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

Percentage Accurate: 58.5% → 98.8%

Time: 23.6s

Alternatives: 19

Speedup: 2.5×

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: 58.5% 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: 98.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771\\ \mathbf{if}\;z \leq -245000000000 \lor \neg \left(z \leq 7.5 \cdot 10^{+30}\right):\\ \;\;\;\;x + \left(\mathsf{fma}\left(\frac{y}{z}, -36.52704169880642, \mathsf{fma}\left(y, 3.13060547623, \frac{y}{\frac{{z}^{2}}{t + 457.9610022158428}}\right)\right) + \frac{y}{\frac{{z}^{3}}{a + \left(-5864.8025282699045 + t \cdot -15.234687407\right)}}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(\frac{b}{t\_1} + \frac{z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right)}{t\_1}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (+
          (*
           z
           (+ (* z (+ (* z (+ z 15.234687407)) 31.4690115749)) 11.9400905721))
          0.607771387771)))
   (if (or (<= z -245000000000.0) (not (<= z 7.5e+30)))
     (+
      x
      (+
       (fma
        (/ y z)
        -36.52704169880642
        (fma y 3.13060547623 (/ y (/ (pow z 2.0) (+ t 457.9610022158428)))))
       (/
        y
        (/ (pow z 3.0) (+ a (+ -5864.8025282699045 (* t -15.234687407)))))))
     (+
      x
      (*
       y
       (+
        (/ b t_1)
        (/
         (* z (+ (* z (+ (* z (+ (* z 3.13060547623) 11.1667541262)) t)) a))
         t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771;
	double tmp;
	if ((z <= -245000000000.0) || !(z <= 7.5e+30)) {
		tmp = x + (fma((y / z), -36.52704169880642, fma(y, 3.13060547623, (y / (pow(z, 2.0) / (t + 457.9610022158428))))) + (y / (pow(z, 3.0) / (a + (-5864.8025282699045 + (t * -15.234687407))))));
	} else {
		tmp = x + (y * ((b / t_1) + ((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) / t_1)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)
	tmp = 0.0
	if ((z <= -245000000000.0) || !(z <= 7.5e+30))
		tmp = Float64(x + Float64(fma(Float64(y / z), -36.52704169880642, fma(y, 3.13060547623, Float64(y / Float64((z ^ 2.0) / Float64(t + 457.9610022158428))))) + Float64(y / Float64((z ^ 3.0) / Float64(a + Float64(-5864.8025282699045 + Float64(t * -15.234687407)))))));
	else
		tmp = Float64(x + Float64(y * Float64(Float64(b / t_1) + Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * 3.13060547623) + 11.1667541262)) + t)) + a)) / t_1))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = 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]}, If[Or[LessEqual[z, -245000000000.0], N[Not[LessEqual[z, 7.5e+30]], $MachinePrecision]], N[(x + N[(N[(N[(y / z), $MachinePrecision] * -36.52704169880642 + N[(y * 3.13060547623 + N[(y / N[(N[Power[z, 2.0], $MachinePrecision] / N[(t + 457.9610022158428), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y / N[(N[Power[z, 3.0], $MachinePrecision] / N[(a + N[(-5864.8025282699045 + N[(t * -15.234687407), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(N[(b / t$95$1), $MachinePrecision] + 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] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.45e11 or 7.49999999999999973e30 < z

   1. Initial program 14.6%

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

   3. Simplified 20.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), t\right), a\right), b\right)}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)}, y, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 80.2%

      \[\leadsto \color{blue}{x + \left(-36.52704169880642 \cdot \frac{y}{z} + \left(3.13060547623 \cdot y + \left(\frac{y \cdot \left(457.9610022158428 + t\right)}{{z}^{2}} + \frac{y \cdot \left(\left(1112.0901850848957 + a\right) - 15.234687407 \cdot \left(457.9610022158428 + t\right)\right)}{{z}^{3}}\right)\right)\right)} \]

   7. Simplified 99.9%

      \[\leadsto \color{blue}{x + \left(\mathsf{fma}\left(\frac{y}{z}, -36.52704169880642, \mathsf{fma}\left(y, 3.13060547623, \frac{y}{\frac{{z}^{2}}{t + 457.9610022158428}}\right)\right) + \frac{y}{\frac{{z}^{3}}{a + \left(-5864.8025282699045 + -15.234687407 \cdot t\right)}}\right)} \]

   if -2.45e11 < z < 7.49999999999999973e30

   1. Initial program 98.9%

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

   3. Simplified 99.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), t\right), a\right), b\right)}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)}, y, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 99.7%

      \[\leadsto \color{blue}{x + y \cdot \left(\frac{b}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(15.234687407 + z\right)\right)\right)} + \frac{z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + 3.13060547623 \cdot z\right)\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(15.234687407 + z\right)\right)\right)}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -245000000000 \lor \neg \left(z \leq 7.5 \cdot 10^{+30}\right):\\ \;\;\;\;x + \left(\mathsf{fma}\left(\frac{y}{z}, -36.52704169880642, \mathsf{fma}\left(y, 3.13060547623, \frac{y}{\frac{{z}^{2}}{t + 457.9610022158428}}\right)\right) + \frac{y}{\frac{{z}^{3}}{a + \left(-5864.8025282699045 + t \cdot -15.234687407\right)}}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(\frac{b}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771} + \frac{z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 99.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771\\ \mathbf{if}\;\frac{y \cdot \left(z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right) + b\right)}{t\_1} \leq \infty:\\ \;\;\;\;x + y \cdot \left(\frac{b}{t\_1} + \frac{z}{\frac{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), t\right), a\right)}}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \mathsf{fma}\left(\frac{y}{z}, -36.52704169880642, y \cdot 3.13060547623 + \frac{y}{{z}^{2}} \cdot \left(t + 457.9610022158428\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (+
          (*
           z
           (+ (* z (+ (* z (+ z 15.234687407)) 31.4690115749)) 11.9400905721))
          0.607771387771)))
   (if (<=
        (/
         (*
          y
          (+
           (* z (+ (* z (+ (* z (+ (* z 3.13060547623) 11.1667541262)) t)) a))
           b))
         t_1)
        INFINITY)
     (+
      x
      (*
       y
       (+
        (/ b t_1)
        (/
         z
         (/
          (fma
           z
           (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721)
           0.607771387771)
          (fma z (fma z (fma z 3.13060547623 11.1667541262) t) a))))))
     (+
      x
      (fma
       (/ y z)
       -36.52704169880642
       (+
        (* y 3.13060547623)
        (* (/ y (pow z 2.0)) (+ t 457.9610022158428))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771;
	double tmp;
	if (((y * ((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / t_1) <= ((double) INFINITY)) {
		tmp = x + (y * ((b / t_1) + (z / (fma(z, fma(z, fma(z, (z + 15.234687407), 31.4690115749), 11.9400905721), 0.607771387771) / fma(z, fma(z, fma(z, 3.13060547623, 11.1667541262), t), a)))));
	} else {
		tmp = x + fma((y / z), -36.52704169880642, ((y * 3.13060547623) + ((y / pow(z, 2.0)) * (t + 457.9610022158428))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)
	tmp = 0.0
	if (Float64(Float64(y * Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / t_1) <= Inf)
		tmp = Float64(x + Float64(y * Float64(Float64(b / t_1) + Float64(z / Float64(fma(z, fma(z, fma(z, Float64(z + 15.234687407), 31.4690115749), 11.9400905721), 0.607771387771) / fma(z, fma(z, fma(z, 3.13060547623, 11.1667541262), t), a))))));
	else
		tmp = Float64(x + fma(Float64(y / z), -36.52704169880642, Float64(Float64(y * 3.13060547623) + Float64(Float64(y / (z ^ 2.0)) * Float64(t + 457.9610022158428)))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = 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]}, If[LessEqual[N[(N[(y * N[(N[(z * N[(N[(z * N[(N[(z * N[(N[(z * 3.13060547623), $MachinePrecision] + 11.1667541262), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], Infinity], N[(x + N[(y * N[(N[(b / t$95$1), $MachinePrecision] + N[(z / N[(N[(z * N[(z * N[(z * N[(z + 15.234687407), $MachinePrecision] + 31.4690115749), $MachinePrecision] + 11.9400905721), $MachinePrecision] + 0.607771387771), $MachinePrecision] / N[(z * N[(z * N[(z * 3.13060547623 + 11.1667541262), $MachinePrecision] + t), $MachinePrecision] + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y / z), $MachinePrecision] * -36.52704169880642 + N[(N[(y * 3.13060547623), $MachinePrecision] + N[(N[(y / N[Power[z, 2.0], $MachinePrecision]), $MachinePrecision] * N[(t + 457.9610022158428), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z 313060547623/100000000000) 55833770631/5000000000) z) t) z) a) z) b)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 z 15234687407/1000000000) z) 314690115749/10000000000) z) 119400905721/10000000000) z) 607771387771/1000000000000)) < +inf.0

   1. Initial program 90.9%

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

   3. Simplified 96.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), t\right), a\right), b\right)}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)}, y, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 96.1%

      \[\leadsto \color{blue}{x + y \cdot \left(\frac{b}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(15.234687407 + z\right)\right)\right)} + \frac{z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + 3.13060547623 \cdot z\right)\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(15.234687407 + z\right)\right)\right)}\right)} \]
   6. Step-by-step derivation

      1. *-un-lft-identity 96.1%

         \[\leadsto x + y \cdot \left(\frac{b}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(15.234687407 + z\right)\right)\right)} + \color{blue}{1 \cdot \frac{z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + 3.13060547623 \cdot z\right)\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(15.234687407 + z\right)\right)\right)}}\right) \]

      2. associate-/l* 98.5%

         \[\leadsto x + y \cdot \left(\frac{b}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(15.234687407 + z\right)\right)\right)} + 1 \cdot \color{blue}{\frac{z}{\frac{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(15.234687407 + z\right)\right)\right)}{a + z \cdot \left(t + z \cdot \left(11.1667541262 + 3.13060547623 \cdot z\right)\right)}}}\right) \]

      3. +-commutative 98.5%

         \[\leadsto x + y \cdot \left(\frac{b}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(15.234687407 + z\right)\right)\right)} + 1 \cdot \frac{z}{\frac{\color{blue}{z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(15.234687407 + z\right)\right)\right) + 0.607771387771}}{a + z \cdot \left(t + z \cdot \left(11.1667541262 + 3.13060547623 \cdot z\right)\right)}}\right) \]

      4. fma-def 98.5%

         \[\leadsto x + y \cdot \left(\frac{b}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(15.234687407 + z\right)\right)\right)} + 1 \cdot \frac{z}{\frac{\color{blue}{\mathsf{fma}\left(z, 11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(15.234687407 + z\right)\right), 0.607771387771\right)}}{a + z \cdot \left(t + z \cdot \left(11.1667541262 + 3.13060547623 \cdot z\right)\right)}}\right) \]

      5. +-commutative 98.5%

         \[\leadsto x + y \cdot \left(\frac{b}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(15.234687407 + z\right)\right)\right)} + 1 \cdot \frac{z}{\frac{\mathsf{fma}\left(z, \color{blue}{z \cdot \left(31.4690115749 + z \cdot \left(15.234687407 + z\right)\right) + 11.9400905721}, 0.607771387771\right)}{a + z \cdot \left(t + z \cdot \left(11.1667541262 + 3.13060547623 \cdot z\right)\right)}}\right) \]

      6. fma-def 98.5%

         \[\leadsto x + y \cdot \left(\frac{b}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(15.234687407 + z\right)\right)\right)} + 1 \cdot \frac{z}{\frac{\mathsf{fma}\left(z, \color{blue}{\mathsf{fma}\left(z, 31.4690115749 + z \cdot \left(15.234687407 + z\right), 11.9400905721\right)}, 0.607771387771\right)}{a + z \cdot \left(t + z \cdot \left(11.1667541262 + 3.13060547623 \cdot z\right)\right)}}\right) \]

      7. +-commutative 98.5%

         \[\leadsto x + y \cdot \left(\frac{b}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(15.234687407 + z\right)\right)\right)} + 1 \cdot \frac{z}{\frac{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \color{blue}{z \cdot \left(15.234687407 + z\right) + 31.4690115749}, 11.9400905721\right), 0.607771387771\right)}{a + z \cdot \left(t + z \cdot \left(11.1667541262 + 3.13060547623 \cdot z\right)\right)}}\right) \]

      8. fma-def 98.5%

         \[\leadsto x + y \cdot \left(\frac{b}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(15.234687407 + z\right)\right)\right)} + 1 \cdot \frac{z}{\frac{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \color{blue}{\mathsf{fma}\left(z, 15.234687407 + z, 31.4690115749\right)}, 11.9400905721\right), 0.607771387771\right)}{a + z \cdot \left(t + z \cdot \left(11.1667541262 + 3.13060547623 \cdot z\right)\right)}}\right) \]

      9. +-commutative 98.5%

         \[\leadsto x + y \cdot \left(\frac{b}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(15.234687407 + z\right)\right)\right)} + 1 \cdot \frac{z}{\frac{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, \color{blue}{z + 15.234687407}, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)}{a + z \cdot \left(t + z \cdot \left(11.1667541262 + 3.13060547623 \cdot z\right)\right)}}\right) \]

      10. +-commutative 98.5%

          \[\leadsto x + y \cdot \left(\frac{b}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(15.234687407 + z\right)\right)\right)} + 1 \cdot \frac{z}{\frac{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)}{\color{blue}{z \cdot \left(t + z \cdot \left(11.1667541262 + 3.13060547623 \cdot z\right)\right) + a}}}\right) \]

      11. fma-def 98.5%

          \[\leadsto x + y \cdot \left(\frac{b}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(15.234687407 + z\right)\right)\right)} + 1 \cdot \frac{z}{\frac{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)}{\color{blue}{\mathsf{fma}\left(z, t + z \cdot \left(11.1667541262 + 3.13060547623 \cdot z\right), a\right)}}}\right) \]

   7. Applied egg-rr 98.5%

      \[\leadsto x + y \cdot \left(\frac{b}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(15.234687407 + z\right)\right)\right)} + \color{blue}{1 \cdot \frac{z}{\frac{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), t\right), a\right)}}}\right) \]

   if +inf.0 < (/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z 313060547623/100000000000) 55833770631/5000000000) z) t) z) a) z) b)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 z 15234687407/1000000000) z) 314690115749/10000000000) z) 119400905721/10000000000) z) 607771387771/1000000000000))

