Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2

Percentage Accurate: 55.9% → 84.4%

Time: 33.8s

Alternatives: 26

Speedup: 2.5×

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: 55.9% 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: 84.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b + y \cdot \left(y + a\right)\\ t_2 := y \cdot t_1\\ t_3 := y \cdot \left(z + y \cdot x\right)\\ t_4 := 27464.7644705 + t_3\\ t_5 := t_1 \cdot t_1\\ t_6 := \frac{x}{\frac{b}{y \cdot y} + \left(1 + \left(\frac{c}{{y}^{3}} + \left(\frac{i}{{y}^{4}} + \frac{a}{y}\right)\right)\right)}\\ t_7 := c + t_2\\ t_8 := t_7 \cdot t_7\\ t_9 := y \cdot t_7\\ \mathbf{if}\;y \leq -4.8 \cdot 10^{+218}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;y \leq -3.15 \cdot 10^{+100}:\\ \;\;\;\;\left(\left(x + \left(\frac{z}{y} + \frac{27464.7644705}{y \cdot y}\right)\right) - \frac{a}{\frac{y \cdot y}{z - x \cdot a}}\right) - \left(\frac{a}{\frac{y}{x}} + \frac{b}{y} \cdot \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -3.3 \cdot 10^{+16}:\\ \;\;\;\;\frac{t}{t_9} + \left(i \cdot \left(\left(230661.510616 \cdot \frac{-1}{y \cdot t_8} + \left(27464.7644705 \cdot \frac{-1}{t_8} - \frac{t_3}{t_8}\right)\right) - \frac{t}{{y}^{2} \cdot t_8}\right) + \left(\frac{t_4}{t_1} + \left(230661.510616 \cdot \frac{1}{t_2} + c \cdot \left(\left(27464.7644705 \cdot \frac{-1}{t_2 \cdot t_1} + \left(230661.510616 \cdot \frac{-1}{t_1 \cdot \left({y}^{2} \cdot t_1\right)} - \frac{y \cdot x}{t_5}\right)\right) - \frac{z}{t_5}\right)\right)\right)\right)\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+24}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot t_4\right)}{i + t_9}\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{+172} \lor \neg \left(y \leq 6.2 \cdot 10^{+260}\right):\\ \;\;\;\;t_6\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ b (* y (+ y a))))
        (t_2 (* y t_1))
        (t_3 (* y (+ z (* y x))))
        (t_4 (+ 27464.7644705 t_3))
        (t_5 (* t_1 t_1))
        (t_6
         (/
          x
          (+
           (/ b (* y y))
           (+ 1.0 (+ (/ c (pow y 3.0)) (+ (/ i (pow y 4.0)) (/ a y)))))))
        (t_7 (+ c t_2))
        (t_8 (* t_7 t_7))
        (t_9 (* y t_7)))
   (if (<= y -4.8e+218)
     t_6
     (if (<= y -3.15e+100)
       (-
        (-
         (+ x (+ (/ z y) (/ 27464.7644705 (* y y))))
         (/ a (/ (* y y) (- z (* x a)))))
        (+ (/ a (/ y x)) (* (/ b y) (/ x y))))
       (if (<= y -3.3e+16)
         (+
          (/ t t_9)
          (+
           (*
            i
            (-
             (+
              (* 230661.510616 (/ -1.0 (* y t_8)))
              (- (* 27464.7644705 (/ -1.0 t_8)) (/ t_3 t_8)))
             (/ t (* (pow y 2.0) t_8))))
           (+
            (/ t_4 t_1)
            (+
             (* 230661.510616 (/ 1.0 t_2))
             (*
              c
              (-
               (+
                (* 27464.7644705 (/ -1.0 (* t_2 t_1)))
                (-
                 (* 230661.510616 (/ -1.0 (* t_1 (* (pow y 2.0) t_1))))
                 (/ (* y x) t_5)))
               (/ z t_5)))))))
         (if (<= y 4.2e+24)
           (/ (+ t (* y (+ 230661.510616 (* y t_4)))) (+ i t_9))
           (if (or (<= y 8.8e+172) (not (<= y 6.2e+260)))
             t_6
             (- (+ x (/ z y)) (/ (* x a) y)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = b + (y * (y + a));
	double t_2 = y * t_1;
	double t_3 = y * (z + (y * x));
	double t_4 = 27464.7644705 + t_3;
	double t_5 = t_1 * t_1;
	double t_6 = x / ((b / (y * y)) + (1.0 + ((c / pow(y, 3.0)) + ((i / pow(y, 4.0)) + (a / y)))));
	double t_7 = c + t_2;
	double t_8 = t_7 * t_7;
	double t_9 = y * t_7;
	double tmp;
	if (y <= -4.8e+218) {
		tmp = t_6;
	} else if (y <= -3.15e+100) {
		tmp = ((x + ((z / y) + (27464.7644705 / (y * y)))) - (a / ((y * y) / (z - (x * a))))) - ((a / (y / x)) + ((b / y) * (x / y)));
	} else if (y <= -3.3e+16) {
		tmp = (t / t_9) + ((i * (((230661.510616 * (-1.0 / (y * t_8))) + ((27464.7644705 * (-1.0 / t_8)) - (t_3 / t_8))) - (t / (pow(y, 2.0) * t_8)))) + ((t_4 / t_1) + ((230661.510616 * (1.0 / t_2)) + (c * (((27464.7644705 * (-1.0 / (t_2 * t_1))) + ((230661.510616 * (-1.0 / (t_1 * (pow(y, 2.0) * t_1)))) - ((y * x) / t_5))) - (z / t_5))))));
	} else if (y <= 4.2e+24) {
		tmp = (t + (y * (230661.510616 + (y * t_4)))) / (i + t_9);
	} else if ((y <= 8.8e+172) || !(y <= 6.2e+260)) {
		tmp = t_6;
	} else {
		tmp = (x + (z / y)) - ((x * a) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: t_8
    real(8) :: t_9
    real(8) :: tmp
    t_1 = b + (y * (y + a))
    t_2 = y * t_1
    t_3 = y * (z + (y * x))
    t_4 = 27464.7644705d0 + t_3
    t_5 = t_1 * t_1
    t_6 = x / ((b / (y * y)) + (1.0d0 + ((c / (y ** 3.0d0)) + ((i / (y ** 4.0d0)) + (a / y)))))
    t_7 = c + t_2
    t_8 = t_7 * t_7
    t_9 = y * t_7
    if (y <= (-4.8d+218)) then
        tmp = t_6
    else if (y <= (-3.15d+100)) then
        tmp = ((x + ((z / y) + (27464.7644705d0 / (y * y)))) - (a / ((y * y) / (z - (x * a))))) - ((a / (y / x)) + ((b / y) * (x / y)))
    else if (y <= (-3.3d+16)) then
        tmp = (t / t_9) + ((i * (((230661.510616d0 * ((-1.0d0) / (y * t_8))) + ((27464.7644705d0 * ((-1.0d0) / t_8)) - (t_3 / t_8))) - (t / ((y ** 2.0d0) * t_8)))) + ((t_4 / t_1) + ((230661.510616d0 * (1.0d0 / t_2)) + (c * (((27464.7644705d0 * ((-1.0d0) / (t_2 * t_1))) + ((230661.510616d0 * ((-1.0d0) / (t_1 * ((y ** 2.0d0) * t_1)))) - ((y * x) / t_5))) - (z / t_5))))))
    else if (y <= 4.2d+24) then
        tmp = (t + (y * (230661.510616d0 + (y * t_4)))) / (i + t_9)
    else if ((y <= 8.8d+172) .or. (.not. (y <= 6.2d+260))) then
        tmp = t_6
    else
        tmp = (x + (z / y)) - ((x * a) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = b + (y * (y + a));
	double t_2 = y * t_1;
	double t_3 = y * (z + (y * x));
	double t_4 = 27464.7644705 + t_3;
	double t_5 = t_1 * t_1;
	double t_6 = x / ((b / (y * y)) + (1.0 + ((c / Math.pow(y, 3.0)) + ((i / Math.pow(y, 4.0)) + (a / y)))));
	double t_7 = c + t_2;
	double t_8 = t_7 * t_7;
	double t_9 = y * t_7;
	double tmp;
	if (y <= -4.8e+218) {
		tmp = t_6;
	} else if (y <= -3.15e+100) {
		tmp = ((x + ((z / y) + (27464.7644705 / (y * y)))) - (a / ((y * y) / (z - (x * a))))) - ((a / (y / x)) + ((b / y) * (x / y)));
	} else if (y <= -3.3e+16) {
		tmp = (t / t_9) + ((i * (((230661.510616 * (-1.0 / (y * t_8))) + ((27464.7644705 * (-1.0 / t_8)) - (t_3 / t_8))) - (t / (Math.pow(y, 2.0) * t_8)))) + ((t_4 / t_1) + ((230661.510616 * (1.0 / t_2)) + (c * (((27464.7644705 * (-1.0 / (t_2 * t_1))) + ((230661.510616 * (-1.0 / (t_1 * (Math.pow(y, 2.0) * t_1)))) - ((y * x) / t_5))) - (z / t_5))))));
	} else if (y <= 4.2e+24) {
		tmp = (t + (y * (230661.510616 + (y * t_4)))) / (i + t_9);
	} else if ((y <= 8.8e+172) || !(y <= 6.2e+260)) {
		tmp = t_6;
	} else {
		tmp = (x + (z / y)) - ((x * a) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = b + (y * (y + a))
	t_2 = y * t_1
	t_3 = y * (z + (y * x))
	t_4 = 27464.7644705 + t_3
	t_5 = t_1 * t_1
	t_6 = x / ((b / (y * y)) + (1.0 + ((c / math.pow(y, 3.0)) + ((i / math.pow(y, 4.0)) + (a / y)))))
	t_7 = c + t_2
	t_8 = t_7 * t_7
	t_9 = y * t_7
	tmp = 0
	if y <= -4.8e+218:
		tmp = t_6
	elif y <= -3.15e+100:
		tmp = ((x + ((z / y) + (27464.7644705 / (y * y)))) - (a / ((y * y) / (z - (x * a))))) - ((a / (y / x)) + ((b / y) * (x / y)))
	elif y <= -3.3e+16:
		tmp = (t / t_9) + ((i * (((230661.510616 * (-1.0 / (y * t_8))) + ((27464.7644705 * (-1.0 / t_8)) - (t_3 / t_8))) - (t / (math.pow(y, 2.0) * t_8)))) + ((t_4 / t_1) + ((230661.510616 * (1.0 / t_2)) + (c * (((27464.7644705 * (-1.0 / (t_2 * t_1))) + ((230661.510616 * (-1.0 / (t_1 * (math.pow(y, 2.0) * t_1)))) - ((y * x) / t_5))) - (z / t_5))))))
	elif y <= 4.2e+24:
		tmp = (t + (y * (230661.510616 + (y * t_4)))) / (i + t_9)
	elif (y <= 8.8e+172) or not (y <= 6.2e+260):
		tmp = t_6
	else:
		tmp = (x + (z / y)) - ((x * a) / y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(b + Float64(y * Float64(y + a)))
	t_2 = Float64(y * t_1)
	t_3 = Float64(y * Float64(z + Float64(y * x)))
	t_4 = Float64(27464.7644705 + t_3)
	t_5 = Float64(t_1 * t_1)
	t_6 = Float64(x / Float64(Float64(b / Float64(y * y)) + Float64(1.0 + Float64(Float64(c / (y ^ 3.0)) + Float64(Float64(i / (y ^ 4.0)) + Float64(a / y))))))
	t_7 = Float64(c + t_2)
	t_8 = Float64(t_7 * t_7)
	t_9 = Float64(y * t_7)
	tmp = 0.0
	if (y <= -4.8e+218)
		tmp = t_6;
	elseif (y <= -3.15e+100)
		tmp = Float64(Float64(Float64(x + Float64(Float64(z / y) + Float64(27464.7644705 / Float64(y * y)))) - Float64(a / Float64(Float64(y * y) / Float64(z - Float64(x * a))))) - Float64(Float64(a / Float64(y / x)) + Float64(Float64(b / y) * Float64(x / y))));
	elseif (y <= -3.3e+16)
		tmp = Float64(Float64(t / t_9) + Float64(Float64(i * Float64(Float64(Float64(230661.510616 * Float64(-1.0 / Float64(y * t_8))) + Float64(Float64(27464.7644705 * Float64(-1.0 / t_8)) - Float64(t_3 / t_8))) - Float64(t / Float64((y ^ 2.0) * t_8)))) + Float64(Float64(t_4 / t_1) + Float64(Float64(230661.510616 * Float64(1.0 / t_2)) + Float64(c * Float64(Float64(Float64(27464.7644705 * Float64(-1.0 / Float64(t_2 * t_1))) + Float64(Float64(230661.510616 * Float64(-1.0 / Float64(t_1 * Float64((y ^ 2.0) * t_1)))) - Float64(Float64(y * x) / t_5))) - Float64(z / t_5)))))));
	elseif (y <= 4.2e+24)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * t_4)))) / Float64(i + t_9));
	elseif ((y <= 8.8e+172) || !(y <= 6.2e+260))
		tmp = t_6;
	else
		tmp = Float64(Float64(x + Float64(z / y)) - Float64(Float64(x * a) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = b + (y * (y + a));
	t_2 = y * t_1;
	t_3 = y * (z + (y * x));
	t_4 = 27464.7644705 + t_3;
	t_5 = t_1 * t_1;
	t_6 = x / ((b / (y * y)) + (1.0 + ((c / (y ^ 3.0)) + ((i / (y ^ 4.0)) + (a / y)))));
	t_7 = c + t_2;
	t_8 = t_7 * t_7;
	t_9 = y * t_7;
	tmp = 0.0;
	if (y <= -4.8e+218)
		tmp = t_6;
	elseif (y <= -3.15e+100)
		tmp = ((x + ((z / y) + (27464.7644705 / (y * y)))) - (a / ((y * y) / (z - (x * a))))) - ((a / (y / x)) + ((b / y) * (x / y)));
	elseif (y <= -3.3e+16)
		tmp = (t / t_9) + ((i * (((230661.510616 * (-1.0 / (y * t_8))) + ((27464.7644705 * (-1.0 / t_8)) - (t_3 / t_8))) - (t / ((y ^ 2.0) * t_8)))) + ((t_4 / t_1) + ((230661.510616 * (1.0 / t_2)) + (c * (((27464.7644705 * (-1.0 / (t_2 * t_1))) + ((230661.510616 * (-1.0 / (t_1 * ((y ^ 2.0) * t_1)))) - ((y * x) / t_5))) - (z / t_5))))));
	elseif (y <= 4.2e+24)
		tmp = (t + (y * (230661.510616 + (y * t_4)))) / (i + t_9);
	elseif ((y <= 8.8e+172) || ~((y <= 6.2e+260)))
		tmp = t_6;
	else
		tmp = (x + (z / y)) - ((x * a) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(y * N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(27464.7644705 + t$95$3), $MachinePrecision]}, Block[{t$95$5 = N[(t$95$1 * t$95$1), $MachinePrecision]}, Block[{t$95$6 = N[(x / N[(N[(b / N[(y * y), $MachinePrecision]), $MachinePrecision] + N[(1.0 + N[(N[(c / N[Power[y, 3.0], $MachinePrecision]), $MachinePrecision] + N[(N[(i / N[Power[y, 4.0], $MachinePrecision]), $MachinePrecision] + N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(c + t$95$2), $MachinePrecision]}, Block[{t$95$8 = N[(t$95$7 * t$95$7), $MachinePrecision]}, Block[{t$95$9 = N[(y * t$95$7), $MachinePrecision]}, If[LessEqual[y, -4.8e+218], t$95$6, If[LessEqual[y, -3.15e+100], N[(N[(N[(x + N[(N[(z / y), $MachinePrecision] + N[(27464.7644705 / N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a / N[(N[(y * y), $MachinePrecision] / N[(z - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision] + N[(N[(b / y), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3.3e+16], N[(N[(t / t$95$9), $MachinePrecision] + N[(N[(i * N[(N[(N[(230661.510616 * N[(-1.0 / N[(y * t$95$8), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(27464.7644705 * N[(-1.0 / t$95$8), $MachinePrecision]), $MachinePrecision] - N[(t$95$3 / t$95$8), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t / N[(N[Power[y, 2.0], $MachinePrecision] * t$95$8), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$4 / t$95$1), $MachinePrecision] + N[(N[(230661.510616 * N[(1.0 / t$95$2), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(N[(27464.7644705 * N[(-1.0 / N[(t$95$2 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(230661.510616 * N[(-1.0 / N[(t$95$1 * N[(N[Power[y, 2.0], $MachinePrecision] * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y * x), $MachinePrecision] / t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z / t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.2e+24], N[(N[(t + N[(y * N[(230661.510616 + N[(y * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + t$95$9), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 8.8e+172], N[Not[LessEqual[y, 6.2e+260]], $MachinePrecision]], t$95$6, N[(N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(N[(x * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -4.79999999999999961e218 or 4.2000000000000003e24 < y < 8.8000000000000005e172 or 6.1999999999999996e260 < y

   1. Initial program 2.2%

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

      1. clear-num 2.2%

         \[\leadsto \color{blue}{\frac{1}{\frac{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}}} \]

      2. inv-pow 2.2%

         \[\leadsto \color{blue}{{\left(\frac{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}\right)}^{-1}} \]

   3. Applied egg-rr 2.2%

      \[\leadsto \color{blue}{{\left(\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right), 230661.510616\right), t\right)}\right)}^{-1}} \]
   4. Step-by-step derivation

