Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2

Percentage Accurate: 55.7% → 81.3%

Time: 24.1s

Alternatives: 15

Speedup: 1.9×

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: 55.7% 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: 81.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\frac{27464.7644705}{y \cdot a} + \frac{z}{a}\right) + \frac{x}{\frac{a}{y}}\\ t_2 := c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\\ t_3 := \frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{if}\;y \leq -2.45 \cdot 10^{+95}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -9 \cdot 10^{+42}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -680000000:\\ \;\;\;\;\frac{y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616}{t_2}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+32}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot t_2}\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{+111}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (+ (/ 27464.7644705 (* y a)) (/ z a)) (/ x (/ a y))))
        (t_2 (+ c (* y (+ (* y (+ y a)) b))))
        (t_3 (+ (/ z y) (- x (/ a (/ y x))))))
   (if (<= y -2.45e+95)
     t_3
     (if (<= y -9e+42)
       t_1
       (if (<= y -680000000.0)
         (/ (+ (* y (+ (* y (+ (* x y) z)) 27464.7644705)) 230661.510616) t_2)
         (if (<= y 3.2e+32)
           (/
            (+ t (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y z))))))
            (+ i (* y t_2)))
           (if (<= y 2.15e+111) t_1 t_3)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = ((27464.7644705 / (y * a)) + (z / a)) + (x / (a / y));
	double t_2 = c + (y * ((y * (y + a)) + b));
	double t_3 = (z / y) + (x - (a / (y / x)));
	double tmp;
	if (y <= -2.45e+95) {
		tmp = t_3;
	} else if (y <= -9e+42) {
		tmp = t_1;
	} else if (y <= -680000000.0) {
		tmp = ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616) / t_2;
	} else if (y <= 3.2e+32) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * t_2));
	} else if (y <= 2.15e+111) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	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 = ((27464.7644705d0 / (y * a)) + (z / a)) + (x / (a / y))
    t_2 = c + (y * ((y * (y + a)) + b))
    t_3 = (z / y) + (x - (a / (y / x)))
    if (y <= (-2.45d+95)) then
        tmp = t_3
    else if (y <= (-9d+42)) then
        tmp = t_1
    else if (y <= (-680000000.0d0)) then
        tmp = ((y * ((y * ((x * y) + z)) + 27464.7644705d0)) + 230661.510616d0) / t_2
    else if (y <= 3.2d+32) then
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * z)))))) / (i + (y * t_2))
    else if (y <= 2.15d+111) then
        tmp = t_1
    else
        tmp = t_3
    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 = ((27464.7644705 / (y * a)) + (z / a)) + (x / (a / y));
	double t_2 = c + (y * ((y * (y + a)) + b));
	double t_3 = (z / y) + (x - (a / (y / x)));
	double tmp;
	if (y <= -2.45e+95) {
		tmp = t_3;
	} else if (y <= -9e+42) {
		tmp = t_1;
	} else if (y <= -680000000.0) {
		tmp = ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616) / t_2;
	} else if (y <= 3.2e+32) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * t_2));
	} else if (y <= 2.15e+111) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = ((27464.7644705 / (y * a)) + (z / a)) + (x / (a / y))
	t_2 = c + (y * ((y * (y + a)) + b))
	t_3 = (z / y) + (x - (a / (y / x)))
	tmp = 0
	if y <= -2.45e+95:
		tmp = t_3
	elif y <= -9e+42:
		tmp = t_1
	elif y <= -680000000.0:
		tmp = ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616) / t_2
	elif y <= 3.2e+32:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * t_2))
	elif y <= 2.15e+111:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(Float64(27464.7644705 / Float64(y * a)) + Float64(z / a)) + Float64(x / Float64(a / y)))
	t_2 = Float64(c + Float64(y * Float64(Float64(y * Float64(y + a)) + b)))
	t_3 = Float64(Float64(z / y) + Float64(x - Float64(a / Float64(y / x))))
	tmp = 0.0
	if (y <= -2.45e+95)
		tmp = t_3;
	elseif (y <= -9e+42)
		tmp = t_1;
	elseif (y <= -680000000.0)
		tmp = Float64(Float64(Float64(y * Float64(Float64(y * Float64(Float64(x * y) + z)) + 27464.7644705)) + 230661.510616) / t_2);
	elseif (y <= 3.2e+32)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * z)))))) / Float64(i + Float64(y * t_2)));
	elseif (y <= 2.15e+111)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = ((27464.7644705 / (y * a)) + (z / a)) + (x / (a / y));
	t_2 = c + (y * ((y * (y + a)) + b));
	t_3 = (z / y) + (x - (a / (y / x)));
	tmp = 0.0;
	if (y <= -2.45e+95)
		tmp = t_3;
	elseif (y <= -9e+42)
		tmp = t_1;
	elseif (y <= -680000000.0)
		tmp = ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616) / t_2;
	elseif (y <= 3.2e+32)
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * t_2));
	elseif (y <= 2.15e+111)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(N[(27464.7644705 / N[(y * a), $MachinePrecision]), $MachinePrecision] + N[(z / a), $MachinePrecision]), $MachinePrecision] + N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c + N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(z / y), $MachinePrecision] + N[(x - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.45e+95], t$95$3, If[LessEqual[y, -9e+42], t$95$1, If[LessEqual[y, -680000000.0], N[(N[(N[(y * N[(N[(y * N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] + 27464.7644705), $MachinePrecision]), $MachinePrecision] + 230661.510616), $MachinePrecision] / t$95$2), $MachinePrecision], If[LessEqual[y, 3.2e+32], 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 * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.15e+111], t$95$1, t$95$3]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.4499999999999999e95 or 2.14999999999999997e111 < y

   1. Initial program 1.2%

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

   2. Taylor expanded in y around inf 76.3%

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

      1. +-commutative 76.3%

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

      2. associate--l+ 76.3%

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

      3. associate-/l* 78.8%

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

   4. Simplified 78.8%

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

   if -2.4499999999999999e95 < y < -9.00000000000000025e42 or 3.1999999999999999e32 < y < 2.14999999999999997e111

   1. Initial program 15.0%

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

   2. Taylor expanded in a around inf 3.5%

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

   3. Taylor expanded in y around inf 47.8%

      \[\leadsto \color{blue}{27464.7644705 \cdot \frac{1}{a \cdot y} + \left(\frac{z}{a} + \frac{x \cdot y}{a}\right)} \]
   4. Step-by-step derivation

      1. associate-+r+ 47.8%

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

      2. associate-*r/ 47.8%

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

      3. metadata-eval 47.8%

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

      4. *-commutative 47.8%

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

      5. associate-/l* 54.0%

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

   5. Simplified 54.0%

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

   if -9.00000000000000025e42 < y < -6.8e8

   1. Initial program 74.5%

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

   2. Taylor expanded in t around 0 74.5%

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

   3. Taylor expanded in i around 0 75.9%

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

   if -6.8e8 < y < 3.1999999999999999e32

   1. Initial program 97.5%

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

   2. Taylor expanded in x around 0 93.3%

      \[\leadsto \frac{\left(\color{blue}{y \cdot \left(27464.7644705 + y \cdot z\right)} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
3. Recombined 4 regimes into one program.

4. Final simplification 83.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.45 \cdot 10^{+95}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq -9 \cdot 10^{+42}:\\ \;\;\;\;\left(\frac{27464.7644705}{y \cdot a} + \frac{z}{a}\right) + \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;y \leq -680000000:\\ \;\;\;\;\frac{y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616}{c + y \cdot \left(y \cdot \left(y + a\right) + b\right)}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+32}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)}\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{+111}:\\ \;\;\;\;\left(\frac{27464.7644705}{y \cdot a} + \frac{z}{a}\right) + \frac{x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]

Alternative 2: 83.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)\\ t_2 := y \cdot \left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616\right)\\ \mathbf{if}\;\frac{t_2 + t}{t_1} \leq 10^{+285}:\\ \;\;\;\;\frac{t}{t_1} + \frac{t_2}{t_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ i (* y (+ c (* y (+ (* y (+ y a)) b))))))
        (t_2
         (* y (+ (* y (+ (* y (+ (* x y) z)) 27464.7644705)) 230661.510616))))
   (if (<= (/ (+ t_2 t) t_1) 1e+285)
     (+ (/ t t_1) (/ t_2 t_1))
     (+ (/ z y) (- x (/ a (/ y x)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = i + (y * (c + (y * ((y * (y + a)) + b))));
	double t_2 = y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616);
	double tmp;
	if (((t_2 + t) / t_1) <= 1e+285) {
		tmp = (t / t_1) + (t_2 / t_1);
	} else {
		tmp = (z / y) + (x - (a / (y / 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = i + (y * (c + (y * ((y * (y + a)) + b))))
    t_2 = y * ((y * ((y * ((x * y) + z)) + 27464.7644705d0)) + 230661.510616d0)
    if (((t_2 + t) / t_1) <= 1d+285) then
        tmp = (t / t_1) + (t_2 / t_1)
    else
        tmp = (z / y) + (x - (a / (y / 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 t_1 = i + (y * (c + (y * ((y * (y + a)) + b))));
	double t_2 = y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616);
	double tmp;
	if (((t_2 + t) / t_1) <= 1e+285) {
		tmp = (t / t_1) + (t_2 / t_1);
	} else {
		tmp = (z / y) + (x - (a / (y / x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = i + (y * (c + (y * ((y * (y + a)) + b))))
	t_2 = y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616)
	tmp = 0
	if ((t_2 + t) / t_1) <= 1e+285:
		tmp = (t / t_1) + (t_2 / t_1)
	else:
		tmp = (z / y) + (x - (a / (y / x)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(i + Float64(y * Float64(c + Float64(y * Float64(Float64(y * Float64(y + a)) + b)))))
	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) <= 1e+285)
		tmp = Float64(Float64(t / t_1) + Float64(t_2 / t_1));
	else
		tmp = Float64(Float64(z / y) + Float64(x - Float64(a / Float64(y / x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = i + (y * (c + (y * ((y * (y + a)) + b))));
	t_2 = y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616);
	tmp = 0.0;
	if (((t_2 + t) / t_1) <= 1e+285)
		tmp = (t / t_1) + (t_2 / t_1);
	else
		tmp = (z / y) + (x - (a / (y / x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(i + N[(y * N[(c + N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision]), $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], 1e+285], N[(N[(t / t$95$1), $MachinePrecision] + N[(t$95$2 / t$95$1), $MachinePrecision]), $MachinePrecision], N[(N[(z / y), $MachinePrecision] + N[(x - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $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)) < 9.9999999999999998e284

