
(FPCore (x y z) :precision binary64 (+ (* x y) (* z (- 1.0 y))))
double code(double x, double y, double z) {
return (x * y) + (z * (1.0 - 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 * (1.0d0 - y))
end function
public static double code(double x, double y, double z) {
return (x * y) + (z * (1.0 - y));
}
def code(x, y, z): return (x * y) + (z * (1.0 - y))
function code(x, y, z) return Float64(Float64(x * y) + Float64(z * Float64(1.0 - y))) end
function tmp = code(x, y, z) tmp = (x * y) + (z * (1.0 - y)); end
code[x_, y_, z_] := N[(N[(x * y), $MachinePrecision] + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
x \cdot y + z \cdot \left(1 - y\right)
\end{array}
Sampling outcomes in binary64 precision:
Herbie found 8 alternatives:
| Alternative | Accuracy | Speedup |
|---|
(FPCore (x y z) :precision binary64 (+ (* x y) (* z (- 1.0 y))))
double code(double x, double y, double z) {
return (x * y) + (z * (1.0 - 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 * (1.0d0 - y))
end function
public static double code(double x, double y, double z) {
return (x * y) + (z * (1.0 - y));
}
def code(x, y, z): return (x * y) + (z * (1.0 - y))
function code(x, y, z) return Float64(Float64(x * y) + Float64(z * Float64(1.0 - y))) end
function tmp = code(x, y, z) tmp = (x * y) + (z * (1.0 - y)); end
code[x_, y_, z_] := N[(N[(x * y), $MachinePrecision] + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
x \cdot y + z \cdot \left(1 - y\right)
\end{array}
(FPCore (x y z) :precision binary64 (fma y (- x z) z))
double code(double x, double y, double z) {
return fma(y, (x - z), z);
}
function code(x, y, z) return fma(y, Float64(x - z), z) end
code[x_, y_, z_] := N[(y * N[(x - z), $MachinePrecision] + z), $MachinePrecision]
\begin{array}{l}
\\
\mathsf{fma}\left(y, x - z, z\right)
\end{array}
(FPCore (x y z)
:precision binary64
(let* ((t_0 (* y (- z))))
(if (<= y -1.1e+204)
(* y x)
(if (<= y -1.2e+91)
t_0
(if (<= y -16500.0)
(* y x)
(if (<= y 1.7e-203)
z
(if (<= y 2.2e-169)
(* y x)
(if (<= y 2e-35)
z
(if (or (<= y 275000000000.0) (not (<= y 1.15e+175)))
(* y x)
t_0)))))))))
double code(double x, double y, double z) {
double t_0 = y * -z;
double tmp;
if (y <= -1.1e+204) {
tmp = y * x;
} else if (y <= -1.2e+91) {
tmp = t_0;
} else if (y <= -16500.0) {
tmp = y * x;
} else if (y <= 1.7e-203) {
tmp = z;
} else if (y <= 2.2e-169) {
tmp = y * x;
} else if (y <= 2e-35) {
tmp = z;
} else if ((y <= 275000000000.0) || !(y <= 1.15e+175)) {
tmp = y * 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 = y * -z
if (y <= (-1.1d+204)) then
tmp = y * x
else if (y <= (-1.2d+91)) then
tmp = t_0
else if (y <= (-16500.0d0)) then
tmp = y * x
else if (y <= 1.7d-203) then
tmp = z
else if (y <= 2.2d-169) then
tmp = y * x
else if (y <= 2d-35) then
tmp = z
else if ((y <= 275000000000.0d0) .or. (.not. (y <= 1.15d+175))) then
tmp = y * x
else
tmp = t_0
end if
