lor \neg \left(x \leq 3.7 \cdot 10^{-35}\right):\\
\;\;\;\;x \cdot y\\
\mathbf{else}:\\
\;\;\;\;z \cdot 5\\
\end{array}
\end{array}
if x < -1.40000000000000007e-15 or 3.6999999999999999e-35 < x Initial program 100.0%
Taylor expanded in y around inf 52.0%
if -1.40000000000000007e-15 < x < 3.6999999999999999e-35Initial program 99.9%
Taylor expanded in x around 0 83.3%
Final simplification66.4%
(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 40.5%
Final simplification40.5%
(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 2024027
(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)))