
(FPCore (x y) :precision binary64 (/ (* x (+ (/ x y) 1.0)) (+ x 1.0)))
double code(double x, double y) {
return (x * ((x / y) + 1.0)) / (x + 1.0);
}
real(8) function code(x, y)
real(8), intent (in) :: x
real(8), intent (in) :: y
code = (x * ((x / y) + 1.0d0)) / (x + 1.0d0)
end function
public static double code(double x, double y) {
return (x * ((x / y) + 1.0)) / (x + 1.0);
}
def code(x, y): return (x * ((x / y) + 1.0)) / (x + 1.0)
function code(x, y) return Float64(Float64(x * Float64(Float64(x / y) + 1.0)) / Float64(x + 1.0)) end
function tmp = code(x, y) tmp = (x * ((x / y) + 1.0)) / (x + 1.0); end
code[x_, y_] := N[(N[(x * N[(N[(x / y), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
\frac{x \cdot \left(\frac{x}{y} + 1\right)}{x + 1}
\end{array}
Sampling outcomes in binary64 precision:
Herbie found 7 alternatives:
| Alternative | Accuracy | Speedup |
|---|
(FPCore (x y) :precision binary64 (/ (* x (+ (/ x y) 1.0)) (+ x 1.0)))
double code(double x, double y) {
return (x * ((x / y) + 1.0)) / (x + 1.0);
}
real(8) function code(x, y)
real(8), intent (in) :: x
real(8), intent (in) :: y
code = (x * ((x / y) + 1.0d0)) / (x + 1.0d0)
end function
public static double code(double x, double y) {
return (x * ((x / y) + 1.0)) / (x + 1.0);
}
def code(x, y): return (x * ((x / y) + 1.0)) / (x + 1.0)
function code(x, y) return Float64(Float64(x * Float64(Float64(x / y) + 1.0)) / Float64(x + 1.0)) end
function tmp = code(x, y) tmp = (x * ((x / y) + 1.0)) / (x + 1.0); end
code[x_, y_] := N[(N[(x * N[(N[(x / y), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
\frac{x \cdot \left(\frac{x}{y} + 1\right)}{x + 1}
\end{array}
(FPCore (x y) :precision binary64 (* (+ (/ x y) 1.0) (/ x (+ x 1.0))))
double code(double x, double y) {
return ((x / y) + 1.0) * (x / (x + 1.0));
}
real(8) function code(x, y)
real(8), intent (in) :: x
real(8), intent (in) :: y
code = ((x / y) + 1.0d0) * (x / (x + 1.0d0))
end function
public static double code(double x, double y) {
return ((x / y) + 1.0) * (x / (x + 1.0));
}
def code(x, y): return ((x / y) + 1.0) * (x / (x + 1.0))
function code(x, y) return Float64(Float64(Float64(x / y) + 1.0) * Float64(x / Float64(x + 1.0))) end
function tmp = code(x, y) tmp = ((x / y) + 1.0) * (x / (x + 1.0)); end
code[x_, y_] := N[(N[(N[(x / y), $MachinePrecision] + 1.0), $MachinePrecision] * N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
\left(\frac{x}{y} + 1\right) \cdot \frac{x}{x + 1}
\end{array}
Initial program 86.8%
Simplified0
(FPCore (x y) :precision binary64 (let* ((t_0 (+ (/ x y) 1.0))) (if (<= x -1.0) t_0 (if (<= x 1.0) (* t_0 x) t_0))))
double code(double x, double y) {
double t_0 = (x / y) + 1.0;
double tmp;
if (x <= -1.0) {
tmp = t_0;
} else if (x <= 1.0) {
tmp = t_0 * x;
} else {
tmp = t_0;
}
return tmp;
}
real(8) function code(x, y)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8) :: t_0
real(8) :: tmp
t_0 = (x / y) + 1.0d0
if (x <= (-1.0d0)) then
tmp = t_0
else if (x <= 1.0d0) then
tmp = t_0 * x
else
tmp = t_0
end if
code = tmp
