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

Percentage Accurate: 59.0% → 98.7%

Time: 28.9s

Alternatives: 24

Speedup: 2.2×

Specification

Math

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

FPCore

(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))))

C

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));
}

Fortran

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

Java

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));
}

Python

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))

Julia

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

MATLAB

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

Wolfram

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]

Initial Program: 59.0% accurate, 1.0× speedup

Math

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

FPCore

(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))))

C

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));
}

Fortran

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

Java

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));
}

Python

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))

Julia

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

MATLAB

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

Wolfram

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]

Alternative 1: 98.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+52}:\\ \;\;\;\;x + \left(3.13060547623 - \frac{36.52704169880642 - \frac{t + 457.9610022158428}{z}}{z}\right) \cdot y\\ \mathbf{elif}\;z \leq 1.26 \cdot 10^{+37}:\\ \;\;\;\;x + \frac{z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right) + b}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771} \cdot y\\ \mathbf{else}:\\ \;\;\;\;x + \left(3.13060547623 - \frac{36.52704169880642 - \frac{\left(t + 457.9610022158428\right) - \frac{-a}{z}}{z}}{z}\right) \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -6e+52)
   (+
    x
    (*
     (-
      3.13060547623
      (/ (- 36.52704169880642 (/ (+ t 457.9610022158428) z)) z))
     y))
   (if (<= z 1.26e+37)
     (+
      x
      (*
       (/
        (+
         (* z (+ (* z (+ (* z (+ (* z 3.13060547623) 11.1667541262)) t)) a))
         b)
        (+
         (*
          z
          (+ (* z (+ (* z (+ z 15.234687407)) 31.4690115749)) 11.9400905721))
         0.607771387771))
       y))
     (+
      x
      (*
       (-
        3.13060547623
        (/
         (- 36.52704169880642 (/ (- (+ t 457.9610022158428) (/ (- a) z)) z))
         z))
       y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -6e+52) {
		tmp = x + ((3.13060547623 - ((36.52704169880642 - ((t + 457.9610022158428) / z)) / z)) * y);
	} else if (z <= 1.26e+37) {
		tmp = x + ((((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)) * y);
	} else {
		tmp = x + ((3.13060547623 - ((36.52704169880642 - (((t + 457.9610022158428) - (-a / z)) / z)) / z)) * y);
	}
	return tmp;
}

Fortran

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 <= (-6d+52)) then
        tmp = x + ((3.13060547623d0 - ((36.52704169880642d0 - ((t + 457.9610022158428d0) / z)) / z)) * y)
    else if (z <= 1.26d+37) then
        tmp = x + ((((z * ((z * ((z * ((z * 3.13060547623d0) + 11.1667541262d0)) + t)) + a)) + b) / ((z * ((z * ((z * (z + 15.234687407d0)) + 31.4690115749d0)) + 11.9400905721d0)) + 0.607771387771d0)) * y)
    else
        tmp = x + ((3.13060547623d0 - ((36.52704169880642d0 - (((t + 457.9610022158428d0) - (-a / z)) / z)) / z)) * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -6e+52) {
		tmp = x + ((3.13060547623 - ((36.52704169880642 - ((t + 457.9610022158428) / z)) / z)) * y);
	} else if (z <= 1.26e+37) {
		tmp = x + ((((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)) * y);
	} else {
		tmp = x + ((3.13060547623 - ((36.52704169880642 - (((t + 457.9610022158428) - (-a / z)) / z)) / z)) * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -6e+52:
		tmp = x + ((3.13060547623 - ((36.52704169880642 - ((t + 457.9610022158428) / z)) / z)) * y)
	elif z <= 1.26e+37:
		tmp = x + ((((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)) * y)
	else:
		tmp = x + ((3.13060547623 - ((36.52704169880642 - (((t + 457.9610022158428) - (-a / z)) / z)) / z)) * y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -6e+52)
		tmp = Float64(x + Float64(Float64(3.13060547623 - Float64(Float64(36.52704169880642 - Float64(Float64(t + 457.9610022158428) / z)) / z)) * y));
	elseif (z <= 1.26e+37)
		tmp = Float64(x + Float64(Float64(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)) * y));
	else
		tmp = Float64(x + Float64(Float64(3.13060547623 - Float64(Float64(36.52704169880642 - Float64(Float64(Float64(t + 457.9610022158428) - Float64(Float64(-a) / z)) / z)) / z)) * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -6e+52)
		tmp = x + ((3.13060547623 - ((36.52704169880642 - ((t + 457.9610022158428) / z)) / z)) * y);
	elseif (z <= 1.26e+37)
		tmp = x + ((((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)) * y);
	else
		tmp = x + ((3.13060547623 - ((36.52704169880642 - (((t + 457.9610022158428) - (-a / z)) / z)) / z)) * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -6e+52], N[(x + N[(N[(3.13060547623 - N[(N[(36.52704169880642 - N[(N[(t + 457.9610022158428), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.26e+37], N[(x + N[(N[(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] / 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] * y), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(3.13060547623 - N[(N[(36.52704169880642 - N[(N[(N[(t + 457.9610022158428), $MachinePrecision] - N[((-a) / z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -6e52

   1. Initial program 4.5%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   2. Add Preprocessing

   4. Applied egg-rr 0

      \[\leadsto expr\]

   5. Taylor expanded in z around -inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if -6e52 < z < 1.26e37

   1. Initial program 98.3%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   2. Add Preprocessing

   4. Applied egg-rr 0

      \[\leadsto expr\]

   if 1.26e37 < z

   1. Initial program 8.1%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   2. Add Preprocessing

   4. Applied egg-rr 0

      \[\leadsto expr\]

   5. Taylor expanded in z around -inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in a around inf 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 2: 98.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+41}:\\ \;\;\;\;x + \left(3.13060547623 - \frac{36.52704169880642 - \frac{t + 457.9610022158428}{z}}{z}\right) \cdot y\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+36}:\\ \;\;\;\;x + \left(z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right) + b\right) \cdot \frac{y}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}\\ \mathbf{else}:\\ \;\;\;\;x + \left(3.13060547623 - \frac{36.52704169880642 - \frac{\left(t + 457.9610022158428\right) - \frac{-a}{z}}{z}}{z}\right) \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -6.8e+41)
   (+
    x
    (*
     (-
      3.13060547623
      (/ (- 36.52704169880642 (/ (+ t 457.9610022158428) z)) z))
     y))
   (if (<= z 8.5e+36)
     (+
      x
      (*
       (+
        (* z (+ (* z (+ (* z (+ (* z 3.13060547623) 11.1667541262)) t)) a))
        b)
       (/
        y
        (+
         (*
          z
          (+ (* z (+ (* z (+ z 15.234687407)) 31.4690115749)) 11.9400905721))
         0.607771387771))))
     (+
      x
      (*
       (-
        3.13060547623
        (/
         (- 36.52704169880642 (/ (- (+ t 457.9610022158428) (/ (- a) z)) z))
         z))
       y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -6.8e+41) {
		tmp = x + ((3.13060547623 - ((36.52704169880642 - ((t + 457.9610022158428) / z)) / z)) * y);
	} else if (z <= 8.5e+36) {
		tmp = x + (((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b) * (y / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)));
	} else {
		tmp = x + ((3.13060547623 - ((36.52704169880642 - (((t + 457.9610022158428) - (-a / z)) / z)) / z)) * y);
	}
	return tmp;
}

Fortran

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 <= (-6.8d+41)) then
        tmp = x + ((3.13060547623d0 - ((36.52704169880642d0 - ((t + 457.9610022158428d0) / z)) / z)) * y)
    else if (z <= 8.5d+36) then
        tmp = x + (((z * ((z * ((z * ((z * 3.13060547623d0) + 11.1667541262d0)) + t)) + a)) + b) * (y / ((z * ((z * ((z * (z + 15.234687407d0)) + 31.4690115749d0)) + 11.9400905721d0)) + 0.607771387771d0)))
    else
        tmp = x + ((3.13060547623d0 - ((36.52704169880642d0 - (((t + 457.9610022158428d0) - (-a / z)) / z)) / z)) * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -6.8e+41) {
		tmp = x + ((3.13060547623 - ((36.52704169880642 - ((t + 457.9610022158428) / z)) / z)) * y);
	} else if (z <= 8.5e+36) {
		tmp = x + (((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b) * (y / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)));
	} else {
		tmp = x + ((3.13060547623 - ((36.52704169880642 - (((t + 457.9610022158428) - (-a / z)) / z)) / z)) * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -6.8e+41:
		tmp = x + ((3.13060547623 - ((36.52704169880642 - ((t + 457.9610022158428) / z)) / z)) * y)
	elif z <= 8.5e+36:
		tmp = x + (((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b) * (y / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)))
	else:
		tmp = x + ((3.13060547623 - ((36.52704169880642 - (((t + 457.9610022158428) - (-a / z)) / z)) / z)) * y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -6.8e+41)
		tmp = Float64(x + Float64(Float64(3.13060547623 - Float64(Float64(36.52704169880642 - Float64(Float64(t + 457.9610022158428) / z)) / z)) * y));
	elseif (z <= 8.5e+36)
		tmp = Float64(x + Float64(Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(Float64(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))));
	else
		tmp = Float64(x + Float64(Float64(3.13060547623 - Float64(Float64(36.52704169880642 - Float64(Float64(Float64(t + 457.9610022158428) - Float64(Float64(-a) / z)) / z)) / z)) * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -6.8e+41)
		tmp = x + ((3.13060547623 - ((36.52704169880642 - ((t + 457.9610022158428) / z)) / z)) * y);
	elseif (z <= 8.5e+36)
		tmp = x + (((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b) * (y / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)));
	else
		tmp = x + ((3.13060547623 - ((36.52704169880642 - (((t + 457.9610022158428) - (-a / z)) / z)) / z)) * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -6.8e+41], N[(x + N[(N[(3.13060547623 - N[(N[(36.52704169880642 - N[(N[(t + 457.9610022158428), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.5e+36], N[(x + N[(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] * 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], N[(x + N[(N[(3.13060547623 - N[(N[(36.52704169880642 - N[(N[(N[(t + 457.9610022158428), $MachinePrecision] - N[((-a) / z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.79999999999999996e41

   1. Initial program 10.0%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   2. Add Preprocessing

   4. Applied egg-rr 0

      \[\leadsto expr\]

   5. Taylor expanded in z around -inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if -6.79999999999999996e41 < z < 8.50000000000000014e36

   1. Initial program 98.3%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   2. Add Preprocessing

   4. Applied egg-rr 0

      \[\leadsto expr\]

   if 8.50000000000000014e36 < z

   1. Initial program 8.1%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   2. Add Preprocessing

   4. Applied egg-rr 0

      \[\leadsto expr\]

   5. Taylor expanded in z around -inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in a around inf 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 3: 97.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+52}:\\ \;\;\;\;x + \left(3.13060547623 - \frac{36.52704169880642 - \frac{t + 457.9610022158428}{z}}{z}\right) \cdot y\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+36}:\\ \;\;\;\;\frac{y}{\frac{1}{\frac{b + z \cdot \left(a + z \cdot t\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}}} + x\\ \mathbf{else}:\\ \;\;\;\;x + \left(3.13060547623 - \frac{36.52704169880642 - \frac{\left(t + 457.9610022158428\right) - \frac{-a}{z}}{z}}{z}\right) \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -3.1e+52)
   (+
    x
    (*
     (-
      3.13060547623
      (/ (- 36.52704169880642 (/ (+ t 457.9610022158428) z)) z))
     y))
   (if (<= z 6.8e+36)
     (+
      (/
       y
       (/
        1.0
        (/
         (+ b (* z (+ a (* z t))))
         (+
          (*
           z
           (+ (* z (+ (* z (+ z 15.234687407)) 31.4690115749)) 11.9400905721))
          0.607771387771))))
      x)
     (+
      x
      (*
       (-
        3.13060547623
        (/
         (- 36.52704169880642 (/ (- (+ t 457.9610022158428) (/ (- a) z)) z))
         z))
       y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -3.1e+52) {
		tmp = x + ((3.13060547623 - ((36.52704169880642 - ((t + 457.9610022158428) / z)) / z)) * y);
	} else if (z <= 6.8e+36) {
		tmp = (y / (1.0 / ((b + (z * (a + (z * t)))) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)))) + x;
	} else {
		tmp = x + ((3.13060547623 - ((36.52704169880642 - (((t + 457.9610022158428) - (-a / z)) / z)) / z)) * y);
	}
	return tmp;
}