      1. unpow-1 2.2%

         \[\leadsto \color{blue}{\frac{1}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right), 230661.510616\right), t\right)}}} \]

      2. fma-udef 2.2%

         \[\leadsto \frac{1}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{x \cdot y + z}, 27464.7644705\right), 230661.510616\right), t\right)}} \]

      3. *-commutative 2.2%

         \[\leadsto \frac{1}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{y \cdot x} + z, 27464.7644705\right), 230661.510616\right), t\right)}} \]

      4. fma-def 2.2%

         \[\leadsto \frac{1}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(y, x, z\right)}, 27464.7644705\right), 230661.510616\right), t\right)}} \]

   5. Simplified 2.2%

      \[\leadsto \color{blue}{\frac{1}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), 27464.7644705\right), 230661.510616\right), t\right)}}} \]

   6. Taylor expanded in i around 0 2.2%

      \[\leadsto \frac{1}{\color{blue}{\frac{y \cdot \left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right)}{y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + \left(y \cdot x + z\right) \cdot y\right)\right) + t} + \frac{i}{y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + \left(y \cdot x + z\right) \cdot y\right)\right) + t}}} \]

   7. Taylor expanded in x around inf 86.4%

      \[\leadsto \color{blue}{\frac{x}{\frac{b}{{y}^{2}} + \left(1 + \left(\frac{c}{{y}^{3}} + \left(\frac{i}{{y}^{4}} + \frac{a}{y}\right)\right)\right)}} \]
   8. Step-by-step derivation

      1. unpow2 86.4%

         \[\leadsto \frac{x}{\frac{b}{\color{blue}{y \cdot y}} + \left(1 + \left(\frac{c}{{y}^{3}} + \left(\frac{i}{{y}^{4}} + \frac{a}{y}\right)\right)\right)} \]

   9. Simplified 86.4%

      \[\leadsto \color{blue}{\frac{x}{\frac{b}{y \cdot y} + \left(1 + \left(\frac{c}{{y}^{3}} + \left(\frac{i}{{y}^{4}} + \frac{a}{y}\right)\right)\right)}} \]

   if -4.79999999999999961e218 < y < -3.1500000000000002e100

   1. Initial program 0.0%

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

   2. Taylor expanded in y around inf 76.9%

      \[\leadsto \color{blue}{\left(\frac{z}{y} + \left(27464.7644705 \cdot \frac{1}{{y}^{2}} + x\right)\right) - \left(\frac{\left(z - a \cdot x\right) \cdot a}{{y}^{2}} + \left(\frac{a \cdot x}{y} + \frac{b \cdot x}{{y}^{2}}\right)\right)} \]
   3. Step-by-step derivation

      1. associate--r+ 76.9%

         \[\leadsto \color{blue}{\left(\left(\frac{z}{y} + \left(27464.7644705 \cdot \frac{1}{{y}^{2}} + x\right)\right) - \frac{\left(z - a \cdot x\right) \cdot a}{{y}^{2}}\right) - \left(\frac{a \cdot x}{y} + \frac{b \cdot x}{{y}^{2}}\right)} \]

      2. associate-+r+ 76.9%

         \[\leadsto \left(\color{blue}{\left(\left(\frac{z}{y} + 27464.7644705 \cdot \frac{1}{{y}^{2}}\right) + x\right)} - \frac{\left(z - a \cdot x\right) \cdot a}{{y}^{2}}\right) - \left(\frac{a \cdot x}{y} + \frac{b \cdot x}{{y}^{2}}\right) \]

      3. associate-*r/ 76.9%

         \[\leadsto \left(\left(\left(\frac{z}{y} + \color{blue}{\frac{27464.7644705 \cdot 1}{{y}^{2}}}\right) + x\right) - \frac{\left(z - a \cdot x\right) \cdot a}{{y}^{2}}\right) - \left(\frac{a \cdot x}{y} + \frac{b \cdot x}{{y}^{2}}\right) \]

      4. metadata-eval 76.9%

         \[\leadsto \left(\left(\left(\frac{z}{y} + \frac{\color{blue}{27464.7644705}}{{y}^{2}}\right) + x\right) - \frac{\left(z - a \cdot x\right) \cdot a}{{y}^{2}}\right) - \left(\frac{a \cdot x}{y} + \frac{b \cdot x}{{y}^{2}}\right) \]

      5. unpow2 76.9%

         \[\leadsto \left(\left(\left(\frac{z}{y} + \frac{27464.7644705}{\color{blue}{y \cdot y}}\right) + x\right) - \frac{\left(z - a \cdot x\right) \cdot a}{{y}^{2}}\right) - \left(\frac{a \cdot x}{y} + \frac{b \cdot x}{{y}^{2}}\right) \]

      6. *-commutative 76.9%

         \[\leadsto \left(\left(\left(\frac{z}{y} + \frac{27464.7644705}{y \cdot y}\right) + x\right) - \frac{\color{blue}{a \cdot \left(z - a \cdot x\right)}}{{y}^{2}}\right) - \left(\frac{a \cdot x}{y} + \frac{b \cdot x}{{y}^{2}}\right) \]

      7. associate-/l* 87.4%

         \[\leadsto \left(\left(\left(\frac{z}{y} + \frac{27464.7644705}{y \cdot y}\right) + x\right) - \color{blue}{\frac{a}{\frac{{y}^{2}}{z - a \cdot x}}}\right) - \left(\frac{a \cdot x}{y} + \frac{b \cdot x}{{y}^{2}}\right) \]

      8. unpow2 87.4%

         \[\leadsto \left(\left(\left(\frac{z}{y} + \frac{27464.7644705}{y \cdot y}\right) + x\right) - \frac{a}{\frac{\color{blue}{y \cdot y}}{z - a \cdot x}}\right) - \left(\frac{a \cdot x}{y} + \frac{b \cdot x}{{y}^{2}}\right) \]

      9. associate-/l* 87.4%

         \[\leadsto \left(\left(\left(\frac{z}{y} + \frac{27464.7644705}{y \cdot y}\right) + x\right) - \frac{a}{\frac{y \cdot y}{z - a \cdot x}}\right) - \left(\color{blue}{\frac{a}{\frac{y}{x}}} + \frac{b \cdot x}{{y}^{2}}\right) \]

      10. unpow2 87.4%

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

      11. times-frac 87.7%

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

   4. Simplified 87.7%

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

   if -3.1500000000000002e100 < y < -3.3e16

   1. Initial program 19.7%

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

   2. Taylor expanded in i around 0 48.9%

      \[\leadsto \color{blue}{\frac{t}{y \cdot \left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right)} + \left(-1 \cdot \left(i \cdot \left(\frac{t}{{y}^{2} \cdot \left(\left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) \cdot \left(c + \left(b + y \cdot \left(a + y\right)\right) \cdot y\right)\right)} + \left(230661.510616 \cdot \frac{1}{y \cdot \left(\left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) \cdot \left(c + \left(b + y \cdot \left(a + y\right)\right) \cdot y\right)\right)} + \left(27464.7644705 \cdot \frac{1}{\left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) \cdot \left(c + \left(b + y \cdot \left(a + y\right)\right) \cdot y\right)} + \frac{\left(y \cdot x + z\right) \cdot y}{\left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) \cdot \left(c + \left(b + y \cdot \left(a + y\right)\right) \cdot y\right)}\right)\right)\right)\right) + \frac{230661.510616 + y \cdot \left(27464.7644705 + \left(y \cdot x + z\right) \cdot y\right)}{c + y \cdot \left(\left(y + a\right) \cdot y + b\right)}\right)} \]

   3. Taylor expanded in c around 0 77.1%

      \[\leadsto \frac{t}{y \cdot \left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right)} + \left(-1 \cdot \left(i \cdot \left(\frac{t}{{y}^{2} \cdot \left(\left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) \cdot \left(c + \left(b + y \cdot \left(a + y\right)\right) \cdot y\right)\right)} + \left(230661.510616 \cdot \frac{1}{y \cdot \left(\left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) \cdot \left(c + \left(b + y \cdot \left(a + y\right)\right) \cdot y\right)\right)} + \left(27464.7644705 \cdot \frac{1}{\left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) \cdot \left(c + \left(b + y \cdot \left(a + y\right)\right) \cdot y\right)} + \frac{\left(y \cdot x + z\right) \cdot y}{\left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) \cdot \left(c + \left(b + y \cdot \left(a + y\right)\right) \cdot y\right)}\right)\right)\right)\right) + \color{blue}{\left(\frac{27464.7644705 + \left(y \cdot x + z\right) \cdot y}{\left(y + a\right) \cdot y + b} + \left(230661.510616 \cdot \frac{1}{y \cdot \left(\left(y + a\right) \cdot y + b\right)} + -1 \cdot \left(c \cdot \left(\frac{z}{\left(b + y \cdot \left(a + y\right)\right) \cdot \left(\left(y + a\right) \cdot y + b\right)} + \left(27464.7644705 \cdot \frac{1}{\left(b + y \cdot \left(a + y\right)\right) \cdot \left(y \cdot \left(\left(y + a\right) \cdot y + b\right)\right)} + \left(230661.510616 \cdot \frac{1}{\left(b + y \cdot \left(a + y\right)\right) \cdot \left({y}^{2} \cdot \left(\left(y + a\right) \cdot y + b\right)\right)} + \frac{y \cdot x}{\left(b + y \cdot \left(a + y\right)\right) \cdot \left(\left(y + a\right) \cdot y + b\right)}\right)\right)\right)\right)\right)\right)}\right) \]

   if -3.3e16 < y < 4.2000000000000003e24

   1. Initial program 97.6%

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

   if 8.8000000000000005e172 < y < 6.1999999999999996e260

   1. Initial program 0.0%

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

   2. Taylor expanded in y around inf 87.1%

      \[\leadsto \color{blue}{\left(\frac{z}{y} + x\right) - \frac{a \cdot x}{y}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{+218}:\\ \;\;\;\;\frac{x}{\frac{b}{y \cdot y} + \left(1 + \left(\frac{c}{{y}^{3}} + \left(\frac{i}{{y}^{4}} + \frac{a}{y}\right)\right)\right)}\\ \mathbf{elif}\;y \leq -3.15 \cdot 10^{+100}:\\ \;\;\;\;\left(\left(x + \left(\frac{z}{y} + \frac{27464.7644705}{y \cdot y}\right)\right) - \frac{a}{\frac{y \cdot y}{z - x \cdot a}}\right) - \left(\frac{a}{\frac{y}{x}} + \frac{b}{y} \cdot \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -3.3 \cdot 10^{+16}:\\ \;\;\;\;\frac{t}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)} + \left(i \cdot \left(\left(230661.510616 \cdot \frac{-1}{y \cdot \left(\left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)\right)} + \left(27464.7644705 \cdot \frac{-1}{\left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)} - \frac{y \cdot \left(z + y \cdot x\right)}{\left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\right)\right) - \frac{t}{{y}^{2} \cdot \left(\left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)\right)}\right) + \left(\frac{27464.7644705 + y \cdot \left(z + y \cdot x\right)}{b + y \cdot \left(y + a\right)} + \left(230661.510616 \cdot \frac{1}{y \cdot \left(b + y \cdot \left(y + a\right)\right)} + c \cdot \left(\left(27464.7644705 \cdot \frac{-1}{\left(y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) \cdot \left(b + y \cdot \left(y + a\right)\right)} + \left(230661.510616 \cdot \frac{-1}{\left(b + y \cdot \left(y + a\right)\right) \cdot \left({y}^{2} \cdot \left(b + y \cdot \left(y + a\right)\right)\right)} - \frac{y \cdot x}{\left(b + y \cdot \left(y + a\right)\right) \cdot \left(b + y \cdot \left(y + a\right)\right)}\right)\right) - \frac{z}{\left(b + y \cdot \left(y + a\right)\right) \cdot \left(b + y \cdot \left(y + a\right)\right)}\right)\right)\right)\right)\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+24}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{+172} \lor \neg \left(y \leq 6.2 \cdot 10^{+260}\right):\\ \;\;\;\;\frac{x}{\frac{b}{y \cdot y} + \left(1 + \left(\frac{c}{{y}^{3}} + \left(\frac{i}{{y}^{4}} + \frac{a}{y}\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \end{array} \]

Alternative 2: 84.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\frac{b}{y \cdot y} + \left(1 + \left(\frac{c}{{y}^{3}} + \left(\frac{i}{{y}^{4}} + \frac{a}{y}\right)\right)\right)}\\ \mathbf{if}\;y \leq -6.4 \cdot 10^{+217}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.85 \cdot 10^{+102}:\\ \;\;\;\;\left(\left(x + \left(\frac{z}{y} + \frac{27464.7644705}{y \cdot y}\right)\right) - \frac{a}{\frac{y \cdot y}{z - x \cdot a}}\right) - \left(\frac{a}{\frac{y}{x}} + \frac{b}{y} \cdot \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{+19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+24}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+173} \lor \neg \left(y \leq 5.5 \cdot 10^{+260}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1
         (/
          x
          (+
           (/ b (* y y))
           (+ 1.0 (+ (/ c (pow y 3.0)) (+ (/ i (pow y 4.0)) (/ a y))))))))
   (if (<= y -6.4e+217)
     t_1
     (if (<= y -1.85e+102)
       (-
        (-
         (+ x (+ (/ z y) (/ 27464.7644705 (* y y))))
         (/ a (/ (* y y) (- z (* x a)))))
        (+ (/ a (/ y x)) (* (/ b y) (/ x y))))
       (if (<= y -6.5e+19)
         t_1
         (if (<= y 2.7e+24)
           (/
            (+
             t
             (*
              y
              (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ z (* y x))))))))
            (+ i (* y (+ c (* y (+ b (* y (+ y a))))))))
           (if (or (<= y 5.5e+173) (not (<= y 5.5e+260)))
             t_1
             (- (+ x (/ z y)) (/ (* x a) y)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x / ((b / (y * y)) + (1.0 + ((c / pow(y, 3.0)) + ((i / pow(y, 4.0)) + (a / y)))));
	double tmp;
	if (y <= -6.4e+217) {
		tmp = t_1;
	} else if (y <= -1.85e+102) {
		tmp = ((x + ((z / y) + (27464.7644705 / (y * y)))) - (a / ((y * y) / (z - (x * a))))) - ((a / (y / x)) + ((b / y) * (x / y)));
	} else if (y <= -6.5e+19) {
		tmp = t_1;
	} else if (y <= 2.7e+24) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / (i + (y * (c + (y * (b + (y * (y + a)))))));
	} else if ((y <= 5.5e+173) || !(y <= 5.5e+260)) {
		tmp = t_1;
	} else {
		tmp = (x + (z / y)) - ((x * a) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / ((b / (y * y)) + (1.0d0 + ((c / (y ** 3.0d0)) + ((i / (y ** 4.0d0)) + (a / y)))))
    if (y <= (-6.4d+217)) then
        tmp = t_1
    else if (y <= (-1.85d+102)) then
        tmp = ((x + ((z / y) + (27464.7644705d0 / (y * y)))) - (a / ((y * y) / (z - (x * a))))) - ((a / (y / x)) + ((b / y) * (x / y)))
    else if (y <= (-6.5d+19)) then
        tmp = t_1
    else if (y <= 2.7d+24) then
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * (z + (y * x)))))))) / (i + (y * (c + (y * (b + (y * (y + a)))))))
    else if ((y <= 5.5d+173) .or. (.not. (y <= 5.5d+260))) then
        tmp = t_1
    else
        tmp = (x + (z / y)) - ((x * a) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x / ((b / (y * y)) + (1.0 + ((c / Math.pow(y, 3.0)) + ((i / Math.pow(y, 4.0)) + (a / y)))));
	double tmp;
	if (y <= -6.4e+217) {
		tmp = t_1;
	} else if (y <= -1.85e+102) {
		tmp = ((x + ((z / y) + (27464.7644705 / (y * y)))) - (a / ((y * y) / (z - (x * a))))) - ((a / (y / x)) + ((b / y) * (x / y)));
	} else if (y <= -6.5e+19) {
		tmp = t_1;
	} else if (y <= 2.7e+24) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / (i + (y * (c + (y * (b + (y * (y + a)))))));
	} else if ((y <= 5.5e+173) || !(y <= 5.5e+260)) {
		tmp = t_1;
	} else {
		tmp = (x + (z / y)) - ((x * a) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x / ((b / (y * y)) + (1.0 + ((c / math.pow(y, 3.0)) + ((i / math.pow(y, 4.0)) + (a / y)))))
	tmp = 0
	if y <= -6.4e+217:
		tmp = t_1
	elif y <= -1.85e+102:
		tmp = ((x + ((z / y) + (27464.7644705 / (y * y)))) - (a / ((y * y) / (z - (x * a))))) - ((a / (y / x)) + ((b / y) * (x / y)))
	elif y <= -6.5e+19:
		tmp = t_1
	elif y <= 2.7e+24:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / (i + (y * (c + (y * (b + (y * (y + a)))))))
	elif (y <= 5.5e+173) or not (y <= 5.5e+260):
		tmp = t_1
	else:
		tmp = (x + (z / y)) - ((x * a) / y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x / Float64(Float64(b / Float64(y * y)) + Float64(1.0 + Float64(Float64(c / (y ^ 3.0)) + Float64(Float64(i / (y ^ 4.0)) + Float64(a / y))))))
	tmp = 0.0
	if (y <= -6.4e+217)
		tmp = t_1;
	elseif (y <= -1.85e+102)
		tmp = Float64(Float64(Float64(x + Float64(Float64(z / y) + Float64(27464.7644705 / Float64(y * y)))) - Float64(a / Float64(Float64(y * y) / Float64(z - Float64(x * a))))) - Float64(Float64(a / Float64(y / x)) + Float64(Float64(b / y) * Float64(x / y))));
	elseif (y <= -6.5e+19)
		tmp = t_1;
	elseif (y <= 2.7e+24)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(z + Float64(y * x)))))))) / Float64(i + Float64(y * Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a))))))));
	elseif ((y <= 5.5e+173) || !(y <= 5.5e+260))
		tmp = t_1;
	else
		tmp = Float64(Float64(x + Float64(z / y)) - Float64(Float64(x * a) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x / ((b / (y * y)) + (1.0 + ((c / (y ^ 3.0)) + ((i / (y ^ 4.0)) + (a / y)))));
	tmp = 0.0;
	if (y <= -6.4e+217)
		tmp = t_1;
	elseif (y <= -1.85e+102)
		tmp = ((x + ((z / y) + (27464.7644705 / (y * y)))) - (a / ((y * y) / (z - (x * a))))) - ((a / (y / x)) + ((b / y) * (x / y)));
	elseif (y <= -6.5e+19)
		tmp = t_1;
	elseif (y <= 2.7e+24)
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / (i + (y * (c + (y * (b + (y * (y + a)))))));
	elseif ((y <= 5.5e+173) || ~((y <= 5.5e+260)))
		tmp = t_1;
	else
		tmp = (x + (z / y)) - ((x * a) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x / N[(N[(b / N[(y * y), $MachinePrecision]), $MachinePrecision] + N[(1.0 + N[(N[(c / N[Power[y, 3.0], $MachinePrecision]), $MachinePrecision] + N[(N[(i / N[Power[y, 4.0], $MachinePrecision]), $MachinePrecision] + N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.4e+217], t$95$1, If[LessEqual[y, -1.85e+102], N[(N[(N[(x + N[(N[(z / y), $MachinePrecision] + N[(27464.7644705 / N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a / N[(N[(y * y), $MachinePrecision] / N[(z - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision] + N[(N[(b / y), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -6.5e+19], t$95$1, If[LessEqual[y, 2.7e+24], N[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 5.5e+173], N[Not[LessEqual[y, 5.5e+260]], $MachinePrecision]], t$95$1, N[(N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(N[(x * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -6.4000000000000001e217 or -1.85000000000000011e102 < y < -6.5e19 or 2.7e24 < y < 5.50000000000000049e173 or 5.49999999999999961e260 < y

