Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, D

Percentage Accurate: 58.0% → 97.8%
Time: 19.2s
Alternatives: 14
Speedup: 7.4×

Specification

?
\[\begin{array}{l} \\ x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \end{array} \]
(FPCore (x y z t a b)
 :precision binary64
 (+
  x
  (/
   (*
    y
    (+ (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z) b))
   (+
    (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z)
    0.607771387771))))
double code(double x, double y, double z, double t, double a, double b) {
	return x + ((y * ((((((((z * 3.13060547623) + 11.1667541262) * z) + t) * z) + a) * z) + b)) / (((((((z + 15.234687407) * z) + 31.4690115749) * z) + 11.9400905721) * z) + 0.607771387771));
}

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = x + ((y * ((((((((z * 3.13060547623d0) + 11.1667541262d0) * z) + t) * z) + a) * z) + b)) / (((((((z + 15.234687407d0) * z) + 31.4690115749d0) * z) + 11.9400905721d0) * z) + 0.607771387771d0))
end function

public static double code(double x, double y, double z, double t, double a, double b) {
	return x + ((y * ((((((((z * 3.13060547623) + 11.1667541262) * z) + t) * z) + a) * z) + b)) / (((((((z + 15.234687407) * z) + 31.4690115749) * z) + 11.9400905721) * z) + 0.607771387771));
}

def code(x, y, z, t, a, b):
	return x + ((y * ((((((((z * 3.13060547623) + 11.1667541262) * z) + t) * z) + a) * z) + b)) / (((((((z + 15.234687407) * z) + 31.4690115749) * z) + 11.9400905721) * z) + 0.607771387771))

function code(x, y, z, t, a, b)
	return Float64(x + Float64(Float64(y * Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(z * 3.13060547623) + 11.1667541262) * z) + t) * z) + a) * z) + b)) / Float64(Float64(Float64(Float64(Float64(Float64(Float64(z + 15.234687407) * z) + 31.4690115749) * z) + 11.9400905721) * z) + 0.607771387771)))
end

function tmp = code(x, y, z, t, a, b)
	tmp = x + ((y * ((((((((z * 3.13060547623) + 11.1667541262) * z) + t) * z) + a) * z) + b)) / (((((((z + 15.234687407) * z) + 31.4690115749) * z) + 11.9400905721) * z) + 0.607771387771));
end

code[x_, y_, z_, t_, a_, b_] := N[(x + N[(N[(y * N[(N[(N[(N[(N[(N[(N[(N[(z * 3.13060547623), $MachinePrecision] + 11.1667541262), $MachinePrecision] * z), $MachinePrecision] + t), $MachinePrecision] * z), $MachinePrecision] + a), $MachinePrecision] * z), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(N[(N[(N[(N[(z + 15.234687407), $MachinePrecision] * z), $MachinePrecision] + 31.4690115749), $MachinePrecision] * z), $MachinePrecision] + 11.9400905721), $MachinePrecision] * z), $MachinePrecision] + 0.607771387771), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

\begin{array}{l}

\\
x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771}
\end{array}

Sampling outcomes in binary64 precision:

Local Percentage Accuracy vs ?

The average percentage accuracy by input value. Horizontal axis shows value of an input variable; the variable is choosen in the title. Vertical axis is accuracy; higher is better. Red represent the original program, while blue represents Herbie's suggestion. These can be toggled with buttons below the plot. The line is an average while dots represent individual samples.

Accuracy vs Speed?

Herbie found 14 alternatives:

AlternativeAccuracySpeedup
The accuracy (vertical axis) and speed (horizontal axis) of each alternatives. Up and to the right is better. The red square shows the initial program, and each blue circle shows an alternative.The line shows the best available speed-accuracy tradeoffs.

Initial Program: 58.0% accurate, 1.0× speedup?

\[\begin{array}{l} \\ x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \end{array} \]
(FPCore (x y z t a b)
 :precision binary64
 (+
  x
  (/
   (*
    y
    (+ (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z) b))
   (+
    (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z)
    0.607771387771))))
double code(double x, double y, double z, double t, double a, double b) {
	return x + ((y * ((((((((z * 3.13060547623) + 11.1667541262) * z) + t) * z) + a) * z) + b)) / (((((((z + 15.234687407) * z) + 31.4690115749) * z) + 11.9400905721) * z) + 0.607771387771));
}

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = x + ((y * ((((((((z * 3.13060547623d0) + 11.1667541262d0) * z) + t) * z) + a) * z) + b)) / (((((((z + 15.234687407d0) * z) + 31.4690115749d0) * z) + 11.9400905721d0) * z) + 0.607771387771d0))
end function

public static double code(double x, double y, double z, double t, double a, double b) {
	return x + ((y * ((((((((z * 3.13060547623) + 11.1667541262) * z) + t) * z) + a) * z) + b)) / (((((((z + 15.234687407) * z) + 31.4690115749) * z) + 11.9400905721) * z) + 0.607771387771));
}

def code(x, y, z, t, a, b):
	return x + ((y * ((((((((z * 3.13060547623) + 11.1667541262) * z) + t) * z) + a) * z) + b)) / (((((((z + 15.234687407) * z) + 31.4690115749) * z) + 11.9400905721) * z) + 0.607771387771))

function code(x, y, z, t, a, b)
	return Float64(x + Float64(Float64(y * Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(z * 3.13060547623) + 11.1667541262) * z) + t) * z) + a) * z) + b)) / Float64(Float64(Float64(Float64(Float64(Float64(Float64(z + 15.234687407) * z) + 31.4690115749) * z) + 11.9400905721) * z) + 0.607771387771)))
end

function tmp = code(x, y, z, t, a, b)
	tmp = x + ((y * ((((((((z * 3.13060547623) + 11.1667541262) * z) + t) * z) + a) * z) + b)) / (((((((z + 15.234687407) * z) + 31.4690115749) * z) + 11.9400905721) * z) + 0.607771387771));
end

code[x_, y_, z_, t_, a_, b_] := N[(x + N[(N[(y * N[(N[(N[(N[(N[(N[(N[(N[(z * 3.13060547623), $MachinePrecision] + 11.1667541262), $MachinePrecision] * z), $MachinePrecision] + t), $MachinePrecision] * z), $MachinePrecision] + a), $MachinePrecision] * z), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(N[(N[(N[(N[(z + 15.234687407), $MachinePrecision] * z), $MachinePrecision] + 31.4690115749), $MachinePrecision] * z), $MachinePrecision] + 11.9400905721), $MachinePrecision] * z), $MachinePrecision] + 0.607771387771), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

\begin{array}{l}

\\
x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771}
\end{array}

Alternative 1: 97.8% accurate, 0.1× speedup?

