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

Percentage Accurate: 58.0% → 97.3%

Time: 16.2s

Alternatives: 10

Speedup: 3.7×

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: 58.0% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (+
  x
  (/
   (*
    y
    (+ (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z) b))
   (+
    (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z)
    0.607771387771))))

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y \cdot 3.13060547623 + t \cdot \frac{y}{z \cdot z}\right)\\ \mathbf{if}\;z \leq -1.1 \cdot 10^{+34}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{+55}:\\ \;\;\;\;\frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right)\right)\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)} + x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (+ (* y 3.13060547623) (* t (/ y (* z z)))))))
   (if (<= z -1.1e+34)
     t_1
     (if (<= z 4.1e+55)
       (+
        (/
         (*
          y
          (+
           b
           (*
            z
            (+ a (* z (+ t (* z (+ (* z 3.13060547623) 11.1667541262))))))))
         (+
          0.607771387771
          (*
           z
           (+
            11.9400905721
            (* z (+ 31.4690115749 (* z (+ z 15.234687407))))))))
        x)
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + ((y * 3.13060547623) + (t * (y / (z * z))));
	double tmp;
	if (z <= -1.1e+34) {
		tmp = t_1;
	} else if (z <= 4.1e+55) {
		tmp = ((y * (b + (z * (a + (z * (t + (z * ((z * 3.13060547623) + 11.1667541262)))))))) / (0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * (z + 15.234687407)))))))) + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y * 3.13060547623d0) + (t * (y / (z * z))))
    if (z <= (-1.1d+34)) then
        tmp = t_1
    else if (z <= 4.1d+55) then
        tmp = ((y * (b + (z * (a + (z * (t + (z * ((z * 3.13060547623d0) + 11.1667541262d0)))))))) / (0.607771387771d0 + (z * (11.9400905721d0 + (z * (31.4690115749d0 + (z * (z + 15.234687407d0)))))))) + x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + ((y * 3.13060547623) + (t * (y / (z * z))));
	double tmp;
	if (z <= -1.1e+34) {
		tmp = t_1;
	} else if (z <= 4.1e+55) {
		tmp = ((y * (b + (z * (a + (z * (t + (z * ((z * 3.13060547623) + 11.1667541262)))))))) / (0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * (z + 15.234687407)))))))) + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + ((y * 3.13060547623) + (t * (y / (z * z))))
	tmp = 0
	if z <= -1.1e+34:
		tmp = t_1
	elif z <= 4.1e+55:
		tmp = ((y * (b + (z * (a + (z * (t + (z * ((z * 3.13060547623) + 11.1667541262)))))))) / (0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * (z + 15.234687407)))))))) + x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(Float64(y * 3.13060547623) + Float64(t * Float64(y / Float64(z * z)))))
	tmp = 0.0
	if (z <= -1.1e+34)
		tmp = t_1;
	elseif (z <= 4.1e+55)
		tmp = Float64(Float64(Float64(y * Float64(b + Float64(z * Float64(a + Float64(z * Float64(t + Float64(z * Float64(Float64(z * 3.13060547623) + 11.1667541262)))))))) / Float64(0.607771387771 + Float64(z * Float64(11.9400905721 + Float64(z * Float64(31.4690115749 + Float64(z * Float64(z + 15.234687407)))))))) + x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + ((y * 3.13060547623) + (t * (y / (z * z))));
	tmp = 0.0;
	if (z <= -1.1e+34)
		tmp = t_1;
	elseif (z <= 4.1e+55)
		tmp = ((y * (b + (z * (a + (z * (t + (z * ((z * 3.13060547623) + 11.1667541262)))))))) / (0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * (z + 15.234687407)))))))) + x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(N[(y * 3.13060547623), $MachinePrecision] + N[(t * N[(y / N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.1e+34], t$95$1, If[LessEqual[z, 4.1e+55], N[(N[(N[(y * N[(b + N[(z * N[(a + N[(z * N[(t + N[(z * N[(N[(z * 3.13060547623), $MachinePrecision] + 11.1667541262), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(0.607771387771 + N[(z * N[(11.9400905721 + N[(z * N[(31.4690115749 + N[(z * N[(z + 15.234687407), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.1000000000000001e34 or 4.09999999999999981e55 < z

   1. Initial program 9.6%

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

   3. Taylor expanded in z around -inf

      \[\leadsto \color{blue}{x + \left(-1 \cdot \frac{\left(\frac{-55833770631}{5000000000} \cdot y + -1 \cdot \frac{t \cdot y - \left(\frac{-15234687407}{1000000000} \cdot \left(\frac{-55833770631}{5000000000} \cdot y - \frac{-4769379582500641883561}{100000000000000000000} \cdot y\right) + \frac{98517059967927196814627}{1000000000000000000000} \cdot y\right)}{z}\right) - \frac{-4769379582500641883561}{100000000000000000000} \cdot y}{z} + \frac{313060547623}{100000000000} \cdot y\right)} \]

   5. Simplified 81.4%

      \[\leadsto \color{blue}{x + \left(y \cdot 3.13060547623 - \frac{\frac{\left(y \cdot t - y \cdot -556.47806218377\right) + -98.5170599679272 \cdot y}{0 - z} + y \cdot 36.52704169880642}{z}\right)} \]

   6. Taylor expanded in t around inf

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right), \color{blue}{\left(-1 \cdot \frac{t \cdot y}{{z}^{2}}\right)}\right)\right) \]
   7. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right), \left(\mathsf{neg}\left(\frac{t \cdot y}{{z}^{2}}\right)\right)\right)\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right), \left(0 - \color{blue}{\frac{t \cdot y}{{z}^{2}}}\right)\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right), \mathsf{\_.f64}\left(0, \color{blue}{\left(\frac{t \cdot y}{{z}^{2}}\right)}\right)\right)\right) \]

      4. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right), \mathsf{\_.f64}\left(0, \left(t \cdot \color{blue}{\frac{y}{{z}^{2}}}\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right), \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(t, \color{blue}{\left(\frac{y}{{z}^{2}}\right)}\right)\right)\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right), \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(y, \color{blue}{\left({z}^{2}\right)}\right)\right)\right)\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right), \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(y, \left(z \cdot \color{blue}{z}\right)\right)\right)\right)\right)\right) \]

      8. *-lowering-*.f64 97.5%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right), \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(y, \mathsf{*.f64}\left(z, \color{blue}{z}\right)\right)\right)\right)\right)\right) \]

   8. Simplified 97.5%

      \[\leadsto x + \left(y \cdot 3.13060547623 - \color{blue}{\left(0 - t \cdot \frac{y}{z \cdot z}\right)}\right) \]

   if -1.1000000000000001e34 < z < 4.09999999999999981e55

   1. Initial program 99.0%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+34}:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 + t \cdot \frac{y}{z \cdot z}\right)\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{+55}:\\ \;\;\;\;\frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right)\right)\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)} + x\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 + t \cdot \frac{y}{z \cdot z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 98.1% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(0.607771387771 + N[(z * N[(11.9400905721 + N[(z * N[(31.4690115749 + N[(z * N[(z + 15.234687407), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b + N[(z * N[(a + N[(z * N[(t + N[(z * N[(N[(z * 3.13060547623), $MachinePrecision] + 11.1667541262), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(y * t$95$2), $MachinePrecision] / t$95$1), $MachinePrecision], Infinity], N[(N[(y * N[(t$95$2 / t$95$1), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(x + N[(N[(y * 3.13060547623), $MachinePrecision] + N[(t * N[(y / N[(z * z), $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 #s(literal 313060547623/100000000000 binary64)) #s(literal 55833770631/5000000000 binary64)) z) t) z) a) z) b)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 z #s(literal 15234687407/1000000000 binary64)) z) #s(literal 314690115749/10000000000 binary64)) z) #s(literal 119400905721/10000000000 binary64)) z) #s(literal 607771387771/1000000000000 binary64))) < +inf.0

