Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2

Percentage Accurate: 56.5% → 85.7%

Time: 31.3s

Alternatives: 17

Speedup: 2.2×

Specification

Math

\[\begin{array}{l} \\ \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (/
  (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t)
  (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return ((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: c
    real(8), intent (in) :: i
    code = ((((((((x * y) + z) * y) + 27464.7644705d0) * y) + 230661.510616d0) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return ((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i);
}

Python

def code(x, y, z, t, a, b, c, i):
	return ((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i)

Julia

function code(x, y, z, t, a, b, c, i)
	return Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / Float64(Float64(Float64(Float64(Float64(Float64(Float64(y + a) * y) + b) * y) + c) * y) + i))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i)
	tmp = ((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(N[(N[(N[(N[(N[(N[(N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision] * y), $MachinePrecision] + 27464.7644705), $MachinePrecision] * y), $MachinePrecision] + 230661.510616), $MachinePrecision] * y), $MachinePrecision] + t), $MachinePrecision] / N[(N[(N[(N[(N[(N[(N[(y + a), $MachinePrecision] * y), $MachinePrecision] + b), $MachinePrecision] * y), $MachinePrecision] + c), $MachinePrecision] * y), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision]

Initial Program: 56.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (/
  (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t)
  (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return ((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: c
    real(8), intent (in) :: i
    code = ((((((((x * y) + z) * y) + 27464.7644705d0) * y) + 230661.510616d0) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return ((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i);
}

Python

def code(x, y, z, t, a, b, c, i):
	return ((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i)

Julia

function code(x, y, z, t, a, b, c, i)
	return Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / Float64(Float64(Float64(Float64(Float64(Float64(Float64(y + a) * y) + b) * y) + c) * y) + i))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i)
	tmp = ((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(N[(N[(N[(N[(N[(N[(N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision] * y), $MachinePrecision] + 27464.7644705), $MachinePrecision] * y), $MachinePrecision] + 230661.510616), $MachinePrecision] * y), $MachinePrecision] + t), $MachinePrecision] / N[(N[(N[(N[(N[(N[(N[(y + a), $MachinePrecision] * y), $MachinePrecision] + b), $MachinePrecision] * y), $MachinePrecision] + c), $MachinePrecision] * y), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision]

Alternative 1: 85.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\\ t_2 := i + y \cdot t\_1\\ t_3 := x \cdot t\_2\\ \mathbf{if}\;y \leq -5.7 \cdot 10^{+75}:\\ \;\;\;\;x + \frac{z + \frac{27464.7644705}{y}}{y}\\ \mathbf{elif}\;y \leq -2.65 \cdot 10^{+38}:\\ \;\;\;\;x \cdot \left(\frac{t}{t\_3} + \left(\frac{y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{t\_3} + \frac{{y}^{3}}{t\_1}\right)\right)\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+56}:\\ \;\;\;\;\frac{t}{t\_2} + \frac{y \cdot \left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616\right)}{t\_2}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* y (+ (* y (+ y a)) b)) c))
        (t_2 (+ i (* y t_1)))
        (t_3 (* x t_2)))
   (if (<= y -5.7e+75)
     (+ x (/ (+ z (/ 27464.7644705 y)) y))
     (if (<= y -2.65e+38)
       (*
        x
        (+
         (/ t t_3)
         (+
          (/ (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y z))))) t_3)
          (/ (pow y 3.0) t_1))))
       (if (<= y 1.55e+56)
         (+
          (/ t t_2)
          (/
           (* y (+ (* y (+ (* y (+ (* x y) z)) 27464.7644705)) 230661.510616))
           t_2))
         (+ x (/ z y)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (y * ((y * (y + a)) + b)) + c;
	double t_2 = i + (y * t_1);
	double t_3 = x * t_2;
	double tmp;
	if (y <= -5.7e+75) {
		tmp = x + ((z + (27464.7644705 / y)) / y);
	} else if (y <= -2.65e+38) {
		tmp = x * ((t / t_3) + (((y * (230661.510616 + (y * (27464.7644705 + (y * z))))) / t_3) + (pow(y, 3.0) / t_1)));
	} else if (y <= 1.55e+56) {
		tmp = (t / t_2) + ((y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616)) / t_2);
	} else {
		tmp = x + (z / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (y * ((y * (y + a)) + b)) + c
    t_2 = i + (y * t_1)
    t_3 = x * t_2
    if (y <= (-5.7d+75)) then
        tmp = x + ((z + (27464.7644705d0 / y)) / y)
    else if (y <= (-2.65d+38)) then
        tmp = x * ((t / t_3) + (((y * (230661.510616d0 + (y * (27464.7644705d0 + (y * z))))) / t_3) + ((y ** 3.0d0) / t_1)))
    else if (y <= 1.55d+56) then
        tmp = (t / t_2) + ((y * ((y * ((y * ((x * y) + z)) + 27464.7644705d0)) + 230661.510616d0)) / t_2)
    else
        tmp = x + (z / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (y * ((y * (y + a)) + b)) + c;
	double t_2 = i + (y * t_1);
	double t_3 = x * t_2;
	double tmp;
	if (y <= -5.7e+75) {
		tmp = x + ((z + (27464.7644705 / y)) / y);
	} else if (y <= -2.65e+38) {
		tmp = x * ((t / t_3) + (((y * (230661.510616 + (y * (27464.7644705 + (y * z))))) / t_3) + (Math.pow(y, 3.0) / t_1)));
	} else if (y <= 1.55e+56) {
		tmp = (t / t_2) + ((y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616)) / t_2);
	} else {
		tmp = x + (z / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (y * ((y * (y + a)) + b)) + c
	t_2 = i + (y * t_1)
	t_3 = x * t_2
	tmp = 0
	if y <= -5.7e+75:
		tmp = x + ((z + (27464.7644705 / y)) / y)
	elif y <= -2.65e+38:
		tmp = x * ((t / t_3) + (((y * (230661.510616 + (y * (27464.7644705 + (y * z))))) / t_3) + (math.pow(y, 3.0) / t_1)))
	elif y <= 1.55e+56:
		tmp = (t / t_2) + ((y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616)) / t_2)
	else:
		tmp = x + (z / y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c)
	t_2 = Float64(i + Float64(y * t_1))
	t_3 = Float64(x * t_2)
	tmp = 0.0
	if (y <= -5.7e+75)
		tmp = Float64(x + Float64(Float64(z + Float64(27464.7644705 / y)) / y));
	elseif (y <= -2.65e+38)
		tmp = Float64(x * Float64(Float64(t / t_3) + Float64(Float64(Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * z))))) / t_3) + Float64((y ^ 3.0) / t_1))));
	elseif (y <= 1.55e+56)
		tmp = Float64(Float64(t / t_2) + Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(Float64(x * y) + z)) + 27464.7644705)) + 230661.510616)) / t_2));
	else
		tmp = Float64(x + Float64(z / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (y * ((y * (y + a)) + b)) + c;
	t_2 = i + (y * t_1);
	t_3 = x * t_2;
	tmp = 0.0;
	if (y <= -5.7e+75)
		tmp = x + ((z + (27464.7644705 / y)) / y);
	elseif (y <= -2.65e+38)
		tmp = x * ((t / t_3) + (((y * (230661.510616 + (y * (27464.7644705 + (y * z))))) / t_3) + ((y ^ 3.0) / t_1)));
	elseif (y <= 1.55e+56)
		tmp = (t / t_2) + ((y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616)) / t_2);
	else
		tmp = x + (z / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]}, Block[{t$95$2 = N[(i + N[(y * t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x * t$95$2), $MachinePrecision]}, If[LessEqual[y, -5.7e+75], N[(x + N[(N[(z + N[(27464.7644705 / y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.65e+38], N[(x * N[(N[(t / t$95$3), $MachinePrecision] + N[(N[(N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$3), $MachinePrecision] + N[(N[Power[y, 3.0], $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.55e+56], N[(N[(t / t$95$2), $MachinePrecision] + N[(N[(y * N[(N[(y * N[(N[(y * N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] + 27464.7644705), $MachinePrecision]), $MachinePrecision] + 230661.510616), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision], N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.7000000000000004e75

   1. Initial program 0.1%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 0.1%

      \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\color{blue}{{y}^{3}} + c\right) \cdot y + i} \]

   4. Taylor expanded in y around -inf 81.2%

      \[\leadsto \color{blue}{x + -1 \cdot \frac{-1 \cdot z - 27464.7644705 \cdot \frac{1}{y}}{y}} \]
   5. Step-by-step derivation

      1. mul-1-neg 81.2%

         \[\leadsto x + \color{blue}{\left(-\frac{-1 \cdot z - 27464.7644705 \cdot \frac{1}{y}}{y}\right)} \]

      2. mul-1-neg 81.2%

         \[\leadsto x + \left(-\frac{\color{blue}{\left(-z\right)} - 27464.7644705 \cdot \frac{1}{y}}{y}\right) \]

      3. associate-*r/ 81.2%

         \[\leadsto x + \left(-\frac{\left(-z\right) - \color{blue}{\frac{27464.7644705 \cdot 1}{y}}}{y}\right) \]

      4. metadata-eval 81.2%

         \[\leadsto x + \left(-\frac{\left(-z\right) - \frac{\color{blue}{27464.7644705}}{y}}{y}\right) \]