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{+64} \lor \neg \left(z \leq 3.8 \cdot 10^{+18}\right):\\ \;\;\;\;x + \mathsf{fma}\left(\frac{y}{z}, -36.52704169880642, \mathsf{fma}\left(y, 3.13060547623, \frac{y}{\frac{{z}^{2}}{t + 457.9610022158428}}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), t\right), a\right), b\right) \cdot \frac{y}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}\\ \end{array} \end{array} \]
(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -5.4e+64) (not (<= z 3.8e+18)))
   (+
    x
    (fma
     (/ y z)
     -36.52704169880642
     (fma y 3.13060547623 (/ y (/ (pow z 2.0) (+ t 457.9610022158428))))))
   (+
    x
    (*
     (fma z (fma z (fma z (fma z 3.13060547623 11.1667541262) t) a) b)
     (/
      y
      (+
       (* z (+ (* z (+ (* z (+ z 15.234687407)) 31.4690115749)) 11.9400905721))
       0.607771387771))))))
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -5.4e+64) || !(z <= 3.8e+18)) {
		tmp = x + fma((y / z), -36.52704169880642, fma(y, 3.13060547623, (y / (pow(z, 2.0) / (t + 457.9610022158428)))));
	} else {
		tmp = x + (fma(z, fma(z, fma(z, fma(z, 3.13060547623, 11.1667541262), t), a), b) * (y / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)));
	}
	return tmp;
}

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -5.4e+64) || !(z <= 3.8e+18))
		tmp = Float64(x + fma(Float64(y / z), -36.52704169880642, fma(y, 3.13060547623, Float64(y / Float64((z ^ 2.0) / Float64(t + 457.9610022158428))))));
	else
		tmp = Float64(x + Float64(fma(z, fma(z, fma(z, fma(z, 3.13060547623, 11.1667541262), t), a), b) * Float64(y / Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771))));
	end
	return tmp
end

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -5.4e+64], N[Not[LessEqual[z, 3.8e+18]], $MachinePrecision]], N[(x + N[(N[(y / z), $MachinePrecision] * -36.52704169880642 + N[(y * 3.13060547623 + N[(y / N[(N[Power[z, 2.0], $MachinePrecision] / N[(t + 457.9610022158428), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z * N[(z * N[(z * N[(z * 3.13060547623 + 11.1667541262), $MachinePrecision] + t), $MachinePrecision] + a), $MachinePrecision] + b), $MachinePrecision] * N[(y / N[(N[(z * N[(N[(z * N[(N[(z * N[(z + 15.234687407), $MachinePrecision]), $MachinePrecision] + 31.4690115749), $MachinePrecision]), $MachinePrecision] + 11.9400905721), $MachinePrecision]), $MachinePrecision] + 0.607771387771), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

\begin{array}{l}

\\
\begin{array}{l}
\mathbf{if}\;z \leq -5.4 \cdot 10^{+64} \lor \neg \left(z \leq 3.8 \cdot 10^{+18}\right):\\
\;\;\;\;x + \mathsf{fma}\left(\frac{y}{z}, -36.52704169880642, \mathsf{fma}\left(y, 3.13060547623, \frac{y}{\frac{{z}^{2}}{t + 457.9610022158428}}\right)\right)\\

\mathbf{else}:\\
\;\;\;\;x + \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), t\right), a\right), b\right) \cdot \frac{y}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}\\


\end{array}
\end{array}
Derivation
    &prev;&pcontext;&pcontext2;&ctx;
  1. Add Preprocessing

Alternative 2: 98.0% accurate, 0.0× speedup?

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right) + b\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771} \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(\frac{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), t\right), a\right), b\right)}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \mathsf{fma}\left(\frac{y}{z}, -36.52704169880642, \mathsf{fma}\left(y, 3.13060547623, \frac{y}{\frac{{z}^{2}}{t + 457.9610022158428}}\right)\right)\\ \end{array} \end{array} \]
(FPCore (x y z t a b)
 :precision binary64
 (if (<=
      (/
       (*
        y
        (+
         (* z (+ (* z (+ (* z (+ (* z 3.13060547623) 11.1667541262)) t)) a))
         b))
       (+
        (*
         z
         (+ (* z (+ (* z (+ z 15.234687407)) 31.4690115749)) 11.9400905721))
        0.607771387771))
      INFINITY)
   (fma
    (/
     (fma z (fma z (fma z (fma z 3.13060547623 11.1667541262) t) a) b)
     (fma
      z
      (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721)
      0.607771387771))
    y
    x)
   (+
    x
    (fma
     (/ y z)
     -36.52704169880642
     (fma y 3.13060547623 (/ y (/ (pow z 2.0) (+ t 457.9610022158428))))))))
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((y * ((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)) <= ((double) INFINITY)) {
		tmp = fma((fma(z, fma(z, fma(z, fma(z, 3.13060547623, 11.1667541262), t), a), b) / fma(z, fma(z, fma(z, (z + 15.234687407), 31.4690115749), 11.9400905721), 0.607771387771)), y, x);
	} else {
		tmp = x + fma((y / z), -36.52704169880642, fma(y, 3.13060547623, (y / (pow(z, 2.0) / (t + 457.9610022158428)))));
	}
	return tmp;
}

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(Float64(y * Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)) <= Inf)
		tmp = fma(Float64(fma(z, fma(z, fma(z, fma(z, 3.13060547623, 11.1667541262), t), a), b) / fma(z, fma(z, fma(z, Float64(z + 15.234687407), 31.4690115749), 11.9400905721), 0.607771387771)), y, x);
	else
		tmp = Float64(x + fma(Float64(y / z), -36.52704169880642, fma(y, 3.13060547623, Float64(y / Float64((z ^ 2.0) / Float64(t + 457.9610022158428))))));
	end
	return tmp
end

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(N[(y * N[(N[(z * N[(N[(z * N[(N[(z * N[(N[(z * 3.13060547623), $MachinePrecision] + 11.1667541262), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / N[(N[(z * N[(N[(z * N[(N[(z * N[(z + 15.234687407), $MachinePrecision]), $MachinePrecision] + 31.4690115749), $MachinePrecision]), $MachinePrecision] + 11.9400905721), $MachinePrecision]), $MachinePrecision] + 0.607771387771), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[(N[(z * N[(z * N[(z * N[(z * 3.13060547623 + 11.1667541262), $MachinePrecision] + t), $MachinePrecision] + a), $MachinePrecision] + b), $MachinePrecision] / N[(z * N[(z * N[(z * N[(z + 15.234687407), $MachinePrecision] + 31.4690115749), $MachinePrecision] + 11.9400905721), $MachinePrecision] + 0.607771387771), $MachinePrecision]), $MachinePrecision] * y + x), $MachinePrecision], N[(x + N[(N[(y / z), $MachinePrecision] * -36.52704169880642 + N[(y * 3.13060547623 + N[(y / N[(N[Power[z, 2.0], $MachinePrecision] / N[(t + 457.9610022158428), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

\begin{array}{l}

\\
\begin{array}{l}
\mathbf{if}\;\frac{y \cdot \left(z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right) + b\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771} \leq \infty:\\
\;\;\;\;\mathsf{fma}\left(\frac{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), t\right), a\right), b\right)}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)}, y, x\right)\\

\mathbf{else}:\\
\;\;\;\;x + \mathsf{fma}\left(\frac{y}{z}, -36.52704169880642, \mathsf{fma}\left(y, 3.13060547623, \frac{y}{\frac{{z}^{2}}{t + 457.9610022158428}}\right)\right)\\


\end{array}
\end{array}
Derivation
    &prev;&pcontext;&pcontext2;&ctx;
  1. Add Preprocessing

Alternative 3: 97.3% accurate, 0.1× speedup?