Fortran

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 <= (-3.1d+52)) then
        tmp = x + ((3.13060547623d0 - ((36.52704169880642d0 - ((t + 457.9610022158428d0) / z)) / z)) * y)
    else if (z <= 6.8d+36) then
        tmp = (y / (1.0d0 / ((b + (z * (a + (z * t)))) / ((z * ((z * ((z * (z + 15.234687407d0)) + 31.4690115749d0)) + 11.9400905721d0)) + 0.607771387771d0)))) + x
    else
        tmp = x + ((3.13060547623d0 - ((36.52704169880642d0 - (((t + 457.9610022158428d0) - (-a / z)) / z)) / z)) * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -3.1e+52) {
		tmp = x + ((3.13060547623 - ((36.52704169880642 - ((t + 457.9610022158428) / z)) / z)) * y);
	} else if (z <= 6.8e+36) {
		tmp = (y / (1.0 / ((b + (z * (a + (z * t)))) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)))) + x;
	} else {
		tmp = x + ((3.13060547623 - ((36.52704169880642 - (((t + 457.9610022158428) - (-a / z)) / z)) / z)) * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -3.1e+52:
		tmp = x + ((3.13060547623 - ((36.52704169880642 - ((t + 457.9610022158428) / z)) / z)) * y)
	elif z <= 6.8e+36:
		tmp = (y / (1.0 / ((b + (z * (a + (z * t)))) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)))) + x
	else:
		tmp = x + ((3.13060547623 - ((36.52704169880642 - (((t + 457.9610022158428) - (-a / z)) / z)) / z)) * y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -3.1e+52)
		tmp = Float64(x + Float64(Float64(3.13060547623 - Float64(Float64(36.52704169880642 - Float64(Float64(t + 457.9610022158428) / z)) / z)) * y));
	elseif (z <= 6.8e+36)
		tmp = Float64(Float64(y / Float64(1.0 / Float64(Float64(b + Float64(z * Float64(a + Float64(z * t)))) / Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)))) + x);
	else
		tmp = Float64(x + Float64(Float64(3.13060547623 - Float64(Float64(36.52704169880642 - Float64(Float64(Float64(t + 457.9610022158428) - Float64(Float64(-a) / z)) / z)) / z)) * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -3.1e+52)
		tmp = x + ((3.13060547623 - ((36.52704169880642 - ((t + 457.9610022158428) / z)) / z)) * y);
	elseif (z <= 6.8e+36)
		tmp = (y / (1.0 / ((b + (z * (a + (z * t)))) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)))) + x;
	else
		tmp = x + ((3.13060547623 - ((36.52704169880642 - (((t + 457.9610022158428) - (-a / z)) / z)) / z)) * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -3.1e+52], N[(x + N[(N[(3.13060547623 - N[(N[(36.52704169880642 - N[(N[(t + 457.9610022158428), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.8e+36], N[(N[(y / N[(1.0 / N[(N[(b + N[(z * N[(a + N[(z * t), $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]), $MachinePrecision] + x), $MachinePrecision], N[(x + N[(N[(3.13060547623 - N[(N[(36.52704169880642 - N[(N[(N[(t + 457.9610022158428), $MachinePrecision] - N[((-a) / z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.1e52

   1. Initial program 4.5%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   2. Add Preprocessing

   4. Applied egg-rr 0

      \[\leadsto expr\]

   5. Taylor expanded in z around -inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if -3.1e52 < z < 6.7999999999999996e36

   1. Initial program 98.3%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   2. Add Preprocessing

   4. Applied egg-rr 0

      \[\leadsto expr\]

   5. Taylor expanded in z around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]

   if 6.7999999999999996e36 < z

   1. Initial program 8.1%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   2. Add Preprocessing

   4. Applied egg-rr 0

      \[\leadsto expr\]

   5. Taylor expanded in z around -inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in a around inf 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 4: 97.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+52}:\\ \;\;\;\;x + \left(3.13060547623 - \frac{36.52704169880642 - \frac{t + 457.9610022158428}{z}}{z}\right) \cdot y\\ \mathbf{elif}\;z \leq 8.4 \cdot 10^{+36}:\\ \;\;\;\;\frac{y}{\frac{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}{b + z \cdot \left(a + z \cdot t\right)}} + x\\ \mathbf{else}:\\ \;\;\;\;x + \left(3.13060547623 - \frac{36.52704169880642 - \frac{\left(t + 457.9610022158428\right) - \frac{-a}{z}}{z}}{z}\right) \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -3.2e+52)
   (+
    x
    (*
     (-
      3.13060547623
      (/ (- 36.52704169880642 (/ (+ t 457.9610022158428) z)) z))
     y))
   (if (<= z 8.4e+36)
     (+
      (/
       y
       (/
        (+
         (*
          z
          (+ (* z (+ (* z (+ z 15.234687407)) 31.4690115749)) 11.9400905721))
         0.607771387771)
        (+ b (* z (+ a (* z t))))))
      x)
     (+
      x
      (*
       (-
        3.13060547623
        (/
         (- 36.52704169880642 (/ (- (+ t 457.9610022158428) (/ (- a) z)) z))
         z))
       y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -3.2e+52) {
		tmp = x + ((3.13060547623 - ((36.52704169880642 - ((t + 457.9610022158428) / z)) / z)) * y);
	} else if (z <= 8.4e+36) {
		tmp = (y / (((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771) / (b + (z * (a + (z * t)))))) + x;
	} else {
		tmp = x + ((3.13060547623 - ((36.52704169880642 - (((t + 457.9610022158428) - (-a / z)) / z)) / z)) * y);
	}
	return tmp;
}

Fortran

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 <= (-3.2d+52)) then
        tmp = x + ((3.13060547623d0 - ((36.52704169880642d0 - ((t + 457.9610022158428d0) / z)) / z)) * y)
    else if (z <= 8.4d+36) then
        tmp = (y / (((z * ((z * ((z * (z + 15.234687407d0)) + 31.4690115749d0)) + 11.9400905721d0)) + 0.607771387771d0) / (b + (z * (a + (z * t)))))) + x
    else
        tmp = x + ((3.13060547623d0 - ((36.52704169880642d0 - (((t + 457.9610022158428d0) - (-a / z)) / z)) / z)) * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -3.2e+52) {
		tmp = x + ((3.13060547623 - ((36.52704169880642 - ((t + 457.9610022158428) / z)) / z)) * y);
	} else if (z <= 8.4e+36) {
		tmp = (y / (((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771) / (b + (z * (a + (z * t)))))) + x;
	} else {
		tmp = x + ((3.13060547623 - ((36.52704169880642 - (((t + 457.9610022158428) - (-a / z)) / z)) / z)) * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -3.2e+52:
		tmp = x + ((3.13060547623 - ((36.52704169880642 - ((t + 457.9610022158428) / z)) / z)) * y)
	elif z <= 8.4e+36:
		tmp = (y / (((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771) / (b + (z * (a + (z * t)))))) + x
	else:
		tmp = x + ((3.13060547623 - ((36.52704169880642 - (((t + 457.9610022158428) - (-a / z)) / z)) / z)) * y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -3.2e+52)
		tmp = Float64(x + Float64(Float64(3.13060547623 - Float64(Float64(36.52704169880642 - Float64(Float64(t + 457.9610022158428) / z)) / z)) * y));
	elseif (z <= 8.4e+36)
		tmp = Float64(Float64(y / Float64(Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771) / Float64(b + Float64(z * Float64(a + Float64(z * t)))))) + x);
	else
		tmp = Float64(x + Float64(Float64(3.13060547623 - Float64(Float64(36.52704169880642 - Float64(Float64(Float64(t + 457.9610022158428) - Float64(Float64(-a) / z)) / z)) / z)) * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -3.2e+52)
		tmp = x + ((3.13060547623 - ((36.52704169880642 - ((t + 457.9610022158428) / z)) / z)) * y);
	elseif (z <= 8.4e+36)
		tmp = (y / (((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771) / (b + (z * (a + (z * t)))))) + x;
	else
		tmp = x + ((3.13060547623 - ((36.52704169880642 - (((t + 457.9610022158428) - (-a / z)) / z)) / z)) * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -3.2e+52], N[(x + N[(N[(3.13060547623 - N[(N[(36.52704169880642 - N[(N[(t + 457.9610022158428), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.4e+36], N[(N[(y / N[(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] / N[(b + N[(z * N[(a + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(x + N[(N[(3.13060547623 - N[(N[(36.52704169880642 - N[(N[(N[(t + 457.9610022158428), $MachinePrecision] - N[((-a) / z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.2e52

   1. Initial program 4.5%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   2. Add Preprocessing

   4. Applied egg-rr 0

      \[\leadsto expr\]

   5. Taylor expanded in z around -inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if -3.2e52 < z < 8.40000000000000018e36

   1. Initial program 98.3%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   2. Add Preprocessing

   4. Applied egg-rr 0

      \[\leadsto expr\]

   5. Taylor expanded in z around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if 8.40000000000000018e36 < z

   1. Initial program 8.1%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   2. Add Preprocessing

   4. Applied egg-rr 0

      \[\leadsto expr\]

   5. Taylor expanded in z around -inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in a around inf 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 5: 98.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(3.13060547623 - \frac{36.52704169880642 - \frac{\left(t + 457.9610022158428\right) - \frac{-a}{z}}{z}}{z}\right) \cdot y\\ \mathbf{if}\;z \leq -5.5 \cdot 10^{+24}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+36}:\\ \;\;\;\;\frac{y}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771} \cdot \left(b + z \cdot \left(a + z \cdot t\right)\right) + x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (+
          x
          (*
           (-
            3.13060547623
            (/
             (-
              36.52704169880642
              (/ (- (+ t 457.9610022158428) (/ (- a) z)) z))
             z))
           y))))
   (if (<= z -5.5e+24)
     t_1
     (if (<= z 8.5e+36)
       (+
        (*
         (/
          y
          (+
           (*
            z
            (+ (* z (+ (* z (+ z 15.234687407)) 31.4690115749)) 11.9400905721))
           0.607771387771))
         (+ b (* z (+ a (* z t)))))
        x)
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + ((3.13060547623 - ((36.52704169880642 - (((t + 457.9610022158428) - (-a / z)) / z)) / z)) * y);
	double tmp;
	if (z <= -5.5e+24) {
		tmp = t_1;
	} else if (z <= 8.5e+36) {
		tmp = ((y / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)) * (b + (z * (a + (z * t))))) + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

