
(FPCore (x y z) :precision binary64 (+ (* x y) (* (- x 1.0) z)))
double code(double x, double y, double z) {
return (x * y) + ((x - 1.0) * z);
}
real(8) function code(x, y, z)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8), intent (in) :: z
code = (x * y) + ((x - 1.0d0) * z)
end function
public static double code(double x, double y, double z) {
return (x * y) + ((x - 1.0) * z);
}
def code(x, y, z): return (x * y) + ((x - 1.0) * z)
function code(x, y, z) return Float64(Float64(x * y) + Float64(Float64(x - 1.0) * z)) end
function tmp = code(x, y, z) tmp = (x * y) + ((x - 1.0) * z); end
code[x_, y_, z_] := N[(N[(x * y), $MachinePrecision] + N[(N[(x - 1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
x \cdot y + \left(x - 1\right) \cdot z
\end{array}
Sampling outcomes in binary64 precision:
Herbie found 7 alternatives:
| Alternative | Accuracy | Speedup |
|---|
(FPCore (x y z) :precision binary64 (+ (* x y) (* (- x 1.0) z)))
double code(double x, double y, double z) {
return (x * y) + ((x - 1.0) * z);
}
real(8) function code(x, y, z)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8), intent (in) :: z
code = (x * y) + ((x - 1.0d0) * z)
end function
public static double code(double x, double y, double z) {
return (x * y) + ((x - 1.0) * z);
}
def code(x, y, z): return (x * y) + ((x - 1.0) * z)
function code(x, y, z) return Float64(Float64(x * y) + Float64(Float64(x - 1.0) * z)) end
function tmp = code(x, y, z) tmp = (x * y) + ((x - 1.0) * z); end
code[x_, y_, z_] := N[(N[(x * y), $MachinePrecision] + N[(N[(x - 1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
x \cdot y + \left(x - 1\right) \cdot z
\end{array}
(FPCore (x y z) :precision binary64 (fma x (+ z y) (- z)))
double code(double x, double y, double z) {
return fma(x, (z + y), -z);
}
function code(x, y, z) return fma(x, Float64(z + y), Float64(-z)) end
code[x_, y_, z_] := N[(x * N[(z + y), $MachinePrecision] + (-z)), $MachinePrecision]
\begin{array}{l}
\\
\mathsf{fma}\left(x, z + y, -z\right)
\end{array}
Initial program 96.1%
Taylor expanded in x around 0
+-commutativeN/A
accelerator-lowering-fma.f64N/A
+-commutativeN/A
+-lowering-+.f64N/A
mul-1-negN/A
neg-lowering-neg.f64100.0
Simplified100.0%
(FPCore (x y z) :precision binary64 (if (<= x -1e+143) (* x y) (if (<= x -760.0) (* x z) (if (<= x 3.8e-29) (- z) (* x y)))))
double code(double x, double y, double z) {
double tmp;
if (x <= -1e+143) {
tmp = x * y;
} else if (x <= -760.0) {
tmp = x * z;
} else if (x <= 3.8e-29) {
tmp = -z;
} else {
tmp = x * y;
}
return tmp;
}
real(8) function code(x, y, z)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8), intent (in) :: z
real(8) :: tmp
if (x <= (-1d+143)) then
tmp = x * y
else if (x <= (-760.0d0)) then
tmp = x * z
else if (x <= 3.8d-29) then
tmp = -z
else
tmp = x * y
end if
code = tmp
end function
public static double code(double x, double y, double z) {
double tmp;
if (x <= -1e+143) {
tmp = x * y;
} else if (x <= -760.0) {
tmp = x * z;
} else if (x <= 3.8e-29) {
tmp = -z;
} else {
tmp = x * y;
}
return tmp;
}
def code(x, y, z): tmp = 0 if x <= -1e+143: tmp = x * y elif x <= -760.0: tmp = x * z elif x <= 3.8e-29: tmp = -z else: tmp = x * y return tmp
function code(x, y, z) tmp = 0.0 if (x <= -1e+143) tmp = Float64(x * y); elseif (x <= -760.0) tmp = Float64(x * z); elseif (x <= 3.8e-29) tmp = Float64(-z); else tmp = Float64(x * y); end return tmp end
function tmp_2 = code(x, y, z) tmp = 0.0; if (x <= -1e+143) tmp = x * y; elseif (x <= -760.0) tmp = x * z; elseif (x <= 3.8e-29) tmp = -z; else tmp = x * y; end tmp_2 = tmp; end