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.45 \cdot 10^{+58} \lor \neg \left(z \leq 3.8 \cdot 10^{+15}\right):\\ \;\;\;\;x + \mathsf{fma}\left(\frac{y}{z}, -36.52704169880642, \mathsf{fma}\left(y, 3.13060547623, \frac{y}{\frac{{z}^{2}}{t + 457.9610022158428}}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right) + b\right)}{0.607771387771 + \left(z \cdot 11.9400905721 + \left(15.234687407 \cdot {z}^{3} + \left(31.4690115749 \cdot {z}^{2} + {z}^{4}\right)\right)\right)}\\ \end{array} \end{array} \]
(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -2.45e+58) (not (<= z 3.8e+15)))
   (+
    x
    (fma
     (/ y z)
     -36.52704169880642
     (fma y 3.13060547623 (/ y (/ (pow z 2.0) (+ t 457.9610022158428))))))
   (+
    x
    (/
     (*
      y
      (+
       (* z (+ (* z (+ (* z (+ (* z 3.13060547623) 11.1667541262)) t)) a))
       b))
     (+
      0.607771387771
      (+
       (* z 11.9400905721)
       (+
        (* 15.234687407 (pow z 3.0))
        (+ (* 31.4690115749 (pow z 2.0)) (pow z 4.0)))))))))
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.45e+58) || !(z <= 3.8e+15)) {
		tmp = x + fma((y / z), -36.52704169880642, fma(y, 3.13060547623, (y / (pow(z, 2.0) / (t + 457.9610022158428)))));
	} else {
		tmp = x + ((y * ((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / (0.607771387771 + ((z * 11.9400905721) + ((15.234687407 * pow(z, 3.0)) + ((31.4690115749 * pow(z, 2.0)) + pow(z, 4.0))))));
	}
	return tmp;
}

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -2.45e+58) || !(z <= 3.8e+15))
		tmp = Float64(x + fma(Float64(y / z), -36.52704169880642, fma(y, 3.13060547623, Float64(y / Float64((z ^ 2.0) / Float64(t + 457.9610022158428))))));
	else
		tmp = Float64(x + Float64(Float64(y * Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / Float64(0.607771387771 + Float64(Float64(z * 11.9400905721) + Float64(Float64(15.234687407 * (z ^ 3.0)) + Float64(Float64(31.4690115749 * (z ^ 2.0)) + (z ^ 4.0)))))));
	end
	return tmp
end

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -2.45e+58], N[Not[LessEqual[z, 3.8e+15]], $MachinePrecision]], N[(x + N[(N[(y / z), $MachinePrecision] * -36.52704169880642 + N[(y * 3.13060547623 + N[(y / N[(N[Power[z, 2.0], $MachinePrecision] / N[(t + 457.9610022158428), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * N[(N[(z * N[(N[(z * N[(N[(z * N[(N[(z * 3.13060547623), $MachinePrecision] + 11.1667541262), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / N[(0.607771387771 + N[(N[(z * 11.9400905721), $MachinePrecision] + N[(N[(15.234687407 * N[Power[z, 3.0], $MachinePrecision]), $MachinePrecision] + N[(N[(31.4690115749 * N[Power[z, 2.0], $MachinePrecision]), $MachinePrecision] + N[Power[z, 4.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

\begin{array}{l}

\\
\begin{array}{l}
\mathbf{if}\;z \leq -2.45 \cdot 10^{+58} \lor \neg \left(z \leq 3.8 \cdot 10^{+15}\right):\\
\;\;\;\;x + \mathsf{fma}\left(\frac{y}{z}, -36.52704169880642, \mathsf{fma}\left(y, 3.13060547623, \frac{y}{\frac{{z}^{2}}{t + 457.9610022158428}}\right)\right)\\

\mathbf{else}:\\
\;\;\;\;x + \frac{y \cdot \left(z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right) + b\right)}{0.607771387771 + \left(z \cdot 11.9400905721 + \left(15.234687407 \cdot {z}^{3} + \left(31.4690115749 \cdot {z}^{2} + {z}^{4}\right)\right)\right)}\\


\end{array}
\end{array}
Derivation
    &prev;&pcontext;&pcontext2;&ctx;
  1. Add Preprocessing

Alternative 4: 97.3% accurate, 0.1× speedup?

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.45 \cdot 10^{+58} \lor \neg \left(z \leq 2.9 \cdot 10^{+18}\right):\\ \;\;\;\;x + \mathsf{fma}\left(\frac{y}{z}, -36.52704169880642, \mathsf{fma}\left(y, 3.13060547623, \frac{y}{\frac{{z}^{2}}{t + 457.9610022158428}}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \left(z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right) + b\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771} + x\\ \end{array} \end{array} \]
(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -2.45e+58) (not (<= z 2.9e+18)))
   (+
    x
    (fma
     (/ y z)
     -36.52704169880642
     (fma y 3.13060547623 (/ y (/ (pow z 2.0) (+ t 457.9610022158428))))))
   (+
    (/
     (*
      y
      (+
       (* z (+ (* z (+ (* z (+ (* z 3.13060547623) 11.1667541262)) t)) a))
       b))
     (+
      (* z (+ (* z (+ (* z (+ z 15.234687407)) 31.4690115749)) 11.9400905721))
      0.607771387771))
    x)))
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.45e+58) || !(z <= 2.9e+18)) {
		tmp = x + fma((y / z), -36.52704169880642, fma(y, 3.13060547623, (y / (pow(z, 2.0) / (t + 457.9610022158428)))));
	} else {
		tmp = ((y * ((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)) + x;
	}
	return tmp;
}

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -2.45e+58) || !(z <= 2.9e+18))
		tmp = Float64(x + fma(Float64(y / z), -36.52704169880642, fma(y, 3.13060547623, Float64(y / Float64((z ^ 2.0) / Float64(t + 457.9610022158428))))));
	else
		tmp = Float64(Float64(Float64(y * Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)) + x);
	end
	return tmp
end

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -2.45e+58], N[Not[LessEqual[z, 2.9e+18]], $MachinePrecision]], N[(x + N[(N[(y / z), $MachinePrecision] * -36.52704169880642 + N[(y * 3.13060547623 + N[(y / N[(N[Power[z, 2.0], $MachinePrecision] / N[(t + 457.9610022158428), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y * N[(N[(z * N[(N[(z * N[(N[(z * N[(N[(z * 3.13060547623), $MachinePrecision] + 11.1667541262), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / N[(N[(z * N[(N[(z * N[(N[(z * N[(z + 15.234687407), $MachinePrecision]), $MachinePrecision] + 31.4690115749), $MachinePrecision]), $MachinePrecision] + 11.9400905721), $MachinePrecision]), $MachinePrecision] + 0.607771387771), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]]

\begin{array}{l}

\\
\begin{array}{l}
\mathbf{if}\;z \leq -2.45 \cdot 10^{+58} \lor \neg \left(z \leq 2.9 \cdot 10^{+18}\right):\\
\;\;\;\;x + \mathsf{fma}\left(\frac{y}{z}, -36.52704169880642, \mathsf{fma}\left(y, 3.13060547623, \frac{y}{\frac{{z}^{2}}{t + 457.9610022158428}}\right)\right)\\

\mathbf{else}:\\
\;\;\;\;\frac{y \cdot \left(z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right) + b\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771} + x\\


\end{array}
\end{array}
Derivation
    &prev;&pcontext;&pcontext2;&ctx;
  1. Add Preprocessing

Alternative 5: 95.1% accurate, 0.5× speedup?