code = tmp
end function
public static double code(double x, double y, double z) {
double t_0 = y * -z;
double tmp;
if (y <= -1.1e+204) {
tmp = y * x;
} else if (y <= -1.2e+91) {
tmp = t_0;
} else if (y <= -16500.0) {
tmp = y * x;
} else if (y <= 1.7e-203) {
tmp = z;
} else if (y <= 2.2e-169) {
tmp = y * x;
} else if (y <= 2e-35) {
tmp = z;
} else if ((y <= 275000000000.0) || !(y <= 1.15e+175)) {
tmp = y * x;
} else {
tmp = t_0;
}
return tmp;
}
def code(x, y, z): t_0 = y * -z tmp = 0 if y <= -1.1e+204: tmp = y * x elif y <= -1.2e+91: tmp = t_0 elif y <= -16500.0: tmp = y * x elif y <= 1.7e-203: tmp = z elif y <= 2.2e-169: tmp = y * x elif y <= 2e-35: tmp = z elif (y <= 275000000000.0) or not (y <= 1.15e+175): tmp = y * x else: tmp = t_0 return tmp
function code(x, y, z) t_0 = Float64(y * Float64(-z)) tmp = 0.0 if (y <= -1.1e+204) tmp = Float64(y * x); elseif (y <= -1.2e+91) tmp = t_0; elseif (y <= -16500.0) tmp = Float64(y * x); elseif (y <= 1.7e-203) tmp = z; elseif (y <= 2.2e-169) tmp = Float64(y * x); elseif (y <= 2e-35) tmp = z; elseif ((y <= 275000000000.0) || !(y <= 1.15e+175)) tmp = Float64(y * x); else tmp = t_0; end return tmp end
function tmp_2 = code(x, y, z) t_0 = y * -z; tmp = 0.0; if (y <= -1.1e+204) tmp = y * x; elseif (y <= -1.2e+91) tmp = t_0; elseif (y <= -16500.0) tmp = y * x; elseif (y <= 1.7e-203) tmp = z; elseif (y <= 2.2e-169) tmp = y * x; elseif (y <= 2e-35) tmp = z; elseif ((y <= 275000000000.0) || ~((y <= 1.15e+175))) tmp = y * x; else tmp = t_0; end tmp_2 = tmp; end
code[x_, y_, z_] := Block[{t$95$0 = N[(y * (-z)), $MachinePrecision]}, If[LessEqual[y, -1.1e+204], N[(y * x), $MachinePrecision], If[LessEqual[y, -1.2e+91], t$95$0, If[LessEqual[y, -16500.0], N[(y * x), $MachinePrecision], If[LessEqual[y, 1.7e-203], z, If[LessEqual[y, 2.2e-169], N[(y * x), $MachinePrecision], If[LessEqual[y, 2e-35], z, If[Or[LessEqual[y, 275000000000.0], N[Not[LessEqual[y, 1.15e+175]], $MachinePrecision]], N[(y * x), $MachinePrecision], t$95$0]]]]]]]]
\begin{array}{l}
\\
\begin{array}{l}
t_0 := y \cdot \left(-z\right)\\
\mathbf{if}\;y \leq -1.1 \cdot 10^{+204}:\\
\;\;\;\;y \cdot x\\
\mathbf{elif}\;y \leq -1.2 \cdot 10^{+91}:\\
\;\;\;\;t_0\\
\mathbf{elif}\;y \leq -16500:\\
\;\;\;\;y \cdot x\\
\mathbf{elif}\;y \leq 1.7 \cdot 10^{-203}:\\
\;\;\;\;z\\
\mathbf{elif}\;y \leq 2.2 \cdot 10^{-169}:\\
\;\;\;\;y \cdot x\\
\mathbf{elif}\;y \leq 2 \cdot 10^{-35}:\\
\;\;\;\;z\\
\mathbf{elif}\;y \leq 275000000000 \lor \neg \left(y \leq 1.15 \cdot 10^{+175}\right):\\
\;\;\;\;y \cdot x\\
\mathbf{else}:\\
\;\;\;\;t_0\\
\end{array}
\end{array}
(FPCore (x y z)
:precision binary64
(let* ((t_0 (* y (- x z))))
(if (<= y -1.46e-9)
t_0
(if (<= y 1.7e-203)
z
(if (<= y 2.2e-169) (* y x) (if (<= y 1.05e-27) z t_0))))))
double code(double x, double y, double z) {
double t_0 = y * (x - z);
double tmp;
if (y <= -1.46e-9) {
tmp = t_0;
} else if (y <= 1.7e-203) {