code[x_, y_, z_] := If[LessEqual[x, -1e+143], N[(x * y), $MachinePrecision], If[LessEqual[x, -760.0], N[(x * z), $MachinePrecision], If[LessEqual[x, 3.8e-29], (-z), N[(x * y), $MachinePrecision]]]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;x \leq -1 \cdot 10^{+143}:\\
\;\;\;\;x \cdot y\\
\mathbf{elif}\;x \leq -760:\\
\;\;\;\;x \cdot z\\
\mathbf{elif}\;x \leq 3.8 \cdot 10^{-29}:\\
\;\;\;\;-z\\
\mathbf{else}:\\
\;\;\;\;x \cdot y\\
\end{array}
\end{array}
if x < -1e143 or 3.79999999999999976e-29 < x Initial program 91.4%
Taylor expanded in y around inf
*-lowering-*.f6463.5
Simplified63.5%
if -1e143 < x < -760Initial program 99.9%
Taylor expanded in x around inf
*-lowering-*.f64N/A
+-commutativeN/A
+-lowering-+.f6496.3
Simplified96.3%
Taylor expanded in z around inf
*-commutativeN/A
*-lowering-*.f6473.6
Simplified73.6%
if -760 < x < 3.79999999999999976e-29Initial program 100.0%
Taylor expanded in x around 0
mul-1-negN/A
neg-lowering-neg.f6482.1
Simplified82.1%
Final simplification73.1%
(FPCore (x y z) :precision binary64 (let* ((t_0 (* x (+ z y)))) (if (<= x -760.0) t_0 (if (<= x 1.0) (fma x y (- z)) t_0))))
double code(double x, double y, double z) {
double t_0 = x * (z + y);
double tmp;
if (x <= -760.0) {
tmp = t_0;
} else if (x <= 1.0) {
tmp = fma(x, y, -z);
} else {
tmp = t_0;
}
return tmp;
}
function code(x, y, z) t_0 = Float64(x * Float64(z + y)) tmp = 0.0 if (x <= -760.0) tmp = t_0; elseif (x <= 1.0) tmp = fma(x, y, Float64(-z)); else tmp = t_0; end return tmp end
code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(z + y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -760.0], t$95$0, If[LessEqual[x, 1.0], N[(x * y + (-z)), $MachinePrecision], t$95$0]]]
\begin{array}{l}
\\
\begin{array}{l}
t_0 := x \cdot \left(z + y\right)\\
\mathbf{if}\;x \leq -760:\\
\;\;\;\;t\_0\\
\mathbf{elif}\;x \leq 1:\\
\;\;\;\;\mathsf{fma}\left(x, y, -z\right)\\
\mathbf{else}:\\
\;\;\;\;t\_0\\
\end{array}
\end{array}
if x < -760 or 1 < x Initial program 92.2%
Taylor expanded in x around inf
*-lowering-*.f64N/A
+-commutativeN/A
+-lowering-+.f6499.5
Simplified99.5%
if -760 < x < 1Initial program 100.0%
Taylor expanded in x around 0
+-commutativeN/A
accelerator-lowering-fma.f64N/A
+-commutativeN/A
+-lowering-+.f64N/A
mul-1-negN/A
neg-lowering-neg.f64100.0
Simplified100.0%
Taylor expanded in z around 0
Simplified98.6%
(FPCore (x y z) :precision binary64 (let* ((t_0 (* x (+ z y)))) (if (<= x -9e-15) t_0 (if (<= x 1.6e-29) (- z) t_0))))
double code(double x, double y, double z) {
double t_0 = x * (z + y);
double tmp;
if (x <= -9e-15) {
tmp = t_0;
} else if (x <= 1.6e-29) {
tmp = -z;
} else {
tmp = t_0;
}
return tmp;
}
real(8) function code(x, y, z)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8), intent (in) :: z
real(8) :: t_0
real(8) :: tmp
t_0 = x * (z + y)
if (x <= (-9d-15)) then
tmp = t_0
else if (x <= 1.6d-29) then
tmp = -z
else
tmp = t_0
end if
code = tmp
end function
public static double code(double x, double y, double z) {
double t_0 = x * (z + y);
double tmp;
if (x <= -9e-15) {
tmp = t_0;
} else if (x <= 1.6e-29) {
tmp = -z;
} else {
tmp = t_0;
}
return tmp;
}
def code(x, y, z): t_0 = x * (z + y) tmp = 0 if x <= -9e-15: tmp = t_0 elif x <= 1.6e-29: tmp = -z else: tmp = t_0 return tmp
function code(x, y, z) t_0 = Float64(x * Float64(z + y)) tmp = 0.0 if (x <= -9e-15) tmp = t_0; elseif (x <= 1.6e-29) tmp = Float64(-z); else tmp = t_0; end return tmp end
function tmp_2 = code(x, y, z) t_0 = x * (z + y); tmp = 0.0; if (x <= -9e-15) tmp = t_0; elseif (x <= 1.6e-29) tmp = -z; else tmp = t_0; end tmp_2 = tmp; end
code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(z + y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -9e-15], t$95$0, If[LessEqual[x, 1.6e-29], (-z), t$95$0]]]
\begin{array}{l}
\\
\begin{array}{l}
