
(FPCore (x y z) :precision binary64 (* (+ x y) (- 1.0 z)))
double code(double x, double y, double z) {
return (x + y) * (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) * (1.0d0 - z)
end function
public static double code(double x, double y, double z) {
return (x + y) * (1.0 - z);
}
def code(x, y, z): return (x + y) * (1.0 - z)
function code(x, y, z) return Float64(Float64(x + y) * Float64(1.0 - z)) end
function tmp = code(x, y, z) tmp = (x + y) * (1.0 - z); end
code[x_, y_, z_] := N[(N[(x + y), $MachinePrecision] * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
\left(x + y\right) \cdot \left(1 - z\right)
\end{array}
Sampling outcomes in binary64 precision:
Herbie found 11 alternatives:
| Alternative | Accuracy | Speedup |
|---|
(FPCore (x y z) :precision binary64 (* (+ x y) (- 1.0 z)))
double code(double x, double y, double z) {
return (x + y) * (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) * (1.0d0 - z)
end function
public static double code(double x, double y, double z) {
return (x + y) * (1.0 - z);
}
def code(x, y, z): return (x + y) * (1.0 - z)
function code(x, y, z) return Float64(Float64(x + y) * Float64(1.0 - z)) end
function tmp = code(x, y, z) tmp = (x + y) * (1.0 - z); end
code[x_, y_, z_] := N[(N[(x + y), $MachinePrecision] * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
\left(x + y\right) \cdot \left(1 - z\right)
\end{array}
(FPCore (x y z) :precision binary64 (- (+ x y) (* z (+ x y))))
double code(double x, double y, double z) {
return (x + y) - (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 + y) - (z * (x + y))
end function
public static double code(double x, double y, double z) {
return (x + y) - (z * (x + y));
}
def code(x, y, z): return (x + y) - (z * (x + y))
function code(x, y, z) return Float64(Float64(x + y) - Float64(z * Float64(x + y))) end
function tmp = code(x, y, z) tmp = (x + y) - (z * (x + y)); end
code[x_, y_, z_] := N[(N[(x + y), $MachinePrecision] - N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
\left(x + y\right) - z \cdot \left(x + y\right)
\end{array}
(FPCore (x y z)
:precision binary64
(let* ((t_0 (* x (- z))))
(if (<= (- 1.0 z) -400.0)
t_0
(if (<= (- 1.0 z) 2.0)
(+ x y)
(if (<= (- 1.0 z) 2e+104) (* y (- 1.0 z)) t_0)))))
double code(double x, double y, double z) {
double t_0 = x * -z;
double tmp;
if ((1.0 - z) <= -400.0) {
tmp = t_0;
} else if ((1.0 - z) <= 2.0) {
tmp = x + y;
} else if ((1.0 - z) <= 2e+104) {
tmp = y * (1.0 - 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
if ((1.0d0 - z) <= (-400.0d0)) then
tmp = t_0
else if ((1.0d0 - z) <= 2.0d0) then
tmp = x + y
else if ((1.0d0 - z) <= 2d+104) then
tmp = y * (1.0d0 - 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;
double tmp;
if ((1.0 - z) <= -400.0) {
tmp = t_0;
} else if ((1.0 - z) <= 2.0) {
tmp = x + y;
} else if ((1.0 - z) <= 2e+104) {
tmp = y * (1.0 - z);
} else {
tmp = t_0;
}
return tmp;
}