   6. Simplified 81.2%

      \[\leadsto \color{blue}{x + \left(-\frac{\left(-z\right) - \frac{27464.7644705}{y}}{y}\right)} \]

   if -5.7000000000000004e75 < y < -2.65000000000000012e38

   1. Initial program 10.3%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 45.7%

      \[\leadsto \color{blue}{x \cdot \left(\frac{t}{x \cdot \left(i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)\right)} + \left(\frac{y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{x \cdot \left(i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)\right)} + \frac{{y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)\right)} \]

   4. Taylor expanded in i around 0 57.9%

      \[\leadsto x \cdot \left(\frac{t}{x \cdot \left(i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)\right)} + \left(\frac{y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{x \cdot \left(i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)\right)} + \color{blue}{\frac{{y}^{3}}{c + y \cdot \left(b + y \cdot \left(a + y\right)\right)}}\right)\right) \]

   if -2.65000000000000012e38 < y < 1.55000000000000002e56

   1. Initial program 95.8%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 95.9%

      \[\leadsto \color{blue}{\frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + x \cdot y\right)\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}} \]

   if 1.55000000000000002e56 < y

   1. Initial program 0.2%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 0.3%

      \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\color{blue}{{y}^{3}} + c\right) \cdot y + i} \]

   4. Taylor expanded in y around inf 66.1%

      \[\leadsto \color{blue}{x + \frac{z}{y}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 85.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.7 \cdot 10^{+75}:\\ \;\;\;\;x + \frac{z + \frac{27464.7644705}{y}}{y}\\ \mathbf{elif}\;y \leq -2.65 \cdot 10^{+38}:\\ \;\;\;\;x \cdot \left(\frac{t}{x \cdot \left(i + y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right)\right)} + \left(\frac{y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{x \cdot \left(i + y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right)\right)} + \frac{{y}^{3}}{y \cdot \left(y \cdot \left(y + a\right) + b\right) + c}\right)\right)\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+56}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right)} + \frac{y \cdot \left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616\right)}{i + y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 85.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i + y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right)\\ t_2 := y \cdot \left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616\right)\\ t_3 := \frac{t\_2 + t}{t\_1}\\ \mathbf{if}\;t\_3 \leq 5 \cdot 10^{+297}:\\ \;\;\;\;\frac{t}{t\_1} + \frac{t\_2}{t\_1}\\ \mathbf{elif}\;t\_3 \leq \infty:\\ \;\;\;\;x \cdot \left(\frac{t}{x \cdot t\_1} + \left(\frac{{y}^{3}}{x} \cdot \frac{z}{t\_1} + \frac{{y}^{4}}{t\_1}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ i (* y (+ (* y (+ (* y (+ y a)) b)) c))))
        (t_2
         (* y (+ (* y (+ (* y (+ (* x y) z)) 27464.7644705)) 230661.510616)))
        (t_3 (/ (+ t_2 t) t_1)))
   (if (<= t_3 5e+297)
     (+ (/ t t_1) (/ t_2 t_1))
     (if (<= t_3 INFINITY)
       (*
        x
        (+
         (/ t (* x t_1))
         (+ (* (/ (pow y 3.0) x) (/ z t_1)) (/ (pow y 4.0) t_1))))
       (+ x (/ z y))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = i + (y * ((y * ((y * (y + a)) + b)) + c));
	double t_2 = y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616);
	double t_3 = (t_2 + t) / t_1;
	double tmp;
	if (t_3 <= 5e+297) {
		tmp = (t / t_1) + (t_2 / t_1);
	} else if (t_3 <= ((double) INFINITY)) {
		tmp = x * ((t / (x * t_1)) + (((pow(y, 3.0) / x) * (z / t_1)) + (pow(y, 4.0) / t_1)));
	} else {
		tmp = x + (z / y);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = i + (y * ((y * ((y * (y + a)) + b)) + c));
	double t_2 = y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616);
	double t_3 = (t_2 + t) / t_1;
	double tmp;
	if (t_3 <= 5e+297) {
		tmp = (t / t_1) + (t_2 / t_1);
	} else if (t_3 <= Double.POSITIVE_INFINITY) {
		tmp = x * ((t / (x * t_1)) + (((Math.pow(y, 3.0) / x) * (z / t_1)) + (Math.pow(y, 4.0) / t_1)));
	} else {
		tmp = x + (z / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = i + (y * ((y * ((y * (y + a)) + b)) + c))
	t_2 = y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616)
	t_3 = (t_2 + t) / t_1
	tmp = 0
	if t_3 <= 5e+297:
		tmp = (t / t_1) + (t_2 / t_1)
	elif t_3 <= math.inf:
		tmp = x * ((t / (x * t_1)) + (((math.pow(y, 3.0) / x) * (z / t_1)) + (math.pow(y, 4.0) / t_1)))
	else:
		tmp = x + (z / y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(i + Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c)))
	t_2 = Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(Float64(x * y) + z)) + 27464.7644705)) + 230661.510616))
	t_3 = Float64(Float64(t_2 + t) / t_1)
	tmp = 0.0
	if (t_3 <= 5e+297)
		tmp = Float64(Float64(t / t_1) + Float64(t_2 / t_1));
	elseif (t_3 <= Inf)
		tmp = Float64(x * Float64(Float64(t / Float64(x * t_1)) + Float64(Float64(Float64((y ^ 3.0) / x) * Float64(z / t_1)) + Float64((y ^ 4.0) / t_1))));
	else
		tmp = Float64(x + Float64(z / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = i + (y * ((y * ((y * (y + a)) + b)) + c));
	t_2 = y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616);
	t_3 = (t_2 + t) / t_1;
	tmp = 0.0;
	if (t_3 <= 5e+297)
		tmp = (t / t_1) + (t_2 / t_1);
	elseif (t_3 <= Inf)
		tmp = x * ((t / (x * t_1)) + ((((y ^ 3.0) / x) * (z / t_1)) + ((y ^ 4.0) / t_1)));
	else
		tmp = x + (z / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(i + N[(y * N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(y * N[(N[(y * N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] + 27464.7644705), $MachinePrecision]), $MachinePrecision] + 230661.510616), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t$95$2 + t), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[t$95$3, 5e+297], N[(N[(t / t$95$1), $MachinePrecision] + N[(t$95$2 / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, Infinity], N[(x * N[(N[(t / N[(x * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(N[Power[y, 3.0], $MachinePrecision] / x), $MachinePrecision] * N[(z / t$95$1), $MachinePrecision]), $MachinePrecision] + N[(N[Power[y, 4.0], $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) 54929528941/2000000) y) 28832688827/125000) y) t) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c) y) i)) < 4.9999999999999998e297

   1. Initial program 91.7%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 91.7%

      \[\leadsto \color{blue}{\frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + x \cdot y\right)\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}} \]

   if 4.9999999999999998e297 < (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) 54929528941/2000000) y) 28832688827/125000) y) t) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c) y) i)) < +inf.0

   1. Initial program 39.3%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 72.7%

      \[\leadsto \color{blue}{x \cdot \left(\frac{t}{x \cdot \left(i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)\right)} + \left(\frac{y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{x \cdot \left(i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)\right)} + \frac{{y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)\right)} \]

   4. Taylor expanded in z around inf 54.5%

      \[\leadsto x \cdot \left(\frac{t}{x \cdot \left(i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)\right)} + \left(\color{blue}{\frac{{y}^{3} \cdot z}{x \cdot \left(i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)\right)}} + \frac{{y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)\right) \]
   5. Step-by-step derivation

      1. times-frac 81.8%

         \[\leadsto x \cdot \left(\frac{t}{x \cdot \left(i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)\right)} + \left(\color{blue}{\frac{{y}^{3}}{x} \cdot \frac{z}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}} + \frac{{y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)\right) \]

   6. Simplified 81.8%

      \[\leadsto x \cdot \left(\frac{t}{x \cdot \left(i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)\right)} + \left(\color{blue}{\frac{{y}^{3}}{x} \cdot \frac{z}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}} + \frac{{y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)\right) \]

   if +inf.0 < (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) 54929528941/2000000) y) 28832688827/125000) y) t) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c) y) i))

   1. Initial program 0.0%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 0.1%

      \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\color{blue}{{y}^{3}} + c\right) \cdot y + i} \]

