
(FPCore (x y z) :precision binary64 (- (* (* x 3.0) y) z))
double code(double x, double y, double z) {
return ((x * 3.0) * y) - z;
}
real(8) function code(x, y, z)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8), intent (in) :: z
code = ((x * 3.0d0) * y) - z
end function
public static double code(double x, double y, double z) {
return ((x * 3.0) * y) - z;
}
def code(x, y, z): return ((x * 3.0) * y) - z
function code(x, y, z) return Float64(Float64(Float64(x * 3.0) * y) - z) end
function tmp = code(x, y, z) tmp = ((x * 3.0) * y) - z; end
code[x_, y_, z_] := N[(N[(N[(x * 3.0), $MachinePrecision] * y), $MachinePrecision] - z), $MachinePrecision]
\begin{array}{l}
\\
\left(x \cdot 3\right) \cdot y - z
\end{array}
Sampling outcomes in binary64 precision:
Herbie found 6 alternatives:
| Alternative | Accuracy | Speedup |
|---|
(FPCore (x y z) :precision binary64 (- (* (* x 3.0) y) z))
double code(double x, double y, double z) {
return ((x * 3.0) * y) - z;
}
real(8) function code(x, y, z)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8), intent (in) :: z
code = ((x * 3.0d0) * y) - z
end function
public static double code(double x, double y, double z) {
return ((x * 3.0) * y) - z;
}
def code(x, y, z): return ((x * 3.0) * y) - z
function code(x, y, z) return Float64(Float64(Float64(x * 3.0) * y) - z) end
function tmp = code(x, y, z) tmp = ((x * 3.0) * y) - z; end
code[x_, y_, z_] := N[(N[(N[(x * 3.0), $MachinePrecision] * y), $MachinePrecision] - z), $MachinePrecision]
\begin{array}{l}
\\
\left(x \cdot 3\right) \cdot y - z
\end{array}
NOTE: x, y, and z should be sorted in increasing order before calling this function. (FPCore (x y z) :precision binary64 (fma (* 3.0 y) x (- z)))
assert(x < y && y < z);
double code(double x, double y, double z) {
return fma((3.0 * y), x, -z);
}
x, y, z = sort([x, y, z]) function code(x, y, z) return fma(Float64(3.0 * y), x, Float64(-z)) end
NOTE: x, y, and z should be sorted in increasing order before calling this function. code[x_, y_, z_] := N[(N[(3.0 * y), $MachinePrecision] * x + (-z)), $MachinePrecision]
\begin{array}{l}
[x, y, z] = \mathsf{sort}([x, y, z])\\
\\
\mathsf{fma}\left(3 \cdot y, x, -z\right)
\end{array}
Initial program 99.9%
associate-*l*99.8%
*-commutative99.8%
fmm-def99.9%
Simplified99.9%
Final simplification99.9%
NOTE: x, y, and z should be sorted in increasing order before calling this function. (FPCore (x y z) :precision binary64 (if (or (<= x -3.7e+47) (not (<= x 1.4e-108))) (* 3.0 (* y x)) (- z)))
assert(x < y && y < z);
double code(double x, double y, double z) {
double tmp;
if ((x <= -3.7e+47) || !(x <= 1.4e-108)) {
tmp = 3.0 * (y * x);
} else {
tmp = -z;
}
return tmp;
}
NOTE: x, y, and z should be sorted in increasing order before calling this function.