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 - ((36.52704169880642d0 - (((t + 457.9610022158428d0) - (-a / z)) / z)) / z)) * y)
    if (z <= (-5.5d+24)) then
        tmp = t_1
    else if (z <= 8.5d+36) then
        tmp = ((y / ((z * ((z * ((z * (z + 15.234687407d0)) + 31.4690115749d0)) + 11.9400905721d0)) + 0.607771387771d0)) * (b + (z * (a + (z * t))))) + x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + ((3.13060547623 - ((36.52704169880642 - (((t + 457.9610022158428) - (-a / z)) / z)) / z)) * y);
	double tmp;
	if (z <= -5.5e+24) {
		tmp = t_1;
	} else if (z <= 8.5e+36) {
		tmp = ((y / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)) * (b + (z * (a + (z * t))))) + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + ((3.13060547623 - ((36.52704169880642 - (((t + 457.9610022158428) - (-a / z)) / z)) / z)) * y)
	tmp = 0
	if z <= -5.5e+24:
		tmp = t_1
	elif z <= 8.5e+36:
		tmp = ((y / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)) * (b + (z * (a + (z * t))))) + x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(Float64(3.13060547623 - Float64(Float64(36.52704169880642 - Float64(Float64(Float64(t + 457.9610022158428) - Float64(Float64(-a) / z)) / z)) / z)) * y))
	tmp = 0.0
	if (z <= -5.5e+24)
		tmp = t_1;
	elseif (z <= 8.5e+36)
		tmp = Float64(Float64(Float64(y / Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)) * Float64(b + Float64(z * Float64(a + Float64(z * t))))) + x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + ((3.13060547623 - ((36.52704169880642 - (((t + 457.9610022158428) - (-a / z)) / z)) / z)) * y);
	tmp = 0.0;
	if (z <= -5.5e+24)
		tmp = t_1;
	elseif (z <= 8.5e+36)
		tmp = ((y / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)) * (b + (z * (a + (z * t))))) + x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(N[(3.13060547623 - N[(N[(36.52704169880642 - N[(N[(N[(t + 457.9610022158428), $MachinePrecision] - N[((-a) / z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.5e+24], t$95$1, If[LessEqual[z, 8.5e+36], N[(N[(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] * N[(b + N[(z * N[(a + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.5000000000000002e24 or 8.50000000000000014e36 < z

   1. Initial program 12.4%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   2. Add Preprocessing

   4. Applied egg-rr 0

      \[\leadsto expr\]

   5. Taylor expanded in z around -inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in a around inf 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   if -5.5000000000000002e24 < z < 8.50000000000000014e36

   1. Initial program 98.3%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   2. Add Preprocessing

   4. Applied egg-rr 0

      \[\leadsto expr\]

   5. Taylor expanded in z around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 97.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -135000000000:\\ \;\;\;\;x + \left(3.13060547623 - \frac{36.52704169880642 - \frac{\left(t + 457.9610022158428\right) - \frac{-a}{z}}{z}}{z}\right) \cdot y\\ \mathbf{elif}\;z \leq 44:\\ \;\;\;\;x + \frac{1}{0.607771387771 + z \cdot 11.9400905721} \cdot \left(y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(3.13060547623 - \frac{36.52704169880642 - \frac{\left(t + 457.9610022158428\right) - \frac{\left(\left(0 - a\right) + -1112.0901850848957\right) + \left(15.234687407 \cdot t + 6976.8927133548\right)}{z}}{z}}{z}\right) \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -135000000000.0)
   (+
    x
    (*
     (-
      3.13060547623
      (/
       (- 36.52704169880642 (/ (- (+ t 457.9610022158428) (/ (- a) z)) z))
       z))
     y))
   (if (<= z 44.0)
     (+
      x
      (*
       (/ 1.0 (+ 0.607771387771 (* z 11.9400905721)))
       (*
        y
        (+
         b
         (*
          z
          (+ a (* z (+ t (* z (+ (* z 3.13060547623) 11.1667541262))))))))))
     (+
      x
      (*
       (-
        3.13060547623
        (/
         (-
          36.52704169880642
          (/
           (-
            (+ t 457.9610022158428)
            (/
             (+
              (+ (- 0.0 a) -1112.0901850848957)
              (+ (* 15.234687407 t) 6976.8927133548))
             z))
           z))
         z))
       y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -135000000000.0) {
		tmp = x + ((3.13060547623 - ((36.52704169880642 - (((t + 457.9610022158428) - (-a / z)) / z)) / z)) * y);
	} else if (z <= 44.0) {
		tmp = x + ((1.0 / (0.607771387771 + (z * 11.9400905721))) * (y * (b + (z * (a + (z * (t + (z * ((z * 3.13060547623) + 11.1667541262)))))))));
	} else {
		tmp = x + ((3.13060547623 - ((36.52704169880642 - (((t + 457.9610022158428) - ((((0.0 - a) + -1112.0901850848957) + ((15.234687407 * t) + 6976.8927133548)) / z)) / z)) / z)) * y);
	}
	return tmp;
}

Fortran

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 <= (-135000000000.0d0)) then
        tmp = x + ((3.13060547623d0 - ((36.52704169880642d0 - (((t + 457.9610022158428d0) - (-a / z)) / z)) / z)) * y)
    else if (z <= 44.0d0) then
        tmp = x + ((1.0d0 / (0.607771387771d0 + (z * 11.9400905721d0))) * (y * (b + (z * (a + (z * (t + (z * ((z * 3.13060547623d0) + 11.1667541262d0)))))))))
    else
        tmp = x + ((3.13060547623d0 - ((36.52704169880642d0 - (((t + 457.9610022158428d0) - ((((0.0d0 - a) + (-1112.0901850848957d0)) + ((15.234687407d0 * t) + 6976.8927133548d0)) / z)) / z)) / z)) * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -135000000000.0) {
		tmp = x + ((3.13060547623 - ((36.52704169880642 - (((t + 457.9610022158428) - (-a / z)) / z)) / z)) * y);
	} else if (z <= 44.0) {
		tmp = x + ((1.0 / (0.607771387771 + (z * 11.9400905721))) * (y * (b + (z * (a + (z * (t + (z * ((z * 3.13060547623) + 11.1667541262)))))))));
	} else {
		tmp = x + ((3.13060547623 - ((36.52704169880642 - (((t + 457.9610022158428) - ((((0.0 - a) + -1112.0901850848957) + ((15.234687407 * t) + 6976.8927133548)) / z)) / z)) / z)) * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -135000000000.0:
		tmp = x + ((3.13060547623 - ((36.52704169880642 - (((t + 457.9610022158428) - (-a / z)) / z)) / z)) * y)
	elif z <= 44.0:
		tmp = x + ((1.0 / (0.607771387771 + (z * 11.9400905721))) * (y * (b + (z * (a + (z * (t + (z * ((z * 3.13060547623) + 11.1667541262)))))))))
	else:
		tmp = x + ((3.13060547623 - ((36.52704169880642 - (((t + 457.9610022158428) - ((((0.0 - a) + -1112.0901850848957) + ((15.234687407 * t) + 6976.8927133548)) / z)) / z)) / z)) * y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -135000000000.0)
		tmp = Float64(x + Float64(Float64(3.13060547623 - Float64(Float64(36.52704169880642 - Float64(Float64(Float64(t + 457.9610022158428) - Float64(Float64(-a) / z)) / z)) / z)) * y));
	elseif (z <= 44.0)
		tmp = Float64(x + Float64(Float64(1.0 / Float64(0.607771387771 + Float64(z * 11.9400905721))) * Float64(y * Float64(b + Float64(z * Float64(a + Float64(z * Float64(t + Float64(z * Float64(Float64(z * 3.13060547623) + 11.1667541262))))))))));
	else
		tmp = Float64(x + Float64(Float64(3.13060547623 - Float64(Float64(36.52704169880642 - Float64(Float64(Float64(t + 457.9610022158428) - Float64(Float64(Float64(Float64(0.0 - a) + -1112.0901850848957) + Float64(Float64(15.234687407 * t) + 6976.8927133548)) / z)) / z)) / z)) * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -135000000000.0)
		tmp = x + ((3.13060547623 - ((36.52704169880642 - (((t + 457.9610022158428) - (-a / z)) / z)) / z)) * y);
	elseif (z <= 44.0)
		tmp = x + ((1.0 / (0.607771387771 + (z * 11.9400905721))) * (y * (b + (z * (a + (z * (t + (z * ((z * 3.13060547623) + 11.1667541262)))))))));
	else
		tmp = x + ((3.13060547623 - ((36.52704169880642 - (((t + 457.9610022158428) - ((((0.0 - a) + -1112.0901850848957) + ((15.234687407 * t) + 6976.8927133548)) / z)) / z)) / z)) * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -135000000000.0], N[(x + N[(N[(3.13060547623 - N[(N[(36.52704169880642 - N[(N[(N[(t + 457.9610022158428), $MachinePrecision] - N[((-a) / z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 44.0], N[(x + N[(N[(1.0 / N[(0.607771387771 + N[(z * 11.9400905721), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(y * N[(b + N[(z * N[(a + N[(z * N[(t + N[(z * N[(N[(z * 3.13060547623), $MachinePrecision] + 11.1667541262), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(3.13060547623 - N[(N[(36.52704169880642 - N[(N[(N[(t + 457.9610022158428), $MachinePrecision] - N[(N[(N[(N[(0.0 - a), $MachinePrecision] + -1112.0901850848957), $MachinePrecision] + N[(N[(15.234687407 * t), $MachinePrecision] + 6976.8927133548), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.35e11

   1. Initial program 17.9%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   2. Add Preprocessing

   4. Applied egg-rr 0

      \[\leadsto expr\]

   5. Taylor expanded in z around -inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in a around inf 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   if -1.35e11 < z < 44

   1. Initial program 99.5%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]

   if 44 < z

   1. Initial program 17.0%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   2. Add Preprocessing

   4. Applied egg-rr 0

      \[\leadsto expr\]

   5. Taylor expanded in z around -inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 7: 97.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -135000000000:\\ \;\;\;\;x + \left(3.13060547623 - \frac{36.52704169880642 - \frac{\left(t + 457.9610022158428\right) - \frac{-a}{z}}{z}}{z}\right) \cdot y\\ \mathbf{elif}\;z \leq 22:\\ \;\;\;\;\left(b + z \cdot \left(a + z \cdot \left(t + z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right)\right)\right)\right) \cdot \frac{y}{0.607771387771 + z \cdot 11.9400905721} + x\\ \mathbf{else}:\\ \;\;\;\;x + \left(3.13060547623 - \frac{36.52704169880642 - \frac{\left(t + 457.9610022158428\right) - \frac{\left(\left(0 - a\right) + -1112.0901850848957\right) + \left(15.234687407 \cdot t + 6976.8927133548\right)}{z}}{z}}{z}\right) \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -135000000000.0)
   (+
    x
    (*
     (-
      3.13060547623
      (/
       (- 36.52704169880642 (/ (- (+ t 457.9610022158428) (/ (- a) z)) z))
       z))
     y))
   (if (<= z 22.0)
     (+
      (*
       (+
        b
        (* z (+ a (* z (+ t (* z (+ (* z 3.13060547623) 11.1667541262)))))))
       (/ y (+ 0.607771387771 (* z 11.9400905721))))
      x)
     (+
      x
      (*
       (-
        3.13060547623
        (/
         (-
          36.52704169880642
          (/
           (-
            (+ t 457.9610022158428)
            (/
             (+
              (+ (- 0.0 a) -1112.0901850848957)
              (+ (* 15.234687407 t) 6976.8927133548))
             z))
           z))
         z))
       y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -135000000000.0) {
		tmp = x + ((3.13060547623 - ((36.52704169880642 - (((t + 457.9610022158428) - (-a / z)) / z)) / z)) * y);
	} else if (z <= 22.0) {
		tmp = ((b + (z * (a + (z * (t + (z * ((z * 3.13060547623) + 11.1667541262))))))) * (y / (0.607771387771 + (z * 11.9400905721)))) + x;
	} else {
		tmp = x + ((3.13060547623 - ((36.52704169880642 - (((t + 457.9610022158428) - ((((0.0 - a) + -1112.0901850848957) + ((15.234687407 * t) + 6976.8927133548)) / z)) / z)) / z)) * y);
	}
	return tmp;
}

