
(FPCore (x y) :precision binary64 (/ (- x y) (- 1.0 y)))
double code(double x, double y) {
return (x - y) / (1.0 - y);
}
real(8) function code(x, y)
real(8), intent (in) :: x
real(8), intent (in) :: y
code = (x - y) / (1.0d0 - y)
end function
public static double code(double x, double y) {
return (x - y) / (1.0 - y);
}
def code(x, y): return (x - y) / (1.0 - y)
function code(x, y) return Float64(Float64(x - y) / Float64(1.0 - y)) end
function tmp = code(x, y) tmp = (x - y) / (1.0 - y); end
code[x_, y_] := N[(N[(x - y), $MachinePrecision] / N[(1.0 - y), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
\frac{x - y}{1 - y}
\end{array}
Sampling outcomes in binary64 precision:
Herbie found 7 alternatives:
| Alternative | Accuracy | Speedup |
|---|
(FPCore (x y) :precision binary64 (/ (- x y) (- 1.0 y)))
double code(double x, double y) {
return (x - y) / (1.0 - y);
}
real(8) function code(x, y)
real(8), intent (in) :: x
real(8), intent (in) :: y
code = (x - y) / (1.0d0 - y)
end function
public static double code(double x, double y) {
return (x - y) / (1.0 - y);
}
def code(x, y): return (x - y) / (1.0 - y)
function code(x, y) return Float64(Float64(x - y) / Float64(1.0 - y)) end
function tmp = code(x, y) tmp = (x - y) / (1.0 - y); end
code[x_, y_] := N[(N[(x - y), $MachinePrecision] / N[(1.0 - y), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
\frac{x - y}{1 - y}
\end{array}
(FPCore (x y) :precision binary64 (/ (- x y) (- 1.0 y)))
double code(double x, double y) {
return (x - y) / (1.0 - y);
}
real(8) function code(x, y)
real(8), intent (in) :: x
real(8), intent (in) :: y
code = (x - y) / (1.0d0 - y)
end function
public static double code(double x, double y) {
return (x - y) / (1.0 - y);
}
def code(x, y): return (x - y) / (1.0 - y)
function code(x, y) return Float64(Float64(x - y) / Float64(1.0 - y)) end
function tmp = code(x, y) tmp = (x - y) / (1.0 - y); end
code[x_, y_] := N[(N[(x - y), $MachinePrecision] / N[(1.0 - y), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
\frac{x - y}{1 - y}
\end{array}
Initial program 100.0%
(FPCore (x y) :precision binary64 (if (or (<= y -1000.0) (not (<= y 102000000000.0))) (+ 1.0 (/ (- 1.0 x) y)) (/ x (- 1.0 y))))
double code(double x, double y) {
double tmp;
if ((y <= -1000.0) || !(y <= 102000000000.0)) {
tmp = 1.0 + ((1.0 - x) / y);
} else {
tmp = x / (1.0 - y);
}
return tmp;
}
real(8) function code(x, y)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8) :: tmp
if ((y <= (-1000.0d0)) .or. (.not. (y <= 102000000000.0d0))) then
tmp = 1.0d0 + ((1.0d0 - x) / y)
else
tmp = x / (1.0d0 - y)
end if
code = tmp
end function
public static double code(double x, double y) {
double tmp;
if ((y <= -1000.0) || !(y <= 102000000000.0)) {
tmp = 1.0 + ((1.0 - x) / y);
} else {
tmp = x / (1.0 - y);
}
return tmp;
}
def code(x, y): tmp = 0 if (y <= -1000.0) or not (y <= 102000000000.0): tmp = 1.0 + ((1.0 - x) / y) else: tmp = x / (1.0 - y) return tmp
function code(x, y) tmp = 0.0 if ((y <= -1000.0) || !(y <= 102000000000.0)) tmp = Float64(1.0 + Float64(Float64(1.0 - x) / y)); else tmp = Float64(x / Float64(1.0 - y)); end return tmp end
function tmp_2 = code(x, y) tmp = 0.0; if ((y <= -1000.0) || ~((y <= 102000000000.0))) tmp = 1.0 + ((1.0 - x) / y); else tmp = x / (1.0 - y); end tmp_2 = tmp; end
code[x_, y_] := If[Or[LessEqual[y, -1000.0], N[Not[LessEqual[y, 102000000000.0]], $MachinePrecision]], N[(1.0 + N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x / N[(1.0 - y), $MachinePrecision]), $MachinePrecision]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;y \leq -1000 \lor \neg \left(y \leq 102000000000\right):\\
\;\;\;\;1 + \frac{1 - x}{y}\\
