
(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 7 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 96.5%
Simplified0
(FPCore (x y z)
:precision binary64
(let* ((t_0 (* x (- z))))
(if (<= x -4.8e+105)
t_0
(if (<= x -3.3e-47)
(* x y)
(if (<= x 0.29) z (if (<= x 4.5e+207) (* x y) t_0))))))
double code(double x, double y, double z) {
double t_0 = x * -z;
double tmp;
if (x <= -4.8e+105) {
tmp = t_0;
} else if (x <= -3.3e-47) {
tmp = x * y;
} else if (x <= 0.29) {
tmp = z;
} else if (x <= 4.5e+207) {
tmp = x * y;
} 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
if (x <= (-4.8d+105)) then
tmp = t_0
else if (x <= (-3.3d-47)) then
tmp = x * y
else if (x <= 0.29d0) then
tmp = z
else if (x <= 4.5d+207) then
tmp = x * y
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;
double tmp;
if (x <= -4.8e+105) {
tmp = t_0;
} else if (x <= -3.3e-47) {
tmp = x * y;
} else if (x <= 0.29) {
tmp = z;
} else if (x <= 4.5e+207) {
tmp = x * y;
} else {
tmp = t_0;
}
return tmp;
}
def code(x, y, z): t_0 = x * -z tmp = 0 if x <= -4.8e+105: tmp = t_0 elif x <= -3.3e-47: tmp = x * y elif x <= 0.29: tmp = z elif x <= 4.5e+207: tmp = x * y else: tmp = t_0 return tmp
function code(x, y, z) t_0 = Float64(x * Float64(-z)) tmp = 0.0 if (x <= -4.8e+105) tmp = t_0; elseif (x <= -3.3e-47) tmp = Float64(x * y); elseif (x <= 0.29) tmp = z; elseif (x <= 4.5e+207) tmp = Float64(x * y); else tmp = t_0; end return tmp end
function tmp_2 = code(x, y, z) t_0 = x * -z; tmp = 0.0; if (x <= -4.8e+105) tmp = t_0; elseif (x <= -3.3e-47) tmp = x * y; elseif (x <= 0.29) tmp = z; elseif (x <= 4.5e+207) tmp = x * y; else tmp = t_0; end tmp_2 = tmp; end
code[x_, y_, z_] := Block[{t$95$0 = N[(x * (-z)), $MachinePrecision]}, If[LessEqual[x, -4.8e+105], t$95$0, If[LessEqual[x, -3.3e-47], N[(x * y), $MachinePrecision], If[LessEqual[x, 0.29], z, If[LessEqual[x, 4.5e+207], N[(x * y), $MachinePrecision], t$95$0]]]]]
\begin{array}{l}
\\
\begin{array}{l}
t_0 := x \cdot \left(-z\right)\\
\mathbf{if}\;x \leq -4.8 \cdot 10^{+105}:\\
\;\;\;\;t\_0\\
\mathbf{elif}\;x \leq -3.3 \cdot 10^{-47}:\\
\;\;\;\;x \cdot y\\
\mathbf{elif}\;x \leq 0.29:\\
\;\;\;\;z\\
\mathbf{elif}\;x \leq 4.5 \cdot 10^{+207}:\\
\;\;\;\;x \cdot y\\
\mathbf{else}:\\
\;\;\;\;t\_0\\
\end{array}
\end{array}
if x < -4.7999999999999995e105 or 4.50000000000000003e207 < x Initial program 90.9%
Simplified0
Taylor expanded in x around inf 0
Simplified0
Taylor expanded in y around 0 0
Simplified0
if -4.7999999999999995e105 < x < -3.30000000000000004e-47 or 0.28999999999999998 < x < 4.50000000000000003e207Initial program 96.0%
Simplified0
Taylor expanded in z around 0 0
Simplified0
if -3.30000000000000004e-47 < x < 0.28999999999999998Initial program 100.0%
Simplified0
Taylor expanded in x around 0 0
Simplified0
(FPCore (x y z) :precision binary64 (let* ((t_0 (* x (- y z)))) (if (<= x -1.0) t_0 (if (<= x 1.0) (+ (* x y) z) t_0))))
double code(double x, double y, double z) {
double t_0 = x * (y - z);
double tmp;
if (x <= -1.0) {
tmp = t_0;
} else if (x <= 1.0) {
tmp = (x * y) + z;
} 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 * (y - z)
if (x <= (-1.0d0)) then
tmp = t_0
else if (x <= 1.0d0) then
tmp = (x * y) + z
else
tmp = t_0
end if
code = tmp
end function
public static double code(double x, double y, double z) {
double t_0 = x * (y - z);
double tmp;
if (x <= -1.0) {
tmp = t_0;
} else if (x <= 1.0) {
tmp = (x * y) + z;
} else {
tmp = t_0;
}
return tmp;
}
