
(FPCore (x y z) :precision binary64 (+ (* x y) (* (- 1.0 x) z)))
double code(double x, double y, double z) {
return (x * y) + ((1.0 - x) * 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 * y) + ((1.0d0 - x) * z)
end function
public static double code(double x, double y, double z) {
return (x * y) + ((1.0 - x) * z);
}
def code(x, y, z): return (x * y) + ((1.0 - x) * z)
function code(x, y, z) return Float64(Float64(x * y) + Float64(Float64(1.0 - x) * z)) end
function tmp = code(x, y, z) tmp = (x * y) + ((1.0 - x) * z); end
code[x_, y_, z_] := N[(N[(x * y), $MachinePrecision] + N[(N[(1.0 - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
x \cdot y + \left(1 - x\right) \cdot z
\end{array}
Sampling outcomes in binary64 precision:
Herbie found 6 alternatives:
| Alternative | Accuracy | Speedup |
|---|
(FPCore (x y z) :precision binary64 (+ (* x y) (* (- 1.0 x) z)))
double code(double x, double y, double z) {
return (x * y) + ((1.0 - x) * 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 * y) + ((1.0d0 - x) * z)
end function
public static double code(double x, double y, double z) {
return (x * y) + ((1.0 - x) * z);
}
def code(x, y, z): return (x * y) + ((1.0 - x) * z)
function code(x, y, z) return Float64(Float64(x * y) + Float64(Float64(1.0 - x) * z)) end
function tmp = code(x, y, z) tmp = (x * y) + ((1.0 - x) * z); end
code[x_, y_, z_] := N[(N[(x * y), $MachinePrecision] + N[(N[(1.0 - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
x \cdot y + \left(1 - x\right) \cdot z
\end{array}
(FPCore (x y z) :precision binary64 (+ z (* x (- y z))))
double code(double x, double y, double z) {
return z + (x * (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 = z + (x * (y - z))
end function
public static double code(double x, double y, double z) {
return z + (x * (y - z));
}
def code(x, y, z): return z + (x * (y - z))
function code(x, y, z) return Float64(z + Float64(x * Float64(y - z))) end
function tmp = code(x, y, z) tmp = z + (x * (y - z)); end
code[x_, y_, z_] := N[(z + N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
z + x \cdot \left(y - z\right)
\end{array}
Initial program 98.4%
+-commutative98.4%
remove-double-neg98.4%
distribute-rgt-neg-out98.4%
neg-sub098.4%
neg-sub098.4%
*-commutative98.4%
distribute-lft-neg-in98.4%
remove-double-neg98.4%
distribute-rgt-out--98.4%
*-lft-identity98.4%
associate-+l-98.4%
distribute-lft-out--100.0%
Simplified100.0%
Final simplification100.0%
(FPCore (x y z) :precision binary64 (if (or (<= x -13000000.0) (not (<= x 0.3))) (* x (- y z)) (+ z (* x y))))
double code(double x, double y, double z) {
double tmp;
if ((x <= -13000000.0) || !(x <= 0.3)) {
tmp = x * (y - z);
} else {
tmp = z + (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 <= (-13000000.0d0)) .or. (.not. (x <= 0.3d0))) then
tmp = x * (y - z)
else
tmp = z + (x * y)
end if
code = tmp
end function
public static double code(double x, double y, double z) {
double tmp;
if ((x <= -13000000.0) || !(x <= 0.3)) {
tmp = x * (y - z);
} else {
tmp = z + (x * y);
}
return tmp;
}
def code(x, y, z): tmp = 0 if (x <= -13000000.0) or not (x <= 0.3): tmp = x * (y - z) else: tmp = z + (x * y) return tmp
function code(x, y, z) tmp = 0.0 if ((x <= -13000000.0) || !(x <= 0.3)) tmp = Float64(x * Float64(y - z)); else tmp = Float64(z + Float64(x * y)); end return tmp end
function tmp_2 = code(x, y, z) tmp = 0.0; if ((x <= -13000000.0) || ~((x <= 0.3))) tmp = x * (y - z); else tmp = z + (x * y); end tmp_2 = tmp; end