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot \left(z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right) + b\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}\\ \mathbf{if}\;t_1 \leq \infty:\\ \;\;\;\;t_1 + x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \end{array} \]
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (/
          (*
           y
           (+
            (* z (+ (* z (+ (* z (+ (* z 3.13060547623) 11.1667541262)) t)) a))
            b))
          (+
           (*
            z
            (+ (* z (+ (* z (+ z 15.234687407)) 31.4690115749)) 11.9400905721))
           0.607771387771))))
   (if (<= t_1 INFINITY) (+ t_1 x) (+ x (* y 3.13060547623)))))
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y * ((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771);
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1 + x;
	} else {
		tmp = x + (y * 3.13060547623);
	}
	return tmp;
}

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y * ((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771);
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1 + x;
	} else {
		tmp = x + (y * 3.13060547623);
	}
	return tmp;
}

def code(x, y, z, t, a, b):
	t_1 = (y * ((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)
	tmp = 0
	if t_1 <= math.inf:
		tmp = t_1 + x
	else:
		tmp = x + (y * 3.13060547623)
	return tmp

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y * Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = Float64(t_1 + x);
	else
		tmp = Float64(x + Float64(y * 3.13060547623));
	end
	return tmp
end

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (y * ((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771);
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1 + x;
	else
		tmp = x + (y * 3.13060547623);
	end
	tmp_2 = tmp;
end

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y * N[(N[(z * N[(N[(z * N[(N[(z * N[(N[(z * 3.13060547623), $MachinePrecision] + 11.1667541262), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / N[(N[(z * N[(N[(z * N[(N[(z * N[(z + 15.234687407), $MachinePrecision]), $MachinePrecision] + 31.4690115749), $MachinePrecision]), $MachinePrecision] + 11.9400905721), $MachinePrecision]), $MachinePrecision] + 0.607771387771), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], N[(t$95$1 + x), $MachinePrecision], N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision]]]

\begin{array}{l}

\\
\begin{array}{l}
t_1 := \frac{y \cdot \left(z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right) + b\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}\\
\mathbf{if}\;t_1 \leq \infty:\\
\;\;\;\;t_1 + x\\

\mathbf{else}:\\
\;\;\;\;x + y \cdot 3.13060547623\\


\end{array}
\end{array}
Derivation
    &prev;&pcontext;&pcontext2;&ctx;
  1. Add Preprocessing

Alternative 6: 94.9% accurate, 1.0× speedup?

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{+58} \lor \neg \left(z \leq 3.5 \cdot 10^{+28}\right):\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot 11.1667541262\right)\right)\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}\\ \end{array} \end{array} \]
(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -6.6e+58) (not (<= z 3.5e+28)))
   (+ x (* y 3.13060547623))
   (+
    x
    (/
     (* y (+ b (* z (+ a (* z (+ t (* z 11.1667541262)))))))
     (+
      (* z (+ (* z (+ (* z (+ z 15.234687407)) 31.4690115749)) 11.9400905721))
      0.607771387771)))))
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -6.6e+58) || !(z <= 3.5e+28)) {
		tmp = x + (y * 3.13060547623);
	} else {
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * 11.1667541262))))))) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771));
	}
	return tmp;
}

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-6.6d+58)) .or. (.not. (z <= 3.5d+28))) then
        tmp = x + (y * 3.13060547623d0)
    else
        tmp = x + ((y * (b + (z * (a + (z * (t + (z * 11.1667541262d0))))))) / ((z * ((z * ((z * (z + 15.234687407d0)) + 31.4690115749d0)) + 11.9400905721d0)) + 0.607771387771d0))
    end if
    code = tmp
end function

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -6.6e+58) || !(z <= 3.5e+28)) {
		tmp = x + (y * 3.13060547623);
	} else {
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * 11.1667541262))))))) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771));
	}
	return tmp;
}

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -6.6e+58) or not (z <= 3.5e+28):
		tmp = x + (y * 3.13060547623)
	else:
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * 11.1667541262))))))) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771))
	return tmp

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -6.6e+58) || !(z <= 3.5e+28))
		tmp = Float64(x + Float64(y * 3.13060547623));
	else
		tmp = Float64(x + Float64(Float64(y * Float64(b + Float64(z * Float64(a + Float64(z * Float64(t + Float64(z * 11.1667541262))))))) / Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)));
	end
	return tmp
end

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -6.6e+58) || ~((z <= 3.5e+28)))
		tmp = x + (y * 3.13060547623);
	else
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * 11.1667541262))))))) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771));
	end
	tmp_2 = tmp;
end

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -6.6e+58], N[Not[LessEqual[z, 3.5e+28]], $MachinePrecision]], N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * N[(b + N[(z * N[(a + N[(z * N[(t + N[(z * 11.1667541262), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(z * N[(N[(z * N[(N[(z * N[(z + 15.234687407), $MachinePrecision]), $MachinePrecision] + 31.4690115749), $MachinePrecision]), $MachinePrecision] + 11.9400905721), $MachinePrecision]), $MachinePrecision] + 0.607771387771), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

\begin{array}{l}

\\
\begin{array}{l}
\mathbf{if}\;z \leq -6.6 \cdot 10^{+58} \lor \neg \left(z \leq 3.5 \cdot 10^{+28}\right):\\
\;\;\;\;x + y \cdot 3.13060547623\\

\mathbf{else}:\\
\;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot 11.1667541262\right)\right)\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}\\


\end{array}
\end{array}
Derivation
    &prev;&pcontext;&pcontext2;&ctx;
  1. Add Preprocessing

Alternative 7: 93.6% accurate, 1.1× speedup?

