
(FPCore (x y z) :precision binary64 (+ (* x y) (* z (- 1.0 y))))
double code(double x, double y, double z) {
return (x * y) + (z * (1.0 - y));
}
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) + (z * (1.0d0 - y))
end function
public static double code(double x, double y, double z) {
return (x * y) + (z * (1.0 - y));
}
def code(x, y, z): return (x * y) + (z * (1.0 - y))
function code(x, y, z) return Float64(Float64(x * y) + Float64(z * Float64(1.0 - y))) end
function tmp = code(x, y, z) tmp = (x * y) + (z * (1.0 - y)); end
code[x_, y_, z_] := N[(N[(x * y), $MachinePrecision] + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
x \cdot y + z \cdot \left(1 - y\right)
\end{array}
Sampling outcomes in binary64 precision:
Herbie found 5 alternatives:
| Alternative | Accuracy | Speedup |
|---|
(FPCore (x y z) :precision binary64 (+ (* x y) (* z (- 1.0 y))))
double code(double x, double y, double z) {
return (x * y) + (z * (1.0 - y));
}
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) + (z * (1.0d0 - y))
end function
public static double code(double x, double y, double z) {
return (x * y) + (z * (1.0 - y));
}
def code(x, y, z): return (x * y) + (z * (1.0 - y))
function code(x, y, z) return Float64(Float64(x * y) + Float64(z * Float64(1.0 - y))) end
function tmp = code(x, y, z) tmp = (x * y) + (z * (1.0 - y)); end
code[x_, y_, z_] := N[(N[(x * y), $MachinePrecision] + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
x \cdot y + z \cdot \left(1 - y\right)
\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(Float64(x - z), y, z) end
code[x_, y_, z_] := N[(N[(x - z), $MachinePrecision] * y + z), $MachinePrecision]
\begin{array}{l}
\\
\mathsf{fma}\left(x - z, y, z\right)
\end{array}
Initial program 98.4%
Taylor expanded in z around 0
+-commutativeN/A
*-commutativeN/A
*-commutativeN/A
distribute-rgt-out--N/A
*-lft-identityN/A
associate-+l-N/A
*-commutativeN/A
distribute-lft-out--N/A
unsub-negN/A
mul-1-negN/A
sub-negN/A
mul-1-negN/A
+-commutativeN/A
mul-1-negN/A
*-commutativeN/A
distribute-lft-neg-inN/A
lower-fma.f64N/A
+-commutativeN/A
distribute-neg-inN/A
mul-1-negN/A
remove-double-negN/A
unsub-negN/A
lower--.f64100.0
Applied rewrites100.0%
(FPCore (x y z) :precision binary64 (let* ((t_0 (* (- x z) y))) (if (<= y -1.45e-105) t_0 (if (<= y 2.55e-15) (* 1.0 z) t_0))))
double code(double x, double y, double z) {
double t_0 = (x - z) * y;
double tmp;
if (y <= -1.45e-105) {
tmp = t_0;
} else if (y <= 2.55e-15) {
tmp = 1.0 * 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 (y <= (-1.45d-105)) then
tmp = t_0
else if (y <= 2.55d-15) then
tmp = 1.0d0 * 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 (y <= -1.45e-105) {
tmp = t_0;
} else if (y <= 2.55e-15) {
tmp = 1.0 * z;
} else {
tmp = t_0;
}
return tmp;
}
def code(x, y, z): t_0 = (x - z) * y tmp = 0 if y <= -1.45e-105: tmp = t_0 elif y <= 2.55e-15: tmp = 1.0 * z else: tmp = t_0 return tmp
function code(x, y, z) t_0 = Float64(Float64(x - z) * y) tmp = 0.0 if (y <= -1.45e-105) tmp = t_0; elseif (y <= 2.55e-15) tmp = Float64(1.0 * 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 (y <= -1.45e-105) tmp = t_0; elseif (y <= 2.55e-15) tmp = 1.0 * z; else tmp = t_0; end tmp_2 = tmp; end
