
(FPCore (x y z t) :precision binary64 (+ (- (- (* x (log y)) y) z) (log t)))
double code(double x, double y, double z, double t) {
return (((x * log(y)) - y) - z) + log(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 * log(y)) - y) - z) + log(t)
end function
public static double code(double x, double y, double z, double t) {
return (((x * Math.log(y)) - y) - z) + Math.log(t);
}
def code(x, y, z, t): return (((x * math.log(y)) - y) - z) + math.log(t)
function code(x, y, z, t) return Float64(Float64(Float64(Float64(x * log(y)) - y) - z) + log(t)) end
function tmp = code(x, y, z, t) tmp = (((x * log(y)) - y) - z) + log(t); end
code[x_, y_, z_, t_] := N[(N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision] - z), $MachinePrecision] + N[Log[t], $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
\left(\left(x \cdot \log y - y\right) - z\right) + \log t
\end{array}
Sampling outcomes in binary64 precision:
Herbie found 11 alternatives:
| Alternative | Accuracy | Speedup |
|---|
(FPCore (x y z t) :precision binary64 (+ (- (- (* x (log y)) y) z) (log t)))
double code(double x, double y, double z, double t) {
return (((x * log(y)) - y) - z) + log(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 * log(y)) - y) - z) + log(t)
end function
public static double code(double x, double y, double z, double t) {
return (((x * Math.log(y)) - y) - z) + Math.log(t);
}
def code(x, y, z, t): return (((x * math.log(y)) - y) - z) + math.log(t)
function code(x, y, z, t) return Float64(Float64(Float64(Float64(x * log(y)) - y) - z) + log(t)) end
function tmp = code(x, y, z, t) tmp = (((x * log(y)) - y) - z) + log(t); end
code[x_, y_, z_, t_] := N[(N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision] - z), $MachinePrecision] + N[Log[t], $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
\left(\left(x \cdot \log y - y\right) - z\right) + \log t
\end{array}
(FPCore (x y z t) :precision binary64 (+ (- (- (* x (log y)) y) z) (log t)))
double code(double x, double y, double z, double t) {
return (((x * log(y)) - y) - z) + log(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 * log(y)) - y) - z) + log(t)
end function
public static double code(double x, double y, double z, double t) {
return (((x * Math.log(y)) - y) - z) + Math.log(t);
}
def code(x, y, z, t): return (((x * math.log(y)) - y) - z) + math.log(t)
function code(x, y, z, t) return Float64(Float64(Float64(Float64(x * log(y)) - y) - z) + log(t)) end
function tmp = code(x, y, z, t) tmp = (((x * log(y)) - y) - z) + log(t); end
code[x_, y_, z_, t_] := N[(N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision] - z), $MachinePrecision] + N[Log[t], $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
\left(\left(x \cdot \log y - y\right) - z\right) + \log t
\end{array}
(FPCore (x y z t)
:precision binary64
(let* ((t_1 (- (* x (log y)) y)))
(if (or (<= t_1 -40000.0) (not (<= t_1 1e-45)))
(- t_1 z)
(- (log (/ t (exp y))) z))))
double code(double x, double y, double z, double t) {
double t_1 = (x * log(y)) - y;
double tmp;
if ((t_1 <= -40000.0) || !(t_1 <= 1e-45)) {
tmp = t_1 - z;
} else {
tmp = log((t / exp(y))) - z;
}
return tmp;
}
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
real(8) :: t_1
real(8) :: tmp
t_1 = (x * log(y)) - y
if ((t_1 <= (-40000.0d0)) .or. (.not. (t_1 <= 1d-45))) then
tmp = t_1 - z
else
tmp = log((t / exp(y))) - z
end if
code = tmp
end function
public static double code(double x, double y, double z, double t) {
double t_1 = (x * Math.log(y)) - y;
double tmp;
if ((t_1 <= -40000.0) || !(t_1 <= 1e-45)) {
tmp = t_1 - z;
} else {
tmp = Math.log((t / Math.exp(y))) - z;
}
return tmp;
}
def code(x, y, z, t): t_1 = (x * math.log(y)) - y tmp = 0 if (t_1 <= -40000.0) or not (t_1 <= 1e-45): tmp = t_1 - z else: tmp = math.log((t / math.exp(y))) - z return tmp
