
(FPCore (x y) :precision binary64 (/ (+ x y) (+ y 1.0)))
double code(double x, double y) {
return (x + y) / (y + 1.0);
}
real(8) function code(x, y)
real(8), intent (in) :: x
real(8), intent (in) :: y
code = (x + y) / (y + 1.0d0)
end function
public static double code(double x, double y) {
return (x + y) / (y + 1.0);
}
def code(x, y): return (x + y) / (y + 1.0)
function code(x, y) return Float64(Float64(x + y) / Float64(y + 1.0)) end
function tmp = code(x, y) tmp = (x + y) / (y + 1.0); end
code[x_, y_] := N[(N[(x + y), $MachinePrecision] / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
\frac{x + y}{y + 1}
\end{array}
Sampling outcomes in binary64 precision:
Herbie found 7 alternatives:
| Alternative | Accuracy | Speedup |
|---|
(FPCore (x y) :precision binary64 (/ (+ x y) (+ y 1.0)))
double code(double x, double y) {
return (x + y) / (y + 1.0);
}
real(8) function code(x, y)
real(8), intent (in) :: x
real(8), intent (in) :: y
code = (x + y) / (y + 1.0d0)
end function
public static double code(double x, double y) {
return (x + y) / (y + 1.0);
}
def code(x, y): return (x + y) / (y + 1.0)
function code(x, y) return Float64(Float64(x + y) / Float64(y + 1.0)) end
function tmp = code(x, y) tmp = (x + y) / (y + 1.0); end
code[x_, y_] := N[(N[(x + y), $MachinePrecision] / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
\frac{x + y}{y + 1}
\end{array}
(FPCore (x y) :precision binary64 (/ (+ x y) (+ y 1.0)))
double code(double x, double y) {
return (x + y) / (y + 1.0);
}
real(8) function code(x, y)
real(8), intent (in) :: x
real(8), intent (in) :: y
code = (x + y) / (y + 1.0d0)
end function
public static double code(double x, double y) {
return (x + y) / (y + 1.0);
}
def code(x, y): return (x + y) / (y + 1.0)
function code(x, y) return Float64(Float64(x + y) / Float64(y + 1.0)) end
function tmp = code(x, y) tmp = (x + y) / (y + 1.0); end
code[x_, y_] := N[(N[(x + y), $MachinePrecision] / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
\frac{x + y}{y + 1}
\end{array}
Initial program 100.0%
(FPCore (x y) :precision binary64 (if (<= y -1.0) (+ 1.0 (/ (+ x -1.0) y)) (if (<= y 0.82) (+ x (* y (- 1.0 x))) (+ 1.0 (/ x y)))))
double code(double x, double y) {
double tmp;
if (y <= -1.0) {
tmp = 1.0 + ((x + -1.0) / y);
} else if (y <= 0.82) {
tmp = x + (y * (1.0 - x));
} else {
tmp = 1.0 + (x / y);
}
return tmp;
}
real(8) function code(x, y)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8) :: tmp
if (y <= (-1.0d0)) then
tmp = 1.0d0 + ((x + (-1.0d0)) / y)
else if (y <= 0.82d0) then
tmp = x + (y * (1.0d0 - x))
else
tmp = 1.0d0 + (x / y)
end if
code = tmp
end function
public static double code(double x, double y) {
double tmp;
if (y <= -1.0) {
tmp = 1.0 + ((x + -1.0) / y);
} else if (y <= 0.82) {
tmp = x + (y * (1.0 - x));
} else {
tmp = 1.0 + (x / y);
}
return tmp;
}