   4. Taylor expanded in y around inf 72.2%

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

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616\right) + t}{i + y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right)} \leq 5 \cdot 10^{+297}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right)} + \frac{y \cdot \left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616\right)}{i + y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right)}\\ \mathbf{elif}\;\frac{y \cdot \left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616\right) + t}{i + y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right)} \leq \infty:\\ \;\;\;\;x \cdot \left(\frac{t}{x \cdot \left(i + y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right)\right)} + \left(\frac{{y}^{3}}{x} \cdot \frac{z}{i + y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right)} + \frac{{y}^{4}}{i + y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right)}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 84.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i + y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right)\\ t_2 := y \cdot \left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616\right)\\ \mathbf{if}\;\frac{t\_2 + t}{t\_1} \leq 5 \cdot 10^{+297}:\\ \;\;\;\;\frac{t}{t\_1} + \frac{t\_2}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z + \frac{27464.7644705}{y}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ i (* y (+ (* y (+ (* y (+ y a)) b)) c))))
        (t_2
         (* y (+ (* y (+ (* y (+ (* x y) z)) 27464.7644705)) 230661.510616))))
   (if (<= (/ (+ t_2 t) t_1) 5e+297)
     (+ (/ t t_1) (/ t_2 t_1))
     (+ x (/ (+ z (/ 27464.7644705 y)) y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = i + (y * ((y * ((y * (y + a)) + b)) + c));
	double t_2 = y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616);
	double tmp;
	if (((t_2 + t) / t_1) <= 5e+297) {
		tmp = (t / t_1) + (t_2 / t_1);
	} else {
		tmp = x + ((z + (27464.7644705 / y)) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = i + (y * ((y * ((y * (y + a)) + b)) + c))
    t_2 = y * ((y * ((y * ((x * y) + z)) + 27464.7644705d0)) + 230661.510616d0)
    if (((t_2 + t) / t_1) <= 5d+297) then
        tmp = (t / t_1) + (t_2 / t_1)
    else
        tmp = x + ((z + (27464.7644705d0 / y)) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = i + (y * ((y * ((y * (y + a)) + b)) + c));
	double t_2 = y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616);
	double tmp;
	if (((t_2 + t) / t_1) <= 5e+297) {
		tmp = (t / t_1) + (t_2 / t_1);
	} else {
		tmp = x + ((z + (27464.7644705 / y)) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = i + (y * ((y * ((y * (y + a)) + b)) + c))
	t_2 = y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616)
	tmp = 0
	if ((t_2 + t) / t_1) <= 5e+297:
		tmp = (t / t_1) + (t_2 / t_1)
	else:
		tmp = x + ((z + (27464.7644705 / y)) / y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(i + Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c)))
	t_2 = Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(Float64(x * y) + z)) + 27464.7644705)) + 230661.510616))
	tmp = 0.0
	if (Float64(Float64(t_2 + t) / t_1) <= 5e+297)
		tmp = Float64(Float64(t / t_1) + Float64(t_2 / t_1));
	else
		tmp = Float64(x + Float64(Float64(z + Float64(27464.7644705 / y)) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = i + (y * ((y * ((y * (y + a)) + b)) + c));
	t_2 = y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616);
	tmp = 0.0;
	if (((t_2 + t) / t_1) <= 5e+297)
		tmp = (t / t_1) + (t_2 / t_1);
	else
		tmp = x + ((z + (27464.7644705 / y)) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(i + N[(y * N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(y * N[(N[(y * N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] + 27464.7644705), $MachinePrecision]), $MachinePrecision] + 230661.510616), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(t$95$2 + t), $MachinePrecision] / t$95$1), $MachinePrecision], 5e+297], N[(N[(t / t$95$1), $MachinePrecision] + N[(t$95$2 / t$95$1), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z + N[(27464.7644705 / y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) 54929528941/2000000) y) 28832688827/125000) y) t) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c) y) i)) < 4.9999999999999998e297

   1. Initial program 91.7%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 91.7%

      \[\leadsto \color{blue}{\frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + x \cdot y\right)\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}} \]

   if 4.9999999999999998e297 < (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) 54929528941/2000000) y) 28832688827/125000) y) t) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c) y) i))

   1. Initial program 4.2%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 4.1%

      \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\color{blue}{{y}^{3}} + c\right) \cdot y + i} \]

   4. Taylor expanded in y around -inf 68.7%

      \[\leadsto \color{blue}{x + -1 \cdot \frac{-1 \cdot z - 27464.7644705 \cdot \frac{1}{y}}{y}} \]
   5. Step-by-step derivation

      1. mul-1-neg 68.7%

         \[\leadsto x + \color{blue}{\left(-\frac{-1 \cdot z - 27464.7644705 \cdot \frac{1}{y}}{y}\right)} \]

      2. mul-1-neg 68.7%

         \[\leadsto x + \left(-\frac{\color{blue}{\left(-z\right)} - 27464.7644705 \cdot \frac{1}{y}}{y}\right) \]

      3. associate-*r/ 68.7%

         \[\leadsto x + \left(-\frac{\left(-z\right) - \color{blue}{\frac{27464.7644705 \cdot 1}{y}}}{y}\right) \]

      4. metadata-eval 68.7%

         \[\leadsto x + \left(-\frac{\left(-z\right) - \frac{\color{blue}{27464.7644705}}{y}}{y}\right) \]

   6. Simplified 68.7%

      \[\leadsto \color{blue}{x + \left(-\frac{\left(-z\right) - \frac{27464.7644705}{y}}{y}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 82.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616\right) + t}{i + y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right)} \leq 5 \cdot 10^{+297}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right)} + \frac{y \cdot \left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616\right)}{i + y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z + \frac{27464.7644705}{y}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot \left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616\right) + t}{i + y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right)}\\ \mathbf{if}\;t\_1 \leq 5 \cdot 10^{+297}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z + \frac{27464.7644705}{y}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1
         (/
          (+
           (* y (+ (* y (+ (* y (+ (* x y) z)) 27464.7644705)) 230661.510616))
           t)
          (+ i (* y (+ (* y (+ (* y (+ y a)) b)) c))))))
   (if (<= t_1 5e+297) t_1 (+ x (/ (+ z (/ 27464.7644705 y)) y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = ((y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616)) + t) / (i + (y * ((y * ((y * (y + a)) + b)) + c)));
	double tmp;
	if (t_1 <= 5e+297) {
		tmp = t_1;
	} else {
		tmp = x + ((z + (27464.7644705 / y)) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((y * ((y * ((y * ((x * y) + z)) + 27464.7644705d0)) + 230661.510616d0)) + t) / (i + (y * ((y * ((y * (y + a)) + b)) + c)))
    if (t_1 <= 5d+297) then
        tmp = t_1
    else
        tmp = x + ((z + (27464.7644705d0 / y)) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = ((y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616)) + t) / (i + (y * ((y * ((y * (y + a)) + b)) + c)));
	double tmp;
	if (t_1 <= 5e+297) {
		tmp = t_1;
	} else {
		tmp = x + ((z + (27464.7644705 / y)) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = ((y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616)) + t) / (i + (y * ((y * ((y * (y + a)) + b)) + c)))
	tmp = 0
	if t_1 <= 5e+297:
		tmp = t_1
	else:
		tmp = x + ((z + (27464.7644705 / y)) / y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(Float64(x * y) + z)) + 27464.7644705)) + 230661.510616)) + t) / Float64(i + Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c))))
	tmp = 0.0
	if (t_1 <= 5e+297)
		tmp = t_1;
	else
		tmp = Float64(x + Float64(Float64(z + Float64(27464.7644705 / y)) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = ((y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616)) + t) / (i + (y * ((y * ((y * (y + a)) + b)) + c)));
	tmp = 0.0;
	if (t_1 <= 5e+297)
		tmp = t_1;
	else
		tmp = x + ((z + (27464.7644705 / y)) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(N[(y * N[(N[(y * N[(N[(y * N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] + 27464.7644705), $MachinePrecision]), $MachinePrecision] + 230661.510616), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision] / N[(i + N[(y * N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 5e+297], t$95$1, N[(x + N[(N[(z + N[(27464.7644705 / y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) 54929528941/2000000) y) 28832688827/125000) y) t) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c) y) i)) < 4.9999999999999998e297

   1. Initial program 91.7%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   if 4.9999999999999998e297 < (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) 54929528941/2000000) y) 28832688827/125000) y) t) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c) y) i))

   1. Initial program 4.2%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 4.1%

      \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\color{blue}{{y}^{3}} + c\right) \cdot y + i} \]

   4. Taylor expanded in y around -inf 68.7%

      \[\leadsto \color{blue}{x + -1 \cdot \frac{-1 \cdot z - 27464.7644705 \cdot \frac{1}{y}}{y}} \]
   5. Step-by-step derivation

      1. mul-1-neg 68.7%

         \[\leadsto x + \color{blue}{\left(-\frac{-1 \cdot z - 27464.7644705 \cdot \frac{1}{y}}{y}\right)} \]

      2. mul-1-neg 68.7%

         \[\leadsto x + \left(-\frac{\color{blue}{\left(-z\right)} - 27464.7644705 \cdot \frac{1}{y}}{y}\right) \]

      3. associate-*r/ 68.7%

         \[\leadsto x + \left(-\frac{\left(-z\right) - \color{blue}{\frac{27464.7644705 \cdot 1}{y}}}{y}\right) \]

      4. metadata-eval 68.7%

         \[\leadsto x + \left(-\frac{\left(-z\right) - \frac{\color{blue}{27464.7644705}}{y}}{y}\right) \]