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot 3.13060547623\\ \mathbf{if}\;z \leq -6.6 \cdot 10^{+58}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-7}:\\ \;\;\;\;x + \frac{y \cdot \left(z \cdot \left(a + z \cdot \left(t + z \cdot 11.1667541262\right)\right)\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+23}:\\ \;\;\;\;x + \frac{y \cdot \left(z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right) + b\right)}{0.607771387771 + z \cdot 11.9400905721}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* y 3.13060547623))))
   (if (<= z -6.6e+58)
     t_1
     (if (<= z -6e-7)
       (+
        x
        (/
         (* y (* z (+ a (* z (+ t (* z 11.1667541262))))))
         (+
          (*
           z
           (+ (* z (+ (* z (+ z 15.234687407)) 31.4690115749)) 11.9400905721))
          0.607771387771)))
       (if (<= z 1.05e+23)
         (+
          x
          (/
           (*
            y
            (+
             (*
              z
              (+ (* z (+ (* z (+ (* z 3.13060547623) 11.1667541262)) t)) a))
             b))
           (+ 0.607771387771 (* z 11.9400905721))))
         t_1)))))
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y * 3.13060547623);
	double tmp;
	if (z <= -6.6e+58) {
		tmp = t_1;
	} else if (z <= -6e-7) {
		tmp = x + ((y * (z * (a + (z * (t + (z * 11.1667541262)))))) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771));
	} else if (z <= 1.05e+23) {
		tmp = x + ((y * ((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / (0.607771387771 + (z * 11.9400905721)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y * 3.13060547623d0)
    if (z <= (-6.6d+58)) then
        tmp = t_1
    else if (z <= (-6d-7)) then
        tmp = x + ((y * (z * (a + (z * (t + (z * 11.1667541262d0)))))) / ((z * ((z * ((z * (z + 15.234687407d0)) + 31.4690115749d0)) + 11.9400905721d0)) + 0.607771387771d0))
    else if (z <= 1.05d+23) then
        tmp = x + ((y * ((z * ((z * ((z * ((z * 3.13060547623d0) + 11.1667541262d0)) + t)) + a)) + b)) / (0.607771387771d0 + (z * 11.9400905721d0)))
    else
        tmp = t_1
    end if
    code = tmp
end function

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y * 3.13060547623);
	double tmp;
	if (z <= -6.6e+58) {
		tmp = t_1;
	} else if (z <= -6e-7) {
		tmp = x + ((y * (z * (a + (z * (t + (z * 11.1667541262)))))) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771));
	} else if (z <= 1.05e+23) {
		tmp = x + ((y * ((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / (0.607771387771 + (z * 11.9400905721)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

def code(x, y, z, t, a, b):
	t_1 = x + (y * 3.13060547623)
	tmp = 0
	if z <= -6.6e+58:
		tmp = t_1
	elif z <= -6e-7:
		tmp = x + ((y * (z * (a + (z * (t + (z * 11.1667541262)))))) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771))
	elif z <= 1.05e+23:
		tmp = x + ((y * ((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / (0.607771387771 + (z * 11.9400905721)))
	else:
		tmp = t_1
	return tmp

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(y * 3.13060547623))
	tmp = 0.0
	if (z <= -6.6e+58)
		tmp = t_1;
	elseif (z <= -6e-7)
		tmp = Float64(x + Float64(Float64(y * Float64(z * Float64(a + Float64(z * Float64(t + Float64(z * 11.1667541262)))))) / Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)));
	elseif (z <= 1.05e+23)
		tmp = Float64(x + Float64(Float64(y * Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / Float64(0.607771387771 + Float64(z * 11.9400905721))));
	else
		tmp = t_1;
	end
	return tmp
end

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (y * 3.13060547623);
	tmp = 0.0;
	if (z <= -6.6e+58)
		tmp = t_1;
	elseif (z <= -6e-7)
		tmp = x + ((y * (z * (a + (z * (t + (z * 11.1667541262)))))) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771));
	elseif (z <= 1.05e+23)
		tmp = x + ((y * ((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / (0.607771387771 + (z * 11.9400905721)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.6e+58], t$95$1, If[LessEqual[z, -6e-7], N[(x + N[(N[(y * N[(z * N[(a + N[(z * N[(t + N[(z * 11.1667541262), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(z * N[(N[(z * N[(N[(z * N[(z + 15.234687407), $MachinePrecision]), $MachinePrecision] + 31.4690115749), $MachinePrecision]), $MachinePrecision] + 11.9400905721), $MachinePrecision]), $MachinePrecision] + 0.607771387771), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.05e+23], N[(x + N[(N[(y * N[(N[(z * N[(N[(z * N[(N[(z * N[(N[(z * 3.13060547623), $MachinePrecision] + 11.1667541262), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / N[(0.607771387771 + N[(z * 11.9400905721), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

\begin{array}{l}

\\
\begin{array}{l}
t_1 := x + y \cdot 3.13060547623\\
\mathbf{if}\;z \leq -6.6 \cdot 10^{+58}:\\
\;\;\;\;t_1\\

\mathbf{elif}\;z \leq -6 \cdot 10^{-7}:\\
\;\;\;\;x + \frac{y \cdot \left(z \cdot \left(a + z \cdot \left(t + z \cdot 11.1667541262\right)\right)\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}\\

\mathbf{elif}\;z \leq 1.05 \cdot 10^{+23}:\\
\;\;\;\;x + \frac{y \cdot \left(z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right) + b\right)}{0.607771387771 + z \cdot 11.9400905721}\\

\mathbf{else}:\\
\;\;\;\;t_1\\


\end{array}
\end{array}
Derivation
    &prev;&pcontext;&pcontext2;&ctx;
  1. Add Preprocessing

Alternative 8: 93.1% accurate, 1.1× speedup?

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot 3.13060547623\\ \mathbf{if}\;z \leq -2.45 \cdot 10^{+58}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -245000:\\ \;\;\;\;x + \frac{a \cdot \left(y \cdot z\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+22}:\\ \;\;\;\;x + \frac{y \cdot \left(z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right) + b\right)}{0.607771387771 + z \cdot 11.9400905721}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* y 3.13060547623))))
   (if (<= z -2.45e+58)
     t_1
     (if (<= z -245000.0)
       (+
        x
        (/
         (* a (* y z))
         (+
          (*
           z
           (+ (* z (+ (* z (+ z 15.234687407)) 31.4690115749)) 11.9400905721))
          0.607771387771)))
       (if (<= z 5e+22)
         (+
          x
          (/
           (*
            y
            (+
             (*
              z
              (+ (* z (+ (* z (+ (* z 3.13060547623) 11.1667541262)) t)) a))
             b))
           (+ 0.607771387771 (* z 11.9400905721))))
         t_1)))))
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y * 3.13060547623);
	double tmp;
	if (z <= -2.45e+58) {
		tmp = t_1;
	} else if (z <= -245000.0) {
		tmp = x + ((a * (y * z)) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771));
	} else if (z <= 5e+22) {
		tmp = x + ((y * ((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / (0.607771387771 + (z * 11.9400905721)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y * 3.13060547623d0)
    if (z <= (-2.45d+58)) then
        tmp = t_1
    else if (z <= (-245000.0d0)) then
        tmp = x + ((a * (y * z)) / ((z * ((z * ((z * (z + 15.234687407d0)) + 31.4690115749d0)) + 11.9400905721d0)) + 0.607771387771d0))
    else if (z <= 5d+22) then
        tmp = x + ((y * ((z * ((z * ((z * ((z * 3.13060547623d0) + 11.1667541262d0)) + t)) + a)) + b)) / (0.607771387771d0 + (z * 11.9400905721d0)))
    else
        tmp = t_1
    end if
    code = tmp
end function

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y * 3.13060547623);
	double tmp;
	if (z <= -2.45e+58) {
		tmp = t_1;
	} else if (z <= -245000.0) {
		tmp = x + ((a * (y * z)) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771));
	} else if (z <= 5e+22) {
		tmp = x + ((y * ((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / (0.607771387771 + (z * 11.9400905721)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

def code(x, y, z, t, a, b):
	t_1 = x + (y * 3.13060547623)
	tmp = 0
	if z <= -2.45e+58:
		tmp = t_1
	elif z <= -245000.0:
		tmp = x + ((a * (y * z)) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771))
	elif z <= 5e+22:
		tmp = x + ((y * ((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / (0.607771387771 + (z * 11.9400905721)))
	else:
		tmp = t_1
	return tmp

