
(FPCore (x y z) :precision binary64 (+ (* x y) (* (- x 1.0) z)))
double code(double x, double y, double z) {
return (x * y) + ((x - 1.0) * 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) + ((x - 1.0d0) * z)
end function
public static double code(double x, double y, double z) {
return (x * y) + ((x - 1.0) * z);
}
def code(x, y, z): return (x * y) + ((x - 1.0) * z)
function code(x, y, z) return Float64(Float64(x * y) + Float64(Float64(x - 1.0) * z)) end
function tmp = code(x, y, z) tmp = (x * y) + ((x - 1.0) * z); end
code[x_, y_, z_] := N[(N[(x * y), $MachinePrecision] + N[(N[(x - 1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
x \cdot y + \left(x - 1\right) \cdot z
\end{array}
Sampling outcomes in binary64 precision:
Herbie found 8 alternatives:
| Alternative | Accuracy | Speedup |
|---|
(FPCore (x y z) :precision binary64 (+ (* x y) (* (- x 1.0) z)))
double code(double x, double y, double z) {
return (x * y) + ((x - 1.0) * 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) + ((x - 1.0d0) * z)
end function
public static double code(double x, double y, double z) {
return (x * y) + ((x - 1.0) * z);
}
def code(x, y, z): return (x * y) + ((x - 1.0) * z)
function code(x, y, z) return Float64(Float64(x * y) + Float64(Float64(x - 1.0) * z)) end
function tmp = code(x, y, z) tmp = (x * y) + ((x - 1.0) * z); end
code[x_, y_, z_] := N[(N[(x * y), $MachinePrecision] + N[(N[(x - 1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
x \cdot y + \left(x - 1\right) \cdot z
\end{array}
(FPCore (x y z) :precision binary64 (- (* x (+ y z)) z))
double code(double x, double y, double z) {
return (x * (y + z)) - 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 + z)) - z
end function
public static double code(double x, double y, double z) {
return (x * (y + z)) - z;
}
def code(x, y, z): return (x * (y + z)) - z
function code(x, y, z) return Float64(Float64(x * Float64(y + z)) - z) end
function tmp = code(x, y, z) tmp = (x * (y + z)) - z; end
code[x_, y_, z_] := N[(N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]
\begin{array}{l}
\\
x \cdot \left(y + z\right) - z
\end{array}
Initial program 98.8%
Simplified0
(FPCore (x y z)
:precision binary64
(if (<= x -4.8e+105)
(* z x)
(if (<= x -3.3e-47)
(* x y)
(if (<= x 2.3e-46)
(- z)
(if (<= x 6e+206) (* x y) (if (<= x 1.8e+260) (* z x) (* x y)))))))
double code(double x, double y, double z) {
double tmp;
if (x <= -4.8e+105) {
tmp = z * x;
} else if (x <= -3.3e-47) {
tmp = x * y;
} else if (x <= 2.3e-46) {
tmp = -z;
} else if (x <= 6e+206) {
tmp = x * y;
} else if (x <= 1.8e+260) {
tmp = z * x;
} 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 <= (-4.8d+105)) then
tmp = z * x
else if (x <= (-3.3d-47)) then
tmp = x * y
else if (x <= 2.3d-46) then
tmp = -z
else if (x <= 6d+206) then
tmp = x * y
else if (x <= 1.8d+260) then
tmp = z * x
else
tmp = x * y
end if
code = tmp
end function
public static double code(double x, double y, double z) {
double tmp;
if (x <= -4.8e+105) {
tmp = z * x;
} else if (x <= -3.3e-47) {
tmp = x * y;
} else if (x <= 2.3e-46) {
tmp = -z;
} else if (x <= 6e+206) {
tmp = x * y;
} else if (x <= 1.8e+260) {
tmp = z * x;
} else {
tmp = x * y;
}
return tmp;
}
def code(x, y, z): tmp = 0 if x <= -4.8e+105: tmp = z * x elif x <= -3.3e-47: tmp = x * y elif x <= 2.3e-46: tmp = -z elif x <= 6e+206: tmp = x * y elif x <= 1.8e+260: tmp = z * x else: tmp = x * y return tmp
function code(x, y, z) tmp = 0.0 if (x <= -4.8e+105) tmp = Float64(z * x); elseif (x <= -3.3e-47) tmp = Float64(x * y); elseif (x <= 2.3e-46) tmp = Float64(-z); elseif (x <= 6e+206) tmp = Float64(x * y); elseif (x <= 1.8e+260) tmp = Float64(z * x); else tmp = Float64(x * y); end return tmp end
function tmp_2 = code(x, y, z) tmp = 0.0; if (x <= -4.8e+105) tmp = z * x; elseif (x <= -3.3e-47) tmp = x * y; elseif (x <= 2.3e-46) tmp = -z; elseif (x <= 6e+206) tmp = x * y; elseif (x <= 1.8e+260) tmp = z * x; else tmp = x * y; end tmp_2 = tmp; end
code[x_, y_, z_] := If[LessEqual[x, -4.8e+105], N[(z * x), $MachinePrecision], If[LessEqual[x, -3.3e-47], N[(x * y), $MachinePrecision], If[LessEqual[x, 2.3e-46], (-z), If[LessEqual[x, 6e+206], N[(x * y), $MachinePrecision], If[LessEqual[x, 1.8e+260], N[(z * x), $MachinePrecision], N[(x * y), $MachinePrecision]]]]]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;x \leq -4.8 \cdot 10^{+105}:\\
\;\;\;\;z \cdot x\\
\mathbf{elif}\;x \leq -3.3 \cdot 10^{-47}:\\
\;\;\;\;x \cdot y\\
\mathbf{elif}\;x \leq 2.3 \cdot 10^{-46}:\\
\;\;\;\;-z\\
\mathbf{elif}\;x \leq 6 \cdot 10^{+206}:\\
\;\;\;\;x \cdot y\\
\mathbf{elif}\;x \leq 1.8 \cdot 10^{+260}:\\
\;\;\;\;z \cdot x\\
\mathbf{else}:\\
\;\;\;\;x \cdot y\\
\end{array}
\end{array}
if x < -4.7999999999999995e105 or 6.0000000000000002e206 < x < 1.7999999999999999e260Initial program 96.4%
Taylor expanded in x around inf 0
Simplified0
Taylor expanded in z around inf 0
Simplified0