function code(x, y, z, t) t_1 = Float64(Float64(x * log(y)) - y) tmp = 0.0 if ((t_1 <= -40000.0) || !(t_1 <= 1e-45)) tmp = Float64(t_1 - z); else tmp = Float64(log(Float64(t / exp(y))) - z); end return tmp end
function tmp_2 = code(x, y, z, t) t_1 = (x * log(y)) - y; tmp = 0.0; if ((t_1 <= -40000.0) || ~((t_1 <= 1e-45))) tmp = t_1 - z; else tmp = log((t / exp(y))) - z; end tmp_2 = tmp; end
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -40000.0], N[Not[LessEqual[t$95$1, 1e-45]], $MachinePrecision]], N[(t$95$1 - z), $MachinePrecision], N[(N[Log[N[(t / N[Exp[y], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - z), $MachinePrecision]]]
\begin{array}{l}
\\
\begin{array}{l}
t_1 := x \cdot \log y - y\\
\mathbf{if}\;t_1 \leq -40000 \lor \neg \left(t_1 \leq 10^{-45}\right):\\
\;\;\;\;t_1 - z\\
\mathbf{else}:\\
\;\;\;\;\log \left(\frac{t}{e^{y}}\right) - z\\
\end{array}
\end{array}
(FPCore (x y z t)
:precision binary64
(let* ((t_1 (- (* x (log y)) y)))
(if (or (<= t_1 -40000.0) (not (<= t_1 1e-45)))
(- t_1 z)
(- (log t) (+ y z)))))
double code(double x, double y, double z, double t) {
double t_1 = (x * log(y)) - y;
double tmp;
if ((t_1 <= -40000.0) || !(t_1 <= 1e-45)) {
tmp = t_1 - z;
} else {
tmp = log(t) - (y + z);
}
return tmp;
}
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
real(8) :: t_1
real(8) :: tmp
t_1 = (x * log(y)) - y
if ((t_1 <= (-40000.0d0)) .or. (.not. (t_1 <= 1d-45))) then
tmp = t_1 - z
else
tmp = log(t) - (y + z)
end if
code = tmp
end function
public static double code(double x, double y, double z, double t) {
double t_1 = (x * Math.log(y)) - y;
double tmp;
if ((t_1 <= -40000.0) || !(t_1 <= 1e-45)) {
tmp = t_1 - z;
} else {
tmp = Math.log(t) - (y + z);
}
return tmp;
}
def code(x, y, z, t): t_1 = (x * math.log(y)) - y tmp = 0 if (t_1 <= -40000.0) or not (t_1 <= 1e-45): tmp = t_1 - z else: tmp = math.log(t) - (y + z) return tmp
function code(x, y, z, t) t_1 = Float64(Float64(x * log(y)) - y) tmp = 0.0 if ((t_1 <= -40000.0) || !(t_1 <= 1e-45)) tmp = Float64(t_1 - z); else tmp = Float64(log(t) - Float64(y + z)); end return tmp end
function tmp_2 = code(x, y, z, t) t_1 = (x * log(y)) - y; tmp = 0.0; if ((t_1 <= -40000.0) || ~((t_1 <= 1e-45))) tmp = t_1 - z; else tmp = log(t) - (y + z); end tmp_2 = tmp; end
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -40000.0], N[Not[LessEqual[t$95$1, 1e-45]], $MachinePrecision]], N[(t$95$1 - z), $MachinePrecision], N[(N[Log[t], $MachinePrecision] - N[(y + z), $MachinePrecision]), $MachinePrecision]]]
\begin{array}{l}
\\
\begin{array}{l}
t_1 := x \cdot \log y - y\\
\mathbf{if}\;t_1 \leq -40000 \lor \neg \left(t_1 \leq 10^{-45}\right):\\
\;\;\;\;t_1 - z\\
\mathbf{else}:\\
\;\;\;\;\log t - \left(y + z\right)\\
\end{array}
\end{array}
(FPCore (x y z t) :precision binary64 (let* ((t_1 (* x (log y)))) (if (<= y 155.0) (- (+ t_1 (log t)) z) (- (- t_1 y) z))))
double code(double x, double y, double z, double t) {
double t_1 = x * log(y);
double tmp;
if (y <= 155.0) {
tmp = (t_1 + log(t)) - z;
} else {
tmp = (t_1 - y) - z;
}
return tmp;
}
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
real(8) :: t_1
real(8) :: tmp
t_1 = x * log(y)
if (y <= 155.0d0) then
tmp = (t_1 + log(t)) - z
else
tmp = (t_1 - y) - z
end if
code = tmp
end function
public static double code(double x, double y, double z, double t) {
double t_1 = x * Math.log(y);
double tmp;
if (y <= 155.0) {
tmp = (t_1 + Math.log(t)) - z;
} else {
tmp = (t_1 - y) - z;
}
return tmp;
}
def code(x, y, z, t): t_1 = x * math.log(y) tmp = 0 if y <= 155.0: tmp = (t_1 + math.log(t)) - z else: tmp = (t_1 - y) - z return tmp
function code(x, y, z, t) t_1 = Float64(x * log(y)) tmp = 0.0 if (y <= 155.0) tmp = Float64(Float64(t_1 + log(t)) - z); else tmp = Float64(Float64(t_1 - y) - z); end return tmp end