code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x - z), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -1.45e-105], t$95$0, If[LessEqual[y, 2.55e-15], N[(1.0 * z), $MachinePrecision], t$95$0]]]
\begin{array}{l}
\\
\begin{array}{l}
t_0 := \left(x - z\right) \cdot y\\
\mathbf{if}\;y \leq -1.45 \cdot 10^{-105}:\\
\;\;\;\;t\_0\\
\mathbf{elif}\;y \leq 2.55 \cdot 10^{-15}:\\
\;\;\;\;1 \cdot z\\
\mathbf{else}:\\
\;\;\;\;t\_0\\
\end{array}
\end{array}
if y < -1.45000000000000002e-105 or 2.55e-15 < y Initial program 97.3%
Taylor expanded in y around inf
*-commutativeN/A
+-commutativeN/A
remove-double-negN/A
mul-1-negN/A
mul-1-negN/A
distribute-neg-inN/A
lower-*.f64N/A
+-commutativeN/A
distribute-neg-inN/A
mul-1-negN/A
remove-double-negN/A
unsub-negN/A
lower--.f6495.1
Applied rewrites95.1%
if -1.45000000000000002e-105 < y < 2.55e-15Initial program 100.0%
Taylor expanded in z around inf
*-commutativeN/A
lower-*.f64N/A
lower--.f6478.4
Applied rewrites78.4%
Taylor expanded in y around 0
Applied rewrites78.4%
(FPCore (x y z) :precision binary64 (if (<= x -8.2e+23) (* y x) (if (<= x 1.16e+66) (* (- 1.0 y) z) (* y x))))
double code(double x, double y, double z) {
double tmp;
if (x <= -8.2e+23) {
tmp = y * x;
} else if (x <= 1.16e+66) {
tmp = (1.0 - y) * z;
} else {
tmp = y * x;
}
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 <= (-8.2d+23)) then
tmp = y * x
else if (x <= 1.16d+66) then
tmp = (1.0d0 - y) * z
else
tmp = y * x
end if
code = tmp
end function
public static double code(double x, double y, double z) {
double tmp;
if (x <= -8.2e+23) {
tmp = y * x;
} else if (x <= 1.16e+66) {
tmp = (1.0 - y) * z;
} else {
tmp = y * x;
}
return tmp;
}
def code(x, y, z): tmp = 0 if x <= -8.2e+23: tmp = y * x elif x <= 1.16e+66: tmp = (1.0 - y) * z else: tmp = y * x return tmp
function code(x, y, z) tmp = 0.0 if (x <= -8.2e+23) tmp = Float64(y * x); elseif (x <= 1.16e+66) tmp = Float64(Float64(1.0 - y) * z); else tmp = Float64(y * x); end return tmp end
function tmp_2 = code(x, y, z) tmp = 0.0; if (x <= -8.2e+23) tmp = y * x; elseif (x <= 1.16e+66) tmp = (1.0 - y) * z; else tmp = y * x; end tmp_2 = tmp; end
code[x_, y_, z_] := If[LessEqual[x, -8.2e+23], N[(y * x), $MachinePrecision], If[LessEqual[x, 1.16e+66], N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision], N[(y * x), $MachinePrecision]]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;x \leq -8.2 \cdot 10^{+23}:\\
\;\;\;\;y \cdot x\\
\mathbf{elif}\;x \leq 1.16 \cdot 10^{+66}:\\
\;\;\;\;\left(1 - y\right) \cdot z\\
\mathbf{else}:\\
\;\;\;\;y \cdot x\\
\end{array}
\end{array}
if x < -8.19999999999999992e23 or 1.16e66 < x Initial program 96.5%
Taylor expanded in z around 0
*-commutativeN/A
lower-*.f6474.8
Applied rewrites74.8%
if -8.19999999999999992e23 < x < 1.16e66Initial program 100.0%
Taylor expanded in z around inf
*-commutativeN/A
lower-*.f64N/A
lower--.f6479.8
Applied rewrites79.8%
(FPCore (x y z) :precision binary64 (if (<= y -1.45e-105) (* y x) (if (<= y 2.55e-15) (* 1.0 z) (* y x))))
double code(double x, double y, double z) {
double tmp;
if (y <= -1.45e-105) {
tmp = y * x;
} else if (y <= 2.55e-15) {