   1. Initial program 93.6%

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

      1. +-commutative N/A

         \[\leadsto \frac{y \cdot \left(\left(\left(\left(z \cdot \frac{313060547623}{100000000000} + \frac{55833770631}{5000000000}\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} + \color{blue}{x} \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{y \cdot \left(\left(\left(\left(z \cdot \frac{313060547623}{100000000000} + \frac{55833770631}{5000000000}\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}}\right), \color{blue}{x}\right) \]

   4. Applied egg-rr 96.8%

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

   if +inf.0 < (/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z #s(literal 313060547623/100000000000 binary64)) #s(literal 55833770631/5000000000 binary64)) z) t) z) a) z) b)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 z #s(literal 15234687407/1000000000 binary64)) z) #s(literal 314690115749/10000000000 binary64)) z) #s(literal 119400905721/10000000000 binary64)) z) #s(literal 607771387771/1000000000000 binary64)))

   1. Initial program 0.0%

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

   3. Taylor expanded in z around -inf

      \[\leadsto \color{blue}{x + \left(-1 \cdot \frac{\left(\frac{-55833770631}{5000000000} \cdot y + -1 \cdot \frac{t \cdot y - \left(\frac{-15234687407}{1000000000} \cdot \left(\frac{-55833770631}{5000000000} \cdot y - \frac{-4769379582500641883561}{100000000000000000000} \cdot y\right) + \frac{98517059967927196814627}{1000000000000000000000} \cdot y\right)}{z}\right) - \frac{-4769379582500641883561}{100000000000000000000} \cdot y}{z} + \frac{313060547623}{100000000000} \cdot y\right)} \]

   5. Simplified 81.4%

      \[\leadsto \color{blue}{x + \left(y \cdot 3.13060547623 - \frac{\frac{\left(y \cdot t - y \cdot -556.47806218377\right) + -98.5170599679272 \cdot y}{0 - z} + y \cdot 36.52704169880642}{z}\right)} \]

   6. Taylor expanded in t around inf

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right), \color{blue}{\left(-1 \cdot \frac{t \cdot y}{{z}^{2}}\right)}\right)\right) \]
   7. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right), \left(\mathsf{neg}\left(\frac{t \cdot y}{{z}^{2}}\right)\right)\right)\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right), \left(0 - \color{blue}{\frac{t \cdot y}{{z}^{2}}}\right)\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right), \mathsf{\_.f64}\left(0, \color{blue}{\left(\frac{t \cdot y}{{z}^{2}}\right)}\right)\right)\right) \]

      4. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right), \mathsf{\_.f64}\left(0, \left(t \cdot \color{blue}{\frac{y}{{z}^{2}}}\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right), \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(t, \color{blue}{\left(\frac{y}{{z}^{2}}\right)}\right)\right)\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right), \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(y, \color{blue}{\left({z}^{2}\right)}\right)\right)\right)\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right), \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(y, \left(z \cdot \color{blue}{z}\right)\right)\right)\right)\right)\right) \]

      8. *-lowering-*.f64 98.9%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right), \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(y, \mathsf{*.f64}\left(z, \color{blue}{z}\right)\right)\right)\right)\right)\right) \]

   8. Simplified 98.9%

      \[\leadsto x + \left(y \cdot 3.13060547623 - \color{blue}{\left(0 - t \cdot \frac{y}{z \cdot z}\right)}\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 97.6%

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

Alternative 3: 97.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y \cdot 3.13060547623 + t \cdot \frac{y}{z \cdot z}\right)\\ \mathbf{if}\;z \leq -1.72 \cdot 10^{+28}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+30}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot t\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (+ (* y 3.13060547623) (* t (/ y (* z z)))))))
   (if (<= z -1.72e+28)
     t_1
     (if (<= z 5.8e+30)
       (+
        x
        (/
         (* y (+ b (* z (+ a (* z t)))))
         (+
          0.607771387771
          (*
           z
           (+
            11.9400905721
            (* z (+ 31.4690115749 (* z (+ z 15.234687407)))))))))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + ((y * 3.13060547623) + (t * (y / (z * z))));
	double tmp;
	if (z <= -1.72e+28) {
		tmp = t_1;
	} else if (z <= 5.8e+30) {
		tmp = x + ((y * (b + (z * (a + (z * t))))) / (0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * (z + 15.234687407))))))));
	} 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 + ((y * 3.13060547623d0) + (t * (y / (z * z))))
    if (z <= (-1.72d+28)) then
        tmp = t_1
    else if (z <= 5.8d+30) then
        tmp = x + ((y * (b + (z * (a + (z * t))))) / (0.607771387771d0 + (z * (11.9400905721d0 + (z * (31.4690115749d0 + (z * (z + 15.234687407d0))))))))
    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 + ((y * 3.13060547623) + (t * (y / (z * z))));
	double tmp;
	if (z <= -1.72e+28) {
		tmp = t_1;
	} else if (z <= 5.8e+30) {
		tmp = x + ((y * (b + (z * (a + (z * t))))) / (0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * (z + 15.234687407))))))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + ((y * 3.13060547623) + (t * (y / (z * z))))
	tmp = 0
	if z <= -1.72e+28:
		tmp = t_1
	elif z <= 5.8e+30:
		tmp = x + ((y * (b + (z * (a + (z * t))))) / (0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * (z + 15.234687407))))))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(Float64(y * 3.13060547623) + Float64(t * Float64(y / Float64(z * z)))))
	tmp = 0.0
	if (z <= -1.72e+28)
		tmp = t_1;
	elseif (z <= 5.8e+30)
		tmp = Float64(x + Float64(Float64(y * Float64(b + Float64(z * Float64(a + Float64(z * t))))) / Float64(0.607771387771 + Float64(z * Float64(11.9400905721 + Float64(z * Float64(31.4690115749 + Float64(z * Float64(z + 15.234687407)))))))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + ((y * 3.13060547623) + (t * (y / (z * z))));
	tmp = 0.0;
	if (z <= -1.72e+28)
		tmp = t_1;
	elseif (z <= 5.8e+30)
		tmp = x + ((y * (b + (z * (a + (z * t))))) / (0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * (z + 15.234687407))))))));
	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[(y * 3.13060547623), $MachinePrecision] + N[(t * N[(y / N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.72e+28], t$95$1, If[LessEqual[z, 5.8e+30], N[(x + N[(N[(y * N[(b + N[(z * N[(a + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(0.607771387771 + N[(z * N[(11.9400905721 + N[(z * N[(31.4690115749 + N[(z * N[(z + 15.234687407), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.72000000000000003e28 or 5.7999999999999996e30 < z

   1. Initial program 16.6%

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

   3. Taylor expanded in z around -inf

      \[\leadsto \color{blue}{x + \left(-1 \cdot \frac{\left(\frac{-55833770631}{5000000000} \cdot y + -1 \cdot \frac{t \cdot y - \left(\frac{-15234687407}{1000000000} \cdot \left(\frac{-55833770631}{5000000000} \cdot y - \frac{-4769379582500641883561}{100000000000000000000} \cdot y\right) + \frac{98517059967927196814627}{1000000000000000000000} \cdot y\right)}{z}\right) - \frac{-4769379582500641883561}{100000000000000000000} \cdot y}{z} + \frac{313060547623}{100000000000} \cdot y\right)} \]