function tmp_2 = code(x, y, z, t) t_1 = x * log(y); tmp = 0.0; if (y <= 155.0) tmp = (t_1 + log(t)) - z; else tmp = (t_1 - y) - z; end tmp_2 = tmp; end
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, 155.0], N[(N[(t$95$1 + N[Log[t], $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision], N[(N[(t$95$1 - y), $MachinePrecision] - z), $MachinePrecision]]]
\begin{array}{l}
\\
\begin{array}{l}
t_1 := x \cdot \log y\\
\mathbf{if}\;y \leq 155:\\
\;\;\;\;\left(t_1 + \log t\right) - z\\
\mathbf{else}:\\
\;\;\;\;\left(t_1 - y\right) - z\\
\end{array}
\end{array}
(FPCore (x y z t) :precision binary64 (if (or (<= x -6500.0) (not (<= x 4.6e+124))) (- (* x (log y)) y) (- (log t) (+ y z))))
double code(double x, double y, double z, double t) {
double tmp;
if ((x <= -6500.0) || !(x <= 4.6e+124)) {
tmp = (x * log(y)) - y;
} else {
tmp = log(t) - (y + z);
}
return tmp;
}
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
real(8) :: tmp
if ((x <= (-6500.0d0)) .or. (.not. (x <= 4.6d+124))) then
tmp = (x * log(y)) - y
else
tmp = log(t) - (y + z)
end if
code = tmp
end function
public static double code(double x, double y, double z, double t) {
double tmp;
if ((x <= -6500.0) || !(x <= 4.6e+124)) {
tmp = (x * Math.log(y)) - y;
} else {
tmp = Math.log(t) - (y + z);
}
return tmp;
}
def code(x, y, z, t): tmp = 0 if (x <= -6500.0) or not (x <= 4.6e+124): tmp = (x * math.log(y)) - y else: tmp = math.log(t) - (y + z) return tmp
function code(x, y, z, t) tmp = 0.0 if ((x <= -6500.0) || !(x <= 4.6e+124)) tmp = Float64(Float64(x * log(y)) - y); else tmp = Float64(log(t) - Float64(y + z)); end return tmp end
function tmp_2 = code(x, y, z, t) tmp = 0.0; if ((x <= -6500.0) || ~((x <= 4.6e+124))) tmp = (x * log(y)) - y; else tmp = log(t) - (y + z); end tmp_2 = tmp; end
code[x_, y_, z_, t_] := If[Or[LessEqual[x, -6500.0], N[Not[LessEqual[x, 4.6e+124]], $MachinePrecision]], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision], N[(N[Log[t], $MachinePrecision] - N[(y + z), $MachinePrecision]), $MachinePrecision]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;x \leq -6500 \lor \neg \left(x \leq 4.6 \cdot 10^{+124}\right):\\
\;\;\;\;x \cdot \log y - y\\
\mathbf{else}:\\
\;\;\;\;\log t - \left(y + z\right)\\
\end{array}
\end{array}
(FPCore (x y z t) :precision binary64 (if (or (<= x -2.1e+34) (not (<= x 6.4e+125))) (- (* x (log y)) z) (- (log t) (+ y z))))
double code(double x, double y, double z, double t) {
double tmp;
if ((x <= -2.1e+34) || !(x <= 6.4e+125)) {
tmp = (x * log(y)) - z;
} else {
tmp = log(t) - (y + z);
}
return tmp;
}
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
real(8) :: tmp
if ((x <= (-2.1d+34)) .or. (.not. (x <= 6.4d+125))) then
tmp = (x * log(y)) - z
else
tmp = log(t) - (y + z)
end if
code = tmp
end function
public static double code(double x, double y, double z, double t) {
double tmp;
if ((x <= -2.1e+34) || !(x <= 6.4e+125)) {
tmp = (x * Math.log(y)) - z;
} else {
tmp = Math.log(t) - (y + z);
}
return tmp;
}
def code(x, y, z, t): tmp = 0 if (x <= -2.1e+34) or not (x <= 6.4e+125): tmp = (x * math.log(y)) - z else: tmp = math.log(t) - (y + z) return tmp
function code(x, y, z, t) tmp = 0.0 if ((x <= -2.1e+34) || !(x <= 6.4e+125)) tmp = Float64(Float64(x * log(y)) - z); else tmp = Float64(log(t) - Float64(y + z)); end return tmp end
function tmp_2 = code(x, y, z, t) tmp = 0.0; if ((x <= -2.1e+34) || ~((x <= 6.4e+125))) tmp = (x * log(y)) - z; else tmp = log(t) - (y + z); end tmp_2 = tmp; end
code[x_, y_, z_, t_] := If[Or[LessEqual[x, -2.1e+34], N[Not[LessEqual[x, 6.4e+125]], $MachinePrecision]], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision], N[(N[Log[t], $MachinePrecision] - N[(y + z), $MachinePrecision]), $MachinePrecision]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;x \leq -2.1 \cdot 10^{+34} \lor \neg \left(x \leq 6.4 \cdot 10^{+125}\right):\\