end function
public static double code(double x, double y) {
double t_0 = (x / y) + 1.0;
double tmp;
if (x <= -1.0) {
tmp = t_0;
} else if (x <= 1.0) {
tmp = t_0 * x;
} else {
tmp = t_0;
}
return tmp;
}
def code(x, y): t_0 = (x / y) + 1.0 tmp = 0 if x <= -1.0: tmp = t_0 elif x <= 1.0: tmp = t_0 * x else: tmp = t_0 return tmp
function code(x, y) t_0 = Float64(Float64(x / y) + 1.0) tmp = 0.0 if (x <= -1.0) tmp = t_0; elseif (x <= 1.0) tmp = Float64(t_0 * x); else tmp = t_0; end return tmp end
function tmp_2 = code(x, y) t_0 = (x / y) + 1.0; tmp = 0.0; if (x <= -1.0) tmp = t_0; elseif (x <= 1.0) tmp = t_0 * x; else tmp = t_0; end tmp_2 = tmp; end
code[x_, y_] := Block[{t$95$0 = N[(N[(x / y), $MachinePrecision] + 1.0), $MachinePrecision]}, If[LessEqual[x, -1.0], t$95$0, If[LessEqual[x, 1.0], N[(t$95$0 * x), $MachinePrecision], t$95$0]]]
\begin{array}{l}
\\
\begin{array}{l}
t_0 := \frac{x}{y} + 1\\
\mathbf{if}\;x \leq -1:\\
\;\;\;\;t\_0\\
\mathbf{elif}\;x \leq 1:\\
\;\;\;\;t\_0 \cdot x\\
\mathbf{else}:\\
\;\;\;\;t\_0\\
\end{array}
\end{array}
if x < -1 or 1 < x Initial program 77.3%
Simplified0
Taylor expanded in x around inf 0
Simplified0
Applied egg-rr0
if -1 < x < 1Initial program 99.8%
Simplified0
Taylor expanded in x around 0 0
Simplified0
(FPCore (x y) :precision binary64 (let* ((t_0 (+ (/ x y) 1.0))) (if (<= x -2060000000.0) t_0 (if (<= x 620000000.0) (/ x (+ x 1.0)) t_0))))
double code(double x, double y) {
double t_0 = (x / y) + 1.0;
double tmp;
if (x <= -2060000000.0) {
tmp = t_0;
} else if (x <= 620000000.0) {
tmp = x / (x + 1.0);
} else {
tmp = t_0;
}
return tmp;
}
real(8) function code(x, y)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8) :: t_0
real(8) :: tmp
t_0 = (x / y) + 1.0d0
if (x <= (-2060000000.0d0)) then
tmp = t_0
else if (x <= 620000000.0d0) then
tmp = x / (x + 1.0d0)
else
tmp = t_0
end if
code = tmp
end function
public static double code(double x, double y) {
double t_0 = (x / y) + 1.0;
double tmp;
if (x <= -2060000000.0) {
tmp = t_0;
} else if (x <= 620000000.0) {
tmp = x / (x + 1.0);
} else {
tmp = t_0;
}
return tmp;
}
def code(x, y): t_0 = (x / y) + 1.0 tmp = 0 if x <= -2060000000.0: tmp = t_0 elif x <= 620000000.0: tmp = x / (x + 1.0) else: tmp = t_0 return tmp
function code(x, y) t_0 = Float64(Float64(x / y) + 1.0) tmp = 0.0 if (x <= -2060000000.0) tmp = t_0; elseif (x <= 620000000.0) tmp = Float64(x / Float64(x + 1.0)); else tmp = t_0; end return tmp end
function tmp_2 = code(x, y) t_0 = (x / y) + 1.0; tmp = 0.0; if (x <= -2060000000.0) tmp = t_0; elseif (x <= 620000000.0) tmp = x / (x + 1.0); else tmp = t_0; end tmp_2 = tmp; end
code[x_, y_] := Block[{t$95$0 = N[(N[(x / y), $MachinePrecision] + 1.0), $MachinePrecision]}, If[LessEqual[x, -2060000000.0], t$95$0, If[LessEqual[x, 620000000.0], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], t$95$0]]]
\begin{array}{l}
\\
\begin{array}{l}
t_0 := \frac{x}{y} + 1\\
\mathbf{if}\;x \leq -2060000000:\\
\;\;\;\;t\_0\\
\mathbf{elif}\;x \leq 620000000:\\
\;\;\;\;\frac{x}{x + 1}\\