tmp = 1.0 * z;
} else {
tmp = y * x;
}
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 (y <= (-1.45d-105)) then
tmp = y * x
else if (y <= 2.55d-15) then
tmp = 1.0d0 * z
else
tmp = y * x
end if
code = tmp
end function
public static double code(double x, double y, double z) {
double tmp;
if (y <= -1.45e-105) {
tmp = y * x;
} else if (y <= 2.55e-15) {
tmp = 1.0 * z;
} else {
tmp = y * x;
}
return tmp;
}
def code(x, y, z): tmp = 0 if y <= -1.45e-105: tmp = y * x elif y <= 2.55e-15: tmp = 1.0 * z else: tmp = y * x return tmp
function code(x, y, z) tmp = 0.0 if (y <= -1.45e-105) tmp = Float64(y * x); elseif (y <= 2.55e-15) tmp = Float64(1.0 * z); else tmp = Float64(y * x); end return tmp end
function tmp_2 = code(x, y, z) tmp = 0.0; if (y <= -1.45e-105) tmp = y * x; elseif (y <= 2.55e-15) tmp = 1.0 * z; else tmp = y * x; end tmp_2 = tmp; end
code[x_, y_, z_] := If[LessEqual[y, -1.45e-105], N[(y * x), $MachinePrecision], If[LessEqual[y, 2.55e-15], N[(1.0 * z), $MachinePrecision], N[(y * x), $MachinePrecision]]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;y \leq -1.45 \cdot 10^{-105}:\\
\;\;\;\;y \cdot x\\
\mathbf{elif}\;y \leq 2.55 \cdot 10^{-15}:\\
\;\;\;\;1 \cdot z\\
\mathbf{else}:\\
\;\;\;\;y \cdot x\\
\end{array}
\end{array}
if y < -1.45000000000000002e-105 or 2.55e-15 < y Initial program 97.3%
Taylor expanded in z around 0
*-commutativeN/A
lower-*.f6461.3
Applied rewrites61.3%
if -1.45000000000000002e-105 < y < 2.55e-15Initial program 100.0%
Taylor expanded in z around inf
*-commutativeN/A
lower-*.f64N/A
lower--.f6478.4
Applied rewrites78.4%
Taylor expanded in y around 0
Applied rewrites78.4%
(FPCore (x y z) :precision binary64 (* y x))
double code(double x, double y, double z) {
return y * x;
}
real(8) function code(x, y, z)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8), intent (in) :: z
code = y * x
end function
public static double code(double x, double y, double z) {
return y * x;
}
def code(x, y, z): return y * x
function code(x, y, z) return Float64(y * x) end
function tmp = code(x, y, z) tmp = y * x; end
code[x_, y_, z_] := N[(y * x), $MachinePrecision]
\begin{array}{l}
\\
y \cdot x
\end{array}
Initial program 98.4%
Taylor expanded in z around 0
*-commutativeN/A
lower-*.f6445.5
Applied rewrites45.5%
(FPCore (x y z) :precision binary64 (- z (* (- z x) y)))
double code(double x, double y, double z) {
return z - ((z - x) * y);
}
real(8) function code(x, y, z)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8), intent (in) :: z
code = z - ((z - x) * y)
end function
public static double code(double x, double y, double z) {
return z - ((z - x) * y);
}
def code(x, y, z): return z - ((z - x) * y)
function code(x, y, z) return Float64(z - Float64(Float64(z - x) * y)) end
function tmp = code(x, y, z) tmp = z - ((z - x) * y); end
code[x_, y_, z_] := N[(z - N[(N[(z - x), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
z - \left(z - x\right) \cdot y
\end{array}
herbie shell --seed 2024235
(FPCore (x y z)
:name "Diagrams.TwoD.Segment:bezierClip from diagrams-lib-1.3.0.3"
:precision binary64
:alt
(! :herbie-platform default (- z (* (- z x) y)))
(+ (* x y) (* z (- 1.0 y))))