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(y * 3.13060547623))
	tmp = 0.0
	if (z <= -2.45e+58)
		tmp = t_1;
	elseif (z <= -245000.0)
		tmp = Float64(x + Float64(Float64(a * Float64(y * z)) / Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)));
	elseif (z <= 5e+22)
		tmp = Float64(x + Float64(Float64(y * Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / Float64(0.607771387771 + Float64(z * 11.9400905721))));
	else
		tmp = t_1;
	end
	return tmp
end

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (y * 3.13060547623);
	tmp = 0.0;
	if (z <= -2.45e+58)
		tmp = t_1;
	elseif (z <= -245000.0)
		tmp = x + ((a * (y * z)) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771));
	elseif (z <= 5e+22)
		tmp = x + ((y * ((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / (0.607771387771 + (z * 11.9400905721)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.45e+58], t$95$1, If[LessEqual[z, -245000.0], N[(x + N[(N[(a * N[(y * z), $MachinePrecision]), $MachinePrecision] / N[(N[(z * N[(N[(z * N[(N[(z * N[(z + 15.234687407), $MachinePrecision]), $MachinePrecision] + 31.4690115749), $MachinePrecision]), $MachinePrecision] + 11.9400905721), $MachinePrecision]), $MachinePrecision] + 0.607771387771), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5e+22], N[(x + N[(N[(y * N[(N[(z * N[(N[(z * N[(N[(z * N[(N[(z * 3.13060547623), $MachinePrecision] + 11.1667541262), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / N[(0.607771387771 + N[(z * 11.9400905721), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

\begin{array}{l}

\\
\begin{array}{l}
t_1 := x + y \cdot 3.13060547623\\
\mathbf{if}\;z \leq -2.45 \cdot 10^{+58}:\\
\;\;\;\;t_1\\

\mathbf{elif}\;z \leq -245000:\\
\;\;\;\;x + \frac{a \cdot \left(y \cdot z\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}\\

\mathbf{elif}\;z \leq 5 \cdot 10^{+22}:\\
\;\;\;\;x + \frac{y \cdot \left(z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right) + b\right)}{0.607771387771 + z \cdot 11.9400905721}\\

\mathbf{else}:\\
\;\;\;\;t_1\\


\end{array}
\end{array}
Derivation
    &prev;&pcontext;&pcontext2;&ctx;
  1. Add Preprocessing

Alternative 9: 88.6% accurate, 1.9× speedup?

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.45 \cdot 10^{+58} \lor \neg \left(z \leq 8.2 \cdot 10^{+21}\right):\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(a \cdot \left(y \cdot z\right)\right) \cdot 1.6453555072203998 + 1.6453555072203998 \cdot \left(y \cdot b\right)\right)\\ \end{array} \end{array} \]
(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -2.45e+58) (not (<= z 8.2e+21)))
   (+ x (* y 3.13060547623))
   (+
    x
    (+ (* (* a (* y z)) 1.6453555072203998) (* 1.6453555072203998 (* y b))))))
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.45e+58) || !(z <= 8.2e+21)) {
		tmp = x + (y * 3.13060547623);
	} else {
		tmp = x + (((a * (y * z)) * 1.6453555072203998) + (1.6453555072203998 * (y * b)));
	}
	return tmp;
}

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-2.45d+58)) .or. (.not. (z <= 8.2d+21))) then
        tmp = x + (y * 3.13060547623d0)
    else
        tmp = x + (((a * (y * z)) * 1.6453555072203998d0) + (1.6453555072203998d0 * (y * b)))
    end if
    code = tmp
end function

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.45e+58) || !(z <= 8.2e+21)) {
		tmp = x + (y * 3.13060547623);
	} else {
		tmp = x + (((a * (y * z)) * 1.6453555072203998) + (1.6453555072203998 * (y * b)));
	}
	return tmp;
}

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -2.45e+58) or not (z <= 8.2e+21):
		tmp = x + (y * 3.13060547623)
	else:
		tmp = x + (((a * (y * z)) * 1.6453555072203998) + (1.6453555072203998 * (y * b)))
	return tmp

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -2.45e+58) || !(z <= 8.2e+21))
		tmp = Float64(x + Float64(y * 3.13060547623));
	else
		tmp = Float64(x + Float64(Float64(Float64(a * Float64(y * z)) * 1.6453555072203998) + Float64(1.6453555072203998 * Float64(y * b))));
	end
	return tmp
end

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -2.45e+58) || ~((z <= 8.2e+21)))
		tmp = x + (y * 3.13060547623);
	else
		tmp = x + (((a * (y * z)) * 1.6453555072203998) + (1.6453555072203998 * (y * b)));
	end
	tmp_2 = tmp;
end

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -2.45e+58], N[Not[LessEqual[z, 8.2e+21]], $MachinePrecision]], N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(N[(a * N[(y * z), $MachinePrecision]), $MachinePrecision] * 1.6453555072203998), $MachinePrecision] + N[(1.6453555072203998 * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

\begin{array}{l}

\\
\begin{array}{l}
\mathbf{if}\;z \leq -2.45 \cdot 10^{+58} \lor \neg \left(z \leq 8.2 \cdot 10^{+21}\right):\\
\;\;\;\;x + y \cdot 3.13060547623\\

\mathbf{else}:\\
\;\;\;\;x + \left(\left(a \cdot \left(y \cdot z\right)\right) \cdot 1.6453555072203998 + 1.6453555072203998 \cdot \left(y \cdot b\right)\right)\\


\end{array}
\end{array}
Derivation
    &prev;&pcontext;&pcontext2;&ctx;
  1. Add Preprocessing

Alternative 10: 82.6% accurate, 3.3× speedup?

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{+58} \lor \neg \left(z \leq 1.18 \cdot 10^{+21}\right):\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot \frac{y}{0.607771387771}\\ \end{array} \end{array} \]
(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -6.6e+58) (not (<= z 1.18e+21)))
   (+ x (* y 3.13060547623))
   (+ x (* b (/ y 0.607771387771)))))
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -6.6e+58) || !(z <= 1.18e+21)) {
		tmp = x + (y * 3.13060547623);
	} else {
		tmp = x + (b * (y / 0.607771387771));
	}
	return tmp;
}

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-6.6d+58)) .or. (.not. (z <= 1.18d+21))) then
        tmp = x + (y * 3.13060547623d0)
    else
        tmp = x + (b * (y / 0.607771387771d0))
    end if
    code = tmp
end function

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -6.6e+58) || !(z <= 1.18e+21)) {
		tmp = x + (y * 3.13060547623);
	} else {
		tmp = x + (b * (y / 0.607771387771));
	}
	return tmp;
}

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -6.6e+58) or not (z <= 1.18e+21):
		tmp = x + (y * 3.13060547623)
	else:
		tmp = x + (b * (y / 0.607771387771))
	return tmp