def code(x, y, z): t_0 = x * -z tmp = 0 if (1.0 - z) <= -400.0: tmp = t_0 elif (1.0 - z) <= 2.0: tmp = x + y elif (1.0 - z) <= 2e+104: tmp = y * (1.0 - z) else: tmp = t_0 return tmp
function code(x, y, z) t_0 = Float64(x * Float64(-z)) tmp = 0.0 if (Float64(1.0 - z) <= -400.0) tmp = t_0; elseif (Float64(1.0 - z) <= 2.0) tmp = Float64(x + y); elseif (Float64(1.0 - z) <= 2e+104) tmp = Float64(y * Float64(1.0 - z)); else tmp = t_0; end return tmp end
function tmp_2 = code(x, y, z) t_0 = x * -z; tmp = 0.0; if ((1.0 - z) <= -400.0) tmp = t_0; elseif ((1.0 - z) <= 2.0) tmp = x + y; elseif ((1.0 - z) <= 2e+104) tmp = y * (1.0 - z); else tmp = t_0; end tmp_2 = tmp; end
code[x_, y_, z_] := Block[{t$95$0 = N[(x * (-z)), $MachinePrecision]}, If[LessEqual[N[(1.0 - z), $MachinePrecision], -400.0], t$95$0, If[LessEqual[N[(1.0 - z), $MachinePrecision], 2.0], N[(x + y), $MachinePrecision], If[LessEqual[N[(1.0 - z), $MachinePrecision], 2e+104], N[(y * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], t$95$0]]]]
\begin{array}{l}
\\
\begin{array}{l}
t_0 := x \cdot \left(-z\right)\\
\mathbf{if}\;1 - z \leq -400:\\
\;\;\;\;t_0\\
\mathbf{elif}\;1 - z \leq 2:\\
\;\;\;\;x + y\\
\mathbf{elif}\;1 - z \leq 2 \cdot 10^{+104}:\\
\;\;\;\;y \cdot \left(1 - z\right)\\
\mathbf{else}:\\
\;\;\;\;t_0\\
\end{array}
\end{array}
(FPCore (x y z)
:precision binary64
(let* ((t_0 (* x (- z))) (t_1 (* y (- z))))
(if (<= z -4e+105)
t_0
(if (<= z -52.0)
t_1
(if (<= z 1.0)
(+ x y)
(if (or (<= z 7.6e+211) (not (<= z 2.1e+270))) t_0 t_1))))))
double code(double x, double y, double z) {
double t_0 = x * -z;
double t_1 = y * -z;
double tmp;
if (z <= -4e+105) {
tmp = t_0;
} else if (z <= -52.0) {
tmp = t_1;
} else if (z <= 1.0) {
tmp = x + y;
} else if ((z <= 7.6e+211) || !(z <= 2.1e+270)) {
tmp = t_0;
} else {
tmp = t_1;
}
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) :: t_1
real(8) :: tmp
t_0 = x * -z
t_1 = y * -z
if (z <= (-4d+105)) then
tmp = t_0
else if (z <= (-52.0d0)) then
tmp = t_1
else if (z <= 1.0d0) then
tmp = x + y
else if ((z <= 7.6d+211) .or. (.not. (z <= 2.1d+270))) then
tmp = t_0
else
tmp = t_1
end if
code = tmp
end function
public static double code(double x, double y, double z) {
double t_0 = x * -z;
double t_1 = y * -z;
double tmp;
if (z <= -4e+105) {
tmp = t_0;
} else if (z <= -52.0) {
tmp = t_1;
} else if (z <= 1.0) {
tmp = x + y;
} else if ((z <= 7.6e+211) || !(z <= 2.1e+270)) {
tmp = t_0;
} else {
tmp = t_1;
}
return tmp;
}
def code(x, y, z): t_0 = x * -z t_1 = y * -z tmp = 0 if z <= -4e+105: tmp = t_0 elif z <= -52.0: tmp = t_1 elif z <= 1.0: tmp = x + y elif (z <= 7.6e+211) or not (z <= 2.1e+270): tmp = t_0 else: tmp = t_1 return tmp
function code(x, y, z) t_0 = Float64(x * Float64(-z)) t_1 = Float64(y * Float64(-z)) tmp = 0.0 if (z <= -4e+105) tmp = t_0; elseif (z <= -52.0) tmp = t_1; elseif (z <= 1.0) tmp = Float64(x + y); elseif ((z <= 7.6e+211) || !(z <= 2.1e+270)) tmp = t_0; else tmp = t_1; end return tmp end