tmp = z;
} else if (y <= 2.2e-169) {
tmp = y * x;
} else if (y <= 1.05e-27) {
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 = y * (x - z)
if (y <= (-1.46d-9)) then
tmp = t_0
else if (y <= 1.7d-203) then
tmp = z
else if (y <= 2.2d-169) then
tmp = y * x
else if (y <= 1.05d-27) 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 = y * (x - z);
double tmp;
if (y <= -1.46e-9) {
tmp = t_0;
} else if (y <= 1.7e-203) {
tmp = z;
} else if (y <= 2.2e-169) {
tmp = y * x;
} else if (y <= 1.05e-27) {
tmp = z;
} else {
tmp = t_0;
}
return tmp;
}
def code(x, y, z): t_0 = y * (x - z) tmp = 0 if y <= -1.46e-9: tmp = t_0 elif y <= 1.7e-203: tmp = z elif y <= 2.2e-169: tmp = y * x elif y <= 1.05e-27: tmp = z else: tmp = t_0 return tmp
function code(x, y, z) t_0 = Float64(y * Float64(x - z)) tmp = 0.0 if (y <= -1.46e-9) tmp = t_0; elseif (y <= 1.7e-203) tmp = z; elseif (y <= 2.2e-169) tmp = Float64(y * x); elseif (y <= 1.05e-27) tmp = z; else tmp = t_0; end return tmp end
function tmp_2 = code(x, y, z) t_0 = y * (x - z); tmp = 0.0; if (y <= -1.46e-9) tmp = t_0; elseif (y <= 1.7e-203) tmp = z; elseif (y <= 2.2e-169) tmp = y * x; elseif (y <= 1.05e-27) tmp = z; else tmp = t_0; end tmp_2 = tmp; end
code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(x - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.46e-9], t$95$0, If[LessEqual[y, 1.7e-203], z, If[LessEqual[y, 2.2e-169], N[(y * x), $MachinePrecision], If[LessEqual[y, 1.05e-27], z, t$95$0]]]]]
\begin{array}{l}
\\
\begin{array}{l}
t_0 := y \cdot \left(x - z\right)\\
\mathbf{if}\;y \leq -1.46 \cdot 10^{-9}:\\
\;\;\;\;t_0\\
\mathbf{elif}\;y \leq 1.7 \cdot 10^{-203}:\\
\;\;\;\;z\\
\mathbf{elif}\;y \leq 2.2 \cdot 10^{-169}:\\
\;\;\;\;y \cdot x\\
\mathbf{elif}\;y \leq 1.05 \cdot 10^{-27}:\\
\;\;\;\;z\\
\mathbf{else}:\\
\;\;\;\;t_0\\
\end{array}
\end{array}
(FPCore (x y z)
:precision binary64
(let* ((t_0 (* y (- x z))))
(if (<= y -16500.0)
t_0
(if (<= y 1.7e-203)
(* z (- 1.0 y))
(if (<= y 2.3e-169) (* y x) (if (<= y 4.2e-26) z t_0))))))
double code(double x, double y, double z) {
double t_0 = y * (x - z);
double tmp;
if (y <= -16500.0) {
tmp = t_0;
} else if (y <= 1.7e-203) {
tmp = z * (1.0 - y);
} else if (y <= 2.3e-169) {
tmp = y * x;
} else if (y <= 4.2e-26) {
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 = y * (x - z)
if (y <= (-16500.0d0)) then
tmp = t_0
else if (y <= 1.7d-203) then
tmp = z * (1.0d0 - y)
else if (y <= 2.3d-169) then
tmp = y * x
else if (y <= 4.2d-26) 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 = y * (x - z);
double tmp;
if (y <= -16500.0) {
tmp = t_0;
} else if (y <= 1.7e-203) {
tmp = z * (1.0 - y);
} else if (y <= 2.3e-169) {
tmp = y * x;
} else if (y <= 4.2e-26) {
tmp = z;
} else {
tmp = t_0;
}
return tmp;
}
def code(x, y, z): t_0 = y * (x - z) tmp = 0 if y <= -16500.0: tmp = t_0 elif y <= 1.7e-203: tmp = z * (1.0 - y) elif y <= 2.3e-169: tmp = y * x elif y <= 4.2e-26: tmp = z else: tmp = t_0 return tmp