   1. Initial program 93.4%

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

   2. Taylor expanded in t around 0 93.5%

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

   if 9.9999999999999998e284 < (/.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 2.1%

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

   2. Taylor expanded in y around inf 62.5%

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

      1. +-commutative 62.5%

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

      2. associate--l+ 62.5%

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

      3. associate-/l* 65.4%

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

   4. Simplified 65.4%

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

4. Final simplification 82.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616\right) + t}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)} \leq 10^{+285}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)} + \frac{y \cdot \left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616\right)}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]

Alternative 3: 83.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot \left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616\right) + t}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)}\\ \mathbf{if}\;t_1 \leq 10^{+285}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \end{array} \]

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 (+ c (* y (+ (* y (+ y a)) b))))))))
   (if (<= t_1 1e+285) t_1 (+ (/ z y) (- x (/ a (/ y x)))))))

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 * (c + (y * ((y * (y + a)) + b)))));
	double tmp;
	if (t_1 <= 1e+285) {
		tmp = t_1;
	} else {
		tmp = (z / y) + (x - (a / (y / 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) :: t_1
    real(8) :: tmp
    t_1 = ((y * ((y * ((y * ((x * y) + z)) + 27464.7644705d0)) + 230661.510616d0)) + t) / (i + (y * (c + (y * ((y * (y + a)) + b)))))
    if (t_1 <= 1d+285) then
        tmp = t_1
    else
        tmp = (z / y) + (x - (a / (y / 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 t_1 = ((y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616)) + t) / (i + (y * (c + (y * ((y * (y + a)) + b)))));
	double tmp;
	if (t_1 <= 1e+285) {
		tmp = t_1;
	} else {
		tmp = (z / y) + (x - (a / (y / x)));
	}
	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 * (c + (y * ((y * (y + a)) + b)))))
	tmp = 0
	if t_1 <= 1e+285:
		tmp = t_1
	else:
		tmp = (z / y) + (x - (a / (y / x)))
	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(c + Float64(y * Float64(Float64(y * Float64(y + a)) + b))))))
	tmp = 0.0
	if (t_1 <= 1e+285)
		tmp = t_1;
	else
		tmp = Float64(Float64(z / y) + Float64(x - Float64(a / Float64(y / x))));
	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 * (c + (y * ((y * (y + a)) + b)))));
	tmp = 0.0;
	if (t_1 <= 1e+285)
		tmp = t_1;
	else
		tmp = (z / y) + (x - (a / (y / x)));
	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[(c + N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 1e+285], t$95$1, N[(N[(z / y), $MachinePrecision] + N[(x - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $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)) < 9.9999999999999998e284

   1. Initial program 93.4%

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

   if 9.9999999999999998e284 < (/.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 2.1%

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

   2. Taylor expanded in y around inf 62.5%

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

      1. +-commutative 62.5%

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

      2. associate--l+ 62.5%

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

      3. associate-/l* 65.4%

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

   4. Simplified 65.4%

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

4. Final simplification 82.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616\right) + t}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)} \leq 10^{+285}:\\ \;\;\;\;\frac{y \cdot \left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616\right) + t}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]

Alternative 4: 77.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(y \cdot \left(y + a\right) + b\right)\\ t_2 := c + t_1\\ t_3 := i + y \cdot t_2\\ t_4 := \frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ t_5 := \frac{x}{\frac{a}{y}}\\ t_6 := \left(\frac{27464.7644705}{y \cdot a} + \frac{z}{a}\right) + t_5\\ \mathbf{if}\;y \leq -1.8 \cdot 10^{+95}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{+38}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;y \leq -7800000000000:\\ \;\;\;\;\frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)}{t_2}\\ \mathbf{elif}\;y \leq -17000000:\\ \;\;\;\;t_5\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-11}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{t_3}\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+31}:\\ \;\;\;\;\frac{y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616}{t_1}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+31}:\\ \;\;\;\;\frac{t}{t_3}\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{+113}:\\ \;\;\;\;t_6\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* y (+ (* y (+ y a)) b)))
        (t_2 (+ c t_1))
        (t_3 (+ i (* y t_2)))
        (t_4 (+ (/ z y) (- x (/ a (/ y x)))))
        (t_5 (/ x (/ a y)))
        (t_6 (+ (+ (/ 27464.7644705 (* y a)) (/ z a)) t_5)))
   (if (<= y -1.8e+95)
     t_4
     (if (<= y -5.2e+38)
       t_6
       (if (<= y -7800000000000.0)
         (/ (+ 230661.510616 (* y (+ 27464.7644705 (* y z)))) t_2)
         (if (<= y -17000000.0)
           t_5
           (if (<= y 1.05e-11)
             (/ (+ t (* y 230661.510616)) t_3)
             (if (<= y 3.1e+31)
               (/
                (+ (* y (+ (* y (+ (* x y) z)) 27464.7644705)) 230661.510616)
                t_1)
               (if (<= y 3.2e+31)
                 (/ t t_3)
                 (if (<= y 5.8e+113) t_6 t_4))))))))))

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);
	double t_2 = c + t_1;
	double t_3 = i + (y * t_2);
	double t_4 = (z / y) + (x - (a / (y / x)));
	double t_5 = x / (a / y);
	double t_6 = ((27464.7644705 / (y * a)) + (z / a)) + t_5;
	double tmp;
	if (y <= -1.8e+95) {
		tmp = t_4;
	} else if (y <= -5.2e+38) {
		tmp = t_6;
	} else if (y <= -7800000000000.0) {
		tmp = (230661.510616 + (y * (27464.7644705 + (y * z)))) / t_2;
	} else if (y <= -17000000.0) {
		tmp = t_5;
	} else if (y <= 1.05e-11) {
		tmp = (t + (y * 230661.510616)) / t_3;
	} else if (y <= 3.1e+31) {
		tmp = ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616) / t_1;
	} else if (y <= 3.2e+31) {
		tmp = t / t_3;
	} else if (y <= 5.8e+113) {
		tmp = t_6;
	} else {
		tmp = t_4;
	}
	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) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: tmp
    t_1 = y * ((y * (y + a)) + b)
    t_2 = c + t_1
    t_3 = i + (y * t_2)
    t_4 = (z / y) + (x - (a / (y / x)))
    t_5 = x / (a / y)
    t_6 = ((27464.7644705d0 / (y * a)) + (z / a)) + t_5
    if (y <= (-1.8d+95)) then
        tmp = t_4
    else if (y <= (-5.2d+38)) then
        tmp = t_6
    else if (y <= (-7800000000000.0d0)) then
        tmp = (230661.510616d0 + (y * (27464.7644705d0 + (y * z)))) / t_2
    else if (y <= (-17000000.0d0)) then
        tmp = t_5
    else if (y <= 1.05d-11) then
        tmp = (t + (y * 230661.510616d0)) / t_3
    else if (y <= 3.1d+31) then
        tmp = ((y * ((y * ((x * y) + z)) + 27464.7644705d0)) + 230661.510616d0) / t_1
    else if (y <= 3.2d+31) then
        tmp = t / t_3
    else if (y <= 5.8d+113) then
        tmp = t_6
    else
        tmp = t_4
    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);
	double t_2 = c + t_1;
	double t_3 = i + (y * t_2);
	double t_4 = (z / y) + (x - (a / (y / x)));
	double t_5 = x / (a / y);
	double t_6 = ((27464.7644705 / (y * a)) + (z / a)) + t_5;
	double tmp;
	if (y <= -1.8e+95) {
		tmp = t_4;
	} else if (y <= -5.2e+38) {
		tmp = t_6;
	} else if (y <= -7800000000000.0) {
		tmp = (230661.510616 + (y * (27464.7644705 + (y * z)))) / t_2;
	} else if (y <= -17000000.0) {
		tmp = t_5;
	} else if (y <= 1.05e-11) {
		tmp = (t + (y * 230661.510616)) / t_3;
	} else if (y <= 3.1e+31) {
		tmp = ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616) / t_1;
	} else if (y <= 3.2e+31) {
		tmp = t / t_3;
	} else if (y <= 5.8e+113) {
		tmp = t_6;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = y * ((y * (y + a)) + b)
	t_2 = c + t_1
	t_3 = i + (y * t_2)
	t_4 = (z / y) + (x - (a / (y / x)))
	t_5 = x / (a / y)
	t_6 = ((27464.7644705 / (y * a)) + (z / a)) + t_5
	tmp = 0
	if y <= -1.8e+95:
		tmp = t_4
	elif y <= -5.2e+38:
		tmp = t_6
	elif y <= -7800000000000.0:
		tmp = (230661.510616 + (y * (27464.7644705 + (y * z)))) / t_2
	elif y <= -17000000.0:
		tmp = t_5
	elif y <= 1.05e-11:
		tmp = (t + (y * 230661.510616)) / t_3
	elif y <= 3.1e+31:
		tmp = ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616) / t_1
	elif y <= 3.2e+31:
		tmp = t / t_3
	elif y <= 5.8e+113:
		tmp = t_6
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(y * Float64(Float64(y * Float64(y + a)) + b))
	t_2 = Float64(c + t_1)
	t_3 = Float64(i + Float64(y * t_2))
	t_4 = Float64(Float64(z / y) + Float64(x - Float64(a / Float64(y / x))))
	t_5 = Float64(x / Float64(a / y))
	t_6 = Float64(Float64(Float64(27464.7644705 / Float64(y * a)) + Float64(z / a)) + t_5)
	tmp = 0.0
	if (y <= -1.8e+95)
		tmp = t_4;
	elseif (y <= -5.2e+38)
		tmp = t_6;
	elseif (y <= -7800000000000.0)
		tmp = Float64(Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * z)))) / t_2);
	elseif (y <= -17000000.0)
		tmp = t_5;
	elseif (y <= 1.05e-11)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / t_3);
	elseif (y <= 3.1e+31)
		tmp = Float64(Float64(Float64(y * Float64(Float64(y * Float64(Float64(x * y) + z)) + 27464.7644705)) + 230661.510616) / t_1);
	elseif (y <= 3.2e+31)
		tmp = Float64(t / t_3);
	elseif (y <= 5.8e+113)
		tmp = t_6;
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = y * ((y * (y + a)) + b);
	t_2 = c + t_1;
	t_3 = i + (y * t_2);
	t_4 = (z / y) + (x - (a / (y / x)));
	t_5 = x / (a / y);
	t_6 = ((27464.7644705 / (y * a)) + (z / a)) + t_5;
	tmp = 0.0;
	if (y <= -1.8e+95)
		tmp = t_4;
	elseif (y <= -5.2e+38)
		tmp = t_6;
	elseif (y <= -7800000000000.0)
		tmp = (230661.510616 + (y * (27464.7644705 + (y * z)))) / t_2;
	elseif (y <= -17000000.0)
		tmp = t_5;
	elseif (y <= 1.05e-11)
		tmp = (t + (y * 230661.510616)) / t_3;
	elseif (y <= 3.1e+31)
		tmp = ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616) / t_1;
	elseif (y <= 3.2e+31)
		tmp = t / t_3;
	elseif (y <= 5.8e+113)
		tmp = t_6;
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c + t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(i + N[(y * t$95$2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(z / y), $MachinePrecision] + N[(x - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(N[(27464.7644705 / N[(y * a), $MachinePrecision]), $MachinePrecision] + N[(z / a), $MachinePrecision]), $MachinePrecision] + t$95$5), $MachinePrecision]}, If[LessEqual[y, -1.8e+95], t$95$4, If[LessEqual[y, -5.2e+38], t$95$6, If[LessEqual[y, -7800000000000.0], N[(N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision], If[LessEqual[y, -17000000.0], t$95$5, If[LessEqual[y, 1.05e-11], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / t$95$3), $MachinePrecision], If[LessEqual[y, 3.1e+31], N[(N[(N[(y * N[(N[(y * N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] + 27464.7644705), $MachinePrecision]), $MachinePrecision] + 230661.510616), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[y, 3.2e+31], N[(t / t$95$3), $MachinePrecision], If[LessEqual[y, 5.8e+113], t$95$6, t$95$4]]]]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y < -1.79999999999999989e95 or 5.79999999999999968e113 < y

