
(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 6 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%
+-commutativeN/A
accelerator-lowering-fma.f64N/A
*-lowering-*.f64N/A
+-lowering-+.f64100.0
Applied egg-rr100.0%
Final simplification100.0%
(FPCore (x y z) :precision binary64 (if (<= x -1e+143) (* x y) (if (<= x -1.05) (* z x) (if (<= x 3.7e-29) (* z 5.0) (* x y)))))
double code(double x, double y, double z) {
double tmp;
if (x <= -1e+143) {
tmp = x * y;
} else if (x <= -1.05) {
tmp = z * x;
} else if (x <= 3.7e-29) {
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 <= (-1d+143)) then
tmp = x * y
else if (x <= (-1.05d0)) then
tmp = z * x
else if (x <= 3.7d-29) 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 <= -1e+143) {
tmp = x * y;
} else if (x <= -1.05) {
tmp = z * x;
} else if (x <= 3.7e-29) {
tmp = z * 5.0;
} else {
tmp = x * y;
}
return tmp;
}
def code(x, y, z): tmp = 0 if x <= -1e+143: tmp = x * y elif x <= -1.05: tmp = z * x elif x <= 3.7e-29: tmp = z * 5.0 else: tmp = x * y return tmp
function code(x, y, z) tmp = 0.0 if (x <= -1e+143) tmp = Float64(x * y); elseif (x <= -1.05) tmp = Float64(z * x); elseif (x <= 3.7e-29) 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 <= -1e+143) tmp = x * y; elseif (x <= -1.05) tmp = z * x; elseif (x <= 3.7e-29) tmp = z * 5.0; else tmp = x * y; end tmp_2 = tmp; end
code[x_, y_, z_] := If[LessEqual[x, -1e+143], N[(x * y), $MachinePrecision], If[LessEqual[x, -1.05], N[(z * x), $MachinePrecision], If[LessEqual[x, 3.7e-29], N[(z * 5.0), $MachinePrecision], N[(x * y), $MachinePrecision]]]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;x \leq -1 \cdot 10^{+143}:\\
\;\;\;\;x \cdot y\\
\mathbf{elif}\;x \leq -1.05:\\
\;\;\;\;z \cdot x\\
\mathbf{elif}\;x \leq 3.7 \cdot 10^{-29}:\\
\;\;\;\;z \cdot 5\\
\mathbf{else}:\\
\;\;\;\;x \cdot y\\
\end{array}
\end{array}
if x < -1e143 or 3.6999999999999997e-29 < x Initial program 100.0%
Taylor expanded in y around inf
*-lowering-*.f6463.5
Simplified63.5%
if -1e143 < x < -1.05000000000000004Initial program 100.0%
Taylor expanded in x around inf
*-lowering-*.f64N/A
+-commutativeN/A
+-lowering-+.f6496.5
Simplified96.5%
Taylor expanded in z around inf
*-lowering-*.f6466.1
Simplified66.1%
if -1.05000000000000004 < x < 3.6999999999999997e-29Initial program 99.9%
Taylor expanded in x around 0
*-lowering-*.f6483.2
Simplified83.2%
Final simplification73.0%
(FPCore (x y z) :precision binary64 (let* ((t_0 (* x (+ z y)))) (if (<= x -760.0) t_0 (if (<= x 5.0) (fma z 5.0 (* x y)) t_0))))
double code(double x, double y, double z) {
double t_0 = x * (z + y);
double tmp;
if (x <= -760.0) {
tmp = t_0;
} else if (x <= 5.0) {
tmp = fma(z, 5.0, (x * y));
} else {
tmp = t_0;
}
return tmp;
}
function code(x, y, z) t_0 = Float64(x * Float64(z + y)) tmp = 0.0 if (x <= -760.0) tmp = t_0; elseif (x <= 5.0) tmp = fma(z, 5.0, Float64(x * y)); else tmp = t_0; end return tmp end
code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(z + y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -760.0], t$95$0, If[LessEqual[x, 5.0], N[(z * 5.0 + N[(x * y), $MachinePrecision]), $MachinePrecision], t$95$0]]]
\begin{array}{l}
\\
\begin{array}{l}
t_0 := x \cdot \left(z + y\right)\\
\mathbf{if}\;x \leq -760:\\
\;\;\;\;t\_0\\
\mathbf{elif}\;x \leq 5:\\
\;\;\;\;\mathsf{fma}\left(z, 5, x \cdot y\right)\\
\mathbf{else}:\\
\;\;\;\;t\_0\\
\end{array}
\end{array}
if x < -760 or 5 < x Initial program 100.0%
Taylor expanded in x around inf
*-lowering-*.f64N/A
+-commutativeN/A
+-lowering-+.f6499.5
Simplified99.5%
if -760 < x < 5Initial program 99.9%
Taylor expanded in y around inf
*-lowering-*.f6498.6
Simplified98.6%
+-commutativeN/A
accelerator-lowering-fma.f64N/A
*-lowering-*.f6498.6
Applied egg-rr98.6%
