
(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%
Final simplification100.0%
(FPCore (x y) :precision binary64 (if (<= y -1.0) 1.0 (if (<= y 1.0) x (if (<= y 3.2e+83) (/ x y) 1.0))))
double code(double x, double y) {
double tmp;
if (y <= -1.0) {
tmp = 1.0;
} else if (y <= 1.0) {
tmp = x;
} else if (y <= 3.2e+83) {
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 <= 1.0d0) then
tmp = x
else if (y <= 3.2d+83) 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 <= 1.0) {
tmp = x;
} else if (y <= 3.2e+83) {
tmp = x / y;
} else {
tmp = 1.0;
}
return tmp;
}
def code(x, y): tmp = 0 if y <= -1.0: tmp = 1.0 elif y <= 1.0: tmp = x elif y <= 3.2e+83: 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 <= 1.0) tmp = x; elseif (y <= 3.2e+83) 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 <= 1.0) tmp = x; elseif (y <= 3.2e+83) 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, 1.0], x, If[LessEqual[y, 3.2e+83], N[(x / y), $MachinePrecision], 1.0]]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;y \leq -1:\\
\;\;\;\;1\\
\mathbf{elif}\;y \leq 1:\\
\;\;\;\;x\\
\mathbf{elif}\;y \leq 3.2 \cdot 10^{+83}:\\
\;\;\;\;\frac{x}{y}\\
\mathbf{else}:\\
\;\;\;\;1\\
\end{array}
\end{array}
if y < -1 or 3.1999999999999999e83 < y Initial program 100.0%
Taylor expanded in y around inf 77.3%
if -1 < y < 1Initial program 100.0%
Taylor expanded in y around 0 78.3%
if 1 < y < 3.1999999999999999e83Initial program 99.9%
Taylor expanded in x around inf 61.5%
+-commutative61.5%
Simplified61.5%
Taylor expanded in y around inf 56.0%
Final simplification76.0%
(FPCore (x y) :precision binary64 (if (or (<= y -185000.0) (not (<= y 12600.0))) (+ 1.0 (/ (+ x -1.0) y)) (/ x (+ y 1.0))))
double code(double x, double y) {
double tmp;
if ((y <= -185000.0) || !(y <= 12600.0)) {
tmp = 1.0 + ((x + -1.0) / y);
} else {
tmp = x / (y + 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 <= (-185000.0d0)) .or. (.not. (y <= 12600.0d0))) then
tmp = 1.0d0 + ((x + (-1.0d0)) / y)
else
tmp = x / (y + 1.0d0)
end if
code = tmp
end function
public static double code(double x, double y) {
double tmp;
if ((y <= -185000.0) || !(y <= 12600.0)) {
tmp = 1.0 + ((x + -1.0) / y);
} else {
tmp = x / (y + 1.0);
}
return tmp;
}
def code(x, y): tmp = 0 if (y <= -185000.0) or not (y <= 12600.0): tmp = 1.0 + ((x + -1.0) / y) else: tmp = x / (y + 1.0) return tmp
function code(x, y) tmp = 0.0 if ((y <= -185000.0) || !(y <= 12600.0)) tmp = Float64(1.0 + Float64(Float64(x + -1.0) / y)); else tmp = Float64(x / Float64(y + 1.0)); end return tmp end
function tmp_2 = code(x, y) tmp = 0.0; if ((y <= -185000.0) || ~((y <= 12600.0))) tmp = 1.0 + ((x + -1.0) / y); else tmp = x / (y + 1.0); end tmp_2 = tmp; end
code[x_, y_] := If[Or[LessEqual[y, -185000.0], N[Not[LessEqual[y, 12600.0]], $MachinePrecision]], N[(1.0 + N[(N[(x + -1.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;y \leq -185000 \lor \neg \left(y \leq 12600\right):\\
\;\;\;\;1 + \frac{x + -1}{y}\\
\mathbf{else}:\\
\;\;\;\;\frac{x}{y + 1}\\
\end{array}
\end{array}
if y < -185000 or 12600 < y Initial program 100.0%
Taylor expanded in y around inf 99.4%
associate--l+99.4%
div-sub99.4%
sub-neg99.4%
metadata-eval99.4%
Simplified99.4%
if -185000 < y < 12600Initial program 100.0%
Taylor expanded in x around inf 79.4%
+-commutative79.4%
Simplified79.4%
Final simplification87.9%
(FPCore (x y) :precision binary64 (if (or (<= x -6.2e-40) (not (<= x 3.1e-148))) (/ x (+ y 1.0)) (/ y (+ y 1.0))))
double code(double x, double y) {
double tmp;
if ((x <= -6.2e-40) || !(x <= 3.1e-148)) {
tmp = x / (y + 1.0);
} else {
tmp = y / (y + 1.0);
}
return tmp;
}
real(8) function code(x, y)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8) :: tmp
if ((x <= (-6.2d-40)) .or. (.not. (x <= 3.1d-148))) then
tmp = x / (y + 1.0d0)
else
tmp = y / (y + 1.0d0)
end if
code = tmp
end function
public static double code(double x, double y) {
double tmp;
if ((x <= -6.2e-40) || !(x <= 3.1e-148)) {
tmp = x / (y + 1.0);
} else {
tmp = y / (y + 1.0);
}
return tmp;
}
def code(x, y): tmp = 0 if (x <= -6.2e-40) or not (x <= 3.1e-148): tmp = x / (y + 1.0) else: tmp = y / (y + 1.0) return tmp