   1. Initial program 1.2%

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

   2. Taylor expanded in y around inf 76.3%

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

      1. +-commutative 76.3%

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

      2. associate--l+ 76.3%

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

      3. associate-/l* 78.8%

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

   4. Simplified 78.8%

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

   if -1.79999999999999989e95 < y < -5.1999999999999998e38 or 3.2000000000000001e31 < y < 5.79999999999999968e113

   1. Initial program 14.2%

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

   2. Taylor expanded in a around inf 3.5%

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

   3. Taylor expanded in y around inf 45.2%

      \[\leadsto \color{blue}{27464.7644705 \cdot \frac{1}{a \cdot y} + \left(\frac{z}{a} + \frac{x \cdot y}{a}\right)} \]
   4. Step-by-step derivation

      1. associate-+r+ 45.2%

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

      2. associate-*r/ 45.2%

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

      3. metadata-eval 45.2%

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

      4. *-commutative 45.2%

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

      5. associate-/l* 51.0%

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

   5. Simplified 51.0%

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

   if -5.1999999999999998e38 < y < -7.8e12

   1. Initial program 98.8%

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

   2. Taylor expanded in t around 0 98.8%

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

   3. Taylor expanded in i around 0 99.1%

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

   4. Taylor expanded in x around 0 99.1%

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

   if -7.8e12 < y < -1.7e7

   1. Initial program 98.4%

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

   2. Taylor expanded in a around inf 98.4%

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

   3. Taylor expanded in y around inf 98.4%

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

      1. associate-/l* 100.0%

         \[\leadsto \color{blue}{\frac{x}{\frac{a}{y}}} \]

   5. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{x}{\frac{a}{y}}} \]

   if -1.7e7 < y < 1.0499999999999999e-11

   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. Taylor expanded in y around 0 89.3%

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

      1. *-commutative 89.3%

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

   4. Simplified 89.3%

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

   if 1.0499999999999999e-11 < y < 3.1000000000000002e31

   1. Initial program 63.4%

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

   2. Taylor expanded in t around 0 55.3%

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

   3. Taylor expanded in i around 0 63.4%

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

   4. Taylor expanded in c around 0 63.0%

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

   if 3.1000000000000002e31 < y < 3.2000000000000001e31

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 100.0%

      \[\leadsto \color{blue}{\frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}} \]
3. Recombined 7 regimes into one program.

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+95}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{+38}:\\ \;\;\;\;\left(\frac{27464.7644705}{y \cdot a} + \frac{z}{a}\right) + \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;y \leq -7800000000000:\\ \;\;\;\;\frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)}{c + y \cdot \left(y \cdot \left(y + a\right) + b\right)}\\ \mathbf{elif}\;y \leq -17000000:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-11}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)}\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+31}:\\ \;\;\;\;\frac{y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616}{y \cdot \left(y \cdot \left(y + a\right) + b\right)}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+31}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)}\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{+113}:\\ \;\;\;\;\left(\frac{27464.7644705}{y \cdot a} + \frac{z}{a}\right) + \frac{x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]

Alternative 5: 78.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\frac{27464.7644705}{y \cdot a} + \frac{z}{a}\right) + \frac{x}{\frac{a}{y}}\\ t_2 := c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\\ t_3 := \frac{y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616}{t_2}\\ t_4 := i + y \cdot t_2\\ t_5 := \frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{if}\;y \leq -7.5 \cdot 10^{+95}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;y \leq -7 \cdot 10^{+42}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -96:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{-11}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{t_4}\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+31}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 3.25 \cdot 10^{+31}:\\ \;\;\;\;\frac{t}{t_4}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+117}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (+ (/ 27464.7644705 (* y a)) (/ z a)) (/ x (/ a y))))
        (t_2 (+ c (* y (+ (* y (+ y a)) b))))
        (t_3
         (/ (+ (* y (+ (* y (+ (* x y) z)) 27464.7644705)) 230661.510616) t_2))
        (t_4 (+ i (* y t_2)))
        (t_5 (+ (/ z y) (- x (/ a (/ y x))))))
   (if (<= y -7.5e+95)
     t_5
     (if (<= y -7e+42)
       t_1
       (if (<= y -96.0)
         t_3
         (if (<= y 4.7e-11)
           (/ (+ t (* y 230661.510616)) t_4)
           (if (<= y 3.1e+31)
             t_3
             (if (<= y 3.25e+31) (/ t t_4) (if (<= y 2.5e+117) t_1 t_5)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = ((27464.7644705 / (y * a)) + (z / a)) + (x / (a / y));
	double t_2 = c + (y * ((y * (y + a)) + b));
	double t_3 = ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616) / t_2;
	double t_4 = i + (y * t_2);
	double t_5 = (z / y) + (x - (a / (y / x)));
	double tmp;
	if (y <= -7.5e+95) {
		tmp = t_5;
	} else if (y <= -7e+42) {
		tmp = t_1;
	} else if (y <= -96.0) {
		tmp = t_3;
	} else if (y <= 4.7e-11) {
		tmp = (t + (y * 230661.510616)) / t_4;
	} else if (y <= 3.1e+31) {
		tmp = t_3;
	} else if (y <= 3.25e+31) {
		tmp = t / t_4;
	} else if (y <= 2.5e+117) {
		tmp = t_1;
	} else {
		tmp = t_5;
	}
	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) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_1 = ((27464.7644705d0 / (y * a)) + (z / a)) + (x / (a / y))
    t_2 = c + (y * ((y * (y + a)) + b))
    t_3 = ((y * ((y * ((x * y) + z)) + 27464.7644705d0)) + 230661.510616d0) / t_2
    t_4 = i + (y * t_2)
    t_5 = (z / y) + (x - (a / (y / x)))
    if (y <= (-7.5d+95)) then
        tmp = t_5
    else if (y <= (-7d+42)) then
        tmp = t_1
    else if (y <= (-96.0d0)) then
        tmp = t_3
    else if (y <= 4.7d-11) then
        tmp = (t + (y * 230661.510616d0)) / t_4
    else if (y <= 3.1d+31) then
        tmp = t_3
    else if (y <= 3.25d+31) then
        tmp = t / t_4
    else if (y <= 2.5d+117) then
        tmp = t_1
    else
        tmp = t_5
    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 = ((27464.7644705 / (y * a)) + (z / a)) + (x / (a / y));
	double t_2 = c + (y * ((y * (y + a)) + b));
	double t_3 = ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616) / t_2;
	double t_4 = i + (y * t_2);
	double t_5 = (z / y) + (x - (a / (y / x)));
	double tmp;
	if (y <= -7.5e+95) {
		tmp = t_5;
	} else if (y <= -7e+42) {
		tmp = t_1;
	} else if (y <= -96.0) {
		tmp = t_3;
	} else if (y <= 4.7e-11) {
		tmp = (t + (y * 230661.510616)) / t_4;
	} else if (y <= 3.1e+31) {
		tmp = t_3;
	} else if (y <= 3.25e+31) {
		tmp = t / t_4;
	} else if (y <= 2.5e+117) {
		tmp = t_1;
	} else {
		tmp = t_5;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = ((27464.7644705 / (y * a)) + (z / a)) + (x / (a / y))
	t_2 = c + (y * ((y * (y + a)) + b))
	t_3 = ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616) / t_2
	t_4 = i + (y * t_2)
	t_5 = (z / y) + (x - (a / (y / x)))
	tmp = 0
	if y <= -7.5e+95:
		tmp = t_5
	elif y <= -7e+42:
		tmp = t_1
	elif y <= -96.0:
		tmp = t_3
	elif y <= 4.7e-11:
		tmp = (t + (y * 230661.510616)) / t_4
	elif y <= 3.1e+31:
		tmp = t_3
	elif y <= 3.25e+31:
		tmp = t / t_4
	elif y <= 2.5e+117:
		tmp = t_1
	else:
		tmp = t_5
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(Float64(27464.7644705 / Float64(y * a)) + Float64(z / a)) + Float64(x / Float64(a / y)))
	t_2 = Float64(c + Float64(y * Float64(Float64(y * Float64(y + a)) + b)))
	t_3 = Float64(Float64(Float64(y * Float64(Float64(y * Float64(Float64(x * y) + z)) + 27464.7644705)) + 230661.510616) / t_2)
	t_4 = Float64(i + Float64(y * t_2))
	t_5 = Float64(Float64(z / y) + Float64(x - Float64(a / Float64(y / x))))
	tmp = 0.0
	if (y <= -7.5e+95)
		tmp = t_5;
	elseif (y <= -7e+42)
		tmp = t_1;
	elseif (y <= -96.0)
		tmp = t_3;
	elseif (y <= 4.7e-11)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / t_4);
	elseif (y <= 3.1e+31)
		tmp = t_3;
	elseif (y <= 3.25e+31)
		tmp = Float64(t / t_4);
	elseif (y <= 2.5e+117)
		tmp = t_1;
	else
		tmp = t_5;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = ((27464.7644705 / (y * a)) + (z / a)) + (x / (a / y));
	t_2 = c + (y * ((y * (y + a)) + b));
	t_3 = ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616) / t_2;
	t_4 = i + (y * t_2);
	t_5 = (z / y) + (x - (a / (y / x)));
	tmp = 0.0;
	if (y <= -7.5e+95)
		tmp = t_5;
	elseif (y <= -7e+42)
		tmp = t_1;
	elseif (y <= -96.0)
		tmp = t_3;
	elseif (y <= 4.7e-11)
		tmp = (t + (y * 230661.510616)) / t_4;
	elseif (y <= 3.1e+31)
		tmp = t_3;
	elseif (y <= 3.25e+31)
		tmp = t / t_4;
	elseif (y <= 2.5e+117)
		tmp = t_1;
	else
		tmp = t_5;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(N[(27464.7644705 / N[(y * a), $MachinePrecision]), $MachinePrecision] + N[(z / a), $MachinePrecision]), $MachinePrecision] + N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c + N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(y * N[(N[(y * N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] + 27464.7644705), $MachinePrecision]), $MachinePrecision] + 230661.510616), $MachinePrecision] / t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(i + N[(y * t$95$2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(z / y), $MachinePrecision] + N[(x - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7.5e+95], t$95$5, If[LessEqual[y, -7e+42], t$95$1, If[LessEqual[y, -96.0], t$95$3, If[LessEqual[y, 4.7e-11], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / t$95$4), $MachinePrecision], If[LessEqual[y, 3.1e+31], t$95$3, If[LessEqual[y, 3.25e+31], N[(t / t$95$4), $MachinePrecision], If[LessEqual[y, 2.5e+117], t$95$1, t$95$5]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -7.5000000000000001e95 or 2.49999999999999992e117 < y