Fortran

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 <= (-135000000000.0d0)) then
        tmp = x + ((3.13060547623d0 - ((36.52704169880642d0 - (((t + 457.9610022158428d0) - (-a / z)) / z)) / z)) * y)
    else if (z <= 22.0d0) then
        tmp = ((b + (z * (a + (z * (t + (z * ((z * 3.13060547623d0) + 11.1667541262d0))))))) * (y / (0.607771387771d0 + (z * 11.9400905721d0)))) + x
    else
        tmp = x + ((3.13060547623d0 - ((36.52704169880642d0 - (((t + 457.9610022158428d0) - ((((0.0d0 - a) + (-1112.0901850848957d0)) + ((15.234687407d0 * t) + 6976.8927133548d0)) / z)) / z)) / z)) * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -135000000000.0) {
		tmp = x + ((3.13060547623 - ((36.52704169880642 - (((t + 457.9610022158428) - (-a / z)) / z)) / z)) * y);
	} else if (z <= 22.0) {
		tmp = ((b + (z * (a + (z * (t + (z * ((z * 3.13060547623) + 11.1667541262))))))) * (y / (0.607771387771 + (z * 11.9400905721)))) + x;
	} else {
		tmp = x + ((3.13060547623 - ((36.52704169880642 - (((t + 457.9610022158428) - ((((0.0 - a) + -1112.0901850848957) + ((15.234687407 * t) + 6976.8927133548)) / z)) / z)) / z)) * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -135000000000.0:
		tmp = x + ((3.13060547623 - ((36.52704169880642 - (((t + 457.9610022158428) - (-a / z)) / z)) / z)) * y)
	elif z <= 22.0:
		tmp = ((b + (z * (a + (z * (t + (z * ((z * 3.13060547623) + 11.1667541262))))))) * (y / (0.607771387771 + (z * 11.9400905721)))) + x
	else:
		tmp = x + ((3.13060547623 - ((36.52704169880642 - (((t + 457.9610022158428) - ((((0.0 - a) + -1112.0901850848957) + ((15.234687407 * t) + 6976.8927133548)) / z)) / z)) / z)) * y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -135000000000.0)
		tmp = Float64(x + Float64(Float64(3.13060547623 - Float64(Float64(36.52704169880642 - Float64(Float64(Float64(t + 457.9610022158428) - Float64(Float64(-a) / z)) / z)) / z)) * y));
	elseif (z <= 22.0)
		tmp = Float64(Float64(Float64(b + Float64(z * Float64(a + Float64(z * Float64(t + Float64(z * Float64(Float64(z * 3.13060547623) + 11.1667541262))))))) * Float64(y / Float64(0.607771387771 + Float64(z * 11.9400905721)))) + x);
	else
		tmp = Float64(x + Float64(Float64(3.13060547623 - Float64(Float64(36.52704169880642 - Float64(Float64(Float64(t + 457.9610022158428) - Float64(Float64(Float64(Float64(0.0 - a) + -1112.0901850848957) + Float64(Float64(15.234687407 * t) + 6976.8927133548)) / z)) / z)) / z)) * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -135000000000.0)
		tmp = x + ((3.13060547623 - ((36.52704169880642 - (((t + 457.9610022158428) - (-a / z)) / z)) / z)) * y);
	elseif (z <= 22.0)
		tmp = ((b + (z * (a + (z * (t + (z * ((z * 3.13060547623) + 11.1667541262))))))) * (y / (0.607771387771 + (z * 11.9400905721)))) + x;
	else
		tmp = x + ((3.13060547623 - ((36.52704169880642 - (((t + 457.9610022158428) - ((((0.0 - a) + -1112.0901850848957) + ((15.234687407 * t) + 6976.8927133548)) / z)) / z)) / z)) * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -135000000000.0], N[(x + N[(N[(3.13060547623 - N[(N[(36.52704169880642 - N[(N[(N[(t + 457.9610022158428), $MachinePrecision] - N[((-a) / z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 22.0], N[(N[(N[(b + N[(z * N[(a + N[(z * N[(t + N[(z * N[(N[(z * 3.13060547623), $MachinePrecision] + 11.1667541262), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(y / N[(0.607771387771 + N[(z * 11.9400905721), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(x + N[(N[(3.13060547623 - N[(N[(36.52704169880642 - N[(N[(N[(t + 457.9610022158428), $MachinePrecision] - N[(N[(N[(N[(0.0 - a), $MachinePrecision] + -1112.0901850848957), $MachinePrecision] + N[(N[(15.234687407 * t), $MachinePrecision] + 6976.8927133548), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.35e11

   1. Initial program 17.9%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   2. Add Preprocessing

   4. Applied egg-rr 0

      \[\leadsto expr\]

   5. Taylor expanded in z around -inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in a around inf 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   if -1.35e11 < z < 22

   1. Initial program 99.5%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]

   if 22 < z

   1. Initial program 17.0%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   2. Add Preprocessing

   4. Applied egg-rr 0

      \[\leadsto expr\]

   5. Taylor expanded in z around -inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 8: 97.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(3.13060547623 - \frac{36.52704169880642 - \frac{\left(t + 457.9610022158428\right) - \frac{-a}{z}}{z}}{z}\right) \cdot y\\ \mathbf{if}\;z \leq -135000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.2:\\ \;\;\;\;\left(b + z \cdot \left(a + z \cdot \left(t + z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right)\right)\right)\right) \cdot \frac{y}{0.607771387771 + z \cdot 11.9400905721} + x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (+
          x
          (*
           (-
            3.13060547623
            (/
             (-
              36.52704169880642
              (/ (- (+ t 457.9610022158428) (/ (- a) z)) z))
             z))
           y))))
   (if (<= z -135000000000.0)
     t_1
     (if (<= z 3.2)
       (+
        (*
         (+
          b
          (* z (+ a (* z (+ t (* z (+ (* z 3.13060547623) 11.1667541262)))))))
         (/ y (+ 0.607771387771 (* z 11.9400905721))))
        x)
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + ((3.13060547623 - ((36.52704169880642 - (((t + 457.9610022158428) - (-a / z)) / z)) / z)) * y);
	double tmp;
	if (z <= -135000000000.0) {
		tmp = t_1;
	} else if (z <= 3.2) {
		tmp = ((b + (z * (a + (z * (t + (z * ((z * 3.13060547623) + 11.1667541262))))))) * (y / (0.607771387771 + (z * 11.9400905721)))) + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

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 - ((36.52704169880642d0 - (((t + 457.9610022158428d0) - (-a / z)) / z)) / z)) * y)
    if (z <= (-135000000000.0d0)) then
        tmp = t_1
    else if (z <= 3.2d0) then
        tmp = ((b + (z * (a + (z * (t + (z * ((z * 3.13060547623d0) + 11.1667541262d0))))))) * (y / (0.607771387771d0 + (z * 11.9400905721d0)))) + x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + ((3.13060547623 - ((36.52704169880642 - (((t + 457.9610022158428) - (-a / z)) / z)) / z)) * y);
	double tmp;
	if (z <= -135000000000.0) {
		tmp = t_1;
	} else if (z <= 3.2) {
		tmp = ((b + (z * (a + (z * (t + (z * ((z * 3.13060547623) + 11.1667541262))))))) * (y / (0.607771387771 + (z * 11.9400905721)))) + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + ((3.13060547623 - ((36.52704169880642 - (((t + 457.9610022158428) - (-a / z)) / z)) / z)) * y)
	tmp = 0
	if z <= -135000000000.0:
		tmp = t_1
	elif z <= 3.2:
		tmp = ((b + (z * (a + (z * (t + (z * ((z * 3.13060547623) + 11.1667541262))))))) * (y / (0.607771387771 + (z * 11.9400905721)))) + x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(Float64(3.13060547623 - Float64(Float64(36.52704169880642 - Float64(Float64(Float64(t + 457.9610022158428) - Float64(Float64(-a) / z)) / z)) / z)) * y))
	tmp = 0.0
	if (z <= -135000000000.0)
		tmp = t_1;
	elseif (z <= 3.2)
		tmp = Float64(Float64(Float64(b + Float64(z * Float64(a + Float64(z * Float64(t + Float64(z * Float64(Float64(z * 3.13060547623) + 11.1667541262))))))) * Float64(y / Float64(0.607771387771 + Float64(z * 11.9400905721)))) + x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + ((3.13060547623 - ((36.52704169880642 - (((t + 457.9610022158428) - (-a / z)) / z)) / z)) * y);
	tmp = 0.0;
	if (z <= -135000000000.0)
		tmp = t_1;
	elseif (z <= 3.2)
		tmp = ((b + (z * (a + (z * (t + (z * ((z * 3.13060547623) + 11.1667541262))))))) * (y / (0.607771387771 + (z * 11.9400905721)))) + x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(N[(3.13060547623 - N[(N[(36.52704169880642 - N[(N[(N[(t + 457.9610022158428), $MachinePrecision] - N[((-a) / z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -135000000000.0], t$95$1, If[LessEqual[z, 3.2], N[(N[(N[(b + N[(z * N[(a + N[(z * N[(t + N[(z * N[(N[(z * 3.13060547623), $MachinePrecision] + 11.1667541262), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(y / N[(0.607771387771 + N[(z * 11.9400905721), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.35e11 or 3.2000000000000002 < z

   1. Initial program 18.1%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   2. Add Preprocessing

   4. Applied egg-rr 0

      \[\leadsto expr\]

   5. Taylor expanded in z around -inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in a around inf 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   if -1.35e11 < z < 3.2000000000000002

   1. Initial program 99.6%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 9: 97.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(3.13060547623 - \frac{36.52704169880642 - \frac{\left(t + 457.9610022158428\right) - \frac{-a}{z}}{z}}{z}\right) \cdot y\\ \mathbf{if}\;z \leq -135000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.2:\\ \;\;\;\;x + \frac{y \cdot \left(\left(\left(z \cdot 11.1667541262 + t\right) \cdot z + a\right) \cdot z + b\right)}{z \cdot 11.9400905721 + 0.607771387771}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (+
          x
          (*
           (-
            3.13060547623
            (/
             (-
              36.52704169880642
              (/ (- (+ t 457.9610022158428) (/ (- a) z)) z))
             z))
           y))))
   (if (<= z -135000000000.0)
     t_1
     (if (<= z 3.2)
       (+
        x
        (/
         (* y (+ (* (+ (* (+ (* z 11.1667541262) t) z) a) z) b))
         (+ (* z 11.9400905721) 0.607771387771)))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + ((3.13060547623 - ((36.52704169880642 - (((t + 457.9610022158428) - (-a / z)) / z)) / z)) * y);
	double tmp;
	if (z <= -135000000000.0) {
		tmp = t_1;
	} else if (z <= 3.2) {
		tmp = x + ((y * ((((((z * 11.1667541262) + t) * z) + a) * z) + b)) / ((z * 11.9400905721) + 0.607771387771));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

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 - ((36.52704169880642d0 - (((t + 457.9610022158428d0) - (-a / z)) / z)) / z)) * y)
    if (z <= (-135000000000.0d0)) then
        tmp = t_1
    else if (z <= 3.2d0) then
        tmp = x + ((y * ((((((z * 11.1667541262d0) + t) * z) + a) * z) + b)) / ((z * 11.9400905721d0) + 0.607771387771d0))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + ((3.13060547623 - ((36.52704169880642 - (((t + 457.9610022158428) - (-a / z)) / z)) / z)) * y);
	double tmp;
	if (z <= -135000000000.0) {
		tmp = t_1;
	} else if (z <= 3.2) {
		tmp = x + ((y * ((((((z * 11.1667541262) + t) * z) + a) * z) + b)) / ((z * 11.9400905721) + 0.607771387771));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + ((3.13060547623 - ((36.52704169880642 - (((t + 457.9610022158428) - (-a / z)) / z)) / z)) * y)
	tmp = 0
	if z <= -135000000000.0:
		tmp = t_1
	elif z <= 3.2:
		tmp = x + ((y * ((((((z * 11.1667541262) + t) * z) + a) * z) + b)) / ((z * 11.9400905721) + 0.607771387771))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(Float64(3.13060547623 - Float64(Float64(36.52704169880642 - Float64(Float64(Float64(t + 457.9610022158428) - Float64(Float64(-a) / z)) / z)) / z)) * y))
	tmp = 0.0
	if (z <= -135000000000.0)
		tmp = t_1;
	elseif (z <= 3.2)
		tmp = Float64(x + Float64(Float64(y * Float64(Float64(Float64(Float64(Float64(Float64(z * 11.1667541262) + t) * z) + a) * z) + b)) / Float64(Float64(z * 11.9400905721) + 0.607771387771)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + ((3.13060547623 - ((36.52704169880642 - (((t + 457.9610022158428) - (-a / z)) / z)) / z)) * y);
	tmp = 0.0;
	if (z <= -135000000000.0)
		tmp = t_1;
	elseif (z <= 3.2)
		tmp = x + ((y * ((((((z * 11.1667541262) + t) * z) + a) * z) + b)) / ((z * 11.9400905721) + 0.607771387771));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(N[(3.13060547623 - N[(N[(36.52704169880642 - N[(N[(N[(t + 457.9610022158428), $MachinePrecision] - N[((-a) / z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -135000000000.0], t$95$1, If[LessEqual[z, 3.2], N[(x + N[(N[(y * N[(N[(N[(N[(N[(N[(z * 11.1667541262), $MachinePrecision] + t), $MachinePrecision] * z), $MachinePrecision] + a), $MachinePrecision] * z), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / N[(N[(z * 11.9400905721), $MachinePrecision] + 0.607771387771), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.35e11 or 3.2000000000000002 < z