def code(x, y, z): t_0 = x * (y - z) tmp = 0 if x <= -1.0: tmp = t_0 elif x <= 1.0: tmp = (x * y) + z else: tmp = t_0 return tmp
function code(x, y, z) t_0 = Float64(x * Float64(y - z)) tmp = 0.0 if (x <= -1.0) tmp = t_0; elseif (x <= 1.0) tmp = Float64(Float64(x * y) + z); else tmp = t_0; end return tmp end
function tmp_2 = code(x, y, z) t_0 = x * (y - z); tmp = 0.0; if (x <= -1.0) tmp = t_0; elseif (x <= 1.0) tmp = (x * y) + z; else tmp = t_0; end tmp_2 = tmp; end
code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.0], t$95$0, If[LessEqual[x, 1.0], N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision], t$95$0]]]
\begin{array}{l}
\\
\begin{array}{l}
t_0 := x \cdot \left(y - z\right)\\
\mathbf{if}\;x \leq -1:\\
\;\;\;\;t\_0\\
\mathbf{elif}\;x \leq 1:\\
\;\;\;\;x \cdot y + z\\
\mathbf{else}:\\
\;\;\;\;t\_0\\
\end{array}
\end{array}
if x < -1 or 1 < x Initial program 93.4%
Simplified0
Taylor expanded in x around inf 0
Simplified0
if -1 < x < 1Initial program 100.0%
Taylor expanded in x around 0 0
Simplified0
(FPCore (x y z) :precision binary64 (let* ((t_0 (* x (- y z)))) (if (<= x -3.4e-47) t_0 (if (<= x 0.78) (* z (- 1.0 x)) t_0))))
double code(double x, double y, double z) {
double t_0 = x * (y - z);
double tmp;
if (x <= -3.4e-47) {
tmp = t_0;
} else if (x <= 0.78) {
tmp = z * (1.0 - x);
} 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 * (y - z)
if (x <= (-3.4d-47)) then
tmp = t_0
else if (x <= 0.78d0) then
tmp = z * (1.0d0 - x)
else
tmp = t_0
end if
code = tmp
end function
public static double code(double x, double y, double z) {
double t_0 = x * (y - z);
double tmp;
if (x <= -3.4e-47) {
tmp = t_0;
} else if (x <= 0.78) {
tmp = z * (1.0 - x);
} else {
tmp = t_0;
}
return tmp;
}
def code(x, y, z): t_0 = x * (y - z) tmp = 0 if x <= -3.4e-47: tmp = t_0 elif x <= 0.78: tmp = z * (1.0 - x) else: tmp = t_0 return tmp
function code(x, y, z) t_0 = Float64(x * Float64(y - z)) tmp = 0.0 if (x <= -3.4e-47) tmp = t_0; elseif (x <= 0.78) tmp = Float64(z * Float64(1.0 - x)); else tmp = t_0; end return tmp end
function tmp_2 = code(x, y, z) t_0 = x * (y - z); tmp = 0.0; if (x <= -3.4e-47) tmp = t_0; elseif (x <= 0.78) tmp = z * (1.0 - x); else tmp = t_0; end tmp_2 = tmp; end
code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.4e-47], t$95$0, If[LessEqual[x, 0.78], N[(z * N[(1.0 - x), $MachinePrecision]), $MachinePrecision], t$95$0]]]
\begin{array}{l}
\\
\begin{array}{l}
t_0 := x \cdot \left(y - z\right)\\
\mathbf{if}\;x \leq -3.4 \cdot 10^{-47}:\\
\;\;\;\;t\_0\\
\mathbf{elif}\;x \leq 0.78:\\
\;\;\;\;z \cdot \left(1 - x\right)\\
\mathbf{else}:\\
\;\;\;\;t\_0\\
\end{array}
\end{array}
if x < -3.4000000000000002e-47 or 0.78000000000000003 < x Initial program 93.6%
Simplified0
Taylor expanded in x around inf 0
Simplified0
if -3.4000000000000002e-47 < x < 0.78000000000000003Initial program 100.0%
Simplified0
Taylor expanded in z around inf 0
Simplified0
(FPCore (x y z) :precision binary64 (let* ((t_0 (* x (- y z)))) (if (<= x -3.4e-47) t_0 (if (<= x 0.29) z t_0))))
double code(double x, double y, double z) {
double t_0 = x * (y - z);
double tmp;
if (x <= -3.4e-47) {
tmp = t_0;
} else if (x <= 0.29) {
tmp = z;
} 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 * (y - z)
if (x <= (-3.4d-47)) then
tmp = t_0
else if (x <= 0.29d0) then
tmp = z
else
tmp = t_0
end if
code = tmp
end function
public static double code(double x, double y, double z) {
double t_0 = x * (y - z);