def code(x, y): tmp = 0 if y <= -1.0: tmp = 1.0 + ((x + -1.0) / y) elif y <= 0.82: tmp = x + (y * (1.0 - x)) else: tmp = 1.0 + (x / y) return tmp
function code(x, y) tmp = 0.0 if (y <= -1.0) tmp = Float64(1.0 + Float64(Float64(x + -1.0) / y)); elseif (y <= 0.82) tmp = Float64(x + Float64(y * Float64(1.0 - x))); else tmp = Float64(1.0 + Float64(x / y)); end return tmp end
function tmp_2 = code(x, y) tmp = 0.0; if (y <= -1.0) tmp = 1.0 + ((x + -1.0) / y); elseif (y <= 0.82) tmp = x + (y * (1.0 - x)); else tmp = 1.0 + (x / y); end tmp_2 = tmp; end
code[x_, y_] := If[LessEqual[y, -1.0], N[(1.0 + N[(N[(x + -1.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 0.82], N[(x + N[(y * N[(1.0 - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(x / y), $MachinePrecision]), $MachinePrecision]]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;y \leq -1:\\
\;\;\;\;1 + \frac{x + -1}{y}\\
\mathbf{elif}\;y \leq 0.82:\\
\;\;\;\;x + y \cdot \left(1 - x\right)\\
\mathbf{else}:\\
\;\;\;\;1 + \frac{x}{y}\\
\end{array}
\end{array}
if y < -1Initial program 100.0%
Taylor expanded in y around inf 98.3%
associate--l+98.3%
div-sub98.3%
sub-neg98.3%
metadata-eval98.3%
Simplified98.3%
if -1 < y < 0.819999999999999951Initial program 100.0%
Taylor expanded in y around 0 98.4%
if 0.819999999999999951 < y Initial program 99.9%
Taylor expanded in y around inf 99.2%
associate--l+99.2%
div-sub99.2%
sub-neg99.2%
metadata-eval99.2%
Simplified99.2%
Taylor expanded in x around inf 99.2%
(FPCore (x y) :precision binary64 (if (or (<= y -1.0) (not (<= y 1.0))) (+ 1.0 (/ x y)) (+ x y)))
double code(double x, double y) {
double tmp;
if ((y <= -1.0) || !(y <= 1.0)) {
tmp = 1.0 + (x / y);
} else {
tmp = x + y;
}
return tmp;
}
real(8) function code(x, y)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8) :: tmp
if ((y <= (-1.0d0)) .or. (.not. (y <= 1.0d0))) then
tmp = 1.0d0 + (x / y)
else
tmp = x + y
end if
code = tmp
end function
public static double code(double x, double y) {
double tmp;
if ((y <= -1.0) || !(y <= 1.0)) {
tmp = 1.0 + (x / y);
} else {
tmp = x + y;
}
return tmp;
}
def code(x, y): tmp = 0 if (y <= -1.0) or not (y <= 1.0): tmp = 1.0 + (x / y) else: tmp = x + y return tmp
function code(x, y) tmp = 0.0 if ((y <= -1.0) || !(y <= 1.0)) tmp = Float64(1.0 + Float64(x / y)); else tmp = Float64(x + y); end return tmp end
function tmp_2 = code(x, y) tmp = 0.0; if ((y <= -1.0) || ~((y <= 1.0))) tmp = 1.0 + (x / y); else tmp = x + y; end tmp_2 = tmp; end
code[x_, y_] := If[Or[LessEqual[y, -1.0], N[Not[LessEqual[y, 1.0]], $MachinePrecision]], N[(1.0 + N[(x / y), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 1\right):\\
\;\;\;\;1 + \frac{x}{y}\\
\mathbf{else}:\\
\;\;\;\;x + y\\
\end{array}
\end{array}
if y < -1 or 1 < y Initial program 100.0%
Taylor expanded in y around inf 98.7%
associate--l+98.7%
div-sub98.7%
sub-neg98.7%
metadata-eval98.7%
Simplified98.7%
Taylor expanded in x around inf 98.5%