   1. Initial program 1.2%

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

   2. Taylor expanded in y around inf 76.3%

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

      1. +-commutative 76.3%

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

      2. associate--l+ 76.3%

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

      3. associate-/l* 78.8%

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

   4. Simplified 78.8%

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

   if -7.5000000000000001e95 < y < -7.00000000000000047e42 or 3.2500000000000002e31 < y < 2.49999999999999992e117

   1. Initial program 15.0%

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

   2. Taylor expanded in a around inf 3.5%

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

   3. Taylor expanded in y around inf 47.8%

      \[\leadsto \color{blue}{27464.7644705 \cdot \frac{1}{a \cdot y} + \left(\frac{z}{a} + \frac{x \cdot y}{a}\right)} \]
   4. Step-by-step derivation

      1. associate-+r+ 47.8%

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

      2. associate-*r/ 47.8%

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

      3. metadata-eval 47.8%

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

      4. *-commutative 47.8%

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

      5. associate-/l* 54.0%

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

   5. Simplified 54.0%

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

   if -7.00000000000000047e42 < y < -96 or 4.69999999999999993e-11 < y < 3.1000000000000002e31

   1. Initial program 69.0%

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

   2. Taylor expanded in t around 0 64.9%

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

   3. Taylor expanded in i around 0 69.7%

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

   if -96 < y < 4.69999999999999993e-11

   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. Taylor expanded in y around 0 89.3%

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

      1. *-commutative 89.3%

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

   4. Simplified 89.3%

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

   if 3.1000000000000002e31 < y < 3.2500000000000002e31

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 100.0%

      \[\leadsto \color{blue}{\frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+95}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq -7 \cdot 10^{+42}:\\ \;\;\;\;\left(\frac{27464.7644705}{y \cdot a} + \frac{z}{a}\right) + \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;y \leq -96:\\ \;\;\;\;\frac{y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616}{c + y \cdot \left(y \cdot \left(y + a\right) + b\right)}\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{-11}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)}\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+31}:\\ \;\;\;\;\frac{y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616}{c + y \cdot \left(y \cdot \left(y + a\right) + b\right)}\\ \mathbf{elif}\;y \leq 3.25 \cdot 10^{+31}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+117}:\\ \;\;\;\;\left(\frac{27464.7644705}{y \cdot a} + \frac{z}{a}\right) + \frac{x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]

Alternative 6: 77.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\frac{27464.7644705}{y \cdot a} + \frac{z}{a}\right) + \frac{x}{\frac{a}{y}}\\ t_2 := c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\\ t_3 := \frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{if}\;y \leq -4.2 \cdot 10^{+95}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -7 \cdot 10^{+42}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -460000000000:\\ \;\;\;\;\frac{y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616}{t_2}\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+32}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{i + y \cdot t_2}\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+114}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (+ (/ 27464.7644705 (* y a)) (/ z a)) (/ x (/ a y))))
        (t_2 (+ c (* y (+ (* y (+ y a)) b))))
        (t_3 (+ (/ z y) (- x (/ a (/ y x))))))
   (if (<= y -4.2e+95)
     t_3
     (if (<= y -7e+42)
       t_1
       (if (<= y -460000000000.0)
         (/ (+ (* y (+ (* y (+ (* x y) z)) 27464.7644705)) 230661.510616) t_2)
         (if (<= y 2.3e+32)
           (/
            (+ t (* y (+ 230661.510616 (* y 27464.7644705))))
            (+ i (* y t_2)))
           (if (<= y 2.2e+114) t_1 t_3)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = ((27464.7644705 / (y * a)) + (z / a)) + (x / (a / y));
	double t_2 = c + (y * ((y * (y + a)) + b));
	double t_3 = (z / y) + (x - (a / (y / x)));
	double tmp;
	if (y <= -4.2e+95) {
		tmp = t_3;
	} else if (y <= -7e+42) {
		tmp = t_1;
	} else if (y <= -460000000000.0) {
		tmp = ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616) / t_2;
	} else if (y <= 2.3e+32) {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * t_2));
	} else if (y <= 2.2e+114) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	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 = ((27464.7644705d0 / (y * a)) + (z / a)) + (x / (a / y))
    t_2 = c + (y * ((y * (y + a)) + b))
    t_3 = (z / y) + (x - (a / (y / x)))
    if (y <= (-4.2d+95)) then
        tmp = t_3
    else if (y <= (-7d+42)) then
        tmp = t_1
    else if (y <= (-460000000000.0d0)) then
        tmp = ((y * ((y * ((x * y) + z)) + 27464.7644705d0)) + 230661.510616d0) / t_2
    else if (y <= 2.3d+32) then
        tmp = (t + (y * (230661.510616d0 + (y * 27464.7644705d0)))) / (i + (y * t_2))
    else if (y <= 2.2d+114) then
        tmp = t_1
    else
        tmp = t_3
    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 = ((27464.7644705 / (y * a)) + (z / a)) + (x / (a / y));
	double t_2 = c + (y * ((y * (y + a)) + b));
	double t_3 = (z / y) + (x - (a / (y / x)));
	double tmp;
	if (y <= -4.2e+95) {
		tmp = t_3;
	} else if (y <= -7e+42) {
		tmp = t_1;
	} else if (y <= -460000000000.0) {
		tmp = ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616) / t_2;
	} else if (y <= 2.3e+32) {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * t_2));
	} else if (y <= 2.2e+114) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = ((27464.7644705 / (y * a)) + (z / a)) + (x / (a / y))
	t_2 = c + (y * ((y * (y + a)) + b))
	t_3 = (z / y) + (x - (a / (y / x)))
	tmp = 0
	if y <= -4.2e+95:
		tmp = t_3
	elif y <= -7e+42:
		tmp = t_1
	elif y <= -460000000000.0:
		tmp = ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616) / t_2
	elif y <= 2.3e+32:
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * t_2))
	elif y <= 2.2e+114:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(Float64(27464.7644705 / Float64(y * a)) + Float64(z / a)) + Float64(x / Float64(a / y)))
	t_2 = Float64(c + Float64(y * Float64(Float64(y * Float64(y + a)) + b)))
	t_3 = Float64(Float64(z / y) + Float64(x - Float64(a / Float64(y / x))))
	tmp = 0.0
	if (y <= -4.2e+95)
		tmp = t_3;
	elseif (y <= -7e+42)
		tmp = t_1;
	elseif (y <= -460000000000.0)
		tmp = Float64(Float64(Float64(y * Float64(Float64(y * Float64(Float64(x * y) + z)) + 27464.7644705)) + 230661.510616) / t_2);
	elseif (y <= 2.3e+32)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * 27464.7644705)))) / Float64(i + Float64(y * t_2)));
	elseif (y <= 2.2e+114)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = ((27464.7644705 / (y * a)) + (z / a)) + (x / (a / y));
	t_2 = c + (y * ((y * (y + a)) + b));
	t_3 = (z / y) + (x - (a / (y / x)));
	tmp = 0.0;
	if (y <= -4.2e+95)
		tmp = t_3;
	elseif (y <= -7e+42)
		tmp = t_1;
	elseif (y <= -460000000000.0)
		tmp = ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616) / t_2;
	elseif (y <= 2.3e+32)
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * t_2));
	elseif (y <= 2.2e+114)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(N[(27464.7644705 / N[(y * a), $MachinePrecision]), $MachinePrecision] + N[(z / a), $MachinePrecision]), $MachinePrecision] + N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c + N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(z / y), $MachinePrecision] + N[(x - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.2e+95], t$95$3, If[LessEqual[y, -7e+42], t$95$1, If[LessEqual[y, -460000000000.0], N[(N[(N[(y * N[(N[(y * N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] + 27464.7644705), $MachinePrecision]), $MachinePrecision] + 230661.510616), $MachinePrecision] / t$95$2), $MachinePrecision], If[LessEqual[y, 2.3e+32], N[(N[(t + N[(y * N[(230661.510616 + N[(y * 27464.7644705), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.2e+114], t$95$1, t$95$3]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.2e95 or 2.2e114 < y

   1. Initial program 1.2%

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

   2. Taylor expanded in y around inf 76.3%

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

      1. +-commutative 76.3%

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

      2. associate--l+ 76.3%

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

      3. associate-/l* 78.8%

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

   4. Simplified 78.8%

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

   if -4.2e95 < y < -7.00000000000000047e42 or 2.3e32 < y < 2.2e114

   1. Initial program 15.0%

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

   2. Taylor expanded in a around inf 3.5%

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

   3. Taylor expanded in y around inf 47.8%

      \[\leadsto \color{blue}{27464.7644705 \cdot \frac{1}{a \cdot y} + \left(\frac{z}{a} + \frac{x \cdot y}{a}\right)} \]
   4. Step-by-step derivation

      1. associate-+r+ 47.8%

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

      2. associate-*r/ 47.8%

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

      3. metadata-eval 47.8%

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

      4. *-commutative 47.8%

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

      5. associate-/l* 54.0%

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

   5. Simplified 54.0%

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

   if -7.00000000000000047e42 < y < -4.6e11

   1. Initial program 74.5%

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

   2. Taylor expanded in t around 0 74.5%

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

   3. Taylor expanded in i around 0 75.9%

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

   if -4.6e11 < y < 2.3e32

   1. Initial program 97.5%

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

   2. Taylor expanded in y around 0 85.7%

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

      1. *-commutative 85.7%

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

   4. Simplified 85.7%

      \[\leadsto \frac{\left(\color{blue}{y \cdot 27464.7644705} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
3. Recombined 4 regimes into one program.