   1. Initial program 0.0%

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

   3. Simplified 0.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), t\right), a\right), b\right)}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)}, y, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 86.7%

      \[\leadsto \color{blue}{x + \left(-36.52704169880642 \cdot \frac{y}{z} + \left(3.13060547623 \cdot y + \frac{y \cdot \left(457.9610022158428 + t\right)}{{z}^{2}}\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 86.7%

         \[\leadsto x + \left(\color{blue}{\frac{y}{z} \cdot -36.52704169880642} + \left(3.13060547623 \cdot y + \frac{y \cdot \left(457.9610022158428 + t\right)}{{z}^{2}}\right)\right) \]

      2. fma-def 86.7%

         \[\leadsto x + \color{blue}{\mathsf{fma}\left(\frac{y}{z}, -36.52704169880642, 3.13060547623 \cdot y + \frac{y \cdot \left(457.9610022158428 + t\right)}{{z}^{2}}\right)} \]

      3. *-commutative 86.7%

         \[\leadsto x + \mathsf{fma}\left(\frac{y}{z}, -36.52704169880642, \color{blue}{y \cdot 3.13060547623} + \frac{y \cdot \left(457.9610022158428 + t\right)}{{z}^{2}}\right) \]

      4. fma-def 86.7%

         \[\leadsto x + \mathsf{fma}\left(\frac{y}{z}, -36.52704169880642, \color{blue}{\mathsf{fma}\left(y, 3.13060547623, \frac{y \cdot \left(457.9610022158428 + t\right)}{{z}^{2}}\right)}\right) \]

      5. associate-/l* 99.9%

         \[\leadsto x + \mathsf{fma}\left(\frac{y}{z}, -36.52704169880642, \mathsf{fma}\left(y, 3.13060547623, \color{blue}{\frac{y}{\frac{{z}^{2}}{457.9610022158428 + t}}}\right)\right) \]

      6. +-commutative 99.9%

         \[\leadsto x + \mathsf{fma}\left(\frac{y}{z}, -36.52704169880642, \mathsf{fma}\left(y, 3.13060547623, \frac{y}{\frac{{z}^{2}}{\color{blue}{t + 457.9610022158428}}}\right)\right) \]

   7. Simplified 99.9%

      \[\leadsto \color{blue}{x + \mathsf{fma}\left(\frac{y}{z}, -36.52704169880642, \mathsf{fma}\left(y, 3.13060547623, \frac{y}{\frac{{z}^{2}}{t + 457.9610022158428}}\right)\right)} \]
   8. Step-by-step derivation

      1. fma-udef 99.9%

         \[\leadsto x + \mathsf{fma}\left(\frac{y}{z}, -36.52704169880642, \color{blue}{y \cdot 3.13060547623 + \frac{y}{\frac{{z}^{2}}{t + 457.9610022158428}}}\right) \]

      2. associate-/r/ 99.9%

         \[\leadsto x + \mathsf{fma}\left(\frac{y}{z}, -36.52704169880642, y \cdot 3.13060547623 + \color{blue}{\frac{y}{{z}^{2}} \cdot \left(t + 457.9610022158428\right)}\right) \]

   9. Applied egg-rr 99.9%

      \[\leadsto x + \mathsf{fma}\left(\frac{y}{z}, -36.52704169880642, \color{blue}{y \cdot 3.13060547623 + \frac{y}{{z}^{2}} \cdot \left(t + 457.9610022158428\right)}\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right) + b\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771} \leq \infty:\\ \;\;\;\;x + y \cdot \left(\frac{b}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771} + \frac{z}{\frac{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), t\right), a\right)}}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \mathsf{fma}\left(\frac{y}{z}, -36.52704169880642, y \cdot 3.13060547623 + \frac{y}{{z}^{2}} \cdot \left(t + 457.9610022158428\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771\\ \mathbf{if}\;z \leq -6 \cdot 10^{+29}:\\ \;\;\;\;x + y \cdot \left(\left(\frac{t + 457.9610022158428}{{z}^{2}} - \frac{36.52704169880642}{z}\right) - -3.13060547623\right)\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+30}:\\ \;\;\;\;x + y \cdot \left(\frac{b}{t\_1} + \frac{z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right)}{t\_1}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \mathsf{fma}\left(\frac{y}{z}, -36.52704169880642, y \cdot 3.13060547623 + \frac{y}{{z}^{2}} \cdot \left(t + 457.9610022158428\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (+
          (*
           z
           (+ (* z (+ (* z (+ z 15.234687407)) 31.4690115749)) 11.9400905721))
          0.607771387771)))
   (if (<= z -6e+29)
     (+
      x
      (*
       y
       (-
        (- (/ (+ t 457.9610022158428) (pow z 2.0)) (/ 36.52704169880642 z))
        -3.13060547623)))
     (if (<= z 2.8e+30)
       (+
        x
        (*
         y
         (+
          (/ b t_1)
          (/
           (* z (+ (* z (+ (* z (+ (* z 3.13060547623) 11.1667541262)) t)) a))
           t_1))))
       (+
        x
        (fma
         (/ y z)
         -36.52704169880642
         (+
          (* y 3.13060547623)
          (* (/ y (pow z 2.0)) (+ t 457.9610022158428)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771;
	double tmp;
	if (z <= -6e+29) {
		tmp = x + (y * ((((t + 457.9610022158428) / pow(z, 2.0)) - (36.52704169880642 / z)) - -3.13060547623));
	} else if (z <= 2.8e+30) {
		tmp = x + (y * ((b / t_1) + ((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) / t_1)));
	} else {
		tmp = x + fma((y / z), -36.52704169880642, ((y * 3.13060547623) + ((y / pow(z, 2.0)) * (t + 457.9610022158428))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)
	tmp = 0.0
	if (z <= -6e+29)
		tmp = Float64(x + Float64(y * Float64(Float64(Float64(Float64(t + 457.9610022158428) / (z ^ 2.0)) - Float64(36.52704169880642 / z)) - -3.13060547623)));
	elseif (z <= 2.8e+30)
		tmp = Float64(x + Float64(y * Float64(Float64(b / t_1) + Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * 3.13060547623) + 11.1667541262)) + t)) + a)) / t_1))));
	else
		tmp = Float64(x + fma(Float64(y / z), -36.52704169880642, Float64(Float64(y * 3.13060547623) + Float64(Float64(y / (z ^ 2.0)) * Float64(t + 457.9610022158428)))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = 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]}, If[LessEqual[z, -6e+29], N[(x + N[(y * N[(N[(N[(N[(t + 457.9610022158428), $MachinePrecision] / N[Power[z, 2.0], $MachinePrecision]), $MachinePrecision] - N[(36.52704169880642 / z), $MachinePrecision]), $MachinePrecision] - -3.13060547623), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.8e+30], N[(x + N[(y * N[(N[(b / t$95$1), $MachinePrecision] + 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] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y / z), $MachinePrecision] * -36.52704169880642 + N[(N[(y * 3.13060547623), $MachinePrecision] + N[(N[(y / N[Power[z, 2.0], $MachinePrecision]), $MachinePrecision] * N[(t + 457.9610022158428), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.9999999999999998e29

   1. Initial program 7.9%

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

   3. Simplified 14.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), t\right), a\right), b\right)}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)}, y, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 91.1%

      \[\leadsto \color{blue}{x + \left(-36.52704169880642 \cdot \frac{y}{z} + \left(3.13060547623 \cdot y + \frac{y \cdot \left(457.9610022158428 + t\right)}{{z}^{2}}\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 91.1%

         \[\leadsto x + \left(\color{blue}{\frac{y}{z} \cdot -36.52704169880642} + \left(3.13060547623 \cdot y + \frac{y \cdot \left(457.9610022158428 + t\right)}{{z}^{2}}\right)\right) \]

      2. fma-def 91.1%

         \[\leadsto x + \color{blue}{\mathsf{fma}\left(\frac{y}{z}, -36.52704169880642, 3.13060547623 \cdot y + \frac{y \cdot \left(457.9610022158428 + t\right)}{{z}^{2}}\right)} \]

      3. *-commutative 91.1%

         \[\leadsto x + \mathsf{fma}\left(\frac{y}{z}, -36.52704169880642, \color{blue}{y \cdot 3.13060547623} + \frac{y \cdot \left(457.9610022158428 + t\right)}{{z}^{2}}\right) \]

      4. fma-def 91.1%

         \[\leadsto x + \mathsf{fma}\left(\frac{y}{z}, -36.52704169880642, \color{blue}{\mathsf{fma}\left(y, 3.13060547623, \frac{y \cdot \left(457.9610022158428 + t\right)}{{z}^{2}}\right)}\right) \]

      5. associate-/l* 99.8%

         \[\leadsto x + \mathsf{fma}\left(\frac{y}{z}, -36.52704169880642, \mathsf{fma}\left(y, 3.13060547623, \color{blue}{\frac{y}{\frac{{z}^{2}}{457.9610022158428 + t}}}\right)\right) \]

      6. +-commutative 99.8%

         \[\leadsto x + \mathsf{fma}\left(\frac{y}{z}, -36.52704169880642, \mathsf{fma}\left(y, 3.13060547623, \frac{y}{\frac{{z}^{2}}{\color{blue}{t + 457.9610022158428}}}\right)\right) \]

   7. Simplified 99.8%

      \[\leadsto \color{blue}{x + \mathsf{fma}\left(\frac{y}{z}, -36.52704169880642, \mathsf{fma}\left(y, 3.13060547623, \frac{y}{\frac{{z}^{2}}{t + 457.9610022158428}}\right)\right)} \]

   8. Taylor expanded in y around -inf 99.9%

      \[\leadsto x + \color{blue}{-1 \cdot \left(y \cdot \left(\left(-1 \cdot \frac{457.9610022158428 + t}{{z}^{2}} + 36.52704169880642 \cdot \frac{1}{z}\right) - 3.13060547623\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 99.9%

         \[\leadsto x + \color{blue}{\left(-y \cdot \left(\left(-1 \cdot \frac{457.9610022158428 + t}{{z}^{2}} + 36.52704169880642 \cdot \frac{1}{z}\right) - 3.13060547623\right)\right)} \]

      2. distribute-rgt-neg-in 99.9%

         \[\leadsto x + \color{blue}{y \cdot \left(-\left(\left(-1 \cdot \frac{457.9610022158428 + t}{{z}^{2}} + 36.52704169880642 \cdot \frac{1}{z}\right) - 3.13060547623\right)\right)} \]

      3. sub-neg 99.9%

         \[\leadsto x + y \cdot \left(-\color{blue}{\left(\left(-1 \cdot \frac{457.9610022158428 + t}{{z}^{2}} + 36.52704169880642 \cdot \frac{1}{z}\right) + \left(-3.13060547623\right)\right)}\right) \]

      4. +-commutative 99.9%

         \[\leadsto x + y \cdot \left(-\left(\color{blue}{\left(36.52704169880642 \cdot \frac{1}{z} + -1 \cdot \frac{457.9610022158428 + t}{{z}^{2}}\right)} + \left(-3.13060547623\right)\right)\right) \]

      5. mul-1-neg 99.9%

         \[\leadsto x + y \cdot \left(-\left(\left(36.52704169880642 \cdot \frac{1}{z} + \color{blue}{\left(-\frac{457.9610022158428 + t}{{z}^{2}}\right)}\right) + \left(-3.13060547623\right)\right)\right) \]

      6. unsub-neg 99.9%

         \[\leadsto x + y \cdot \left(-\left(\color{blue}{\left(36.52704169880642 \cdot \frac{1}{z} - \frac{457.9610022158428 + t}{{z}^{2}}\right)} + \left(-3.13060547623\right)\right)\right) \]

      7. associate-*r/ 99.9%

         \[\leadsto x + y \cdot \left(-\left(\left(\color{blue}{\frac{36.52704169880642 \cdot 1}{z}} - \frac{457.9610022158428 + t}{{z}^{2}}\right) + \left(-3.13060547623\right)\right)\right) \]

      8. metadata-eval 99.9%

         \[\leadsto x + y \cdot \left(-\left(\left(\frac{\color{blue}{36.52704169880642}}{z} - \frac{457.9610022158428 + t}{{z}^{2}}\right) + \left(-3.13060547623\right)\right)\right) \]

      9. +-commutative 99.9%

         \[\leadsto x + y \cdot \left(-\left(\left(\frac{36.52704169880642}{z} - \frac{\color{blue}{t + 457.9610022158428}}{{z}^{2}}\right) + \left(-3.13060547623\right)\right)\right) \]

      10. metadata-eval 99.9%

          \[\leadsto x + y \cdot \left(-\left(\left(\frac{36.52704169880642}{z} - \frac{t + 457.9610022158428}{{z}^{2}}\right) + \color{blue}{-3.13060547623}\right)\right) \]

   10. Simplified 99.9%

       \[\leadsto x + \color{blue}{y \cdot \left(-\left(\left(\frac{36.52704169880642}{z} - \frac{t + 457.9610022158428}{{z}^{2}}\right) + -3.13060547623\right)\right)} \]

   if -5.9999999999999998e29 < z < 2.79999999999999983e30

   1. Initial program 96.3%

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

   3. Simplified 99.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), t\right), a\right), b\right)}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)}, y, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 99.6%

      \[\leadsto \color{blue}{x + y \cdot \left(\frac{b}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(15.234687407 + z\right)\right)\right)} + \frac{z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + 3.13060547623 \cdot z\right)\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(15.234687407 + z\right)\right)\right)}\right)} \]

   if 2.79999999999999983e30 < z

   1. Initial program 14.2%

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

   3. Simplified 14.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), t\right), a\right), b\right)}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)}, y, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 83.3%

      \[\leadsto \color{blue}{x + \left(-36.52704169880642 \cdot \frac{y}{z} + \left(3.13060547623 \cdot y + \frac{y \cdot \left(457.9610022158428 + t\right)}{{z}^{2}}\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 83.3%

         \[\leadsto x + \left(\color{blue}{\frac{y}{z} \cdot -36.52704169880642} + \left(3.13060547623 \cdot y + \frac{y \cdot \left(457.9610022158428 + t\right)}{{z}^{2}}\right)\right) \]