if -1 < y < 1Initial program 100.0%
Taylor expanded in y around 0 98.4%
Taylor expanded in x around 0 97.7%
Final simplification98.1%
(FPCore (x y) :precision binary64 (if (<= y -1.0) (+ 1.0 (/ (+ x -1.0) y)) (if (<= y 1.0) (+ x y) (+ 1.0 (/ x y)))))
double code(double x, double y) {
double tmp;
if (y <= -1.0) {
tmp = 1.0 + ((x + -1.0) / y);
} else if (y <= 1.0) {
tmp = x + y;
} else {
tmp = 1.0 + (x / y);
}
return tmp;
}
real(8) function code(x, y)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8) :: tmp
if (y <= (-1.0d0)) then
tmp = 1.0d0 + ((x + (-1.0d0)) / y)
else if (y <= 1.0d0) then
tmp = x + y
else
tmp = 1.0d0 + (x / y)
end if
code = tmp
end function
public static double code(double x, double y) {
double tmp;
if (y <= -1.0) {
tmp = 1.0 + ((x + -1.0) / y);
} else if (y <= 1.0) {
tmp = x + y;
} else {
tmp = 1.0 + (x / y);
}
return tmp;
}
def code(x, y): tmp = 0 if y <= -1.0: tmp = 1.0 + ((x + -1.0) / y) elif y <= 1.0: tmp = x + y else: tmp = 1.0 + (x / y) return tmp
function code(x, y) tmp = 0.0 if (y <= -1.0) tmp = Float64(1.0 + Float64(Float64(x + -1.0) / y)); elseif (y <= 1.0) tmp = Float64(x + y); else tmp = Float64(1.0 + Float64(x / y)); end return tmp end
function tmp_2 = code(x, y) tmp = 0.0; if (y <= -1.0) tmp = 1.0 + ((x + -1.0) / y); elseif (y <= 1.0) tmp = x + y; else tmp = 1.0 + (x / y); end tmp_2 = tmp; end
code[x_, y_] := If[LessEqual[y, -1.0], N[(1.0 + N[(N[(x + -1.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.0], N[(x + y), $MachinePrecision], N[(1.0 + N[(x / y), $MachinePrecision]), $MachinePrecision]]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;y \leq -1:\\
\;\;\;\;1 + \frac{x + -1}{y}\\
\mathbf{elif}\;y \leq 1:\\
\;\;\;\;x + y\\
\mathbf{else}:\\
\;\;\;\;1 + \frac{x}{y}\\
\end{array}
\end{array}
if y < -1Initial program 100.0%
Taylor expanded in y around inf 98.3%
associate--l+98.3%
div-sub98.3%
sub-neg98.3%
metadata-eval98.3%
Simplified98.3%
if -1 < y < 1Initial program 100.0%
Taylor expanded in y around 0 98.4%
Taylor expanded in x around 0 97.7%
if 1 < y Initial program 99.9%
Taylor expanded in y around inf 99.2%
associate--l+99.2%
div-sub99.2%
sub-neg99.2%
metadata-eval99.2%
Simplified99.2%
Taylor expanded in x around inf 99.2%
(FPCore (x y) :precision binary64 (if (<= y -1.0) 1.0 (if (<= y 3350000.0) (+ x y) 1.0)))
double code(double x, double y) {
double tmp;
if (y <= -1.0) {
tmp = 1.0;
} else if (y <= 3350000.0) {
tmp = x + y;
} else {
tmp = 1.0;
}
return tmp;
}
real(8) function code(x, y)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8) :: tmp
if (y <= (-1.0d0)) then
tmp = 1.0d0
else if (y <= 3350000.0d0) then
tmp = x + y
else
tmp = 1.0d0
end if
code = tmp
end function
public static double code(double x, double y) {
double tmp;
if (y <= -1.0) {
tmp = 1.0;
} else if (y <= 3350000.0) {
tmp = x + y;
} else {
tmp = 1.0;
}
return tmp;
}