t_0 := x \cdot \left(z + y\right)\\
\mathbf{if}\;x \leq -9 \cdot 10^{-15}:\\
\;\;\;\;t\_0\\
\mathbf{elif}\;x \leq 1.6 \cdot 10^{-29}:\\
\;\;\;\;-z\\
\mathbf{else}:\\
\;\;\;\;t\_0\\
\end{array}
\end{array}
if x < -8.9999999999999995e-15 or 1.6e-29 < x Initial program 92.8%
Taylor expanded in x around inf
*-lowering-*.f64N/A
+-commutativeN/A
+-lowering-+.f6497.5
Simplified97.5%
if -8.9999999999999995e-15 < x < 1.6e-29Initial program 100.0%
Taylor expanded in x around 0
mul-1-negN/A
neg-lowering-neg.f6485.3
Simplified85.3%
(FPCore (x y z) :precision binary64 (if (<= x -1.45e-16) (* x y) (if (<= x 1.65e-34) (- z) (* x y))))
double code(double x, double y, double z) {
double tmp;
if (x <= -1.45e-16) {
tmp = x * y;
} else if (x <= 1.65e-34) {
tmp = -z;
} else {
tmp = x * y;
}
return tmp;
}
real(8) function code(x, y, z)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8), intent (in) :: z
real(8) :: tmp
if (x <= (-1.45d-16)) then
tmp = x * y
else if (x <= 1.65d-34) then
tmp = -z
else
tmp = x * y
end if
code = tmp
end function
public static double code(double x, double y, double z) {
double tmp;
if (x <= -1.45e-16) {
tmp = x * y;
} else if (x <= 1.65e-34) {
tmp = -z;
} else {
tmp = x * y;
}
return tmp;
}
def code(x, y, z): tmp = 0 if x <= -1.45e-16: tmp = x * y elif x <= 1.65e-34: tmp = -z else: tmp = x * y return tmp
function code(x, y, z) tmp = 0.0 if (x <= -1.45e-16) tmp = Float64(x * y); elseif (x <= 1.65e-34) tmp = Float64(-z); else tmp = Float64(x * y); end return tmp end
function tmp_2 = code(x, y, z) tmp = 0.0; if (x <= -1.45e-16) tmp = x * y; elseif (x <= 1.65e-34) tmp = -z; else tmp = x * y; end tmp_2 = tmp; end
code[x_, y_, z_] := If[LessEqual[x, -1.45e-16], N[(x * y), $MachinePrecision], If[LessEqual[x, 1.65e-34], (-z), N[(x * y), $MachinePrecision]]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;x \leq -1.45 \cdot 10^{-16}:\\
\;\;\;\;x \cdot y\\
\mathbf{elif}\;x \leq 1.65 \cdot 10^{-34}:\\
\;\;\;\;-z\\
\mathbf{else}:\\
\;\;\;\;x \cdot y\\
\end{array}
\end{array}
if x < -1.4499999999999999e-16 or 1.64999999999999991e-34 < x Initial program 92.8%
Taylor expanded in y around inf
*-lowering-*.f6459.2
Simplified59.2%
if -1.4499999999999999e-16 < x < 1.64999999999999991e-34Initial program 100.0%
Taylor expanded in x around 0
mul-1-negN/A
neg-lowering-neg.f6485.3
Simplified85.3%
(FPCore (x y z) :precision binary64 (- z))
double code(double x, double y, double z) {
return -z;
}
real(8) function code(x, y, z)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8), intent (in) :: z
code = -z
end function
public static double code(double x, double y, double z) {
return -z;
}
def code(x, y, z): return -z
function code(x, y, z) return Float64(-z) end
function tmp = code(x, y, z) tmp = -z; end
code[x_, y_, z_] := (-z)
\begin{array}{l}
\\
-z
\end{array}
Initial program 96.1%
Taylor expanded in x around 0
mul-1-negN/A
neg-lowering-neg.f6441.0
Simplified41.0%
(FPCore (x y z) :precision binary64 z)
double code(double x, double y, double z) {
return z;
}
real(8) function code(x, y, z)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8), intent (in) :: z
code = z
end function
public static double code(double x, double y, double z) {
return z;
}
def code(x, y, z): return z
function code(x, y, z) return z end
function tmp = code(x, y, z) tmp = z; end
code[x_, y_, z_] := z
\begin{array}{l}
\\
z
\end{array}
Initial program 96.1%
Taylor expanded in x around 0
mul-1-negN/A
neg-lowering-neg.f6441.0
Simplified41.0%
neg-sub0N/A
flip--N/A
Applied egg-rr2.3%
herbie shell --seed 2024199
(FPCore (x y z)
:name "Graphics.Rendering.Chart.Drawing:drawTextsR from Chart-1.5.3"
:precision binary64
(+ (* x y) (* (- x 1.0) z)))