      2. fma-def 83.3%

         \[\leadsto x + \color{blue}{\mathsf{fma}\left(\frac{y}{z}, -36.52704169880642, 3.13060547623 \cdot y + \frac{y \cdot \left(457.9610022158428 + t\right)}{{z}^{2}}\right)} \]

      3. *-commutative 83.3%

         \[\leadsto x + \mathsf{fma}\left(\frac{y}{z}, -36.52704169880642, \color{blue}{y \cdot 3.13060547623} + \frac{y \cdot \left(457.9610022158428 + t\right)}{{z}^{2}}\right) \]

      4. fma-def 83.3%

         \[\leadsto x + \mathsf{fma}\left(\frac{y}{z}, -36.52704169880642, \color{blue}{\mathsf{fma}\left(y, 3.13060547623, \frac{y \cdot \left(457.9610022158428 + t\right)}{{z}^{2}}\right)}\right) \]

      5. associate-/l* 98.5%

         \[\leadsto x + \mathsf{fma}\left(\frac{y}{z}, -36.52704169880642, \mathsf{fma}\left(y, 3.13060547623, \color{blue}{\frac{y}{\frac{{z}^{2}}{457.9610022158428 + t}}}\right)\right) \]

      6. +-commutative 98.5%

         \[\leadsto x + \mathsf{fma}\left(\frac{y}{z}, -36.52704169880642, \mathsf{fma}\left(y, 3.13060547623, \frac{y}{\frac{{z}^{2}}{\color{blue}{t + 457.9610022158428}}}\right)\right) \]

   7. Simplified 98.5%

      \[\leadsto \color{blue}{x + \mathsf{fma}\left(\frac{y}{z}, -36.52704169880642, \mathsf{fma}\left(y, 3.13060547623, \frac{y}{\frac{{z}^{2}}{t + 457.9610022158428}}\right)\right)} \]
   8. Step-by-step derivation

      1. fma-udef 98.5%

         \[\leadsto x + \mathsf{fma}\left(\frac{y}{z}, -36.52704169880642, \color{blue}{y \cdot 3.13060547623 + \frac{y}{\frac{{z}^{2}}{t + 457.9610022158428}}}\right) \]

      2. associate-/r/ 98.5%

         \[\leadsto x + \mathsf{fma}\left(\frac{y}{z}, -36.52704169880642, y \cdot 3.13060547623 + \color{blue}{\frac{y}{{z}^{2}} \cdot \left(t + 457.9610022158428\right)}\right) \]

   9. Applied egg-rr 98.5%

      \[\leadsto x + \mathsf{fma}\left(\frac{y}{z}, -36.52704169880642, \color{blue}{y \cdot 3.13060547623 + \frac{y}{{z}^{2}} \cdot \left(t + 457.9610022158428\right)}\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+29}:\\ \;\;\;\;x + y \cdot \left(\left(\frac{t + 457.9610022158428}{{z}^{2}} - \frac{36.52704169880642}{z}\right) - -3.13060547623\right)\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+30}:\\ \;\;\;\;x + y \cdot \left(\frac{b}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771} + \frac{z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \mathsf{fma}\left(\frac{y}{z}, -36.52704169880642, y \cdot 3.13060547623 + \frac{y}{{z}^{2}} \cdot \left(t + 457.9610022158428\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 98.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771\\ \mathbf{if}\;z \leq -6 \cdot 10^{+29} \lor \neg \left(z \leq 2.2 \cdot 10^{+31}\right):\\ \;\;\;\;x + y \cdot \left(\left(\frac{t + 457.9610022158428}{{z}^{2}} - \frac{36.52704169880642}{z}\right) - -3.13060547623\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(\frac{b}{t\_1} + \frac{z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right)}{t\_1}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (+
          (*
           z
           (+ (* z (+ (* z (+ z 15.234687407)) 31.4690115749)) 11.9400905721))
          0.607771387771)))
   (if (or (<= z -6e+29) (not (<= z 2.2e+31)))
     (+
      x
      (*
       y
       (-
        (- (/ (+ t 457.9610022158428) (pow z 2.0)) (/ 36.52704169880642 z))
        -3.13060547623)))
     (+
      x
      (*
       y
       (+
        (/ b t_1)
        (/
         (* z (+ (* z (+ (* z (+ (* z 3.13060547623) 11.1667541262)) t)) a))
         t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771;
	double tmp;
	if ((z <= -6e+29) || !(z <= 2.2e+31)) {
		tmp = x + (y * ((((t + 457.9610022158428) / pow(z, 2.0)) - (36.52704169880642 / z)) - -3.13060547623));
	} else {
		tmp = x + (y * ((b / t_1) + ((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) / 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 = (z * ((z * ((z * (z + 15.234687407d0)) + 31.4690115749d0)) + 11.9400905721d0)) + 0.607771387771d0
    if ((z <= (-6d+29)) .or. (.not. (z <= 2.2d+31))) then
        tmp = x + (y * ((((t + 457.9610022158428d0) / (z ** 2.0d0)) - (36.52704169880642d0 / z)) - (-3.13060547623d0)))
    else
        tmp = x + (y * ((b / t_1) + ((z * ((z * ((z * ((z * 3.13060547623d0) + 11.1667541262d0)) + t)) + a)) / 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 = (z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771;
	double tmp;
	if ((z <= -6e+29) || !(z <= 2.2e+31)) {
		tmp = x + (y * ((((t + 457.9610022158428) / Math.pow(z, 2.0)) - (36.52704169880642 / z)) - -3.13060547623));
	} else {
		tmp = x + (y * ((b / t_1) + ((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) / t_1)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771
	tmp = 0
	if (z <= -6e+29) or not (z <= 2.2e+31):
		tmp = x + (y * ((((t + 457.9610022158428) / math.pow(z, 2.0)) - (36.52704169880642 / z)) - -3.13060547623))
	else:
		tmp = x + (y * ((b / t_1) + ((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) / t_1)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)
	tmp = 0.0
	if ((z <= -6e+29) || !(z <= 2.2e+31))
		tmp = Float64(x + Float64(y * Float64(Float64(Float64(Float64(t + 457.9610022158428) / (z ^ 2.0)) - Float64(36.52704169880642 / z)) - -3.13060547623)));
	else
		tmp = Float64(x + Float64(y * Float64(Float64(b / t_1) + Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * 3.13060547623) + 11.1667541262)) + t)) + a)) / t_1))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771;
	tmp = 0.0;
	if ((z <= -6e+29) || ~((z <= 2.2e+31)))
		tmp = x + (y * ((((t + 457.9610022158428) / (z ^ 2.0)) - (36.52704169880642 / z)) - -3.13060547623));
	else
		tmp = x + (y * ((b / t_1) + ((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) / t_1)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = 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]}, If[Or[LessEqual[z, -6e+29], N[Not[LessEqual[z, 2.2e+31]], $MachinePrecision]], N[(x + N[(y * N[(N[(N[(N[(t + 457.9610022158428), $MachinePrecision] / N[Power[z, 2.0], $MachinePrecision]), $MachinePrecision] - N[(36.52704169880642 / z), $MachinePrecision]), $MachinePrecision] - -3.13060547623), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(N[(b / t$95$1), $MachinePrecision] + 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] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.9999999999999998e29 or 2.2000000000000001e31 < z

   1. Initial program 11.3%

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

   3. Simplified 14.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), t\right), a\right), b\right)}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)}, y, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 86.9%

      \[\leadsto \color{blue}{x + \left(-36.52704169880642 \cdot \frac{y}{z} + \left(3.13060547623 \cdot y + \frac{y \cdot \left(457.9610022158428 + t\right)}{{z}^{2}}\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 86.9%

         \[\leadsto x + \left(\color{blue}{\frac{y}{z} \cdot -36.52704169880642} + \left(3.13060547623 \cdot y + \frac{y \cdot \left(457.9610022158428 + t\right)}{{z}^{2}}\right)\right) \]

      2. fma-def 86.9%

         \[\leadsto x + \color{blue}{\mathsf{fma}\left(\frac{y}{z}, -36.52704169880642, 3.13060547623 \cdot y + \frac{y \cdot \left(457.9610022158428 + t\right)}{{z}^{2}}\right)} \]

      3. *-commutative 86.9%

         \[\leadsto x + \mathsf{fma}\left(\frac{y}{z}, -36.52704169880642, \color{blue}{y \cdot 3.13060547623} + \frac{y \cdot \left(457.9610022158428 + t\right)}{{z}^{2}}\right) \]

      4. fma-def 86.9%

         \[\leadsto x + \mathsf{fma}\left(\frac{y}{z}, -36.52704169880642, \color{blue}{\mathsf{fma}\left(y, 3.13060547623, \frac{y \cdot \left(457.9610022158428 + t\right)}{{z}^{2}}\right)}\right) \]

      5. associate-/l* 99.1%

         \[\leadsto x + \mathsf{fma}\left(\frac{y}{z}, -36.52704169880642, \mathsf{fma}\left(y, 3.13060547623, \color{blue}{\frac{y}{\frac{{z}^{2}}{457.9610022158428 + t}}}\right)\right) \]

      6. +-commutative 99.1%

         \[\leadsto x + \mathsf{fma}\left(\frac{y}{z}, -36.52704169880642, \mathsf{fma}\left(y, 3.13060547623, \frac{y}{\frac{{z}^{2}}{\color{blue}{t + 457.9610022158428}}}\right)\right) \]

   7. Simplified 99.1%

      \[\leadsto \color{blue}{x + \mathsf{fma}\left(\frac{y}{z}, -36.52704169880642, \mathsf{fma}\left(y, 3.13060547623, \frac{y}{\frac{{z}^{2}}{t + 457.9610022158428}}\right)\right)} \]

   8. Taylor expanded in y around -inf 99.1%

      \[\leadsto x + \color{blue}{-1 \cdot \left(y \cdot \left(\left(-1 \cdot \frac{457.9610022158428 + t}{{z}^{2}} + 36.52704169880642 \cdot \frac{1}{z}\right) - 3.13060547623\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 99.1%

         \[\leadsto x + \color{blue}{\left(-y \cdot \left(\left(-1 \cdot \frac{457.9610022158428 + t}{{z}^{2}} + 36.52704169880642 \cdot \frac{1}{z}\right) - 3.13060547623\right)\right)} \]

      2. distribute-rgt-neg-in 99.1%

         \[\leadsto x + \color{blue}{y \cdot \left(-\left(\left(-1 \cdot \frac{457.9610022158428 + t}{{z}^{2}} + 36.52704169880642 \cdot \frac{1}{z}\right) - 3.13060547623\right)\right)} \]

      3. sub-neg 99.1%

         \[\leadsto x + y \cdot \left(-\color{blue}{\left(\left(-1 \cdot \frac{457.9610022158428 + t}{{z}^{2}} + 36.52704169880642 \cdot \frac{1}{z}\right) + \left(-3.13060547623\right)\right)}\right) \]

      4. +-commutative 99.1%

         \[\leadsto x + y \cdot \left(-\left(\color{blue}{\left(36.52704169880642 \cdot \frac{1}{z} + -1 \cdot \frac{457.9610022158428 + t}{{z}^{2}}\right)} + \left(-3.13060547623\right)\right)\right) \]

      5. mul-1-neg 99.1%

         \[\leadsto x + y \cdot \left(-\left(\left(36.52704169880642 \cdot \frac{1}{z} + \color{blue}{\left(-\frac{457.9610022158428 + t}{{z}^{2}}\right)}\right) + \left(-3.13060547623\right)\right)\right) \]

      6. unsub-neg 99.1%

         \[\leadsto x + y \cdot \left(-\left(\color{blue}{\left(36.52704169880642 \cdot \frac{1}{z} - \frac{457.9610022158428 + t}{{z}^{2}}\right)} + \left(-3.13060547623\right)\right)\right) \]

      7. associate-*r/ 99.1%

         \[\leadsto x + y \cdot \left(-\left(\left(\color{blue}{\frac{36.52704169880642 \cdot 1}{z}} - \frac{457.9610022158428 + t}{{z}^{2}}\right) + \left(-3.13060547623\right)\right)\right) \]

      8. metadata-eval 99.1%

         \[\leadsto x + y \cdot \left(-\left(\left(\frac{\color{blue}{36.52704169880642}}{z} - \frac{457.9610022158428 + t}{{z}^{2}}\right) + \left(-3.13060547623\right)\right)\right) \]

      9. +-commutative 99.1%

         \[\leadsto x + y \cdot \left(-\left(\left(\frac{36.52704169880642}{z} - \frac{\color{blue}{t + 457.9610022158428}}{{z}^{2}}\right) + \left(-3.13060547623\right)\right)\right) \]

      10. metadata-eval 99.1%

          \[\leadsto x + y \cdot \left(-\left(\left(\frac{36.52704169880642}{z} - \frac{t + 457.9610022158428}{{z}^{2}}\right) + \color{blue}{-3.13060547623}\right)\right) \]