   1. Initial program 6.9%

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

      1. clear-num 6.9%

         \[\leadsto \color{blue}{\frac{1}{\frac{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}}} \]

      2. inv-pow 6.9%

         \[\leadsto \color{blue}{{\left(\frac{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}\right)}^{-1}} \]

   3. Applied egg-rr 6.9%

      \[\leadsto \color{blue}{{\left(\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right), 230661.510616\right), t\right)}\right)}^{-1}} \]
   4. Step-by-step derivation

      1. unpow-1 6.9%

         \[\leadsto \color{blue}{\frac{1}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right), 230661.510616\right), t\right)}}} \]

      2. fma-udef 6.9%

         \[\leadsto \frac{1}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{x \cdot y + z}, 27464.7644705\right), 230661.510616\right), t\right)}} \]

      3. *-commutative 6.9%

         \[\leadsto \frac{1}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{y \cdot x} + z, 27464.7644705\right), 230661.510616\right), t\right)}} \]

      4. fma-def 6.9%

         \[\leadsto \frac{1}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(y, x, z\right)}, 27464.7644705\right), 230661.510616\right), t\right)}} \]

   5. Simplified 6.9%

      \[\leadsto \color{blue}{\frac{1}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), 27464.7644705\right), 230661.510616\right), t\right)}}} \]

   6. Taylor expanded in i around 0 6.9%

      \[\leadsto \frac{1}{\color{blue}{\frac{y \cdot \left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right)}{y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + \left(y \cdot x + z\right) \cdot y\right)\right) + t} + \frac{i}{y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + \left(y \cdot x + z\right) \cdot y\right)\right) + t}}} \]

   7. Taylor expanded in x around inf 81.0%

      \[\leadsto \color{blue}{\frac{x}{\frac{b}{{y}^{2}} + \left(1 + \left(\frac{c}{{y}^{3}} + \left(\frac{i}{{y}^{4}} + \frac{a}{y}\right)\right)\right)}} \]
   8. Step-by-step derivation

      1. unpow2 81.0%

         \[\leadsto \frac{x}{\frac{b}{\color{blue}{y \cdot y}} + \left(1 + \left(\frac{c}{{y}^{3}} + \left(\frac{i}{{y}^{4}} + \frac{a}{y}\right)\right)\right)} \]

   9. Simplified 81.0%

      \[\leadsto \color{blue}{\frac{x}{\frac{b}{y \cdot y} + \left(1 + \left(\frac{c}{{y}^{3}} + \left(\frac{i}{{y}^{4}} + \frac{a}{y}\right)\right)\right)}} \]

   if -6.4000000000000001e217 < y < -1.85000000000000011e102

   1. Initial program 0.0%

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

   2. Taylor expanded in y around inf 76.9%

      \[\leadsto \color{blue}{\left(\frac{z}{y} + \left(27464.7644705 \cdot \frac{1}{{y}^{2}} + x\right)\right) - \left(\frac{\left(z - a \cdot x\right) \cdot a}{{y}^{2}} + \left(\frac{a \cdot x}{y} + \frac{b \cdot x}{{y}^{2}}\right)\right)} \]
   3. Step-by-step derivation

      1. associate--r+ 76.9%

         \[\leadsto \color{blue}{\left(\left(\frac{z}{y} + \left(27464.7644705 \cdot \frac{1}{{y}^{2}} + x\right)\right) - \frac{\left(z - a \cdot x\right) \cdot a}{{y}^{2}}\right) - \left(\frac{a \cdot x}{y} + \frac{b \cdot x}{{y}^{2}}\right)} \]

      2. associate-+r+ 76.9%

         \[\leadsto \left(\color{blue}{\left(\left(\frac{z}{y} + 27464.7644705 \cdot \frac{1}{{y}^{2}}\right) + x\right)} - \frac{\left(z - a \cdot x\right) \cdot a}{{y}^{2}}\right) - \left(\frac{a \cdot x}{y} + \frac{b \cdot x}{{y}^{2}}\right) \]

      3. associate-*r/ 76.9%

         \[\leadsto \left(\left(\left(\frac{z}{y} + \color{blue}{\frac{27464.7644705 \cdot 1}{{y}^{2}}}\right) + x\right) - \frac{\left(z - a \cdot x\right) \cdot a}{{y}^{2}}\right) - \left(\frac{a \cdot x}{y} + \frac{b \cdot x}{{y}^{2}}\right) \]

      4. metadata-eval 76.9%

         \[\leadsto \left(\left(\left(\frac{z}{y} + \frac{\color{blue}{27464.7644705}}{{y}^{2}}\right) + x\right) - \frac{\left(z - a \cdot x\right) \cdot a}{{y}^{2}}\right) - \left(\frac{a \cdot x}{y} + \frac{b \cdot x}{{y}^{2}}\right) \]

      5. unpow2 76.9%

         \[\leadsto \left(\left(\left(\frac{z}{y} + \frac{27464.7644705}{\color{blue}{y \cdot y}}\right) + x\right) - \frac{\left(z - a \cdot x\right) \cdot a}{{y}^{2}}\right) - \left(\frac{a \cdot x}{y} + \frac{b \cdot x}{{y}^{2}}\right) \]

      6. *-commutative 76.9%

         \[\leadsto \left(\left(\left(\frac{z}{y} + \frac{27464.7644705}{y \cdot y}\right) + x\right) - \frac{\color{blue}{a \cdot \left(z - a \cdot x\right)}}{{y}^{2}}\right) - \left(\frac{a \cdot x}{y} + \frac{b \cdot x}{{y}^{2}}\right) \]

      7. associate-/l* 87.4%

         \[\leadsto \left(\left(\left(\frac{z}{y} + \frac{27464.7644705}{y \cdot y}\right) + x\right) - \color{blue}{\frac{a}{\frac{{y}^{2}}{z - a \cdot x}}}\right) - \left(\frac{a \cdot x}{y} + \frac{b \cdot x}{{y}^{2}}\right) \]

      8. unpow2 87.4%

         \[\leadsto \left(\left(\left(\frac{z}{y} + \frac{27464.7644705}{y \cdot y}\right) + x\right) - \frac{a}{\frac{\color{blue}{y \cdot y}}{z - a \cdot x}}\right) - \left(\frac{a \cdot x}{y} + \frac{b \cdot x}{{y}^{2}}\right) \]

      9. associate-/l* 87.4%

         \[\leadsto \left(\left(\left(\frac{z}{y} + \frac{27464.7644705}{y \cdot y}\right) + x\right) - \frac{a}{\frac{y \cdot y}{z - a \cdot x}}\right) - \left(\color{blue}{\frac{a}{\frac{y}{x}}} + \frac{b \cdot x}{{y}^{2}}\right) \]

      10. unpow2 87.4%

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

      11. times-frac 87.7%

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

   4. Simplified 87.7%

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

   if -6.5e19 < y < 2.7e24

   1. Initial program 96.9%

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

   if 5.50000000000000049e173 < y < 5.49999999999999961e260

   1. Initial program 0.0%

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

   2. Taylor expanded in y around inf 87.1%

      \[\leadsto \color{blue}{\left(\frac{z}{y} + x\right) - \frac{a \cdot x}{y}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.4 \cdot 10^{+217}:\\ \;\;\;\;\frac{x}{\frac{b}{y \cdot y} + \left(1 + \left(\frac{c}{{y}^{3}} + \left(\frac{i}{{y}^{4}} + \frac{a}{y}\right)\right)\right)}\\ \mathbf{elif}\;y \leq -1.85 \cdot 10^{+102}:\\ \;\;\;\;\left(\left(x + \left(\frac{z}{y} + \frac{27464.7644705}{y \cdot y}\right)\right) - \frac{a}{\frac{y \cdot y}{z - x \cdot a}}\right) - \left(\frac{a}{\frac{y}{x}} + \frac{b}{y} \cdot \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{+19}:\\ \;\;\;\;\frac{x}{\frac{b}{y \cdot y} + \left(1 + \left(\frac{c}{{y}^{3}} + \left(\frac{i}{{y}^{4}} + \frac{a}{y}\right)\right)\right)}\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+24}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+173} \lor \neg \left(y \leq 5.5 \cdot 10^{+260}\right):\\ \;\;\;\;\frac{x}{\frac{b}{y \cdot y} + \left(1 + \left(\frac{c}{{y}^{3}} + \left(\frac{i}{{y}^{4}} + \frac{a}{y}\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \end{array} \]

Alternative 3: 82.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot y\right)\\ t_2 := y \cdot \left(y + a\right)\\ t_3 := c + y \cdot \left(b + t_2\right)\\ t_4 := t_3 \cdot t_3\\ t_5 := y \cdot \left(z + y \cdot x\right)\\ t_6 := 230661.510616 + y \cdot \left(27464.7644705 + t_5\right)\\ t_7 := \left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ t_8 := c + y \cdot t_2\\ \mathbf{if}\;y \leq -6.2 \cdot 10^{+101}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;y \leq -7 \cdot 10^{+22}:\\ \;\;\;\;\frac{1}{\frac{a}{y \cdot x} + \left(\left(\frac{1}{x} + \frac{b}{t_1}\right) + \left(\frac{\frac{z}{x \cdot x} - \frac{a}{x}}{\frac{t_1}{z}} - \left(\frac{z}{y \cdot \left(x \cdot x\right)} + \frac{27464.7644705}{\left(y \cdot y\right) \cdot \left(x \cdot x\right)}\right)\right)\right)}\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{+18}:\\ \;\;\;\;\frac{t + y \cdot t_6}{i + y \cdot t_3}\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+95}:\\ \;\;\;\;\frac{\frac{t}{y}}{t_8} + \left(\frac{t_6}{t_3} - i \cdot \left(\left(230661.510616 \cdot \frac{1}{y \cdot t_4} + \left(27464.7644705 \cdot \frac{1}{t_4} + \frac{t_5}{t_4}\right)\right) + \frac{t}{t_8 \cdot \left(\left(y \cdot y\right) \cdot t_8\right)}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_7\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* x (* y y)))
        (t_2 (* y (+ y a)))
        (t_3 (+ c (* y (+ b t_2))))
        (t_4 (* t_3 t_3))
        (t_5 (* y (+ z (* y x))))
        (t_6 (+ 230661.510616 (* y (+ 27464.7644705 t_5))))
        (t_7 (- (+ x (/ z y)) (/ (* x a) y)))
        (t_8 (+ c (* y t_2))))
   (if (<= y -6.2e+101)
     t_7
     (if (<= y -7e+22)
       (/
        1.0
        (+
         (/ a (* y x))
         (+
          (+ (/ 1.0 x) (/ b t_1))
          (-
           (/ (- (/ z (* x x)) (/ a x)) (/ t_1 z))
           (+ (/ z (* y (* x x))) (/ 27464.7644705 (* (* y y) (* x x))))))))
       (if (<= y 2.15e+18)
         (/ (+ t (* y t_6)) (+ i (* y t_3)))
         (if (<= y 8e+95)
           (+
            (/ (/ t y) t_8)
            (-
             (/ t_6 t_3)
             (*
              i
              (+
               (+
                (* 230661.510616 (/ 1.0 (* y t_4)))
                (+ (* 27464.7644705 (/ 1.0 t_4)) (/ t_5 t_4)))
               (/ t (* t_8 (* (* y y) t_8)))))))
           t_7))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x * (y * y);
	double t_2 = y * (y + a);
	double t_3 = c + (y * (b + t_2));
	double t_4 = t_3 * t_3;
	double t_5 = y * (z + (y * x));
	double t_6 = 230661.510616 + (y * (27464.7644705 + t_5));
	double t_7 = (x + (z / y)) - ((x * a) / y);
	double t_8 = c + (y * t_2);
	double tmp;
	if (y <= -6.2e+101) {
		tmp = t_7;
	} else if (y <= -7e+22) {
		tmp = 1.0 / ((a / (y * x)) + (((1.0 / x) + (b / t_1)) + ((((z / (x * x)) - (a / x)) / (t_1 / z)) - ((z / (y * (x * x))) + (27464.7644705 / ((y * y) * (x * x)))))));
	} else if (y <= 2.15e+18) {
		tmp = (t + (y * t_6)) / (i + (y * t_3));
	} else if (y <= 8e+95) {
		tmp = ((t / y) / t_8) + ((t_6 / t_3) - (i * (((230661.510616 * (1.0 / (y * t_4))) + ((27464.7644705 * (1.0 / t_4)) + (t_5 / t_4))) + (t / (t_8 * ((y * y) * t_8))))));
	} else {
		tmp = t_7;
	}
	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) :: t_7
    real(8) :: t_8
    real(8) :: tmp
    t_1 = x * (y * y)
    t_2 = y * (y + a)
    t_3 = c + (y * (b + t_2))
    t_4 = t_3 * t_3
    t_5 = y * (z + (y * x))
    t_6 = 230661.510616d0 + (y * (27464.7644705d0 + t_5))
    t_7 = (x + (z / y)) - ((x * a) / y)
    t_8 = c + (y * t_2)
    if (y <= (-6.2d+101)) then
        tmp = t_7
    else if (y <= (-7d+22)) then
        tmp = 1.0d0 / ((a / (y * x)) + (((1.0d0 / x) + (b / t_1)) + ((((z / (x * x)) - (a / x)) / (t_1 / z)) - ((z / (y * (x * x))) + (27464.7644705d0 / ((y * y) * (x * x)))))))
    else if (y <= 2.15d+18) then
        tmp = (t + (y * t_6)) / (i + (y * t_3))
    else if (y <= 8d+95) then
        tmp = ((t / y) / t_8) + ((t_6 / t_3) - (i * (((230661.510616d0 * (1.0d0 / (y * t_4))) + ((27464.7644705d0 * (1.0d0 / t_4)) + (t_5 / t_4))) + (t / (t_8 * ((y * y) * t_8))))))
    else
        tmp = t_7
    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 = x * (y * y);
	double t_2 = y * (y + a);
	double t_3 = c + (y * (b + t_2));
	double t_4 = t_3 * t_3;
	double t_5 = y * (z + (y * x));
	double t_6 = 230661.510616 + (y * (27464.7644705 + t_5));
	double t_7 = (x + (z / y)) - ((x * a) / y);
	double t_8 = c + (y * t_2);
	double tmp;
	if (y <= -6.2e+101) {
		tmp = t_7;
	} else if (y <= -7e+22) {
		tmp = 1.0 / ((a / (y * x)) + (((1.0 / x) + (b / t_1)) + ((((z / (x * x)) - (a / x)) / (t_1 / z)) - ((z / (y * (x * x))) + (27464.7644705 / ((y * y) * (x * x)))))));
	} else if (y <= 2.15e+18) {
		tmp = (t + (y * t_6)) / (i + (y * t_3));
	} else if (y <= 8e+95) {
		tmp = ((t / y) / t_8) + ((t_6 / t_3) - (i * (((230661.510616 * (1.0 / (y * t_4))) + ((27464.7644705 * (1.0 / t_4)) + (t_5 / t_4))) + (t / (t_8 * ((y * y) * t_8))))));
	} else {
		tmp = t_7;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x * (y * y)
	t_2 = y * (y + a)
	t_3 = c + (y * (b + t_2))
	t_4 = t_3 * t_3
	t_5 = y * (z + (y * x))
	t_6 = 230661.510616 + (y * (27464.7644705 + t_5))
	t_7 = (x + (z / y)) - ((x * a) / y)
	t_8 = c + (y * t_2)
	tmp = 0
	if y <= -6.2e+101:
		tmp = t_7
	elif y <= -7e+22:
		tmp = 1.0 / ((a / (y * x)) + (((1.0 / x) + (b / t_1)) + ((((z / (x * x)) - (a / x)) / (t_1 / z)) - ((z / (y * (x * x))) + (27464.7644705 / ((y * y) * (x * x)))))))
	elif y <= 2.15e+18:
		tmp = (t + (y * t_6)) / (i + (y * t_3))
	elif y <= 8e+95:
		tmp = ((t / y) / t_8) + ((t_6 / t_3) - (i * (((230661.510616 * (1.0 / (y * t_4))) + ((27464.7644705 * (1.0 / t_4)) + (t_5 / t_4))) + (t / (t_8 * ((y * y) * t_8))))))
	else:
		tmp = t_7
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x * Float64(y * y))
	t_2 = Float64(y * Float64(y + a))
	t_3 = Float64(c + Float64(y * Float64(b + t_2)))
	t_4 = Float64(t_3 * t_3)
	t_5 = Float64(y * Float64(z + Float64(y * x)))
	t_6 = Float64(230661.510616 + Float64(y * Float64(27464.7644705 + t_5)))
	t_7 = Float64(Float64(x + Float64(z / y)) - Float64(Float64(x * a) / y))
	t_8 = Float64(c + Float64(y * t_2))
	tmp = 0.0
	if (y <= -6.2e+101)
		tmp = t_7;
	elseif (y <= -7e+22)
		tmp = Float64(1.0 / Float64(Float64(a / Float64(y * x)) + Float64(Float64(Float64(1.0 / x) + Float64(b / t_1)) + Float64(Float64(Float64(Float64(z / Float64(x * x)) - Float64(a / x)) / Float64(t_1 / z)) - Float64(Float64(z / Float64(y * Float64(x * x))) + Float64(27464.7644705 / Float64(Float64(y * y) * Float64(x * x))))))));
	elseif (y <= 2.15e+18)
		tmp = Float64(Float64(t + Float64(y * t_6)) / Float64(i + Float64(y * t_3)));
	elseif (y <= 8e+95)
		tmp = Float64(Float64(Float64(t / y) / t_8) + Float64(Float64(t_6 / t_3) - Float64(i * Float64(Float64(Float64(230661.510616 * Float64(1.0 / Float64(y * t_4))) + Float64(Float64(27464.7644705 * Float64(1.0 / t_4)) + Float64(t_5 / t_4))) + Float64(t / Float64(t_8 * Float64(Float64(y * y) * t_8)))))));
	else
		tmp = t_7;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x * (y * y);
	t_2 = y * (y + a);
	t_3 = c + (y * (b + t_2));
	t_4 = t_3 * t_3;
	t_5 = y * (z + (y * x));
	t_6 = 230661.510616 + (y * (27464.7644705 + t_5));
	t_7 = (x + (z / y)) - ((x * a) / y);
	t_8 = c + (y * t_2);
	tmp = 0.0;
	if (y <= -6.2e+101)
		tmp = t_7;
	elseif (y <= -7e+22)
		tmp = 1.0 / ((a / (y * x)) + (((1.0 / x) + (b / t_1)) + ((((z / (x * x)) - (a / x)) / (t_1 / z)) - ((z / (y * (x * x))) + (27464.7644705 / ((y * y) * (x * x)))))));
	elseif (y <= 2.15e+18)
		tmp = (t + (y * t_6)) / (i + (y * t_3));
	elseif (y <= 8e+95)
		tmp = ((t / y) / t_8) + ((t_6 / t_3) - (i * (((230661.510616 * (1.0 / (y * t_4))) + ((27464.7644705 * (1.0 / t_4)) + (t_5 / t_4))) + (t / (t_8 * ((y * y) * t_8))))));
	else
		tmp = t_7;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x * N[(y * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(c + N[(y * N[(b + t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$3 * t$95$3), $MachinePrecision]}, Block[{t$95$5 = N[(y * N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(230661.510616 + N[(y * N[(27464.7644705 + t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(N[(x * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$8 = N[(c + N[(y * t$95$2), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.2e+101], t$95$7, If[LessEqual[y, -7e+22], N[(1.0 / N[(N[(a / N[(y * x), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(1.0 / x), $MachinePrecision] + N[(b / t$95$1), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(N[(z / N[(x * x), $MachinePrecision]), $MachinePrecision] - N[(a / x), $MachinePrecision]), $MachinePrecision] / N[(t$95$1 / z), $MachinePrecision]), $MachinePrecision] - N[(N[(z / N[(y * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(27464.7644705 / N[(N[(y * y), $MachinePrecision] * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.15e+18], N[(N[(t + N[(y * t$95$6), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8e+95], N[(N[(N[(t / y), $MachinePrecision] / t$95$8), $MachinePrecision] + N[(N[(t$95$6 / t$95$3), $MachinePrecision] - N[(i * N[(N[(N[(230661.510616 * N[(1.0 / N[(y * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(27464.7644705 * N[(1.0 / t$95$4), $MachinePrecision]), $MachinePrecision] + N[(t$95$5 / t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t / N[(t$95$8 * N[(N[(y * y), $MachinePrecision] * t$95$8), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$7]]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -6.19999999999999998e101 or 8.00000000000000016e95 < y

