
(FPCore (x y) :precision binary64 (* 2.0 (- (* x x) (* x y))))
double code(double x, double y) {
return 2.0 * ((x * x) - (x * y));
}
real(8) function code(x, y)
real(8), intent (in) :: x
real(8), intent (in) :: y
code = 2.0d0 * ((x * x) - (x * y))
end function
public static double code(double x, double y) {
return 2.0 * ((x * x) - (x * y));
}
def code(x, y): return 2.0 * ((x * x) - (x * y))
function code(x, y) return Float64(2.0 * Float64(Float64(x * x) - Float64(x * y))) end
function tmp = code(x, y) tmp = 2.0 * ((x * x) - (x * y)); end
code[x_, y_] := N[(2.0 * N[(N[(x * x), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
2 \cdot \left(x \cdot x - x \cdot y\right)
\end{array}
Sampling outcomes in binary64 precision:
Herbie found 5 alternatives:
| Alternative | Accuracy | Speedup |
|---|
(FPCore (x y) :precision binary64 (* 2.0 (- (* x x) (* x y))))
double code(double x, double y) {
return 2.0 * ((x * x) - (x * y));
}
real(8) function code(x, y)
real(8), intent (in) :: x
real(8), intent (in) :: y
code = 2.0d0 * ((x * x) - (x * y))
end function
public static double code(double x, double y) {
return 2.0 * ((x * x) - (x * y));
}
def code(x, y): return 2.0 * ((x * x) - (x * y))
function code(x, y) return Float64(2.0 * Float64(Float64(x * x) - Float64(x * y))) end
function tmp = code(x, y) tmp = 2.0 * ((x * x) - (x * y)); end
code[x_, y_] := N[(2.0 * N[(N[(x * x), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
2 \cdot \left(x \cdot x - x \cdot y\right)
\end{array}
(FPCore (x y) :precision binary64 (* 2.0 (* x (- x y))))
double code(double x, double y) {
return 2.0 * (x * (x - y));
}
real(8) function code(x, y)
real(8), intent (in) :: x
real(8), intent (in) :: y
code = 2.0d0 * (x * (x - y))
end function
public static double code(double x, double y) {
return 2.0 * (x * (x - y));
}
def code(x, y): return 2.0 * (x * (x - y))
function code(x, y) return Float64(2.0 * Float64(x * Float64(x - y))) end
function tmp = code(x, y) tmp = 2.0 * (x * (x - y)); end
code[x_, y_] := N[(2.0 * N[(x * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
2 \cdot \left(x \cdot \left(x - y\right)\right)
\end{array}
Initial program 93.7%
*-lowering-*.f64N/A
distribute-lft-out--N/A
*-lowering-*.f64N/A
--lowering--.f64100.0%
Simplified100.0%
(FPCore (x y) :precision binary64 (let* ((t_0 (* y (* x -2.0)))) (if (<= y -1.55e+100) t_0 (if (<= y 1.6e+14) (* 2.0 (* x x)) t_0))))
double code(double x, double y) {
double t_0 = y * (x * -2.0);
double tmp;
if (y <= -1.55e+100) {
tmp = t_0;
} else if (y <= 1.6e+14) {
tmp = 2.0 * (x * 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 = y * (x * (-2.0d0))
if (y <= (-1.55d+100)) then
tmp = t_0
else if (y <= 1.6d+14) then
tmp = 2.0d0 * (x * x)
else
tmp = t_0
end if
code = tmp
end function
public static double code(double x, double y) {
double t_0 = y * (x * -2.0);
double tmp;
if (y <= -1.55e+100) {
tmp = t_0;
} else if (y <= 1.6e+14) {
tmp = 2.0 * (x * x);
} else {
tmp = t_0;
}
return tmp;
}
def code(x, y): t_0 = y * (x * -2.0) tmp = 0 if y <= -1.55e+100: tmp = t_0 elif y <= 1.6e+14: tmp = 2.0 * (x * x) else: tmp = t_0 return tmp
function code(x, y) t_0 = Float64(y * Float64(x * -2.0)) tmp = 0.0 if (y <= -1.55e+100) tmp = t_0; elseif (y <= 1.6e+14) tmp = Float64(2.0 * Float64(x * x)); else tmp = t_0; end return tmp end
function tmp_2 = code(x, y) t_0 = y * (x * -2.0); tmp = 0.0; if (y <= -1.55e+100) tmp = t_0; elseif (y <= 1.6e+14) tmp = 2.0 * (x * x); else tmp = t_0; end tmp_2 = tmp; end
code[x_, y_] := Block[{t$95$0 = N[(y * N[(x * -2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.55e+100], t$95$0, If[LessEqual[y, 1.6e+14], N[(2.0 * N[(x * x), $MachinePrecision]), $MachinePrecision], t$95$0]]]
\begin{array}{l}
\\
\begin{array}{l}
t_0 := y \cdot \left(x \cdot -2\right)\\
\mathbf{if}\;y \leq -1.55 \cdot 10^{+100}:\\
\;\;\;\;t\_0\\
\mathbf{elif}\;y \leq 1.6 \cdot 10^{+14}:\\
\;\;\;\;2 \cdot \left(x \cdot x\right)\\