   10. Simplified 99.1%

       \[\leadsto x + \color{blue}{y \cdot \left(-\left(\left(\frac{36.52704169880642}{z} - \frac{t + 457.9610022158428}{{z}^{2}}\right) + -3.13060547623\right)\right)} \]

   if -5.9999999999999998e29 < z < 2.2000000000000001e31

   1. Initial program 96.3%

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

   3. Simplified 99.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), t\right), a\right), b\right)}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)}, y, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 99.6%

      \[\leadsto \color{blue}{x + y \cdot \left(\frac{b}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(15.234687407 + z\right)\right)\right)} + \frac{z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + 3.13060547623 \cdot z\right)\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(15.234687407 + z\right)\right)\right)}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+29} \lor \neg \left(z \leq 2.2 \cdot 10^{+31}\right):\\ \;\;\;\;x + y \cdot \left(\left(\frac{t + 457.9610022158428}{{z}^{2}} - \frac{36.52704169880642}{z}\right) - -3.13060547623\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(\frac{b}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771} + \frac{z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 97.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771\\ t_2 := z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right)\\ \mathbf{if}\;\frac{y \cdot \left(t\_2 + b\right)}{t\_1} \leq \infty:\\ \;\;\;\;x + y \cdot \left(\frac{b}{t\_1} + \frac{t\_2}{t\_1}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(3.13060547623 + \frac{b}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot 15.234687407\right)\right)}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (+
          (*
           z
           (+ (* z (+ (* z (+ z 15.234687407)) 31.4690115749)) 11.9400905721))
          0.607771387771))
        (t_2
         (* z (+ (* z (+ (* z (+ (* z 3.13060547623) 11.1667541262)) t)) a))))
   (if (<= (/ (* y (+ t_2 b)) t_1) INFINITY)
     (+ x (* y (+ (/ b t_1) (/ t_2 t_1))))
     (+
      x
      (*
       y
       (+
        3.13060547623
        (/
         b
         (+
          0.607771387771
          (*
           z
           (+
            11.9400905721
            (* z (+ 31.4690115749 (* z 15.234687407)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771;
	double t_2 = z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a);
	double tmp;
	if (((y * (t_2 + b)) / t_1) <= ((double) INFINITY)) {
		tmp = x + (y * ((b / t_1) + (t_2 / t_1)));
	} else {
		tmp = x + (y * (3.13060547623 + (b / (0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * 15.234687407)))))))));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771;
	double t_2 = z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a);
	double tmp;
	if (((y * (t_2 + b)) / t_1) <= Double.POSITIVE_INFINITY) {
		tmp = x + (y * ((b / t_1) + (t_2 / t_1)));
	} else {
		tmp = x + (y * (3.13060547623 + (b / (0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * 15.234687407)))))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771
	t_2 = z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)
	tmp = 0
	if ((y * (t_2 + b)) / t_1) <= math.inf:
		tmp = x + (y * ((b / t_1) + (t_2 / t_1)))
	else:
		tmp = x + (y * (3.13060547623 + (b / (0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * 15.234687407)))))))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)
	t_2 = Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * 3.13060547623) + 11.1667541262)) + t)) + a))
	tmp = 0.0
	if (Float64(Float64(y * Float64(t_2 + b)) / t_1) <= Inf)
		tmp = Float64(x + Float64(y * Float64(Float64(b / t_1) + Float64(t_2 / t_1))));
	else
		tmp = Float64(x + Float64(y * Float64(3.13060547623 + Float64(b / Float64(0.607771387771 + Float64(z * Float64(11.9400905721 + Float64(z * Float64(31.4690115749 + Float64(z * 15.234687407))))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771;
	t_2 = z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a);
	tmp = 0.0;
	if (((y * (t_2 + b)) / t_1) <= Inf)
		tmp = x + (y * ((b / t_1) + (t_2 / t_1)));
	else
		tmp = x + (y * (3.13060547623 + (b / (0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * 15.234687407)))))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = 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]}, Block[{t$95$2 = N[(z * N[(N[(z * N[(N[(z * N[(N[(z * 3.13060547623), $MachinePrecision] + 11.1667541262), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(y * N[(t$95$2 + b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], Infinity], N[(x + N[(y * N[(N[(b / t$95$1), $MachinePrecision] + N[(t$95$2 / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(3.13060547623 + N[(b / N[(0.607771387771 + N[(z * N[(11.9400905721 + N[(z * N[(31.4690115749 + N[(z * 15.234687407), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z 313060547623/100000000000) 55833770631/5000000000) z) t) z) a) z) b)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 z 15234687407/1000000000) z) 314690115749/10000000000) z) 119400905721/10000000000) z) 607771387771/1000000000000)) < +inf.0

   1. Initial program 90.9%

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

   3. Simplified 96.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), t\right), a\right), b\right)}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)}, y, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 96.1%

      \[\leadsto \color{blue}{x + y \cdot \left(\frac{b}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(15.234687407 + z\right)\right)\right)} + \frac{z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + 3.13060547623 \cdot z\right)\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(15.234687407 + z\right)\right)\right)}\right)} \]

   if +inf.0 < (/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z 313060547623/100000000000) 55833770631/5000000000) z) t) z) a) z) b)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 z 15234687407/1000000000) z) 314690115749/10000000000) z) 119400905721/10000000000) z) 607771387771/1000000000000))

   1. Initial program 0.0%

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

   3. Simplified 0.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), t\right), a\right), b\right)}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)}, y, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 0.0%

      \[\leadsto \color{blue}{x + y \cdot \left(\frac{b}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(15.234687407 + z\right)\right)\right)} + \frac{z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + 3.13060547623 \cdot z\right)\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(15.234687407 + z\right)\right)\right)}\right)} \]

   6. Taylor expanded in z around inf 98.3%

      \[\leadsto x + y \cdot \left(\frac{b}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(15.234687407 + z\right)\right)\right)} + \color{blue}{3.13060547623}\right) \]

   7. Taylor expanded in z around 0 98.3%

      \[\leadsto x + y \cdot \left(\frac{b}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + \color{blue}{15.234687407 \cdot z}\right)\right)} + 3.13060547623\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 97.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right) + b\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771} \leq \infty:\\ \;\;\;\;x + y \cdot \left(\frac{b}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771} + \frac{z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(3.13060547623 + \frac{b}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot 15.234687407\right)\right)}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 94.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771\\ t_2 := \frac{y \cdot \left(z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right) + b\right)}{t\_1}\\ \mathbf{if}\;t\_2 \leq 10^{+276}:\\ \;\;\;\;t\_2 + x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(3.13060547623 + \frac{b}{t\_1}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (+
          (*
           z
           (+ (* z (+ (* z (+ z 15.234687407)) 31.4690115749)) 11.9400905721))
          0.607771387771))
        (t_2
         (/
          (*
           y
           (+
            (* z (+ (* z (+ (* z (+ (* z 3.13060547623) 11.1667541262)) t)) a))
            b))
          t_1)))
   (if (<= t_2 1e+276) (+ t_2 x) (+ x (* y (+ 3.13060547623 (/ b t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771;
	double t_2 = (y * ((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / t_1;
	double tmp;
	if (t_2 <= 1e+276) {
		tmp = t_2 + x;
	} else {
		tmp = x + (y * (3.13060547623 + (b / 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) :: t_2
    real(8) :: tmp
    t_1 = (z * ((z * ((z * (z + 15.234687407d0)) + 31.4690115749d0)) + 11.9400905721d0)) + 0.607771387771d0
    t_2 = (y * ((z * ((z * ((z * ((z * 3.13060547623d0) + 11.1667541262d0)) + t)) + a)) + b)) / t_1
    if (t_2 <= 1d+276) then
        tmp = t_2 + x
    else
        tmp = x + (y * (3.13060547623d0 + (b / 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 = (z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771;
	double t_2 = (y * ((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / t_1;
	double tmp;
	if (t_2 <= 1e+276) {
		tmp = t_2 + x;
	} else {
		tmp = x + (y * (3.13060547623 + (b / t_1)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771
	t_2 = (y * ((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / t_1
	tmp = 0
	if t_2 <= 1e+276:
		tmp = t_2 + x
	else:
		tmp = x + (y * (3.13060547623 + (b / t_1)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)
	t_2 = Float64(Float64(y * Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / t_1)
	tmp = 0.0
	if (t_2 <= 1e+276)
		tmp = Float64(t_2 + x);
	else
		tmp = Float64(x + Float64(y * Float64(3.13060547623 + Float64(b / t_1))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771;
	t_2 = (y * ((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / t_1;
	tmp = 0.0;
	if (t_2 <= 1e+276)
		tmp = t_2 + x;
	else
		tmp = x + (y * (3.13060547623 + (b / t_1)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = 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]}, Block[{t$95$2 = N[(N[(y * N[(N[(z * N[(N[(z * N[(N[(z * N[(N[(z * 3.13060547623), $MachinePrecision] + 11.1667541262), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[t$95$2, 1e+276], N[(t$95$2 + x), $MachinePrecision], N[(x + N[(y * N[(3.13060547623 + N[(b / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z 313060547623/100000000000) 55833770631/5000000000) z) t) z) a) z) b)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 z 15234687407/1000000000) z) 314690115749/10000000000) z) 119400905721/10000000000) z) 607771387771/1000000000000)) < 1.0000000000000001e276

   1. Initial program 97.0%

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

   if 1.0000000000000001e276 < (/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z 313060547623/100000000000) 55833770631/5000000000) z) t) z) a) z) b)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 z 15234687407/1000000000) z) 314690115749/10000000000) z) 119400905721/10000000000) z) 607771387771/1000000000000))

   1. Initial program 9.1%

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

   3. Simplified 14.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), t\right), a\right), b\right)}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)}, y, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 14.4%

      \[\leadsto \color{blue}{x + y \cdot \left(\frac{b}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(15.234687407 + z\right)\right)\right)} + \frac{z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + 3.13060547623 \cdot z\right)\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(15.234687407 + z\right)\right)\right)}\right)} \]

   6. Taylor expanded in z around inf 92.2%

      \[\leadsto x + y \cdot \left(\frac{b}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(15.234687407 + z\right)\right)\right)} + \color{blue}{3.13060547623}\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 94.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right) + b\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771} \leq 10^{+276}:\\ \;\;\;\;\frac{y \cdot \left(z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right) + b\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771} + x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(3.13060547623 + \frac{b}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 95.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771\\ \mathbf{if}\;z \leq -5.8 \cdot 10^{+41}:\\ \;\;\;\;x + y \cdot \left(3.13060547623 + \frac{b}{t\_1}\right)\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+45}:\\ \;\;\;\;x + y \cdot \left(\frac{z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right)}{t\_1} + b \cdot 1.6453555072203998\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(3.13060547623 + \frac{b}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot 15.234687407\right)\right)}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (+
          (*
           z
           (+ (* z (+ (* z (+ z 15.234687407)) 31.4690115749)) 11.9400905721))
          0.607771387771)))
   (if (<= z -5.8e+41)
     (+ x (* y (+ 3.13060547623 (/ b t_1))))
     (if (<= z 3.4e+45)
       (+
        x
        (*
         y
         (+
          (/
           (* z (+ (* z (+ (* z (+ (* z 3.13060547623) 11.1667541262)) t)) a))
           t_1)
          (* b 1.6453555072203998))))
       (+
        x
        (*
         y
         (+
          3.13060547623
          (/
           b
           (+
            0.607771387771
            (*
             z
             (+
              11.9400905721
              (* z (+ 31.4690115749 (* z 15.234687407))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771;
	double tmp;
	if (z <= -5.8e+41) {
		tmp = x + (y * (3.13060547623 + (b / t_1)));
	} else if (z <= 3.4e+45) {
		tmp = x + (y * (((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) / t_1) + (b * 1.6453555072203998)));
	} else {
		tmp = x + (y * (3.13060547623 + (b / (0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * 15.234687407)))))))));
	}
	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 = (z * ((z * ((z * (z + 15.234687407d0)) + 31.4690115749d0)) + 11.9400905721d0)) + 0.607771387771d0
    if (z <= (-5.8d+41)) then
        tmp = x + (y * (3.13060547623d0 + (b / t_1)))
    else if (z <= 3.4d+45) then
        tmp = x + (y * (((z * ((z * ((z * ((z * 3.13060547623d0) + 11.1667541262d0)) + t)) + a)) / t_1) + (b * 1.6453555072203998d0)))
    else
        tmp = x + (y * (3.13060547623d0 + (b / (0.607771387771d0 + (z * (11.9400905721d0 + (z * (31.4690115749d0 + (z * 15.234687407d0)))))))))
    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 = (z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771;
	double tmp;
	if (z <= -5.8e+41) {
		tmp = x + (y * (3.13060547623 + (b / t_1)));
	} else if (z <= 3.4e+45) {
		tmp = x + (y * (((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) / t_1) + (b * 1.6453555072203998)));
	} else {
		tmp = x + (y * (3.13060547623 + (b / (0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * 15.234687407)))))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771
	tmp = 0
	if z <= -5.8e+41:
		tmp = x + (y * (3.13060547623 + (b / t_1)))
	elif z <= 3.4e+45:
		tmp = x + (y * (((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) / t_1) + (b * 1.6453555072203998)))
	else:
		tmp = x + (y * (3.13060547623 + (b / (0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * 15.234687407)))))))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)
	tmp = 0.0
	if (z <= -5.8e+41)
		tmp = Float64(x + Float64(y * Float64(3.13060547623 + Float64(b / t_1))));
	elseif (z <= 3.4e+45)
		tmp = Float64(x + Float64(y * Float64(Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * 3.13060547623) + 11.1667541262)) + t)) + a)) / t_1) + Float64(b * 1.6453555072203998))));
	else
		tmp = Float64(x + Float64(y * Float64(3.13060547623 + Float64(b / Float64(0.607771387771 + Float64(z * Float64(11.9400905721 + Float64(z * Float64(31.4690115749 + Float64(z * 15.234687407))))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771;
	tmp = 0.0;
	if (z <= -5.8e+41)
		tmp = x + (y * (3.13060547623 + (b / t_1)));
	elseif (z <= 3.4e+45)
		tmp = x + (y * (((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) / t_1) + (b * 1.6453555072203998)));
	else
		tmp = x + (y * (3.13060547623 + (b / (0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * 15.234687407)))))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = 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]}, If[LessEqual[z, -5.8e+41], N[(x + N[(y * N[(3.13060547623 + N[(b / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.4e+45], N[(x + N[(y * 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] / t$95$1), $MachinePrecision] + N[(b * 1.6453555072203998), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(3.13060547623 + N[(b / N[(0.607771387771 + N[(z * N[(11.9400905721 + N[(z * N[(31.4690115749 + N[(z * 15.234687407), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.79999999999999977e41

   1. Initial program 6.2%

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

   3. Simplified 9.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), t\right), a\right), b\right)}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)}, y, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 9.7%

      \[\leadsto \color{blue}{x + y \cdot \left(\frac{b}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(15.234687407 + z\right)\right)\right)} + \frac{z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + 3.13060547623 \cdot z\right)\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(15.234687407 + z\right)\right)\right)}\right)} \]

   6. Taylor expanded in z around inf 96.6%

      \[\leadsto x + y \cdot \left(\frac{b}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(15.234687407 + z\right)\right)\right)} + \color{blue}{3.13060547623}\right) \]

   if -5.79999999999999977e41 < z < 3.4e45

   1. Initial program 94.5%

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

   3. Simplified 99.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), t\right), a\right), b\right)}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)}, y, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 99.0%

      \[\leadsto \color{blue}{x + y \cdot \left(\frac{b}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(15.234687407 + z\right)\right)\right)} + \frac{z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + 3.13060547623 \cdot z\right)\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(15.234687407 + z\right)\right)\right)}\right)} \]