   1. Initial program 0.1%

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

   2. Taylor expanded in y around inf 81.9%

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

   if -6.19999999999999998e101 < y < -7e22

   1. Initial program 17.3%

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

      1. clear-num 17.2%

         \[\leadsto \color{blue}{\frac{1}{\frac{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}}} \]

      2. inv-pow 17.2%

         \[\leadsto \color{blue}{{\left(\frac{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}\right)}^{-1}} \]

   3. Applied egg-rr 17.3%

      \[\leadsto \color{blue}{{\left(\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right), 230661.510616\right), t\right)}\right)}^{-1}} \]
   4. Step-by-step derivation

      1. unpow-1 17.3%

         \[\leadsto \color{blue}{\frac{1}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right), 230661.510616\right), t\right)}}} \]

      2. fma-udef 17.3%

         \[\leadsto \frac{1}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{x \cdot y + z}, 27464.7644705\right), 230661.510616\right), t\right)}} \]

      3. *-commutative 17.3%

         \[\leadsto \frac{1}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{y \cdot x} + z, 27464.7644705\right), 230661.510616\right), t\right)}} \]

      4. fma-def 17.3%

         \[\leadsto \frac{1}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(y, x, z\right)}, 27464.7644705\right), 230661.510616\right), t\right)}} \]

   5. Simplified 17.3%

      \[\leadsto \color{blue}{\frac{1}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), 27464.7644705\right), 230661.510616\right), t\right)}}} \]

   6. Taylor expanded in y around inf 59.9%

      \[\leadsto \frac{1}{\color{blue}{\left(\frac{a}{y \cdot x} + \left(\frac{1}{x} + \frac{b}{{y}^{2} \cdot x}\right)\right) - \left(\frac{\left(\frac{a}{x} - \frac{z}{{x}^{2}}\right) \cdot z}{{y}^{2} \cdot x} + \left(27464.7644705 \cdot \frac{1}{{y}^{2} \cdot {x}^{2}} + \frac{z}{y \cdot {x}^{2}}\right)\right)}} \]
   7. Step-by-step derivation

      1. associate--l+ 59.9%

         \[\leadsto \frac{1}{\color{blue}{\frac{a}{y \cdot x} + \left(\left(\frac{1}{x} + \frac{b}{{y}^{2} \cdot x}\right) - \left(\frac{\left(\frac{a}{x} - \frac{z}{{x}^{2}}\right) \cdot z}{{y}^{2} \cdot x} + \left(27464.7644705 \cdot \frac{1}{{y}^{2} \cdot {x}^{2}} + \frac{z}{y \cdot {x}^{2}}\right)\right)\right)}} \]

      2. unpow2 59.9%

         \[\leadsto \frac{1}{\frac{a}{y \cdot x} + \left(\left(\frac{1}{x} + \frac{b}{\color{blue}{\left(y \cdot y\right)} \cdot x}\right) - \left(\frac{\left(\frac{a}{x} - \frac{z}{{x}^{2}}\right) \cdot z}{{y}^{2} \cdot x} + \left(27464.7644705 \cdot \frac{1}{{y}^{2} \cdot {x}^{2}} + \frac{z}{y \cdot {x}^{2}}\right)\right)\right)} \]

      3. associate-/l* 59.9%

         \[\leadsto \frac{1}{\frac{a}{y \cdot x} + \left(\left(\frac{1}{x} + \frac{b}{\left(y \cdot y\right) \cdot x}\right) - \left(\color{blue}{\frac{\frac{a}{x} - \frac{z}{{x}^{2}}}{\frac{{y}^{2} \cdot x}{z}}} + \left(27464.7644705 \cdot \frac{1}{{y}^{2} \cdot {x}^{2}} + \frac{z}{y \cdot {x}^{2}}\right)\right)\right)} \]

      4. unpow2 59.9%

         \[\leadsto \frac{1}{\frac{a}{y \cdot x} + \left(\left(\frac{1}{x} + \frac{b}{\left(y \cdot y\right) \cdot x}\right) - \left(\frac{\frac{a}{x} - \frac{z}{\color{blue}{x \cdot x}}}{\frac{{y}^{2} \cdot x}{z}} + \left(27464.7644705 \cdot \frac{1}{{y}^{2} \cdot {x}^{2}} + \frac{z}{y \cdot {x}^{2}}\right)\right)\right)} \]

      5. unpow2 59.9%

         \[\leadsto \frac{1}{\frac{a}{y \cdot x} + \left(\left(\frac{1}{x} + \frac{b}{\left(y \cdot y\right) \cdot x}\right) - \left(\frac{\frac{a}{x} - \frac{z}{x \cdot x}}{\frac{\color{blue}{\left(y \cdot y\right)} \cdot x}{z}} + \left(27464.7644705 \cdot \frac{1}{{y}^{2} \cdot {x}^{2}} + \frac{z}{y \cdot {x}^{2}}\right)\right)\right)} \]

   8. Simplified 59.9%

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

   if -7e22 < y < 2.15e18

   1. Initial program 97.6%

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

   if 2.15e18 < y < 8.00000000000000016e95

   1. Initial program 14.3%

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

   2. Taylor expanded in i around 0 43.0%

      \[\leadsto \color{blue}{\frac{t}{y \cdot \left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right)} + \left(-1 \cdot \left(i \cdot \left(\frac{t}{{y}^{2} \cdot \left(\left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) \cdot \left(c + \left(b + y \cdot \left(a + y\right)\right) \cdot y\right)\right)} + \left(230661.510616 \cdot \frac{1}{y \cdot \left(\left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) \cdot \left(c + \left(b + y \cdot \left(a + y\right)\right) \cdot y\right)\right)} + \left(27464.7644705 \cdot \frac{1}{\left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) \cdot \left(c + \left(b + y \cdot \left(a + y\right)\right) \cdot y\right)} + \frac{\left(y \cdot x + z\right) \cdot y}{\left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) \cdot \left(c + \left(b + y \cdot \left(a + y\right)\right) \cdot y\right)}\right)\right)\right)\right) + \frac{230661.510616 + y \cdot \left(27464.7644705 + \left(y \cdot x + z\right) \cdot y\right)}{c + y \cdot \left(\left(y + a\right) \cdot y + b\right)}\right)} \]

   3. Taylor expanded in b around 0 43.0%

      \[\leadsto \frac{t}{y \cdot \left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right)} + \left(-1 \cdot \left(i \cdot \left(\frac{t}{\color{blue}{\left(c + \left(y + a\right) \cdot {y}^{2}\right) \cdot \left({y}^{2} \cdot \left(c + {y}^{2} \cdot \left(a + y\right)\right)\right)}} + \left(230661.510616 \cdot \frac{1}{y \cdot \left(\left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) \cdot \left(c + \left(b + y \cdot \left(a + y\right)\right) \cdot y\right)\right)} + \left(27464.7644705 \cdot \frac{1}{\left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) \cdot \left(c + \left(b + y \cdot \left(a + y\right)\right) \cdot y\right)} + \frac{\left(y \cdot x + z\right) \cdot y}{\left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) \cdot \left(c + \left(b + y \cdot \left(a + y\right)\right) \cdot y\right)}\right)\right)\right)\right) + \frac{230661.510616 + y \cdot \left(27464.7644705 + \left(y \cdot x + z\right) \cdot y\right)}{c + y \cdot \left(\left(y + a\right) \cdot y + b\right)}\right) \]
   4. Step-by-step derivation

      1. *-commutative 43.0%

         \[\leadsto \frac{t}{y \cdot \left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right)} + \left(-1 \cdot \left(i \cdot \left(\frac{t}{\left(c + \color{blue}{{y}^{2} \cdot \left(y + a\right)}\right) \cdot \left({y}^{2} \cdot \left(c + {y}^{2} \cdot \left(a + y\right)\right)\right)} + \left(230661.510616 \cdot \frac{1}{y \cdot \left(\left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) \cdot \left(c + \left(b + y \cdot \left(a + y\right)\right) \cdot y\right)\right)} + \left(27464.7644705 \cdot \frac{1}{\left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) \cdot \left(c + \left(b + y \cdot \left(a + y\right)\right) \cdot y\right)} + \frac{\left(y \cdot x + z\right) \cdot y}{\left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) \cdot \left(c + \left(b + y \cdot \left(a + y\right)\right) \cdot y\right)}\right)\right)\right)\right) + \frac{230661.510616 + y \cdot \left(27464.7644705 + \left(y \cdot x + z\right) \cdot y\right)}{c + y \cdot \left(\left(y + a\right) \cdot y + b\right)}\right) \]

      2. unpow2 43.0%

         \[\leadsto \frac{t}{y \cdot \left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right)} + \left(-1 \cdot \left(i \cdot \left(\frac{t}{\left(c + \color{blue}{\left(y \cdot y\right)} \cdot \left(y + a\right)\right) \cdot \left({y}^{2} \cdot \left(c + {y}^{2} \cdot \left(a + y\right)\right)\right)} + \left(230661.510616 \cdot \frac{1}{y \cdot \left(\left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) \cdot \left(c + \left(b + y \cdot \left(a + y\right)\right) \cdot y\right)\right)} + \left(27464.7644705 \cdot \frac{1}{\left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) \cdot \left(c + \left(b + y \cdot \left(a + y\right)\right) \cdot y\right)} + \frac{\left(y \cdot x + z\right) \cdot y}{\left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) \cdot \left(c + \left(b + y \cdot \left(a + y\right)\right) \cdot y\right)}\right)\right)\right)\right) + \frac{230661.510616 + y \cdot \left(27464.7644705 + \left(y \cdot x + z\right) \cdot y\right)}{c + y \cdot \left(\left(y + a\right) \cdot y + b\right)}\right) \]

      3. associate-*r* 43.0%

         \[\leadsto \frac{t}{y \cdot \left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right)} + \left(-1 \cdot \left(i \cdot \left(\frac{t}{\left(c + \color{blue}{y \cdot \left(y \cdot \left(y + a\right)\right)}\right) \cdot \left({y}^{2} \cdot \left(c + {y}^{2} \cdot \left(a + y\right)\right)\right)} + \left(230661.510616 \cdot \frac{1}{y \cdot \left(\left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) \cdot \left(c + \left(b + y \cdot \left(a + y\right)\right) \cdot y\right)\right)} + \left(27464.7644705 \cdot \frac{1}{\left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) \cdot \left(c + \left(b + y \cdot \left(a + y\right)\right) \cdot y\right)} + \frac{\left(y \cdot x + z\right) \cdot y}{\left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) \cdot \left(c + \left(b + y \cdot \left(a + y\right)\right) \cdot y\right)}\right)\right)\right)\right) + \frac{230661.510616 + y \cdot \left(27464.7644705 + \left(y \cdot x + z\right) \cdot y\right)}{c + y \cdot \left(\left(y + a\right) \cdot y + b\right)}\right) \]

      4. unpow2 43.0%

         \[\leadsto \frac{t}{y \cdot \left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right)} + \left(-1 \cdot \left(i \cdot \left(\frac{t}{\left(c + y \cdot \left(y \cdot \left(y + a\right)\right)\right) \cdot \left(\color{blue}{\left(y \cdot y\right)} \cdot \left(c + {y}^{2} \cdot \left(a + y\right)\right)\right)} + \left(230661.510616 \cdot \frac{1}{y \cdot \left(\left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) \cdot \left(c + \left(b + y \cdot \left(a + y\right)\right) \cdot y\right)\right)} + \left(27464.7644705 \cdot \frac{1}{\left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) \cdot \left(c + \left(b + y \cdot \left(a + y\right)\right) \cdot y\right)} + \frac{\left(y \cdot x + z\right) \cdot y}{\left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) \cdot \left(c + \left(b + y \cdot \left(a + y\right)\right) \cdot y\right)}\right)\right)\right)\right) + \frac{230661.510616 + y \cdot \left(27464.7644705 + \left(y \cdot x + z\right) \cdot y\right)}{c + y \cdot \left(\left(y + a\right) \cdot y + b\right)}\right) \]