   5. Simplified 81.5%

      \[\leadsto \color{blue}{x + \left(y \cdot 3.13060547623 - \frac{\frac{\left(y \cdot t - y \cdot -556.47806218377\right) + -98.5170599679272 \cdot y}{0 - z} + y \cdot 36.52704169880642}{z}\right)} \]

   6. Taylor expanded in t around inf

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right), \color{blue}{\left(-1 \cdot \frac{t \cdot y}{{z}^{2}}\right)}\right)\right) \]
   7. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right), \left(\mathsf{neg}\left(\frac{t \cdot y}{{z}^{2}}\right)\right)\right)\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right), \left(0 - \color{blue}{\frac{t \cdot y}{{z}^{2}}}\right)\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right), \mathsf{\_.f64}\left(0, \color{blue}{\left(\frac{t \cdot y}{{z}^{2}}\right)}\right)\right)\right) \]

      4. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right), \mathsf{\_.f64}\left(0, \left(t \cdot \color{blue}{\frac{y}{{z}^{2}}}\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right), \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(t, \color{blue}{\left(\frac{y}{{z}^{2}}\right)}\right)\right)\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right), \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(y, \color{blue}{\left({z}^{2}\right)}\right)\right)\right)\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right), \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(y, \left(z \cdot \color{blue}{z}\right)\right)\right)\right)\right)\right) \]

      8. *-lowering-*.f64 96.3%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right), \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(y, \mathsf{*.f64}\left(z, \color{blue}{z}\right)\right)\right)\right)\right)\right) \]

   8. Simplified 96.3%

      \[\leadsto x + \left(y \cdot 3.13060547623 - \color{blue}{\left(0 - t \cdot \frac{y}{z \cdot z}\right)}\right) \]

   if -1.72000000000000003e28 < z < 5.7999999999999996e30

   1. Initial program 99.6%

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

   3. Taylor expanded in z around 0

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \color{blue}{\left(b + z \cdot \left(a + t \cdot z\right)\right)}\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(z, \frac{15234687407}{1000000000}\right), z\right), \frac{314690115749}{10000000000}\right), z\right), \frac{119400905721}{10000000000}\right), z\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]
   4. Step-by-step derivation

      1. distribute-rgt-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(b + \left(a \cdot z + \left(t \cdot z\right) \cdot z\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(z, \frac{15234687407}{1000000000}\right), z\right), \frac{314690115749}{10000000000}\right), z\right), \frac{119400905721}{10000000000}\right), z\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      2. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(b + \left(a \cdot z + t \cdot \left(z \cdot z\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(z, \frac{15234687407}{1000000000}\right), z\right), \frac{314690115749}{10000000000}\right), z\right), \frac{119400905721}{10000000000}\right), z\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      3. unpow2 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(b + \left(a \cdot z + t \cdot {z}^{2}\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(z, \frac{15234687407}{1000000000}\right), z\right), \frac{314690115749}{10000000000}\right), z\right), \frac{119400905721}{10000000000}\right), z\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(b, \left(a \cdot z + t \cdot {z}^{2}\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(z, \frac{15234687407}{1000000000}\right), z\right), \frac{314690115749}{10000000000}\right), z\right), \frac{119400905721}{10000000000}\right), \color{blue}{z}\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      5. unpow2 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(b, \left(a \cdot z + t \cdot \left(z \cdot z\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(z, \frac{15234687407}{1000000000}\right), z\right), \frac{314690115749}{10000000000}\right), z\right), \frac{119400905721}{10000000000}\right), z\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(b, \left(a \cdot z + \left(t \cdot z\right) \cdot z\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(z, \frac{15234687407}{1000000000}\right), z\right), \frac{314690115749}{10000000000}\right), z\right), \frac{119400905721}{10000000000}\right), z\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      7. distribute-rgt-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(b, \left(z \cdot \left(a + t \cdot z\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(z, \frac{15234687407}{1000000000}\right), z\right), \frac{314690115749}{10000000000}\right), z\right), \frac{119400905721}{10000000000}\right), z\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(b, \mathsf{*.f64}\left(z, \left(a + t \cdot z\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(z, \frac{15234687407}{1000000000}\right), z\right), \frac{314690115749}{10000000000}\right), z\right), \frac{119400905721}{10000000000}\right), z\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      9. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(b, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(a, \left(t \cdot z\right)\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(z, \frac{15234687407}{1000000000}\right), z\right), \frac{314690115749}{10000000000}\right), z\right), \frac{119400905721}{10000000000}\right), z\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(b, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(a, \left(z \cdot t\right)\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(z, \frac{15234687407}{1000000000}\right), z\right), \frac{314690115749}{10000000000}\right), z\right), \frac{119400905721}{10000000000}\right), z\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      11. *-lowering-*.f64 98.9%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(b, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(z, t\right)\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(z, \frac{15234687407}{1000000000}\right), z\right), \frac{314690115749}{10000000000}\right), z\right), \frac{119400905721}{10000000000}\right), z\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

   5. Simplified 98.9%

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

4. Final simplification 97.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.72 \cdot 10^{+28}:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 + t \cdot \frac{y}{z \cdot z}\right)\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+30}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot t\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 + t \cdot \frac{y}{z \cdot z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 93.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y \cdot 3.13060547623 + t \cdot \frac{y}{z \cdot z}\right)\\ \mathbf{if}\;z \leq -1.35 \cdot 10^{+28}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 10^{+30}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot a\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (+ (* y 3.13060547623) (* t (/ y (* z z)))))))
   (if (<= z -1.35e+28)
     t_1
     (if (<= z 1e+30)
       (+
        x
        (/
         (* y (+ b (* z a)))
         (+
          0.607771387771
          (*
           z
           (+
            11.9400905721
            (* z (+ 31.4690115749 (* z (+ z 15.234687407)))))))))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + ((y * 3.13060547623) + (t * (y / (z * z))));
	double tmp;
	if (z <= -1.35e+28) {
		tmp = t_1;
	} else if (z <= 1e+30) {
		tmp = x + ((y * (b + (z * a))) / (0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * (z + 15.234687407))))))));
	} 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 + ((y * 3.13060547623d0) + (t * (y / (z * z))))
    if (z <= (-1.35d+28)) then
        tmp = t_1
    else if (z <= 1d+30) then
        tmp = x + ((y * (b + (z * a))) / (0.607771387771d0 + (z * (11.9400905721d0 + (z * (31.4690115749d0 + (z * (z + 15.234687407d0))))))))
    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 + ((y * 3.13060547623) + (t * (y / (z * z))));
	double tmp;
	if (z <= -1.35e+28) {
		tmp = t_1;
	} else if (z <= 1e+30) {
		tmp = x + ((y * (b + (z * a))) / (0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * (z + 15.234687407))))))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + ((y * 3.13060547623) + (t * (y / (z * z))))
	tmp = 0
	if z <= -1.35e+28:
		tmp = t_1
	elif z <= 1e+30:
		tmp = x + ((y * (b + (z * a))) / (0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * (z + 15.234687407))))))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(Float64(y * 3.13060547623) + Float64(t * Float64(y / Float64(z * z)))))
	tmp = 0.0
	if (z <= -1.35e+28)
		tmp = t_1;
	elseif (z <= 1e+30)
		tmp = Float64(x + Float64(Float64(y * Float64(b + Float64(z * a))) / Float64(0.607771387771 + Float64(z * Float64(11.9400905721 + Float64(z * Float64(31.4690115749 + Float64(z * Float64(z + 15.234687407)))))))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + ((y * 3.13060547623) + (t * (y / (z * z))));
	tmp = 0.0;
	if (z <= -1.35e+28)
		tmp = t_1;
	elseif (z <= 1e+30)
		tmp = x + ((y * (b + (z * a))) / (0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * (z + 15.234687407))))))));
	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[(y * 3.13060547623), $MachinePrecision] + N[(t * N[(y / N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.35e+28], t$95$1, If[LessEqual[z, 1e+30], N[(x + N[(N[(y * N[(b + N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(0.607771387771 + N[(z * N[(11.9400905721 + N[(z * N[(31.4690115749 + N[(z * N[(z + 15.234687407), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.3500000000000001e28 or 1e30 < z