   6. Taylor expanded in z around 0 98.0%

      \[\leadsto x + y \cdot \left(\color{blue}{1.6453555072203998 \cdot b} + \frac{z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + 3.13060547623 \cdot z\right)\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(15.234687407 + z\right)\right)\right)}\right) \]

   if 3.4e45 < z

   1. Initial program 10.0%

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

   3. Simplified 10.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), t\right), a\right), b\right)}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)}, y, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 10.0%

      \[\leadsto \color{blue}{x + y \cdot \left(\frac{b}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(15.234687407 + z\right)\right)\right)} + \frac{z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + 3.13060547623 \cdot z\right)\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(15.234687407 + z\right)\right)\right)}\right)} \]

   6. Taylor expanded in z around inf 96.0%

      \[\leadsto x + y \cdot \left(\frac{b}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(15.234687407 + z\right)\right)\right)} + \color{blue}{3.13060547623}\right) \]

   7. Taylor expanded in z around 0 96.0%

      \[\leadsto x + y \cdot \left(\frac{b}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + \color{blue}{15.234687407 \cdot z}\right)\right)} + 3.13060547623\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 97.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+41}:\\ \;\;\;\;x + y \cdot \left(3.13060547623 + \frac{b}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}\right)\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+45}:\\ \;\;\;\;x + y \cdot \left(\frac{z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771} + b \cdot 1.6453555072203998\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(3.13060547623 + \frac{b}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot 15.234687407\right)\right)}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 94.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771\\ \mathbf{if}\;z \leq -6 \cdot 10^{+29} \lor \neg \left(z \leq 3850000\right):\\ \;\;\;\;x + y \cdot \left(3.13060547623 + \frac{b}{t\_1}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(b \cdot 1.6453555072203998 + \frac{z \cdot \left(a + z \cdot \left(t + z \cdot 11.1667541262\right)\right)}{t\_1}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (+
          (*
           z
           (+ (* z (+ (* z (+ z 15.234687407)) 31.4690115749)) 11.9400905721))
          0.607771387771)))
   (if (or (<= z -6e+29) (not (<= z 3850000.0)))
     (+ x (* y (+ 3.13060547623 (/ b t_1))))
     (+
      x
      (*
       y
       (+
        (* b 1.6453555072203998)
        (/ (* z (+ a (* z (+ t (* z 11.1667541262))))) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771;
	double tmp;
	if ((z <= -6e+29) || !(z <= 3850000.0)) {
		tmp = x + (y * (3.13060547623 + (b / t_1)));
	} else {
		tmp = x + (y * ((b * 1.6453555072203998) + ((z * (a + (z * (t + (z * 11.1667541262))))) / 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 = (z * ((z * ((z * (z + 15.234687407d0)) + 31.4690115749d0)) + 11.9400905721d0)) + 0.607771387771d0
    if ((z <= (-6d+29)) .or. (.not. (z <= 3850000.0d0))) then
        tmp = x + (y * (3.13060547623d0 + (b / t_1)))
    else
        tmp = x + (y * ((b * 1.6453555072203998d0) + ((z * (a + (z * (t + (z * 11.1667541262d0))))) / 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 = (z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771;
	double tmp;
	if ((z <= -6e+29) || !(z <= 3850000.0)) {
		tmp = x + (y * (3.13060547623 + (b / t_1)));
	} else {
		tmp = x + (y * ((b * 1.6453555072203998) + ((z * (a + (z * (t + (z * 11.1667541262))))) / t_1)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771
	tmp = 0
	if (z <= -6e+29) or not (z <= 3850000.0):
		tmp = x + (y * (3.13060547623 + (b / t_1)))
	else:
		tmp = x + (y * ((b * 1.6453555072203998) + ((z * (a + (z * (t + (z * 11.1667541262))))) / t_1)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)
	tmp = 0.0
	if ((z <= -6e+29) || !(z <= 3850000.0))
		tmp = Float64(x + Float64(y * Float64(3.13060547623 + Float64(b / t_1))));
	else
		tmp = Float64(x + Float64(y * Float64(Float64(b * 1.6453555072203998) + Float64(Float64(z * Float64(a + Float64(z * Float64(t + Float64(z * 11.1667541262))))) / t_1))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771;
	tmp = 0.0;
	if ((z <= -6e+29) || ~((z <= 3850000.0)))
		tmp = x + (y * (3.13060547623 + (b / t_1)));
	else
		tmp = x + (y * ((b * 1.6453555072203998) + ((z * (a + (z * (t + (z * 11.1667541262))))) / t_1)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = 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]}, If[Or[LessEqual[z, -6e+29], N[Not[LessEqual[z, 3850000.0]], $MachinePrecision]], N[(x + N[(y * N[(3.13060547623 + N[(b / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(N[(b * 1.6453555072203998), $MachinePrecision] + N[(N[(z * N[(a + N[(z * N[(t + N[(z * 11.1667541262), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.9999999999999998e29 or 3.85e6 < z

   1. Initial program 14.7%

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

   3. Simplified 18.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), t\right), a\right), b\right)}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)}, y, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 18.3%

      \[\leadsto \color{blue}{x + y \cdot \left(\frac{b}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(15.234687407 + z\right)\right)\right)} + \frac{z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + 3.13060547623 \cdot z\right)\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(15.234687407 + z\right)\right)\right)}\right)} \]

   6. Taylor expanded in z around inf 93.8%

      \[\leadsto x + y \cdot \left(\frac{b}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(15.234687407 + z\right)\right)\right)} + \color{blue}{3.13060547623}\right) \]

   if -5.9999999999999998e29 < z < 3.85e6

   1. Initial program 96.8%

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

   3. Simplified 99.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), t\right), a\right), b\right)}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)}, y, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 99.7%

      \[\leadsto \color{blue}{x + y \cdot \left(\frac{b}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(15.234687407 + z\right)\right)\right)} + \frac{z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + 3.13060547623 \cdot z\right)\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(15.234687407 + z\right)\right)\right)}\right)} \]

   6. Taylor expanded in z around 0 98.9%

      \[\leadsto x + y \cdot \left(\frac{b}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(15.234687407 + z\right)\right)\right)} + \frac{z \cdot \left(a + z \cdot \left(t + \color{blue}{11.1667541262 \cdot z}\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(15.234687407 + z\right)\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-commutative 98.9%

         \[\leadsto x + y \cdot \left(\frac{b}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(15.234687407 + z\right)\right)\right)} + \frac{z \cdot \left(a + z \cdot \left(t + \color{blue}{z \cdot 11.1667541262}\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(15.234687407 + z\right)\right)\right)}\right) \]

   8. Simplified 98.9%

      \[\leadsto x + y \cdot \left(\frac{b}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(15.234687407 + z\right)\right)\right)} + \frac{z \cdot \left(a + z \cdot \left(t + \color{blue}{z \cdot 11.1667541262}\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(15.234687407 + z\right)\right)\right)}\right) \]

   9. Taylor expanded in z around 0 98.5%

      \[\leadsto x + y \cdot \left(\color{blue}{1.6453555072203998 \cdot b} + \frac{z \cdot \left(a + z \cdot \left(t + z \cdot 11.1667541262\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(15.234687407 + z\right)\right)\right)}\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 96.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+29} \lor \neg \left(z \leq 3850000\right):\\ \;\;\;\;x + y \cdot \left(3.13060547623 + \frac{b}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(b \cdot 1.6453555072203998 + \frac{z \cdot \left(a + z \cdot \left(t + z \cdot 11.1667541262\right)\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 95.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771\\ \mathbf{if}\;z \leq -5.8 \cdot 10^{+29}:\\ \;\;\;\;x + y \cdot \left(3.13060547623 + \frac{b}{t\_1}\right)\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+23}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot 11.1667541262\right)\right)\right)}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(3.13060547623 + \frac{b}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot 15.234687407\right)\right)}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (+
          (*
           z
           (+ (* z (+ (* z (+ z 15.234687407)) 31.4690115749)) 11.9400905721))
          0.607771387771)))
   (if (<= z -5.8e+29)
     (+ x (* y (+ 3.13060547623 (/ b t_1))))
     (if (<= z 3.8e+23)
       (+ x (/ (* y (+ b (* z (+ a (* z (+ t (* z 11.1667541262))))))) t_1))
       (+
        x
        (*
         y
         (+
          3.13060547623
          (/
           b
           (+
            0.607771387771
            (*
             z
             (+
              11.9400905721
              (* z (+ 31.4690115749 (* z 15.234687407))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771;
	double tmp;
	if (z <= -5.8e+29) {
		tmp = x + (y * (3.13060547623 + (b / t_1)));
	} else if (z <= 3.8e+23) {
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * 11.1667541262))))))) / t_1);
	} else {
		tmp = x + (y * (3.13060547623 + (b / (0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * 15.234687407)))))))));
	}
	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 = (z * ((z * ((z * (z + 15.234687407d0)) + 31.4690115749d0)) + 11.9400905721d0)) + 0.607771387771d0
    if (z <= (-5.8d+29)) then
        tmp = x + (y * (3.13060547623d0 + (b / t_1)))
    else if (z <= 3.8d+23) then
        tmp = x + ((y * (b + (z * (a + (z * (t + (z * 11.1667541262d0))))))) / t_1)
    else
        tmp = x + (y * (3.13060547623d0 + (b / (0.607771387771d0 + (z * (11.9400905721d0 + (z * (31.4690115749d0 + (z * 15.234687407d0)))))))))
    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 = (z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771;
	double tmp;
	if (z <= -5.8e+29) {
		tmp = x + (y * (3.13060547623 + (b / t_1)));
	} else if (z <= 3.8e+23) {
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * 11.1667541262))))))) / t_1);
	} else {
		tmp = x + (y * (3.13060547623 + (b / (0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * 15.234687407)))))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771
	tmp = 0
	if z <= -5.8e+29:
		tmp = x + (y * (3.13060547623 + (b / t_1)))
	elif z <= 3.8e+23:
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * 11.1667541262))))))) / t_1)
	else:
		tmp = x + (y * (3.13060547623 + (b / (0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * 15.234687407)))))))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)
	tmp = 0.0
	if (z <= -5.8e+29)
		tmp = Float64(x + Float64(y * Float64(3.13060547623 + Float64(b / t_1))));
	elseif (z <= 3.8e+23)
		tmp = Float64(x + Float64(Float64(y * Float64(b + Float64(z * Float64(a + Float64(z * Float64(t + Float64(z * 11.1667541262))))))) / t_1));
	else
		tmp = Float64(x + Float64(y * Float64(3.13060547623 + Float64(b / Float64(0.607771387771 + Float64(z * Float64(11.9400905721 + Float64(z * Float64(31.4690115749 + Float64(z * 15.234687407))))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771;
	tmp = 0.0;
	if (z <= -5.8e+29)
		tmp = x + (y * (3.13060547623 + (b / t_1)));
	elseif (z <= 3.8e+23)
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * 11.1667541262))))))) / t_1);
	else
		tmp = x + (y * (3.13060547623 + (b / (0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * 15.234687407)))))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = 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]}, If[LessEqual[z, -5.8e+29], N[(x + N[(y * N[(3.13060547623 + N[(b / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.8e+23], N[(x + N[(N[(y * N[(b + N[(z * N[(a + N[(z * N[(t + N[(z * 11.1667541262), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(3.13060547623 + N[(b / N[(0.607771387771 + N[(z * N[(11.9400905721 + N[(z * N[(31.4690115749 + N[(z * 15.234687407), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.7999999999999999e29

   1. Initial program 7.9%

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

   3. Simplified 16.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), t\right), a\right), b\right)}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)}, y, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 16.0%

      \[\leadsto \color{blue}{x + y \cdot \left(\frac{b}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(15.234687407 + z\right)\right)\right)} + \frac{z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + 3.13060547623 \cdot z\right)\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(15.234687407 + z\right)\right)\right)}\right)} \]

   6. Taylor expanded in z around inf 93.6%

      \[\leadsto x + y \cdot \left(\frac{b}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(15.234687407 + z\right)\right)\right)} + \color{blue}{3.13060547623}\right) \]

   if -5.7999999999999999e29 < z < 3.79999999999999975e23

   1. Initial program 96.9%

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

   3. Taylor expanded in z around 0 96.8%

      \[\leadsto x + \frac{y \cdot \left(\left(\left(\color{blue}{11.1667541262 \cdot z} + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   4. Step-by-step derivation

      1. *-commutative 96.8%

         \[\leadsto x + \frac{y \cdot \left(\left(\left(\color{blue}{z \cdot 11.1667541262} + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]

   5. Simplified 96.8%

      \[\leadsto x + \frac{y \cdot \left(\left(\left(\color{blue}{z \cdot 11.1667541262} + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]

   if 3.79999999999999975e23 < z

   1. Initial program 17.9%

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

   3. Simplified 17.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), t\right), a\right), b\right)}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)}, y, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 17.9%

      \[\leadsto \color{blue}{x + y \cdot \left(\frac{b}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(15.234687407 + z\right)\right)\right)} + \frac{z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + 3.13060547623 \cdot z\right)\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(15.234687407 + z\right)\right)\right)}\right)} \]

   6. Taylor expanded in z around inf 94.0%

      \[\leadsto x + y \cdot \left(\frac{b}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(15.234687407 + z\right)\right)\right)} + \color{blue}{3.13060547623}\right) \]

