
(FPCore (x y z t) :precision binary64 (+ (* (+ (* x y) z) y) t))
double code(double x, double y, double z, double t) {
return (((x * y) + z) * y) + t;
}
real(8) function code(x, y, z, t)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8), intent (in) :: z
real(8), intent (in) :: t
code = (((x * y) + z) * y) + t
end function
public static double code(double x, double y, double z, double t) {
return (((x * y) + z) * y) + t;
}
def code(x, y, z, t): return (((x * y) + z) * y) + t
function code(x, y, z, t) return Float64(Float64(Float64(Float64(x * y) + z) * y) + t) end
function tmp = code(x, y, z, t) tmp = (((x * y) + z) * y) + t; end
code[x_, y_, z_, t_] := N[(N[(N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision] * y), $MachinePrecision] + t), $MachinePrecision]
\begin{array}{l}
\\
\left(x \cdot y + z\right) \cdot y + t
\end{array}
Sampling outcomes in binary64 precision:
Herbie found 6 alternatives:
| Alternative | Accuracy | Speedup |
|---|
(FPCore (x y z t) :precision binary64 (+ (* (+ (* x y) z) y) t))
double code(double x, double y, double z, double t) {
return (((x * y) + z) * y) + t;
}
real(8) function code(x, y, z, t)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8), intent (in) :: z
real(8), intent (in) :: t
code = (((x * y) + z) * y) + t
end function
public static double code(double x, double y, double z, double t) {
return (((x * y) + z) * y) + t;
}
def code(x, y, z, t): return (((x * y) + z) * y) + t
function code(x, y, z, t) return Float64(Float64(Float64(Float64(x * y) + z) * y) + t) end
function tmp = code(x, y, z, t) tmp = (((x * y) + z) * y) + t; end
code[x_, y_, z_, t_] := N[(N[(N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision] * y), $MachinePrecision] + t), $MachinePrecision]
\begin{array}{l}
\\
\left(x \cdot y + z\right) \cdot y + t
\end{array}
(FPCore (x y z t) :precision binary64 (+ (* y (+ (* x y) z)) t))
double code(double x, double y, double z, double t) {
return (y * ((x * y) + z)) + t;
}
real(8) function code(x, y, z, t)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8), intent (in) :: z
real(8), intent (in) :: t
code = (y * ((x * y) + z)) + t
end function
public static double code(double x, double y, double z, double t) {
return (y * ((x * y) + z)) + t;
}
def code(x, y, z, t): return (y * ((x * y) + z)) + t
function code(x, y, z, t) return Float64(Float64(y * Float64(Float64(x * y) + z)) + t) end
function tmp = code(x, y, z, t) tmp = (y * ((x * y) + z)) + t; end
code[x_, y_, z_, t_] := N[(N[(y * N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]
\begin{array}{l}
\\
y \cdot \left(x \cdot y + z\right) + t
\end{array}
Initial program 99.9%
Final simplification99.9%
(FPCore (x y z t) :precision binary64 (let* ((t_1 (* y (+ (* x y) z))) (t_2 (* y (fma y x z)))) (if (<= t_1 -1e+51) t_2 (if (<= t_1 5e+195) (fma y z t) t_2))))
double code(double x, double y, double z, double t) {
double t_1 = y * ((x * y) + z);
double t_2 = y * fma(y, x, z);
double tmp;
if (t_1 <= -1e+51) {
tmp = t_2;
} else if (t_1 <= 5e+195) {
tmp = fma(y, z, t);