      5. unpow2 43.0%

         \[\leadsto \frac{t}{y \cdot \left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right)} + \left(-1 \cdot \left(i \cdot \left(\frac{t}{\left(c + y \cdot \left(y \cdot \left(y + a\right)\right)\right) \cdot \left(\left(y \cdot y\right) \cdot \left(c + \color{blue}{\left(y \cdot y\right)} \cdot \left(a + y\right)\right)\right)} + \left(230661.510616 \cdot \frac{1}{y \cdot \left(\left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) \cdot \left(c + \left(b + y \cdot \left(a + y\right)\right) \cdot y\right)\right)} + \left(27464.7644705 \cdot \frac{1}{\left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) \cdot \left(c + \left(b + y \cdot \left(a + y\right)\right) \cdot y\right)} + \frac{\left(y \cdot x + z\right) \cdot y}{\left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) \cdot \left(c + \left(b + y \cdot \left(a + y\right)\right) \cdot y\right)}\right)\right)\right)\right) + \frac{230661.510616 + y \cdot \left(27464.7644705 + \left(y \cdot x + z\right) \cdot y\right)}{c + y \cdot \left(\left(y + a\right) \cdot y + b\right)}\right) \]

      6. +-commutative 43.0%

         \[\leadsto \frac{t}{y \cdot \left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right)} + \left(-1 \cdot \left(i \cdot \left(\frac{t}{\left(c + y \cdot \left(y \cdot \left(y + a\right)\right)\right) \cdot \left(\left(y \cdot y\right) \cdot \left(c + \left(y \cdot y\right) \cdot \color{blue}{\left(y + a\right)}\right)\right)} + \left(230661.510616 \cdot \frac{1}{y \cdot \left(\left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) \cdot \left(c + \left(b + y \cdot \left(a + y\right)\right) \cdot y\right)\right)} + \left(27464.7644705 \cdot \frac{1}{\left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) \cdot \left(c + \left(b + y \cdot \left(a + y\right)\right) \cdot y\right)} + \frac{\left(y \cdot x + z\right) \cdot y}{\left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) \cdot \left(c + \left(b + y \cdot \left(a + y\right)\right) \cdot y\right)}\right)\right)\right)\right) + \frac{230661.510616 + y \cdot \left(27464.7644705 + \left(y \cdot x + z\right) \cdot y\right)}{c + y \cdot \left(\left(y + a\right) \cdot y + b\right)}\right) \]

      7. associate-*r* 43.0%

         \[\leadsto \frac{t}{y \cdot \left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right)} + \left(-1 \cdot \left(i \cdot \left(\frac{t}{\left(c + y \cdot \left(y \cdot \left(y + a\right)\right)\right) \cdot \left(\left(y \cdot y\right) \cdot \left(c + \color{blue}{y \cdot \left(y \cdot \left(y + a\right)\right)}\right)\right)} + \left(230661.510616 \cdot \frac{1}{y \cdot \left(\left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) \cdot \left(c + \left(b + y \cdot \left(a + y\right)\right) \cdot y\right)\right)} + \left(27464.7644705 \cdot \frac{1}{\left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) \cdot \left(c + \left(b + y \cdot \left(a + y\right)\right) \cdot y\right)} + \frac{\left(y \cdot x + z\right) \cdot y}{\left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) \cdot \left(c + \left(b + y \cdot \left(a + y\right)\right) \cdot y\right)}\right)\right)\right)\right) + \frac{230661.510616 + y \cdot \left(27464.7644705 + \left(y \cdot x + z\right) \cdot y\right)}{c + y \cdot \left(\left(y + a\right) \cdot y + b\right)}\right) \]

   5. Simplified 43.0%

      \[\leadsto \frac{t}{y \cdot \left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right)} + \left(-1 \cdot \left(i \cdot \left(\frac{t}{\color{blue}{\left(c + y \cdot \left(y \cdot \left(y + a\right)\right)\right) \cdot \left(\left(y \cdot y\right) \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right)\right)\right)\right)}} + \left(230661.510616 \cdot \frac{1}{y \cdot \left(\left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) \cdot \left(c + \left(b + y \cdot \left(a + y\right)\right) \cdot y\right)\right)} + \left(27464.7644705 \cdot \frac{1}{\left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) \cdot \left(c + \left(b + y \cdot \left(a + y\right)\right) \cdot y\right)} + \frac{\left(y \cdot x + z\right) \cdot y}{\left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) \cdot \left(c + \left(b + y \cdot \left(a + y\right)\right) \cdot y\right)}\right)\right)\right)\right) + \frac{230661.510616 + y \cdot \left(27464.7644705 + \left(y \cdot x + z\right) \cdot y\right)}{c + y \cdot \left(\left(y + a\right) \cdot y + b\right)}\right) \]

   6. Taylor expanded in b around 0 43.0%

      \[\leadsto \color{blue}{\frac{t}{y \cdot \left(c + {y}^{2} \cdot \left(a + y\right)\right)}} + \left(-1 \cdot \left(i \cdot \left(\frac{t}{\left(c + y \cdot \left(y \cdot \left(y + a\right)\right)\right) \cdot \left(\left(y \cdot y\right) \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right)\right)\right)\right)} + \left(230661.510616 \cdot \frac{1}{y \cdot \left(\left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) \cdot \left(c + \left(b + y \cdot \left(a + y\right)\right) \cdot y\right)\right)} + \left(27464.7644705 \cdot \frac{1}{\left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) \cdot \left(c + \left(b + y \cdot \left(a + y\right)\right) \cdot y\right)} + \frac{\left(y \cdot x + z\right) \cdot y}{\left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) \cdot \left(c + \left(b + y \cdot \left(a + y\right)\right) \cdot y\right)}\right)\right)\right)\right) + \frac{230661.510616 + y \cdot \left(27464.7644705 + \left(y \cdot x + z\right) \cdot y\right)}{c + y \cdot \left(\left(y + a\right) \cdot y + b\right)}\right) \]
   7. Step-by-step derivation

      1. associate-/r* 48.6%

         \[\leadsto \color{blue}{\frac{\frac{t}{y}}{c + {y}^{2} \cdot \left(a + y\right)}} + \left(-1 \cdot \left(i \cdot \left(\frac{t}{\left(c + y \cdot \left(y \cdot \left(y + a\right)\right)\right) \cdot \left(\left(y \cdot y\right) \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right)\right)\right)\right)} + \left(230661.510616 \cdot \frac{1}{y \cdot \left(\left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) \cdot \left(c + \left(b + y \cdot \left(a + y\right)\right) \cdot y\right)\right)} + \left(27464.7644705 \cdot \frac{1}{\left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) \cdot \left(c + \left(b + y \cdot \left(a + y\right)\right) \cdot y\right)} + \frac{\left(y \cdot x + z\right) \cdot y}{\left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) \cdot \left(c + \left(b + y \cdot \left(a + y\right)\right) \cdot y\right)}\right)\right)\right)\right) + \frac{230661.510616 + y \cdot \left(27464.7644705 + \left(y \cdot x + z\right) \cdot y\right)}{c + y \cdot \left(\left(y + a\right) \cdot y + b\right)}\right) \]

      2. unpow2 48.6%

         \[\leadsto \frac{\frac{t}{y}}{c + \color{blue}{\left(y \cdot y\right)} \cdot \left(a + y\right)} + \left(-1 \cdot \left(i \cdot \left(\frac{t}{\left(c + y \cdot \left(y \cdot \left(y + a\right)\right)\right) \cdot \left(\left(y \cdot y\right) \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right)\right)\right)\right)} + \left(230661.510616 \cdot \frac{1}{y \cdot \left(\left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) \cdot \left(c + \left(b + y \cdot \left(a + y\right)\right) \cdot y\right)\right)} + \left(27464.7644705 \cdot \frac{1}{\left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) \cdot \left(c + \left(b + y \cdot \left(a + y\right)\right) \cdot y\right)} + \frac{\left(y \cdot x + z\right) \cdot y}{\left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) \cdot \left(c + \left(b + y \cdot \left(a + y\right)\right) \cdot y\right)}\right)\right)\right)\right) + \frac{230661.510616 + y \cdot \left(27464.7644705 + \left(y \cdot x + z\right) \cdot y\right)}{c + y \cdot \left(\left(y + a\right) \cdot y + b\right)}\right) \]

      3. +-commutative 48.6%

         \[\leadsto \frac{\frac{t}{y}}{c + \left(y \cdot y\right) \cdot \color{blue}{\left(y + a\right)}} + \left(-1 \cdot \left(i \cdot \left(\frac{t}{\left(c + y \cdot \left(y \cdot \left(y + a\right)\right)\right) \cdot \left(\left(y \cdot y\right) \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right)\right)\right)\right)} + \left(230661.510616 \cdot \frac{1}{y \cdot \left(\left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) \cdot \left(c + \left(b + y \cdot \left(a + y\right)\right) \cdot y\right)\right)} + \left(27464.7644705 \cdot \frac{1}{\left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) \cdot \left(c + \left(b + y \cdot \left(a + y\right)\right) \cdot y\right)} + \frac{\left(y \cdot x + z\right) \cdot y}{\left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) \cdot \left(c + \left(b + y \cdot \left(a + y\right)\right) \cdot y\right)}\right)\right)\right)\right) + \frac{230661.510616 + y \cdot \left(27464.7644705 + \left(y \cdot x + z\right) \cdot y\right)}{c + y \cdot \left(\left(y + a\right) \cdot y + b\right)}\right) \]

      4. associate-*r* 48.6%

         \[\leadsto \frac{\frac{t}{y}}{c + \color{blue}{y \cdot \left(y \cdot \left(y + a\right)\right)}} + \left(-1 \cdot \left(i \cdot \left(\frac{t}{\left(c + y \cdot \left(y \cdot \left(y + a\right)\right)\right) \cdot \left(\left(y \cdot y\right) \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right)\right)\right)\right)} + \left(230661.510616 \cdot \frac{1}{y \cdot \left(\left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) \cdot \left(c + \left(b + y \cdot \left(a + y\right)\right) \cdot y\right)\right)} + \left(27464.7644705 \cdot \frac{1}{\left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) \cdot \left(c + \left(b + y \cdot \left(a + y\right)\right) \cdot y\right)} + \frac{\left(y \cdot x + z\right) \cdot y}{\left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) \cdot \left(c + \left(b + y \cdot \left(a + y\right)\right) \cdot y\right)}\right)\right)\right)\right) + \frac{230661.510616 + y \cdot \left(27464.7644705 + \left(y \cdot x + z\right) \cdot y\right)}{c + y \cdot \left(\left(y + a\right) \cdot y + b\right)}\right) \]

   8. Simplified 48.6%

      \[\leadsto \color{blue}{\frac{\frac{t}{y}}{c + y \cdot \left(y \cdot \left(y + a\right)\right)}} + \left(-1 \cdot \left(i \cdot \left(\frac{t}{\left(c + y \cdot \left(y \cdot \left(y + a\right)\right)\right) \cdot \left(\left(y \cdot y\right) \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right)\right)\right)\right)} + \left(230661.510616 \cdot \frac{1}{y \cdot \left(\left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) \cdot \left(c + \left(b + y \cdot \left(a + y\right)\right) \cdot y\right)\right)} + \left(27464.7644705 \cdot \frac{1}{\left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) \cdot \left(c + \left(b + y \cdot \left(a + y\right)\right) \cdot y\right)} + \frac{\left(y \cdot x + z\right) \cdot y}{\left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) \cdot \left(c + \left(b + y \cdot \left(a + y\right)\right) \cdot y\right)}\right)\right)\right)\right) + \frac{230661.510616 + y \cdot \left(27464.7644705 + \left(y \cdot x + z\right) \cdot y\right)}{c + y \cdot \left(\left(y + a\right) \cdot y + b\right)}\right) \]
3. Recombined 4 regimes into one program.

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+101}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{elif}\;y \leq -7 \cdot 10^{+22}:\\ \;\;\;\;\frac{1}{\frac{a}{y \cdot x} + \left(\left(\frac{1}{x} + \frac{b}{x \cdot \left(y \cdot y\right)}\right) + \left(\frac{\frac{z}{x \cdot x} - \frac{a}{x}}{\frac{x \cdot \left(y \cdot y\right)}{z}} - \left(\frac{z}{y \cdot \left(x \cdot x\right)} + \frac{27464.7644705}{\left(y \cdot y\right) \cdot \left(x \cdot x\right)}\right)\right)\right)}\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{+18}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+95}:\\ \;\;\;\;\frac{\frac{t}{y}}{c + y \cdot \left(y \cdot \left(y + a\right)\right)} + \left(\frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)}{c + y \cdot \left(b + y \cdot \left(y + a\right)\right)} - i \cdot \left(\left(230661.510616 \cdot \frac{1}{y \cdot \left(\left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)\right)} + \left(27464.7644705 \cdot \frac{1}{\left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)} + \frac{y \cdot \left(z + y \cdot x\right)}{\left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\right)\right) + \frac{t}{\left(c + y \cdot \left(y \cdot \left(y + a\right)\right)\right) \cdot \left(\left(y \cdot y\right) \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right)\right)\right)\right)}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \end{array} \]

Alternative 4: 82.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot y\right)\\ \mathbf{if}\;y \leq -2 \cdot 10^{+102}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{elif}\;y \leq -7 \cdot 10^{+22}:\\ \;\;\;\;\frac{1}{\frac{a}{y \cdot x} + \left(\left(\frac{1}{x} + \frac{b}{t_1}\right) + \left(\frac{\frac{z}{x \cdot x} - \frac{a}{x}}{\frac{t_1}{z}} - \left(\frac{z}{y \cdot \left(x \cdot x\right)} + \frac{27464.7644705}{\left(y \cdot y\right) \cdot \left(x \cdot x\right)}\right)\right)\right)}\\ \mathbf{elif}\;y \leq 2.55 \cdot 10^{+76}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x + \left(\frac{z}{y} + \frac{27464.7644705}{y \cdot y}\right)\right) - \frac{a}{\frac{y \cdot y}{z - x \cdot a}}\right) - \left(\frac{a}{\frac{y}{x}} + \frac{b}{y} \cdot \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* x (* y y))))
   (if (<= y -2e+102)
     (- (+ x (/ z y)) (/ (* x a) y))
     (if (<= y -7e+22)
       (/
        1.0
        (+
         (/ a (* y x))
         (+
          (+ (/ 1.0 x) (/ b t_1))
          (-
           (/ (- (/ z (* x x)) (/ a x)) (/ t_1 z))
           (+ (/ z (* y (* x x))) (/ 27464.7644705 (* (* y y) (* x x))))))))
       (if (<= y 2.55e+76)
         (/
          (+
           t
           (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ z (* y x))))))))
          (+ i (* y (+ c (* y (+ b (* y (+ y a))))))))
         (-
          (-
           (+ x (+ (/ z y) (/ 27464.7644705 (* y y))))
           (/ a (/ (* y y) (- z (* x a)))))
          (+ (/ a (/ y x)) (* (/ b y) (/ x y)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x * (y * y);
	double tmp;
	if (y <= -2e+102) {
		tmp = (x + (z / y)) - ((x * a) / y);
	} else if (y <= -7e+22) {
		tmp = 1.0 / ((a / (y * x)) + (((1.0 / x) + (b / t_1)) + ((((z / (x * x)) - (a / x)) / (t_1 / z)) - ((z / (y * (x * x))) + (27464.7644705 / ((y * y) * (x * x)))))));
	} else if (y <= 2.55e+76) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / (i + (y * (c + (y * (b + (y * (y + a)))))));
	} else {
		tmp = ((x + ((z / y) + (27464.7644705 / (y * y)))) - (a / ((y * y) / (z - (x * a))))) - ((a / (y / x)) + ((b / y) * (x / y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (y * y)
    if (y <= (-2d+102)) then
        tmp = (x + (z / y)) - ((x * a) / y)
    else if (y <= (-7d+22)) then
        tmp = 1.0d0 / ((a / (y * x)) + (((1.0d0 / x) + (b / t_1)) + ((((z / (x * x)) - (a / x)) / (t_1 / z)) - ((z / (y * (x * x))) + (27464.7644705d0 / ((y * y) * (x * x)))))))
    else if (y <= 2.55d+76) then
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * (z + (y * x)))))))) / (i + (y * (c + (y * (b + (y * (y + a)))))))
    else
        tmp = ((x + ((z / y) + (27464.7644705d0 / (y * y)))) - (a / ((y * y) / (z - (x * a))))) - ((a / (y / x)) + ((b / y) * (x / y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x * (y * y);
	double tmp;
	if (y <= -2e+102) {
		tmp = (x + (z / y)) - ((x * a) / y);
	} else if (y <= -7e+22) {
		tmp = 1.0 / ((a / (y * x)) + (((1.0 / x) + (b / t_1)) + ((((z / (x * x)) - (a / x)) / (t_1 / z)) - ((z / (y * (x * x))) + (27464.7644705 / ((y * y) * (x * x)))))));
	} else if (y <= 2.55e+76) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / (i + (y * (c + (y * (b + (y * (y + a)))))));
	} else {
		tmp = ((x + ((z / y) + (27464.7644705 / (y * y)))) - (a / ((y * y) / (z - (x * a))))) - ((a / (y / x)) + ((b / y) * (x / y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x * (y * y)
	tmp = 0
	if y <= -2e+102:
		tmp = (x + (z / y)) - ((x * a) / y)
	elif y <= -7e+22:
		tmp = 1.0 / ((a / (y * x)) + (((1.0 / x) + (b / t_1)) + ((((z / (x * x)) - (a / x)) / (t_1 / z)) - ((z / (y * (x * x))) + (27464.7644705 / ((y * y) * (x * x)))))))
	elif y <= 2.55e+76:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / (i + (y * (c + (y * (b + (y * (y + a)))))))
	else:
		tmp = ((x + ((z / y) + (27464.7644705 / (y * y)))) - (a / ((y * y) / (z - (x * a))))) - ((a / (y / x)) + ((b / y) * (x / y)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x * Float64(y * y))
	tmp = 0.0
	if (y <= -2e+102)
		tmp = Float64(Float64(x + Float64(z / y)) - Float64(Float64(x * a) / y));
	elseif (y <= -7e+22)
		tmp = Float64(1.0 / Float64(Float64(a / Float64(y * x)) + Float64(Float64(Float64(1.0 / x) + Float64(b / t_1)) + Float64(Float64(Float64(Float64(z / Float64(x * x)) - Float64(a / x)) / Float64(t_1 / z)) - Float64(Float64(z / Float64(y * Float64(x * x))) + Float64(27464.7644705 / Float64(Float64(y * y) * Float64(x * x))))))));
	elseif (y <= 2.55e+76)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(z + Float64(y * x)))))))) / Float64(i + Float64(y * Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a))))))));
	else
		tmp = Float64(Float64(Float64(x + Float64(Float64(z / y) + Float64(27464.7644705 / Float64(y * y)))) - Float64(a / Float64(Float64(y * y) / Float64(z - Float64(x * a))))) - Float64(Float64(a / Float64(y / x)) + Float64(Float64(b / y) * Float64(x / y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x * (y * y);
	tmp = 0.0;
	if (y <= -2e+102)
		tmp = (x + (z / y)) - ((x * a) / y);
	elseif (y <= -7e+22)
		tmp = 1.0 / ((a / (y * x)) + (((1.0 / x) + (b / t_1)) + ((((z / (x * x)) - (a / x)) / (t_1 / z)) - ((z / (y * (x * x))) + (27464.7644705 / ((y * y) * (x * x)))))));
	elseif (y <= 2.55e+76)
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / (i + (y * (c + (y * (b + (y * (y + a)))))));
	else
		tmp = ((x + ((z / y) + (27464.7644705 / (y * y)))) - (a / ((y * y) / (z - (x * a))))) - ((a / (y / x)) + ((b / y) * (x / y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x * N[(y * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2e+102], N[(N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(N[(x * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -7e+22], N[(1.0 / N[(N[(a / N[(y * x), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(1.0 / x), $MachinePrecision] + N[(b / t$95$1), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(N[(z / N[(x * x), $MachinePrecision]), $MachinePrecision] - N[(a / x), $MachinePrecision]), $MachinePrecision] / N[(t$95$1 / z), $MachinePrecision]), $MachinePrecision] - N[(N[(z / N[(y * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(27464.7644705 / N[(N[(y * y), $MachinePrecision] * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.55e+76], N[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x + N[(N[(z / y), $MachinePrecision] + N[(27464.7644705 / N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a / N[(N[(y * y), $MachinePrecision] / N[(z - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision] + N[(N[(b / y), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.99999999999999995e102