   6. Simplified 68.7%

      \[\leadsto \color{blue}{x + \left(-\frac{\left(-z\right) - \frac{27464.7644705}{y}}{y}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 82.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616\right) + t}{i + y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right)} \leq 5 \cdot 10^{+297}:\\ \;\;\;\;\frac{y \cdot \left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616\right) + t}{i + y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z + \frac{27464.7644705}{y}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(c + y \cdot b\right)\\ t_2 := \frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{i + t\_1}\\ \mathbf{if}\;y \leq -3.6 \cdot 10^{+22}:\\ \;\;\;\;x + \frac{z + \frac{27464.7644705}{y}}{y}\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{-68}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+14}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{t\_1}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+51}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* y (+ c (* y b))))
        (t_2 (/ (+ t (* y (+ 230661.510616 (* y 27464.7644705)))) (+ i t_1))))
   (if (<= y -3.6e+22)
     (+ x (/ (+ z (/ 27464.7644705 y)) y))
     (if (<= y 9.2e-68)
       t_2
       (if (<= y 5.2e+14)
         (/ (+ t (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y z)))))) t_1)
         (if (<= y 3e+51) t_2 (+ x (/ z y))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = y * (c + (y * b));
	double t_2 = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + t_1);
	double tmp;
	if (y <= -3.6e+22) {
		tmp = x + ((z + (27464.7644705 / y)) / y);
	} else if (y <= 9.2e-68) {
		tmp = t_2;
	} else if (y <= 5.2e+14) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / t_1;
	} else if (y <= 3e+51) {
		tmp = t_2;
	} else {
		tmp = x + (z / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * (c + (y * b))
    t_2 = (t + (y * (230661.510616d0 + (y * 27464.7644705d0)))) / (i + t_1)
    if (y <= (-3.6d+22)) then
        tmp = x + ((z + (27464.7644705d0 / y)) / y)
    else if (y <= 9.2d-68) then
        tmp = t_2
    else if (y <= 5.2d+14) then
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * z)))))) / t_1
    else if (y <= 3d+51) then
        tmp = t_2
    else
        tmp = x + (z / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = y * (c + (y * b));
	double t_2 = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + t_1);
	double tmp;
	if (y <= -3.6e+22) {
		tmp = x + ((z + (27464.7644705 / y)) / y);
	} else if (y <= 9.2e-68) {
		tmp = t_2;
	} else if (y <= 5.2e+14) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / t_1;
	} else if (y <= 3e+51) {
		tmp = t_2;
	} else {
		tmp = x + (z / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = y * (c + (y * b))
	t_2 = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + t_1)
	tmp = 0
	if y <= -3.6e+22:
		tmp = x + ((z + (27464.7644705 / y)) / y)
	elif y <= 9.2e-68:
		tmp = t_2
	elif y <= 5.2e+14:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / t_1
	elif y <= 3e+51:
		tmp = t_2
	else:
		tmp = x + (z / y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(y * Float64(c + Float64(y * b)))
	t_2 = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * 27464.7644705)))) / Float64(i + t_1))
	tmp = 0.0
	if (y <= -3.6e+22)
		tmp = Float64(x + Float64(Float64(z + Float64(27464.7644705 / y)) / y));
	elseif (y <= 9.2e-68)
		tmp = t_2;
	elseif (y <= 5.2e+14)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * z)))))) / t_1);
	elseif (y <= 3e+51)
		tmp = t_2;
	else
		tmp = Float64(x + Float64(z / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = y * (c + (y * b));
	t_2 = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + t_1);
	tmp = 0.0;
	if (y <= -3.6e+22)
		tmp = x + ((z + (27464.7644705 / y)) / y);
	elseif (y <= 9.2e-68)
		tmp = t_2;
	elseif (y <= 5.2e+14)
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / t_1;
	elseif (y <= 3e+51)
		tmp = t_2;
	else
		tmp = x + (z / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(y * N[(c + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t + N[(y * N[(230661.510616 + N[(y * 27464.7644705), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.6e+22], N[(x + N[(N[(z + N[(27464.7644705 / y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.2e-68], t$95$2, If[LessEqual[y, 5.2e+14], N[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[y, 3e+51], t$95$2, N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.6e22

   1. Initial program 7.0%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 6.9%

      \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\color{blue}{{y}^{3}} + c\right) \cdot y + i} \]

   4. Taylor expanded in y around -inf 65.5%

      \[\leadsto \color{blue}{x + -1 \cdot \frac{-1 \cdot z - 27464.7644705 \cdot \frac{1}{y}}{y}} \]
   5. Step-by-step derivation

      1. mul-1-neg 65.5%

         \[\leadsto x + \color{blue}{\left(-\frac{-1 \cdot z - 27464.7644705 \cdot \frac{1}{y}}{y}\right)} \]

      2. mul-1-neg 65.5%

         \[\leadsto x + \left(-\frac{\color{blue}{\left(-z\right)} - 27464.7644705 \cdot \frac{1}{y}}{y}\right) \]

      3. associate-*r/ 65.5%

         \[\leadsto x + \left(-\frac{\left(-z\right) - \color{blue}{\frac{27464.7644705 \cdot 1}{y}}}{y}\right) \]

      4. metadata-eval 65.5%

         \[\leadsto x + \left(-\frac{\left(-z\right) - \frac{\color{blue}{27464.7644705}}{y}}{y}\right) \]

   6. Simplified 65.5%

      \[\leadsto \color{blue}{x + \left(-\frac{\left(-z\right) - \frac{27464.7644705}{y}}{y}\right)} \]

   if -3.6e22 < y < 9.19999999999999987e-68 or 5.2e14 < y < 3e51

   1. Initial program 97.4%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 93.8%

      \[\leadsto \frac{\left(\color{blue}{y \cdot \left(27464.7644705 + y \cdot z\right)} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   4. Taylor expanded in y around 0 88.4%

      \[\leadsto \frac{\left(y \cdot \left(27464.7644705 + y \cdot z\right) + 230661.510616\right) \cdot y + t}{\left(\color{blue}{b \cdot y} + c\right) \cdot y + i} \]
   5. Step-by-step derivation

      1. *-commutative 88.4%

         \[\leadsto \frac{\left(y \cdot \left(27464.7644705 + y \cdot z\right) + 230661.510616\right) \cdot y + t}{\left(\color{blue}{y \cdot b} + c\right) \cdot y + i} \]

   6. Simplified 88.4%

      \[\leadsto \frac{\left(y \cdot \left(27464.7644705 + y \cdot z\right) + 230661.510616\right) \cdot y + t}{\left(\color{blue}{y \cdot b} + c\right) \cdot y + i} \]

   7. Taylor expanded in z around 0 82.1%

      \[\leadsto \color{blue}{\frac{t + y \cdot \left(230661.510616 + 27464.7644705 \cdot y\right)}{i + y \cdot \left(c + b \cdot y\right)}} \]

   if 9.19999999999999987e-68 < y < 5.2e14

   1. Initial program 94.0%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 83.2%

      \[\leadsto \frac{\left(\color{blue}{y \cdot \left(27464.7644705 + y \cdot z\right)} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   4. Taylor expanded in y around 0 65.9%

      \[\leadsto \frac{\left(y \cdot \left(27464.7644705 + y \cdot z\right) + 230661.510616\right) \cdot y + t}{\left(\color{blue}{b \cdot y} + c\right) \cdot y + i} \]
   5. Step-by-step derivation

      1. *-commutative 65.9%

         \[\leadsto \frac{\left(y \cdot \left(27464.7644705 + y \cdot z\right) + 230661.510616\right) \cdot y + t}{\left(\color{blue}{y \cdot b} + c\right) \cdot y + i} \]

   6. Simplified 65.9%

      \[\leadsto \frac{\left(y \cdot \left(27464.7644705 + y \cdot z\right) + 230661.510616\right) \cdot y + t}{\left(\color{blue}{y \cdot b} + c\right) \cdot y + i} \]

   7. Taylor expanded in i around 0 53.6%

      \[\leadsto \color{blue}{\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{y \cdot \left(c + b \cdot y\right)}} \]

   if 3e51 < y

   1. Initial program 2.5%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 2.5%

      \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\color{blue}{{y}^{3}} + c\right) \cdot y + i} \]

   4. Taylor expanded in y around inf 65.4%

      \[\leadsto \color{blue}{x + \frac{z}{y}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+22}:\\ \;\;\;\;x + \frac{z + \frac{27464.7644705}{y}}{y}\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{-68}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+14}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{y \cdot \left(c + y \cdot b\right)}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+51}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 81.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+38}:\\ \;\;\;\;x + \frac{z + \frac{27464.7644705}{y}}{y}\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+49}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -2.4e+38)
   (+ x (/ (+ z (/ 27464.7644705 y)) y))
   (if (<= y 6.8e+49)
     (/
      (+ t (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y z))))))
      (+ i (* y (+ (* y (+ (* y (+ y a)) b)) c))))
     (+ x (/ z y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -2.4e+38) {
		tmp = x + ((z + (27464.7644705 / y)) / y);
	} else if (y <= 6.8e+49) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * ((y * ((y * (y + a)) + b)) + c)));
	} else {
		tmp = x + (z / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= (-2.4d+38)) then
        tmp = x + ((z + (27464.7644705d0 / y)) / y)
    else if (y <= 6.8d+49) then
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * z)))))) / (i + (y * ((y * ((y * (y + a)) + b)) + c)))
    else
        tmp = x + (z / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -2.4e+38) {
		tmp = x + ((z + (27464.7644705 / y)) / y);
	} else if (y <= 6.8e+49) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * ((y * ((y * (y + a)) + b)) + c)));
	} else {
		tmp = x + (z / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -2.4e+38:
		tmp = x + ((z + (27464.7644705 / y)) / y)
	elif y <= 6.8e+49:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * ((y * ((y * (y + a)) + b)) + c)))
	else:
		tmp = x + (z / y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -2.4e+38)
		tmp = Float64(x + Float64(Float64(z + Float64(27464.7644705 / y)) / y));
	elseif (y <= 6.8e+49)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * z)))))) / Float64(i + Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c))));
	else
		tmp = Float64(x + Float64(z / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -2.4e+38)
		tmp = x + ((z + (27464.7644705 / y)) / y);
	elseif (y <= 6.8e+49)
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * ((y * ((y * (y + a)) + b)) + c)));
	else
		tmp = x + (z / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -2.4e+38], N[(x + N[(N[(z + N[(27464.7644705 / y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.8e+49], N[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.40000000000000017e38

   1. Initial program 2.7%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 2.5%

      \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\color{blue}{{y}^{3}} + c\right) \cdot y + i} \]

   4. Taylor expanded in y around -inf 67.8%

      \[\leadsto \color{blue}{x + -1 \cdot \frac{-1 \cdot z - 27464.7644705 \cdot \frac{1}{y}}{y}} \]
   5. Step-by-step derivation