   7. Taylor expanded in z around 0 94.1%

      \[\leadsto x + y \cdot \left(\frac{b}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + \color{blue}{15.234687407 \cdot z}\right)\right)} + 3.13060547623\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 95.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+29}:\\ \;\;\;\;x + y \cdot \left(3.13060547623 + \frac{b}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}\right)\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+23}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot 11.1667541262\right)\right)\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(3.13060547623 + \frac{b}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot 15.234687407\right)\right)}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 93.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-7} \lor \neg \left(z \leq 3700000\right):\\ \;\;\;\;x + y \cdot \left(3.13060547623 + \frac{b}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right) + b\right)}{0.607771387771 + z \cdot 11.9400905721}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -2e-7) (not (<= z 3700000.0)))
   (+
    x
    (*
     y
     (+
      3.13060547623
      (/
       b
       (+
        (*
         z
         (+ (* z (+ (* z (+ z 15.234687407)) 31.4690115749)) 11.9400905721))
        0.607771387771)))))
   (+
    x
    (/
     (*
      y
      (+
       (* z (+ (* z (+ (* z (+ (* z 3.13060547623) 11.1667541262)) t)) a))
       b))
     (+ 0.607771387771 (* z 11.9400905721))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2e-7) || !(z <= 3700000.0)) {
		tmp = x + (y * (3.13060547623 + (b / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771))));
	} else {
		tmp = x + ((y * ((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / (0.607771387771 + (z * 11.9400905721)));
	}
	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 <= (-2d-7)) .or. (.not. (z <= 3700000.0d0))) then
        tmp = x + (y * (3.13060547623d0 + (b / ((z * ((z * ((z * (z + 15.234687407d0)) + 31.4690115749d0)) + 11.9400905721d0)) + 0.607771387771d0))))
    else
        tmp = x + ((y * ((z * ((z * ((z * ((z * 3.13060547623d0) + 11.1667541262d0)) + t)) + a)) + b)) / (0.607771387771d0 + (z * 11.9400905721d0)))
    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 <= -2e-7) || !(z <= 3700000.0)) {
		tmp = x + (y * (3.13060547623 + (b / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771))));
	} else {
		tmp = x + ((y * ((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / (0.607771387771 + (z * 11.9400905721)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -2e-7) or not (z <= 3700000.0):
		tmp = x + (y * (3.13060547623 + (b / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771))))
	else:
		tmp = x + ((y * ((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / (0.607771387771 + (z * 11.9400905721)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -2e-7) || !(z <= 3700000.0))
		tmp = Float64(x + Float64(y * Float64(3.13060547623 + Float64(b / 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(y * Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / Float64(0.607771387771 + Float64(z * 11.9400905721))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -2e-7) || ~((z <= 3700000.0)))
		tmp = x + (y * (3.13060547623 + (b / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771))));
	else
		tmp = x + ((y * ((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / (0.607771387771 + (z * 11.9400905721)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -2e-7], N[Not[LessEqual[z, 3700000.0]], $MachinePrecision]], N[(x + N[(y * N[(3.13060547623 + N[(b / 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]), $MachinePrecision], N[(x + N[(N[(y * N[(N[(z * N[(N[(z * N[(N[(z * N[(N[(z * 3.13060547623), $MachinePrecision] + 11.1667541262), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / N[(0.607771387771 + N[(z * 11.9400905721), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.9999999999999999e-7 or 3.7e6 < z

   1. Initial program 20.6%

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

   3. Simplified 26.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), t\right), a\right), b\right)}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)}, y, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 26.4%

      \[\leadsto \color{blue}{x + y \cdot \left(\frac{b}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(15.234687407 + z\right)\right)\right)} + \frac{z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + 3.13060547623 \cdot z\right)\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(15.234687407 + z\right)\right)\right)}\right)} \]

   6. Taylor expanded in z around inf 89.6%

      \[\leadsto x + y \cdot \left(\frac{b}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(15.234687407 + z\right)\right)\right)} + \color{blue}{3.13060547623}\right) \]

   if -1.9999999999999999e-7 < z < 3.7e6

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 0 98.7%

      \[\leadsto x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\color{blue}{11.9400905721 \cdot z} + 0.607771387771} \]
   4. Step-by-step derivation

      1. *-commutative 98.7%

         \[\leadsto x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\color{blue}{z \cdot 11.9400905721} + 0.607771387771} \]

   5. Simplified 98.7%

      \[\leadsto x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\color{blue}{z \cdot 11.9400905721} + 0.607771387771} \]
3. Recombined 2 regimes into one program.

4. Final simplification 93.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-7} \lor \neg \left(z \leq 3700000\right):\\ \;\;\;\;x + y \cdot \left(3.13060547623 + \frac{b}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right) + b\right)}{0.607771387771 + z \cdot 11.9400905721}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 91.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771\\ \mathbf{if}\;z \leq -3.3 \cdot 10^{+14}:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 + \frac{y}{z} \cdot -36.52704169880642\right)\\ \mathbf{elif}\;z \leq 3800000:\\ \;\;\;\;x + y \cdot \left(b \cdot 1.6453555072203998 + \frac{z \cdot a}{t\_1}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(3.13060547623 + \frac{b}{t\_1}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (+
          (*
           z
           (+ (* z (+ (* z (+ z 15.234687407)) 31.4690115749)) 11.9400905721))
          0.607771387771)))
   (if (<= z -3.3e+14)
     (+ x (+ (* y 3.13060547623) (* (/ y z) -36.52704169880642)))
     (if (<= z 3800000.0)
       (+ x (* y (+ (* b 1.6453555072203998) (/ (* z a) t_1))))
       (+ x (* y (+ 3.13060547623 (/ b t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771;
	double tmp;
	if (z <= -3.3e+14) {
		tmp = x + ((y * 3.13060547623) + ((y / z) * -36.52704169880642));
	} else if (z <= 3800000.0) {
		tmp = x + (y * ((b * 1.6453555072203998) + ((z * a) / t_1)));
	} else {
		tmp = x + (y * (3.13060547623 + (b / 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 = (z * ((z * ((z * (z + 15.234687407d0)) + 31.4690115749d0)) + 11.9400905721d0)) + 0.607771387771d0
    if (z <= (-3.3d+14)) then
        tmp = x + ((y * 3.13060547623d0) + ((y / z) * (-36.52704169880642d0)))
    else if (z <= 3800000.0d0) then
        tmp = x + (y * ((b * 1.6453555072203998d0) + ((z * a) / t_1)))
    else
        tmp = x + (y * (3.13060547623d0 + (b / 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 = (z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771;
	double tmp;
	if (z <= -3.3e+14) {
		tmp = x + ((y * 3.13060547623) + ((y / z) * -36.52704169880642));
	} else if (z <= 3800000.0) {
		tmp = x + (y * ((b * 1.6453555072203998) + ((z * a) / t_1)));
	} else {
		tmp = x + (y * (3.13060547623 + (b / t_1)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771
	tmp = 0
	if z <= -3.3e+14:
		tmp = x + ((y * 3.13060547623) + ((y / z) * -36.52704169880642))
	elif z <= 3800000.0:
		tmp = x + (y * ((b * 1.6453555072203998) + ((z * a) / t_1)))
	else:
		tmp = x + (y * (3.13060547623 + (b / t_1)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)
	tmp = 0.0
	if (z <= -3.3e+14)
		tmp = Float64(x + Float64(Float64(y * 3.13060547623) + Float64(Float64(y / z) * -36.52704169880642)));
	elseif (z <= 3800000.0)
		tmp = Float64(x + Float64(y * Float64(Float64(b * 1.6453555072203998) + Float64(Float64(z * a) / t_1))));
	else
		tmp = Float64(x + Float64(y * Float64(3.13060547623 + Float64(b / t_1))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771;
	tmp = 0.0;
	if (z <= -3.3e+14)
		tmp = x + ((y * 3.13060547623) + ((y / z) * -36.52704169880642));
	elseif (z <= 3800000.0)
		tmp = x + (y * ((b * 1.6453555072203998) + ((z * a) / t_1)));
	else
		tmp = x + (y * (3.13060547623 + (b / t_1)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = 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]}, If[LessEqual[z, -3.3e+14], N[(x + N[(N[(y * 3.13060547623), $MachinePrecision] + N[(N[(y / z), $MachinePrecision] * -36.52704169880642), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3800000.0], N[(x + N[(y * N[(N[(b * 1.6453555072203998), $MachinePrecision] + N[(N[(z * a), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(3.13060547623 + N[(b / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.3e14

   1. Initial program 13.7%

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

   3. Simplified 24.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), t\right), a\right), b\right)}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)}, y, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 89.5%

      \[\leadsto \color{blue}{x + \left(-36.52704169880642 \cdot \frac{y}{z} + 3.13060547623 \cdot y\right)} \]

   if -3.3e14 < z < 3.8e6

   1. Initial program 98.9%

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

   3. Simplified 99.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), t\right), a\right), b\right)}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)}, y, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 99.7%

      \[\leadsto \color{blue}{x + y \cdot \left(\frac{b}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(15.234687407 + z\right)\right)\right)} + \frac{z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + 3.13060547623 \cdot z\right)\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(15.234687407 + z\right)\right)\right)}\right)} \]

   6. Taylor expanded in z around 0 99.3%

      \[\leadsto x + y \cdot \left(\color{blue}{1.6453555072203998 \cdot b} + \frac{z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + 3.13060547623 \cdot z\right)\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(15.234687407 + z\right)\right)\right)}\right) \]

   7. Taylor expanded in a around inf 93.0%

      \[\leadsto x + y \cdot \left(1.6453555072203998 \cdot b + \color{blue}{\frac{a \cdot z}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(15.234687407 + z\right)\right)\right)}}\right) \]

   if 3.8e6 < z

   1. Initial program 20.1%

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

   3. Simplified 21.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), t\right), a\right), b\right)}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)}, y, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 21.3%

      \[\leadsto \color{blue}{x + y \cdot \left(\frac{b}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(15.234687407 + z\right)\right)\right)} + \frac{z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + 3.13060547623 \cdot z\right)\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(15.234687407 + z\right)\right)\right)}\right)} \]

   6. Taylor expanded in z around inf 92.8%

      \[\leadsto x + y \cdot \left(\frac{b}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(15.234687407 + z\right)\right)\right)} + \color{blue}{3.13060547623}\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 92.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+14}:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 + \frac{y}{z} \cdot -36.52704169880642\right)\\ \mathbf{elif}\;z \leq 3800000:\\ \;\;\;\;x + y \cdot \left(b \cdot 1.6453555072203998 + \frac{z \cdot a}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(3.13060547623 + \frac{b}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 90.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6000000000000:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 + \frac{y}{z} \cdot -36.52704169880642\right)\\ \mathbf{elif}\;z \leq 3450000:\\ \;\;\;\;x + y \cdot \left(b \cdot 1.6453555072203998 - z \cdot \left(b \cdot 32.324150453290734 - a \cdot 1.6453555072203998\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(3.13060547623 + \frac{b}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -6000000000000.0)
   (+ x (+ (* y 3.13060547623) (* (/ y z) -36.52704169880642)))
   (if (<= z 3450000.0)
     (+
      x
      (*
       y
       (-
        (* b 1.6453555072203998)
        (* z (- (* b 32.324150453290734) (* a 1.6453555072203998))))))
     (+
      x
      (*
       y
       (+
        3.13060547623
        (/
         b
         (+
          (*
           z
           (+ (* z (+ (* z (+ z 15.234687407)) 31.4690115749)) 11.9400905721))
          0.607771387771))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -6000000000000.0) {
		tmp = x + ((y * 3.13060547623) + ((y / z) * -36.52704169880642));
	} else if (z <= 3450000.0) {
		tmp = x + (y * ((b * 1.6453555072203998) - (z * ((b * 32.324150453290734) - (a * 1.6453555072203998)))));
	} else {
		tmp = x + (y * (3.13060547623 + (b / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771))));
	}
	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 <= (-6000000000000.0d0)) then
        tmp = x + ((y * 3.13060547623d0) + ((y / z) * (-36.52704169880642d0)))
    else if (z <= 3450000.0d0) then
        tmp = x + (y * ((b * 1.6453555072203998d0) - (z * ((b * 32.324150453290734d0) - (a * 1.6453555072203998d0)))))
    else
        tmp = x + (y * (3.13060547623d0 + (b / ((z * ((z * ((z * (z + 15.234687407d0)) + 31.4690115749d0)) + 11.9400905721d0)) + 0.607771387771d0))))
    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 <= -6000000000000.0) {
		tmp = x + ((y * 3.13060547623) + ((y / z) * -36.52704169880642));
	} else if (z <= 3450000.0) {
		tmp = x + (y * ((b * 1.6453555072203998) - (z * ((b * 32.324150453290734) - (a * 1.6453555072203998)))));
	} else {
		tmp = x + (y * (3.13060547623 + (b / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -6000000000000.0:
		tmp = x + ((y * 3.13060547623) + ((y / z) * -36.52704169880642))
	elif z <= 3450000.0:
		tmp = x + (y * ((b * 1.6453555072203998) - (z * ((b * 32.324150453290734) - (a * 1.6453555072203998)))))
	else:
		tmp = x + (y * (3.13060547623 + (b / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -6000000000000.0)
		tmp = Float64(x + Float64(Float64(y * 3.13060547623) + Float64(Float64(y / z) * -36.52704169880642)));
	elseif (z <= 3450000.0)
		tmp = Float64(x + Float64(y * Float64(Float64(b * 1.6453555072203998) - Float64(z * Float64(Float64(b * 32.324150453290734) - Float64(a * 1.6453555072203998))))));
	else
		tmp = Float64(x + Float64(y * Float64(3.13060547623 + Float64(b / Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -6000000000000.0)
		tmp = x + ((y * 3.13060547623) + ((y / z) * -36.52704169880642));
	elseif (z <= 3450000.0)
		tmp = x + (y * ((b * 1.6453555072203998) - (z * ((b * 32.324150453290734) - (a * 1.6453555072203998)))));
	else
		tmp = x + (y * (3.13060547623 + (b / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -6000000000000.0], N[(x + N[(N[(y * 3.13060547623), $MachinePrecision] + N[(N[(y / z), $MachinePrecision] * -36.52704169880642), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3450000.0], N[(x + N[(y * N[(N[(b * 1.6453555072203998), $MachinePrecision] - N[(z * N[(N[(b * 32.324150453290734), $MachinePrecision] - N[(a * 1.6453555072203998), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(3.13060547623 + N[(b / 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]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -6e12

   1. Initial program 13.7%

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

   3. Simplified 24.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), t\right), a\right), b\right)}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)}, y, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 89.5%

      \[\leadsto \color{blue}{x + \left(-36.52704169880642 \cdot \frac{y}{z} + 3.13060547623 \cdot y\right)} \]

   if -6e12 < z < 3.45e6

   1. Initial program 98.9%

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

   3. Simplified 99.6%

      \[\leadsto \color{blue}{x + \frac{y}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)} \cdot \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), t\right), a\right), b\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 78.5%

      \[\leadsto x + \color{blue}{\left(1.6453555072203998 \cdot \left(b \cdot y\right) + z \cdot \left(1.6453555072203998 \cdot \left(a \cdot y\right) - 32.324150453290734 \cdot \left(b \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y around 0 92.0%

      \[\leadsto x + \color{blue}{y \cdot \left(1.6453555072203998 \cdot b + z \cdot \left(1.6453555072203998 \cdot a - 32.324150453290734 \cdot b\right)\right)} \]

   if 3.45e6 < z

   1. Initial program 20.1%

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

   3. Simplified 21.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), t\right), a\right), b\right)}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)}, y, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 21.3%

      \[\leadsto \color{blue}{x + y \cdot \left(\frac{b}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(15.234687407 + z\right)\right)\right)} + \frac{z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + 3.13060547623 \cdot z\right)\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(15.234687407 + z\right)\right)\right)}\right)} \]