   1. Initial program 0.0%

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

   2. Taylor expanded in y around inf 82.0%

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

   if -1.99999999999999995e102 < y < -7e22

   1. Initial program 17.3%

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

      1. clear-num 17.2%

         \[\leadsto \color{blue}{\frac{1}{\frac{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}}} \]

      2. inv-pow 17.2%

         \[\leadsto \color{blue}{{\left(\frac{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}\right)}^{-1}} \]

   3. Applied egg-rr 17.3%

      \[\leadsto \color{blue}{{\left(\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right), 230661.510616\right), t\right)}\right)}^{-1}} \]
   4. Step-by-step derivation

      1. unpow-1 17.3%

         \[\leadsto \color{blue}{\frac{1}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right), 230661.510616\right), t\right)}}} \]

      2. fma-udef 17.3%

         \[\leadsto \frac{1}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{x \cdot y + z}, 27464.7644705\right), 230661.510616\right), t\right)}} \]

      3. *-commutative 17.3%

         \[\leadsto \frac{1}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{y \cdot x} + z, 27464.7644705\right), 230661.510616\right), t\right)}} \]

      4. fma-def 17.3%

         \[\leadsto \frac{1}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(y, x, z\right)}, 27464.7644705\right), 230661.510616\right), t\right)}} \]

   5. Simplified 17.3%

      \[\leadsto \color{blue}{\frac{1}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), 27464.7644705\right), 230661.510616\right), t\right)}}} \]

   6. Taylor expanded in y around inf 59.9%

      \[\leadsto \frac{1}{\color{blue}{\left(\frac{a}{y \cdot x} + \left(\frac{1}{x} + \frac{b}{{y}^{2} \cdot x}\right)\right) - \left(\frac{\left(\frac{a}{x} - \frac{z}{{x}^{2}}\right) \cdot z}{{y}^{2} \cdot x} + \left(27464.7644705 \cdot \frac{1}{{y}^{2} \cdot {x}^{2}} + \frac{z}{y \cdot {x}^{2}}\right)\right)}} \]
   7. Step-by-step derivation

      1. associate--l+ 59.9%

         \[\leadsto \frac{1}{\color{blue}{\frac{a}{y \cdot x} + \left(\left(\frac{1}{x} + \frac{b}{{y}^{2} \cdot x}\right) - \left(\frac{\left(\frac{a}{x} - \frac{z}{{x}^{2}}\right) \cdot z}{{y}^{2} \cdot x} + \left(27464.7644705 \cdot \frac{1}{{y}^{2} \cdot {x}^{2}} + \frac{z}{y \cdot {x}^{2}}\right)\right)\right)}} \]

      2. unpow2 59.9%

         \[\leadsto \frac{1}{\frac{a}{y \cdot x} + \left(\left(\frac{1}{x} + \frac{b}{\color{blue}{\left(y \cdot y\right)} \cdot x}\right) - \left(\frac{\left(\frac{a}{x} - \frac{z}{{x}^{2}}\right) \cdot z}{{y}^{2} \cdot x} + \left(27464.7644705 \cdot \frac{1}{{y}^{2} \cdot {x}^{2}} + \frac{z}{y \cdot {x}^{2}}\right)\right)\right)} \]

      3. associate-/l* 59.9%

         \[\leadsto \frac{1}{\frac{a}{y \cdot x} + \left(\left(\frac{1}{x} + \frac{b}{\left(y \cdot y\right) \cdot x}\right) - \left(\color{blue}{\frac{\frac{a}{x} - \frac{z}{{x}^{2}}}{\frac{{y}^{2} \cdot x}{z}}} + \left(27464.7644705 \cdot \frac{1}{{y}^{2} \cdot {x}^{2}} + \frac{z}{y \cdot {x}^{2}}\right)\right)\right)} \]

      4. unpow2 59.9%

         \[\leadsto \frac{1}{\frac{a}{y \cdot x} + \left(\left(\frac{1}{x} + \frac{b}{\left(y \cdot y\right) \cdot x}\right) - \left(\frac{\frac{a}{x} - \frac{z}{\color{blue}{x \cdot x}}}{\frac{{y}^{2} \cdot x}{z}} + \left(27464.7644705 \cdot \frac{1}{{y}^{2} \cdot {x}^{2}} + \frac{z}{y \cdot {x}^{2}}\right)\right)\right)} \]

      5. unpow2 59.9%

         \[\leadsto \frac{1}{\frac{a}{y \cdot x} + \left(\left(\frac{1}{x} + \frac{b}{\left(y \cdot y\right) \cdot x}\right) - \left(\frac{\frac{a}{x} - \frac{z}{x \cdot x}}{\frac{\color{blue}{\left(y \cdot y\right)} \cdot x}{z}} + \left(27464.7644705 \cdot \frac{1}{{y}^{2} \cdot {x}^{2}} + \frac{z}{y \cdot {x}^{2}}\right)\right)\right)} \]

   8. Simplified 59.9%

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

   if -7e22 < y < 2.5500000000000001e76

   1. Initial program 90.6%

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

   if 2.5500000000000001e76 < y

   1. Initial program 0.4%

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

   2. Taylor expanded in y around inf 53.9%

      \[\leadsto \color{blue}{\left(\frac{z}{y} + \left(27464.7644705 \cdot \frac{1}{{y}^{2}} + x\right)\right) - \left(\frac{\left(z - a \cdot x\right) \cdot a}{{y}^{2}} + \left(\frac{a \cdot x}{y} + \frac{b \cdot x}{{y}^{2}}\right)\right)} \]
   3. Step-by-step derivation

      1. associate--r+ 53.9%

         \[\leadsto \color{blue}{\left(\left(\frac{z}{y} + \left(27464.7644705 \cdot \frac{1}{{y}^{2}} + x\right)\right) - \frac{\left(z - a \cdot x\right) \cdot a}{{y}^{2}}\right) - \left(\frac{a \cdot x}{y} + \frac{b \cdot x}{{y}^{2}}\right)} \]

      2. associate-+r+ 53.9%

         \[\leadsto \left(\color{blue}{\left(\left(\frac{z}{y} + 27464.7644705 \cdot \frac{1}{{y}^{2}}\right) + x\right)} - \frac{\left(z - a \cdot x\right) \cdot a}{{y}^{2}}\right) - \left(\frac{a \cdot x}{y} + \frac{b \cdot x}{{y}^{2}}\right) \]

      3. associate-*r/ 53.8%

         \[\leadsto \left(\left(\left(\frac{z}{y} + \color{blue}{\frac{27464.7644705 \cdot 1}{{y}^{2}}}\right) + x\right) - \frac{\left(z - a \cdot x\right) \cdot a}{{y}^{2}}\right) - \left(\frac{a \cdot x}{y} + \frac{b \cdot x}{{y}^{2}}\right) \]

      4. metadata-eval 53.8%

         \[\leadsto \left(\left(\left(\frac{z}{y} + \frac{\color{blue}{27464.7644705}}{{y}^{2}}\right) + x\right) - \frac{\left(z - a \cdot x\right) \cdot a}{{y}^{2}}\right) - \left(\frac{a \cdot x}{y} + \frac{b \cdot x}{{y}^{2}}\right) \]

      5. unpow2 53.8%

         \[\leadsto \left(\left(\left(\frac{z}{y} + \frac{27464.7644705}{\color{blue}{y \cdot y}}\right) + x\right) - \frac{\left(z - a \cdot x\right) \cdot a}{{y}^{2}}\right) - \left(\frac{a \cdot x}{y} + \frac{b \cdot x}{{y}^{2}}\right) \]

      6. *-commutative 53.8%

         \[\leadsto \left(\left(\left(\frac{z}{y} + \frac{27464.7644705}{y \cdot y}\right) + x\right) - \frac{\color{blue}{a \cdot \left(z - a \cdot x\right)}}{{y}^{2}}\right) - \left(\frac{a \cdot x}{y} + \frac{b \cdot x}{{y}^{2}}\right) \]

      7. associate-/l* 73.6%

         \[\leadsto \left(\left(\left(\frac{z}{y} + \frac{27464.7644705}{y \cdot y}\right) + x\right) - \color{blue}{\frac{a}{\frac{{y}^{2}}{z - a \cdot x}}}\right) - \left(\frac{a \cdot x}{y} + \frac{b \cdot x}{{y}^{2}}\right) \]

      8. unpow2 73.6%

         \[\leadsto \left(\left(\left(\frac{z}{y} + \frac{27464.7644705}{y \cdot y}\right) + x\right) - \frac{a}{\frac{\color{blue}{y \cdot y}}{z - a \cdot x}}\right) - \left(\frac{a \cdot x}{y} + \frac{b \cdot x}{{y}^{2}}\right) \]

      9. associate-/l* 73.6%

         \[\leadsto \left(\left(\left(\frac{z}{y} + \frac{27464.7644705}{y \cdot y}\right) + x\right) - \frac{a}{\frac{y \cdot y}{z - a \cdot x}}\right) - \left(\color{blue}{\frac{a}{\frac{y}{x}}} + \frac{b \cdot x}{{y}^{2}}\right) \]

      10. unpow2 73.6%

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

      11. times-frac 78.4%

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

   4. Simplified 78.4%

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

4. Final simplification 84.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+102}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{elif}\;y \leq -7 \cdot 10^{+22}:\\ \;\;\;\;\frac{1}{\frac{a}{y \cdot x} + \left(\left(\frac{1}{x} + \frac{b}{x \cdot \left(y \cdot y\right)}\right) + \left(\frac{\frac{z}{x \cdot x} - \frac{a}{x}}{\frac{x \cdot \left(y \cdot y\right)}{z}} - \left(\frac{z}{y \cdot \left(x \cdot x\right)} + \frac{27464.7644705}{\left(y \cdot y\right) \cdot \left(x \cdot x\right)}\right)\right)\right)}\\ \mathbf{elif}\;y \leq 2.55 \cdot 10^{+76}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x + \left(\frac{z}{y} + \frac{27464.7644705}{y \cdot y}\right)\right) - \frac{a}{\frac{y \cdot y}{z - x \cdot a}}\right) - \left(\frac{a}{\frac{y}{x}} + \frac{b}{y} \cdot \frac{x}{y}\right)\\ \end{array} \]

Alternative 5: 82.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.9 \cdot 10^{+103}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{elif}\;y \leq -7 \cdot 10^{+22}:\\ \;\;\;\;\frac{1}{\frac{1}{x} - \frac{\frac{z}{x \cdot x} - \frac{a}{x}}{y}}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+76}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x + \left(\frac{z}{y} + \frac{27464.7644705}{y \cdot y}\right)\right) - \frac{a}{\frac{y \cdot y}{z - x \cdot a}}\right) - \left(\frac{a}{\frac{y}{x}} + \frac{b}{y} \cdot \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -6.9e+103)
   (- (+ x (/ z y)) (/ (* x a) y))
   (if (<= y -7e+22)
     (/ 1.0 (- (/ 1.0 x) (/ (- (/ z (* x x)) (/ a x)) y)))
     (if (<= y 1.2e+76)
       (/
        (+
         t
         (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ z (* y x))))))))
        (+ i (* y (+ c (* y (+ b (* y (+ y a))))))))
       (-
        (-
         (+ x (+ (/ z y) (/ 27464.7644705 (* y y))))
         (/ a (/ (* y y) (- z (* x a)))))
        (+ (/ a (/ y x)) (* (/ b y) (/ x y))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -6.9e+103) {
		tmp = (x + (z / y)) - ((x * a) / y);
	} else if (y <= -7e+22) {
		tmp = 1.0 / ((1.0 / x) - (((z / (x * x)) - (a / x)) / y));
	} else if (y <= 1.2e+76) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / (i + (y * (c + (y * (b + (y * (y + a)))))));
	} else {
		tmp = ((x + ((z / y) + (27464.7644705 / (y * y)))) - (a / ((y * y) / (z - (x * a))))) - ((a / (y / x)) + ((b / y) * (x / y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= (-6.9d+103)) then
        tmp = (x + (z / y)) - ((x * a) / y)
    else if (y <= (-7d+22)) then
        tmp = 1.0d0 / ((1.0d0 / x) - (((z / (x * x)) - (a / x)) / y))
    else if (y <= 1.2d+76) then
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * (z + (y * x)))))))) / (i + (y * (c + (y * (b + (y * (y + a)))))))
    else
        tmp = ((x + ((z / y) + (27464.7644705d0 / (y * y)))) - (a / ((y * y) / (z - (x * a))))) - ((a / (y / x)) + ((b / y) * (x / y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -6.9e+103) {
		tmp = (x + (z / y)) - ((x * a) / y);
	} else if (y <= -7e+22) {
		tmp = 1.0 / ((1.0 / x) - (((z / (x * x)) - (a / x)) / y));
	} else if (y <= 1.2e+76) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / (i + (y * (c + (y * (b + (y * (y + a)))))));
	} else {
		tmp = ((x + ((z / y) + (27464.7644705 / (y * y)))) - (a / ((y * y) / (z - (x * a))))) - ((a / (y / x)) + ((b / y) * (x / y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -6.9e+103:
		tmp = (x + (z / y)) - ((x * a) / y)
	elif y <= -7e+22:
		tmp = 1.0 / ((1.0 / x) - (((z / (x * x)) - (a / x)) / y))
	elif y <= 1.2e+76:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / (i + (y * (c + (y * (b + (y * (y + a)))))))
	else:
		tmp = ((x + ((z / y) + (27464.7644705 / (y * y)))) - (a / ((y * y) / (z - (x * a))))) - ((a / (y / x)) + ((b / y) * (x / y)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -6.9e+103)
		tmp = Float64(Float64(x + Float64(z / y)) - Float64(Float64(x * a) / y));
	elseif (y <= -7e+22)
		tmp = Float64(1.0 / Float64(Float64(1.0 / x) - Float64(Float64(Float64(z / Float64(x * x)) - Float64(a / x)) / y)));
	elseif (y <= 1.2e+76)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(z + Float64(y * x)))))))) / Float64(i + Float64(y * Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a))))))));
	else
		tmp = Float64(Float64(Float64(x + Float64(Float64(z / y) + Float64(27464.7644705 / Float64(y * y)))) - Float64(a / Float64(Float64(y * y) / Float64(z - Float64(x * a))))) - Float64(Float64(a / Float64(y / x)) + Float64(Float64(b / y) * Float64(x / y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -6.9e+103)
		tmp = (x + (z / y)) - ((x * a) / y);
	elseif (y <= -7e+22)
		tmp = 1.0 / ((1.0 / x) - (((z / (x * x)) - (a / x)) / y));
	elseif (y <= 1.2e+76)
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / (i + (y * (c + (y * (b + (y * (y + a)))))));
	else
		tmp = ((x + ((z / y) + (27464.7644705 / (y * y)))) - (a / ((y * y) / (z - (x * a))))) - ((a / (y / x)) + ((b / y) * (x / y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -6.9e+103], N[(N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(N[(x * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -7e+22], N[(1.0 / N[(N[(1.0 / x), $MachinePrecision] - N[(N[(N[(z / N[(x * x), $MachinePrecision]), $MachinePrecision] - N[(a / x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.2e+76], N[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x + N[(N[(z / y), $MachinePrecision] + N[(27464.7644705 / N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a / N[(N[(y * y), $MachinePrecision] / N[(z - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision] + N[(N[(b / y), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -6.8999999999999999e103