if -4.7999999999999995e105 < x < -3.30000000000000004e-47 or 2.2999999999999999e-46 < x < 6.0000000000000002e206 or 1.7999999999999999e260 < x Initial program 98.9%
Taylor expanded in y around inf 0
Simplified0
if -3.30000000000000004e-47 < x < 2.2999999999999999e-46Initial program 100.0%
Taylor expanded in x around 0 0
Simplified0
Applied egg-rr0
(FPCore (x y z) :precision binary64 (let* ((t_0 (* x (+ z y)))) (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 * (z + y);
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 * (z + y)
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 * (z + y);
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 * (z + y) 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(z + y)) 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 * (z + y); 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[(z + y), $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(z + y\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 97.8%
Taylor expanded in x around inf 0
Simplified0
if -1 < x < 1Initial program 100.0%
Simplified0
Taylor expanded in y around inf 0
Simplified0
(FPCore (x y z) :precision binary64 (let* ((t_0 (* x (+ z y)))) (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 * (z + y);
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 * (z + y)
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 * (z + y);
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 * (z + y) 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(z + y)) 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 * (z + y); 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[(z + y), $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(z + y\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 97.9%
Taylor expanded in x around inf 0
Simplified0
if -3.4000000000000002e-47 < x < 0.78000000000000003Initial program 100.0%
Taylor expanded in y around 0 0
Simplified0
(FPCore (x y z) :precision binary64 (let* ((t_0 (* x (+ z y)))) (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 * (z + y);
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 * (z + y)
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 * (z + y);
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 * (z + y) 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(z + y)) tmp = 0.0 if (x <= -3.4e-47) tmp = t_0; elseif (x <= 0.29) tmp = Float64(-z); 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 <= -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[(z + y), $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(z + y\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 97.9%
Taylor expanded in x around inf 0
Simplified0
if -3.4000000000000002e-47 < x < 0.28999999999999998Initial program 100.0%
Taylor expanded in x around 0 0
Simplified0
Applied egg-rr0
(FPCore (x y z) :precision binary64 (if (<= x -3.4e-47) (* x y) (if (<= x 6.2e-47) (- z) (* x y))))
double code(double x, double y, double z) {
double tmp;
if (x <= -3.4e-47) {
tmp = x * y;
} else if (x <= 6.2e-47) {
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 <= (-3.4d-47)) then
tmp = x * y
else if (x <= 6.2d-47) 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 <= -3.4e-47) {
tmp = x * y;
} else if (x <= 6.2e-47) {
tmp = -z;
} else {
tmp = x * y;
}
return tmp;
}
def code(x, y, z): tmp = 0 if x <= -3.4e-47: tmp = x * y elif x <= 6.2e-47: tmp = -z else: tmp = x * y return tmp
function code(x, y, z) tmp = 0.0 if (x <= -3.4e-47) tmp = Float64(x * y); elseif (x <= 6.2e-47) tmp = Float64(-z); else tmp = Float64(x * y); end return tmp end
function tmp_2 = code(x, y, z) tmp = 0.0; if (x <= -3.4e-47) tmp = x * y; elseif (x <= 6.2e-47) tmp = -z; else tmp = x * y; end tmp_2 = tmp; end
code[x_, y_, z_] := If[LessEqual[x, -3.4e-47], N[(x * y), $MachinePrecision], If[LessEqual[x, 6.2e-47], (-z), N[(x * y), $MachinePrecision]]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;x \leq -3.4 \cdot 10^{-47}:\\
\;\;\;\;x \cdot y\\
\mathbf{elif}\;x \leq 6.2 \cdot 10^{-47}:\\
\;\;\;\;-z\\
\mathbf{else}:\\
\;\;\;\;x \cdot y\\
\end{array}
\end{array}
if x < -3.4000000000000002e-47 or 6.1999999999999996e-47 < x Initial program 97.9%
Taylor expanded in y around inf 0
Simplified0
if -3.4000000000000002e-47 < x < 6.1999999999999996e-47Initial program 100.0%
Taylor expanded in x around 0 0
Simplified0
Applied egg-rr0
(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 Float64(-z) end
function tmp = code(x, y, z) tmp = -z; end
code[x_, y_, z_] := (-z)
\begin{array}{l}
\\
-z
\end{array}
Initial program 98.8%
Taylor expanded in x around 0 0
Simplified0
Applied egg-rr0
(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 98.8%
Taylor expanded in x around 0 0
Simplified0
Applied egg-rr0
herbie shell --seed 2024110
(FPCore (x y z)
:name "Graphics.Rendering.Chart.Drawing:drawTextsR from Chart-1.5.3"
:precision binary64
(+ (* x y) (* (- x 1.0) z)))