   1. Initial program 18.1%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   2. Add Preprocessing

   4. Applied egg-rr 0

      \[\leadsto expr\]

   5. Taylor expanded in z around -inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in a around inf 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   if -1.35e11 < z < 3.2000000000000002

   1. Initial program 99.6%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in z around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 10: 97.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(3.13060547623 - \frac{36.52704169880642 - \frac{\left(t + 457.9610022158428\right) - \frac{-a}{z}}{z}}{z}\right) \cdot y\\ \mathbf{if}\;z \leq -6.5 \cdot 10^{+17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.2:\\ \;\;\;\;x + \frac{z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right) + b}{0.607771387771} \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (+
          x
          (*
           (-
            3.13060547623
            (/
             (-
              36.52704169880642
              (/ (- (+ t 457.9610022158428) (/ (- a) z)) z))
             z))
           y))))
   (if (<= z -6.5e+17)
     t_1
     (if (<= z 3.2)
       (+
        x
        (*
         (/
          (+
           (* z (+ (* z (+ (* z (+ (* z 3.13060547623) 11.1667541262)) t)) a))
           b)
          0.607771387771)
         y))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + ((3.13060547623 - ((36.52704169880642 - (((t + 457.9610022158428) - (-a / z)) / z)) / z)) * y);
	double tmp;
	if (z <= -6.5e+17) {
		tmp = t_1;
	} else if (z <= 3.2) {
		tmp = x + ((((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b) / 0.607771387771) * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

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 - ((36.52704169880642d0 - (((t + 457.9610022158428d0) - (-a / z)) / z)) / z)) * y)
    if (z <= (-6.5d+17)) then
        tmp = t_1
    else if (z <= 3.2d0) then
        tmp = x + ((((z * ((z * ((z * ((z * 3.13060547623d0) + 11.1667541262d0)) + t)) + a)) + b) / 0.607771387771d0) * y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + ((3.13060547623 - ((36.52704169880642 - (((t + 457.9610022158428) - (-a / z)) / z)) / z)) * y);
	double tmp;
	if (z <= -6.5e+17) {
		tmp = t_1;
	} else if (z <= 3.2) {
		tmp = x + ((((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b) / 0.607771387771) * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + ((3.13060547623 - ((36.52704169880642 - (((t + 457.9610022158428) - (-a / z)) / z)) / z)) * y)
	tmp = 0
	if z <= -6.5e+17:
		tmp = t_1
	elif z <= 3.2:
		tmp = x + ((((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b) / 0.607771387771) * y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(Float64(3.13060547623 - Float64(Float64(36.52704169880642 - Float64(Float64(Float64(t + 457.9610022158428) - Float64(Float64(-a) / z)) / z)) / z)) * y))
	tmp = 0.0
	if (z <= -6.5e+17)
		tmp = t_1;
	elseif (z <= 3.2)
		tmp = Float64(x + Float64(Float64(Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b) / 0.607771387771) * y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + ((3.13060547623 - ((36.52704169880642 - (((t + 457.9610022158428) - (-a / z)) / z)) / z)) * y);
	tmp = 0.0;
	if (z <= -6.5e+17)
		tmp = t_1;
	elseif (z <= 3.2)
		tmp = x + ((((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b) / 0.607771387771) * y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(N[(3.13060547623 - N[(N[(36.52704169880642 - N[(N[(N[(t + 457.9610022158428), $MachinePrecision] - N[((-a) / z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.5e+17], t$95$1, If[LessEqual[z, 3.2], N[(x + N[(N[(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] / 0.607771387771), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -6.5e17 or 3.2000000000000002 < z

   1. Initial program 17.4%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   2. Add Preprocessing

   4. Applied egg-rr 0

      \[\leadsto expr\]

   5. Taylor expanded in z around -inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in a around inf 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   if -6.5e17 < z < 3.2000000000000002

   1. Initial program 99.6%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   2. Add Preprocessing

   4. Applied egg-rr 0

      \[\leadsto expr\]

   5. Taylor expanded in z around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 11: 97.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(3.13060547623 - \frac{36.52704169880642 - \frac{\left(t + 457.9610022158428\right) - \frac{-a}{z}}{z}}{z}\right) \cdot y\\ \mathbf{if}\;z \leq -135000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.2:\\ \;\;\;\;\frac{y}{\frac{1}{\frac{b + z \cdot \left(a + z \cdot t\right)}{z \cdot 11.9400905721 + 0.607771387771}}} + x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (+
          x
          (*
           (-
            3.13060547623
            (/
             (-
              36.52704169880642
              (/ (- (+ t 457.9610022158428) (/ (- a) z)) z))
             z))
           y))))
   (if (<= z -135000000000.0)
     t_1
     (if (<= z 3.2)
       (+
        (/
         y
         (/
          1.0
          (/
           (+ b (* z (+ a (* z t))))
           (+ (* z 11.9400905721) 0.607771387771))))
        x)
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + ((3.13060547623 - ((36.52704169880642 - (((t + 457.9610022158428) - (-a / z)) / z)) / z)) * y);
	double tmp;
	if (z <= -135000000000.0) {
		tmp = t_1;
	} else if (z <= 3.2) {
		tmp = (y / (1.0 / ((b + (z * (a + (z * t)))) / ((z * 11.9400905721) + 0.607771387771)))) + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

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 - ((36.52704169880642d0 - (((t + 457.9610022158428d0) - (-a / z)) / z)) / z)) * y)
    if (z <= (-135000000000.0d0)) then
        tmp = t_1
    else if (z <= 3.2d0) then
        tmp = (y / (1.0d0 / ((b + (z * (a + (z * t)))) / ((z * 11.9400905721d0) + 0.607771387771d0)))) + x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + ((3.13060547623 - ((36.52704169880642 - (((t + 457.9610022158428) - (-a / z)) / z)) / z)) * y);
	double tmp;
	if (z <= -135000000000.0) {
		tmp = t_1;
	} else if (z <= 3.2) {
		tmp = (y / (1.0 / ((b + (z * (a + (z * t)))) / ((z * 11.9400905721) + 0.607771387771)))) + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + ((3.13060547623 - ((36.52704169880642 - (((t + 457.9610022158428) - (-a / z)) / z)) / z)) * y)
	tmp = 0
	if z <= -135000000000.0:
		tmp = t_1
	elif z <= 3.2:
		tmp = (y / (1.0 / ((b + (z * (a + (z * t)))) / ((z * 11.9400905721) + 0.607771387771)))) + x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(Float64(3.13060547623 - Float64(Float64(36.52704169880642 - Float64(Float64(Float64(t + 457.9610022158428) - Float64(Float64(-a) / z)) / z)) / z)) * y))
	tmp = 0.0
	if (z <= -135000000000.0)
		tmp = t_1;
	elseif (z <= 3.2)
		tmp = Float64(Float64(y / Float64(1.0 / Float64(Float64(b + Float64(z * Float64(a + Float64(z * t)))) / Float64(Float64(z * 11.9400905721) + 0.607771387771)))) + x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + ((3.13060547623 - ((36.52704169880642 - (((t + 457.9610022158428) - (-a / z)) / z)) / z)) * y);
	tmp = 0.0;
	if (z <= -135000000000.0)
		tmp = t_1;
	elseif (z <= 3.2)
		tmp = (y / (1.0 / ((b + (z * (a + (z * t)))) / ((z * 11.9400905721) + 0.607771387771)))) + x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(N[(3.13060547623 - N[(N[(36.52704169880642 - N[(N[(N[(t + 457.9610022158428), $MachinePrecision] - N[((-a) / z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -135000000000.0], t$95$1, If[LessEqual[z, 3.2], N[(N[(y / N[(1.0 / N[(N[(b + N[(z * N[(a + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(z * 11.9400905721), $MachinePrecision] + 0.607771387771), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.35e11 or 3.2000000000000002 < z

   1. Initial program 18.1%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   2. Add Preprocessing

   4. Applied egg-rr 0

      \[\leadsto expr\]

   5. Taylor expanded in z around -inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in a around inf 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   if -1.35e11 < z < 3.2000000000000002

   1. Initial program 99.6%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   2. Add Preprocessing

   4. Applied egg-rr 0

      \[\leadsto expr\]

   5. Taylor expanded in z around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]

   10. Taylor expanded in z around 0 0

       \[\leadsto expr\]

   12. Simplified 0

       \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 12: 97.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(3.13060547623 - \frac{36.52704169880642 - \frac{\left(t + 457.9610022158428\right) - \frac{-a}{z}}{z}}{z}\right) \cdot y\\ \mathbf{if}\;z \leq -135000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.15:\\ \;\;\;\;x + \frac{y \cdot \left(z \cdot \left(a + z \cdot t\right) + b\right)}{z \cdot 11.9400905721 + 0.607771387771}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (+
          x
          (*
           (-
            3.13060547623
            (/
             (-
              36.52704169880642
              (/ (- (+ t 457.9610022158428) (/ (- a) z)) z))
             z))
           y))))
   (if (<= z -135000000000.0)
     t_1
     (if (<= z 2.15)
       (+
        x
        (/
         (* y (+ (* z (+ a (* z t))) b))
         (+ (* z 11.9400905721) 0.607771387771)))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + ((3.13060547623 - ((36.52704169880642 - (((t + 457.9610022158428) - (-a / z)) / z)) / z)) * y);
	double tmp;
	if (z <= -135000000000.0) {
		tmp = t_1;
	} else if (z <= 2.15) {
		tmp = x + ((y * ((z * (a + (z * t))) + b)) / ((z * 11.9400905721) + 0.607771387771));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

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 - ((36.52704169880642d0 - (((t + 457.9610022158428d0) - (-a / z)) / z)) / z)) * y)
    if (z <= (-135000000000.0d0)) then
        tmp = t_1
    else if (z <= 2.15d0) then
        tmp = x + ((y * ((z * (a + (z * t))) + b)) / ((z * 11.9400905721d0) + 0.607771387771d0))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + ((3.13060547623 - ((36.52704169880642 - (((t + 457.9610022158428) - (-a / z)) / z)) / z)) * y);
	double tmp;
	if (z <= -135000000000.0) {
		tmp = t_1;
	} else if (z <= 2.15) {
		tmp = x + ((y * ((z * (a + (z * t))) + b)) / ((z * 11.9400905721) + 0.607771387771));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + ((3.13060547623 - ((36.52704169880642 - (((t + 457.9610022158428) - (-a / z)) / z)) / z)) * y)
	tmp = 0
	if z <= -135000000000.0:
		tmp = t_1
	elif z <= 2.15:
		tmp = x + ((y * ((z * (a + (z * t))) + b)) / ((z * 11.9400905721) + 0.607771387771))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(Float64(3.13060547623 - Float64(Float64(36.52704169880642 - Float64(Float64(Float64(t + 457.9610022158428) - Float64(Float64(-a) / z)) / z)) / z)) * y))
	tmp = 0.0
	if (z <= -135000000000.0)
		tmp = t_1;
	elseif (z <= 2.15)
		tmp = Float64(x + Float64(Float64(y * Float64(Float64(z * Float64(a + Float64(z * t))) + b)) / Float64(Float64(z * 11.9400905721) + 0.607771387771)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + ((3.13060547623 - ((36.52704169880642 - (((t + 457.9610022158428) - (-a / z)) / z)) / z)) * y);
	tmp = 0.0;
	if (z <= -135000000000.0)
		tmp = t_1;
	elseif (z <= 2.15)
		tmp = x + ((y * ((z * (a + (z * t))) + b)) / ((z * 11.9400905721) + 0.607771387771));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(N[(3.13060547623 - N[(N[(36.52704169880642 - N[(N[(N[(t + 457.9610022158428), $MachinePrecision] - N[((-a) / z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -135000000000.0], t$95$1, If[LessEqual[z, 2.15], N[(x + N[(N[(y * N[(N[(z * N[(a + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / N[(N[(z * 11.9400905721), $MachinePrecision] + 0.607771387771), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.35e11 or 2.14999999999999991 < z