code[x_, y_, z_] := If[Or[LessEqual[x, -13000000.0], N[Not[LessEqual[x, 0.3]], $MachinePrecision]], N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision], N[(z + N[(x * y), $MachinePrecision]), $MachinePrecision]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;x \leq -13000000 \lor \neg \left(x \leq 0.3\right):\\
\;\;\;\;x \cdot \left(y - z\right)\\
\mathbf{else}:\\
\;\;\;\;z + x \cdot y\\
\end{array}
\end{array}
if x < -1.3e7 or 0.299999999999999989 < x Initial program 96.7%
Taylor expanded in x around inf 99.2%
mul-1-neg99.2%
sub-neg99.2%
Simplified99.2%
if -1.3e7 < x < 0.299999999999999989Initial program 100.0%
+-commutative100.0%
remove-double-neg100.0%
distribute-rgt-neg-out100.0%
neg-sub0100.0%
neg-sub0100.0%
*-commutative100.0%
distribute-lft-neg-in100.0%
remove-double-neg100.0%
distribute-rgt-out--100.0%
*-lft-identity100.0%
associate-+l-100.0%
distribute-lft-out--100.0%
Simplified100.0%
Taylor expanded in z around 0 99.0%
mul-1-neg99.0%
distribute-rgt-neg-out99.0%
Simplified99.0%
sub-neg99.0%
+-commutative99.0%
distribute-rgt-neg-out99.0%
remove-double-neg99.0%
Applied egg-rr99.0%
Final simplification99.1%
(FPCore (x y z) :precision binary64 (if (or (<= x -4.6e-66) (not (<= x 1.05e-9))) (* x (- y z)) (* z (- 1.0 x))))
double code(double x, double y, double z) {
double tmp;
if ((x <= -4.6e-66) || !(x <= 1.05e-9)) {
tmp = x * (y - z);
} else {
tmp = z * (1.0 - 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 <= (-4.6d-66)) .or. (.not. (x <= 1.05d-9))) then
tmp = x * (y - z)
else
tmp = z * (1.0d0 - x)
end if
code = tmp
end function
public static double code(double x, double y, double z) {
double tmp;
if ((x <= -4.6e-66) || !(x <= 1.05e-9)) {
tmp = x * (y - z);
} else {
tmp = z * (1.0 - x);
}
return tmp;
}
def code(x, y, z): tmp = 0 if (x <= -4.6e-66) or not (x <= 1.05e-9): tmp = x * (y - z) else: tmp = z * (1.0 - x) return tmp
function code(x, y, z) tmp = 0.0 if ((x <= -4.6e-66) || !(x <= 1.05e-9)) tmp = Float64(x * Float64(y - z)); else tmp = Float64(z * Float64(1.0 - x)); end return tmp end
function tmp_2 = code(x, y, z) tmp = 0.0; if ((x <= -4.6e-66) || ~((x <= 1.05e-9))) tmp = x * (y - z); else tmp = z * (1.0 - x); end tmp_2 = tmp; end
code[x_, y_, z_] := If[Or[LessEqual[x, -4.6e-66], N[Not[LessEqual[x, 1.05e-9]], $MachinePrecision]], N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision], N[(z * N[(1.0 - x), $MachinePrecision]), $MachinePrecision]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;x \leq -4.6 \cdot 10^{-66} \lor \neg \left(x \leq 1.05 \cdot 10^{-9}\right):\\
\;\;\;\;x \cdot \left(y - z\right)\\
\mathbf{else}:\\
\;\;\;\;z \cdot \left(1 - x\right)\\
\end{array}
\end{array}
if x < -4.59999999999999984e-66 or 1.0500000000000001e-9 < x Initial program 97.0%
Taylor expanded in x around inf 96.2%
mul-1-neg96.2%
sub-neg96.2%
Simplified96.2%
if -4.59999999999999984e-66 < x < 1.0500000000000001e-9Initial program 100.0%
Taylor expanded in y around 0 81.6%
Final simplification89.4%
(FPCore (x y z) :precision binary64 (if (or (<= x -4.3e-66) (not (<= x 8e-9))) (* x (- y z)) z))
double code(double x, double y, double z) {
double tmp;
if ((x <= -4.3e-66) || !(x <= 8e-9)) {
tmp = x * (y - z);
} else {
tmp = z;
}
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 <= (-4.3d-66)) .or. (.not. (x <= 8d-9))) then
tmp = x * (y - z)
else
tmp = z
end if
code = tmp
end function