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+95}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq -7 \cdot 10^{+42}:\\ \;\;\;\;\left(\frac{27464.7644705}{y \cdot a} + \frac{z}{a}\right) + \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;y \leq -460000000000:\\ \;\;\;\;\frac{y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616}{c + y \cdot \left(y \cdot \left(y + a\right) + b\right)}\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+32}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)}\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+114}:\\ \;\;\;\;\left(\frac{27464.7644705}{y \cdot a} + \frac{z}{a}\right) + \frac{x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]

Alternative 7: 76.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\\ t_2 := \frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ t_3 := \frac{x}{\frac{a}{y}}\\ t_4 := \left(\frac{27464.7644705}{y \cdot a} + \frac{z}{a}\right) + t_3\\ \mathbf{if}\;y \leq -4 \cdot 10^{+95}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -2.85 \cdot 10^{+38}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y \leq -7800000000000:\\ \;\;\;\;\frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)}{t_1}\\ \mathbf{elif}\;y \leq -7300000000000:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+31}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot t_1}\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+111}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ c (* y (+ (* y (+ y a)) b))))
        (t_2 (+ (/ z y) (- x (/ a (/ y x)))))
        (t_3 (/ x (/ a y)))
        (t_4 (+ (+ (/ 27464.7644705 (* y a)) (/ z a)) t_3)))
   (if (<= y -4e+95)
     t_2
     (if (<= y -2.85e+38)
       t_4
       (if (<= y -7800000000000.0)
         (/ (+ 230661.510616 (* y (+ 27464.7644705 (* y z)))) t_1)
         (if (<= y -7300000000000.0)
           t_3
           (if (<= y 7.8e+31)
             (/ (+ t (* y 230661.510616)) (+ i (* y t_1)))
             (if (<= y 5.5e+111) t_4 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c + (y * ((y * (y + a)) + b));
	double t_2 = (z / y) + (x - (a / (y / x)));
	double t_3 = x / (a / y);
	double t_4 = ((27464.7644705 / (y * a)) + (z / a)) + t_3;
	double tmp;
	if (y <= -4e+95) {
		tmp = t_2;
	} else if (y <= -2.85e+38) {
		tmp = t_4;
	} else if (y <= -7800000000000.0) {
		tmp = (230661.510616 + (y * (27464.7644705 + (y * z)))) / t_1;
	} else if (y <= -7300000000000.0) {
		tmp = t_3;
	} else if (y <= 7.8e+31) {
		tmp = (t + (y * 230661.510616)) / (i + (y * t_1));
	} else if (y <= 5.5e+111) {
		tmp = t_4;
	} else {
		tmp = t_2;
	}
	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) :: t_4
    real(8) :: tmp
    t_1 = c + (y * ((y * (y + a)) + b))
    t_2 = (z / y) + (x - (a / (y / x)))
    t_3 = x / (a / y)
    t_4 = ((27464.7644705d0 / (y * a)) + (z / a)) + t_3
    if (y <= (-4d+95)) then
        tmp = t_2
    else if (y <= (-2.85d+38)) then
        tmp = t_4
    else if (y <= (-7800000000000.0d0)) then
        tmp = (230661.510616d0 + (y * (27464.7644705d0 + (y * z)))) / t_1
    else if (y <= (-7300000000000.0d0)) then
        tmp = t_3
    else if (y <= 7.8d+31) then
        tmp = (t + (y * 230661.510616d0)) / (i + (y * t_1))
    else if (y <= 5.5d+111) then
        tmp = t_4
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c + (y * ((y * (y + a)) + b));
	double t_2 = (z / y) + (x - (a / (y / x)));
	double t_3 = x / (a / y);
	double t_4 = ((27464.7644705 / (y * a)) + (z / a)) + t_3;
	double tmp;
	if (y <= -4e+95) {
		tmp = t_2;
	} else if (y <= -2.85e+38) {
		tmp = t_4;
	} else if (y <= -7800000000000.0) {
		tmp = (230661.510616 + (y * (27464.7644705 + (y * z)))) / t_1;
	} else if (y <= -7300000000000.0) {
		tmp = t_3;
	} else if (y <= 7.8e+31) {
		tmp = (t + (y * 230661.510616)) / (i + (y * t_1));
	} else if (y <= 5.5e+111) {
		tmp = t_4;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = c + (y * ((y * (y + a)) + b))
	t_2 = (z / y) + (x - (a / (y / x)))
	t_3 = x / (a / y)
	t_4 = ((27464.7644705 / (y * a)) + (z / a)) + t_3
	tmp = 0
	if y <= -4e+95:
		tmp = t_2
	elif y <= -2.85e+38:
		tmp = t_4
	elif y <= -7800000000000.0:
		tmp = (230661.510616 + (y * (27464.7644705 + (y * z)))) / t_1
	elif y <= -7300000000000.0:
		tmp = t_3
	elif y <= 7.8e+31:
		tmp = (t + (y * 230661.510616)) / (i + (y * t_1))
	elif y <= 5.5e+111:
		tmp = t_4
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(c + Float64(y * Float64(Float64(y * Float64(y + a)) + b)))
	t_2 = Float64(Float64(z / y) + Float64(x - Float64(a / Float64(y / x))))
	t_3 = Float64(x / Float64(a / y))
	t_4 = Float64(Float64(Float64(27464.7644705 / Float64(y * a)) + Float64(z / a)) + t_3)
	tmp = 0.0
	if (y <= -4e+95)
		tmp = t_2;
	elseif (y <= -2.85e+38)
		tmp = t_4;
	elseif (y <= -7800000000000.0)
		tmp = Float64(Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * z)))) / t_1);
	elseif (y <= -7300000000000.0)
		tmp = t_3;
	elseif (y <= 7.8e+31)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(i + Float64(y * t_1)));
	elseif (y <= 5.5e+111)
		tmp = t_4;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = c + (y * ((y * (y + a)) + b));
	t_2 = (z / y) + (x - (a / (y / x)));
	t_3 = x / (a / y);
	t_4 = ((27464.7644705 / (y * a)) + (z / a)) + t_3;
	tmp = 0.0;
	if (y <= -4e+95)
		tmp = t_2;
	elseif (y <= -2.85e+38)
		tmp = t_4;
	elseif (y <= -7800000000000.0)
		tmp = (230661.510616 + (y * (27464.7644705 + (y * z)))) / t_1;
	elseif (y <= -7300000000000.0)
		tmp = t_3;
	elseif (y <= 7.8e+31)
		tmp = (t + (y * 230661.510616)) / (i + (y * t_1));
	elseif (y <= 5.5e+111)
		tmp = t_4;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(c + N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z / y), $MachinePrecision] + N[(x - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(27464.7644705 / N[(y * a), $MachinePrecision]), $MachinePrecision] + N[(z / a), $MachinePrecision]), $MachinePrecision] + t$95$3), $MachinePrecision]}, If[LessEqual[y, -4e+95], t$95$2, If[LessEqual[y, -2.85e+38], t$95$4, If[LessEqual[y, -7800000000000.0], N[(N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[y, -7300000000000.0], t$95$3, If[LessEqual[y, 7.8e+31], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.5e+111], t$95$4, t$95$2]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -4.00000000000000008e95 or 5.4999999999999998e111 < y

   1. Initial program 1.2%

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

   2. Taylor expanded in y around inf 76.3%

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

      1. +-commutative 76.3%

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

      2. associate--l+ 76.3%

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

      3. associate-/l* 78.8%

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

   4. Simplified 78.8%

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

   if -4.00000000000000008e95 < y < -2.8499999999999999e38 or 7.79999999999999999e31 < y < 5.4999999999999998e111

   1. Initial program 14.2%

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

   2. Taylor expanded in a around inf 3.5%

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

   3. Taylor expanded in y around inf 45.2%

      \[\leadsto \color{blue}{27464.7644705 \cdot \frac{1}{a \cdot y} + \left(\frac{z}{a} + \frac{x \cdot y}{a}\right)} \]
   4. Step-by-step derivation

      1. associate-+r+ 45.2%

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

      2. associate-*r/ 45.2%

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

      3. metadata-eval 45.2%

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

      4. *-commutative 45.2%

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

      5. associate-/l* 51.0%

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

   5. Simplified 51.0%

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

   if -2.8499999999999999e38 < y < -7.8e12

   1. Initial program 98.8%

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

   2. Taylor expanded in t around 0 98.8%

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

   3. Taylor expanded in i around 0 99.1%

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

   4. Taylor expanded in x around 0 99.1%

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

   if -7.8e12 < y < -7.3e12

   1. Initial program 98.4%

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

   2. Taylor expanded in a around inf 98.4%

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

   3. Taylor expanded in y around inf 98.4%

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

      1. associate-/l* 100.0%

         \[\leadsto \color{blue}{\frac{x}{\frac{a}{y}}} \]

   5. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{x}{\frac{a}{y}}} \]

   if -7.3e12 < y < 7.79999999999999999e31

   1. Initial program 97.5%

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

   2. Taylor expanded in y around 0 84.4%

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

      1. *-commutative 84.4%

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

   4. Simplified 84.4%

      \[\leadsto \frac{\color{blue}{y \cdot 230661.510616} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
3. Recombined 5 regimes into one program.