   1. Initial program 16.6%

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

   3. Taylor expanded in z around -inf

      \[\leadsto \color{blue}{x + \left(-1 \cdot \frac{\left(\frac{-55833770631}{5000000000} \cdot y + -1 \cdot \frac{t \cdot y - \left(\frac{-15234687407}{1000000000} \cdot \left(\frac{-55833770631}{5000000000} \cdot y - \frac{-4769379582500641883561}{100000000000000000000} \cdot y\right) + \frac{98517059967927196814627}{1000000000000000000000} \cdot y\right)}{z}\right) - \frac{-4769379582500641883561}{100000000000000000000} \cdot y}{z} + \frac{313060547623}{100000000000} \cdot y\right)} \]

   5. Simplified 81.5%

      \[\leadsto \color{blue}{x + \left(y \cdot 3.13060547623 - \frac{\frac{\left(y \cdot t - y \cdot -556.47806218377\right) + -98.5170599679272 \cdot y}{0 - z} + y \cdot 36.52704169880642}{z}\right)} \]

   6. Taylor expanded in t around inf

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right), \color{blue}{\left(-1 \cdot \frac{t \cdot y}{{z}^{2}}\right)}\right)\right) \]
   7. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right), \left(\mathsf{neg}\left(\frac{t \cdot y}{{z}^{2}}\right)\right)\right)\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right), \left(0 - \color{blue}{\frac{t \cdot y}{{z}^{2}}}\right)\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right), \mathsf{\_.f64}\left(0, \color{blue}{\left(\frac{t \cdot y}{{z}^{2}}\right)}\right)\right)\right) \]

      4. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right), \mathsf{\_.f64}\left(0, \left(t \cdot \color{blue}{\frac{y}{{z}^{2}}}\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right), \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(t, \color{blue}{\left(\frac{y}{{z}^{2}}\right)}\right)\right)\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right), \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(y, \color{blue}{\left({z}^{2}\right)}\right)\right)\right)\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right), \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(y, \left(z \cdot \color{blue}{z}\right)\right)\right)\right)\right)\right) \]

      8. *-lowering-*.f64 96.3%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right), \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(y, \mathsf{*.f64}\left(z, \color{blue}{z}\right)\right)\right)\right)\right)\right) \]

   8. Simplified 96.3%

      \[\leadsto x + \left(y \cdot 3.13060547623 - \color{blue}{\left(0 - t \cdot \frac{y}{z \cdot z}\right)}\right) \]

   if -1.3500000000000001e28 < z < 1e30

   1. Initial program 99.6%

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

   3. Taylor expanded in z around 0

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \color{blue}{\left(b + a \cdot z\right)}\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(z, \frac{15234687407}{1000000000}\right), z\right), \frac{314690115749}{10000000000}\right), z\right), \frac{119400905721}{10000000000}\right), z\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]
   4. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(b, \left(a \cdot z\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(z, \frac{15234687407}{1000000000}\right), z\right), \frac{314690115749}{10000000000}\right), z\right), \frac{119400905721}{10000000000}\right), \color{blue}{z}\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(b, \left(z \cdot a\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(z, \frac{15234687407}{1000000000}\right), z\right), \frac{314690115749}{10000000000}\right), z\right), \frac{119400905721}{10000000000}\right), z\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      3. *-lowering-*.f64 92.9%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(b, \mathsf{*.f64}\left(z, a\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(z, \frac{15234687407}{1000000000}\right), z\right), \frac{314690115749}{10000000000}\right), z\right), \frac{119400905721}{10000000000}\right), z\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

   5. Simplified 92.9%

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

4. Final simplification 94.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+28}:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 + t \cdot \frac{y}{z \cdot z}\right)\\ \mathbf{elif}\;z \leq 10^{+30}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot a\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 + t \cdot \frac{y}{z \cdot z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 86.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y \cdot 3.13060547623 + t \cdot \frac{y}{z \cdot z}\right)\\ \mathbf{if}\;z \leq -1.35 \cdot 10^{+28}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{-31}:\\ \;\;\;\;b \cdot \left(y \cdot 1.6453555072203998\right) + \left(x + z \cdot \left(y \cdot \left(a \cdot 1.6453555072203998 - b \cdot 32.324150453290734\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (+ (* y 3.13060547623) (* t (/ y (* z z)))))))
   (if (<= z -1.35e+28)
     t_1
     (if (<= z 6.4e-31)
       (+
        (* b (* y 1.6453555072203998))
        (+
         x
         (* z (* y (- (* a 1.6453555072203998) (* b 32.324150453290734))))))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + ((y * 3.13060547623) + (t * (y / (z * z))));
	double tmp;
	if (z <= -1.35e+28) {
		tmp = t_1;
	} else if (z <= 6.4e-31) {
		tmp = (b * (y * 1.6453555072203998)) + (x + (z * (y * ((a * 1.6453555072203998) - (b * 32.324150453290734)))));
	} 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 + ((y * 3.13060547623d0) + (t * (y / (z * z))))
    if (z <= (-1.35d+28)) then
        tmp = t_1
    else if (z <= 6.4d-31) then
        tmp = (b * (y * 1.6453555072203998d0)) + (x + (z * (y * ((a * 1.6453555072203998d0) - (b * 32.324150453290734d0)))))
    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 + ((y * 3.13060547623) + (t * (y / (z * z))));
	double tmp;
	if (z <= -1.35e+28) {
		tmp = t_1;
	} else if (z <= 6.4e-31) {
		tmp = (b * (y * 1.6453555072203998)) + (x + (z * (y * ((a * 1.6453555072203998) - (b * 32.324150453290734)))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + ((y * 3.13060547623) + (t * (y / (z * z))))
	tmp = 0
	if z <= -1.35e+28:
		tmp = t_1
	elif z <= 6.4e-31:
		tmp = (b * (y * 1.6453555072203998)) + (x + (z * (y * ((a * 1.6453555072203998) - (b * 32.324150453290734)))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(Float64(y * 3.13060547623) + Float64(t * Float64(y / Float64(z * z)))))
	tmp = 0.0
	if (z <= -1.35e+28)
		tmp = t_1;
	elseif (z <= 6.4e-31)
		tmp = Float64(Float64(b * Float64(y * 1.6453555072203998)) + Float64(x + Float64(z * Float64(y * Float64(Float64(a * 1.6453555072203998) - Float64(b * 32.324150453290734))))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + ((y * 3.13060547623) + (t * (y / (z * z))));
	tmp = 0.0;
	if (z <= -1.35e+28)
		tmp = t_1;
	elseif (z <= 6.4e-31)
		tmp = (b * (y * 1.6453555072203998)) + (x + (z * (y * ((a * 1.6453555072203998) - (b * 32.324150453290734)))));
	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[(y * 3.13060547623), $MachinePrecision] + N[(t * N[(y / N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.35e+28], t$95$1, If[LessEqual[z, 6.4e-31], N[(N[(b * N[(y * 1.6453555072203998), $MachinePrecision]), $MachinePrecision] + N[(x + N[(z * N[(y * N[(N[(a * 1.6453555072203998), $MachinePrecision] - N[(b * 32.324150453290734), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.3500000000000001e28 or 6.40000000000000036e-31 < z