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 <= (-3.7d+47)) .or. (.not. (x <= 1.4d-108))) then
tmp = 3.0d0 * (y * x)
else
tmp = -z
end if
code = tmp
end function
assert x < y && y < z;
public static double code(double x, double y, double z) {
double tmp;
if ((x <= -3.7e+47) || !(x <= 1.4e-108)) {
tmp = 3.0 * (y * x);
} else {
tmp = -z;
}
return tmp;
}
[x, y, z] = sort([x, y, z]) def code(x, y, z): tmp = 0 if (x <= -3.7e+47) or not (x <= 1.4e-108): tmp = 3.0 * (y * x) else: tmp = -z return tmp
x, y, z = sort([x, y, z]) function code(x, y, z) tmp = 0.0 if ((x <= -3.7e+47) || !(x <= 1.4e-108)) tmp = Float64(3.0 * Float64(y * x)); else tmp = Float64(-z); end return tmp end
x, y, z = num2cell(sort([x, y, z])){:}
function tmp_2 = code(x, y, z)
tmp = 0.0;
if ((x <= -3.7e+47) || ~((x <= 1.4e-108)))
tmp = 3.0 * (y * x);
else
tmp = -z;
end
tmp_2 = tmp;
end
NOTE: x, y, and z should be sorted in increasing order before calling this function. code[x_, y_, z_] := If[Or[LessEqual[x, -3.7e+47], N[Not[LessEqual[x, 1.4e-108]], $MachinePrecision]], N[(3.0 * N[(y * x), $MachinePrecision]), $MachinePrecision], (-z)]
\begin{array}{l}
[x, y, z] = \mathsf{sort}([x, y, z])\\
\\
\begin{array}{l}
\mathbf{if}\;x \leq -3.7 \cdot 10^{+47} \lor \neg \left(x \leq 1.4 \cdot 10^{-108}\right):\\
\;\;\;\;3 \cdot \left(y \cdot x\right)\\
\mathbf{else}:\\
\;\;\;\;-z\\
\end{array}
\end{array}
if x < -3.70000000000000041e47 or 1.4e-108 < x Initial program 99.8%
associate-*l*99.8%
*-commutative99.8%
fmm-def99.8%
Simplified99.8%
Taylor expanded in y around inf 91.5%
+-commutative91.5%
fma-define91.5%
mul-1-neg91.5%
fmm-def91.5%
Simplified91.5%
Taylor expanded in y around inf 65.6%
if -3.70000000000000041e47 < x < 1.4e-108Initial program 99.9%
associate-*l*99.9%
*-commutative99.9%
fmm-def99.9%
Simplified99.9%
Taylor expanded in y around 0 75.8%
mul-1-neg75.8%
Simplified75.8%
Final simplification70.4%
NOTE: x, y, and z should be sorted in increasing order before calling this function. (FPCore (x y z) :precision binary64 (if (or (<= x -8.5e+47) (not (<= x 1.4e-108))) (* (* 3.0 y) x) (- z)))
assert(x < y && y < z);
double code(double x, double y, double z) {
double tmp;
if ((x <= -8.5e+47) || !(x <= 1.4e-108)) {
tmp = (3.0 * y) * x;
} else {
tmp = -z;
}
return tmp;
}
NOTE: x, y, and z should be sorted in increasing order before calling this function.
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 <= (-8.5d+47)) .or. (.not. (x <= 1.4d-108))) then
tmp = (3.0d0 * y) * x
else
tmp = -z
end if
code = tmp
end function
assert x < y && y < z;
public static double code(double x, double y, double z) {
double tmp;
if ((x <= -8.5e+47) || !(x <= 1.4e-108)) {
tmp = (3.0 * y) * x;
} else {
tmp = -z;
}
return tmp;
}
[x, y, z] = sort([x, y, z]) def code(x, y, z): tmp = 0 if (x <= -8.5e+47) or not (x <= 1.4e-108): tmp = (3.0 * y) * x else: tmp = -z return tmp
x, y, z = sort([x, y, z]) function code(x, y, z) tmp = 0.0 if ((x <= -8.5e+47) || !(x <= 1.4e-108)) tmp = Float64(Float64(3.0 * y) * x); else tmp = Float64(-z); end return tmp end
x, y, z = num2cell(sort([x, y, z])){:}
function tmp_2 = code(x, y, z)
tmp = 0.0;
if ((x <= -8.5e+47) || ~((x <= 1.4e-108)))
tmp = (3.0 * y) * x;
else
tmp = -z;
end
tmp_2 = tmp;
end
NOTE: x, y, and z should be sorted in increasing order before calling this function. code[x_, y_, z_] := If[Or[LessEqual[x, -8.5e+47], N[Not[LessEqual[x, 1.4e-108]], $MachinePrecision]], N[(N[(3.0 * y), $MachinePrecision] * x), $MachinePrecision], (-z)]
\begin{array}{l}
[x, y, z] = \mathsf{sort}([x, y, z])\\
\\
\begin{array}{l}
\mathbf{if}\;x \leq -8.5 \cdot 10^{+47} \lor \neg \left(x \leq 1.4 \cdot 10^{-108}\right):\\
\;\;\;\;\left(3 \cdot y\right) \cdot x\\
\mathbf{else}:\\
\;\;\;\;-z\\
\end{array}
\end{array}
if x < -8.5000000000000008e47 or 1.4e-108 < x Initial program 99.8%
associate-*l*99.8%
*-commutative99.8%
fmm-def99.8%
Simplified99.8%
Taylor expanded in y around inf 91.5%
+-commutative91.5%
fma-define91.5%
mul-1-neg91.5%
fmm-def91.5%
Simplified91.5%
Taylor expanded in y around inf 65.6%
associate-*r*65.6%
*-commutative65.6%
associate-*r*65.7%
Simplified65.7%
if -8.5000000000000008e47 < x < 1.4e-108Initial program 99.9%
associate-*l*99.9%
*-commutative99.9%
fmm-def99.9%
Simplified99.9%
Taylor expanded in y around 0 75.8%