function code(x, y, z) t_0 = Float64(y * Float64(x - z)) tmp = 0.0 if (y <= -16500.0) tmp = t_0; elseif (y <= 1.7e-203) tmp = Float64(z * Float64(1.0 - y)); elseif (y <= 2.3e-169) tmp = Float64(y * x); elseif (y <= 4.2e-26) tmp = z; else tmp = t_0; end return tmp end
function tmp_2 = code(x, y, z) t_0 = y * (x - z); tmp = 0.0; if (y <= -16500.0) tmp = t_0; elseif (y <= 1.7e-203) tmp = z * (1.0 - y); elseif (y <= 2.3e-169) tmp = y * x; elseif (y <= 4.2e-26) tmp = z; else tmp = t_0; end tmp_2 = tmp; end
code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(x - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -16500.0], t$95$0, If[LessEqual[y, 1.7e-203], N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.3e-169], N[(y * x), $MachinePrecision], If[LessEqual[y, 4.2e-26], z, t$95$0]]]]]
\begin{array}{l}
\\
\begin{array}{l}
t_0 := y \cdot \left(x - z\right)\\
\mathbf{if}\;y \leq -16500:\\
\;\;\;\;t_0\\
\mathbf{elif}\;y \leq 1.7 \cdot 10^{-203}:\\
\;\;\;\;z \cdot \left(1 - y\right)\\
\mathbf{elif}\;y \leq 2.3 \cdot 10^{-169}:\\
\;\;\;\;y \cdot x\\
\mathbf{elif}\;y \leq 4.2 \cdot 10^{-26}:\\
\;\;\;\;z\\
\mathbf{else}:\\
\;\;\;\;t_0\\
\end{array}
\end{array}
(FPCore (x y z)
:precision binary64
(if (or (<= y -16500.0)
(and (not (<= y 1.7e-203)) (or (<= y 2.2e-169) (not (<= y 1.5e-35)))))
(* y x)
z))
double code(double x, double y, double z) {
double tmp;
if ((y <= -16500.0) || (!(y <= 1.7e-203) && ((y <= 2.2e-169) || !(y <= 1.5e-35)))) {
tmp = y * x;
} 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 ((y <= (-16500.0d0)) .or. (.not. (y <= 1.7d-203)) .and. (y <= 2.2d-169) .or. (.not. (y <= 1.5d-35))) then
tmp = y * x
else
tmp = z
end if
code = tmp
end function
public static double code(double x, double y, double z) {
double tmp;
if ((y <= -16500.0) || (!(y <= 1.7e-203) && ((y <= 2.2e-169) || !(y <= 1.5e-35)))) {
tmp = y * x;
} else {
tmp = z;
}
return tmp;
}
def code(x, y, z): tmp = 0 if (y <= -16500.0) or (not (y <= 1.7e-203) and ((y <= 2.2e-169) or not (y <= 1.5e-35))): tmp = y * x else: tmp = z return tmp
function code(x, y, z) tmp = 0.0 if ((y <= -16500.0) || (!(y <= 1.7e-203) && ((y <= 2.2e-169) || !(y <= 1.5e-35)))) tmp = Float64(y * x); else tmp = z; end return tmp end
function tmp_2 = code(x, y, z) tmp = 0.0; if ((y <= -16500.0) || (~((y <= 1.7e-203)) && ((y <= 2.2e-169) || ~((y <= 1.5e-35))))) tmp = y * x; else tmp = z; end tmp_2 = tmp; end
code[x_, y_, z_] := If[Or[LessEqual[y, -16500.0], And[N[Not[LessEqual[y, 1.7e-203]], $MachinePrecision], Or[LessEqual[y, 2.2e-169], N[Not[LessEqual[y, 1.5e-35]], $MachinePrecision]]]], N[(y * x), $MachinePrecision], z]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;y \leq -16500 \lor \neg \left(y \leq 1.7 \cdot 10^{-203}\right) \land \left(y \leq 2.2 \cdot 10^{-169} \lor \neg \left(y \leq 1.5 \cdot 10^{-35}\right)\right):\\
