
(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 -4e+87)
(* x y)
(if (<= x -4500000000.0)
(* z x)
(if (<= x -1.15e-65) (* x y) (if (<= x 5.0) (* z 5.0) (* z x))))))
double code(double x, double y, double z) {
double tmp;
if (x <= -4e+87) {
tmp = x * y;
} else if (x <= -4500000000.0) {
tmp = z * x;
} else if (x <= -1.15e-65) {
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 <= (-4d+87)) then
tmp = x * y
else if (x <= (-4500000000.0d0)) then
tmp = z * x
else if (x <= (-1.15d-65)) 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 <= -4e+87) {
tmp = x * y;
} else if (x <= -4500000000.0) {
tmp = z * x;
} else if (x <= -1.15e-65) {
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 <= -4e+87: tmp = x * y elif x <= -4500000000.0: tmp = z * x elif x <= -1.15e-65: 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 <= -4e+87) tmp = Float64(x * y); elseif (x <= -4500000000.0) tmp = Float64(z * x); elseif (x <= -1.15e-65) 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 <= -4e+87) tmp = x * y; elseif (x <= -4500000000.0) tmp = z * x; elseif (x <= -1.15e-65) 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, -4e+87], N[(x * y), $MachinePrecision], If[LessEqual[x, -4500000000.0], N[(z * x), $MachinePrecision], If[LessEqual[x, -1.15e-65], 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 -4 \cdot 10^{+87}:\\
\;\;\;\;x \cdot y\\
\mathbf{elif}\;x \leq -4500000000:\\
\;\;\;\;z \cdot x\\
\mathbf{elif}\;x \leq -1.15 \cdot 10^{-65}:\\
\;\;\;\;x \cdot y\\
\mathbf{elif}\;x \leq 5:\\
\;\;\;\;z \cdot 5\\
\mathbf{else}:\\
\;\;\;\;z \cdot x\\
\end{array}
\end{array}
if x < -3.9999999999999998e87 or -4.5e9 < x < -1.15e-65Initial program 99.9%
Taylor expanded in y around inf 60.9%
if -3.9999999999999998e87 < x < -4.5e9 or 5 < x Initial program 99.9%
Taylor expanded in x around inf 97.9%
+-commutative97.9%
Simplified97.9%
Taylor expanded in z around inf 56.4%
if -1.15e-65 < x < 5Initial program 99.8%
Taylor expanded in x around 0 75.4%
Final simplification66.6%
(FPCore (x y z) :precision binary64 (if (or (<= x -5.6e-67) (not (<= x 0.00075))) (* x (+ z y)) (* z 5.0)))
double code(double x, double y, double z) {
double tmp;
if ((x <= -5.6e-67) || !(x <= 0.00075)) {
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 <= (-5.6d-67)) .or. (.not. (x <= 0.00075d0))) 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 <= -5.6e-67) || !(x <= 0.00075)) {
tmp = x * (z + y);
} else {
tmp = z * 5.0;
}
return tmp;
}
def code(x, y, z): tmp = 0 if (x <= -5.6e-67) or not (x <= 0.00075): tmp = x * (z + y) else: tmp = z * 5.0 return tmp
function code(x, y, z) tmp = 0.0 if ((x <= -5.6e-67) || !(x <= 0.00075)) 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 <= -5.6e-67) || ~((x <= 0.00075))) tmp = x * (z + y); else tmp = z * 5.0; end tmp_2 = tmp; end
code[x_, y_, z_] := If[Or[LessEqual[x, -5.6e-67], N[Not[LessEqual[x, 0.00075]], $MachinePrecision]], N[(x * N[(z + y), $MachinePrecision]), $MachinePrecision], N[(z * 5.0), $MachinePrecision]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;x \leq -5.6 \cdot 10^{-67} \lor \neg \left(x \leq 0.00075\right):\\
\;\;\;\;x \cdot \left(z + y\right)\\
\mathbf{else}:\\
\;\;\;\;z \cdot 5\\
\end{array}
\end{array}
if x < -5.60000000000000021e-67 or 7.5000000000000002e-4 < x Initial program 99.9%
Taylor expanded in x around inf 95.1%