\mathbf{else}:\\
\;\;\;\;\frac{x}{1 - y}\\
\end{array}
\end{array}
if y < -1e3 or 1.02e11 < y Initial program 100.0%
Taylor expanded in y around inf 98.9%
+-commutative98.9%
mul-1-neg98.9%
sub-neg98.9%
div-sub98.9%
Simplified98.9%
if -1e3 < y < 1.02e11Initial program 100.0%
Taylor expanded in x around inf 78.6%
Final simplification88.5%
(FPCore (x y) :precision binary64 (if (or (<= y -0.000215) (not (<= y 102000000000.0))) (- 1.0 (/ x y)) (/ x (- 1.0 y))))
double code(double x, double y) {
double tmp;
if ((y <= -0.000215) || !(y <= 102000000000.0)) {
tmp = 1.0 - (x / y);
} else {
tmp = x / (1.0 - y);
}
return tmp;
}
real(8) function code(x, y)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8) :: tmp
if ((y <= (-0.000215d0)) .or. (.not. (y <= 102000000000.0d0))) then
tmp = 1.0d0 - (x / y)
else
tmp = x / (1.0d0 - y)
end if
code = tmp
end function
public static double code(double x, double y) {
double tmp;
if ((y <= -0.000215) || !(y <= 102000000000.0)) {
tmp = 1.0 - (x / y);
} else {
tmp = x / (1.0 - y);
}
return tmp;
}
def code(x, y): tmp = 0 if (y <= -0.000215) or not (y <= 102000000000.0): tmp = 1.0 - (x / y) else: tmp = x / (1.0 - y) return tmp
function code(x, y) tmp = 0.0 if ((y <= -0.000215) || !(y <= 102000000000.0)) tmp = Float64(1.0 - Float64(x / y)); else tmp = Float64(x / Float64(1.0 - y)); end return tmp end
function tmp_2 = code(x, y) tmp = 0.0; if ((y <= -0.000215) || ~((y <= 102000000000.0))) tmp = 1.0 - (x / y); else tmp = x / (1.0 - y); end tmp_2 = tmp; end
code[x_, y_] := If[Or[LessEqual[y, -0.000215], N[Not[LessEqual[y, 102000000000.0]], $MachinePrecision]], N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision], N[(x / N[(1.0 - y), $MachinePrecision]), $MachinePrecision]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;y \leq -0.000215 \lor \neg \left(y \leq 102000000000\right):\\
\;\;\;\;1 - \frac{x}{y}\\
\mathbf{else}:\\
\;\;\;\;\frac{x}{1 - y}\\
\end{array}
\end{array}
if y < -2.14999999999999995e-4 or 1.02e11 < y Initial program 100.0%
Taylor expanded in y around inf 97.3%
+-commutative97.3%
mul-1-neg97.3%
sub-neg97.3%
div-sub97.3%
Simplified97.3%
Taylor expanded in x around inf 97.0%
mul-1-neg97.0%
Simplified97.0%
Taylor expanded in x around 0 97.0%
mul-1-neg97.0%
sub-neg97.0%
Simplified97.0%
if -2.14999999999999995e-4 < y < 1.02e11Initial program 100.0%
Taylor expanded in x around inf 79.7%
Final simplification88.3%
(FPCore (x y) :precision binary64 (if (or (<= y -0.000215) (not (<= y 1.0))) (- 1.0 (/ x y)) (+ x (* x y))))
double code(double x, double y) {
double tmp;
if ((y <= -0.000215) || !(y <= 1.0)) {
tmp = 1.0 - (x / y);
} else {
tmp = x + (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 <= (-0.000215d0)) .or. (.not. (y <= 1.0d0))) then
tmp = 1.0d0 - (x / y)
else
tmp = x + (x * y)
end if
code = tmp
end function
public static double code(double x, double y) {
double tmp;
if ((y <= -0.000215) || !(y <= 1.0)) {
tmp = 1.0 - (x / y);
} else {
tmp = x + (x * y);
}
return tmp;
}
def code(x, y): tmp = 0 if (y <= -0.000215) or not (y <= 1.0): tmp = 1.0 - (x / y) else: tmp = x + (x * y) return tmp
function code(x, y) tmp = 0.0 if ((y <= -0.000215) || !(y <= 1.0)) tmp = Float64(1.0 - Float64(x / y)); else tmp = Float64(x + Float64(x * y)); end return tmp end
function tmp_2 = code(x, y) tmp = 0.0; if ((y <= -0.000215) || ~((y <= 1.0))) tmp = 1.0 - (x / y); else tmp = x + (x * y); end tmp_2 = tmp; end
code[x_, y_] := If[Or[LessEqual[y, -0.000215], N[Not[LessEqual[y, 1.0]], $MachinePrecision]], N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision], N[(x + N[(x * y), $MachinePrecision]), $MachinePrecision]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;y \leq -0.000215 \lor \neg \left(y \leq 1\right):\\