   1. Initial program 18.1%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   2. Add Preprocessing

   4. Applied egg-rr 0

      \[\leadsto expr\]

   5. Taylor expanded in z around -inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in a around inf 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   if -1.35e11 < z < 2.14999999999999991

   1. Initial program 99.6%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in z around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 13: 95.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -135000000000:\\ \;\;\;\;x + \left(3.13060547623 - \frac{36.52704169880642 - \frac{t + 457.9610022158428}{z}}{z}\right) \cdot y\\ \mathbf{elif}\;z \leq 3.2:\\ \;\;\;\;x + \frac{y \cdot \left(z \cdot \left(a + z \cdot t\right) + b\right)}{z \cdot 11.9400905721 + 0.607771387771}\\ \mathbf{else}:\\ \;\;\;\;x + \left(3.13060547623 + \frac{t}{z \cdot z}\right) \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -135000000000.0)
   (+
    x
    (*
     (-
      3.13060547623
      (/ (- 36.52704169880642 (/ (+ t 457.9610022158428) z)) z))
     y))
   (if (<= z 3.2)
     (+
      x
      (/
       (* y (+ (* z (+ a (* z t))) b))
       (+ (* z 11.9400905721) 0.607771387771)))
     (+ x (* (+ 3.13060547623 (/ t (* z z))) y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -135000000000.0) {
		tmp = x + ((3.13060547623 - ((36.52704169880642 - ((t + 457.9610022158428) / z)) / z)) * y);
	} else if (z <= 3.2) {
		tmp = x + ((y * ((z * (a + (z * t))) + b)) / ((z * 11.9400905721) + 0.607771387771));
	} else {
		tmp = x + ((3.13060547623 + (t / (z * z))) * y);
	}
	return tmp;
}

Fortran

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 <= (-135000000000.0d0)) then
        tmp = x + ((3.13060547623d0 - ((36.52704169880642d0 - ((t + 457.9610022158428d0) / z)) / z)) * y)
    else if (z <= 3.2d0) then
        tmp = x + ((y * ((z * (a + (z * t))) + b)) / ((z * 11.9400905721d0) + 0.607771387771d0))
    else
        tmp = x + ((3.13060547623d0 + (t / (z * z))) * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -135000000000.0) {
		tmp = x + ((3.13060547623 - ((36.52704169880642 - ((t + 457.9610022158428) / z)) / z)) * y);
	} else if (z <= 3.2) {
		tmp = x + ((y * ((z * (a + (z * t))) + b)) / ((z * 11.9400905721) + 0.607771387771));
	} else {
		tmp = x + ((3.13060547623 + (t / (z * z))) * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -135000000000.0:
		tmp = x + ((3.13060547623 - ((36.52704169880642 - ((t + 457.9610022158428) / z)) / z)) * y)
	elif z <= 3.2:
		tmp = x + ((y * ((z * (a + (z * t))) + b)) / ((z * 11.9400905721) + 0.607771387771))
	else:
		tmp = x + ((3.13060547623 + (t / (z * z))) * y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -135000000000.0)
		tmp = Float64(x + Float64(Float64(3.13060547623 - Float64(Float64(36.52704169880642 - Float64(Float64(t + 457.9610022158428) / z)) / z)) * y));
	elseif (z <= 3.2)
		tmp = Float64(x + Float64(Float64(y * Float64(Float64(z * Float64(a + Float64(z * t))) + b)) / Float64(Float64(z * 11.9400905721) + 0.607771387771)));
	else
		tmp = Float64(x + Float64(Float64(3.13060547623 + Float64(t / Float64(z * z))) * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -135000000000.0)
		tmp = x + ((3.13060547623 - ((36.52704169880642 - ((t + 457.9610022158428) / z)) / z)) * y);
	elseif (z <= 3.2)
		tmp = x + ((y * ((z * (a + (z * t))) + b)) / ((z * 11.9400905721) + 0.607771387771));
	else
		tmp = x + ((3.13060547623 + (t / (z * z))) * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -135000000000.0], N[(x + N[(N[(3.13060547623 - N[(N[(36.52704169880642 - N[(N[(t + 457.9610022158428), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.2], N[(x + N[(N[(y * N[(N[(z * N[(a + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / N[(N[(z * 11.9400905721), $MachinePrecision] + 0.607771387771), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(3.13060547623 + N[(t / N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.35e11

   1. Initial program 17.9%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   2. Add Preprocessing

   4. Applied egg-rr 0

      \[\leadsto expr\]

   5. Taylor expanded in z around -inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if -1.35e11 < z < 3.2000000000000002

   1. Initial program 99.6%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in z around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   if 3.2000000000000002 < z

   1. Initial program 18.3%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   2. Add Preprocessing

   4. Applied egg-rr 0

      \[\leadsto expr\]

   5. Taylor expanded in z around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in t around inf 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 14: 63.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 1.6453555072203998 \cdot \left(b \cdot y\right)\\ t_2 := y \cdot 3.13060547623 + x\\ \mathbf{if}\;z \leq -7.8 \cdot 10^{-13}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{-95}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{-214}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-16}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* 1.6453555072203998 (* b y))) (t_2 (+ (* y 3.13060547623) x)))
   (if (<= z -7.8e-13)
     t_2
     (if (<= z -1.35e-95)
       t_1
       (if (<= z -1.65e-214) x (if (<= z 2.1e-16) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 1.6453555072203998 * (b * y);
	double t_2 = (y * 3.13060547623) + x;
	double tmp;
	if (z <= -7.8e-13) {
		tmp = t_2;
	} else if (z <= -1.35e-95) {
		tmp = t_1;
	} else if (z <= -1.65e-214) {
		tmp = x;
	} else if (z <= 2.1e-16) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

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) :: t_2
    real(8) :: tmp
    t_1 = 1.6453555072203998d0 * (b * y)
    t_2 = (y * 3.13060547623d0) + x
    if (z <= (-7.8d-13)) then
        tmp = t_2
    else if (z <= (-1.35d-95)) then
        tmp = t_1
    else if (z <= (-1.65d-214)) then
        tmp = x
    else if (z <= 2.1d-16) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 1.6453555072203998 * (b * y);
	double t_2 = (y * 3.13060547623) + x;
	double tmp;
	if (z <= -7.8e-13) {
		tmp = t_2;
	} else if (z <= -1.35e-95) {
		tmp = t_1;
	} else if (z <= -1.65e-214) {
		tmp = x;
	} else if (z <= 2.1e-16) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = 1.6453555072203998 * (b * y)
	t_2 = (y * 3.13060547623) + x
	tmp = 0
	if z <= -7.8e-13:
		tmp = t_2
	elif z <= -1.35e-95:
		tmp = t_1
	elif z <= -1.65e-214:
		tmp = x
	elif z <= 2.1e-16:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(1.6453555072203998 * Float64(b * y))
	t_2 = Float64(Float64(y * 3.13060547623) + x)
	tmp = 0.0
	if (z <= -7.8e-13)
		tmp = t_2;
	elseif (z <= -1.35e-95)
		tmp = t_1;
	elseif (z <= -1.65e-214)
		tmp = x;
	elseif (z <= 2.1e-16)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = 1.6453555072203998 * (b * y);
	t_2 = (y * 3.13060547623) + x;
	tmp = 0.0;
	if (z <= -7.8e-13)
		tmp = t_2;
	elseif (z <= -1.35e-95)
		tmp = t_1;
	elseif (z <= -1.65e-214)
		tmp = x;
	elseif (z <= 2.1e-16)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(1.6453555072203998 * N[(b * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * 3.13060547623), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[z, -7.8e-13], t$95$2, If[LessEqual[z, -1.35e-95], t$95$1, If[LessEqual[z, -1.65e-214], x, If[LessEqual[z, 2.1e-16], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.80000000000000009e-13 or 2.1000000000000001e-16 < z

   1. Initial program 23.2%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -7.80000000000000009e-13 < z < -1.35e-95 or -1.6499999999999999e-214 < z < 2.1000000000000001e-16

   1. Initial program 99.6%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in z around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   9. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   11. Simplified 0

       \[\leadsto expr\]

   if -1.35e-95 < z < -1.6499999999999999e-214

   1. Initial program 99.5%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 15: 95.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+17}:\\ \;\;\;\;x + \left(3.13060547623 - \frac{36.52704169880642 - \frac{t + 457.9610022158428}{z}}{z}\right) \cdot y\\ \mathbf{elif}\;z \leq 3.2:\\ \;\;\;\;\frac{y}{\frac{0.607771387771}{b + z \cdot \left(a + z \cdot t\right)}} + x\\ \mathbf{else}:\\ \;\;\;\;x + \left(3.13060547623 + \frac{t}{z \cdot z}\right) \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -6.5e+17)
   (+
    x
    (*
     (-
      3.13060547623
      (/ (- 36.52704169880642 (/ (+ t 457.9610022158428) z)) z))
     y))
   (if (<= z 3.2)
     (+ (/ y (/ 0.607771387771 (+ b (* z (+ a (* z t)))))) x)
     (+ x (* (+ 3.13060547623 (/ t (* z z))) y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -6.5e+17) {
		tmp = x + ((3.13060547623 - ((36.52704169880642 - ((t + 457.9610022158428) / z)) / z)) * y);
	} else if (z <= 3.2) {
		tmp = (y / (0.607771387771 / (b + (z * (a + (z * t)))))) + x;
	} else {
		tmp = x + ((3.13060547623 + (t / (z * z))) * y);
	}
	return tmp;
}

Fortran

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 <= (-6.5d+17)) then
        tmp = x + ((3.13060547623d0 - ((36.52704169880642d0 - ((t + 457.9610022158428d0) / z)) / z)) * y)
    else if (z <= 3.2d0) then
        tmp = (y / (0.607771387771d0 / (b + (z * (a + (z * t)))))) + x
    else
        tmp = x + ((3.13060547623d0 + (t / (z * z))) * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -6.5e+17) {
		tmp = x + ((3.13060547623 - ((36.52704169880642 - ((t + 457.9610022158428) / z)) / z)) * y);
	} else if (z <= 3.2) {
		tmp = (y / (0.607771387771 / (b + (z * (a + (z * t)))))) + x;
	} else {
		tmp = x + ((3.13060547623 + (t / (z * z))) * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -6.5e+17:
		tmp = x + ((3.13060547623 - ((36.52704169880642 - ((t + 457.9610022158428) / z)) / z)) * y)
	elif z <= 3.2:
		tmp = (y / (0.607771387771 / (b + (z * (a + (z * t)))))) + x
	else:
		tmp = x + ((3.13060547623 + (t / (z * z))) * y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -6.5e+17)
		tmp = Float64(x + Float64(Float64(3.13060547623 - Float64(Float64(36.52704169880642 - Float64(Float64(t + 457.9610022158428) / z)) / z)) * y));
	elseif (z <= 3.2)
		tmp = Float64(Float64(y / Float64(0.607771387771 / Float64(b + Float64(z * Float64(a + Float64(z * t)))))) + x);
	else
		tmp = Float64(x + Float64(Float64(3.13060547623 + Float64(t / Float64(z * z))) * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -6.5e+17)
		tmp = x + ((3.13060547623 - ((36.52704169880642 - ((t + 457.9610022158428) / z)) / z)) * y);
	elseif (z <= 3.2)
		tmp = (y / (0.607771387771 / (b + (z * (a + (z * t)))))) + x;
	else
		tmp = x + ((3.13060547623 + (t / (z * z))) * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -6.5e+17], N[(x + N[(N[(3.13060547623 - N[(N[(36.52704169880642 - N[(N[(t + 457.9610022158428), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.2], N[(N[(y / N[(0.607771387771 / N[(b + N[(z * N[(a + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(x + N[(N[(3.13060547623 + N[(t / N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.5e17