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+95}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq -2.85 \cdot 10^{+38}:\\ \;\;\;\;\left(\frac{27464.7644705}{y \cdot a} + \frac{z}{a}\right) + \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;y \leq -7800000000000:\\ \;\;\;\;\frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)}{c + y \cdot \left(y \cdot \left(y + a\right) + b\right)}\\ \mathbf{elif}\;y \leq -7300000000000:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+31}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)}\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+111}:\\ \;\;\;\;\left(\frac{27464.7644705}{y \cdot a} + \frac{z}{a}\right) + \frac{x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]

Alternative 8: 69.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\\ t_2 := \frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ t_3 := \frac{x}{\frac{a}{y}}\\ t_4 := \left(\frac{27464.7644705}{y \cdot a} + \frac{z}{a}\right) + t_3\\ \mathbf{if}\;y \leq -7.5 \cdot 10^{+95}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{+37}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y \leq -7800000000000:\\ \;\;\;\;\frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)}{t_1}\\ \mathbf{elif}\;y \leq -2200000000000:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+31}:\\ \;\;\;\;\frac{t}{i + y \cdot t_1}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+111}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ c (* y (+ (* y (+ y a)) b))))
        (t_2 (+ (/ z y) (- x (/ a (/ y x)))))
        (t_3 (/ x (/ a y)))
        (t_4 (+ (+ (/ 27464.7644705 (* y a)) (/ z a)) t_3)))
   (if (<= y -7.5e+95)
     t_2
     (if (<= y -1.1e+37)
       t_4
       (if (<= y -7800000000000.0)
         (/ (+ 230661.510616 (* y (+ 27464.7644705 (* y z)))) t_1)
         (if (<= y -2200000000000.0)
           t_3
           (if (<= y 7.8e+31)
             (/ t (+ i (* y t_1)))
             (if (<= y 1.15e+111) t_4 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c + (y * ((y * (y + a)) + b));
	double t_2 = (z / y) + (x - (a / (y / x)));
	double t_3 = x / (a / y);
	double t_4 = ((27464.7644705 / (y * a)) + (z / a)) + t_3;
	double tmp;
	if (y <= -7.5e+95) {
		tmp = t_2;
	} else if (y <= -1.1e+37) {
		tmp = t_4;
	} else if (y <= -7800000000000.0) {
		tmp = (230661.510616 + (y * (27464.7644705 + (y * z)))) / t_1;
	} else if (y <= -2200000000000.0) {
		tmp = t_3;
	} else if (y <= 7.8e+31) {
		tmp = t / (i + (y * t_1));
	} else if (y <= 1.15e+111) {
		tmp = t_4;
	} else {
		tmp = t_2;
	}
	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) :: t_4
    real(8) :: tmp
    t_1 = c + (y * ((y * (y + a)) + b))
    t_2 = (z / y) + (x - (a / (y / x)))
    t_3 = x / (a / y)
    t_4 = ((27464.7644705d0 / (y * a)) + (z / a)) + t_3
    if (y <= (-7.5d+95)) then
        tmp = t_2
    else if (y <= (-1.1d+37)) then
        tmp = t_4
    else if (y <= (-7800000000000.0d0)) then
        tmp = (230661.510616d0 + (y * (27464.7644705d0 + (y * z)))) / t_1
    else if (y <= (-2200000000000.0d0)) then
        tmp = t_3
    else if (y <= 7.8d+31) then
        tmp = t / (i + (y * t_1))
    else if (y <= 1.15d+111) then
        tmp = t_4
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c + (y * ((y * (y + a)) + b));
	double t_2 = (z / y) + (x - (a / (y / x)));
	double t_3 = x / (a / y);
	double t_4 = ((27464.7644705 / (y * a)) + (z / a)) + t_3;
	double tmp;
	if (y <= -7.5e+95) {
		tmp = t_2;
	} else if (y <= -1.1e+37) {
		tmp = t_4;
	} else if (y <= -7800000000000.0) {
		tmp = (230661.510616 + (y * (27464.7644705 + (y * z)))) / t_1;
	} else if (y <= -2200000000000.0) {
		tmp = t_3;
	} else if (y <= 7.8e+31) {
		tmp = t / (i + (y * t_1));
	} else if (y <= 1.15e+111) {
		tmp = t_4;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = c + (y * ((y * (y + a)) + b))
	t_2 = (z / y) + (x - (a / (y / x)))
	t_3 = x / (a / y)
	t_4 = ((27464.7644705 / (y * a)) + (z / a)) + t_3
	tmp = 0
	if y <= -7.5e+95:
		tmp = t_2
	elif y <= -1.1e+37:
		tmp = t_4
	elif y <= -7800000000000.0:
		tmp = (230661.510616 + (y * (27464.7644705 + (y * z)))) / t_1
	elif y <= -2200000000000.0:
		tmp = t_3
	elif y <= 7.8e+31:
		tmp = t / (i + (y * t_1))
	elif y <= 1.15e+111:
		tmp = t_4
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(c + Float64(y * Float64(Float64(y * Float64(y + a)) + b)))
	t_2 = Float64(Float64(z / y) + Float64(x - Float64(a / Float64(y / x))))
	t_3 = Float64(x / Float64(a / y))
	t_4 = Float64(Float64(Float64(27464.7644705 / Float64(y * a)) + Float64(z / a)) + t_3)
	tmp = 0.0
	if (y <= -7.5e+95)
		tmp = t_2;
	elseif (y <= -1.1e+37)
		tmp = t_4;
	elseif (y <= -7800000000000.0)
		tmp = Float64(Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * z)))) / t_1);
	elseif (y <= -2200000000000.0)
		tmp = t_3;
	elseif (y <= 7.8e+31)
		tmp = Float64(t / Float64(i + Float64(y * t_1)));
	elseif (y <= 1.15e+111)
		tmp = t_4;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = c + (y * ((y * (y + a)) + b));
	t_2 = (z / y) + (x - (a / (y / x)));
	t_3 = x / (a / y);
	t_4 = ((27464.7644705 / (y * a)) + (z / a)) + t_3;
	tmp = 0.0;
	if (y <= -7.5e+95)
		tmp = t_2;
	elseif (y <= -1.1e+37)
		tmp = t_4;
	elseif (y <= -7800000000000.0)
		tmp = (230661.510616 + (y * (27464.7644705 + (y * z)))) / t_1;
	elseif (y <= -2200000000000.0)
		tmp = t_3;
	elseif (y <= 7.8e+31)
		tmp = t / (i + (y * t_1));
	elseif (y <= 1.15e+111)
		tmp = t_4;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(c + N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z / y), $MachinePrecision] + N[(x - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(27464.7644705 / N[(y * a), $MachinePrecision]), $MachinePrecision] + N[(z / a), $MachinePrecision]), $MachinePrecision] + t$95$3), $MachinePrecision]}, If[LessEqual[y, -7.5e+95], t$95$2, If[LessEqual[y, -1.1e+37], t$95$4, If[LessEqual[y, -7800000000000.0], N[(N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[y, -2200000000000.0], t$95$3, If[LessEqual[y, 7.8e+31], N[(t / N[(i + N[(y * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.15e+111], t$95$4, t$95$2]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -7.5000000000000001e95 or 1.15000000000000001e111 < y

   1. Initial program 1.2%

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

   2. Taylor expanded in y around inf 76.3%

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

      1. +-commutative 76.3%

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

      2. associate--l+ 76.3%

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

      3. associate-/l* 78.8%

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

   4. Simplified 78.8%

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

   if -7.5000000000000001e95 < y < -1.1e37 or 7.79999999999999999e31 < y < 1.15000000000000001e111

   1. Initial program 14.2%

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

   2. Taylor expanded in a around inf 3.5%

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

   3. Taylor expanded in y around inf 45.2%

      \[\leadsto \color{blue}{27464.7644705 \cdot \frac{1}{a \cdot y} + \left(\frac{z}{a} + \frac{x \cdot y}{a}\right)} \]
   4. Step-by-step derivation

      1. associate-+r+ 45.2%

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

      2. associate-*r/ 45.2%

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

      3. metadata-eval 45.2%

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

      4. *-commutative 45.2%

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

      5. associate-/l* 51.0%

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

   5. Simplified 51.0%

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

   if -1.1e37 < y < -7.8e12

   1. Initial program 98.8%

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

   2. Taylor expanded in t around 0 98.8%

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

   3. Taylor expanded in i around 0 99.1%

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

   4. Taylor expanded in x around 0 99.1%

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

   if -7.8e12 < y < -2.2e12

   1. Initial program 98.4%

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

   2. Taylor expanded in a around inf 98.4%

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

   3. Taylor expanded in y around inf 98.4%

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

      1. associate-/l* 100.0%

         \[\leadsto \color{blue}{\frac{x}{\frac{a}{y}}} \]

   5. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{x}{\frac{a}{y}}} \]

   if -2.2e12 < y < 7.79999999999999999e31

   1. Initial program 97.5%

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

   2. Taylor expanded in t around inf 72.0%

      \[\leadsto \color{blue}{\frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 72.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+95}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{+37}:\\ \;\;\;\;\left(\frac{27464.7644705}{y \cdot a} + \frac{z}{a}\right) + \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;y \leq -7800000000000:\\ \;\;\;\;\frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)}{c + y \cdot \left(y \cdot \left(y + a\right) + b\right)}\\ \mathbf{elif}\;y \leq -2200000000000:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+31}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+111}:\\ \;\;\;\;\left(\frac{27464.7644705}{y \cdot a} + \frac{z}{a}\right) + \frac{x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]