} else {
tmp = t_2;
}
return tmp;
}
function code(x, y, z, t) t_1 = Float64(y * Float64(Float64(x * y) + z)) t_2 = Float64(y * fma(y, x, z)) tmp = 0.0 if (t_1 <= -1e+51) tmp = t_2; elseif (t_1 <= 5e+195) tmp = fma(y, z, t); else tmp = t_2; end return tmp end
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(y * x + z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+51], t$95$2, If[LessEqual[t$95$1, 5e+195], N[(y * z + t), $MachinePrecision], t$95$2]]]]
\begin{array}{l}
\\
\begin{array}{l}
t_1 := y \cdot \left(x \cdot y + z\right)\\
t_2 := y \cdot \mathsf{fma}\left(y, x, z\right)\\
\mathbf{if}\;t\_1 \leq -1 \cdot 10^{+51}:\\
\;\;\;\;t\_2\\
\mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+195}:\\
\;\;\;\;\mathsf{fma}\left(y, z, t\right)\\
\mathbf{else}:\\
\;\;\;\;t\_2\\
\end{array}
\end{array}
if (*.f64 (+.f64 (*.f64 x y) z) y) < -1e51 or 4.9999999999999998e195 < (*.f64 (+.f64 (*.f64 x y) z) y) Initial program 99.9%
Taylor expanded in y around inf
Applied rewrites92.8%
if -1e51 < (*.f64 (+.f64 (*.f64 x y) z) y) < 4.9999999999999998e195Initial program 99.9%
Taylor expanded in x around 0
+-commutativeN/A
lower-fma.f6493.1
Applied rewrites93.1%
Final simplification93.0%
(FPCore (x y z t)
:precision binary64
(let* ((t_1 (* y (+ (* x y) z))))
(if (<= t_1 -2e+238)
(* y (* x y))
(if (<= t_1 4e+278) (fma y z t) (* x (* y y))))))
double code(double x, double y, double z, double t) {
double t_1 = y * ((x * y) + z);
double tmp;
if (t_1 <= -2e+238) {
tmp = y * (x * y);
} else if (t_1 <= 4e+278) {
tmp = fma(y, z, t);
} else {
tmp = x * (y * y);
}
return tmp;
}
function code(x, y, z, t) t_1 = Float64(y * Float64(Float64(x * y) + z)) tmp = 0.0 if (t_1 <= -2e+238) tmp = Float64(y * Float64(x * y)); elseif (t_1 <= 4e+278) tmp = fma(y, z, t); else tmp = Float64(x * Float64(y * y)); end return tmp end
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+238], N[(y * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 4e+278], N[(y * z + t), $MachinePrecision], N[(x * N[(y * y), $MachinePrecision]), $MachinePrecision]]]]
\begin{array}{l}
\\
\begin{array}{l}
t_1 := y \cdot \left(x \cdot y + z\right)\\
\mathbf{if}\;t\_1 \leq -2 \cdot 10^{+238}:\\
\;\;\;\;y \cdot \left(x \cdot y\right)\\
\mathbf{elif}\;t\_1 \leq 4 \cdot 10^{+278}:\\
\;\;\;\;\mathsf{fma}\left(y, z, t\right)\\
\mathbf{else}:\\
\;\;\;\;x \cdot \left(y \cdot y\right)\\
\end{array}
\end{array}
if (*.f64 (+.f64 (*.f64 x y) z) y) < -2.0000000000000001e238Initial program 100.0%
Taylor expanded in x around inf
unpow2N/A
associate-*r*N/A
*-commutativeN/A
lower-*.f64N/A
*-commutativeN/A
lower-*.f6477.0
Applied rewrites77.0%
if -2.0000000000000001e238 < (*.f64 (+.f64 (*.f64 x y) z) y) < 3.99999999999999985e278Initial program 99.9%
Taylor expanded in x around 0
+-commutativeN/A
lower-fma.f6485.7
Applied rewrites85.7%
if 3.99999999999999985e278 < (*.f64 (+.f64 (*.f64 x y) z) y) Initial program 100.0%
lift-+.f64N/A
flip3-+N/A
clear-numN/A
lower-/.f64N/A
clear-numN/A
flip3-+N/A
lift-+.f64N/A
lower-/.f64100.0
lift-+.f64N/A
lift-*.f64N/A
*-commutativeN/A