      1. mul-1-neg 67.8%

         \[\leadsto x + \color{blue}{\left(-\frac{-1 \cdot z - 27464.7644705 \cdot \frac{1}{y}}{y}\right)} \]

      2. mul-1-neg 67.8%

         \[\leadsto x + \left(-\frac{\color{blue}{\left(-z\right)} - 27464.7644705 \cdot \frac{1}{y}}{y}\right) \]

      3. associate-*r/ 67.8%

         \[\leadsto x + \left(-\frac{\left(-z\right) - \color{blue}{\frac{27464.7644705 \cdot 1}{y}}}{y}\right) \]

      4. metadata-eval 67.8%

         \[\leadsto x + \left(-\frac{\left(-z\right) - \frac{\color{blue}{27464.7644705}}{y}}{y}\right) \]

   6. Simplified 67.8%

      \[\leadsto \color{blue}{x + \left(-\frac{\left(-z\right) - \frac{27464.7644705}{y}}{y}\right)} \]

   if -2.40000000000000017e38 < y < 6.8000000000000001e49

   1. Initial program 96.4%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 91.2%

      \[\leadsto \frac{\left(\color{blue}{y \cdot \left(27464.7644705 + y \cdot z\right)} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   if 6.8000000000000001e49 < y

   1. Initial program 2.5%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 2.5%

      \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\color{blue}{{y}^{3}} + c\right) \cdot y + i} \]

   4. Taylor expanded in y around inf 65.4%

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

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+38}:\\ \;\;\;\;x + \frac{z + \frac{27464.7644705}{y}}{y}\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+49}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 81.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.75 \cdot 10^{+35}:\\ \;\;\;\;x + \frac{z + \frac{27464.7644705}{y}}{y}\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+51}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot a\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -2.75e+35)
   (+ x (/ (+ z (/ 27464.7644705 y)) y))
   (if (<= y 3.6e+51)
     (/
      (+ t (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y z))))))
      (+ i (* y (+ c (* y (+ b (* y a)))))))
     (+ x (/ z y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -2.75e+35) {
		tmp = x + ((z + (27464.7644705 / y)) / y);
	} else if (y <= 3.6e+51) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * (b + (y * a))))));
	} else {
		tmp = x + (z / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= (-2.75d+35)) then
        tmp = x + ((z + (27464.7644705d0 / y)) / y)
    else if (y <= 3.6d+51) then
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * z)))))) / (i + (y * (c + (y * (b + (y * a))))))
    else
        tmp = x + (z / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -2.75e+35) {
		tmp = x + ((z + (27464.7644705 / y)) / y);
	} else if (y <= 3.6e+51) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * (b + (y * a))))));
	} else {
		tmp = x + (z / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -2.75e+35:
		tmp = x + ((z + (27464.7644705 / y)) / y)
	elif y <= 3.6e+51:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * (b + (y * a))))))
	else:
		tmp = x + (z / y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -2.75e+35)
		tmp = Float64(x + Float64(Float64(z + Float64(27464.7644705 / y)) / y));
	elseif (y <= 3.6e+51)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * z)))))) / Float64(i + Float64(y * Float64(c + Float64(y * Float64(b + Float64(y * a)))))));
	else
		tmp = Float64(x + Float64(z / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -2.75e+35)
		tmp = x + ((z + (27464.7644705 / y)) / y);
	elseif (y <= 3.6e+51)
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * (b + (y * a))))));
	else
		tmp = x + (z / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -2.75e+35], N[(x + N[(N[(z + N[(27464.7644705 / y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.6e+51], N[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * N[(b + N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.75000000000000001e35

   1. Initial program 4.2%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 4.0%

      \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\color{blue}{{y}^{3}} + c\right) \cdot y + i} \]

   4. Taylor expanded in y around -inf 66.9%

      \[\leadsto \color{blue}{x + -1 \cdot \frac{-1 \cdot z - 27464.7644705 \cdot \frac{1}{y}}{y}} \]
   5. Step-by-step derivation

      1. mul-1-neg 66.9%

         \[\leadsto x + \color{blue}{\left(-\frac{-1 \cdot z - 27464.7644705 \cdot \frac{1}{y}}{y}\right)} \]

      2. mul-1-neg 66.9%

         \[\leadsto x + \left(-\frac{\color{blue}{\left(-z\right)} - 27464.7644705 \cdot \frac{1}{y}}{y}\right) \]

      3. associate-*r/ 66.9%

         \[\leadsto x + \left(-\frac{\left(-z\right) - \color{blue}{\frac{27464.7644705 \cdot 1}{y}}}{y}\right) \]

      4. metadata-eval 66.9%

         \[\leadsto x + \left(-\frac{\left(-z\right) - \frac{\color{blue}{27464.7644705}}{y}}{y}\right) \]

   6. Simplified 66.9%

      \[\leadsto \color{blue}{x + \left(-\frac{\left(-z\right) - \frac{27464.7644705}{y}}{y}\right)} \]

   if -2.75000000000000001e35 < y < 3.60000000000000011e51

   1. Initial program 96.4%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 91.3%

      \[\leadsto \frac{\left(\color{blue}{y \cdot \left(27464.7644705 + y \cdot z\right)} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   4. Taylor expanded in y around 0 90.6%

      \[\leadsto \frac{\left(y \cdot \left(27464.7644705 + y \cdot z\right) + 230661.510616\right) \cdot y + t}{\left(\color{blue}{y \cdot \left(b + a \cdot y\right)} + c\right) \cdot y + i} \]
   5. Step-by-step derivation

      1. *-commutative 90.6%

         \[\leadsto \frac{\left(y \cdot \left(27464.7644705 + y \cdot z\right) + 230661.510616\right) \cdot y + t}{\left(y \cdot \left(b + \color{blue}{y \cdot a}\right) + c\right) \cdot y + i} \]

   6. Simplified 90.6%

      \[\leadsto \frac{\left(y \cdot \left(27464.7644705 + y \cdot z\right) + 230661.510616\right) \cdot y + t}{\left(\color{blue}{y \cdot \left(b + y \cdot a\right)} + c\right) \cdot y + i} \]

   if 3.60000000000000011e51 < y

   1. Initial program 2.5%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 2.5%

      \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\color{blue}{{y}^{3}} + c\right) \cdot y + i} \]

   4. Taylor expanded in y around inf 65.4%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.75 \cdot 10^{+35}:\\ \;\;\;\;x + \frac{z + \frac{27464.7644705}{y}}{y}\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+51}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot a\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 78.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+35}:\\ \;\;\;\;x + \frac{z + \frac{27464.7644705}{y}}{y}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+49}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -1.4e+35)
   (+ x (/ (+ z (/ 27464.7644705 y)) y))
   (if (<= y 3.2e+49)
     (/
      (+ t (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y z))))))
      (+ i (* y (+ c (* y b)))))
     (+ x (/ z y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -1.4e+35) {
		tmp = x + ((z + (27464.7644705 / y)) / y);
	} else if (y <= 3.2e+49) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * b))));
	} else {
		tmp = x + (z / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= (-1.4d+35)) then
        tmp = x + ((z + (27464.7644705d0 / y)) / y)
    else if (y <= 3.2d+49) then
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * z)))))) / (i + (y * (c + (y * b))))
    else
        tmp = x + (z / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -1.4e+35) {
		tmp = x + ((z + (27464.7644705 / y)) / y);
	} else if (y <= 3.2e+49) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * b))));
	} else {
		tmp = x + (z / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -1.4e+35:
		tmp = x + ((z + (27464.7644705 / y)) / y)
	elif y <= 3.2e+49:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * b))))
	else:
		tmp = x + (z / y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -1.4e+35)
		tmp = Float64(x + Float64(Float64(z + Float64(27464.7644705 / y)) / y));
	elseif (y <= 3.2e+49)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * z)))))) / Float64(i + Float64(y * Float64(c + Float64(y * b)))));
	else
		tmp = Float64(x + Float64(z / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -1.4e+35)
		tmp = x + ((z + (27464.7644705 / y)) / y);
	elseif (y <= 3.2e+49)
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * b))));
	else
		tmp = x + (z / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -1.4e+35], N[(x + N[(N[(z + N[(27464.7644705 / y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.2e+49], N[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.39999999999999999e35

   1. Initial program 4.2%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 4.0%

      \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\color{blue}{{y}^{3}} + c\right) \cdot y + i} \]

   4. Taylor expanded in y around -inf 66.9%

      \[\leadsto \color{blue}{x + -1 \cdot \frac{-1 \cdot z - 27464.7644705 \cdot \frac{1}{y}}{y}} \]
   5. Step-by-step derivation

      1. mul-1-neg 66.9%

         \[\leadsto x + \color{blue}{\left(-\frac{-1 \cdot z - 27464.7644705 \cdot \frac{1}{y}}{y}\right)} \]

      2. mul-1-neg 66.9%

         \[\leadsto x + \left(-\frac{\color{blue}{\left(-z\right)} - 27464.7644705 \cdot \frac{1}{y}}{y}\right) \]

      3. associate-*r/ 66.9%

         \[\leadsto x + \left(-\frac{\left(-z\right) - \color{blue}{\frac{27464.7644705 \cdot 1}{y}}}{y}\right) \]

      4. metadata-eval 66.9%

         \[\leadsto x + \left(-\frac{\left(-z\right) - \frac{\color{blue}{27464.7644705}}{y}}{y}\right) \]

