
(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 6 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 (- (* x (+ y z)) z))
double code(double x, double y, double z) {
return (x * (y + z)) - 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 + z)) - z
end function
public static double code(double x, double y, double z) {
return (x * (y + z)) - z;
}
def code(x, y, z): return (x * (y + z)) - z
function code(x, y, z) return Float64(Float64(x * Float64(y + z)) - z) end
function tmp = code(x, y, z) tmp = (x * (y + z)) - z; end
code[x_, y_, z_] := N[(N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]
\begin{array}{l}
\\
x \cdot \left(y + z\right) - z
\end{array}
Initial program 98.4%
*-commutative98.4%
sub-neg98.4%
distribute-rgt-in98.4%
metadata-eval98.4%
neg-mul-198.4%
associate-+r+98.4%
unsub-neg98.4%
distribute-lft-out100.0%
Simplified100.0%
(FPCore (x y z)
:precision binary64
(if (<= x -6.8e+77)
(* x z)
(if (<= x -5.1e-30)
(* x y)
(if (<= x 1.75e-58) (- z) (if (<= x 9.2e+117) (* x y) (* x z))))))
double code(double x, double y, double z) {
double tmp;
if (x <= -6.8e+77) {
tmp = x * z;
} else if (x <= -5.1e-30) {
tmp = x * y;
} else if (x <= 1.75e-58) {
tmp = -z;
} else if (x <= 9.2e+117) {
tmp = x * y;
} else {
tmp = x * z;
}
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 <= (-6.8d+77)) then
tmp = x * z
else if (x <= (-5.1d-30)) then
tmp = x * y
else if (x <= 1.75d-58) then
tmp = -z
else if (x <= 9.2d+117) then
tmp = x * y
else
tmp = x * z
end if
code = tmp
end function
public static double code(double x, double y, double z) {
double tmp;
if (x <= -6.8e+77) {
tmp = x * z;
} else if (x <= -5.1e-30) {
tmp = x * y;
} else if (x <= 1.75e-58) {
tmp = -z;
} else if (x <= 9.2e+117) {
tmp = x * y;
} else {
tmp = x * z;
}
return tmp;
}
def code(x, y, z): tmp = 0 if x <= -6.8e+77: tmp = x * z elif x <= -5.1e-30: tmp = x * y elif x <= 1.75e-58: tmp = -z elif x <= 9.2e+117: tmp = x * y else: tmp = x * z return tmp
function code(x, y, z) tmp = 0.0 if (x <= -6.8e+77) tmp = Float64(x * z); elseif (x <= -5.1e-30) tmp = Float64(x * y); elseif (x <= 1.75e-58) tmp = Float64(-z); elseif (x <= 9.2e+117) tmp = Float64(x * y); else tmp = Float64(x * z); end return tmp end
function tmp_2 = code(x, y, z) tmp = 0.0; if (x <= -6.8e+77) tmp = x * z; elseif (x <= -5.1e-30) tmp = x * y; elseif (x <= 1.75e-58) tmp = -z; elseif (x <= 9.2e+117) tmp = x * y; else tmp = x * z; end tmp_2 = tmp; end
code[x_, y_, z_] := If[LessEqual[x, -6.8e+77], N[(x * z), $MachinePrecision], If[LessEqual[x, -5.1e-30], N[(x * y), $MachinePrecision], If[LessEqual[x, 1.75e-58], (-z), If[LessEqual[x, 9.2e+117], N[(x * y), $MachinePrecision], N[(x * z), $MachinePrecision]]]]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;x \leq -6.8 \cdot 10^{+77}:\\
\;\;\;\;x \cdot z\\
\mathbf{elif}\;x \leq -5.1 \cdot 10^{-30}:\\
\;\;\;\;x \cdot y\\
\mathbf{elif}\;x \leq 1.75 \cdot 10^{-58}:\\
\;\;\;\;-z\\
\mathbf{elif}\;x \leq 9.2 \cdot 10^{+117}:\\
\;\;\;\;x \cdot y\\