function tmp_2 = code(x, y, z) t_0 = x * -z; t_1 = y * -z; tmp = 0.0; if (z <= -4e+105) tmp = t_0; elseif (z <= -52.0) tmp = t_1; elseif (z <= 1.0) tmp = x + y; elseif ((z <= 7.6e+211) || ~((z <= 2.1e+270))) tmp = t_0; else tmp = t_1; end tmp_2 = tmp; end
code[x_, y_, z_] := Block[{t$95$0 = N[(x * (-z)), $MachinePrecision]}, Block[{t$95$1 = N[(y * (-z)), $MachinePrecision]}, If[LessEqual[z, -4e+105], t$95$0, If[LessEqual[z, -52.0], t$95$1, If[LessEqual[z, 1.0], N[(x + y), $MachinePrecision], If[Or[LessEqual[z, 7.6e+211], N[Not[LessEqual[z, 2.1e+270]], $MachinePrecision]], t$95$0, t$95$1]]]]]]
\begin{array}{l}
\\
\begin{array}{l}
t_0 := x \cdot \left(-z\right)\\
t_1 := y \cdot \left(-z\right)\\
\mathbf{if}\;z \leq -4 \cdot 10^{+105}:\\
\;\;\;\;t_0\\
\mathbf{elif}\;z \leq -52:\\
\;\;\;\;t_1\\
\mathbf{elif}\;z \leq 1:\\
\;\;\;\;x + y\\
\mathbf{elif}\;z \leq 7.6 \cdot 10^{+211} \lor \neg \left(z \leq 2.1 \cdot 10^{+270}\right):\\
\;\;\;\;t_0\\
\mathbf{else}:\\
\;\;\;\;t_1\\
\end{array}
\end{array}
(FPCore (x y z) :precision binary64 (if (or (<= (- 1.0 z) -400.0) (not (<= (- 1.0 z) 2.0))) (* z (- (- x) y)) (+ x y)))
double code(double x, double y, double z) {
double tmp;
if (((1.0 - z) <= -400.0) || !((1.0 - z) <= 2.0)) {
tmp = z * (-x - y);
} 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 (((1.0d0 - z) <= (-400.0d0)) .or. (.not. ((1.0d0 - z) <= 2.0d0))) then
tmp = z * (-x - y)
else
tmp = x + y
end if
code = tmp
end function
public static double code(double x, double y, double z) {
double tmp;
if (((1.0 - z) <= -400.0) || !((1.0 - z) <= 2.0)) {
tmp = z * (-x - y);
} else {
tmp = x + y;
}
return tmp;
}
def code(x, y, z): tmp = 0 if ((1.0 - z) <= -400.0) or not ((1.0 - z) <= 2.0): tmp = z * (-x - y) else: tmp = x + y return tmp
function code(x, y, z) tmp = 0.0 if ((Float64(1.0 - z) <= -400.0) || !(Float64(1.0 - z) <= 2.0)) tmp = Float64(z * Float64(Float64(-x) - y)); else tmp = Float64(x + y); end return tmp end
function tmp_2 = code(x, y, z) tmp = 0.0; if (((1.0 - z) <= -400.0) || ~(((1.0 - z) <= 2.0))) tmp = z * (-x - y); else tmp = x + y; end tmp_2 = tmp; end
code[x_, y_, z_] := If[Or[LessEqual[N[(1.0 - z), $MachinePrecision], -400.0], N[Not[LessEqual[N[(1.0 - z), $MachinePrecision], 2.0]], $MachinePrecision]], N[(z * N[((-x) - y), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;1 - z \leq -400 \lor \neg \left(1 - z \leq 2\right):\\
\;\;\;\;z \cdot \left(\left(-x\right) - y\right)\\
\mathbf{else}:\\
\;\;\;\;x + y\\
\end{array}
\end{array}
(FPCore (x y z) :precision binary64 (if (or (<= z -300000000000.0) (not (<= z 1.0))) (* x (- z)) (+ x y)))
double code(double x, double y, double z) {
double tmp;
if ((z <= -300000000000.0) || !(z <= 1.0)) {
tmp = x * -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 ((z <= (-300000000000.0d0)) .or. (.not. (z <= 1.0d0))) then
tmp = x * -z
else
tmp = x + y
end if
code = tmp
end function
public static double code(double x, double y, double z) {
double tmp;
if ((z <= -300000000000.0) || !(z <= 1.0)) {