   6. Simplified 66.9%

      \[\leadsto \color{blue}{x + \left(-\frac{\left(-z\right) - \frac{27464.7644705}{y}}{y}\right)} \]

   if -1.39999999999999999e35 < y < 3.20000000000000014e49

   1. Initial program 96.4%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 91.3%

      \[\leadsto \frac{\left(\color{blue}{y \cdot \left(27464.7644705 + y \cdot z\right)} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   4. Taylor expanded in y around 0 84.7%

      \[\leadsto \frac{\left(y \cdot \left(27464.7644705 + y \cdot z\right) + 230661.510616\right) \cdot y + t}{\left(\color{blue}{b \cdot y} + c\right) \cdot y + i} \]
   5. Step-by-step derivation

      1. *-commutative 84.7%

         \[\leadsto \frac{\left(y \cdot \left(27464.7644705 + y \cdot z\right) + 230661.510616\right) \cdot y + t}{\left(\color{blue}{y \cdot b} + c\right) \cdot y + i} \]

   6. Simplified 84.7%

      \[\leadsto \frac{\left(y \cdot \left(27464.7644705 + y \cdot z\right) + 230661.510616\right) \cdot y + t}{\left(\color{blue}{y \cdot b} + c\right) \cdot y + i} \]

   if 3.20000000000000014e49 < y

   1. Initial program 2.5%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 2.5%

      \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\color{blue}{{y}^{3}} + c\right) \cdot y + i} \]

   4. Taylor expanded in y around inf 65.4%

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

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+35}:\\ \;\;\;\;x + \frac{z + \frac{27464.7644705}{y}}{y}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+49}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 76.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+16}:\\ \;\;\;\;x + \frac{z + \frac{27464.7644705}{y}}{y}\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+49}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -2.8e+16)
   (+ x (/ (+ z (/ 27464.7644705 y)) y))
   (if (<= y 3.1e+49)
     (/ (+ t (* y 230661.510616)) (+ i (* y (+ (* y (+ (* y (+ y a)) b)) c))))
     (+ x (/ z y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -2.8e+16) {
		tmp = x + ((z + (27464.7644705 / y)) / y);
	} else if (y <= 3.1e+49) {
		tmp = (t + (y * 230661.510616)) / (i + (y * ((y * ((y * (y + a)) + b)) + c)));
	} else {
		tmp = x + (z / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= (-2.8d+16)) then
        tmp = x + ((z + (27464.7644705d0 / y)) / y)
    else if (y <= 3.1d+49) then
        tmp = (t + (y * 230661.510616d0)) / (i + (y * ((y * ((y * (y + a)) + b)) + c)))
    else
        tmp = x + (z / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -2.8e+16) {
		tmp = x + ((z + (27464.7644705 / y)) / y);
	} else if (y <= 3.1e+49) {
		tmp = (t + (y * 230661.510616)) / (i + (y * ((y * ((y * (y + a)) + b)) + c)));
	} else {
		tmp = x + (z / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -2.8e+16:
		tmp = x + ((z + (27464.7644705 / y)) / y)
	elif y <= 3.1e+49:
		tmp = (t + (y * 230661.510616)) / (i + (y * ((y * ((y * (y + a)) + b)) + c)))
	else:
		tmp = x + (z / y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -2.8e+16)
		tmp = Float64(x + Float64(Float64(z + Float64(27464.7644705 / y)) / y));
	elseif (y <= 3.1e+49)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(i + Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c))));
	else
		tmp = Float64(x + Float64(z / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -2.8e+16)
		tmp = x + ((z + (27464.7644705 / y)) / y);
	elseif (y <= 3.1e+49)
		tmp = (t + (y * 230661.510616)) / (i + (y * ((y * ((y * (y + a)) + b)) + c)));
	else
		tmp = x + (z / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -2.8e+16], N[(x + N[(N[(z + N[(27464.7644705 / y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.1e+49], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.8e16

   1. Initial program 8.3%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 8.2%

      \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\color{blue}{{y}^{3}} + c\right) \cdot y + i} \]

   4. Taylor expanded in y around -inf 64.6%

      \[\leadsto \color{blue}{x + -1 \cdot \frac{-1 \cdot z - 27464.7644705 \cdot \frac{1}{y}}{y}} \]
   5. Step-by-step derivation

      1. mul-1-neg 64.6%

         \[\leadsto x + \color{blue}{\left(-\frac{-1 \cdot z - 27464.7644705 \cdot \frac{1}{y}}{y}\right)} \]

      2. mul-1-neg 64.6%

         \[\leadsto x + \left(-\frac{\color{blue}{\left(-z\right)} - 27464.7644705 \cdot \frac{1}{y}}{y}\right) \]

      3. associate-*r/ 64.6%

         \[\leadsto x + \left(-\frac{\left(-z\right) - \color{blue}{\frac{27464.7644705 \cdot 1}{y}}}{y}\right) \]

      4. metadata-eval 64.6%

         \[\leadsto x + \left(-\frac{\left(-z\right) - \frac{\color{blue}{27464.7644705}}{y}}{y}\right) \]

   6. Simplified 64.6%

      \[\leadsto \color{blue}{x + \left(-\frac{\left(-z\right) - \frac{27464.7644705}{y}}{y}\right)} \]

   if -2.8e16 < y < 3.09999999999999992e49

   1. Initial program 97.0%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 79.6%

      \[\leadsto \frac{\color{blue}{230661.510616 \cdot y} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   4. Step-by-step derivation

      1. *-commutative 79.6%

         \[\leadsto \frac{\color{blue}{y \cdot 230661.510616} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   5. Simplified 79.6%

      \[\leadsto \frac{\color{blue}{y \cdot 230661.510616} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   if 3.09999999999999992e49 < y

   1. Initial program 2.5%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 2.5%

      \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\color{blue}{{y}^{3}} + c\right) \cdot y + i} \]

   4. Taylor expanded in y around inf 65.4%

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

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+16}:\\ \;\;\;\;x + \frac{z + \frac{27464.7644705}{y}}{y}\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+49}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 74.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+24}:\\ \;\;\;\;x + \frac{z + \frac{27464.7644705}{y}}{y}\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+49}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -2.5e+24)
   (+ x (/ (+ z (/ 27464.7644705 y)) y))
   (if (<= y 3.1e+49)
     (/
      (+ t (* y (+ 230661.510616 (* y 27464.7644705))))
      (+ i (* y (+ c (* y b)))))
     (+ x (/ z y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -2.5e+24) {
		tmp = x + ((z + (27464.7644705 / y)) / y);
	} else if (y <= 3.1e+49) {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * (c + (y * b))));
	} else {
		tmp = x + (z / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= (-2.5d+24)) then
        tmp = x + ((z + (27464.7644705d0 / y)) / y)
    else if (y <= 3.1d+49) then
        tmp = (t + (y * (230661.510616d0 + (y * 27464.7644705d0)))) / (i + (y * (c + (y * b))))
    else
        tmp = x + (z / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -2.5e+24) {
		tmp = x + ((z + (27464.7644705 / y)) / y);
	} else if (y <= 3.1e+49) {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * (c + (y * b))));
	} else {
		tmp = x + (z / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -2.5e+24:
		tmp = x + ((z + (27464.7644705 / y)) / y)
	elif y <= 3.1e+49:
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * (c + (y * b))))
	else:
		tmp = x + (z / y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -2.5e+24)
		tmp = Float64(x + Float64(Float64(z + Float64(27464.7644705 / y)) / y));
	elseif (y <= 3.1e+49)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * 27464.7644705)))) / Float64(i + Float64(y * Float64(c + Float64(y * b)))));
	else
		tmp = Float64(x + Float64(z / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -2.5e+24)
		tmp = x + ((z + (27464.7644705 / y)) / y);
	elseif (y <= 3.1e+49)
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * (c + (y * b))));
	else
		tmp = x + (z / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -2.5e+24], N[(x + N[(N[(z + N[(27464.7644705 / y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.1e+49], N[(N[(t + N[(y * N[(230661.510616 + N[(y * 27464.7644705), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.50000000000000023e24

   1. Initial program 7.0%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 6.9%

      \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\color{blue}{{y}^{3}} + c\right) \cdot y + i} \]

   4. Taylor expanded in y around -inf 65.5%

      \[\leadsto \color{blue}{x + -1 \cdot \frac{-1 \cdot z - 27464.7644705 \cdot \frac{1}{y}}{y}} \]
   5. Step-by-step derivation

      1. mul-1-neg 65.5%

         \[\leadsto x + \color{blue}{\left(-\frac{-1 \cdot z - 27464.7644705 \cdot \frac{1}{y}}{y}\right)} \]

      2. mul-1-neg 65.5%

         \[\leadsto x + \left(-\frac{\color{blue}{\left(-z\right)} - 27464.7644705 \cdot \frac{1}{y}}{y}\right) \]

      3. associate-*r/ 65.5%

         \[\leadsto x + \left(-\frac{\left(-z\right) - \color{blue}{\frac{27464.7644705 \cdot 1}{y}}}{y}\right) \]

      4. metadata-eval 65.5%

         \[\leadsto x + \left(-\frac{\left(-z\right) - \frac{\color{blue}{27464.7644705}}{y}}{y}\right) \]