\mathbf{else}:\\
\;\;\;\;x \cdot z\\
\end{array}
\end{array}
if x < -6.79999999999999993e77 or 9.19999999999999951e117 < x Initial program 95.3%
Taylor expanded in x around inf 100.0%
+-commutative100.0%
Simplified100.0%
Taylor expanded in z around inf 65.6%
*-commutative65.6%
Simplified65.6%
if -6.79999999999999993e77 < x < -5.09999999999999972e-30 or 1.75e-58 < x < 9.19999999999999951e117Initial program 100.0%
Taylor expanded in y around inf 69.7%
if -5.09999999999999972e-30 < x < 1.75e-58Initial program 100.0%
Taylor expanded in x around 0 78.7%
neg-mul-178.7%
Simplified78.7%
Final simplification72.3%
(FPCore (x y z) :precision binary64 (if (or (<= x -8.6e+23) (not (<= x 1.0))) (* x (+ y z)) (- (* x y) z)))
double code(double x, double y, double z) {
double tmp;
if ((x <= -8.6e+23) || !(x <= 1.0)) {
tmp = x * (y + z);
} else {
tmp = (x * y) - z;
}
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 <= (-8.6d+23)) .or. (.not. (x <= 1.0d0))) then
tmp = x * (y + z)
else
tmp = (x * y) - z
end if
code = tmp
end function
public static double code(double x, double y, double z) {
double tmp;
if ((x <= -8.6e+23) || !(x <= 1.0)) {
tmp = x * (y + z);
} else {
tmp = (x * y) - z;
}
return tmp;
}
def code(x, y, z): tmp = 0 if (x <= -8.6e+23) or not (x <= 1.0): tmp = x * (y + z) else: tmp = (x * y) - z return tmp
function code(x, y, z) tmp = 0.0 if ((x <= -8.6e+23) || !(x <= 1.0)) tmp = Float64(x * Float64(y + z)); else tmp = Float64(Float64(x * y) - z); end return tmp end
function tmp_2 = code(x, y, z) tmp = 0.0; if ((x <= -8.6e+23) || ~((x <= 1.0))) tmp = x * (y + z); else tmp = (x * y) - z; end tmp_2 = tmp; end
code[x_, y_, z_] := If[Or[LessEqual[x, -8.6e+23], N[Not[LessEqual[x, 1.0]], $MachinePrecision]], N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] - z), $MachinePrecision]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;x \leq -8.6 \cdot 10^{+23} \lor \neg \left(x \leq 1\right):\\
\;\;\;\;x \cdot \left(y + z\right)\\
\mathbf{else}:\\
\;\;\;\;x \cdot y - z\\
\end{array}
\end{array}
if x < -8.5999999999999997e23 or 1 < x Initial program 96.7%
Taylor expanded in x around inf 99.3%
+-commutative99.3%
Simplified99.3%
if -8.5999999999999997e23 < x < 1Initial program 100.0%
*-commutative100.0%
sub-neg100.0%
distribute-rgt-in100.0%
metadata-eval100.0%
neg-mul-1100.0%
associate-+r+100.0%
unsub-neg100.0%
distribute-lft-out100.0%
Simplified100.0%
Taylor expanded in y around inf 99.7%
Final simplification99.5%
(FPCore (x y z) :precision binary64 (if (or (<= x -7.8e-31) (not (<= x 1.75e-58))) (* x (+ y z)) (- z)))
double code(double x, double y, double z) {
double tmp;
if ((x <= -7.8e-31) || !(x <= 1.75e-58)) {
tmp = x * (y + z);
} else {
tmp = -z;
}
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 <= (-7.8d-31)) .or. (.not. (x <= 1.75d-58))) then
tmp = x * (y + z)
else
tmp = -z
end if
code = tmp
end function
public static double code(double x, double y, double z) {
double tmp;
if ((x <= -7.8e-31) || !(x <= 1.75e-58)) {