   1. Initial program 16.4%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   2. Add Preprocessing

   4. Applied egg-rr 0

      \[\leadsto expr\]

   5. Taylor expanded in z around -inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if -6.5e17 < z < 3.2000000000000002

   1. Initial program 99.6%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   2. Add Preprocessing

   4. Applied egg-rr 0

      \[\leadsto expr\]

   5. Taylor expanded in z around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in z around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   if 3.2000000000000002 < z

   1. Initial program 18.3%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   2. Add Preprocessing

   4. Applied egg-rr 0

      \[\leadsto expr\]

   5. Taylor expanded in z around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in t around inf 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 16: 90.3% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot 3.13060547623 + x\\ \mathbf{if}\;z \leq -3.3 \cdot 10^{+21}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.2:\\ \;\;\;\;x + y \cdot \left(\left(b + z \cdot a\right) \cdot 1.6453555072203998\right)\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+74}:\\ \;\;\;\;x + \frac{t}{z \cdot z} \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (* y 3.13060547623) x)))
   (if (<= z -3.3e+21)
     t_1
     (if (<= z 3.2)
       (+ x (* y (* (+ b (* z a)) 1.6453555072203998)))
       (if (<= z 3.5e+74) (+ x (* (/ t (* z z)) y)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y * 3.13060547623) + x;
	double tmp;
	if (z <= -3.3e+21) {
		tmp = t_1;
	} else if (z <= 3.2) {
		tmp = x + (y * ((b + (z * a)) * 1.6453555072203998));
	} else if (z <= 3.5e+74) {
		tmp = x + ((t / (z * z)) * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

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 = (y * 3.13060547623d0) + x
    if (z <= (-3.3d+21)) then
        tmp = t_1
    else if (z <= 3.2d0) then
        tmp = x + (y * ((b + (z * a)) * 1.6453555072203998d0))
    else if (z <= 3.5d+74) then
        tmp = x + ((t / (z * z)) * y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y * 3.13060547623) + x;
	double tmp;
	if (z <= -3.3e+21) {
		tmp = t_1;
	} else if (z <= 3.2) {
		tmp = x + (y * ((b + (z * a)) * 1.6453555072203998));
	} else if (z <= 3.5e+74) {
		tmp = x + ((t / (z * z)) * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (y * 3.13060547623) + x
	tmp = 0
	if z <= -3.3e+21:
		tmp = t_1
	elif z <= 3.2:
		tmp = x + (y * ((b + (z * a)) * 1.6453555072203998))
	elif z <= 3.5e+74:
		tmp = x + ((t / (z * z)) * y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y * 3.13060547623) + x)
	tmp = 0.0
	if (z <= -3.3e+21)
		tmp = t_1;
	elseif (z <= 3.2)
		tmp = Float64(x + Float64(y * Float64(Float64(b + Float64(z * a)) * 1.6453555072203998)));
	elseif (z <= 3.5e+74)
		tmp = Float64(x + Float64(Float64(t / Float64(z * z)) * y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (y * 3.13060547623) + x;
	tmp = 0.0;
	if (z <= -3.3e+21)
		tmp = t_1;
	elseif (z <= 3.2)
		tmp = x + (y * ((b + (z * a)) * 1.6453555072203998));
	elseif (z <= 3.5e+74)
		tmp = x + ((t / (z * z)) * y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y * 3.13060547623), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[z, -3.3e+21], t$95$1, If[LessEqual[z, 3.2], N[(x + N[(y * N[(N[(b + N[(z * a), $MachinePrecision]), $MachinePrecision] * 1.6453555072203998), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.5e+74], N[(x + N[(N[(t / N[(z * z), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.3e21 or 3.50000000000000014e74 < z

   1. Initial program 9.1%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -3.3e21 < z < 3.2000000000000002

   1. Initial program 99.6%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in z around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   10. Applied egg-rr 0

       \[\leadsto expr\]

   if 3.2000000000000002 < z < 3.50000000000000014e74

   1. Initial program 66.6%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   2. Add Preprocessing

   4. Applied egg-rr 0

      \[\leadsto expr\]

   5. Taylor expanded in z around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in t around inf 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 17: 83.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot 3.13060547623 + x\\ \mathbf{if}\;z \leq -6 \cdot 10^{+18}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-16}:\\ \;\;\;\;1.6453555072203998 \cdot \left(y \cdot b\right) + x\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+74}:\\ \;\;\;\;x + \frac{t}{z \cdot z} \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (* y 3.13060547623) x)))
   (if (<= z -6e+18)
     t_1
     (if (<= z 2.2e-16)
       (+ (* 1.6453555072203998 (* y b)) x)
       (if (<= z 3.3e+74) (+ x (* (/ t (* z z)) y)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y * 3.13060547623) + x;
	double tmp;
	if (z <= -6e+18) {
		tmp = t_1;
	} else if (z <= 2.2e-16) {
		tmp = (1.6453555072203998 * (y * b)) + x;
	} else if (z <= 3.3e+74) {
		tmp = x + ((t / (z * z)) * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

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 = (y * 3.13060547623d0) + x
    if (z <= (-6d+18)) then
        tmp = t_1
    else if (z <= 2.2d-16) then
        tmp = (1.6453555072203998d0 * (y * b)) + x
    else if (z <= 3.3d+74) then
        tmp = x + ((t / (z * z)) * y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y * 3.13060547623) + x;
	double tmp;
	if (z <= -6e+18) {
		tmp = t_1;
	} else if (z <= 2.2e-16) {
		tmp = (1.6453555072203998 * (y * b)) + x;
	} else if (z <= 3.3e+74) {
		tmp = x + ((t / (z * z)) * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (y * 3.13060547623) + x
	tmp = 0
	if z <= -6e+18:
		tmp = t_1
	elif z <= 2.2e-16:
		tmp = (1.6453555072203998 * (y * b)) + x
	elif z <= 3.3e+74:
		tmp = x + ((t / (z * z)) * y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y * 3.13060547623) + x)
	tmp = 0.0
	if (z <= -6e+18)
		tmp = t_1;
	elseif (z <= 2.2e-16)
		tmp = Float64(Float64(1.6453555072203998 * Float64(y * b)) + x);
	elseif (z <= 3.3e+74)
		tmp = Float64(x + Float64(Float64(t / Float64(z * z)) * y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (y * 3.13060547623) + x;
	tmp = 0.0;
	if (z <= -6e+18)
		tmp = t_1;
	elseif (z <= 2.2e-16)
		tmp = (1.6453555072203998 * (y * b)) + x;
	elseif (z <= 3.3e+74)
		tmp = x + ((t / (z * z)) * y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y * 3.13060547623), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[z, -6e+18], t$95$1, If[LessEqual[z, 2.2e-16], N[(N[(1.6453555072203998 * N[(y * b), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[z, 3.3e+74], N[(x + N[(N[(t / N[(z * z), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6e18 or 3.3000000000000002e74 < z

   1. Initial program 9.1%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -6e18 < z < 2.2e-16

   1. Initial program 99.6%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if 2.2e-16 < z < 3.3000000000000002e74

   1. Initial program 71.4%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   2. Add Preprocessing

   4. Applied egg-rr 0

      \[\leadsto expr\]

   5. Taylor expanded in z around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in t around inf 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 18: 93.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+17}:\\ \;\;\;\;x + \left(3.13060547623 - \frac{36.52704169880642 - \frac{t + 457.9610022158428}{z}}{z}\right) \cdot y\\ \mathbf{elif}\;z \leq 0.092:\\ \;\;\;\;x + y \cdot \left(\left(b + z \cdot a\right) \cdot 1.6453555072203998\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(3.13060547623 + \frac{t}{z \cdot z}\right) \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -6.5e+17)
   (+
    x
    (*
     (-
      3.13060547623
      (/ (- 36.52704169880642 (/ (+ t 457.9610022158428) z)) z))
     y))
   (if (<= z 0.092)
     (+ x (* y (* (+ b (* z a)) 1.6453555072203998)))
     (+ x (* (+ 3.13060547623 (/ t (* z z))) y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -6.5e+17) {
		tmp = x + ((3.13060547623 - ((36.52704169880642 - ((t + 457.9610022158428) / z)) / z)) * y);
	} else if (z <= 0.092) {
		tmp = x + (y * ((b + (z * a)) * 1.6453555072203998));
	} else {
		tmp = x + ((3.13060547623 + (t / (z * z))) * y);
	}
	return tmp;
}

Fortran

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 <= (-6.5d+17)) then
        tmp = x + ((3.13060547623d0 - ((36.52704169880642d0 - ((t + 457.9610022158428d0) / z)) / z)) * y)
    else if (z <= 0.092d0) then
        tmp = x + (y * ((b + (z * a)) * 1.6453555072203998d0))
    else
        tmp = x + ((3.13060547623d0 + (t / (z * z))) * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -6.5e+17) {
		tmp = x + ((3.13060547623 - ((36.52704169880642 - ((t + 457.9610022158428) / z)) / z)) * y);
	} else if (z <= 0.092) {
		tmp = x + (y * ((b + (z * a)) * 1.6453555072203998));
	} else {
		tmp = x + ((3.13060547623 + (t / (z * z))) * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -6.5e+17:
		tmp = x + ((3.13060547623 - ((36.52704169880642 - ((t + 457.9610022158428) / z)) / z)) * y)
	elif z <= 0.092:
		tmp = x + (y * ((b + (z * a)) * 1.6453555072203998))
	else:
		tmp = x + ((3.13060547623 + (t / (z * z))) * y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -6.5e+17)
		tmp = Float64(x + Float64(Float64(3.13060547623 - Float64(Float64(36.52704169880642 - Float64(Float64(t + 457.9610022158428) / z)) / z)) * y));
	elseif (z <= 0.092)
		tmp = Float64(x + Float64(y * Float64(Float64(b + Float64(z * a)) * 1.6453555072203998)));
	else
		tmp = Float64(x + Float64(Float64(3.13060547623 + Float64(t / Float64(z * z))) * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -6.5e+17)
		tmp = x + ((3.13060547623 - ((36.52704169880642 - ((t + 457.9610022158428) / z)) / z)) * y);
	elseif (z <= 0.092)
		tmp = x + (y * ((b + (z * a)) * 1.6453555072203998));
	else
		tmp = x + ((3.13060547623 + (t / (z * z))) * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -6.5e+17], N[(x + N[(N[(3.13060547623 - N[(N[(36.52704169880642 - N[(N[(t + 457.9610022158428), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.092], N[(x + N[(y * N[(N[(b + N[(z * a), $MachinePrecision]), $MachinePrecision] * 1.6453555072203998), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(3.13060547623 + N[(t / N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.5e17

   1. Initial program 16.4%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   2. Add Preprocessing

   4. Applied egg-rr 0

      \[\leadsto expr\]

   5. Taylor expanded in z around -inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if -6.5e17 < z < 0.091999999999999998