mul-1-neg75.8%
Simplified75.8%
Final simplification70.4%
NOTE: x, y, and z should be sorted in increasing order before calling this function. (FPCore (x y z) :precision binary64 (- (* 3.0 (* y x)) z))
assert(x < y && y < z);
double code(double x, double y, double z) {
return (3.0 * (y * x)) - z;
}
NOTE: x, y, and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8), intent (in) :: z
code = (3.0d0 * (y * x)) - z
end function
assert x < y && y < z;
public static double code(double x, double y, double z) {
return (3.0 * (y * x)) - z;
}
[x, y, z] = sort([x, y, z]) def code(x, y, z): return (3.0 * (y * x)) - z
x, y, z = sort([x, y, z]) function code(x, y, z) return Float64(Float64(3.0 * Float64(y * x)) - z) end
x, y, z = num2cell(sort([x, y, z])){:}
function tmp = code(x, y, z)
tmp = (3.0 * (y * x)) - z;
end
NOTE: x, y, and z should be sorted in increasing order before calling this function. code[x_, y_, z_] := N[(N[(3.0 * N[(y * x), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]
\begin{array}{l}
[x, y, z] = \mathsf{sort}([x, y, z])\\
\\
3 \cdot \left(y \cdot x\right) - z
\end{array}
Initial program 99.9%
associate-*l*99.8%
Simplified99.8%
Taylor expanded in x around 0 99.8%
Final simplification99.8%
NOTE: x, y, and z should be sorted in increasing order before calling this function. (FPCore (x y z) :precision binary64 (- (* (* 3.0 y) x) z))
assert(x < y && y < z);
double code(double x, double y, double z) {
return ((3.0 * y) * x) - z;
}
NOTE: x, y, and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8), intent (in) :: z
code = ((3.0d0 * y) * x) - z
end function
assert x < y && y < z;
public static double code(double x, double y, double z) {
return ((3.0 * y) * x) - z;
}
[x, y, z] = sort([x, y, z]) def code(x, y, z): return ((3.0 * y) * x) - z
x, y, z = sort([x, y, z]) function code(x, y, z) return Float64(Float64(Float64(3.0 * y) * x) - z) end
x, y, z = num2cell(sort([x, y, z])){:}
function tmp = code(x, y, z)
tmp = ((3.0 * y) * x) - z;
end
NOTE: x, y, and z should be sorted in increasing order before calling this function. code[x_, y_, z_] := N[(N[(N[(3.0 * y), $MachinePrecision] * x), $MachinePrecision] - z), $MachinePrecision]
\begin{array}{l}
[x, y, z] = \mathsf{sort}([x, y, z])\\
\\
\left(3 \cdot y\right) \cdot x - z
\end{array}
Initial program 99.9%
associate-*l*99.8%
Simplified99.8%
Final simplification99.8%
NOTE: x, y, and z should be sorted in increasing order before calling this function. (FPCore (x y z) :precision binary64 (- z))
assert(x < y && y < z);
double code(double x, double y, double z) {
return -z;
}
NOTE: x, y, and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8), intent (in) :: z
code = -z
end function
assert x < y && y < z;
public static double code(double x, double y, double z) {
return -z;
}
[x, y, z] = sort([x, y, z]) def code(x, y, z): return -z
x, y, z = sort([x, y, z]) function code(x, y, z) return Float64(-z) end
x, y, z = num2cell(sort([x, y, z])){:}
function tmp = code(x, y, z)
tmp = -z;
end
NOTE: x, y, and z should be sorted in increasing order before calling this function. code[x_, y_, z_] := (-z)
\begin{array}{l}
[x, y, z] = \mathsf{sort}([x, y, z])\\
\\
-z
\end{array}
Initial program 99.9%
associate-*l*99.8%
*-commutative99.8%
fmm-def99.9%
Simplified99.9%
Taylor expanded in y around 0 54.6%
mul-1-neg54.6%
Simplified54.6%
Final simplification54.6%
(FPCore (x y z) :precision binary64 (- (* x (* 3.0 y)) z))
double code(double x, double y, double z) {
return (x * (3.0 * y)) - z;
}
real(8) function code(x, y, z)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8), intent (in) :: z
code = (x * (3.0d0 * y)) - z
end function
public static double code(double x, double y, double z) {
return (x * (3.0 * y)) - z;
}
def code(x, y, z): return (x * (3.0 * y)) - z
function code(x, y, z) return Float64(Float64(x * Float64(3.0 * y)) - z) end
function tmp = code(x, y, z) tmp = (x * (3.0 * y)) - z; end
code[x_, y_, z_] := N[(N[(x * N[(3.0 * y), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]
\begin{array}{l}
\\
x \cdot \left(3 \cdot y\right) - z
\end{array}
herbie shell --seed 2024095
(FPCore (x y z)
:name "Diagrams.Solve.Polynomial:cubForm from diagrams-solve-0.1, B"
:precision binary64
:alt
(- (* x (* 3.0 y)) z)
(- (* (* x 3.0) y) z))