   1. Initial program 0.0%

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

   2. Taylor expanded in y around inf 82.0%

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

   if -6.8999999999999999e103 < y < -7e22

   1. Initial program 17.3%

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

      1. clear-num 17.2%

         \[\leadsto \color{blue}{\frac{1}{\frac{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}}} \]

      2. inv-pow 17.2%

         \[\leadsto \color{blue}{{\left(\frac{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}\right)}^{-1}} \]

   3. Applied egg-rr 17.3%

      \[\leadsto \color{blue}{{\left(\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right), 230661.510616\right), t\right)}\right)}^{-1}} \]
   4. Step-by-step derivation

      1. unpow-1 17.3%

         \[\leadsto \color{blue}{\frac{1}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right), 230661.510616\right), t\right)}}} \]

      2. fma-udef 17.3%

         \[\leadsto \frac{1}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{x \cdot y + z}, 27464.7644705\right), 230661.510616\right), t\right)}} \]

      3. *-commutative 17.3%

         \[\leadsto \frac{1}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{y \cdot x} + z, 27464.7644705\right), 230661.510616\right), t\right)}} \]

      4. fma-def 17.3%

         \[\leadsto \frac{1}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(y, x, z\right)}, 27464.7644705\right), 230661.510616\right), t\right)}} \]

   5. Simplified 17.3%

      \[\leadsto \color{blue}{\frac{1}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), 27464.7644705\right), 230661.510616\right), t\right)}}} \]

   6. Taylor expanded in y around -inf 54.8%

      \[\leadsto \frac{1}{\color{blue}{\frac{1}{x} + -1 \cdot \frac{-1 \cdot \frac{a}{x} - -1 \cdot \frac{z}{{x}^{2}}}{y}}} \]
   7. Step-by-step derivation

      1. mul-1-neg 54.8%

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

      2. distribute-lft-out-- 54.8%

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

      3. unpow2 54.8%

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

   8. Simplified 54.8%

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

   if -7e22 < y < 1.2e76

   1. Initial program 90.6%

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

   if 1.2e76 < y

   1. Initial program 0.4%

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

   2. Taylor expanded in y around inf 53.9%

      \[\leadsto \color{blue}{\left(\frac{z}{y} + \left(27464.7644705 \cdot \frac{1}{{y}^{2}} + x\right)\right) - \left(\frac{\left(z - a \cdot x\right) \cdot a}{{y}^{2}} + \left(\frac{a \cdot x}{y} + \frac{b \cdot x}{{y}^{2}}\right)\right)} \]
   3. Step-by-step derivation

      1. associate--r+ 53.9%

         \[\leadsto \color{blue}{\left(\left(\frac{z}{y} + \left(27464.7644705 \cdot \frac{1}{{y}^{2}} + x\right)\right) - \frac{\left(z - a \cdot x\right) \cdot a}{{y}^{2}}\right) - \left(\frac{a \cdot x}{y} + \frac{b \cdot x}{{y}^{2}}\right)} \]

      2. associate-+r+ 53.9%

         \[\leadsto \left(\color{blue}{\left(\left(\frac{z}{y} + 27464.7644705 \cdot \frac{1}{{y}^{2}}\right) + x\right)} - \frac{\left(z - a \cdot x\right) \cdot a}{{y}^{2}}\right) - \left(\frac{a \cdot x}{y} + \frac{b \cdot x}{{y}^{2}}\right) \]

      3. associate-*r/ 53.8%

         \[\leadsto \left(\left(\left(\frac{z}{y} + \color{blue}{\frac{27464.7644705 \cdot 1}{{y}^{2}}}\right) + x\right) - \frac{\left(z - a \cdot x\right) \cdot a}{{y}^{2}}\right) - \left(\frac{a \cdot x}{y} + \frac{b \cdot x}{{y}^{2}}\right) \]

      4. metadata-eval 53.8%

         \[\leadsto \left(\left(\left(\frac{z}{y} + \frac{\color{blue}{27464.7644705}}{{y}^{2}}\right) + x\right) - \frac{\left(z - a \cdot x\right) \cdot a}{{y}^{2}}\right) - \left(\frac{a \cdot x}{y} + \frac{b \cdot x}{{y}^{2}}\right) \]

      5. unpow2 53.8%

         \[\leadsto \left(\left(\left(\frac{z}{y} + \frac{27464.7644705}{\color{blue}{y \cdot y}}\right) + x\right) - \frac{\left(z - a \cdot x\right) \cdot a}{{y}^{2}}\right) - \left(\frac{a \cdot x}{y} + \frac{b \cdot x}{{y}^{2}}\right) \]

      6. *-commutative 53.8%

         \[\leadsto \left(\left(\left(\frac{z}{y} + \frac{27464.7644705}{y \cdot y}\right) + x\right) - \frac{\color{blue}{a \cdot \left(z - a \cdot x\right)}}{{y}^{2}}\right) - \left(\frac{a \cdot x}{y} + \frac{b \cdot x}{{y}^{2}}\right) \]

      7. associate-/l* 73.6%

         \[\leadsto \left(\left(\left(\frac{z}{y} + \frac{27464.7644705}{y \cdot y}\right) + x\right) - \color{blue}{\frac{a}{\frac{{y}^{2}}{z - a \cdot x}}}\right) - \left(\frac{a \cdot x}{y} + \frac{b \cdot x}{{y}^{2}}\right) \]

      8. unpow2 73.6%

         \[\leadsto \left(\left(\left(\frac{z}{y} + \frac{27464.7644705}{y \cdot y}\right) + x\right) - \frac{a}{\frac{\color{blue}{y \cdot y}}{z - a \cdot x}}\right) - \left(\frac{a \cdot x}{y} + \frac{b \cdot x}{{y}^{2}}\right) \]

      9. associate-/l* 73.6%

         \[\leadsto \left(\left(\left(\frac{z}{y} + \frac{27464.7644705}{y \cdot y}\right) + x\right) - \frac{a}{\frac{y \cdot y}{z - a \cdot x}}\right) - \left(\color{blue}{\frac{a}{\frac{y}{x}}} + \frac{b \cdot x}{{y}^{2}}\right) \]

      10. unpow2 73.6%

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

      11. times-frac 78.4%

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

   4. Simplified 78.4%

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

4. Final simplification 84.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.9 \cdot 10^{+103}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{elif}\;y \leq -7 \cdot 10^{+22}:\\ \;\;\;\;\frac{1}{\frac{1}{x} - \frac{\frac{z}{x \cdot x} - \frac{a}{x}}{y}}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+76}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x + \left(\frac{z}{y} + \frac{27464.7644705}{y \cdot y}\right)\right) - \frac{a}{\frac{y \cdot y}{z - x \cdot a}}\right) - \left(\frac{a}{\frac{y}{x}} + \frac{b}{y} \cdot \frac{x}{y}\right)\\ \end{array} \]

Alternative 6: 82.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{if}\;y \leq -1.3 \cdot 10^{+103}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -7 \cdot 10^{+22}:\\ \;\;\;\;\frac{1}{\frac{1}{x} - \frac{\frac{z}{x \cdot x} - \frac{a}{x}}{y}}\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+52}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (- (+ x (/ z y)) (/ (* x a) y))))
   (if (<= y -1.3e+103)
     t_1
     (if (<= y -7e+22)
       (/ 1.0 (- (/ 1.0 x) (/ (- (/ z (* x x)) (/ a x)) y)))
       (if (<= y 2.2e+52)
         (/
          (+
           t
           (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ z (* y x))))))))
          (+ i (* y (+ c (* y (+ b (* y (+ 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 = (x + (z / y)) - ((x * a) / y);
	double tmp;
	if (y <= -1.3e+103) {
		tmp = t_1;
	} else if (y <= -7e+22) {
		tmp = 1.0 / ((1.0 / x) - (((z / (x * x)) - (a / x)) / y));
	} else if (y <= 2.2e+52) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / (i + (y * (c + (y * (b + (y * (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 = (x + (z / y)) - ((x * a) / y)
    if (y <= (-1.3d+103)) then
        tmp = t_1
    else if (y <= (-7d+22)) then
        tmp = 1.0d0 / ((1.0d0 / x) - (((z / (x * x)) - (a / x)) / y))
    else if (y <= 2.2d+52) then
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * (z + (y * x)))))))) / (i + (y * (c + (y * (b + (y * (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 = (x + (z / y)) - ((x * a) / y);
	double tmp;
	if (y <= -1.3e+103) {
		tmp = t_1;
	} else if (y <= -7e+22) {
		tmp = 1.0 / ((1.0 / x) - (((z / (x * x)) - (a / x)) / y));
	} else if (y <= 2.2e+52) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / (i + (y * (c + (y * (b + (y * (y + a)))))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x + (z / y)) - ((x * a) / y)
	tmp = 0
	if y <= -1.3e+103:
		tmp = t_1
	elif y <= -7e+22:
		tmp = 1.0 / ((1.0 / x) - (((z / (x * x)) - (a / x)) / y))
	elif y <= 2.2e+52:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / (i + (y * (c + (y * (b + (y * (y + a)))))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x + Float64(z / y)) - Float64(Float64(x * a) / y))
	tmp = 0.0
	if (y <= -1.3e+103)
		tmp = t_1;
	elseif (y <= -7e+22)
		tmp = Float64(1.0 / Float64(Float64(1.0 / x) - Float64(Float64(Float64(z / Float64(x * x)) - Float64(a / x)) / y)));
	elseif (y <= 2.2e+52)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(z + Float64(y * x)))))))) / Float64(i + Float64(y * Float64(c + Float64(y * Float64(b + Float64(y * Float64(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 = (x + (z / y)) - ((x * a) / y);
	tmp = 0.0;
	if (y <= -1.3e+103)
		tmp = t_1;
	elseif (y <= -7e+22)
		tmp = 1.0 / ((1.0 / x) - (((z / (x * x)) - (a / x)) / y));
	elseif (y <= 2.2e+52)
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / (i + (y * (c + (y * (b + (y * (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[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(N[(x * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.3e+103], t$95$1, If[LessEqual[y, -7e+22], N[(1.0 / N[(N[(1.0 / x), $MachinePrecision] - N[(N[(N[(z / N[(x * x), $MachinePrecision]), $MachinePrecision] - N[(a / x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.2e+52], N[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.3000000000000001e103 or 2.2e52 < y

   1. Initial program 0.3%

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

   2. Taylor expanded in y around inf 75.3%

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

   if -1.3000000000000001e103 < y < -7e22

   1. Initial program 17.3%

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

      1. clear-num 17.2%

         \[\leadsto \color{blue}{\frac{1}{\frac{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}}} \]

      2. inv-pow 17.2%

         \[\leadsto \color{blue}{{\left(\frac{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}\right)}^{-1}} \]

   3. Applied egg-rr 17.3%

      \[\leadsto \color{blue}{{\left(\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right), 230661.510616\right), t\right)}\right)}^{-1}} \]
   4. Step-by-step derivation

      1. unpow-1 17.3%

         \[\leadsto \color{blue}{\frac{1}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right), 230661.510616\right), t\right)}}} \]

      2. fma-udef 17.3%

         \[\leadsto \frac{1}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{x \cdot y + z}, 27464.7644705\right), 230661.510616\right), t\right)}} \]

      3. *-commutative 17.3%

         \[\leadsto \frac{1}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{y \cdot x} + z, 27464.7644705\right), 230661.510616\right), t\right)}} \]

      4. fma-def 17.3%

         \[\leadsto \frac{1}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(y, x, z\right)}, 27464.7644705\right), 230661.510616\right), t\right)}} \]

   5. Simplified 17.3%

      \[\leadsto \color{blue}{\frac{1}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), 27464.7644705\right), 230661.510616\right), t\right)}}} \]

   6. Taylor expanded in y around -inf 54.8%

      \[\leadsto \frac{1}{\color{blue}{\frac{1}{x} + -1 \cdot \frac{-1 \cdot \frac{a}{x} - -1 \cdot \frac{z}{{x}^{2}}}{y}}} \]
   7. Step-by-step derivation

      1. mul-1-neg 54.8%

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

      2. distribute-lft-out-- 54.8%

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

      3. unpow2 54.8%

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

   8. Simplified 54.8%

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

   if -7e22 < y < 2.2e52

   1. Initial program 93.7%

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

4. Final simplification 84.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+103}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{elif}\;y \leq -7 \cdot 10^{+22}:\\ \;\;\;\;\frac{1}{\frac{1}{x} - \frac{\frac{z}{x \cdot x} - \frac{a}{x}}{y}}\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+52}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \end{array} \]

Alternative 7: 78.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{if}\;y \leq -1.25 \cdot 10^{+104}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{+19}:\\ \;\;\;\;\frac{1}{\frac{1}{x} - \frac{\frac{z}{x \cdot x} - \frac{a}{x}}{y}}\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{+24}:\\ \;\;\;\;\frac{1}{\frac{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (- (+ x (/ z y)) (/ (* x a) y))))
   (if (<= y -1.25e+104)
     t_1
     (if (<= y -6.5e+19)
       (/ 1.0 (- (/ 1.0 x) (/ (- (/ z (* x x)) (/ a x)) y)))
       (if (<= y 4.6e+24)
         (/
          1.0
          (/
           (+ i (* y (+ c (* y (+ b (* y (+ y a)))))))
           (+ t (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y z))))))))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x + (z / y)) - ((x * a) / y);
	double tmp;
	if (y <= -1.25e+104) {
		tmp = t_1;
	} else if (y <= -6.5e+19) {
		tmp = 1.0 / ((1.0 / x) - (((z / (x * x)) - (a / x)) / y));
	} else if (y <= 4.6e+24) {
		tmp = 1.0 / ((i + (y * (c + (y * (b + (y * (y + a))))))) / (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))));
	} 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 = (x + (z / y)) - ((x * a) / y)
    if (y <= (-1.25d+104)) then
        tmp = t_1
    else if (y <= (-6.5d+19)) then
        tmp = 1.0d0 / ((1.0d0 / x) - (((z / (x * x)) - (a / x)) / y))
    else if (y <= 4.6d+24) then
        tmp = 1.0d0 / ((i + (y * (c + (y * (b + (y * (y + a))))))) / (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * z)))))))
    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 = (x + (z / y)) - ((x * a) / y);
	double tmp;
	if (y <= -1.25e+104) {
		tmp = t_1;
	} else if (y <= -6.5e+19) {
		tmp = 1.0 / ((1.0 / x) - (((z / (x * x)) - (a / x)) / y));
	} else if (y <= 4.6e+24) {
		tmp = 1.0 / ((i + (y * (c + (y * (b + (y * (y + a))))))) / (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x + (z / y)) - ((x * a) / y)
	tmp = 0
	if y <= -1.25e+104:
		tmp = t_1
	elif y <= -6.5e+19:
		tmp = 1.0 / ((1.0 / x) - (((z / (x * x)) - (a / x)) / y))
	elif y <= 4.6e+24:
		tmp = 1.0 / ((i + (y * (c + (y * (b + (y * (y + a))))))) / (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x + Float64(z / y)) - Float64(Float64(x * a) / y))
	tmp = 0.0
	if (y <= -1.25e+104)
		tmp = t_1;
	elseif (y <= -6.5e+19)
		tmp = Float64(1.0 / Float64(Float64(1.0 / x) - Float64(Float64(Float64(z / Float64(x * x)) - Float64(a / x)) / y)));
	elseif (y <= 4.6e+24)
		tmp = Float64(1.0 / Float64(Float64(i + Float64(y * Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a))))))) / Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * z))))))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x + (z / y)) - ((x * a) / y);
	tmp = 0.0;
	if (y <= -1.25e+104)
		tmp = t_1;
	elseif (y <= -6.5e+19)
		tmp = 1.0 / ((1.0 / x) - (((z / (x * x)) - (a / x)) / y));
	elseif (y <= 4.6e+24)
		tmp = 1.0 / ((i + (y * (c + (y * (b + (y * (y + a))))))) / (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))));
	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[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(N[(x * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.25e+104], t$95$1, If[LessEqual[y, -6.5e+19], N[(1.0 / N[(N[(1.0 / x), $MachinePrecision] - N[(N[(N[(z / N[(x * x), $MachinePrecision]), $MachinePrecision] - N[(a / x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.6e+24], N[(1.0 / N[(N[(i + N[(y * N[(c + N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.2499999999999999e104 or 4.5999999999999998e24 < y