   1. Initial program 21.5%

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

   3. Taylor expanded in z around -inf

      \[\leadsto \color{blue}{x + \left(-1 \cdot \frac{\left(\frac{-55833770631}{5000000000} \cdot y + -1 \cdot \frac{t \cdot y - \left(\frac{-15234687407}{1000000000} \cdot \left(\frac{-55833770631}{5000000000} \cdot y - \frac{-4769379582500641883561}{100000000000000000000} \cdot y\right) + \frac{98517059967927196814627}{1000000000000000000000} \cdot y\right)}{z}\right) - \frac{-4769379582500641883561}{100000000000000000000} \cdot y}{z} + \frac{313060547623}{100000000000} \cdot y\right)} \]

   5. Simplified 80.5%

      \[\leadsto \color{blue}{x + \left(y \cdot 3.13060547623 - \frac{\frac{\left(y \cdot t - y \cdot -556.47806218377\right) + -98.5170599679272 \cdot y}{0 - z} + y \cdot 36.52704169880642}{z}\right)} \]

   6. Taylor expanded in t around inf

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right), \color{blue}{\left(-1 \cdot \frac{t \cdot y}{{z}^{2}}\right)}\right)\right) \]
   7. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right), \left(\mathsf{neg}\left(\frac{t \cdot y}{{z}^{2}}\right)\right)\right)\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right), \left(0 - \color{blue}{\frac{t \cdot y}{{z}^{2}}}\right)\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right), \mathsf{\_.f64}\left(0, \color{blue}{\left(\frac{t \cdot y}{{z}^{2}}\right)}\right)\right)\right) \]

      4. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right), \mathsf{\_.f64}\left(0, \left(t \cdot \color{blue}{\frac{y}{{z}^{2}}}\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right), \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(t, \color{blue}{\left(\frac{y}{{z}^{2}}\right)}\right)\right)\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right), \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(y, \color{blue}{\left({z}^{2}\right)}\right)\right)\right)\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right), \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(y, \left(z \cdot \color{blue}{z}\right)\right)\right)\right)\right)\right) \]

      8. *-lowering-*.f64 94.4%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right), \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(y, \mathsf{*.f64}\left(z, \color{blue}{z}\right)\right)\right)\right)\right)\right) \]

   8. Simplified 94.4%

      \[\leadsto x + \left(y \cdot 3.13060547623 - \color{blue}{\left(0 - t \cdot \frac{y}{z \cdot z}\right)}\right) \]

   if -1.3500000000000001e28 < z < 6.40000000000000036e-31

   1. Initial program 99.6%

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

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x + \left(\frac{1000000000000}{607771387771} \cdot \left(b \cdot y\right) + z \cdot \left(\frac{1000000000000}{607771387771} \cdot \left(a \cdot y\right) - \frac{11940090572100000000000000}{369386059793087248348441} \cdot \left(b \cdot y\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-+r+ N/A

         \[\leadsto \left(x + \frac{1000000000000}{607771387771} \cdot \left(b \cdot y\right)\right) + \color{blue}{z \cdot \left(\frac{1000000000000}{607771387771} \cdot \left(a \cdot y\right) - \frac{11940090572100000000000000}{369386059793087248348441} \cdot \left(b \cdot y\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto \left(\frac{1000000000000}{607771387771} \cdot \left(b \cdot y\right) + x\right) + \color{blue}{z} \cdot \left(\frac{1000000000000}{607771387771} \cdot \left(a \cdot y\right) - \frac{11940090572100000000000000}{369386059793087248348441} \cdot \left(b \cdot y\right)\right) \]

      3. associate-+l+ N/A

         \[\leadsto \frac{1000000000000}{607771387771} \cdot \left(b \cdot y\right) + \color{blue}{\left(x + z \cdot \left(\frac{1000000000000}{607771387771} \cdot \left(a \cdot y\right) - \frac{11940090572100000000000000}{369386059793087248348441} \cdot \left(b \cdot y\right)\right)\right)} \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{1000000000000}{607771387771} \cdot \left(b \cdot y\right)\right), \color{blue}{\left(x + z \cdot \left(\frac{1000000000000}{607771387771} \cdot \left(a \cdot y\right) - \frac{11940090572100000000000000}{369386059793087248348441} \cdot \left(b \cdot y\right)\right)\right)}\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(b \cdot y\right) \cdot \frac{1000000000000}{607771387771}\right), \left(\color{blue}{x} + z \cdot \left(\frac{1000000000000}{607771387771} \cdot \left(a \cdot y\right) - \frac{11940090572100000000000000}{369386059793087248348441} \cdot \left(b \cdot y\right)\right)\right)\right) \]

      6. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(b \cdot \left(y \cdot \frac{1000000000000}{607771387771}\right)\right), \left(\color{blue}{x} + z \cdot \left(\frac{1000000000000}{607771387771} \cdot \left(a \cdot y\right) - \frac{11940090572100000000000000}{369386059793087248348441} \cdot \left(b \cdot y\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \left(y \cdot \frac{1000000000000}{607771387771}\right)\right), \left(\color{blue}{x} + z \cdot \left(\frac{1000000000000}{607771387771} \cdot \left(a \cdot y\right) - \frac{11940090572100000000000000}{369386059793087248348441} \cdot \left(b \cdot y\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{*.f64}\left(y, \frac{1000000000000}{607771387771}\right)\right), \left(x + z \cdot \left(\frac{1000000000000}{607771387771} \cdot \left(a \cdot y\right) - \frac{11940090572100000000000000}{369386059793087248348441} \cdot \left(b \cdot y\right)\right)\right)\right) \]

      9. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{*.f64}\left(y, \frac{1000000000000}{607771387771}\right)\right), \mathsf{+.f64}\left(x, \color{blue}{\left(z \cdot \left(\frac{1000000000000}{607771387771} \cdot \left(a \cdot y\right) - \frac{11940090572100000000000000}{369386059793087248348441} \cdot \left(b \cdot y\right)\right)\right)}\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{*.f64}\left(y, \frac{1000000000000}{607771387771}\right)\right), \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \color{blue}{\left(\frac{1000000000000}{607771387771} \cdot \left(a \cdot y\right) - \frac{11940090572100000000000000}{369386059793087248348441} \cdot \left(b \cdot y\right)\right)}\right)\right)\right) \]

      11. associate-*r* N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{*.f64}\left(y, \frac{1000000000000}{607771387771}\right)\right), \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \left(\left(\frac{1000000000000}{607771387771} \cdot a\right) \cdot y - \color{blue}{\frac{11940090572100000000000000}{369386059793087248348441}} \cdot \left(b \cdot y\right)\right)\right)\right)\right) \]