\mathbf{else}:\\
\;\;\;\;t\_0\\
\end{array}
\end{array}
if x < -2.06e9 or 6.2e8 < x Initial program 76.5%
Simplified0
Taylor expanded in x around inf 0
Simplified0
Applied egg-rr0
if -2.06e9 < x < 6.2e8Initial program 99.8%
Simplified0
Taylor expanded in x around 0 0
Simplified0
Applied egg-rr0
(FPCore (x y) :precision binary64 (let* ((t_0 (+ (/ x y) 1.0))) (if (<= x -1.0) t_0 (if (<= x 0.052) x t_0))))
double code(double x, double y) {
double t_0 = (x / y) + 1.0;
double tmp;
if (x <= -1.0) {
tmp = t_0;
} else if (x <= 0.052) {
tmp = x;
} else {
tmp = t_0;
}
return tmp;
}
real(8) function code(x, y)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8) :: t_0
real(8) :: tmp
t_0 = (x / y) + 1.0d0
if (x <= (-1.0d0)) then
tmp = t_0
else if (x <= 0.052d0) then
tmp = x
else
tmp = t_0
end if
code = tmp
end function
public static double code(double x, double y) {
double t_0 = (x / y) + 1.0;
double tmp;
if (x <= -1.0) {
tmp = t_0;
} else if (x <= 0.052) {
tmp = x;
} else {
tmp = t_0;
}
return tmp;
}
def code(x, y): t_0 = (x / y) + 1.0 tmp = 0 if x <= -1.0: tmp = t_0 elif x <= 0.052: tmp = x else: tmp = t_0 return tmp
function code(x, y) t_0 = Float64(Float64(x / y) + 1.0) tmp = 0.0 if (x <= -1.0) tmp = t_0; elseif (x <= 0.052) tmp = x; else tmp = t_0; end return tmp end
function tmp_2 = code(x, y) t_0 = (x / y) + 1.0; tmp = 0.0; if (x <= -1.0) tmp = t_0; elseif (x <= 0.052) tmp = x; else tmp = t_0; end tmp_2 = tmp; end
code[x_, y_] := Block[{t$95$0 = N[(N[(x / y), $MachinePrecision] + 1.0), $MachinePrecision]}, If[LessEqual[x, -1.0], t$95$0, If[LessEqual[x, 0.052], x, t$95$0]]]
\begin{array}{l}
\\
\begin{array}{l}
t_0 := \frac{x}{y} + 1\\
\mathbf{if}\;x \leq -1:\\
\;\;\;\;t\_0\\
\mathbf{elif}\;x \leq 0.052:\\
\;\;\;\;x\\
\mathbf{else}:\\
\;\;\;\;t\_0\\
\end{array}
\end{array}
if x < -1 or 0.0519999999999999976 < x Initial program 77.3%
Simplified0
Taylor expanded in x around inf 0
Simplified0
Applied egg-rr0
if -1 < x < 0.0519999999999999976Initial program 99.8%
Simplified0
Taylor expanded in x around 0 0
Simplified0
(FPCore (x y) :precision binary64 (if (<= x -1.0) (/ x y) (if (<= x 610000000.0) x (/ x y))))
double code(double x, double y) {
double tmp;
if (x <= -1.0) {
tmp = x / y;
} else if (x <= 610000000.0) {
tmp = x;
} 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 (x <= (-1.0d0)) then
tmp = x / y
else if (x <= 610000000.0d0) then
tmp = x
else
tmp = x / y
end if
code = tmp
end function
public static double code(double x, double y) {
double tmp;
if (x <= -1.0) {
tmp = x / y;
} else if (x <= 610000000.0) {
tmp = x;
} else {
tmp = x / y;
}
return tmp;
}
def code(x, y): tmp = 0 if x <= -1.0: tmp = x / y elif x <= 610000000.0: tmp = x else: tmp = x / y return tmp
function code(x, y) tmp = 0.0 if (x <= -1.0) tmp = Float64(x / y); elseif (x <= 610000000.0) tmp = x; else tmp = Float64(x / y); end return tmp end
function tmp_2 = code(x, y) tmp = 0.0; if (x <= -1.0) tmp = x / y; elseif (x <= 610000000.0) tmp = x; else tmp = x / y; end tmp_2 = tmp; end