+-commutative95.1%
Simplified95.1%
if -5.60000000000000021e-67 < x < 7.5000000000000002e-4Initial program 99.8%
Taylor expanded in x around 0 76.0%
Final simplification85.9%
(FPCore (x y z) :precision binary64 (if (or (<= x -6.2e-59) (not (<= x 2.1e+14))) (* x (+ z y)) (* z (+ 5.0 x))))
double code(double x, double y, double z) {
double tmp;
if ((x <= -6.2e-59) || !(x <= 2.1e+14)) {
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 <= (-6.2d-59)) .or. (.not. (x <= 2.1d+14))) 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 <= -6.2e-59) || !(x <= 2.1e+14)) {
tmp = x * (z + y);
} else {
tmp = z * (5.0 + x);
}
return tmp;
}
def code(x, y, z): tmp = 0 if (x <= -6.2e-59) or not (x <= 2.1e+14): tmp = x * (z + y) else: tmp = z * (5.0 + x) return tmp
function code(x, y, z) tmp = 0.0 if ((x <= -6.2e-59) || !(x <= 2.1e+14)) 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 <= -6.2e-59) || ~((x <= 2.1e+14))) tmp = x * (z + y); else tmp = z * (5.0 + x); end tmp_2 = tmp; end
code[x_, y_, z_] := If[Or[LessEqual[x, -6.2e-59], N[Not[LessEqual[x, 2.1e+14]], $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 -6.2 \cdot 10^{-59} \lor \neg \left(x \leq 2.1 \cdot 10^{+14}\right):\\
\;\;\;\;x \cdot \left(z + y\right)\\
\mathbf{else}:\\
\;\;\;\;z \cdot \left(5 + x\right)\\
\end{array}
\end{array}
if x < -6.19999999999999998e-59 or 2.1e14 < x Initial program 99.9%
Taylor expanded in x around inf 95.9%
+-commutative95.9%
Simplified95.9%
if -6.19999999999999998e-59 < x < 2.1e14Initial program 99.8%
Taylor expanded in y around 0 76.5%
distribute-rgt-in76.5%
Simplified76.5%
Final simplification86.3%
(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 -7e-66) (* x y) (if (<= x 0.00075) (* z 5.0) (* x y))))
double code(double x, double y, double z) {
double tmp;
if (x <= -7e-66) {
tmp = x * y;
} else if (x <= 0.00075) {
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 <= (-7d-66)) then
tmp = x * y
else if (x <= 0.00075d0) 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 <= -7e-66) {
tmp = x * y;
} else if (x <= 0.00075) {
tmp = z * 5.0;
} else {
tmp = x * y;
}
return tmp;
}
def code(x, y, z): tmp = 0 if x <= -7e-66: tmp = x * y elif x <= 0.00075: tmp = z * 5.0 else: tmp = x * y return tmp
function code(x, y, z) tmp = 0.0 if (x <= -7e-66) tmp = Float64(x * y); elseif (x <= 0.00075) 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 <= -7e-66) tmp = x * y; elseif (x <= 0.00075) tmp = z * 5.0; else tmp = x * y; end tmp_2 = tmp; end
code[x_, y_, z_] := If[LessEqual[x, -7e-66], N[(x * y), $MachinePrecision], If[LessEqual[x, 0.00075], N[(z * 5.0), $MachinePrecision], N[(x * y), $MachinePrecision]]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;x \leq -7 \cdot 10^{-66}:\\
\;\;\;\;x \cdot y\\
\mathbf{elif}\;x \leq 0.00075:\\
\;\;\;\;z \cdot 5\\
\mathbf{else}:\\
\;\;\;\;x \cdot y\\
\end{array}
\end{array}
if x < -7.0000000000000001e-66 or 7.5000000000000002e-4 < x Initial program 99.9%
Taylor expanded in y around inf 53.2%
if -7.0000000000000001e-66 < x < 7.5000000000000002e-4Initial program 99.8%
Taylor expanded in x around 0 76.0%
Final simplification64.2%
(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 39.8%
Final simplification39.8%
(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 2023290
(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)))