Alternative 9: 62.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\frac{27464.7644705}{y \cdot a} + \frac{z}{a}\right) + \frac{x}{\frac{a}{y}}\\ t_2 := \frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{if}\;y \leq -4.5 \cdot 10^{+95}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -13:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{-26}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{+111}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (+ (/ 27464.7644705 (* y a)) (/ z a)) (/ x (/ a y))))
        (t_2 (+ (/ z y) (- x (/ a (/ y x))))))
   (if (<= y -4.5e+95)
     t_2
     (if (<= y -13.0)
       t_1
       (if (<= y 4.9e-26)
         (/ (+ t (* y 230661.510616)) i)
         (if (<= y 1.02e+111) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = ((27464.7644705 / (y * a)) + (z / a)) + (x / (a / y));
	double t_2 = (z / y) + (x - (a / (y / x)));
	double tmp;
	if (y <= -4.5e+95) {
		tmp = t_2;
	} else if (y <= -13.0) {
		tmp = t_1;
	} else if (y <= 4.9e-26) {
		tmp = (t + (y * 230661.510616)) / i;
	} else if (y <= 1.02e+111) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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 = ((27464.7644705d0 / (y * a)) + (z / a)) + (x / (a / y))
    t_2 = (z / y) + (x - (a / (y / x)))
    if (y <= (-4.5d+95)) then
        tmp = t_2
    else if (y <= (-13.0d0)) then
        tmp = t_1
    else if (y <= 4.9d-26) then
        tmp = (t + (y * 230661.510616d0)) / i
    else if (y <= 1.02d+111) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = ((27464.7644705 / (y * a)) + (z / a)) + (x / (a / y));
	double t_2 = (z / y) + (x - (a / (y / x)));
	double tmp;
	if (y <= -4.5e+95) {
		tmp = t_2;
	} else if (y <= -13.0) {
		tmp = t_1;
	} else if (y <= 4.9e-26) {
		tmp = (t + (y * 230661.510616)) / i;
	} else if (y <= 1.02e+111) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = ((27464.7644705 / (y * a)) + (z / a)) + (x / (a / y))
	t_2 = (z / y) + (x - (a / (y / x)))
	tmp = 0
	if y <= -4.5e+95:
		tmp = t_2
	elif y <= -13.0:
		tmp = t_1
	elif y <= 4.9e-26:
		tmp = (t + (y * 230661.510616)) / i
	elif y <= 1.02e+111:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(Float64(27464.7644705 / Float64(y * a)) + Float64(z / a)) + Float64(x / Float64(a / y)))
	t_2 = Float64(Float64(z / y) + Float64(x - Float64(a / Float64(y / x))))
	tmp = 0.0
	if (y <= -4.5e+95)
		tmp = t_2;
	elseif (y <= -13.0)
		tmp = t_1;
	elseif (y <= 4.9e-26)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / i);
	elseif (y <= 1.02e+111)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = ((27464.7644705 / (y * a)) + (z / a)) + (x / (a / y));
	t_2 = (z / y) + (x - (a / (y / x)));
	tmp = 0.0;
	if (y <= -4.5e+95)
		tmp = t_2;
	elseif (y <= -13.0)
		tmp = t_1;
	elseif (y <= 4.9e-26)
		tmp = (t + (y * 230661.510616)) / i;
	elseif (y <= 1.02e+111)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(N[(27464.7644705 / N[(y * a), $MachinePrecision]), $MachinePrecision] + N[(z / a), $MachinePrecision]), $MachinePrecision] + N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z / y), $MachinePrecision] + N[(x - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.5e+95], t$95$2, If[LessEqual[y, -13.0], t$95$1, If[LessEqual[y, 4.9e-26], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / i), $MachinePrecision], If[LessEqual[y, 1.02e+111], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.50000000000000017e95 or 1.02e111 < y

   1. Initial program 1.2%

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

   2. Taylor expanded in y around inf 76.3%

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

      1. +-commutative 76.3%

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

      2. associate--l+ 76.3%

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

      3. associate-/l* 78.8%

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

   4. Simplified 78.8%

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

   if -4.50000000000000017e95 < y < -13 or 4.8999999999999999e-26 < y < 1.02e111

   1. Initial program 40.9%

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

   2. Taylor expanded in a around inf 8.5%

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

   3. Taylor expanded in y around inf 34.2%

      \[\leadsto \color{blue}{27464.7644705 \cdot \frac{1}{a \cdot y} + \left(\frac{z}{a} + \frac{x \cdot y}{a}\right)} \]
   4. Step-by-step derivation

      1. associate-+r+ 34.2%

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

      2. associate-*r/ 34.2%

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

      3. metadata-eval 34.2%

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

      4. *-commutative 34.2%

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

      5. associate-/l* 37.8%

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

   5. Simplified 37.8%

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

   if -13 < y < 4.8999999999999999e-26

   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. Taylor expanded in y around 0 48.4%

      \[\leadsto \color{blue}{y \cdot \left(230661.510616 \cdot \frac{1}{i} - \frac{c \cdot t}{{i}^{2}}\right) + \frac{t}{i}} \]

   3. Taylor expanded in i around inf 62.2%

      \[\leadsto \color{blue}{\frac{t + 230661.510616 \cdot y}{i}} \]
   4. Step-by-step derivation

      1. *-commutative 62.2%

         \[\leadsto \frac{t + \color{blue}{y \cdot 230661.510616}}{i} \]

   5. Simplified 62.2%

      \[\leadsto \color{blue}{\frac{t + y \cdot 230661.510616}{i}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 62.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+95}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq -13:\\ \;\;\;\;\left(\frac{27464.7644705}{y \cdot a} + \frac{z}{a}\right) + \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{-26}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{+111}:\\ \;\;\;\;\left(\frac{27464.7644705}{y \cdot a} + \frac{z}{a}\right) + \frac{x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]

Alternative 10: 69.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\frac{27464.7644705}{y \cdot a} + \frac{z}{a}\right) + \frac{x}{\frac{a}{y}}\\ t_2 := \frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{if}\;y \leq -1.06 \cdot 10^{+96}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -21000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+31}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)}\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+113}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (+ (/ 27464.7644705 (* y a)) (/ z a)) (/ x (/ a y))))
        (t_2 (+ (/ z y) (- x (/ a (/ y x))))))
   (if (<= y -1.06e+96)
     t_2
     (if (<= y -21000.0)
       t_1
       (if (<= y 3.2e+31)
         (/ t (+ i (* y (+ c (* y (+ (* y (+ y a)) b))))))
         (if (<= y 2.3e+113) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = ((27464.7644705 / (y * a)) + (z / a)) + (x / (a / y));
	double t_2 = (z / y) + (x - (a / (y / x)));
	double tmp;
	if (y <= -1.06e+96) {
		tmp = t_2;
	} else if (y <= -21000.0) {
		tmp = t_1;
	} else if (y <= 3.2e+31) {
		tmp = t / (i + (y * (c + (y * ((y * (y + a)) + b)))));
	} else if (y <= 2.3e+113) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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 = ((27464.7644705d0 / (y * a)) + (z / a)) + (x / (a / y))
    t_2 = (z / y) + (x - (a / (y / x)))
    if (y <= (-1.06d+96)) then
        tmp = t_2
    else if (y <= (-21000.0d0)) then
        tmp = t_1
    else if (y <= 3.2d+31) then
        tmp = t / (i + (y * (c + (y * ((y * (y + a)) + b)))))
    else if (y <= 2.3d+113) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = ((27464.7644705 / (y * a)) + (z / a)) + (x / (a / y));
	double t_2 = (z / y) + (x - (a / (y / x)));
	double tmp;
	if (y <= -1.06e+96) {
		tmp = t_2;
	} else if (y <= -21000.0) {
		tmp = t_1;
	} else if (y <= 3.2e+31) {
		tmp = t / (i + (y * (c + (y * ((y * (y + a)) + b)))));
	} else if (y <= 2.3e+113) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = ((27464.7644705 / (y * a)) + (z / a)) + (x / (a / y))
	t_2 = (z / y) + (x - (a / (y / x)))
	tmp = 0
	if y <= -1.06e+96:
		tmp = t_2
	elif y <= -21000.0:
		tmp = t_1
	elif y <= 3.2e+31:
		tmp = t / (i + (y * (c + (y * ((y * (y + a)) + b)))))
	elif y <= 2.3e+113:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(Float64(27464.7644705 / Float64(y * a)) + Float64(z / a)) + Float64(x / Float64(a / y)))
	t_2 = Float64(Float64(z / y) + Float64(x - Float64(a / Float64(y / x))))
	tmp = 0.0
	if (y <= -1.06e+96)
		tmp = t_2;
	elseif (y <= -21000.0)
		tmp = t_1;
	elseif (y <= 3.2e+31)
		tmp = Float64(t / Float64(i + Float64(y * Float64(c + Float64(y * Float64(Float64(y * Float64(y + a)) + b))))));
	elseif (y <= 2.3e+113)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = ((27464.7644705 / (y * a)) + (z / a)) + (x / (a / y));
	t_2 = (z / y) + (x - (a / (y / x)));
	tmp = 0.0;
	if (y <= -1.06e+96)
		tmp = t_2;
	elseif (y <= -21000.0)
		tmp = t_1;
	elseif (y <= 3.2e+31)
		tmp = t / (i + (y * (c + (y * ((y * (y + a)) + b)))));
	elseif (y <= 2.3e+113)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(N[(27464.7644705 / N[(y * a), $MachinePrecision]), $MachinePrecision] + N[(z / a), $MachinePrecision]), $MachinePrecision] + N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z / y), $MachinePrecision] + N[(x - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.06e+96], t$95$2, If[LessEqual[y, -21000.0], t$95$1, If[LessEqual[y, 3.2e+31], N[(t / N[(i + N[(y * N[(c + N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.3e+113], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.06e96 or 2.29999999999999997e113 < y

   1. Initial program 1.2%

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

   2. Taylor expanded in y around inf 76.3%

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

      1. +-commutative 76.3%

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

      2. associate--l+ 76.3%

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

      3. associate-/l* 78.8%

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

   4. Simplified 78.8%

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

   if -1.06e96 < y < -21000 or 3.2000000000000001e31 < y < 2.29999999999999997e113

   1. Initial program 27.2%

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

   2. Taylor expanded in a around inf 5.9%

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

   3. Taylor expanded in y around inf 41.2%

      \[\leadsto \color{blue}{27464.7644705 \cdot \frac{1}{a \cdot y} + \left(\frac{z}{a} + \frac{x \cdot y}{a}\right)} \]
   4. Step-by-step derivation

      1. associate-+r+ 41.2%

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

      2. associate-*r/ 41.2%

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

      3. metadata-eval 41.2%

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

      4. *-commutative 41.2%

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

      5. associate-/l* 46.0%

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

   5. Simplified 46.0%

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

   if -21000 < y < 3.2000000000000001e31

   1. Initial program 97.5%

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

   2. Taylor expanded in t around inf 72.0%

      \[\leadsto \color{blue}{\frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 70.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.06 \cdot 10^{+96}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq -21000:\\ \;\;\;\;\left(\frac{27464.7644705}{y \cdot a} + \frac{z}{a}\right) + \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+31}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)}\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+113}:\\ \;\;\;\;\left(\frac{27464.7644705}{y \cdot a} + \frac{z}{a}\right) + \frac{x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]