function code(x, y) tmp = 0.0 if ((x <= -6.2e-40) || !(x <= 3.1e-148)) tmp = Float64(x / Float64(y + 1.0)); else tmp = Float64(y / Float64(y + 1.0)); end return tmp end
function tmp_2 = code(x, y) tmp = 0.0; if ((x <= -6.2e-40) || ~((x <= 3.1e-148))) tmp = x / (y + 1.0); else tmp = y / (y + 1.0); end tmp_2 = tmp; end
code[x_, y_] := If[Or[LessEqual[x, -6.2e-40], N[Not[LessEqual[x, 3.1e-148]], $MachinePrecision]], N[(x / N[(y + 1.0), $MachinePrecision]), $MachinePrecision], N[(y / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;x \leq -6.2 \cdot 10^{-40} \lor \neg \left(x \leq 3.1 \cdot 10^{-148}\right):\\
\;\;\;\;\frac{x}{y + 1}\\
\mathbf{else}:\\
\;\;\;\;\frac{y}{y + 1}\\
\end{array}
\end{array}
if x < -6.20000000000000021e-40 or 3.1000000000000001e-148 < x Initial program 100.0%
Taylor expanded in x around inf 76.8%
+-commutative76.8%
Simplified76.8%
if -6.20000000000000021e-40 < x < 3.1000000000000001e-148Initial program 100.0%
Taylor expanded in x around 0 82.5%
+-commutative82.5%
Simplified82.5%
Final simplification78.6%
(FPCore (x y) :precision binary64 (if (<= y -1.05e+55) 1.0 (if (<= y 3.3e+83) (/ x (+ y 1.0)) 1.0)))
double code(double x, double y) {
double tmp;
if (y <= -1.05e+55) {
tmp = 1.0;
} else if (y <= 3.3e+83) {
tmp = x / (y + 1.0);
} 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 <= (-1.05d+55)) then
tmp = 1.0d0
else if (y <= 3.3d+83) then
tmp = x / (y + 1.0d0)
else
tmp = 1.0d0
end if
code = tmp
end function
public static double code(double x, double y) {
double tmp;
if (y <= -1.05e+55) {
tmp = 1.0;
} else if (y <= 3.3e+83) {
tmp = x / (y + 1.0);
} else {
tmp = 1.0;
}
return tmp;
}
def code(x, y): tmp = 0 if y <= -1.05e+55: tmp = 1.0 elif y <= 3.3e+83: tmp = x / (y + 1.0) else: tmp = 1.0 return tmp
function code(x, y) tmp = 0.0 if (y <= -1.05e+55) tmp = 1.0; elseif (y <= 3.3e+83) tmp = Float64(x / Float64(y + 1.0)); else tmp = 1.0; end return tmp end
function tmp_2 = code(x, y) tmp = 0.0; if (y <= -1.05e+55) tmp = 1.0; elseif (y <= 3.3e+83) tmp = x / (y + 1.0); else tmp = 1.0; end tmp_2 = tmp; end
code[x_, y_] := If[LessEqual[y, -1.05e+55], 1.0, If[LessEqual[y, 3.3e+83], N[(x / N[(y + 1.0), $MachinePrecision]), $MachinePrecision], 1.0]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;y \leq -1.05 \cdot 10^{+55}:\\
\;\;\;\;1\\
\mathbf{elif}\;y \leq 3.3 \cdot 10^{+83}:\\
\;\;\;\;\frac{x}{y + 1}\\
\mathbf{else}:\\
\;\;\;\;1\\
\end{array}
\end{array}
if y < -1.05e55 or 3.29999999999999985e83 < y Initial program 100.0%
Taylor expanded in y around inf 78.6%
if -1.05e55 < y < 3.29999999999999985e83Initial program 100.0%
Taylor expanded in x around inf 76.3%
+-commutative76.3%
Simplified76.3%
Final simplification77.1%
(FPCore (x y) :precision binary64 (if (<= y -1.0) 1.0 (if (<= y 1750.0) x 1.0)))
double code(double x, double y) {
double tmp;
if (y <= -1.0) {
tmp = 1.0;
} else if (y <= 1750.0) {
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 <= 1750.0d0) 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 <= 1750.0) {
tmp = x;
} else {
tmp = 1.0;
}
return tmp;
}
def code(x, y): tmp = 0 if y <= -1.0: tmp = 1.0 elif y <= 1750.0: tmp = x else: tmp = 1.0 return tmp
function code(x, y) tmp = 0.0 if (y <= -1.0) tmp = 1.0; elseif (y <= 1750.0) 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 <= 1750.0) tmp = x; else tmp = 1.0; end tmp_2 = tmp; end
code[x_, y_] := If[LessEqual[y, -1.0], 1.0, If[LessEqual[y, 1750.0], x, 1.0]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;y \leq -1:\\
\;\;\;\;1\\
\mathbf{elif}\;y \leq 1750:\\
\;\;\;\;x\\
\mathbf{else}:\\
\;\;\;\;1\\
\end{array}
\end{array}
if y < -1 or 1750 < y Initial program 100.0%
Taylor expanded in y around inf 69.0%
if -1 < y < 1750Initial program 100.0%
Taylor expanded in y around 0 77.9%
Final simplification74.1%
(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 31.4%
Final simplification31.4%
herbie shell --seed 2024071
(FPCore (x y)
:name "Data.Colour.SRGB:invTransferFunction from colour-2.3.3"
:precision binary64
(/ (+ x y) (+ y 1.0)))