\;\;\;\;1 - \frac{x}{y}\\
\mathbf{else}:\\
\;\;\;\;x + x \cdot y\\
\end{array}
\end{array}
if y < -2.14999999999999995e-4 or 1 < y Initial program 100.0%
Taylor expanded in y around inf 96.1%
+-commutative96.1%
mul-1-neg96.1%
sub-neg96.1%
div-sub96.1%
Simplified96.1%
Taylor expanded in x around inf 95.7%
mul-1-neg95.7%
Simplified95.7%
Taylor expanded in x around 0 95.7%
mul-1-neg95.7%
sub-neg95.7%
Simplified95.7%
if -2.14999999999999995e-4 < y < 1Initial program 100.0%
Taylor expanded in x around inf 79.2%
Taylor expanded in y around 0 78.6%
Final simplification87.3%
(FPCore (x y) :precision binary64 (if (<= y -0.000215) 1.0 (if (<= y 1.0) (+ x (* x y)) 1.0)))
double code(double x, double y) {
double tmp;
if (y <= -0.000215) {
tmp = 1.0;
} else if (y <= 1.0) {
tmp = x + (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 <= (-0.000215d0)) then
tmp = 1.0d0
else if (y <= 1.0d0) then
tmp = x + (x * y)
else
tmp = 1.0d0
end if
code = tmp
end function
public static double code(double x, double y) {
double tmp;
if (y <= -0.000215) {
tmp = 1.0;
} else if (y <= 1.0) {
tmp = x + (x * y);
} else {
tmp = 1.0;
}
return tmp;
}
def code(x, y): tmp = 0 if y <= -0.000215: tmp = 1.0 elif y <= 1.0: tmp = x + (x * y) else: tmp = 1.0 return tmp
function code(x, y) tmp = 0.0 if (y <= -0.000215) tmp = 1.0; elseif (y <= 1.0) tmp = Float64(x + Float64(x * y)); else tmp = 1.0; end return tmp end
function tmp_2 = code(x, y) tmp = 0.0; if (y <= -0.000215) tmp = 1.0; elseif (y <= 1.0) tmp = x + (x * y); else tmp = 1.0; end tmp_2 = tmp; end
code[x_, y_] := If[LessEqual[y, -0.000215], 1.0, If[LessEqual[y, 1.0], N[(x + N[(x * y), $MachinePrecision]), $MachinePrecision], 1.0]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;y \leq -0.000215:\\
\;\;\;\;1\\
\mathbf{elif}\;y \leq 1:\\
\;\;\;\;x + x \cdot y\\
\mathbf{else}:\\
\;\;\;\;1\\
\end{array}
\end{array}
if y < -2.14999999999999995e-4 or 1 < y Initial program 100.0%
Taylor expanded in y around inf 66.8%
if -2.14999999999999995e-4 < y < 1Initial program 100.0%
Taylor expanded in x around inf 79.2%
Taylor expanded in y around 0 78.6%
(FPCore (x y) :precision binary64 (if (<= y -0.000215) 1.0 (if (<= y 1.0) x 1.0)))
double code(double x, double y) {
double tmp;
if (y <= -0.000215) {
tmp = 1.0;
} else if (y <= 1.0) {
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 <= (-0.000215d0)) then
tmp = 1.0d0
else if (y <= 1.0d0) 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 <= -0.000215) {
tmp = 1.0;
} else if (y <= 1.0) {
tmp = x;
} else {
tmp = 1.0;
}
return tmp;
}
def code(x, y): tmp = 0 if y <= -0.000215: tmp = 1.0 elif y <= 1.0: tmp = x else: tmp = 1.0 return tmp
function code(x, y) tmp = 0.0 if (y <= -0.000215) tmp = 1.0; elseif (y <= 1.0) tmp = x; else tmp = 1.0; end return tmp end
function tmp_2 = code(x, y) tmp = 0.0; if (y <= -0.000215) tmp = 1.0; elseif (y <= 1.0) tmp = x; else tmp = 1.0; end tmp_2 = tmp; end
code[x_, y_] := If[LessEqual[y, -0.000215], 1.0, If[LessEqual[y, 1.0], x, 1.0]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;y \leq -0.000215:\\
\;\;\;\;1\\
\mathbf{elif}\;y \leq 1:\\
\;\;\;\;x\\
\mathbf{else}:\\
\;\;\;\;1\\
\end{array}
\end{array}
if y < -2.14999999999999995e-4 or 1 < y Initial program 100.0%
Taylor expanded in y around inf 66.8%
if -2.14999999999999995e-4 < y < 1Initial program 100.0%
Taylor expanded in y around 0 77.8%
(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 35.8%
herbie shell --seed 2024181
(FPCore (x y)
:name "Diagrams.Trail:splitAtParam from diagrams-lib-1.3.0.3, C"
:precision binary64
(/ (- x y) (- 1.0 y)))