\mathbf{else}:\\
\;\;\;\;t\_0\\
\end{array}
\end{array}
if y < -1.55000000000000003e100 or 1.6e14 < y Initial program 84.4%
*-lowering-*.f64N/A
distribute-lft-out--N/A
*-lowering-*.f64N/A
--lowering--.f64100.0%
Simplified100.0%
Taylor expanded in x around 0
associate-*r*N/A
*-commutativeN/A
*-lowering-*.f64N/A
*-lowering-*.f6484.7%
Simplified84.7%
if -1.55000000000000003e100 < y < 1.6e14Initial program 99.3%
*-lowering-*.f64N/A
distribute-lft-out--N/A
*-lowering-*.f64N/A
--lowering--.f64100.0%
Simplified100.0%
Taylor expanded in x around inf
*-lowering-*.f64N/A
unpow2N/A
*-lowering-*.f6485.0%
Simplified85.0%
Final simplification84.9%
(FPCore (x y) :precision binary64 (* 2.0 (* x x)))
double code(double x, double y) {
return 2.0 * (x * x);
}
real(8) function code(x, y)
real(8), intent (in) :: x
real(8), intent (in) :: y
code = 2.0d0 * (x * x)
end function
public static double code(double x, double y) {
return 2.0 * (x * x);
}
def code(x, y): return 2.0 * (x * x)
function code(x, y) return Float64(2.0 * Float64(x * x)) end
function tmp = code(x, y) tmp = 2.0 * (x * x); end
code[x_, y_] := N[(2.0 * N[(x * x), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
2 \cdot \left(x \cdot x\right)
\end{array}
Initial program 93.7%
*-lowering-*.f64N/A
distribute-lft-out--N/A
*-lowering-*.f64N/A
--lowering--.f64100.0%
Simplified100.0%
Taylor expanded in x around inf
*-lowering-*.f64N/A
unpow2N/A
*-lowering-*.f6463.9%
Simplified63.9%
(FPCore (x y) :precision binary64 (* 2.0 x))
double code(double x, double y) {
return 2.0 * x;
}
real(8) function code(x, y)
real(8), intent (in) :: x
real(8), intent (in) :: y
code = 2.0d0 * x
end function
public static double code(double x, double y) {
return 2.0 * x;
}
def code(x, y): return 2.0 * x
function code(x, y) return Float64(2.0 * x) end
function tmp = code(x, y) tmp = 2.0 * x; end
code[x_, y_] := N[(2.0 * x), $MachinePrecision]
\begin{array}{l}
\\
2 \cdot x
\end{array}
Initial program 93.7%
*-lowering-*.f64N/A
distribute-lft-out--N/A
*-lowering-*.f64N/A
--lowering--.f64100.0%
Simplified100.0%
Taylor expanded in x around inf
*-lowering-*.f64N/A
unpow2N/A
*-lowering-*.f6463.9%
Simplified63.9%
pow2N/A
pow-to-expN/A
*-commutativeN/A
count-2N/A
flip-+N/A
+-inversesN/A
+-inversesN/A
+-inversesN/A
+-inversesN/A
flip-+N/A
log-prodN/A
sqr-powN/A
metadata-evalN/A
unpow1N/A
rem-exp-log4.3%
Applied egg-rr4.3%
(FPCore (x y) :precision binary64 2.0)
double code(double x, double y) {
return 2.0;
}
real(8) function code(x, y)
real(8), intent (in) :: x
real(8), intent (in) :: y
code = 2.0d0
end function
public static double code(double x, double y) {
return 2.0;
}
def code(x, y): return 2.0
function code(x, y) return 2.0 end
function tmp = code(x, y) tmp = 2.0; end
code[x_, y_] := 2.0
\begin{array}{l}
\\
2
\end{array}
Initial program 93.7%
*-lowering-*.f64N/A
distribute-lft-out--N/A
*-lowering-*.f64N/A
--lowering--.f64100.0%
Simplified100.0%
Taylor expanded in x around inf
*-lowering-*.f64N/A
unpow2N/A
*-lowering-*.f6463.9%
Simplified63.9%
Applied egg-rr3.7%
(FPCore (x y) :precision binary64 (* (* x 2.0) (- x y)))
double code(double x, double y) {
return (x * 2.0) * (x - y);
}
real(8) function code(x, y)
real(8), intent (in) :: x
real(8), intent (in) :: y
code = (x * 2.0d0) * (x - y)
end function
public static double code(double x, double y) {
return (x * 2.0) * (x - y);
}
def code(x, y): return (x * 2.0) * (x - y)
function code(x, y) return Float64(Float64(x * 2.0) * Float64(x - y)) end
function tmp = code(x, y) tmp = (x * 2.0) * (x - y); end
code[x_, y_] := N[(N[(x * 2.0), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
\left(x \cdot 2\right) \cdot \left(x - y\right)
\end{array}
herbie shell --seed 2024161
(FPCore (x y)
:name "Linear.Matrix:fromQuaternion from linear-1.19.1.3, A"
:precision binary64
:alt
(! :herbie-platform default (* (* x 2) (- x y)))
(* 2.0 (- (* x x) (* x y))))