   6. Taylor expanded in z around inf 92.8%

      \[\leadsto x + y \cdot \left(\frac{b}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(15.234687407 + z\right)\right)\right)} + \color{blue}{3.13060547623}\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6000000000000:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 + \frac{y}{z} \cdot -36.52704169880642\right)\\ \mathbf{elif}\;z \leq 3450000:\\ \;\;\;\;x + y \cdot \left(b \cdot 1.6453555072203998 - z \cdot \left(b \cdot 32.324150453290734 - a \cdot 1.6453555072203998\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(3.13060547623 + \frac{b}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 89.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6200000000000:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 + \frac{y}{z} \cdot -36.52704169880642\right)\\ \mathbf{elif}\;z \leq 3000000:\\ \;\;\;\;x + y \cdot \left(b \cdot 1.6453555072203998 - z \cdot \left(b \cdot 32.324150453290734 - a \cdot 1.6453555072203998\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(3.13060547623 + \frac{b}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot 15.234687407\right)\right)}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -6200000000000.0)
   (+ x (+ (* y 3.13060547623) (* (/ y z) -36.52704169880642)))
   (if (<= z 3000000.0)
     (+
      x
      (*
       y
       (-
        (* b 1.6453555072203998)
        (* z (- (* b 32.324150453290734) (* a 1.6453555072203998))))))
     (+
      x
      (*
       y
       (+
        3.13060547623
        (/
         b
         (+
          0.607771387771
          (*
           z
           (+
            11.9400905721
            (* z (+ 31.4690115749 (* z 15.234687407)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -6200000000000.0) {
		tmp = x + ((y * 3.13060547623) + ((y / z) * -36.52704169880642));
	} else if (z <= 3000000.0) {
		tmp = x + (y * ((b * 1.6453555072203998) - (z * ((b * 32.324150453290734) - (a * 1.6453555072203998)))));
	} else {
		tmp = x + (y * (3.13060547623 + (b / (0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * 15.234687407)))))))));
	}
	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 <= (-6200000000000.0d0)) then
        tmp = x + ((y * 3.13060547623d0) + ((y / z) * (-36.52704169880642d0)))
    else if (z <= 3000000.0d0) then
        tmp = x + (y * ((b * 1.6453555072203998d0) - (z * ((b * 32.324150453290734d0) - (a * 1.6453555072203998d0)))))
    else
        tmp = x + (y * (3.13060547623d0 + (b / (0.607771387771d0 + (z * (11.9400905721d0 + (z * (31.4690115749d0 + (z * 15.234687407d0)))))))))
    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 <= -6200000000000.0) {
		tmp = x + ((y * 3.13060547623) + ((y / z) * -36.52704169880642));
	} else if (z <= 3000000.0) {
		tmp = x + (y * ((b * 1.6453555072203998) - (z * ((b * 32.324150453290734) - (a * 1.6453555072203998)))));
	} else {
		tmp = x + (y * (3.13060547623 + (b / (0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * 15.234687407)))))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -6200000000000.0:
		tmp = x + ((y * 3.13060547623) + ((y / z) * -36.52704169880642))
	elif z <= 3000000.0:
		tmp = x + (y * ((b * 1.6453555072203998) - (z * ((b * 32.324150453290734) - (a * 1.6453555072203998)))))
	else:
		tmp = x + (y * (3.13060547623 + (b / (0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * 15.234687407)))))))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -6200000000000.0)
		tmp = Float64(x + Float64(Float64(y * 3.13060547623) + Float64(Float64(y / z) * -36.52704169880642)));
	elseif (z <= 3000000.0)
		tmp = Float64(x + Float64(y * Float64(Float64(b * 1.6453555072203998) - Float64(z * Float64(Float64(b * 32.324150453290734) - Float64(a * 1.6453555072203998))))));
	else
		tmp = Float64(x + Float64(y * Float64(3.13060547623 + Float64(b / Float64(0.607771387771 + Float64(z * Float64(11.9400905721 + Float64(z * Float64(31.4690115749 + Float64(z * 15.234687407))))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -6200000000000.0)
		tmp = x + ((y * 3.13060547623) + ((y / z) * -36.52704169880642));
	elseif (z <= 3000000.0)
		tmp = x + (y * ((b * 1.6453555072203998) - (z * ((b * 32.324150453290734) - (a * 1.6453555072203998)))));
	else
		tmp = x + (y * (3.13060547623 + (b / (0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * 15.234687407)))))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -6200000000000.0], N[(x + N[(N[(y * 3.13060547623), $MachinePrecision] + N[(N[(y / z), $MachinePrecision] * -36.52704169880642), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3000000.0], N[(x + N[(y * N[(N[(b * 1.6453555072203998), $MachinePrecision] - N[(z * N[(N[(b * 32.324150453290734), $MachinePrecision] - N[(a * 1.6453555072203998), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(3.13060547623 + N[(b / N[(0.607771387771 + N[(z * N[(11.9400905721 + N[(z * N[(31.4690115749 + N[(z * 15.234687407), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.2e12

   1. Initial program 13.7%

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

   3. Simplified 24.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), t\right), a\right), b\right)}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)}, y, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 89.5%

      \[\leadsto \color{blue}{x + \left(-36.52704169880642 \cdot \frac{y}{z} + 3.13060547623 \cdot y\right)} \]

   if -6.2e12 < z < 3e6

   1. Initial program 98.9%

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

   3. Simplified 99.6%

      \[\leadsto \color{blue}{x + \frac{y}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)} \cdot \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), t\right), a\right), b\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 78.5%

      \[\leadsto x + \color{blue}{\left(1.6453555072203998 \cdot \left(b \cdot y\right) + z \cdot \left(1.6453555072203998 \cdot \left(a \cdot y\right) - 32.324150453290734 \cdot \left(b \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y around 0 92.0%

      \[\leadsto x + \color{blue}{y \cdot \left(1.6453555072203998 \cdot b + z \cdot \left(1.6453555072203998 \cdot a - 32.324150453290734 \cdot b\right)\right)} \]

   if 3e6 < z

   1. Initial program 20.1%

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

   3. Simplified 21.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), t\right), a\right), b\right)}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)}, y, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 21.3%

      \[\leadsto \color{blue}{x + y \cdot \left(\frac{b}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(15.234687407 + z\right)\right)\right)} + \frac{z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + 3.13060547623 \cdot z\right)\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(15.234687407 + z\right)\right)\right)}\right)} \]

   6. Taylor expanded in z around inf 92.8%

      \[\leadsto x + y \cdot \left(\frac{b}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(15.234687407 + z\right)\right)\right)} + \color{blue}{3.13060547623}\right) \]

   7. Taylor expanded in z around 0 91.7%

      \[\leadsto x + y \cdot \left(\frac{b}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + \color{blue}{15.234687407 \cdot z}\right)\right)} + 3.13060547623\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6200000000000:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 + \frac{y}{z} \cdot -36.52704169880642\right)\\ \mathbf{elif}\;z \leq 3000000:\\ \;\;\;\;x + y \cdot \left(b \cdot 1.6453555072203998 - z \cdot \left(b \cdot 32.324150453290734 - a \cdot 1.6453555072203998\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(3.13060547623 + \frac{b}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot 15.234687407\right)\right)}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 86.4% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -38000000000000:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 + \frac{y}{z} \cdot -36.52704169880642\right)\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+29}:\\ \;\;\;\;x + 1.6453555072203998 \cdot \left(z \cdot \left(y \cdot a\right) + y \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -38000000000000.0)
   (+ x (+ (* y 3.13060547623) (* (/ y z) -36.52704169880642)))
   (if (<= z 1.2e+29)
     (+ x (* 1.6453555072203998 (+ (* z (* y a)) (* y b))))
     (+ x (* y 3.13060547623)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -38000000000000.0) {
		tmp = x + ((y * 3.13060547623) + ((y / z) * -36.52704169880642));
	} else if (z <= 1.2e+29) {
		tmp = x + (1.6453555072203998 * ((z * (y * a)) + (y * b)));
	} else {
		tmp = x + (y * 3.13060547623);
	}
	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 <= (-38000000000000.0d0)) then
        tmp = x + ((y * 3.13060547623d0) + ((y / z) * (-36.52704169880642d0)))
    else if (z <= 1.2d+29) then
        tmp = x + (1.6453555072203998d0 * ((z * (y * a)) + (y * b)))
    else
        tmp = x + (y * 3.13060547623d0)
    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 <= -38000000000000.0) {
		tmp = x + ((y * 3.13060547623) + ((y / z) * -36.52704169880642));
	} else if (z <= 1.2e+29) {
		tmp = x + (1.6453555072203998 * ((z * (y * a)) + (y * b)));
	} else {
		tmp = x + (y * 3.13060547623);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -38000000000000.0:
		tmp = x + ((y * 3.13060547623) + ((y / z) * -36.52704169880642))
	elif z <= 1.2e+29:
		tmp = x + (1.6453555072203998 * ((z * (y * a)) + (y * b)))
	else:
		tmp = x + (y * 3.13060547623)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -38000000000000.0)
		tmp = Float64(x + Float64(Float64(y * 3.13060547623) + Float64(Float64(y / z) * -36.52704169880642)));
	elseif (z <= 1.2e+29)
		tmp = Float64(x + Float64(1.6453555072203998 * Float64(Float64(z * Float64(y * a)) + Float64(y * b))));
	else
		tmp = Float64(x + Float64(y * 3.13060547623));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -38000000000000.0)
		tmp = x + ((y * 3.13060547623) + ((y / z) * -36.52704169880642));
	elseif (z <= 1.2e+29)
		tmp = x + (1.6453555072203998 * ((z * (y * a)) + (y * b)));
	else
		tmp = x + (y * 3.13060547623);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -38000000000000.0], N[(x + N[(N[(y * 3.13060547623), $MachinePrecision] + N[(N[(y / z), $MachinePrecision] * -36.52704169880642), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.2e+29], N[(x + N[(1.6453555072203998 * N[(N[(z * N[(y * a), $MachinePrecision]), $MachinePrecision] + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.8e13

   1. Initial program 13.7%

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

   3. Simplified 24.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), t\right), a\right), b\right)}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)}, y, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 89.5%

      \[\leadsto \color{blue}{x + \left(-36.52704169880642 \cdot \frac{y}{z} + 3.13060547623 \cdot y\right)} \]

   if -3.8e13 < z < 1.2e29

   1. Initial program 98.3%

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

   3. Simplified 99.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), t\right), a\right), b\right)}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)}, y, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 99.6%

      \[\leadsto \color{blue}{x + y \cdot \left(\frac{b}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(15.234687407 + z\right)\right)\right)} + \frac{z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + 3.13060547623 \cdot z\right)\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(15.234687407 + z\right)\right)\right)}\right)} \]

   6. Taylor expanded in z around 0 98.6%

      \[\leadsto x + y \cdot \left(\color{blue}{1.6453555072203998 \cdot b} + \frac{z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + 3.13060547623 \cdot z\right)\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(15.234687407 + z\right)\right)\right)}\right) \]

   7. Taylor expanded in z around 0 88.5%

      \[\leadsto x + \color{blue}{\left(1.6453555072203998 \cdot \left(a \cdot \left(y \cdot z\right)\right) + 1.6453555072203998 \cdot \left(b \cdot y\right)\right)} \]
   8. Step-by-step derivation

      1. distribute-lft-out 88.5%

         \[\leadsto x + \color{blue}{1.6453555072203998 \cdot \left(a \cdot \left(y \cdot z\right) + b \cdot y\right)} \]

      2. associate-*r* 81.0%

         \[\leadsto x + 1.6453555072203998 \cdot \left(\color{blue}{\left(a \cdot y\right) \cdot z} + b \cdot y\right) \]

      3. *-commutative 81.0%

         \[\leadsto x + 1.6453555072203998 \cdot \left(\color{blue}{\left(y \cdot a\right)} \cdot z + b \cdot y\right) \]

   9. Simplified 81.0%

      \[\leadsto x + \color{blue}{1.6453555072203998 \cdot \left(\left(y \cdot a\right) \cdot z + b \cdot y\right)} \]

   if 1.2e29 < z

   1. Initial program 14.2%

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

   3. Simplified 14.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), t\right), a\right), b\right)}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)}, y, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 94.6%

      \[\leadsto \color{blue}{x + 3.13060547623 \cdot y} \]
   6. Step-by-step derivation

      1. +-commutative 94.6%

         \[\leadsto \color{blue}{3.13060547623 \cdot y + x} \]

      2. *-commutative 94.6%

         \[\leadsto \color{blue}{y \cdot 3.13060547623} + x \]

   7. Simplified 94.6%

      \[\leadsto \color{blue}{y \cdot 3.13060547623 + x} \]
3. Recombined 3 regimes into one program.