tmp = x * -z;
} else {
tmp = x + y;
}
return tmp;
}
def code(x, y, z): tmp = 0 if (z <= -300000000000.0) or not (z <= 1.0): tmp = x * -z else: tmp = x + y return tmp
function code(x, y, z) tmp = 0.0 if ((z <= -300000000000.0) || !(z <= 1.0)) tmp = Float64(x * Float64(-z)); else tmp = Float64(x + y); end return tmp end
function tmp_2 = code(x, y, z) tmp = 0.0; if ((z <= -300000000000.0) || ~((z <= 1.0))) tmp = x * -z; else tmp = x + y; end tmp_2 = tmp; end
code[x_, y_, z_] := If[Or[LessEqual[z, -300000000000.0], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(x * (-z)), $MachinePrecision], N[(x + y), $MachinePrecision]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;z \leq -300000000000 \lor \neg \left(z \leq 1\right):\\
\;\;\;\;x \cdot \left(-z\right)\\
\mathbf{else}:\\
\;\;\;\;x + y\\
\end{array}
\end{array}
(FPCore (x y z) :precision binary64 (if (<= x -4e-46) (* x (- 1.0 z)) (* y (- 1.0 z))))
double code(double x, double y, double z) {
double tmp;
if (x <= -4e-46) {
tmp = x * (1.0 - z);
} else {
tmp = y * (1.0 - 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 <= (-4d-46)) then
tmp = x * (1.0d0 - z)
else
tmp = y * (1.0d0 - z)
end if
code = tmp
end function
public static double code(double x, double y, double z) {
double tmp;
if (x <= -4e-46) {
tmp = x * (1.0 - z);
} else {
tmp = y * (1.0 - z);
}
return tmp;
}
def code(x, y, z): tmp = 0 if x <= -4e-46: tmp = x * (1.0 - z) else: tmp = y * (1.0 - z) return tmp
function code(x, y, z) tmp = 0.0 if (x <= -4e-46) tmp = Float64(x * Float64(1.0 - z)); else tmp = Float64(y * Float64(1.0 - z)); end return tmp end
function tmp_2 = code(x, y, z) tmp = 0.0; if (x <= -4e-46) tmp = x * (1.0 - z); else tmp = y * (1.0 - z); end tmp_2 = tmp; end
code[x_, y_, z_] := If[LessEqual[x, -4e-46], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(y * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;x \leq -4 \cdot 10^{-46}:\\
\;\;\;\;x \cdot \left(1 - z\right)\\
\mathbf{else}:\\
\;\;\;\;y \cdot \left(1 - z\right)\\
\end{array}
\end{array}
(FPCore (x y z) :precision binary64 (if (<= x -1.65e-47) (* x (- 1.0 z)) (- y (* y z))))
double code(double x, double y, double z) {
double tmp;
if (x <= -1.65e-47) {
tmp = x * (1.0 - z);
} else {
tmp = y - (y * 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 <= (-1.65d-47)) then
tmp = x * (1.0d0 - z)
else
tmp = y - (y * z)
end if
code = tmp
end function
public static double code(double x, double y, double z) {
double tmp;
if (x <= -1.65e-47) {
tmp = x * (1.0 - z);
} else {
tmp = y - (y * z);
}
return tmp;
}
def code(x, y, z): tmp = 0 if x <= -1.65e-47: tmp = x * (1.0 - z) else: tmp = y - (y * z) return tmp
function code(x, y, z) tmp = 0.0 if (x <= -1.65e-47) tmp = Float64(x * Float64(1.0 - z)); else tmp = Float64(y - Float64(y * z)); end return tmp end
function tmp_2 = code(x, y, z) tmp = 0.0; if (x <= -1.65e-47) tmp = x * (1.0 - z); else tmp = y - (y * z); end tmp_2 = tmp; end