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -6.6e+58) || !(z <= 1.18e+21))
		tmp = Float64(x + Float64(y * 3.13060547623));
	else
		tmp = Float64(x + Float64(b * Float64(y / 0.607771387771)));
	end
	return tmp
end

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -6.6e+58) || ~((z <= 1.18e+21)))
		tmp = x + (y * 3.13060547623);
	else
		tmp = x + (b * (y / 0.607771387771));
	end
	tmp_2 = tmp;
end

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -6.6e+58], N[Not[LessEqual[z, 1.18e+21]], $MachinePrecision]], N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision], N[(x + N[(b * N[(y / 0.607771387771), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

\begin{array}{l}

\\
\begin{array}{l}
\mathbf{if}\;z \leq -6.6 \cdot 10^{+58} \lor \neg \left(z \leq 1.18 \cdot 10^{+21}\right):\\
\;\;\;\;x + y \cdot 3.13060547623\\

\mathbf{else}:\\
\;\;\;\;x + b \cdot \frac{y}{0.607771387771}\\


\end{array}
\end{array}
Derivation
    &prev;&pcontext;&pcontext2;&ctx;
  1. Add Preprocessing

Alternative 11: 82.6% accurate, 3.3× speedup?

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{+58} \lor \neg \left(z \leq 2.2 \cdot 10^{+21}\right):\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot \left(y \cdot 1.6453555072203998\right)\\ \end{array} \end{array} \]
(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -6.6e+58) (not (<= z 2.2e+21)))
   (+ x (* y 3.13060547623))
   (+ x (* b (* y 1.6453555072203998)))))
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -6.6e+58) || !(z <= 2.2e+21)) {
		tmp = x + (y * 3.13060547623);
	} else {
		tmp = x + (b * (y * 1.6453555072203998));
	}
	return tmp;
}

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-6.6d+58)) .or. (.not. (z <= 2.2d+21))) then
        tmp = x + (y * 3.13060547623d0)
    else
        tmp = x + (b * (y * 1.6453555072203998d0))
    end if
    code = tmp
end function

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -6.6e+58) || !(z <= 2.2e+21)) {
		tmp = x + (y * 3.13060547623);
	} else {
		tmp = x + (b * (y * 1.6453555072203998));
	}
	return tmp;
}

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -6.6e+58) or not (z <= 2.2e+21):
		tmp = x + (y * 3.13060547623)
	else:
		tmp = x + (b * (y * 1.6453555072203998))
	return tmp

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -6.6e+58) || !(z <= 2.2e+21))
		tmp = Float64(x + Float64(y * 3.13060547623));
	else
		tmp = Float64(x + Float64(b * Float64(y * 1.6453555072203998)));
	end
	return tmp
end

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -6.6e+58) || ~((z <= 2.2e+21)))
		tmp = x + (y * 3.13060547623);
	else
		tmp = x + (b * (y * 1.6453555072203998));
	end
	tmp_2 = tmp;
end

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -6.6e+58], N[Not[LessEqual[z, 2.2e+21]], $MachinePrecision]], N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision], N[(x + N[(b * N[(y * 1.6453555072203998), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

\begin{array}{l}

\\
\begin{array}{l}
\mathbf{if}\;z \leq -6.6 \cdot 10^{+58} \lor \neg \left(z \leq 2.2 \cdot 10^{+21}\right):\\
\;\;\;\;x + y \cdot 3.13060547623\\

\mathbf{else}:\\
\;\;\;\;x + b \cdot \left(y \cdot 1.6453555072203998\right)\\


\end{array}
\end{array}
Derivation
    &prev;&pcontext;&pcontext2;&ctx;
  1. Add Preprocessing

Alternative 12: 82.6% accurate, 3.3× speedup?

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{+58} \lor \neg \left(z \leq 2.26 \cdot 10^{+21}\right):\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x + 1.6453555072203998 \cdot \left(y \cdot b\right)\\ \end{array} \end{array} \]
(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -6.6e+58) (not (<= z 2.26e+21)))
   (+ x (* y 3.13060547623))
   (+ x (* 1.6453555072203998 (* y b)))))
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -6.6e+58) || !(z <= 2.26e+21)) {
		tmp = x + (y * 3.13060547623);
	} else {
		tmp = x + (1.6453555072203998 * (y * b));
	}
	return tmp;
}

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-6.6d+58)) .or. (.not. (z <= 2.26d+21))) then
        tmp = x + (y * 3.13060547623d0)
    else
        tmp = x + (1.6453555072203998d0 * (y * b))
    end if
    code = tmp
end function

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -6.6e+58) || !(z <= 2.26e+21)) {
		tmp = x + (y * 3.13060547623);
	} else {
		tmp = x + (1.6453555072203998 * (y * b));
	}
	return tmp;
}

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -6.6e+58) or not (z <= 2.26e+21):
		tmp = x + (y * 3.13060547623)
	else:
		tmp = x + (1.6453555072203998 * (y * b))
	return tmp

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -6.6e+58) || !(z <= 2.26e+21))
		tmp = Float64(x + Float64(y * 3.13060547623));
	else
		tmp = Float64(x + Float64(1.6453555072203998 * Float64(y * b)));
	end
	return tmp
end

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -6.6e+58) || ~((z <= 2.26e+21)))
		tmp = x + (y * 3.13060547623);
	else
		tmp = x + (1.6453555072203998 * (y * b));
	end
	tmp_2 = tmp;
end

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -6.6e+58], N[Not[LessEqual[z, 2.26e+21]], $MachinePrecision]], N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision], N[(x + N[(1.6453555072203998 * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

\begin{array}{l}

\\
\begin{array}{l}
\mathbf{if}\;z \leq -6.6 \cdot 10^{+58} \lor \neg \left(z \leq 2.26 \cdot 10^{+21}\right):\\
\;\;\;\;x + y \cdot 3.13060547623\\

\mathbf{else}:\\
\;\;\;\;x + 1.6453555072203998 \cdot \left(y \cdot b\right)\\


\end{array}
\end{array}
Derivation
    &prev;&pcontext;&pcontext2;&ctx;
  1. Add Preprocessing

Alternative 13: 62.4% accurate, 7.4× speedup?

\[\begin{array}{l} \\ x + y \cdot 3.13060547623 \end{array} \]
(FPCore (x y z t a b) :precision binary64 (+ x (* y 3.13060547623)))
double code(double x, double y, double z, double t, double a, double b) {
	return x + (y * 3.13060547623);
}

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = x + (y * 3.13060547623d0)
end function

public static double code(double x, double y, double z, double t, double a, double b) {
	return x + (y * 3.13060547623);
}

def code(x, y, z, t, a, b):
	return x + (y * 3.13060547623)

function code(x, y, z, t, a, b)
	return Float64(x + Float64(y * 3.13060547623))
end

function tmp = code(x, y, z, t, a, b)
	tmp = x + (y * 3.13060547623);
end

code[x_, y_, z_, t_, a_, b_] := N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision]

\begin{array}{l}

\\
x + y \cdot 3.13060547623
\end{array}
Derivation
    &prev;&pcontext;&pcontext2;&ctx;
  1. Add Preprocessing

Alternative 14: 45.0% accurate, 37.0× speedup?

\[\begin{array}{l} \\ x \end{array} \]
(FPCore (x y z t a b) :precision binary64 x)
double code(double x, double y, double z, double t, double a, double b) {
	return x;
}

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = x
end function

public static double code(double x, double y, double z, double t, double a, double b) {
	return x;
}

def code(x, y, z, t, a, b):
	return x

function code(x, y, z, t, a, b)
	return x
end

function tmp = code(x, y, z, t, a, b)
	tmp = x;
end

code[x_, y_, z_, t_, a_, b_] := x

\begin{array}{l}

\\
x
\end{array}
Derivation
    &prev;&pcontext;&pcontext2;&ctx;
  1. Add Preprocessing

Developer target: 98.6% accurate, 0.9× speedup?