   6. Simplified 65.5%

      \[\leadsto \color{blue}{x + \left(-\frac{\left(-z\right) - \frac{27464.7644705}{y}}{y}\right)} \]

   if -2.50000000000000023e24 < y < 3.09999999999999992e49

   1. Initial program 97.0%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 92.5%

      \[\leadsto \frac{\left(\color{blue}{y \cdot \left(27464.7644705 + y \cdot z\right)} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   4. Taylor expanded in y around 0 85.7%

      \[\leadsto \frac{\left(y \cdot \left(27464.7644705 + y \cdot z\right) + 230661.510616\right) \cdot y + t}{\left(\color{blue}{b \cdot y} + c\right) \cdot y + i} \]
   5. Step-by-step derivation

      1. *-commutative 85.7%

         \[\leadsto \frac{\left(y \cdot \left(27464.7644705 + y \cdot z\right) + 230661.510616\right) \cdot y + t}{\left(\color{blue}{y \cdot b} + c\right) \cdot y + i} \]

   6. Simplified 85.7%

      \[\leadsto \frac{\left(y \cdot \left(27464.7644705 + y \cdot z\right) + 230661.510616\right) \cdot y + t}{\left(\color{blue}{y \cdot b} + c\right) \cdot y + i} \]

   7. Taylor expanded in z around 0 75.4%

      \[\leadsto \color{blue}{\frac{t + y \cdot \left(230661.510616 + 27464.7644705 \cdot y\right)}{i + y \cdot \left(c + b \cdot y\right)}} \]

   if 3.09999999999999992e49 < y

   1. Initial program 2.5%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 2.5%

      \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\color{blue}{{y}^{3}} + c\right) \cdot y + i} \]

   4. Taylor expanded in y around inf 65.4%

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

4. Final simplification 71.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+24}:\\ \;\;\;\;x + \frac{z + \frac{27464.7644705}{y}}{y}\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+49}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 69.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+24}:\\ \;\;\;\;x + \frac{z + \frac{27464.7644705}{y}}{y}\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+49}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -1.8e+24)
   (+ x (/ (+ z (/ 27464.7644705 y)) y))
   (if (<= y 3.8e+49)
     (/ t (+ i (* y (+ (* y (+ (* y (+ y a)) b)) c))))
     (+ x (/ z y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -1.8e+24) {
		tmp = x + ((z + (27464.7644705 / y)) / y);
	} else if (y <= 3.8e+49) {
		tmp = t / (i + (y * ((y * ((y * (y + a)) + b)) + c)));
	} else {
		tmp = x + (z / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= (-1.8d+24)) then
        tmp = x + ((z + (27464.7644705d0 / y)) / y)
    else if (y <= 3.8d+49) then
        tmp = t / (i + (y * ((y * ((y * (y + a)) + b)) + c)))
    else
        tmp = x + (z / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -1.8e+24) {
		tmp = x + ((z + (27464.7644705 / y)) / y);
	} else if (y <= 3.8e+49) {
		tmp = t / (i + (y * ((y * ((y * (y + a)) + b)) + c)));
	} else {
		tmp = x + (z / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -1.8e+24:
		tmp = x + ((z + (27464.7644705 / y)) / y)
	elif y <= 3.8e+49:
		tmp = t / (i + (y * ((y * ((y * (y + a)) + b)) + c)))
	else:
		tmp = x + (z / y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -1.8e+24)
		tmp = Float64(x + Float64(Float64(z + Float64(27464.7644705 / y)) / y));
	elseif (y <= 3.8e+49)
		tmp = Float64(t / Float64(i + Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c))));
	else
		tmp = Float64(x + Float64(z / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -1.8e+24)
		tmp = x + ((z + (27464.7644705 / y)) / y);
	elseif (y <= 3.8e+49)
		tmp = t / (i + (y * ((y * ((y * (y + a)) + b)) + c)));
	else
		tmp = x + (z / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -1.8e+24], N[(x + N[(N[(z + N[(27464.7644705 / y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.8e+49], N[(t / N[(i + N[(y * N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.79999999999999992e24

   1. Initial program 7.0%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 6.9%

      \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\color{blue}{{y}^{3}} + c\right) \cdot y + i} \]

   4. Taylor expanded in y around -inf 65.5%

      \[\leadsto \color{blue}{x + -1 \cdot \frac{-1 \cdot z - 27464.7644705 \cdot \frac{1}{y}}{y}} \]
   5. Step-by-step derivation

      1. mul-1-neg 65.5%

         \[\leadsto x + \color{blue}{\left(-\frac{-1 \cdot z - 27464.7644705 \cdot \frac{1}{y}}{y}\right)} \]

      2. mul-1-neg 65.5%

         \[\leadsto x + \left(-\frac{\color{blue}{\left(-z\right)} - 27464.7644705 \cdot \frac{1}{y}}{y}\right) \]

      3. associate-*r/ 65.5%

         \[\leadsto x + \left(-\frac{\left(-z\right) - \color{blue}{\frac{27464.7644705 \cdot 1}{y}}}{y}\right) \]

      4. metadata-eval 65.5%

         \[\leadsto x + \left(-\frac{\left(-z\right) - \frac{\color{blue}{27464.7644705}}{y}}{y}\right) \]

   6. Simplified 65.5%

      \[\leadsto \color{blue}{x + \left(-\frac{\left(-z\right) - \frac{27464.7644705}{y}}{y}\right)} \]

   if -1.79999999999999992e24 < y < 3.7999999999999999e49

   1. Initial program 97.0%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 68.7%

      \[\leadsto \color{blue}{\frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}} \]

   if 3.7999999999999999e49 < y

   1. Initial program 2.5%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 2.5%

      \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\color{blue}{{y}^{3}} + c\right) \cdot y + i} \]

   4. Taylor expanded in y around inf 65.4%

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

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+24}:\\ \;\;\;\;x + \frac{z + \frac{27464.7644705}{y}}{y}\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+49}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 68.0% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+20}:\\ \;\;\;\;x + \frac{z + \frac{27464.7644705}{y}}{y}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+49}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -6.5e+20)
   (+ x (/ (+ z (/ 27464.7644705 y)) y))
   (if (<= y 3.2e+49) (/ t (+ i (* y (+ c (* y b))))) (+ x (/ z y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -6.5e+20) {
		tmp = x + ((z + (27464.7644705 / y)) / y);
	} else if (y <= 3.2e+49) {
		tmp = t / (i + (y * (c + (y * b))));
	} else {
		tmp = x + (z / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= (-6.5d+20)) then
        tmp = x + ((z + (27464.7644705d0 / y)) / y)
    else if (y <= 3.2d+49) then
        tmp = t / (i + (y * (c + (y * b))))
    else
        tmp = x + (z / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -6.5e+20) {
		tmp = x + ((z + (27464.7644705 / y)) / y);
	} else if (y <= 3.2e+49) {
		tmp = t / (i + (y * (c + (y * b))));
	} else {
		tmp = x + (z / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -6.5e+20:
		tmp = x + ((z + (27464.7644705 / y)) / y)
	elif y <= 3.2e+49:
		tmp = t / (i + (y * (c + (y * b))))
	else:
		tmp = x + (z / y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -6.5e+20)
		tmp = Float64(x + Float64(Float64(z + Float64(27464.7644705 / y)) / y));
	elseif (y <= 3.2e+49)
		tmp = Float64(t / Float64(i + Float64(y * Float64(c + Float64(y * b)))));
	else
		tmp = Float64(x + Float64(z / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -6.5e+20)
		tmp = x + ((z + (27464.7644705 / y)) / y);
	elseif (y <= 3.2e+49)
		tmp = t / (i + (y * (c + (y * b))));
	else
		tmp = x + (z / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -6.5e+20], N[(x + N[(N[(z + N[(27464.7644705 / y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.2e+49], N[(t / N[(i + N[(y * N[(c + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.5e20

   1. Initial program 7.0%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 6.9%

      \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\color{blue}{{y}^{3}} + c\right) \cdot y + i} \]

   4. Taylor expanded in y around -inf 65.5%

      \[\leadsto \color{blue}{x + -1 \cdot \frac{-1 \cdot z - 27464.7644705 \cdot \frac{1}{y}}{y}} \]
   5. Step-by-step derivation

      1. mul-1-neg 65.5%

         \[\leadsto x + \color{blue}{\left(-\frac{-1 \cdot z - 27464.7644705 \cdot \frac{1}{y}}{y}\right)} \]

      2. mul-1-neg 65.5%

         \[\leadsto x + \left(-\frac{\color{blue}{\left(-z\right)} - 27464.7644705 \cdot \frac{1}{y}}{y}\right) \]

      3. associate-*r/ 65.5%

         \[\leadsto x + \left(-\frac{\left(-z\right) - \color{blue}{\frac{27464.7644705 \cdot 1}{y}}}{y}\right) \]

      4. metadata-eval 65.5%

         \[\leadsto x + \left(-\frac{\left(-z\right) - \frac{\color{blue}{27464.7644705}}{y}}{y}\right) \]

   6. Simplified 65.5%

      \[\leadsto \color{blue}{x + \left(-\frac{\left(-z\right) - \frac{27464.7644705}{y}}{y}\right)} \]

   if -6.5e20 < y < 3.20000000000000014e49

   1. Initial program 97.0%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 92.5%

      \[\leadsto \frac{\left(\color{blue}{y \cdot \left(27464.7644705 + y \cdot z\right)} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   4. Taylor expanded in y around 0 85.7%

      \[\leadsto \frac{\left(y \cdot \left(27464.7644705 + y \cdot z\right) + 230661.510616\right) \cdot y + t}{\left(\color{blue}{b \cdot y} + c\right) \cdot y + i} \]
   5. Step-by-step derivation