tmp = x * (y + z);
} else {
tmp = -z;
}
return tmp;
}
def code(x, y, z): tmp = 0 if (x <= -7.8e-31) or not (x <= 1.75e-58): tmp = x * (y + z) else: tmp = -z return tmp
function code(x, y, z) tmp = 0.0 if ((x <= -7.8e-31) || !(x <= 1.75e-58)) tmp = Float64(x * Float64(y + z)); else tmp = Float64(-z); end return tmp end
function tmp_2 = code(x, y, z) tmp = 0.0; if ((x <= -7.8e-31) || ~((x <= 1.75e-58))) tmp = x * (y + z); else tmp = -z; end tmp_2 = tmp; end
code[x_, y_, z_] := If[Or[LessEqual[x, -7.8e-31], N[Not[LessEqual[x, 1.75e-58]], $MachinePrecision]], N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision], (-z)]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;x \leq -7.8 \cdot 10^{-31} \lor \neg \left(x \leq 1.75 \cdot 10^{-58}\right):\\
\;\;\;\;x \cdot \left(y + z\right)\\
\mathbf{else}:\\
\;\;\;\;-z\\
\end{array}
\end{array}
if x < -7.8000000000000003e-31 or 1.75e-58 < x Initial program 97.2%
Taylor expanded in x around inf 96.0%
+-commutative96.0%
Simplified96.0%
if -7.8000000000000003e-31 < x < 1.75e-58Initial program 100.0%
Taylor expanded in x around 0 78.7%
neg-mul-178.7%
Simplified78.7%
Final simplification88.3%
(FPCore (x y z) :precision binary64 (if (or (<= x -5.4e-30) (not (<= x 1.75e-58))) (* x y) (- z)))
double code(double x, double y, double z) {
double tmp;
if ((x <= -5.4e-30) || !(x <= 1.75e-58)) {
tmp = x * y;
} else {
tmp = -z;
}
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 <= (-5.4d-30)) .or. (.not. (x <= 1.75d-58))) then
tmp = x * y
else
tmp = -z
end if
code = tmp
end function
public static double code(double x, double y, double z) {
double tmp;
if ((x <= -5.4e-30) || !(x <= 1.75e-58)) {
tmp = x * y;
} else {
tmp = -z;
}
return tmp;
}
def code(x, y, z): tmp = 0 if (x <= -5.4e-30) or not (x <= 1.75e-58): tmp = x * y else: tmp = -z return tmp
function code(x, y, z) tmp = 0.0 if ((x <= -5.4e-30) || !(x <= 1.75e-58)) tmp = Float64(x * y); else tmp = Float64(-z); end return tmp end
function tmp_2 = code(x, y, z) tmp = 0.0; if ((x <= -5.4e-30) || ~((x <= 1.75e-58))) tmp = x * y; else tmp = -z; end tmp_2 = tmp; end
code[x_, y_, z_] := If[Or[LessEqual[x, -5.4e-30], N[Not[LessEqual[x, 1.75e-58]], $MachinePrecision]], N[(x * y), $MachinePrecision], (-z)]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;x \leq -5.4 \cdot 10^{-30} \lor \neg \left(x \leq 1.75 \cdot 10^{-58}\right):\\
\;\;\;\;x \cdot y\\
\mathbf{else}:\\
\;\;\;\;-z\\
\end{array}
\end{array}
if x < -5.39999999999999975e-30 or 1.75e-58 < x Initial program 97.2%
Taylor expanded in y around inf 52.8%
if -5.39999999999999975e-30 < x < 1.75e-58Initial program 100.0%
Taylor expanded in x around 0 78.7%
neg-mul-178.7%
Simplified78.7%
Final simplification64.2%
(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 98.4%
Taylor expanded in x around 0 38.0%
neg-mul-138.0%
Simplified38.0%
herbie shell --seed 2024185
(FPCore (x y z)
:name "Graphics.Rendering.Chart.Drawing:drawTextsR from Chart-1.5.3"
:precision binary64
(+ (* x y) (* (- x 1.0) z)))