\;\;\;\;y \cdot x\\
\mathbf{else}:\\
\;\;\;\;z\\
\end{array}
\end{array}
(FPCore (x y z) :precision binary64 (if (or (<= y -1.0) (not (<= y 1.0))) (* y (- x z)) (+ z (* y x))))
double code(double x, double y, double z) {
double tmp;
if ((y <= -1.0) || !(y <= 1.0)) {
tmp = y * (x - z);
} else {
tmp = z + (y * 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 ((y <= (-1.0d0)) .or. (.not. (y <= 1.0d0))) then
tmp = y * (x - z)
else
tmp = z + (y * x)
end if
code = tmp
end function
public static double code(double x, double y, double z) {
double tmp;
if ((y <= -1.0) || !(y <= 1.0)) {
tmp = y * (x - z);
} else {
tmp = z + (y * x);
}
return tmp;
}
def code(x, y, z): tmp = 0 if (y <= -1.0) or not (y <= 1.0): tmp = y * (x - z) else: tmp = z + (y * x) return tmp
function code(x, y, z) tmp = 0.0 if ((y <= -1.0) || !(y <= 1.0)) tmp = Float64(y * Float64(x - z)); else tmp = Float64(z + Float64(y * x)); end return tmp end
function tmp_2 = code(x, y, z) tmp = 0.0; if ((y <= -1.0) || ~((y <= 1.0))) tmp = y * (x - z); else tmp = z + (y * x); end tmp_2 = tmp; end
code[x_, y_, z_] := If[Or[LessEqual[y, -1.0], N[Not[LessEqual[y, 1.0]], $MachinePrecision]], N[(y * N[(x - z), $MachinePrecision]), $MachinePrecision], N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 1\right):\\
\;\;\;\;y \cdot \left(x - z\right)\\
\mathbf{else}:\\
\;\;\;\;z + y \cdot x\\
\end{array}
\end{array}
(FPCore (x y z) :precision binary64 (+ z (* y (- x z))))
double code(double x, double y, double z) {
return z + (y * (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 = z + (y * (x - z))
end function
public static double code(double x, double y, double z) {
return z + (y * (x - z));
}
def code(x, y, z): return z + (y * (x - z))
function code(x, y, z) return Float64(z + Float64(y * Float64(x - z))) end
function tmp = code(x, y, z) tmp = z + (y * (x - z)); end
code[x_, y_, z_] := N[(z + N[(y * N[(x - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
z + y \cdot \left(x - z\right)
\end{array}
(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}
(FPCore (x y z) :precision binary64 (- z (* (- z x) y)))
double code(double x, double y, double z) {
return z - ((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 = z - ((z - x) * y)
end function
public static double code(double x, double y, double z) {
return z - ((z - x) * y);
}
def code(x, y, z): return z - ((z - x) * y)
function code(x, y, z) return Float64(z - Float64(Float64(z - x) * y)) end
function tmp = code(x, y, z) tmp = z - ((z - x) * y); end
code[x_, y_, z_] := N[(z - N[(N[(z - x), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
z - \left(z - x\right) \cdot y
\end{array}
herbie shell --seed 2023348
(FPCore (x y z)
:name "Diagrams.TwoD.Segment:bezierClip from diagrams-lib-1.3.0.3"
:precision binary64
:herbie-target
(- z (* (- z x) y))
(+ (* x y) (* z (- 1.0 y))))