Alternative 11: 61.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{if}\;y \leq -9 \cdot 10^{-22}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-31}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{+111}:\\ \;\;\;\;\frac{z}{a} + \frac{x \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (/ z y) (- x (/ a (/ y x))))))
   (if (<= y -9e-22)
     t_1
     (if (<= y 1.25e-31)
       (/ (+ t (* y 230661.510616)) i)
       (if (<= y 1.02e+111) (+ (/ z a) (/ (* x y) a)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (z / y) + (x - (a / (y / x)));
	double tmp;
	if (y <= -9e-22) {
		tmp = t_1;
	} else if (y <= 1.25e-31) {
		tmp = (t + (y * 230661.510616)) / i;
	} else if (y <= 1.02e+111) {
		tmp = (z / a) + ((x * y) / a);
	} else {
		tmp = t_1;
	}
	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 = (z / y) + (x - (a / (y / x)))
    if (y <= (-9d-22)) then
        tmp = t_1
    else if (y <= 1.25d-31) then
        tmp = (t + (y * 230661.510616d0)) / i
    else if (y <= 1.02d+111) then
        tmp = (z / a) + ((x * y) / a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (z / y) + (x - (a / (y / x)));
	double tmp;
	if (y <= -9e-22) {
		tmp = t_1;
	} else if (y <= 1.25e-31) {
		tmp = (t + (y * 230661.510616)) / i;
	} else if (y <= 1.02e+111) {
		tmp = (z / a) + ((x * y) / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (z / y) + (x - (a / (y / x)))
	tmp = 0
	if y <= -9e-22:
		tmp = t_1
	elif y <= 1.25e-31:
		tmp = (t + (y * 230661.510616)) / i
	elif y <= 1.02e+111:
		tmp = (z / a) + ((x * y) / a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(z / y) + Float64(x - Float64(a / Float64(y / x))))
	tmp = 0.0
	if (y <= -9e-22)
		tmp = t_1;
	elseif (y <= 1.25e-31)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / i);
	elseif (y <= 1.02e+111)
		tmp = Float64(Float64(z / a) + Float64(Float64(x * y) / a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (z / y) + (x - (a / (y / x)));
	tmp = 0.0;
	if (y <= -9e-22)
		tmp = t_1;
	elseif (y <= 1.25e-31)
		tmp = (t + (y * 230661.510616)) / i;
	elseif (y <= 1.02e+111)
		tmp = (z / a) + ((x * y) / a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(z / y), $MachinePrecision] + N[(x - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9e-22], t$95$1, If[LessEqual[y, 1.25e-31], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / i), $MachinePrecision], If[LessEqual[y, 1.02e+111], N[(N[(z / a), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.99999999999999973e-22 or 1.02e111 < y

   1. Initial program 15.0%

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

   2. Taylor expanded in y around inf 60.7%

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

      1. +-commutative 60.7%

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

      2. associate--l+ 60.7%

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

      3. associate-/l* 62.6%

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

   4. Simplified 62.6%

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

   if -8.99999999999999973e-22 < y < 1.25e-31

   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. Taylor expanded in y around 0 50.4%

      \[\leadsto \color{blue}{y \cdot \left(230661.510616 \cdot \frac{1}{i} - \frac{c \cdot t}{{i}^{2}}\right) + \frac{t}{i}} \]

   3. Taylor expanded in i around inf 64.7%

      \[\leadsto \color{blue}{\frac{t + 230661.510616 \cdot y}{i}} \]
   4. Step-by-step derivation

      1. *-commutative 64.7%

         \[\leadsto \frac{t + \color{blue}{y \cdot 230661.510616}}{i} \]

   5. Simplified 64.7%

      \[\leadsto \color{blue}{\frac{t + y \cdot 230661.510616}{i}} \]

   if 1.25e-31 < y < 1.02e111

   1. Initial program 36.9%

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

   2. Taylor expanded in a around inf 9.3%

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

   3. Taylor expanded in y around inf 33.2%

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

4. Final simplification 60.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{-22}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-31}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{+111}:\\ \;\;\;\;\frac{z}{a} + \frac{x \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]

Alternative 12: 55.6% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{+46}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-29}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{+112}:\\ \;\;\;\;\frac{z}{a} + \frac{x \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -8.2e+46)
   x
   (if (<= y 8e-29)
     (/ (+ t (* y 230661.510616)) i)
     (if (<= y 5.8e+112) (+ (/ z a) (/ (* x y) 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 <= -8.2e+46) {
		tmp = x;
	} else if (y <= 8e-29) {
		tmp = (t + (y * 230661.510616)) / i;
	} else if (y <= 5.8e+112) {
		tmp = (z / a) + ((x * y) / 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 <= (-8.2d+46)) then
        tmp = x
    else if (y <= 8d-29) then
        tmp = (t + (y * 230661.510616d0)) / i
    else if (y <= 5.8d+112) then
        tmp = (z / a) + ((x * y) / 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 <= -8.2e+46) {
		tmp = x;
	} else if (y <= 8e-29) {
		tmp = (t + (y * 230661.510616)) / i;
	} else if (y <= 5.8e+112) {
		tmp = (z / a) + ((x * y) / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -8.2e+46:
		tmp = x
	elif y <= 8e-29:
		tmp = (t + (y * 230661.510616)) / i
	elif y <= 5.8e+112:
		tmp = (z / a) + ((x * y) / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -8.2e+46)
		tmp = x;
	elseif (y <= 8e-29)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / i);
	elseif (y <= 5.8e+112)
		tmp = Float64(Float64(z / a) + Float64(Float64(x * y) / 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 <= -8.2e+46)
		tmp = x;
	elseif (y <= 8e-29)
		tmp = (t + (y * 230661.510616)) / i;
	elseif (y <= 5.8e+112)
		tmp = (z / a) + ((x * y) / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -8.2e+46], x, If[LessEqual[y, 8e-29], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / i), $MachinePrecision], If[LessEqual[y, 5.8e+112], N[(N[(z / a), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.19999999999999999e46 or 5.8000000000000004e112 < y

   1. Initial program 2.4%

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

   2. Taylor expanded in y around inf 62.2%

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

   if -8.19999999999999999e46 < y < 7.99999999999999955e-29

   1. Initial program 97.5%

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

   2. Taylor expanded in y around 0 45.1%

      \[\leadsto \color{blue}{y \cdot \left(230661.510616 \cdot \frac{1}{i} - \frac{c \cdot t}{{i}^{2}}\right) + \frac{t}{i}} \]

   3. Taylor expanded in i around inf 57.7%

      \[\leadsto \color{blue}{\frac{t + 230661.510616 \cdot y}{i}} \]
   4. Step-by-step derivation

      1. *-commutative 57.7%

         \[\leadsto \frac{t + \color{blue}{y \cdot 230661.510616}}{i} \]

   5. Simplified 57.7%

      \[\leadsto \color{blue}{\frac{t + y \cdot 230661.510616}{i}} \]

   if 7.99999999999999955e-29 < y < 5.8000000000000004e112

   1. Initial program 36.9%

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

   2. Taylor expanded in a around inf 9.3%

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

   3. Taylor expanded in y around inf 33.2%

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

4. Final simplification 56.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{+46}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-29}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{+112}:\\ \;\;\;\;\frac{z}{a} + \frac{x \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 13: 55.4% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.6 \cdot 10^{+45}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+18}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -5.6e+45) x (if (<= y 3.5e+18) (/ (+ t (* y 230661.510616)) 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 <= -5.6e+45) {
		tmp = x;
	} else if (y <= 3.5e+18) {
		tmp = (t + (y * 230661.510616)) / 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 <= (-5.6d+45)) then
        tmp = x
    else if (y <= 3.5d+18) then
        tmp = (t + (y * 230661.510616d0)) / 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 <= -5.6e+45) {
		tmp = x;
	} else if (y <= 3.5e+18) {
		tmp = (t + (y * 230661.510616)) / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -5.6e+45:
		tmp = x
	elif y <= 3.5e+18:
		tmp = (t + (y * 230661.510616)) / i
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -5.6e+45)
		tmp = x;
	elseif (y <= 3.5e+18)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / 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 <= -5.6e+45)
		tmp = x;
	elseif (y <= 3.5e+18)
		tmp = (t + (y * 230661.510616)) / i;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -5.6e+45], x, If[LessEqual[y, 3.5e+18], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / i), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -5.5999999999999999e45 or 3.5e18 < y

   1. Initial program 5.8%

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

   2. Taylor expanded in y around inf 52.2%

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

   if -5.5999999999999999e45 < y < 3.5e18

   1. Initial program 96.3%

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

   2. Taylor expanded in y around 0 43.2%

      \[\leadsto \color{blue}{y \cdot \left(230661.510616 \cdot \frac{1}{i} - \frac{c \cdot t}{{i}^{2}}\right) + \frac{t}{i}} \]

   3. Taylor expanded in i around inf 55.0%

      \[\leadsto \color{blue}{\frac{t + 230661.510616 \cdot y}{i}} \]
   4. Step-by-step derivation

      1. *-commutative 55.0%

         \[\leadsto \frac{t + \color{blue}{y \cdot 230661.510616}}{i} \]

   5. Simplified 55.0%

      \[\leadsto \color{blue}{\frac{t + y \cdot 230661.510616}{i}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 53.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.6 \cdot 10^{+45}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+18}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 14: 51.8% accurate, 4.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+45}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.16 \cdot 10^{+44}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -5.5e+45) x (if (<= y 1.16e+44) (/ 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 <= -5.5e+45) {
		tmp = x;
	} else if (y <= 1.16e+44) {
		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 <= (-5.5d+45)) then
        tmp = x
    else if (y <= 1.16d+44) 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 <= -5.5e+45) {
		tmp = x;
	} else if (y <= 1.16e+44) {
		tmp = t / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -5.5e+45:
		tmp = x
	elif y <= 1.16e+44:
		tmp = t / i
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -5.5e+45)
		tmp = x;
	elseif (y <= 1.16e+44)
		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 <= -5.5e+45)
		tmp = x;
	elseif (y <= 1.16e+44)
		tmp = t / i;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -5.5e+45], x, If[LessEqual[y, 1.16e+44], N[(t / i), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -5.5000000000000001e45 or 1.1600000000000001e44 < y

   1. Initial program 3.2%

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

   2. Taylor expanded in y around inf 56.0%

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

   if -5.5000000000000001e45 < y < 1.1600000000000001e44

   1. Initial program 93.3%

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

   2. Taylor expanded in y around 0 46.4%

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

4. Final simplification 50.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+45}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.16 \cdot 10^{+44}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 15: 26.8% 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 56.4%

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

2. Taylor expanded in y around inf 24.9%

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

3. Final simplification 24.9%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023336 
(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)))