(FPCore (x y z) :precision binary64 (let* ((t_0 (* x (+ z y)))) (if (<= x -2.6e-14) t_0 (if (<= x 9e-64) (* z 5.0) t_0))))
double code(double x, double y, double z) {
double t_0 = x * (z + y);
double tmp;
if (x <= -2.6e-14) {
tmp = t_0;
} else if (x <= 9e-64) {
tmp = z * 5.0;
} else {
tmp = t_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) :: t_0
real(8) :: tmp
t_0 = x * (z + y)
if (x <= (-2.6d-14)) then
tmp = t_0
else if (x <= 9d-64) then
tmp = z * 5.0d0
else
tmp = t_0
end if
code = tmp
end function
public static double code(double x, double y, double z) {
double t_0 = x * (z + y);
double tmp;
if (x <= -2.6e-14) {
tmp = t_0;
} else if (x <= 9e-64) {
tmp = z * 5.0;
} else {
tmp = t_0;
}
return tmp;
}
def code(x, y, z): t_0 = x * (z + y) tmp = 0 if x <= -2.6e-14: tmp = t_0 elif x <= 9e-64: tmp = z * 5.0 else: tmp = t_0 return tmp
function code(x, y, z) t_0 = Float64(x * Float64(z + y)) tmp = 0.0 if (x <= -2.6e-14) tmp = t_0; elseif (x <= 9e-64) tmp = Float64(z * 5.0); else tmp = t_0; end return tmp end
function tmp_2 = code(x, y, z) t_0 = x * (z + y); tmp = 0.0; if (x <= -2.6e-14) tmp = t_0; elseif (x <= 9e-64) tmp = z * 5.0; else tmp = t_0; end tmp_2 = tmp; end
code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(z + y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.6e-14], t$95$0, If[LessEqual[x, 9e-64], N[(z * 5.0), $MachinePrecision], t$95$0]]]
\begin{array}{l}
\\
\begin{array}{l}
t_0 := x \cdot \left(z + y\right)\\
\mathbf{if}\;x \leq -2.6 \cdot 10^{-14}:\\
\;\;\;\;t\_0\\
\mathbf{elif}\;x \leq 9 \cdot 10^{-64}:\\
\;\;\;\;z \cdot 5\\
\mathbf{else}:\\
\;\;\;\;t\_0\\
\end{array}
\end{array}
if x < -2.59999999999999997e-14 or 9.00000000000000019e-64 < x Initial program 100.0%
Taylor expanded in x around inf
*-lowering-*.f64N/A
+-commutativeN/A
+-lowering-+.f6494.6
Simplified94.6%
if -2.59999999999999997e-14 < x < 9.00000000000000019e-64Initial program 99.9%
Taylor expanded in x around 0
*-lowering-*.f6488.2
Simplified88.2%
Final simplification91.9%
(FPCore (x y z) :precision binary64 (if (<= x -2.4e-16) (* x y) (if (<= x 1.7e-31) (* z 5.0) (* x y))))
double code(double x, double y, double z) {
double tmp;
if (x <= -2.4e-16) {
tmp = x * y;
} else if (x <= 1.7e-31) {
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 <= (-2.4d-16)) then
tmp = x * y
else if (x <= 1.7d-31) 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 <= -2.4e-16) {
tmp = x * y;
} else if (x <= 1.7e-31) {
tmp = z * 5.0;
} else {
tmp = x * y;
}
return tmp;
}
def code(x, y, z): tmp = 0 if x <= -2.4e-16: tmp = x * y elif x <= 1.7e-31: tmp = z * 5.0 else: tmp = x * y return tmp
function code(x, y, z) tmp = 0.0 if (x <= -2.4e-16) tmp = Float64(x * y); elseif (x <= 1.7e-31) 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 <= -2.4e-16) tmp = x * y; elseif (x <= 1.7e-31) tmp = z * 5.0; else tmp = x * y; end tmp_2 = tmp; end
code[x_, y_, z_] := If[LessEqual[x, -2.4e-16], N[(x * y), $MachinePrecision], If[LessEqual[x, 1.7e-31], N[(z * 5.0), $MachinePrecision], N[(x * y), $MachinePrecision]]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;x \leq -2.4 \cdot 10^{-16}:\\
\;\;\;\;x \cdot y\\
\mathbf{elif}\;x \leq 1.7 \cdot 10^{-31}:\\
\;\;\;\;z \cdot 5\\
\mathbf{else}:\\
\;\;\;\;x \cdot y\\
\end{array}
\end{array}
if x < -2.40000000000000005e-16 or 1.7000000000000001e-31 < x Initial program 100.0%
Taylor expanded in y around inf
*-lowering-*.f6459.2
Simplified59.2%
if -2.40000000000000005e-16 < x < 1.7000000000000001e-31Initial program 99.9%
Taylor expanded in x around 0
*-lowering-*.f6485.1
Simplified85.1%
Final simplification71.0%
(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
*-lowering-*.f6440.9
Simplified40.9%
Final simplification40.9%
(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 2024199
(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)))