   1. Initial program 99.6%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in z around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   10. Applied egg-rr 0

       \[\leadsto expr\]

   if 0.091999999999999998 < z

   1. Initial program 18.3%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   2. Add Preprocessing

   4. Applied egg-rr 0

      \[\leadsto expr\]

   5. Taylor expanded in z around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in t around inf 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 19: 93.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(3.13060547623 + \frac{t}{z \cdot z}\right) \cdot y\\ \mathbf{if}\;z \leq -6.5 \cdot 10^{+17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.8:\\ \;\;\;\;x + y \cdot \left(\left(b + z \cdot a\right) \cdot 1.6453555072203998\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* (+ 3.13060547623 (/ t (* z z))) y))))
   (if (<= z -6.5e+17)
     t_1
     (if (<= z 2.8) (+ x (* y (* (+ b (* z a)) 1.6453555072203998))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + ((3.13060547623 + (t / (z * z))) * y);
	double tmp;
	if (z <= -6.5e+17) {
		tmp = t_1;
	} else if (z <= 2.8) {
		tmp = x + (y * ((b + (z * a)) * 1.6453555072203998));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

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 + (t / (z * z))) * y)
    if (z <= (-6.5d+17)) then
        tmp = t_1
    else if (z <= 2.8d0) then
        tmp = x + (y * ((b + (z * a)) * 1.6453555072203998d0))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + ((3.13060547623 + (t / (z * z))) * y);
	double tmp;
	if (z <= -6.5e+17) {
		tmp = t_1;
	} else if (z <= 2.8) {
		tmp = x + (y * ((b + (z * a)) * 1.6453555072203998));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + ((3.13060547623 + (t / (z * z))) * y)
	tmp = 0
	if z <= -6.5e+17:
		tmp = t_1
	elif z <= 2.8:
		tmp = x + (y * ((b + (z * a)) * 1.6453555072203998))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(Float64(3.13060547623 + Float64(t / Float64(z * z))) * y))
	tmp = 0.0
	if (z <= -6.5e+17)
		tmp = t_1;
	elseif (z <= 2.8)
		tmp = Float64(x + Float64(y * Float64(Float64(b + Float64(z * a)) * 1.6453555072203998)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + ((3.13060547623 + (t / (z * z))) * y);
	tmp = 0.0;
	if (z <= -6.5e+17)
		tmp = t_1;
	elseif (z <= 2.8)
		tmp = x + (y * ((b + (z * a)) * 1.6453555072203998));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(N[(3.13060547623 + N[(t / N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.5e+17], t$95$1, If[LessEqual[z, 2.8], N[(x + N[(y * N[(N[(b + N[(z * a), $MachinePrecision]), $MachinePrecision] * 1.6453555072203998), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -6.5e17 or 2.7999999999999998 < z

   1. Initial program 17.4%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   2. Add Preprocessing

   4. Applied egg-rr 0

      \[\leadsto expr\]

   5. Taylor expanded in z around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in t around inf 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   if -6.5e17 < z < 2.7999999999999998

   1. Initial program 99.6%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in z around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   10. Applied egg-rr 0

       \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 20: 50.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 1.6453555072203998 \cdot \left(b \cdot y\right)\\ \mathbf{if}\;y \leq -4 \cdot 10^{+212}:\\ \;\;\;\;y \cdot 3.13060547623\\ \mathbf{elif}\;y \leq -5 \cdot 10^{+124}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{+104}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* 1.6453555072203998 (* b y))))
   (if (<= y -4e+212)
     (* y 3.13060547623)
     (if (<= y -5e+124) t_1 (if (<= y 2.15e+104) x t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 1.6453555072203998 * (b * y);
	double tmp;
	if (y <= -4e+212) {
		tmp = y * 3.13060547623;
	} else if (y <= -5e+124) {
		tmp = t_1;
	} else if (y <= 2.15e+104) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

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 = 1.6453555072203998d0 * (b * y)
    if (y <= (-4d+212)) then
        tmp = y * 3.13060547623d0
    else if (y <= (-5d+124)) then
        tmp = t_1
    else if (y <= 2.15d+104) then
        tmp = x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 1.6453555072203998 * (b * y);
	double tmp;
	if (y <= -4e+212) {
		tmp = y * 3.13060547623;
	} else if (y <= -5e+124) {
		tmp = t_1;
	} else if (y <= 2.15e+104) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = 1.6453555072203998 * (b * y)
	tmp = 0
	if y <= -4e+212:
		tmp = y * 3.13060547623
	elif y <= -5e+124:
		tmp = t_1
	elif y <= 2.15e+104:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(1.6453555072203998 * Float64(b * y))
	tmp = 0.0
	if (y <= -4e+212)
		tmp = Float64(y * 3.13060547623);
	elseif (y <= -5e+124)
		tmp = t_1;
	elseif (y <= 2.15e+104)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = 1.6453555072203998 * (b * y);
	tmp = 0.0;
	if (y <= -4e+212)
		tmp = y * 3.13060547623;
	elseif (y <= -5e+124)
		tmp = t_1;
	elseif (y <= 2.15e+104)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(1.6453555072203998 * N[(b * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4e+212], N[(y * 3.13060547623), $MachinePrecision], If[LessEqual[y, -5e+124], t$95$1, If[LessEqual[y, 2.15e+104], x, t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.9999999999999996e212

   1. Initial program 48.0%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   if -3.9999999999999996e212 < y < -4.9999999999999996e124 or 2.1500000000000001e104 < y

   1. Initial program 73.0%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in z around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   9. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   11. Simplified 0

       \[\leadsto expr\]

   if -4.9999999999999996e124 < y < 2.1500000000000001e104

   1. Initial program 59.4%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 21: 83.5% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot 3.13060547623 + x\\ \mathbf{if}\;z \leq -1.2 \cdot 10^{+18}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{+36}:\\ \;\;\;\;1.6453555072203998 \cdot \left(y \cdot b\right) + x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (* y 3.13060547623) x)))
   (if (<= z -1.2e+18)
     t_1
     (if (<= z 6.4e+36) (+ (* 1.6453555072203998 (* y b)) x) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y * 3.13060547623) + x;
	double tmp;
	if (z <= -1.2e+18) {
		tmp = t_1;
	} else if (z <= 6.4e+36) {
		tmp = (1.6453555072203998 * (y * b)) + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

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 = (y * 3.13060547623d0) + x
    if (z <= (-1.2d+18)) then
        tmp = t_1
    else if (z <= 6.4d+36) then
        tmp = (1.6453555072203998d0 * (y * b)) + x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y * 3.13060547623) + x;
	double tmp;
	if (z <= -1.2e+18) {
		tmp = t_1;
	} else if (z <= 6.4e+36) {
		tmp = (1.6453555072203998 * (y * b)) + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (y * 3.13060547623) + x
	tmp = 0
	if z <= -1.2e+18:
		tmp = t_1
	elif z <= 6.4e+36:
		tmp = (1.6453555072203998 * (y * b)) + x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y * 3.13060547623) + x)
	tmp = 0.0
	if (z <= -1.2e+18)
		tmp = t_1;
	elseif (z <= 6.4e+36)
		tmp = Float64(Float64(1.6453555072203998 * Float64(y * b)) + x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (y * 3.13060547623) + x;
	tmp = 0.0;
	if (z <= -1.2e+18)
		tmp = t_1;
	elseif (z <= 6.4e+36)
		tmp = (1.6453555072203998 * (y * b)) + x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y * 3.13060547623), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[z, -1.2e+18], t$95$1, If[LessEqual[z, 6.4e+36], N[(N[(1.6453555072203998 * N[(y * b), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.2e18 or 6.3999999999999998e36 < z

   1. Initial program 12.4%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -1.2e18 < z < 6.3999999999999998e36

   1. Initial program 98.3%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 22: 83.5% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot 3.13060547623 + x\\ \mathbf{if}\;z \leq -6.2 \cdot 10^{+18}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{+36}:\\ \;\;\;\;x + \left(1.6453555072203998 \cdot b\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (* y 3.13060547623) x)))
   (if (<= z -6.2e+18)
     t_1
     (if (<= z 6.4e+36) (+ x (* (* 1.6453555072203998 b) y)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y * 3.13060547623) + x;
	double tmp;
	if (z <= -6.2e+18) {
		tmp = t_1;
	} else if (z <= 6.4e+36) {
		tmp = x + ((1.6453555072203998 * b) * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

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 = (y * 3.13060547623d0) + x
    if (z <= (-6.2d+18)) then
        tmp = t_1
    else if (z <= 6.4d+36) then
        tmp = x + ((1.6453555072203998d0 * b) * y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y * 3.13060547623) + x;
	double tmp;
	if (z <= -6.2e+18) {
		tmp = t_1;
	} else if (z <= 6.4e+36) {
		tmp = x + ((1.6453555072203998 * b) * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (y * 3.13060547623) + x
	tmp = 0
	if z <= -6.2e+18:
		tmp = t_1
	elif z <= 6.4e+36:
		tmp = x + ((1.6453555072203998 * b) * y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y * 3.13060547623) + x)
	tmp = 0.0
	if (z <= -6.2e+18)
		tmp = t_1;
	elseif (z <= 6.4e+36)
		tmp = Float64(x + Float64(Float64(1.6453555072203998 * b) * y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (y * 3.13060547623) + x;
	tmp = 0.0;
	if (z <= -6.2e+18)
		tmp = t_1;
	elseif (z <= 6.4e+36)
		tmp = x + ((1.6453555072203998 * b) * y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y * 3.13060547623), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[z, -6.2e+18], t$95$1, If[LessEqual[z, 6.4e+36], N[(x + N[(N[(1.6453555072203998 * b), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -6.2e18 or 6.3999999999999998e36 < z

   1. Initial program 12.4%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -6.2e18 < z < 6.3999999999999998e36

   1. Initial program 98.3%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   2. Add Preprocessing

   4. Applied egg-rr 0

      \[\leadsto expr\]

   5. Taylor expanded in z around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 23: 49.2% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{-254}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{-165}:\\ \;\;\;\;y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -1.65e-254) x (if (<= x 1.25e-165) (* y 3.13060547623) x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.65e-254) {
		tmp = x;
	} else if (x <= 1.25e-165) {
		tmp = y * 3.13060547623;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

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 (x <= (-1.65d-254)) then
        tmp = x
    else if (x <= 1.25d-165) then
        tmp = y * 3.13060547623d0
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.65e-254) {
		tmp = x;
	} else if (x <= 1.25e-165) {
		tmp = y * 3.13060547623;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -1.65e-254:
		tmp = x
	elif x <= 1.25e-165:
		tmp = y * 3.13060547623
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -1.65e-254)
		tmp = x;
	elseif (x <= 1.25e-165)
		tmp = Float64(y * 3.13060547623);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -1.65e-254)
		tmp = x;
	elseif (x <= 1.25e-165)
		tmp = y * 3.13060547623;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -1.65e-254], x, If[LessEqual[x, 1.25e-165], N[(y * 3.13060547623), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -1.65000000000000008e-254 or 1.24999999999999995e-165 < x

   1. Initial program 63.7%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -1.65000000000000008e-254 < x < 1.24999999999999995e-165

   1. Initial program 54.4%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 24: 45.0% accurate, 37.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 x)

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 61.7%

   \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
2. Add Preprocessing

3. Taylor expanded in x around inf 0

   \[\leadsto expr\]

5. Simplified 0

   \[\leadsto expr\]
6. Add Preprocessing

Developer target: 98.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\left(3.13060547623 - \frac{36.527041698806414}{z}\right) + \frac{t}{z \cdot z}\right) \cdot \frac{y}{1}\\ \mathbf{if}\;z < -6.499344996252632 \cdot 10^{+53}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z < 7.066965436914287 \cdot 10^{+59}:\\ \;\;\;\;x + \frac{y}{\frac{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771}{\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(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))))

C

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;
}

Fortran

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

Java

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;
}

Python

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

Julia

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

MATLAB

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

Wolfram

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]]]

Reproduce

herbie shell --seed 2024110 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, D"
  :precision binary64

  :alt
  (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))))