code[x_, y_] := If[LessEqual[x, -1.0], N[(x / y), $MachinePrecision], If[LessEqual[x, 610000000.0], x, N[(x / y), $MachinePrecision]]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;x \leq -1:\\
\;\;\;\;\frac{x}{y}\\
\mathbf{elif}\;x \leq 610000000:\\
\;\;\;\;x\\
\mathbf{else}:\\
\;\;\;\;\frac{x}{y}\\
\end{array}
\end{array}
if x < -1 or 6.1e8 < x Initial program 77.1%
Simplified0
Taylor expanded in x around inf 0
Simplified0
if -1 < x < 6.1e8Initial program 99.8%
Simplified0
Taylor expanded in x around 0 0
Simplified0
(FPCore (x y) :precision binary64 (if (<= x -1.0) 1.0 (if (<= x 1.0) x 1.0)))
double code(double x, double y) {
double tmp;
if (x <= -1.0) {
tmp = 1.0;
} else if (x <= 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 (x <= (-1.0d0)) then
tmp = 1.0d0
else if (x <= 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 (x <= -1.0) {
tmp = 1.0;
} else if (x <= 1.0) {
tmp = x;
} else {
tmp = 1.0;
}
return tmp;
}
def code(x, y): tmp = 0 if x <= -1.0: tmp = 1.0 elif x <= 1.0: tmp = x else: tmp = 1.0 return tmp
function code(x, y) tmp = 0.0 if (x <= -1.0) tmp = 1.0; elseif (x <= 1.0) tmp = x; else tmp = 1.0; end return tmp end
function tmp_2 = code(x, y) tmp = 0.0; if (x <= -1.0) tmp = 1.0; elseif (x <= 1.0) tmp = x; else tmp = 1.0; end tmp_2 = tmp; end
code[x_, y_] := If[LessEqual[x, -1.0], 1.0, If[LessEqual[x, 1.0], x, 1.0]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;x \leq -1:\\
\;\;\;\;1\\
\mathbf{elif}\;x \leq 1:\\
\;\;\;\;x\\
\mathbf{else}:\\
\;\;\;\;1\\
\end{array}
\end{array}
if x < -1 or 1 < x Initial program 77.3%
Simplified0
Taylor expanded in x around 0 0
Simplified0
Taylor expanded in x around inf 0
Simplified0
if -1 < x < 1Initial program 99.8%
Simplified0
Taylor expanded in x around 0 0
Simplified0
(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 86.8%
Simplified0
Taylor expanded in x around 0 0
Simplified0
Taylor expanded in x around inf 0
Simplified0
(FPCore (x y) :precision binary64 (* (/ x 1.0) (/ (+ (/ x y) 1.0) (+ x 1.0))))
double code(double x, double y) {
return (x / 1.0) * (((x / y) + 1.0) / (x + 1.0));
}
real(8) function code(x, y)
real(8), intent (in) :: x
real(8), intent (in) :: y
code = (x / 1.0d0) * (((x / y) + 1.0d0) / (x + 1.0d0))
end function
public static double code(double x, double y) {
return (x / 1.0) * (((x / y) + 1.0) / (x + 1.0));
}
def code(x, y): return (x / 1.0) * (((x / y) + 1.0) / (x + 1.0))
function code(x, y) return Float64(Float64(x / 1.0) * Float64(Float64(Float64(x / y) + 1.0) / Float64(x + 1.0))) end
function tmp = code(x, y) tmp = (x / 1.0) * (((x / y) + 1.0) / (x + 1.0)); end
code[x_, y_] := N[(N[(x / 1.0), $MachinePrecision] * N[(N[(N[(x / y), $MachinePrecision] + 1.0), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
\frac{x}{1} \cdot \frac{\frac{x}{y} + 1}{x + 1}
\end{array}
herbie shell --seed 2024110
(FPCore (x y)
:name "Codec.Picture.Types:toneMapping from JuicyPixels-3.2.6.1"
:precision binary64
:alt
(* (/ x 1.0) (/ (+ (/ x y) 1.0) (+ x 1.0)))
(/ (* x (+ (/ x y) 1.0)) (+ x 1.0)))