      12. associate-*r* N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{*.f64}\left(y, \frac{1000000000000}{607771387771}\right)\right), \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \left(\left(\frac{1000000000000}{607771387771} \cdot a\right) \cdot y - \left(\frac{11940090572100000000000000}{369386059793087248348441} \cdot b\right) \cdot \color{blue}{y}\right)\right)\right)\right) \]

      13. distribute-rgt-out-- N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{*.f64}\left(y, \frac{1000000000000}{607771387771}\right)\right), \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \left(y \cdot \color{blue}{\left(\frac{1000000000000}{607771387771} \cdot a - \frac{11940090572100000000000000}{369386059793087248348441} \cdot b\right)}\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{*.f64}\left(y, \frac{1000000000000}{607771387771}\right)\right), \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{1000000000000}{607771387771} \cdot a - \frac{11940090572100000000000000}{369386059793087248348441} \cdot b\right)}\right)\right)\right)\right) \]

      15. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{*.f64}\left(y, \frac{1000000000000}{607771387771}\right)\right), \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\left(\frac{1000000000000}{607771387771} \cdot a\right), \color{blue}{\left(\frac{11940090572100000000000000}{369386059793087248348441} \cdot b\right)}\right)\right)\right)\right)\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{*.f64}\left(y, \frac{1000000000000}{607771387771}\right)\right), \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\left(a \cdot \frac{1000000000000}{607771387771}\right), \left(\color{blue}{\frac{11940090572100000000000000}{369386059793087248348441}} \cdot b\right)\right)\right)\right)\right)\right) \]

      17. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{*.f64}\left(y, \frac{1000000000000}{607771387771}\right)\right), \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, \frac{1000000000000}{607771387771}\right), \left(\color{blue}{\frac{11940090572100000000000000}{369386059793087248348441}} \cdot b\right)\right)\right)\right)\right)\right) \]

      18. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{*.f64}\left(y, \frac{1000000000000}{607771387771}\right)\right), \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, \frac{1000000000000}{607771387771}\right), \left(b \cdot \color{blue}{\frac{11940090572100000000000000}{369386059793087248348441}}\right)\right)\right)\right)\right)\right) \]

      19. *-lowering-*.f64 83.0%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{*.f64}\left(y, \frac{1000000000000}{607771387771}\right)\right), \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, \frac{1000000000000}{607771387771}\right), \mathsf{*.f64}\left(b, \color{blue}{\frac{11940090572100000000000000}{369386059793087248348441}}\right)\right)\right)\right)\right)\right) \]

   5. Simplified 83.0%

      \[\leadsto \color{blue}{b \cdot \left(y \cdot 1.6453555072203998\right) + \left(x + z \cdot \left(y \cdot \left(a \cdot 1.6453555072203998 - b \cdot 32.324150453290734\right)\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+28}:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 + t \cdot \frac{y}{z \cdot z}\right)\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{-31}:\\ \;\;\;\;b \cdot \left(y \cdot 1.6453555072203998\right) + \left(x + z \cdot \left(y \cdot \left(a \cdot 1.6453555072203998 - b \cdot 32.324150453290734\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 + t \cdot \frac{y}{z \cdot z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 86.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y \cdot 3.13060547623 + t \cdot \frac{y}{z \cdot z}\right)\\ \mathbf{if}\;z \leq -0.6:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2000000:\\ \;\;\;\;x + b \cdot \left(y \cdot 1.6453555072203998\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (+ (* y 3.13060547623) (* t (/ y (* z z)))))))
   (if (<= z -0.6)
     t_1
     (if (<= z 2000000.0) (+ x (* b (* y 1.6453555072203998))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + ((y * 3.13060547623) + (t * (y / (z * z))));
	double tmp;
	if (z <= -0.6) {
		tmp = t_1;
	} else if (z <= 2000000.0) {
		tmp = x + (b * (y * 1.6453555072203998));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y * 3.13060547623d0) + (t * (y / (z * z))))
    if (z <= (-0.6d0)) then
        tmp = t_1
    else if (z <= 2000000.0d0) then
        tmp = x + (b * (y * 1.6453555072203998d0))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + ((y * 3.13060547623) + (t * (y / (z * z))));
	double tmp;
	if (z <= -0.6) {
		tmp = t_1;
	} else if (z <= 2000000.0) {
		tmp = x + (b * (y * 1.6453555072203998));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + ((y * 3.13060547623) + (t * (y / (z * z))))
	tmp = 0
	if z <= -0.6:
		tmp = t_1
	elif z <= 2000000.0:
		tmp = x + (b * (y * 1.6453555072203998))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(Float64(y * 3.13060547623) + Float64(t * Float64(y / Float64(z * z)))))
	tmp = 0.0
	if (z <= -0.6)
		tmp = t_1;
	elseif (z <= 2000000.0)
		tmp = Float64(x + Float64(b * Float64(y * 1.6453555072203998)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + ((y * 3.13060547623) + (t * (y / (z * z))));
	tmp = 0.0;
	if (z <= -0.6)
		tmp = t_1;
	elseif (z <= 2000000.0)
		tmp = x + (b * (y * 1.6453555072203998));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(N[(y * 3.13060547623), $MachinePrecision] + N[(t * N[(y / N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.6], t$95$1, If[LessEqual[z, 2000000.0], N[(x + N[(b * N[(y * 1.6453555072203998), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -0.599999999999999978 or 2e6 < z

   1. Initial program 21.5%

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

   3. Taylor expanded in z around -inf

      \[\leadsto \color{blue}{x + \left(-1 \cdot \frac{\left(\frac{-55833770631}{5000000000} \cdot y + -1 \cdot \frac{t \cdot y - \left(\frac{-15234687407}{1000000000} \cdot \left(\frac{-55833770631}{5000000000} \cdot y - \frac{-4769379582500641883561}{100000000000000000000} \cdot y\right) + \frac{98517059967927196814627}{1000000000000000000000} \cdot y\right)}{z}\right) - \frac{-4769379582500641883561}{100000000000000000000} \cdot y}{z} + \frac{313060547623}{100000000000} \cdot y\right)} \]

   5. Simplified 79.8%

      \[\leadsto \color{blue}{x + \left(y \cdot 3.13060547623 - \frac{\frac{\left(y \cdot t - y \cdot -556.47806218377\right) + -98.5170599679272 \cdot y}{0 - z} + y \cdot 36.52704169880642}{z}\right)} \]

   6. Taylor expanded in t around inf

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right), \color{blue}{\left(-1 \cdot \frac{t \cdot y}{{z}^{2}}\right)}\right)\right) \]
   7. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right), \left(\mathsf{neg}\left(\frac{t \cdot y}{{z}^{2}}\right)\right)\right)\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right), \left(0 - \color{blue}{\frac{t \cdot y}{{z}^{2}}}\right)\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right), \mathsf{\_.f64}\left(0, \color{blue}{\left(\frac{t \cdot y}{{z}^{2}}\right)}\right)\right)\right) \]

      4. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right), \mathsf{\_.f64}\left(0, \left(t \cdot \color{blue}{\frac{y}{{z}^{2}}}\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right), \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(t, \color{blue}{\left(\frac{y}{{z}^{2}}\right)}\right)\right)\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right), \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(y, \color{blue}{\left({z}^{2}\right)}\right)\right)\right)\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right), \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(y, \left(z \cdot \color{blue}{z}\right)\right)\right)\right)\right)\right) \]

      8. *-lowering-*.f64 93.7%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right), \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(y, \mathsf{*.f64}\left(z, \color{blue}{z}\right)\right)\right)\right)\right)\right) \]

