
(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-define100.0%
Applied egg-rr100.0%
Final simplification100.0%
(FPCore (x y z) :precision binary64 (if (<= x -1.4e-67) (* x y) (if (<= x 3e-79) (* z 5.0) (if (<= x 3.5e+256) (* x y) (* z x)))))
double code(double x, double y, double z) {
double tmp;
if (x <= -1.4e-67) {
tmp = x * y;
} else if (x <= 3e-79) {
tmp = z * 5.0;
} else if (x <= 3.5e+256) {
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 <= (-1.4d-67)) then
tmp = x * y
else if (x <= 3d-79) then
tmp = z * 5.0d0
else if (x <= 3.5d+256) 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 <= -1.4e-67) {
tmp = x * y;
} else if (x <= 3e-79) {
tmp = z * 5.0;
} else if (x <= 3.5e+256) {
tmp = x * y;
} else {
tmp = z * x;
}
return tmp;
}
def code(x, y, z): tmp = 0 if x <= -1.4e-67: tmp = x * y elif x <= 3e-79: tmp = z * 5.0 elif x <= 3.5e+256: tmp = x * y else: tmp = z * x return tmp
function code(x, y, z) tmp = 0.0 if (x <= -1.4e-67) tmp = Float64(x * y); elseif (x <= 3e-79) tmp = Float64(z * 5.0); elseif (x <= 3.5e+256) 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 <= -1.4e-67) tmp = x * y; elseif (x <= 3e-79) tmp = z * 5.0; elseif (x <= 3.5e+256) tmp = x * y; else tmp = z * x; end tmp_2 = tmp; end
code[x_, y_, z_] := If[LessEqual[x, -1.4e-67], N[(x * y), $MachinePrecision], If[LessEqual[x, 3e-79], N[(z * 5.0), $MachinePrecision], If[LessEqual[x, 3.5e+256], N[(x * y), $MachinePrecision], N[(z * x), $MachinePrecision]]]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;x \leq -1.4 \cdot 10^{-67}:\\
\;\;\;\;x \cdot y\\
\mathbf{elif}\;x \leq 3 \cdot 10^{-79}:\\
\;\;\;\;z \cdot 5\\
\mathbf{elif}\;x \leq 3.5 \cdot 10^{+256}:\\
\;\;\;\;x \cdot y\\
\mathbf{else}:\\
\;\;\;\;z \cdot x\\
\end{array}
\end{array}
if x < -1.40000000000000005e-67 or 3e-79 < x < 3.4999999999999998e256Initial program 100.0%
Taylor expanded in y around inf 61.3%
if -1.40000000000000005e-67 < x < 3e-79Initial program 99.9%
Taylor expanded in x around 0 79.7%
if 3.4999999999999998e256 < x Initial program 100.0%
Taylor expanded in x around inf 100.0%
+-commutative100.0%
Simplified100.0%
Taylor expanded in z around inf 82.3%
Final simplification69.3%
(FPCore (x y z) :precision binary64 (if (or (<= x -5.0) (not (<= x 0.0155))) (* x (+ z y)) (+ (* x y) (* z 5.0))))
double code(double x, double y, double z) {
double tmp;
if ((x <= -5.0) || !(x <= 0.0155)) {
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 <= (-5.0d0)) .or. (.not. (x <= 0.0155d0))) 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 <= -5.0) || !(x <= 0.0155)) {
tmp = x * (z + y);
} else {
tmp = (x * y) + (z * 5.0);
}
return tmp;
}
def code(x, y, z): tmp = 0 if (x <= -5.0) or not (x <= 0.0155): tmp = x * (z + y) else: tmp = (x * y) + (z * 5.0) return tmp
function code(x, y, z) tmp = 0.0 if ((x <= -5.0) || !(x <= 0.0155)) 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 <= -5.0) || ~((x <= 0.0155))) tmp = x * (z + y); else tmp = (x * y) + (z * 5.0); end tmp_2 = tmp; end
code[x_, y_, z_] := If[Or[LessEqual[x, -5.0], N[Not[LessEqual[x, 0.0155]], $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 -5 \lor \neg \left(x \leq 0.0155\right):\\
\;\;\;\;x \cdot \left(z + y\right)\\
\mathbf{else}:\\
\;\;\;\;x \cdot y + z \cdot 5\\
\end{array}
\end{array}
if x < -5 or 0.0155 < x Initial program 100.0%
Taylor expanded in x around inf 99.5%
+-commutative99.5%
Simplified99.5%