def code(x, y): tmp = 0 if y <= -1.0: tmp = 1.0 elif y <= 3350000.0: tmp = x + y else: tmp = 1.0 return tmp
function code(x, y) tmp = 0.0 if (y <= -1.0) tmp = 1.0; elseif (y <= 3350000.0) tmp = Float64(x + y); else tmp = 1.0; end return tmp end
function tmp_2 = code(x, y) tmp = 0.0; if (y <= -1.0) tmp = 1.0; elseif (y <= 3350000.0) tmp = x + y; else tmp = 1.0; end tmp_2 = tmp; end
code[x_, y_] := If[LessEqual[y, -1.0], 1.0, If[LessEqual[y, 3350000.0], N[(x + y), $MachinePrecision], 1.0]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;y \leq -1:\\
\;\;\;\;1\\
\mathbf{elif}\;y \leq 3350000:\\
\;\;\;\;x + y\\
\mathbf{else}:\\
\;\;\;\;1\\
\end{array}
\end{array}
if y < -1 or 3.35e6 < y Initial program 100.0%
Taylor expanded in y around inf 69.9%
if -1 < y < 3.35e6Initial program 100.0%
Taylor expanded in y around 0 97.6%
Taylor expanded in x around 0 97.0%
(FPCore (x y) :precision binary64 (if (<= y -1.0) 1.0 (if (<= y 3350000.0) x 1.0)))
double code(double x, double y) {
double tmp;
if (y <= -1.0) {
tmp = 1.0;
} else if (y <= 3350000.0) {
tmp = x;
} else {
tmp = 1.0;
}
return tmp;
}
real(8) function code(x, y)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8) :: tmp
if (y <= (-1.0d0)) then
tmp = 1.0d0
else if (y <= 3350000.0d0) then
tmp = x
else
tmp = 1.0d0
end if
code = tmp
end function
public static double code(double x, double y) {
double tmp;
if (y <= -1.0) {
tmp = 1.0;
} else if (y <= 3350000.0) {
tmp = x;
} else {
tmp = 1.0;
}
return tmp;
}
def code(x, y): tmp = 0 if y <= -1.0: tmp = 1.0 elif y <= 3350000.0: tmp = x else: tmp = 1.0 return tmp
function code(x, y) tmp = 0.0 if (y <= -1.0) tmp = 1.0; elseif (y <= 3350000.0) tmp = x; else tmp = 1.0; end return tmp end
function tmp_2 = code(x, y) tmp = 0.0; if (y <= -1.0) tmp = 1.0; elseif (y <= 3350000.0) tmp = x; else tmp = 1.0; end tmp_2 = tmp; end
code[x_, y_] := If[LessEqual[y, -1.0], 1.0, If[LessEqual[y, 3350000.0], x, 1.0]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;y \leq -1:\\
\;\;\;\;1\\
\mathbf{elif}\;y \leq 3350000:\\
\;\;\;\;x\\
\mathbf{else}:\\
\;\;\;\;1\\
\end{array}
\end{array}
if y < -1 or 3.35e6 < y Initial program 100.0%
Taylor expanded in y around inf 69.9%
if -1 < y < 3.35e6Initial program 100.0%
Taylor expanded in y around 0 74.1%
(FPCore (x y) :precision binary64 1.0)
double code(double x, double y) {
return 1.0;
}
real(8) function code(x, y)
real(8), intent (in) :: x
real(8), intent (in) :: y
code = 1.0d0
end function
public static double code(double x, double y) {
return 1.0;
}
def code(x, y): return 1.0
function code(x, y) return 1.0 end
function tmp = code(x, y) tmp = 1.0; end
code[x_, y_] := 1.0
\begin{array}{l}
\\
1
\end{array}
Initial program 100.0%
Taylor expanded in y around inf 36.5%
herbie shell --seed 2024146
(FPCore (x y)
:name "Data.Colour.SRGB:invTransferFunction from colour-2.3.3"
:precision binary64
(/ (+ x y) (+ y 1.0)))