   8. Simplified 93.7%

      \[\leadsto x + \left(y \cdot 3.13060547623 - \color{blue}{\left(0 - t \cdot \frac{y}{z \cdot z}\right)}\right) \]

   if -0.599999999999999978 < z < 2e6

   1. Initial program 99.6%

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

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x + \frac{1000000000000}{607771387771} \cdot \left(b \cdot y\right)} \]
   4. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{1000000000000}{607771387771} \cdot \left(b \cdot y\right)\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(b \cdot y\right) \cdot \color{blue}{\frac{1000000000000}{607771387771}}\right)\right) \]

      3. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(b \cdot \color{blue}{\left(y \cdot \frac{1000000000000}{607771387771}\right)}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \color{blue}{\left(y \cdot \frac{1000000000000}{607771387771}\right)}\right)\right) \]

      5. *-lowering-*.f64 78.9%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(y, \color{blue}{\frac{1000000000000}{607771387771}}\right)\right)\right) \]

   5. Simplified 78.9%

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

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.6:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 + t \cdot \frac{y}{z \cdot z}\right)\\ \mathbf{elif}\;z \leq 2000000:\\ \;\;\;\;x + b \cdot \left(y \cdot 1.6453555072203998\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 + t \cdot \frac{y}{z \cdot z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 84.3% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot 3.13060547623\\ \mathbf{if}\;z \leq -0.98:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 10500000:\\ \;\;\;\;x + b \cdot \left(y \cdot 1.6453555072203998\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* y 3.13060547623))))
   (if (<= z -0.98)
     t_1
     (if (<= z 10500000.0) (+ x (* b (* y 1.6453555072203998))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y * 3.13060547623);
	double tmp;
	if (z <= -0.98) {
		tmp = t_1;
	} else if (z <= 10500000.0) {
		tmp = x + (b * (y * 1.6453555072203998));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y * 3.13060547623d0)
    if (z <= (-0.98d0)) then
        tmp = t_1
    else if (z <= 10500000.0d0) then
        tmp = x + (b * (y * 1.6453555072203998d0))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y * 3.13060547623);
	double tmp;
	if (z <= -0.98) {
		tmp = t_1;
	} else if (z <= 10500000.0) {
		tmp = x + (b * (y * 1.6453555072203998));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (y * 3.13060547623)
	tmp = 0
	if z <= -0.98:
		tmp = t_1
	elif z <= 10500000.0:
		tmp = x + (b * (y * 1.6453555072203998))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(y * 3.13060547623))
	tmp = 0.0
	if (z <= -0.98)
		tmp = t_1;
	elseif (z <= 10500000.0)
		tmp = Float64(x + Float64(b * Float64(y * 1.6453555072203998)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (y * 3.13060547623);
	tmp = 0.0;
	if (z <= -0.98)
		tmp = t_1;
	elseif (z <= 10500000.0)
		tmp = x + (b * (y * 1.6453555072203998));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.98], t$95$1, If[LessEqual[z, 10500000.0], N[(x + N[(b * N[(y * 1.6453555072203998), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -0.97999999999999998 or 1.05e7 < z

   1. Initial program 21.5%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{x + \frac{313060547623}{100000000000} \cdot y} \]
   4. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{313060547623}{100000000000} \cdot y\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\frac{313060547623}{100000000000}}\right)\right) \]

      3. *-lowering-*.f64 84.3%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\frac{313060547623}{100000000000}}\right)\right) \]

   5. Simplified 84.3%

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

   if -0.97999999999999998 < z < 1.05e7

   1. Initial program 99.6%

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

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x + \frac{1000000000000}{607771387771} \cdot \left(b \cdot y\right)} \]
   4. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{1000000000000}{607771387771} \cdot \left(b \cdot y\right)\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(b \cdot y\right) \cdot \color{blue}{\frac{1000000000000}{607771387771}}\right)\right) \]

      3. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(b \cdot \color{blue}{\left(y \cdot \frac{1000000000000}{607771387771}\right)}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \color{blue}{\left(y \cdot \frac{1000000000000}{607771387771}\right)}\right)\right) \]

      5. *-lowering-*.f64 78.9%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(y, \color{blue}{\frac{1000000000000}{607771387771}}\right)\right)\right) \]

   5. Simplified 78.9%

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

Alternative 8: 52.3% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+41}:\\ \;\;\;\;y \cdot 3.13060547623\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+82}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot 3.13060547623\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -3.4e+41)
   (* y 3.13060547623)
   (if (<= y 3.6e+82) x (* y 3.13060547623))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -3.4e+41) {
		tmp = y * 3.13060547623;
	} else if (y <= 3.6e+82) {
		tmp = x;
	} else {
		tmp = 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 (y <= (-3.4d+41)) then
        tmp = y * 3.13060547623d0
    else if (y <= 3.6d+82) then
        tmp = x
    else
        tmp = 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 (y <= -3.4e+41) {
		tmp = y * 3.13060547623;
	} else if (y <= 3.6e+82) {
		tmp = x;
	} else {
		tmp = y * 3.13060547623;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -3.4e+41:
		tmp = y * 3.13060547623
	elif y <= 3.6e+82:
		tmp = x
	else:
		tmp = y * 3.13060547623
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -3.4e+41)
		tmp = Float64(y * 3.13060547623);
	elseif (y <= 3.6e+82)
		tmp = x;
	else
		tmp = Float64(y * 3.13060547623);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -3.4e+41)
		tmp = y * 3.13060547623;
	elseif (y <= 3.6e+82)
		tmp = x;
	else
		tmp = y * 3.13060547623;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -3.4e+41], N[(y * 3.13060547623), $MachinePrecision], If[LessEqual[y, 3.6e+82], x, N[(y * 3.13060547623), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.39999999999999998e41 or 3.60000000000000014e82 < y

   1. Initial program 50.6%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{x + \frac{313060547623}{100000000000} \cdot y} \]
   4. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{313060547623}{100000000000} \cdot y\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\frac{313060547623}{100000000000}}\right)\right) \]

      3. *-lowering-*.f64 49.6%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\frac{313060547623}{100000000000}}\right)\right) \]

   5. Simplified 49.6%

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

   6. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{313060547623}{100000000000} \cdot y} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 41.6%

         \[\leadsto \mathsf{*.f64}\left(\frac{313060547623}{100000000000}, \color{blue}{y}\right) \]

   8. Simplified 41.6%

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

   if -3.39999999999999998e41 < y < 3.60000000000000014e82

   1. Initial program 62.3%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 66.0%

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

4. Final simplification 56.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+41}:\\ \;\;\;\;y \cdot 3.13060547623\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+82}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot 3.13060547623\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 63.7% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5.5 \cdot 10^{+272}:\\ \;\;\;\;y \cdot \left(b \cdot 1.6453555072203998\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -5.5e+272)
   (* 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 (b <= -5.5e+272) {
		tmp = 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 (b <= (-5.5d+272)) then
        tmp = 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 (b <= -5.5e+272) {
		tmp = y * (b * 1.6453555072203998);
	} else {
		tmp = x + (y * 3.13060547623);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -5.5e+272:
		tmp = 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 (b <= -5.5e+272)
		tmp = 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 (b <= -5.5e+272)
		tmp = 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[b, -5.5e+272], N[(y * N[(b * 1.6453555072203998), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -5.4999999999999998e272