4. Final simplification 86.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -38000000000000:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 + \frac{y}{z} \cdot -36.52704169880642\right)\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+29}:\\ \;\;\;\;x + 1.6453555072203998 \cdot \left(z \cdot \left(y \cdot a\right) + y \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 90.1% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8800000000000:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 + \frac{y}{z} \cdot -36.52704169880642\right)\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+26}:\\ \;\;\;\;x + y \cdot \left(b \cdot 1.6453555072203998 + 1.6453555072203998 \cdot \left(z \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -8800000000000.0)
   (+ x (+ (* y 3.13060547623) (* (/ y z) -36.52704169880642)))
   (if (<= z 6.2e+26)
     (+ x (* y (+ (* b 1.6453555072203998) (* 1.6453555072203998 (* z a)))))
     (+ x (* y 3.13060547623)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -8800000000000.0) {
		tmp = x + ((y * 3.13060547623) + ((y / z) * -36.52704169880642));
	} else if (z <= 6.2e+26) {
		tmp = x + (y * ((b * 1.6453555072203998) + (1.6453555072203998 * (z * a))));
	} else {
		tmp = x + (y * 3.13060547623);
	}
	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 <= (-8800000000000.0d0)) then
        tmp = x + ((y * 3.13060547623d0) + ((y / z) * (-36.52704169880642d0)))
    else if (z <= 6.2d+26) then
        tmp = x + (y * ((b * 1.6453555072203998d0) + (1.6453555072203998d0 * (z * a))))
    else
        tmp = x + (y * 3.13060547623d0)
    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 <= -8800000000000.0) {
		tmp = x + ((y * 3.13060547623) + ((y / z) * -36.52704169880642));
	} else if (z <= 6.2e+26) {
		tmp = x + (y * ((b * 1.6453555072203998) + (1.6453555072203998 * (z * a))));
	} else {
		tmp = x + (y * 3.13060547623);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -8800000000000.0:
		tmp = x + ((y * 3.13060547623) + ((y / z) * -36.52704169880642))
	elif z <= 6.2e+26:
		tmp = x + (y * ((b * 1.6453555072203998) + (1.6453555072203998 * (z * a))))
	else:
		tmp = x + (y * 3.13060547623)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -8800000000000.0)
		tmp = Float64(x + Float64(Float64(y * 3.13060547623) + Float64(Float64(y / z) * -36.52704169880642)));
	elseif (z <= 6.2e+26)
		tmp = Float64(x + Float64(y * Float64(Float64(b * 1.6453555072203998) + Float64(1.6453555072203998 * Float64(z * a)))));
	else
		tmp = Float64(x + Float64(y * 3.13060547623));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -8800000000000.0)
		tmp = x + ((y * 3.13060547623) + ((y / z) * -36.52704169880642));
	elseif (z <= 6.2e+26)
		tmp = x + (y * ((b * 1.6453555072203998) + (1.6453555072203998 * (z * a))));
	else
		tmp = x + (y * 3.13060547623);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -8800000000000.0], N[(x + N[(N[(y * 3.13060547623), $MachinePrecision] + N[(N[(y / z), $MachinePrecision] * -36.52704169880642), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.2e+26], N[(x + N[(y * N[(N[(b * 1.6453555072203998), $MachinePrecision] + N[(1.6453555072203998 * N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.8e12

   1. Initial program 13.7%

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

   3. Simplified 24.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), t\right), a\right), b\right)}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)}, y, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 89.5%

      \[\leadsto \color{blue}{x + \left(-36.52704169880642 \cdot \frac{y}{z} + 3.13060547623 \cdot y\right)} \]

   if -8.8e12 < z < 6.1999999999999999e26

   1. Initial program 98.3%

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

   3. Simplified 99.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), t\right), a\right), b\right)}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)}, y, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 99.6%

      \[\leadsto \color{blue}{x + y \cdot \left(\frac{b}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(15.234687407 + z\right)\right)\right)} + \frac{z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + 3.13060547623 \cdot z\right)\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(15.234687407 + z\right)\right)\right)}\right)} \]

   6. Taylor expanded in z around 0 98.6%

      \[\leadsto x + y \cdot \left(\color{blue}{1.6453555072203998 \cdot b} + \frac{z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + 3.13060547623 \cdot z\right)\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(15.234687407 + z\right)\right)\right)}\right) \]

   7. Taylor expanded in z around 0 90.0%

      \[\leadsto x + y \cdot \left(1.6453555072203998 \cdot b + \color{blue}{1.6453555072203998 \cdot \left(a \cdot z\right)}\right) \]
   8. Step-by-step derivation

      1. *-commutative 90.0%

         \[\leadsto x + y \cdot \left(1.6453555072203998 \cdot b + 1.6453555072203998 \cdot \color{blue}{\left(z \cdot a\right)}\right) \]

   9. Simplified 90.0%

      \[\leadsto x + y \cdot \left(1.6453555072203998 \cdot b + \color{blue}{1.6453555072203998 \cdot \left(z \cdot a\right)}\right) \]

   if 6.1999999999999999e26 < z

   1. Initial program 14.2%

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

   3. Simplified 14.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), t\right), a\right), b\right)}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)}, y, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 94.6%

      \[\leadsto \color{blue}{x + 3.13060547623 \cdot y} \]
   6. Step-by-step derivation

      1. +-commutative 94.6%

         \[\leadsto \color{blue}{3.13060547623 \cdot y + x} \]

      2. *-commutative 94.6%

         \[\leadsto \color{blue}{y \cdot 3.13060547623} + x \]

   7. Simplified 94.6%

      \[\leadsto \color{blue}{y \cdot 3.13060547623 + x} \]
3. Recombined 3 regimes into one program.

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8800000000000:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 + \frac{y}{z} \cdot -36.52704169880642\right)\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+26}:\\ \;\;\;\;x + y \cdot \left(b \cdot 1.6453555072203998 + 1.6453555072203998 \cdot \left(z \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 83.0% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+14} \lor \neg \left(z \leq 3.8 \cdot 10^{+27}\right):\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(b \cdot 1.6453555072203998\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -3e+14) (not (<= z 3.8e+27)))
   (+ x (* y 3.13060547623))
   (+ x (* y (* b 1.6453555072203998)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -3e+14) || !(z <= 3.8e+27)) {
		tmp = x + (y * 3.13060547623);
	} else {
		tmp = x + (y * (b * 1.6453555072203998));
	}
	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 <= (-3d+14)) .or. (.not. (z <= 3.8d+27))) then
        tmp = x + (y * 3.13060547623d0)
    else
        tmp = x + (y * (b * 1.6453555072203998d0))
    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 <= -3e+14) || !(z <= 3.8e+27)) {
		tmp = x + (y * 3.13060547623);
	} else {
		tmp = x + (y * (b * 1.6453555072203998));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -3e+14) or not (z <= 3.8e+27):
		tmp = x + (y * 3.13060547623)
	else:
		tmp = x + (y * (b * 1.6453555072203998))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -3e+14) || !(z <= 3.8e+27))
		tmp = Float64(x + Float64(y * 3.13060547623));
	else
		tmp = Float64(x + Float64(y * Float64(b * 1.6453555072203998)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -3e+14) || ~((z <= 3.8e+27)))
		tmp = x + (y * 3.13060547623);
	else
		tmp = x + (y * (b * 1.6453555072203998));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -3e+14], N[Not[LessEqual[z, 3.8e+27]], $MachinePrecision]], N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(b * 1.6453555072203998), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3e14 or 3.80000000000000022e27 < z

   1. Initial program 13.9%

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

   3. Simplified 19.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), t\right), a\right), b\right)}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)}, y, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 92.0%

      \[\leadsto \color{blue}{x + 3.13060547623 \cdot y} \]
   6. Step-by-step derivation

      1. +-commutative 92.0%

         \[\leadsto \color{blue}{3.13060547623 \cdot y + x} \]

      2. *-commutative 92.0%

         \[\leadsto \color{blue}{y \cdot 3.13060547623} + x \]

   7. Simplified 92.0%

      \[\leadsto \color{blue}{y \cdot 3.13060547623 + x} \]

   if -3e14 < z < 3.80000000000000022e27

   1. Initial program 98.3%

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

   3. Simplified 99.6%

      \[\leadsto \color{blue}{x + \frac{y}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)} \cdot \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), t\right), a\right), b\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 78.0%

      \[\leadsto x + \color{blue}{1.6453555072203998 \cdot \left(b \cdot y\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 78.1%

         \[\leadsto x + \color{blue}{\left(1.6453555072203998 \cdot b\right) \cdot y} \]

      2. *-commutative 78.1%

         \[\leadsto x + \color{blue}{\left(b \cdot 1.6453555072203998\right)} \cdot y \]

   7. Simplified 78.1%

      \[\leadsto x + \color{blue}{\left(b \cdot 1.6453555072203998\right) \cdot y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 85.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+14} \lor \neg \left(z \leq 3.8 \cdot 10^{+27}\right):\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(b \cdot 1.6453555072203998\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 83.0% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6200000000000:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 + \frac{y}{z} \cdot -36.52704169880642\right)\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+28}:\\ \;\;\;\;x + y \cdot \left(b \cdot 1.6453555072203998\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -6200000000000.0)
   (+ x (+ (* y 3.13060547623) (* (/ y z) -36.52704169880642)))
   (if (<= z 2.9e+28)
     (+ x (* y (* b 1.6453555072203998)))
     (+ x (* y 3.13060547623)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -6200000000000.0) {
		tmp = x + ((y * 3.13060547623) + ((y / z) * -36.52704169880642));
	} else if (z <= 2.9e+28) {
		tmp = x + (y * (b * 1.6453555072203998));
	} else {
		tmp = x + (y * 3.13060547623);
	}
	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 <= (-6200000000000.0d0)) then
        tmp = x + ((y * 3.13060547623d0) + ((y / z) * (-36.52704169880642d0)))
    else if (z <= 2.9d+28) then
        tmp = x + (y * (b * 1.6453555072203998d0))
    else
        tmp = x + (y * 3.13060547623d0)
    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 <= -6200000000000.0) {
		tmp = x + ((y * 3.13060547623) + ((y / z) * -36.52704169880642));
	} else if (z <= 2.9e+28) {
		tmp = x + (y * (b * 1.6453555072203998));
	} else {
		tmp = x + (y * 3.13060547623);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -6200000000000.0:
		tmp = x + ((y * 3.13060547623) + ((y / z) * -36.52704169880642))
	elif z <= 2.9e+28:
		tmp = x + (y * (b * 1.6453555072203998))
	else:
		tmp = x + (y * 3.13060547623)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -6200000000000.0)
		tmp = Float64(x + Float64(Float64(y * 3.13060547623) + Float64(Float64(y / z) * -36.52704169880642)));
	elseif (z <= 2.9e+28)
		tmp = Float64(x + Float64(y * Float64(b * 1.6453555072203998)));
	else
		tmp = Float64(x + Float64(y * 3.13060547623));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -6200000000000.0)
		tmp = x + ((y * 3.13060547623) + ((y / z) * -36.52704169880642));
	elseif (z <= 2.9e+28)
		tmp = x + (y * (b * 1.6453555072203998));
	else
		tmp = x + (y * 3.13060547623);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -6200000000000.0], N[(x + N[(N[(y * 3.13060547623), $MachinePrecision] + N[(N[(y / z), $MachinePrecision] * -36.52704169880642), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.9e+28], N[(x + N[(y * N[(b * 1.6453555072203998), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.2e12

   1. Initial program 13.7%

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

   3. Simplified 24.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), t\right), a\right), b\right)}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)}, y, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 89.5%

      \[\leadsto \color{blue}{x + \left(-36.52704169880642 \cdot \frac{y}{z} + 3.13060547623 \cdot y\right)} \]

   if -6.2e12 < z < 2.9000000000000001e28

   1. Initial program 98.3%

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

   3. Simplified 99.6%

      \[\leadsto \color{blue}{x + \frac{y}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)} \cdot \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), t\right), a\right), b\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 78.0%

      \[\leadsto x + \color{blue}{1.6453555072203998 \cdot \left(b \cdot y\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 78.1%

         \[\leadsto x + \color{blue}{\left(1.6453555072203998 \cdot b\right) \cdot y} \]

      2. *-commutative 78.1%

         \[\leadsto x + \color{blue}{\left(b \cdot 1.6453555072203998\right)} \cdot y \]

   7. Simplified 78.1%

      \[\leadsto x + \color{blue}{\left(b \cdot 1.6453555072203998\right) \cdot y} \]

   if 2.9000000000000001e28 < z

   1. Initial program 14.2%

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

   3. Simplified 14.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), t\right), a\right), b\right)}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)}, y, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 94.6%

      \[\leadsto \color{blue}{x + 3.13060547623 \cdot y} \]
   6. Step-by-step derivation

      1. +-commutative 94.6%

         \[\leadsto \color{blue}{3.13060547623 \cdot y + x} \]

      2. *-commutative 94.6%

         \[\leadsto \color{blue}{y \cdot 3.13060547623} + x \]

   7. Simplified 94.6%

      \[\leadsto \color{blue}{y \cdot 3.13060547623 + x} \]
3. Recombined 3 regimes into one program.

4. Final simplification 85.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6200000000000:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 + \frac{y}{z} \cdot -36.52704169880642\right)\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+28}:\\ \;\;\;\;x + y \cdot \left(b \cdot 1.6453555072203998\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 63.6% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7500000 \lor \neg \left(z \leq 10^{-39}\right):\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -7500000.0) (not (<= z 1e-39))) (+ x (* y 3.13060547623)) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -7500000.0) || !(z <= 1e-39)) {
		tmp = x + (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 ((z <= (-7500000.0d0)) .or. (.not. (z <= 1d-39))) then
        tmp = x + (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 ((z <= -7500000.0) || !(z <= 1e-39)) {
		tmp = x + (y * 3.13060547623);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -7500000.0) or not (z <= 1e-39):
		tmp = x + (y * 3.13060547623)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -7500000.0) || !(z <= 1e-39))
		tmp = Float64(x + 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 ((z <= -7500000.0) || ~((z <= 1e-39)))
		tmp = x + (y * 3.13060547623);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -7500000.0], N[Not[LessEqual[z, 1e-39]], $MachinePrecision]], N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -7.5e6 or 9.99999999999999929e-40 < z

   1. Initial program 22.8%

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

   3. Simplified 28.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), t\right), a\right), b\right)}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)}, y, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 85.2%

      \[\leadsto \color{blue}{x + 3.13060547623 \cdot y} \]
   6. Step-by-step derivation

      1. +-commutative 85.2%

         \[\leadsto \color{blue}{3.13060547623 \cdot y + x} \]

      2. *-commutative 85.2%

         \[\leadsto \color{blue}{y \cdot 3.13060547623} + x \]

   7. Simplified 85.2%

      \[\leadsto \color{blue}{y \cdot 3.13060547623 + x} \]

   if -7.5e6 < z < 9.99999999999999929e-40

   1. Initial program 99.6%

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

   3. Simplified 99.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), t\right), a\right), b\right)}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)}, y, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 44.8%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 67.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7500000 \lor \neg \left(z \leq 10^{-39}\right):\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 44.7% 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 56.1%

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

3. Simplified 59.3%

   \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), t\right), a\right), b\right)}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)}, y, x\right)} \]
4. Add Preprocessing

5. Taylor expanded in y around 0 47.1%

   \[\leadsto \color{blue}{x} \]

6. Final simplification 47.1%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 98.5% 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 2024026 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, D"
  :precision binary64

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

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