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\left(3.13060547623 - \frac{36.527041698806414}{z}\right) + \frac{t}{z \cdot z}\right) \cdot \frac{y}{1}\\ \mathbf{if}\;z < -6.499344996252632 \cdot 10^{+53}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z < 7.066965436914287 \cdot 10^{+59}:\\ \;\;\;\;x + \frac{y}{\frac{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771}{\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (+
          x
          (*
           (+ (- 3.13060547623 (/ 36.527041698806414 z)) (/ t (* z z)))
           (/ y 1.0)))))
   (if (< z -6.499344996252632e+53)
     t_1
     (if (< z 7.066965436914287e+59)
       (+
        x
        (/
         y
         (/
          (+
           (*
            (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721)
            z)
           0.607771387771)
          (+
           (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z)
           b))))
       t_1))))
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (((3.13060547623 - (36.527041698806414 / z)) + (t / (z * z))) * (y / 1.0));
	double tmp;
	if (z < -6.499344996252632e+53) {
		tmp = t_1;
	} else if (z < 7.066965436914287e+59) {
		tmp = x + (y / ((((((((z + 15.234687407) * z) + 31.4690115749) * z) + 11.9400905721) * z) + 0.607771387771) / ((((((((z * 3.13060547623) + 11.1667541262) * z) + t) * z) + a) * z) + b)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (((3.13060547623d0 - (36.527041698806414d0 / z)) + (t / (z * z))) * (y / 1.0d0))
    if (z < (-6.499344996252632d+53)) then
        tmp = t_1
    else if (z < 7.066965436914287d+59) then
        tmp = x + (y / ((((((((z + 15.234687407d0) * z) + 31.4690115749d0) * z) + 11.9400905721d0) * z) + 0.607771387771d0) / ((((((((z * 3.13060547623d0) + 11.1667541262d0) * z) + t) * z) + a) * z) + b)))
    else
        tmp = t_1
    end if
    code = tmp
end function

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (((3.13060547623 - (36.527041698806414 / z)) + (t / (z * z))) * (y / 1.0));
	double tmp;
	if (z < -6.499344996252632e+53) {
		tmp = t_1;
	} else if (z < 7.066965436914287e+59) {
		tmp = x + (y / ((((((((z + 15.234687407) * z) + 31.4690115749) * z) + 11.9400905721) * z) + 0.607771387771) / ((((((((z * 3.13060547623) + 11.1667541262) * z) + t) * z) + a) * z) + b)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

def code(x, y, z, t, a, b):
	t_1 = x + (((3.13060547623 - (36.527041698806414 / z)) + (t / (z * z))) * (y / 1.0))
	tmp = 0
	if z < -6.499344996252632e+53:
		tmp = t_1
	elif z < 7.066965436914287e+59:
		tmp = x + (y / ((((((((z + 15.234687407) * z) + 31.4690115749) * z) + 11.9400905721) * z) + 0.607771387771) / ((((((((z * 3.13060547623) + 11.1667541262) * z) + t) * z) + a) * z) + b)))
	else:
		tmp = t_1
	return tmp

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(Float64(Float64(3.13060547623 - Float64(36.527041698806414 / z)) + Float64(t / Float64(z * z))) * Float64(y / 1.0)))
	tmp = 0.0
	if (z < -6.499344996252632e+53)
		tmp = t_1;
	elseif (z < 7.066965436914287e+59)
		tmp = Float64(x + Float64(y / Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(z + 15.234687407) * z) + 31.4690115749) * z) + 11.9400905721) * z) + 0.607771387771) / Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(z * 3.13060547623) + 11.1667541262) * z) + t) * z) + a) * z) + b))));
	else
		tmp = t_1;
	end
	return tmp
end

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (((3.13060547623 - (36.527041698806414 / z)) + (t / (z * z))) * (y / 1.0));
	tmp = 0.0;
	if (z < -6.499344996252632e+53)
		tmp = t_1;
	elseif (z < 7.066965436914287e+59)
		tmp = x + (y / ((((((((z + 15.234687407) * z) + 31.4690115749) * z) + 11.9400905721) * z) + 0.607771387771) / ((((((((z * 3.13060547623) + 11.1667541262) * z) + t) * z) + a) * z) + b)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(N[(N[(3.13060547623 - N[(36.527041698806414 / z), $MachinePrecision]), $MachinePrecision] + N[(t / N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(y / 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[z, -6.499344996252632e+53], t$95$1, If[Less[z, 7.066965436914287e+59], N[(x + N[(y / N[(N[(N[(N[(N[(N[(N[(N[(z + 15.234687407), $MachinePrecision] * z), $MachinePrecision] + 31.4690115749), $MachinePrecision] * z), $MachinePrecision] + 11.9400905721), $MachinePrecision] * z), $MachinePrecision] + 0.607771387771), $MachinePrecision] / N[(N[(N[(N[(N[(N[(N[(N[(z * 3.13060547623), $MachinePrecision] + 11.1667541262), $MachinePrecision] * z), $MachinePrecision] + t), $MachinePrecision] * z), $MachinePrecision] + a), $MachinePrecision] * z), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

\begin{array}{l}

\\
\begin{array}{l}
t_1 := x + \left(\left(3.13060547623 - \frac{36.527041698806414}{z}\right) + \frac{t}{z \cdot z}\right) \cdot \frac{y}{1}\\
\mathbf{if}\;z < -6.499344996252632 \cdot 10^{+53}:\\
\;\;\;\;t_1\\

\mathbf{elif}\;z < 7.066965436914287 \cdot 10^{+59}:\\
\;\;\;\;x + \frac{y}{\frac{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771}{\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}\\

\mathbf{else}:\\
\;\;\;\;t_1\\


\end{array}
\end{array}

Reproduce

?
herbie shell --seed 2024008 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, D"
  :precision binary64

  :herbie-target
  (if (< z -6.499344996252632e+53) (+ x (* (+ (- 3.13060547623 (/ 36.527041698806414 z)) (/ t (* z z))) (/ y 1.0))) (if (< z 7.066965436914287e+59) (+ x (/ y (/ (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771) (+ (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z) b)))) (+ x (* (+ (- 3.13060547623 (/ 36.527041698806414 z)) (/ t (* z z))) (/ y 1.0)))))

  (+ x (/ (* y (+ (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z) b)) (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771))))