code[x_, y_, z_] := If[LessEqual[x, -1.65e-47], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(y - N[(y * z), $MachinePrecision]), $MachinePrecision]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;x \leq -1.65 \cdot 10^{-47}:\\
\;\;\;\;x \cdot \left(1 - z\right)\\
\mathbf{else}:\\
\;\;\;\;y - y \cdot z\\
\end{array}
\end{array}
(FPCore (x y z) :precision binary64 (* (- 1.0 z) (+ x y)))
double code(double x, double y, double z) {
return (1.0 - 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 = (1.0d0 - z) * (x + y)
end function
public static double code(double x, double y, double z) {
return (1.0 - z) * (x + y);
}
def code(x, y, z): return (1.0 - z) * (x + y)
function code(x, y, z) return Float64(Float64(1.0 - z) * Float64(x + y)) end
function tmp = code(x, y, z) tmp = (1.0 - z) * (x + y); end
code[x_, y_, z_] := N[(N[(1.0 - z), $MachinePrecision] * N[(x + y), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
\left(1 - z\right) \cdot \left(x + y\right)
\end{array}
(FPCore (x y z) :precision binary64 (if (<= y 1.2e-22) x y))
double code(double x, double y, double z) {
double tmp;
if (y <= 1.2e-22) {
tmp = x;
} else {
tmp = 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 (y <= 1.2d-22) then
tmp = x
else
tmp = y
end if
code = tmp
end function
public static double code(double x, double y, double z) {
double tmp;
if (y <= 1.2e-22) {
tmp = x;
} else {
tmp = y;
}
return tmp;
}
def code(x, y, z): tmp = 0 if y <= 1.2e-22: tmp = x else: tmp = y return tmp
function code(x, y, z) tmp = 0.0 if (y <= 1.2e-22) tmp = x; else tmp = y; end return tmp end
function tmp_2 = code(x, y, z) tmp = 0.0; if (y <= 1.2e-22) tmp = x; else tmp = y; end tmp_2 = tmp; end
code[x_, y_, z_] := If[LessEqual[y, 1.2e-22], x, y]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;y \leq 1.2 \cdot 10^{-22}:\\
\;\;\;\;x\\
\mathbf{else}:\\
\;\;\;\;y\\
\end{array}
\end{array}
(FPCore (x y z) :precision binary64 (+ x y))
double code(double x, double y, double z) {
return 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 + y
end function
public static double code(double x, double y, double z) {
return x + y;
}
def code(x, y, z): return x + y
function code(x, y, z) return Float64(x + y) end
function tmp = code(x, y, z) tmp = x + y; end
code[x_, y_, z_] := N[(x + y), $MachinePrecision]
\begin{array}{l}
\\
x + y
\end{array}
(FPCore (x y z) :precision binary64 x)
double code(double x, double y, double z) {
return x;
}
real(8) function code(x, y, z)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8), intent (in) :: z
code = x
end function
public static double code(double x, double y, double z) {
return x;
}
def code(x, y, z): return x
function code(x, y, z) return x end
function tmp = code(x, y, z) tmp = x; end
code[x_, y_, z_] := x
\begin{array}{l}
\\
x
\end{array}
herbie shell --seed 2024010
(FPCore (x y z)
:name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, H"
:precision binary64
(* (+ x y) (- 1.0 z)))