public static double code(double x, double y, double z) {
double tmp;
if ((x <= -4.3e-66) || !(x <= 8e-9)) {
tmp = x * (y - z);
} else {
tmp = z;
}
return tmp;
}
def code(x, y, z): tmp = 0 if (x <= -4.3e-66) or not (x <= 8e-9): tmp = x * (y - z) else: tmp = z return tmp
function code(x, y, z) tmp = 0.0 if ((x <= -4.3e-66) || !(x <= 8e-9)) tmp = Float64(x * Float64(y - z)); else tmp = z; end return tmp end
function tmp_2 = code(x, y, z) tmp = 0.0; if ((x <= -4.3e-66) || ~((x <= 8e-9))) tmp = x * (y - z); else tmp = z; end tmp_2 = tmp; end
code[x_, y_, z_] := If[Or[LessEqual[x, -4.3e-66], N[Not[LessEqual[x, 8e-9]], $MachinePrecision]], N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision], z]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;x \leq -4.3 \cdot 10^{-66} \lor \neg \left(x \leq 8 \cdot 10^{-9}\right):\\
\;\;\;\;x \cdot \left(y - z\right)\\
\mathbf{else}:\\
\;\;\;\;z\\
\end{array}
\end{array}
if x < -4.30000000000000013e-66 or 8.0000000000000005e-9 < x Initial program 97.0%
Taylor expanded in x around inf 96.2%
mul-1-neg96.2%
sub-neg96.2%
Simplified96.2%
if -4.30000000000000013e-66 < x < 8.0000000000000005e-9Initial program 100.0%
Taylor expanded in x around 0 81.6%
Final simplification89.4%
(FPCore (x y z) :precision binary64 (if (or (<= x -3.7e-66) (not (<= x 7.8e-16))) (* x y) z))
double code(double x, double y, double z) {
double tmp;
if ((x <= -3.7e-66) || !(x <= 7.8e-16)) {
tmp = x * y;
} else {
tmp = z;
}
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 <= (-3.7d-66)) .or. (.not. (x <= 7.8d-16))) then
tmp = x * y
else
tmp = z
end if
code = tmp
end function
public static double code(double x, double y, double z) {
double tmp;
if ((x <= -3.7e-66) || !(x <= 7.8e-16)) {
tmp = x * y;
} else {
tmp = z;
}
return tmp;
}
def code(x, y, z): tmp = 0 if (x <= -3.7e-66) or not (x <= 7.8e-16): tmp = x * y else: tmp = z return tmp
function code(x, y, z) tmp = 0.0 if ((x <= -3.7e-66) || !(x <= 7.8e-16)) tmp = Float64(x * y); else tmp = z; end return tmp end
function tmp_2 = code(x, y, z) tmp = 0.0; if ((x <= -3.7e-66) || ~((x <= 7.8e-16))) tmp = x * y; else tmp = z; end tmp_2 = tmp; end
code[x_, y_, z_] := If[Or[LessEqual[x, -3.7e-66], N[Not[LessEqual[x, 7.8e-16]], $MachinePrecision]], N[(x * y), $MachinePrecision], z]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;x \leq -3.7 \cdot 10^{-66} \lor \neg \left(x \leq 7.8 \cdot 10^{-16}\right):\\
\;\;\;\;x \cdot y\\
\mathbf{else}:\\
\;\;\;\;z\\
\end{array}
\end{array}
if x < -3.7000000000000002e-66 or 7.79999999999999954e-16 < x Initial program 97.0%
Taylor expanded in y around inf 61.1%
if -3.7000000000000002e-66 < x < 7.79999999999999954e-16Initial program 100.0%
Taylor expanded in x around 0 81.6%
Final simplification70.6%
(FPCore (x y z) :precision binary64 z)
double code(double x, double y, double z) {
return z;
}
real(8) function code(x, y, z)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8), intent (in) :: z
code = z
end function
public static double code(double x, double y, double z) {
return z;
}
def code(x, y, z): return z
function code(x, y, z) return z end
function tmp = code(x, y, z) tmp = z; end
code[x_, y_, z_] := z
\begin{array}{l}
\\
z
\end{array}
Initial program 98.4%
Taylor expanded in x around 0 40.7%
herbie shell --seed 2024112
(FPCore (x y z)
:name "Diagrams.Backend.Rasterific:$crender from diagrams-rasterific-1.3.1.3"
:precision binary64
(+ (* x y) (* (- 1.0 x) z)))