double tmp;
if (x <= -3.4e-47) {
tmp = t_0;
} else if (x <= 0.29) {
tmp = z;
} else {
tmp = t_0;
}
return tmp;
}
def code(x, y, z): t_0 = x * (y - z) tmp = 0 if x <= -3.4e-47: tmp = t_0 elif x <= 0.29: tmp = z else: tmp = t_0 return tmp
function code(x, y, z) t_0 = Float64(x * Float64(y - z)) tmp = 0.0 if (x <= -3.4e-47) tmp = t_0; elseif (x <= 0.29) tmp = z; else tmp = t_0; end return tmp end
function tmp_2 = code(x, y, z) t_0 = x * (y - z); tmp = 0.0; if (x <= -3.4e-47) tmp = t_0; elseif (x <= 0.29) tmp = z; else tmp = t_0; end tmp_2 = tmp; end
code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.4e-47], t$95$0, If[LessEqual[x, 0.29], z, t$95$0]]]
\begin{array}{l}
\\
\begin{array}{l}
t_0 := x \cdot \left(y - z\right)\\
\mathbf{if}\;x \leq -3.4 \cdot 10^{-47}:\\
\;\;\;\;t\_0\\
\mathbf{elif}\;x \leq 0.29:\\
\;\;\;\;z\\
\mathbf{else}:\\
\;\;\;\;t\_0\\
\end{array}
\end{array}
if x < -3.4000000000000002e-47 or 0.28999999999999998 < x Initial program 93.6%
Simplified0
Taylor expanded in x around inf 0
Simplified0
if -3.4000000000000002e-47 < x < 0.28999999999999998Initial program 100.0%
Simplified0
Taylor expanded in x around 0 0
Simplified0
(FPCore (x y z) :precision binary64 (if (<= x -3.3e-47) (* x y) (if (<= x 0.29) z (* x y))))
double code(double x, double y, double z) {
double tmp;
if (x <= -3.3e-47) {
tmp = x * y;
} else if (x <= 0.29) {
tmp = z;
} 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 <= (-3.3d-47)) then
tmp = x * y
else if (x <= 0.29d0) then
tmp = z
else
tmp = x * y
end if
code = tmp
end function
public static double code(double x, double y, double z) {
double tmp;
if (x <= -3.3e-47) {
tmp = x * y;
} else if (x <= 0.29) {
tmp = z;
} else {
tmp = x * y;
}
return tmp;
}
def code(x, y, z): tmp = 0 if x <= -3.3e-47: tmp = x * y elif x <= 0.29: tmp = z else: tmp = x * y return tmp
function code(x, y, z) tmp = 0.0 if (x <= -3.3e-47) tmp = Float64(x * y); elseif (x <= 0.29) tmp = z; else tmp = Float64(x * y); end return tmp end
function tmp_2 = code(x, y, z) tmp = 0.0; if (x <= -3.3e-47) tmp = x * y; elseif (x <= 0.29) tmp = z; else tmp = x * y; end tmp_2 = tmp; end
code[x_, y_, z_] := If[LessEqual[x, -3.3e-47], N[(x * y), $MachinePrecision], If[LessEqual[x, 0.29], z, N[(x * y), $MachinePrecision]]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;x \leq -3.3 \cdot 10^{-47}:\\
\;\;\;\;x \cdot y\\
\mathbf{elif}\;x \leq 0.29:\\
\;\;\;\;z\\
\mathbf{else}:\\
\;\;\;\;x \cdot y\\
\end{array}
\end{array}
if x < -3.30000000000000004e-47 or 0.28999999999999998 < x Initial program 93.6%
Simplified0
Taylor expanded in z around 0 0
Simplified0
if -3.30000000000000004e-47 < x < 0.28999999999999998Initial program 100.0%
Simplified0
Taylor expanded in x around 0 0
Simplified0
(FPCore (x y z) :precision binary64 z)
double code(double x, double y, double z) {
return z;
}
real(8) function code(x, y, z)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8), intent (in) :: z
code = z
end function
public static double code(double x, double y, double z) {
return z;
}
def code(x, y, z): return z
function code(x, y, z) return z end
function tmp = code(x, y, z) tmp = z; end
code[x_, y_, z_] := z
\begin{array}{l}
\\
z
\end{array}
Initial program 96.5%
Simplified0
Taylor expanded in x around 0 0
Simplified0
herbie shell --seed 2024110
(FPCore (x y z)
:name "Diagrams.Backend.Rasterific:$crender from diagrams-rasterific-1.3.1.3"
:precision binary64
(+ (* x y) (* (- 1.0 x) z)))