      1. *-commutative 85.7%

         \[\leadsto \frac{\left(y \cdot \left(27464.7644705 + y \cdot z\right) + 230661.510616\right) \cdot y + t}{\left(\color{blue}{y \cdot b} + c\right) \cdot y + i} \]

   6. Simplified 85.7%

      \[\leadsto \frac{\left(y \cdot \left(27464.7644705 + y \cdot z\right) + 230661.510616\right) \cdot y + t}{\left(\color{blue}{y \cdot b} + c\right) \cdot y + i} \]

   7. Taylor expanded in t around inf 64.0%

      \[\leadsto \color{blue}{\frac{t}{i + y \cdot \left(c + b \cdot y\right)}} \]

   if 3.20000000000000014e49 < y

   1. Initial program 2.5%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 2.5%

      \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\color{blue}{{y}^{3}} + c\right) \cdot y + i} \]

   4. Taylor expanded in y around inf 65.4%

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

4. Final simplification 64.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+20}:\\ \;\;\;\;x + \frac{z + \frac{27464.7644705}{y}}{y}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+49}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 58.5% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.3 \cdot 10^{+20} \lor \neg \left(y \leq 33000000000000\right):\\ \;\;\;\;x + \frac{z + \frac{27464.7644705}{y}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -4.3e+20) (not (<= y 33000000000000.0)))
   (+ x (/ (+ z (/ 27464.7644705 y)) y))
   (/ t i)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -4.3e+20) || !(y <= 33000000000000.0)) {
		tmp = x + ((z + (27464.7644705 / y)) / y);
	} else {
		tmp = t / i;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-4.3d+20)) .or. (.not. (y <= 33000000000000.0d0))) then
        tmp = x + ((z + (27464.7644705d0 / y)) / y)
    else
        tmp = t / i
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -4.3e+20) || !(y <= 33000000000000.0)) {
		tmp = x + ((z + (27464.7644705 / y)) / y);
	} else {
		tmp = t / i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -4.3e+20) or not (y <= 33000000000000.0):
		tmp = x + ((z + (27464.7644705 / y)) / y)
	else:
		tmp = t / i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -4.3e+20) || !(y <= 33000000000000.0))
		tmp = Float64(x + Float64(Float64(z + Float64(27464.7644705 / y)) / y));
	else
		tmp = Float64(t / i);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -4.3e+20) || ~((y <= 33000000000000.0)))
		tmp = x + ((z + (27464.7644705 / y)) / y);
	else
		tmp = t / i;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -4.3e+20], N[Not[LessEqual[y, 33000000000000.0]], $MachinePrecision]], N[(x + N[(N[(z + N[(27464.7644705 / y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(t / i), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.3e20 or 3.3e13 < y

   1. Initial program 9.1%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 6.6%

      \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\color{blue}{{y}^{3}} + c\right) \cdot y + i} \]

   4. Taylor expanded in y around -inf 62.0%

      \[\leadsto \color{blue}{x + -1 \cdot \frac{-1 \cdot z - 27464.7644705 \cdot \frac{1}{y}}{y}} \]
   5. Step-by-step derivation

      1. mul-1-neg 62.0%

         \[\leadsto x + \color{blue}{\left(-\frac{-1 \cdot z - 27464.7644705 \cdot \frac{1}{y}}{y}\right)} \]

      2. mul-1-neg 62.0%

         \[\leadsto x + \left(-\frac{\color{blue}{\left(-z\right)} - 27464.7644705 \cdot \frac{1}{y}}{y}\right) \]

      3. associate-*r/ 62.0%

         \[\leadsto x + \left(-\frac{\left(-z\right) - \color{blue}{\frac{27464.7644705 \cdot 1}{y}}}{y}\right) \]

      4. metadata-eval 62.0%

         \[\leadsto x + \left(-\frac{\left(-z\right) - \frac{\color{blue}{27464.7644705}}{y}}{y}\right) \]

   6. Simplified 62.0%

      \[\leadsto \color{blue}{x + \left(-\frac{\left(-z\right) - \frac{27464.7644705}{y}}{y}\right)} \]

   if -4.3e20 < y < 3.3e13

   1. Initial program 98.3%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 48.1%

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

4. Final simplification 54.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.3 \cdot 10^{+20} \lor \neg \left(y \leq 33000000000000\right):\\ \;\;\;\;x + \frac{z + \frac{27464.7644705}{y}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 49.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.3:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+15}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{+141}:\\ \;\;\;\;\frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -0.3) x (if (<= y 4e+15) (/ t i) (if (<= y 1.85e+141) (/ z a) x))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -0.3) {
		tmp = x;
	} else if (y <= 4e+15) {
		tmp = t / i;
	} else if (y <= 1.85e+141) {
		tmp = z / a;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= (-0.3d0)) then
        tmp = x
    else if (y <= 4d+15) then
        tmp = t / i
    else if (y <= 1.85d+141) then
        tmp = z / a
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -0.3) {
		tmp = x;
	} else if (y <= 4e+15) {
		tmp = t / i;
	} else if (y <= 1.85e+141) {
		tmp = z / a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -0.3:
		tmp = x
	elif y <= 4e+15:
		tmp = t / i
	elif y <= 1.85e+141:
		tmp = z / a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -0.3)
		tmp = x;
	elseif (y <= 4e+15)
		tmp = Float64(t / i);
	elseif (y <= 1.85e+141)
		tmp = Float64(z / a);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -0.3)
		tmp = x;
	elseif (y <= 4e+15)
		tmp = t / i;
	elseif (y <= 1.85e+141)
		tmp = z / a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -0.3], x, If[LessEqual[y, 4e+15], N[(t / i), $MachinePrecision], If[LessEqual[y, 1.85e+141], N[(z / a), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if y < -0.299999999999999989 or 1.8500000000000001e141 < y

   1. Initial program 10.1%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 49.9%

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

   if -0.299999999999999989 < y < 4e15

   1. Initial program 99.0%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 49.7%

      \[\leadsto \color{blue}{\frac{t}{i}} \]

   if 4e15 < y < 1.8500000000000001e141

   1. Initial program 22.4%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 16.5%

      \[\leadsto \frac{\left(\color{blue}{y \cdot \left(27464.7644705 + y \cdot z\right)} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   4. Taylor expanded in a around inf 7.2%

      \[\leadsto \color{blue}{\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{a \cdot {y}^{3}}} \]

   5. Taylor expanded in y around inf 34.0%

      \[\leadsto \color{blue}{\frac{z}{a}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 48.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.3:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+15}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{+141}:\\ \;\;\;\;\frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 58.2% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+17} \lor \neg \left(y \leq 17000000000000\right):\\ \;\;\;\;x + \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -1.6e+17) (not (<= y 17000000000000.0))) (+ x (/ z y)) (/ t i)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -1.6e+17) || !(y <= 17000000000000.0)) {
		tmp = x + (z / y);
	} else {
		tmp = t / i;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-1.6d+17)) .or. (.not. (y <= 17000000000000.0d0))) then
        tmp = x + (z / y)
    else
        tmp = t / i
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -1.6e+17) || !(y <= 17000000000000.0)) {
		tmp = x + (z / y);
	} else {
		tmp = t / i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -1.6e+17) or not (y <= 17000000000000.0):
		tmp = x + (z / y)
	else:
		tmp = t / i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -1.6e+17) || !(y <= 17000000000000.0))
		tmp = Float64(x + Float64(z / y));
	else
		tmp = Float64(t / i);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -1.6e+17) || ~((y <= 17000000000000.0)))
		tmp = x + (z / y);
	else
		tmp = t / i;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -1.6e+17], N[Not[LessEqual[y, 17000000000000.0]], $MachinePrecision]], N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision], N[(t / i), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.6e17 or 1.7e13 < y

   1. Initial program 9.8%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 7.3%

      \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\color{blue}{{y}^{3}} + c\right) \cdot y + i} \]

   4. Taylor expanded in y around inf 60.6%

      \[\leadsto \color{blue}{x + \frac{z}{y}} \]

   if -1.6e17 < y < 1.7e13

   1. Initial program 98.3%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 48.4%

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

4. Final simplification 54.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+17} \lor \neg \left(y \leq 17000000000000\right):\\ \;\;\;\;x + \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 50.6% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.32:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-34}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -0.32) x (if (<= y 1.05e-34) (/ t i) x)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -0.32) {
		tmp = x;
	} else if (y <= 1.05e-34) {
		tmp = t / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= (-0.32d0)) then
        tmp = x
    else if (y <= 1.05d-34) then
        tmp = t / i
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -0.32) {
		tmp = x;
	} else if (y <= 1.05e-34) {
		tmp = t / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -0.32:
		tmp = x
	elif y <= 1.05e-34:
		tmp = t / i
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -0.32)
		tmp = x;
	elseif (y <= 1.05e-34)
		tmp = Float64(t / i);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -0.32)
		tmp = x;
	elseif (y <= 1.05e-34)
		tmp = t / i;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -0.32], x, If[LessEqual[y, 1.05e-34], N[(t / i), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -0.320000000000000007 or 1.05e-34 < y

   1. Initial program 16.4%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 41.3%

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

   if -0.320000000000000007 < y < 1.05e-34

   1. Initial program 99.7%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 52.7%

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

4. Final simplification 46.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.32:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-34}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 25.4% accurate, 33.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 56.1%

   \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
2. Add Preprocessing

3. Taylor expanded in y around inf 23.2%

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

4. Final simplification 23.2%

   \[\leadsto x \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024055 
(FPCore (x y z t a b c i)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2"
  :precision binary64
  (/ (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)))