\;\;\;\;x \cdot \log y - z\\
\mathbf{else}:\\
\;\;\;\;\log t - \left(y + z\right)\\
\end{array}
\end{array}
(FPCore (x y z t) :precision binary64 (if (<= y 155.0) (- (log t) z) (- (- y) z)))
double code(double x, double y, double z, double t) {
double tmp;
if (y <= 155.0) {
tmp = log(t) - z;
} else {
tmp = -y - z;
}
return tmp;
}
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
real(8) :: tmp
if (y <= 155.0d0) then
tmp = log(t) - z
else
tmp = -y - z
end if
code = tmp
end function
public static double code(double x, double y, double z, double t) {
double tmp;
if (y <= 155.0) {
tmp = Math.log(t) - z;
} else {
tmp = -y - z;
}
return tmp;
}
def code(x, y, z, t): tmp = 0 if y <= 155.0: tmp = math.log(t) - z else: tmp = -y - z return tmp
function code(x, y, z, t) tmp = 0.0 if (y <= 155.0) tmp = Float64(log(t) - z); else tmp = Float64(Float64(-y) - z); end return tmp end
function tmp_2 = code(x, y, z, t) tmp = 0.0; if (y <= 155.0) tmp = log(t) - z; else tmp = -y - z; end tmp_2 = tmp; end
code[x_, y_, z_, t_] := If[LessEqual[y, 155.0], N[(N[Log[t], $MachinePrecision] - z), $MachinePrecision], N[((-y) - z), $MachinePrecision]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;y \leq 155:\\
\;\;\;\;\log t - z\\
\mathbf{else}:\\
\;\;\;\;\left(-y\right) - z\\
\end{array}
\end{array}
(FPCore (x y z t) :precision binary64 (- (log t) (+ y z)))
double code(double x, double y, double z, double t) {
return log(t) - (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 = log(t) - (y + z)
end function
public static double code(double x, double y, double z, double t) {
return Math.log(t) - (y + z);
}
def code(x, y, z, t): return math.log(t) - (y + z)
function code(x, y, z, t) return Float64(log(t) - Float64(y + z)) end
function tmp = code(x, y, z, t) tmp = log(t) - (y + z); end
code[x_, y_, z_, t_] := N[(N[Log[t], $MachinePrecision] - N[(y + z), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
\log t - \left(y + z\right)
\end{array}
(FPCore (x y z t) :precision binary64 (if (<= y 4e+72) (- z) (- y)))
double code(double x, double y, double z, double t) {
double tmp;
if (y <= 4e+72) {
tmp = -z;
} else {
tmp = -y;
}
return tmp;
}
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
real(8) :: tmp
if (y <= 4d+72) then
tmp = -z
else
tmp = -y
end if
code = tmp
end function
public static double code(double x, double y, double z, double t) {
double tmp;
if (y <= 4e+72) {
tmp = -z;
} else {
tmp = -y;
}
return tmp;
}
def code(x, y, z, t): tmp = 0 if y <= 4e+72: tmp = -z else: tmp = -y return tmp
function code(x, y, z, t) tmp = 0.0 if (y <= 4e+72) tmp = Float64(-z); else tmp = Float64(-y); end return tmp end
function tmp_2 = code(x, y, z, t) tmp = 0.0; if (y <= 4e+72) tmp = -z; else tmp = -y; end tmp_2 = tmp; end
code[x_, y_, z_, t_] := If[LessEqual[y, 4e+72], (-z), (-y)]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;y \leq 4 \cdot 10^{+72}:\\
\;\;\;\;-z\\
\mathbf{else}:\\
\;\;\;\;-y\\
\end{array}
\end{array}
(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(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}
\\
\left(-y\right) - z
\end{array}
(FPCore (x y z t) :precision binary64 (- y))
double code(double x, double y, double z, double t) {
return -y;
}
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
end function
public static double code(double x, double y, double z, double t) {
return -y;
}
def code(x, y, z, t): return -y
function code(x, y, z, t) return Float64(-y) end
function tmp = code(x, y, z, t) tmp = -y; end
code[x_, y_, z_, t_] := (-y)
\begin{array}{l}
\\
-y
\end{array}
herbie shell --seed 2023343
(FPCore (x y z t)
:name "Numeric.SpecFunctions:incompleteGamma from math-functions-0.1.5.2, A"
:precision binary64
(+ (- (- (* x (log y)) y) z) (log t)))