   1. Initial program 88.5%

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

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{\frac{b \cdot y}{\frac{607771387771}{1000000000000} + z \cdot \left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)}} \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(b \cdot y\right), \color{blue}{\left(\frac{607771387771}{1000000000000} + z \cdot \left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot b\right), \left(\color{blue}{\frac{607771387771}{1000000000000}} + z \cdot \left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), \left(\color{blue}{\frac{607771387771}{1000000000000}} + z \cdot \left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), \mathsf{+.f64}\left(\frac{607771387771}{1000000000000}, \color{blue}{\left(z \cdot \left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)\right)}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), \mathsf{+.f64}\left(\frac{607771387771}{1000000000000}, \mathsf{*.f64}\left(z, \color{blue}{\left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)}\right)\right)\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), \mathsf{+.f64}\left(\frac{607771387771}{1000000000000}, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{119400905721}{10000000000}, \color{blue}{\left(z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)}\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), \mathsf{+.f64}\left(\frac{607771387771}{1000000000000}, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{119400905721}{10000000000}, \mathsf{*.f64}\left(z, \color{blue}{\left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)}\right)\right)\right)\right)\right) \]

      8. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), \mathsf{+.f64}\left(\frac{607771387771}{1000000000000}, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{119400905721}{10000000000}, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{314690115749}{10000000000}, \color{blue}{\left(z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)}\right)\right)\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), \mathsf{+.f64}\left(\frac{607771387771}{1000000000000}, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{119400905721}{10000000000}, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{314690115749}{10000000000}, \mathsf{*.f64}\left(z, \color{blue}{\left(\frac{15234687407}{1000000000} + z\right)}\right)\right)\right)\right)\right)\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), \mathsf{+.f64}\left(\frac{607771387771}{1000000000000}, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{119400905721}{10000000000}, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{314690115749}{10000000000}, \mathsf{*.f64}\left(z, \left(z + \color{blue}{\frac{15234687407}{1000000000}}\right)\right)\right)\right)\right)\right)\right)\right) \]

      11. +-lowering-+.f64 88.5%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), \mathsf{+.f64}\left(\frac{607771387771}{1000000000000}, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{119400905721}{10000000000}, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{314690115749}{10000000000}, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(z, \color{blue}{\frac{15234687407}{1000000000}}\right)\right)\right)\right)\right)\right)\right)\right) \]

   5. Simplified 88.5%

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

   6. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\frac{-11940090572100000000000000}{369386059793087248348441} \cdot \left(b \cdot \left(y \cdot z\right)\right) + \frac{1000000000000}{607771387771} \cdot \left(b \cdot y\right)} \]
   7. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \frac{1000000000000}{607771387771} \cdot \left(b \cdot y\right) + \color{blue}{\frac{-11940090572100000000000000}{369386059793087248348441} \cdot \left(b \cdot \left(y \cdot z\right)\right)} \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{1000000000000}{607771387771} \cdot \left(b \cdot y\right)\right), \color{blue}{\left(\frac{-11940090572100000000000000}{369386059793087248348441} \cdot \left(b \cdot \left(y \cdot z\right)\right)\right)}\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(b \cdot y\right) \cdot \frac{1000000000000}{607771387771}\right), \left(\color{blue}{\frac{-11940090572100000000000000}{369386059793087248348441}} \cdot \left(b \cdot \left(y \cdot z\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(b \cdot y\right), \frac{1000000000000}{607771387771}\right), \left(\color{blue}{\frac{-11940090572100000000000000}{369386059793087248348441}} \cdot \left(b \cdot \left(y \cdot z\right)\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(y \cdot b\right), \frac{1000000000000}{607771387771}\right), \left(\frac{-11940090572100000000000000}{369386059793087248348441} \cdot \left(b \cdot \left(y \cdot z\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(y, b\right), \frac{1000000000000}{607771387771}\right), \left(\frac{-11940090572100000000000000}{369386059793087248348441} \cdot \left(b \cdot \left(y \cdot z\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(y, b\right), \frac{1000000000000}{607771387771}\right), \mathsf{*.f64}\left(\frac{-11940090572100000000000000}{369386059793087248348441}, \color{blue}{\left(b \cdot \left(y \cdot z\right)\right)}\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(y, b\right), \frac{1000000000000}{607771387771}\right), \mathsf{*.f64}\left(\frac{-11940090572100000000000000}{369386059793087248348441}, \left(\left(y \cdot z\right) \cdot \color{blue}{b}\right)\right)\right) \]

      9. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(y, b\right), \frac{1000000000000}{607771387771}\right), \mathsf{*.f64}\left(\frac{-11940090572100000000000000}{369386059793087248348441}, \left(y \cdot \color{blue}{\left(z \cdot b\right)}\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(y, b\right), \frac{1000000000000}{607771387771}\right), \mathsf{*.f64}\left(\frac{-11940090572100000000000000}{369386059793087248348441}, \mathsf{*.f64}\left(y, \color{blue}{\left(z \cdot b\right)}\right)\right)\right) \]

      11. *-lowering-*.f64 66.3%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(y, b\right), \frac{1000000000000}{607771387771}\right), \mathsf{*.f64}\left(\frac{-11940090572100000000000000}{369386059793087248348441}, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, \color{blue}{b}\right)\right)\right)\right) \]

   8. Simplified 66.3%

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

   9. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\frac{1000000000000}{607771387771} \cdot \left(b \cdot y\right)} \]
   10. Step-by-step derivation

       1. associate-*r* N/A

          \[\leadsto \left(\frac{1000000000000}{607771387771} \cdot b\right) \cdot \color{blue}{y} \]

       2. *-commutative N/A

          \[\leadsto y \cdot \color{blue}{\left(\frac{1000000000000}{607771387771} \cdot b\right)} \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{1000000000000}{607771387771} \cdot b\right)}\right) \]

       4. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(y, \left(b \cdot \color{blue}{\frac{1000000000000}{607771387771}}\right)\right) \]

       5. *-lowering-*.f64 88.6%

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(b, \color{blue}{\frac{1000000000000}{607771387771}}\right)\right) \]

   11. Simplified 88.6%

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

   if -5.4999999999999998e272 < b

   1. Initial program 56.7%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{x + \frac{313060547623}{100000000000} \cdot y} \]
   4. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{313060547623}{100000000000} \cdot y\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\frac{313060547623}{100000000000}}\right)\right) \]

      3. *-lowering-*.f64 67.0%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\frac{313060547623}{100000000000}}\right)\right) \]

   5. Simplified 67.0%

      \[\leadsto \color{blue}{x + y \cdot 3.13060547623} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 10: 45.9% 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 57.8%

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

3. Taylor expanded in x around inf

   \[\leadsto \color{blue}{x} \]
4. Step-by-step derivation

5. Simplified 45.4%

   \[\leadsto \color{blue}{x} \]
6. Add Preprocessing

Developer Target 1: 98.6% 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 2024161 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, D"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< z -649934499625263200000000000000000000000000000000000000) (+ x (* (+ (- 313060547623/100000000000 (/ 18263520849403207/500000000000000 z)) (/ t (* z z))) (/ y 1))) (if (< z 706696543691428700000000000000000000000000000000000000000000) (+ x (/ y (/ (+ (* (+ (* (+ (* (+ z 15234687407/1000000000) z) 314690115749/10000000000) z) 119400905721/10000000000) z) 607771387771/1000000000000) (+ (* (+ (* (+ (* (+ (* z 313060547623/100000000000) 55833770631/5000000000) z) t) z) a) z) b)))) (+ x (* (+ (- 313060547623/100000000000 (/ 18263520849403207/500000000000000 z)) (/ t (* z z))) (/ y 1))))))

  (+ 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))))