lower-fma.f64100.0
Applied rewrites100.0%
Taylor expanded in y around inf
lower-*.f64N/A
unpow2N/A
lower-*.f6494.7
Applied rewrites94.7%
Final simplification85.6%
(FPCore (x y z t) :precision binary64 (let* ((t_1 (* y (+ (* x y) z))) (t_2 (* y (* x y)))) (if (<= t_1 -2e+238) t_2 (if (<= t_1 5e+195) (fma y z t) t_2))))
double code(double x, double y, double z, double t) {
double t_1 = y * ((x * y) + z);
double t_2 = y * (x * y);
double tmp;
if (t_1 <= -2e+238) {
tmp = t_2;
} else if (t_1 <= 5e+195) {
tmp = fma(y, z, t);
} else {
tmp = t_2;
}
return tmp;
}
function code(x, y, z, t) t_1 = Float64(y * Float64(Float64(x * y) + z)) t_2 = Float64(y * Float64(x * y)) tmp = 0.0 if (t_1 <= -2e+238) tmp = t_2; elseif (t_1 <= 5e+195) tmp = fma(y, z, t); else tmp = t_2; end return tmp end
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+238], t$95$2, If[LessEqual[t$95$1, 5e+195], N[(y * z + t), $MachinePrecision], t$95$2]]]]
\begin{array}{l}
\\
\begin{array}{l}
t_1 := y \cdot \left(x \cdot y + z\right)\\
t_2 := y \cdot \left(x \cdot y\right)\\
\mathbf{if}\;t\_1 \leq -2 \cdot 10^{+238}:\\
\;\;\;\;t\_2\\
\mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+195}:\\
\;\;\;\;\mathsf{fma}\left(y, z, t\right)\\
\mathbf{else}:\\
\;\;\;\;t\_2\\
\end{array}
\end{array}
if (*.f64 (+.f64 (*.f64 x y) z) y) < -2.0000000000000001e238 or 4.9999999999999998e195 < (*.f64 (+.f64 (*.f64 x y) z) y) Initial program 99.9%
Taylor expanded in x around inf
unpow2N/A
associate-*r*N/A
*-commutativeN/A
lower-*.f64N/A
*-commutativeN/A
lower-*.f6479.8
Applied rewrites79.8%
if -2.0000000000000001e238 < (*.f64 (+.f64 (*.f64 x y) z) y) < 4.9999999999999998e195Initial program 99.9%
Taylor expanded in x around 0
+-commutativeN/A
lower-fma.f6488.3
Applied rewrites88.3%
Final simplification85.2%
(FPCore (x y z t) :precision binary64 (fma y z t))
double code(double x, double y, double z, double t) {
return fma(y, z, t);
}
function code(x, y, z, t) return fma(y, z, t) end
code[x_, y_, z_, t_] := N[(y * z + t), $MachinePrecision]
\begin{array}{l}
\\
\mathsf{fma}\left(y, z, t\right)
\end{array}
Initial program 99.9%
Taylor expanded in x around 0
+-commutativeN/A
lower-fma.f6469.9
Applied rewrites69.9%
(FPCore (x y z t) :precision binary64 (* y z))
double code(double x, double y, double z, double t) {
return y * z;
}
real(8) function code(x, y, z, t)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8), intent (in) :: z
real(8), intent (in) :: t
code = y * z
end function
public static double code(double x, double y, double z, double t) {
return y * z;
}
def code(x, y, z, t): return y * z
function code(x, y, z, t) return Float64(y * z) end
function tmp = code(x, y, z, t) tmp = y * z; end
code[x_, y_, z_, t_] := N[(y * z), $MachinePrecision]
\begin{array}{l}
\\
y \cdot z
\end{array}
Initial program 99.9%
Taylor expanded in z around inf
lower-*.f6427.8
Applied rewrites27.8%
herbie shell --seed 2024220
(FPCore (x y z t)
:name "Language.Haskell.HsColour.ColourHighlight:unbase from hscolour-1.23"
:precision binary64
(+ (* (+ (* x y) z) y) t))