if -5 < x < 0.0155Initial program 99.9%
Taylor expanded in y around inf 99.5%
Final simplification99.5%
(FPCore (x y z) :precision binary64 (if (or (<= x -4.9e-65) (not (<= x 4.6e-85))) (* x (+ z y)) (* z 5.0)))
double code(double x, double y, double z) {
double tmp;
if ((x <= -4.9e-65) || !(x <= 4.6e-85)) {
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 <= (-4.9d-65)) .or. (.not. (x <= 4.6d-85))) 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 <= -4.9e-65) || !(x <= 4.6e-85)) {
tmp = x * (z + y);
} else {
tmp = z * 5.0;
}
return tmp;
}
def code(x, y, z): tmp = 0 if (x <= -4.9e-65) or not (x <= 4.6e-85): tmp = x * (z + y) else: tmp = z * 5.0 return tmp
function code(x, y, z) tmp = 0.0 if ((x <= -4.9e-65) || !(x <= 4.6e-85)) 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 <= -4.9e-65) || ~((x <= 4.6e-85))) tmp = x * (z + y); else tmp = z * 5.0; end tmp_2 = tmp; end
code[x_, y_, z_] := If[Or[LessEqual[x, -4.9e-65], N[Not[LessEqual[x, 4.6e-85]], $MachinePrecision]], N[(x * N[(z + y), $MachinePrecision]), $MachinePrecision], N[(z * 5.0), $MachinePrecision]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;x \leq -4.9 \cdot 10^{-65} \lor \neg \left(x \leq 4.6 \cdot 10^{-85}\right):\\
\;\;\;\;x \cdot \left(z + y\right)\\
\mathbf{else}:\\
\;\;\;\;z \cdot 5\\
\end{array}
\end{array}
if x < -4.89999999999999964e-65 or 4.6000000000000001e-85 < x Initial program 100.0%
Taylor expanded in x around inf 91.2%
+-commutative91.2%
Simplified91.2%
if -4.89999999999999964e-65 < x < 4.6000000000000001e-85Initial program 99.9%
Taylor expanded in x around 0 80.3%
Final simplification87.1%
(FPCore (x y z) :precision binary64 (if (or (<= x -3.2e-63) (not (<= x 3.5e-80))) (* x y) (* z 5.0)))
double code(double x, double y, double z) {
double tmp;
if ((x <= -3.2e-63) || !(x <= 3.5e-80)) {
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 <= (-3.2d-63)) .or. (.not. (x <= 3.5d-80))) 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 <= -3.2e-63) || !(x <= 3.5e-80)) {
tmp = x * y;
} else {
tmp = z * 5.0;
}
return tmp;
}
def code(x, y, z): tmp = 0 if (x <= -3.2e-63) or not (x <= 3.5e-80): tmp = x * y else: tmp = z * 5.0 return tmp
function code(x, y, z) tmp = 0.0 if ((x <= -3.2e-63) || !(x <= 3.5e-80)) 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 <= -3.2e-63) || ~((x <= 3.5e-80))) tmp = x * y; else tmp = z * 5.0; end tmp_2 = tmp; end
code[x_, y_, z_] := If[Or[LessEqual[x, -3.2e-63], N[Not[LessEqual[x, 3.5e-80]], $MachinePrecision]], N[(x * y), $MachinePrecision], N[(z * 5.0), $MachinePrecision]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;x \leq -3.2 \cdot 10^{-63} \lor \neg \left(x \leq 3.5 \cdot 10^{-80}\right):\\
\;\;\;\;x \cdot y\\
\mathbf{else}:\\
\;\;\;\;z \cdot 5\\
\end{array}
\end{array}
if x < -3.19999999999999989e-63 or 3.50000000000000015e-80 < x Initial program 100.0%
Taylor expanded in y around inf 59.6%
if -3.19999999999999989e-63 < x < 3.50000000000000015e-80Initial program 99.9%
Taylor expanded in x around 0 79.7%
Final simplification67.4%
(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 36.9%
Final simplification36.9%
(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 2024135
(FPCore (x y z)
:name "Graphics.Rendering.Plot.Render.Plot.Legend:renderLegendOutside from plot-0.2.3.4, C"
:precision binary64
:alt
(! :herbie-platform default (+ (* (+ x 5) z) (* x y)))
(+ (* x (+ y z)) (* z 5.0)))