   1. Initial program 1.4%

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

   2. Taylor expanded in y around inf 71.8%

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

   if -1.2499999999999999e104 < y < -6.5e19

   1. Initial program 20.3%

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

      1. clear-num 20.2%

         \[\leadsto \color{blue}{\frac{1}{\frac{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}}} \]

      2. inv-pow 20.2%

         \[\leadsto \color{blue}{{\left(\frac{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}\right)}^{-1}} \]

   3. Applied egg-rr 20.3%

      \[\leadsto \color{blue}{{\left(\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right), 230661.510616\right), t\right)}\right)}^{-1}} \]
   4. Step-by-step derivation

      1. unpow-1 20.3%

         \[\leadsto \color{blue}{\frac{1}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right), 230661.510616\right), t\right)}}} \]

      2. fma-udef 20.3%

         \[\leadsto \frac{1}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{x \cdot y + z}, 27464.7644705\right), 230661.510616\right), t\right)}} \]

      3. *-commutative 20.3%

         \[\leadsto \frac{1}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{y \cdot x} + z, 27464.7644705\right), 230661.510616\right), t\right)}} \]

      4. fma-def 20.3%

         \[\leadsto \frac{1}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(y, x, z\right)}, 27464.7644705\right), 230661.510616\right), t\right)}} \]

   5. Simplified 20.3%

      \[\leadsto \color{blue}{\frac{1}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), 27464.7644705\right), 230661.510616\right), t\right)}}} \]

   6. Taylor expanded in y around -inf 54.3%

      \[\leadsto \frac{1}{\color{blue}{\frac{1}{x} + -1 \cdot \frac{-1 \cdot \frac{a}{x} - -1 \cdot \frac{z}{{x}^{2}}}{y}}} \]
   7. Step-by-step derivation

      1. mul-1-neg 54.3%

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

      2. distribute-lft-out-- 54.3%

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

      3. unpow2 54.3%

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

   8. Simplified 54.3%

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

   if -6.5e19 < y < 4.5999999999999998e24

   1. Initial program 96.9%

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

      1. clear-num 96.6%

         \[\leadsto \color{blue}{\frac{1}{\frac{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}}} \]

      2. inv-pow 96.6%

         \[\leadsto \color{blue}{{\left(\frac{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}\right)}^{-1}} \]

   3. Applied egg-rr 96.6%

      \[\leadsto \color{blue}{{\left(\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right), 230661.510616\right), t\right)}\right)}^{-1}} \]
   4. Step-by-step derivation

      1. unpow-1 96.6%

         \[\leadsto \color{blue}{\frac{1}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right), 230661.510616\right), t\right)}}} \]

      2. fma-udef 96.6%

         \[\leadsto \frac{1}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{x \cdot y + z}, 27464.7644705\right), 230661.510616\right), t\right)}} \]

      3. *-commutative 96.6%

         \[\leadsto \frac{1}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{y \cdot x} + z, 27464.7644705\right), 230661.510616\right), t\right)}} \]

      4. fma-def 96.6%

         \[\leadsto \frac{1}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(y, x, z\right)}, 27464.7644705\right), 230661.510616\right), t\right)}} \]

   5. Simplified 96.6%

      \[\leadsto \color{blue}{\frac{1}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), 27464.7644705\right), 230661.510616\right), t\right)}}} \]

   6. Taylor expanded in x around 0 91.1%

      \[\leadsto \frac{1}{\color{blue}{\frac{y \cdot \left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) + i}{y \cdot \left(230661.510616 + y \cdot \left(y \cdot z + 27464.7644705\right)\right) + t}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+104}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{+19}:\\ \;\;\;\;\frac{1}{\frac{1}{x} - \frac{\frac{z}{x \cdot x} - \frac{a}{x}}{y}}\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{+24}:\\ \;\;\;\;\frac{1}{\frac{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \end{array} \]

Alternative 8: 78.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{if}\;y \leq -1.05 \cdot 10^{+102}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{+19}:\\ \;\;\;\;\frac{1}{\frac{1}{x} - \frac{\frac{z}{x \cdot x} - \frac{a}{x}}{y}}\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{+24}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + \left(y \cdot y\right) \cdot z\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (- (+ x (/ z y)) (/ (* x a) y))))
   (if (<= y -1.05e+102)
     t_1
     (if (<= y -6.5e+19)
       (/ 1.0 (- (/ 1.0 x) (/ (- (/ z (* x x)) (/ a x)) y)))
       (if (<= y 4.6e+24)
         (/
          (+ t (* y (+ 230661.510616 (* (* y y) z))))
          (+ i (* y (+ c (* y (+ b (* y (+ 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 = (x + (z / y)) - ((x * a) / y);
	double tmp;
	if (y <= -1.05e+102) {
		tmp = t_1;
	} else if (y <= -6.5e+19) {
		tmp = 1.0 / ((1.0 / x) - (((z / (x * x)) - (a / x)) / y));
	} else if (y <= 4.6e+24) {
		tmp = (t + (y * (230661.510616 + ((y * y) * z)))) / (i + (y * (c + (y * (b + (y * (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 = (x + (z / y)) - ((x * a) / y)
    if (y <= (-1.05d+102)) then
        tmp = t_1
    else if (y <= (-6.5d+19)) then
        tmp = 1.0d0 / ((1.0d0 / x) - (((z / (x * x)) - (a / x)) / y))
    else if (y <= 4.6d+24) then
        tmp = (t + (y * (230661.510616d0 + ((y * y) * z)))) / (i + (y * (c + (y * (b + (y * (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 = (x + (z / y)) - ((x * a) / y);
	double tmp;
	if (y <= -1.05e+102) {
		tmp = t_1;
	} else if (y <= -6.5e+19) {
		tmp = 1.0 / ((1.0 / x) - (((z / (x * x)) - (a / x)) / y));
	} else if (y <= 4.6e+24) {
		tmp = (t + (y * (230661.510616 + ((y * y) * z)))) / (i + (y * (c + (y * (b + (y * (y + a)))))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x + (z / y)) - ((x * a) / y)
	tmp = 0
	if y <= -1.05e+102:
		tmp = t_1
	elif y <= -6.5e+19:
		tmp = 1.0 / ((1.0 / x) - (((z / (x * x)) - (a / x)) / y))
	elif y <= 4.6e+24:
		tmp = (t + (y * (230661.510616 + ((y * y) * z)))) / (i + (y * (c + (y * (b + (y * (y + a)))))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x + Float64(z / y)) - Float64(Float64(x * a) / y))
	tmp = 0.0
	if (y <= -1.05e+102)
		tmp = t_1;
	elseif (y <= -6.5e+19)
		tmp = Float64(1.0 / Float64(Float64(1.0 / x) - Float64(Float64(Float64(z / Float64(x * x)) - Float64(a / x)) / y)));
	elseif (y <= 4.6e+24)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(Float64(y * y) * z)))) / Float64(i + Float64(y * Float64(c + Float64(y * Float64(b + Float64(y * Float64(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 = (x + (z / y)) - ((x * a) / y);
	tmp = 0.0;
	if (y <= -1.05e+102)
		tmp = t_1;
	elseif (y <= -6.5e+19)
		tmp = 1.0 / ((1.0 / x) - (((z / (x * x)) - (a / x)) / y));
	elseif (y <= 4.6e+24)
		tmp = (t + (y * (230661.510616 + ((y * y) * z)))) / (i + (y * (c + (y * (b + (y * (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[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(N[(x * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.05e+102], t$95$1, If[LessEqual[y, -6.5e+19], N[(1.0 / N[(N[(1.0 / x), $MachinePrecision] - N[(N[(N[(z / N[(x * x), $MachinePrecision]), $MachinePrecision] - N[(a / x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.6e+24], N[(N[(t + N[(y * N[(230661.510616 + N[(N[(y * y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.05000000000000001e102 or 4.5999999999999998e24 < y

   1. Initial program 1.4%

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

   2. Taylor expanded in y around inf 71.8%

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

   if -1.05000000000000001e102 < y < -6.5e19

   1. Initial program 20.3%

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

      1. clear-num 20.2%

         \[\leadsto \color{blue}{\frac{1}{\frac{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}}} \]

      2. inv-pow 20.2%

         \[\leadsto \color{blue}{{\left(\frac{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}\right)}^{-1}} \]

   3. Applied egg-rr 20.3%

      \[\leadsto \color{blue}{{\left(\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right), 230661.510616\right), t\right)}\right)}^{-1}} \]
   4. Step-by-step derivation

      1. unpow-1 20.3%

         \[\leadsto \color{blue}{\frac{1}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right), 230661.510616\right), t\right)}}} \]

      2. fma-udef 20.3%

         \[\leadsto \frac{1}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{x \cdot y + z}, 27464.7644705\right), 230661.510616\right), t\right)}} \]

      3. *-commutative 20.3%

         \[\leadsto \frac{1}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{y \cdot x} + z, 27464.7644705\right), 230661.510616\right), t\right)}} \]

      4. fma-def 20.3%

         \[\leadsto \frac{1}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(y, x, z\right)}, 27464.7644705\right), 230661.510616\right), t\right)}} \]

   5. Simplified 20.3%

      \[\leadsto \color{blue}{\frac{1}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), 27464.7644705\right), 230661.510616\right), t\right)}}} \]

   6. Taylor expanded in y around -inf 54.3%

      \[\leadsto \frac{1}{\color{blue}{\frac{1}{x} + -1 \cdot \frac{-1 \cdot \frac{a}{x} - -1 \cdot \frac{z}{{x}^{2}}}{y}}} \]
   7. Step-by-step derivation

      1. mul-1-neg 54.3%

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

      2. distribute-lft-out-- 54.3%

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

      3. unpow2 54.3%

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

   8. Simplified 54.3%

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

   if -6.5e19 < y < 4.5999999999999998e24

   1. Initial program 96.9%

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

   2. Taylor expanded in z around inf 88.5%

      \[\leadsto \frac{\left(\color{blue}{{y}^{2} \cdot z} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   3. Step-by-step derivation

      1. *-commutative 88.5%

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

      2. unpow2 88.5%

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

   4. Simplified 88.5%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+102}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{+19}:\\ \;\;\;\;\frac{1}{\frac{1}{x} - \frac{\frac{z}{x \cdot x} - \frac{a}{x}}{y}}\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{+24}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + \left(y \cdot y\right) \cdot z\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \end{array} \]

Alternative 9: 78.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{if}\;y \leq -6 \cdot 10^{+101}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -4 \cdot 10^{+19}:\\ \;\;\;\;\frac{1}{\frac{1}{x} - \frac{\frac{z}{x \cdot x} - \frac{a}{x}}{y}}\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+51}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (- (+ x (/ z y)) (/ (* x a) y))))
   (if (<= y -6e+101)
     t_1
     (if (<= y -4e+19)
       (/ 1.0 (- (/ 1.0 x) (/ (- (/ z (* x x)) (/ a x)) y)))
       (if (<= y 3.6e+51)
         (/
          (+
           t
           (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ z (* y x))))))))
          (+ i (* y (+ c (* y b)))))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x + (z / y)) - ((x * a) / y);
	double tmp;
	if (y <= -6e+101) {
		tmp = t_1;
	} else if (y <= -4e+19) {
		tmp = 1.0 / ((1.0 / x) - (((z / (x * x)) - (a / x)) / y));
	} else if (y <= 3.6e+51) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / (i + (y * (c + (y * b))));
	} 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 = (x + (z / y)) - ((x * a) / y)
    if (y <= (-6d+101)) then
        tmp = t_1
    else if (y <= (-4d+19)) then
        tmp = 1.0d0 / ((1.0d0 / x) - (((z / (x * x)) - (a / x)) / y))
    else if (y <= 3.6d+51) then
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * (z + (y * x)))))))) / (i + (y * (c + (y * b))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x + (z / y)) - ((x * a) / y);
	double tmp;
	if (y <= -6e+101) {
		tmp = t_1;
	} else if (y <= -4e+19) {
		tmp = 1.0 / ((1.0 / x) - (((z / (x * x)) - (a / x)) / y));
	} else if (y <= 3.6e+51) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / (i + (y * (c + (y * b))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x + (z / y)) - ((x * a) / y)
	tmp = 0
	if y <= -6e+101:
		tmp = t_1
	elif y <= -4e+19:
		tmp = 1.0 / ((1.0 / x) - (((z / (x * x)) - (a / x)) / y))
	elif y <= 3.6e+51:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / (i + (y * (c + (y * b))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x + Float64(z / y)) - Float64(Float64(x * a) / y))
	tmp = 0.0
	if (y <= -6e+101)
		tmp = t_1;
	elseif (y <= -4e+19)
		tmp = Float64(1.0 / Float64(Float64(1.0 / x) - Float64(Float64(Float64(z / Float64(x * x)) - Float64(a / x)) / y)));
	elseif (y <= 3.6e+51)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(z + Float64(y * x)))))))) / Float64(i + Float64(y * Float64(c + Float64(y * b)))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x + (z / y)) - ((x * a) / y);
	tmp = 0.0;
	if (y <= -6e+101)
		tmp = t_1;
	elseif (y <= -4e+19)
		tmp = 1.0 / ((1.0 / x) - (((z / (x * x)) - (a / x)) / y));
	elseif (y <= 3.6e+51)
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / (i + (y * (c + (y * b))));
	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[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(N[(x * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6e+101], t$95$1, If[LessEqual[y, -4e+19], N[(1.0 / N[(N[(1.0 / x), $MachinePrecision] - N[(N[(N[(z / N[(x * x), $MachinePrecision]), $MachinePrecision] - N[(a / x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.6e+51], N[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.99999999999999986e101 or 3.60000000000000011e51 < y

   1. Initial program 0.3%

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

   2. Taylor expanded in y around inf 75.3%

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

   if -5.99999999999999986e101 < y < -4e19

   1. Initial program 20.3%

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

      1. clear-num 20.2%

         \[\leadsto \color{blue}{\frac{1}{\frac{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}}} \]

      2. inv-pow 20.2%

         \[\leadsto \color{blue}{{\left(\frac{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}\right)}^{-1}} \]

   3. Applied egg-rr 20.3%

      \[\leadsto \color{blue}{{\left(\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right), 230661.510616\right), t\right)}\right)}^{-1}} \]
   4. Step-by-step derivation

      1. unpow-1 20.3%

         \[\leadsto \color{blue}{\frac{1}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right), 230661.510616\right), t\right)}}} \]

      2. fma-udef 20.3%

         \[\leadsto \frac{1}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{x \cdot y + z}, 27464.7644705\right), 230661.510616\right), t\right)}} \]

      3. *-commutative 20.3%

         \[\leadsto \frac{1}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{y \cdot x} + z, 27464.7644705\right), 230661.510616\right), t\right)}} \]

      4. fma-def 20.3%

         \[\leadsto \frac{1}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(y, x, z\right)}, 27464.7644705\right), 230661.510616\right), t\right)}} \]

   5. Simplified 20.3%

      \[\leadsto \color{blue}{\frac{1}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), 27464.7644705\right), 230661.510616\right), t\right)}}} \]

   6. Taylor expanded in y around -inf 54.3%

      \[\leadsto \frac{1}{\color{blue}{\frac{1}{x} + -1 \cdot \frac{-1 \cdot \frac{a}{x} - -1 \cdot \frac{z}{{x}^{2}}}{y}}} \]
   7. Step-by-step derivation

      1. mul-1-neg 54.3%

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

      2. distribute-lft-out-- 54.3%

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

      3. unpow2 54.3%

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

   8. Simplified 54.3%

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

   if -4e19 < y < 3.60000000000000011e51

   1. Initial program 94.3%

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

   2. Taylor expanded in y around 0 87.4%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+101}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{elif}\;y \leq -4 \cdot 10^{+19}:\\ \;\;\;\;\frac{1}{\frac{1}{x} - \frac{\frac{z}{x \cdot x} - \frac{a}{x}}{y}}\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+51}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \end{array} \]

Alternative 10: 73.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{if}\;y \leq -1.35 \cdot 10^{+103}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -3.3 \cdot 10^{+16}:\\ \;\;\;\;\frac{1}{\frac{1}{x} - \frac{\frac{z}{x \cdot x} - \frac{a}{x}}{y}}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+24}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot y\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (- (+ x (/ z y)) (/ (* x a) y))))
   (if (<= y -1.35e+103)
     t_1
     (if (<= y -3.3e+16)
       (/ 1.0 (- (/ 1.0 x) (/ (- (/ z (* x x)) (/ a x)) y)))
       (if (<= y 4.2e+24)
         (/
          (+ t (* y (+ 230661.510616 (* y 27464.7644705))))
          (+ i (* y (+ c (* y (+ b (* y y)))))))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x + (z / y)) - ((x * a) / y);
	double tmp;
	if (y <= -1.35e+103) {
		tmp = t_1;
	} else if (y <= -3.3e+16) {
		tmp = 1.0 / ((1.0 / x) - (((z / (x * x)) - (a / x)) / y));
	} else if (y <= 4.2e+24) {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * (c + (y * (b + (y * y))))));
	} 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 = (x + (z / y)) - ((x * a) / y)
    if (y <= (-1.35d+103)) then
        tmp = t_1
    else if (y <= (-3.3d+16)) then
        tmp = 1.0d0 / ((1.0d0 / x) - (((z / (x * x)) - (a / x)) / y))
    else if (y <= 4.2d+24) then
        tmp = (t + (y * (230661.510616d0 + (y * 27464.7644705d0)))) / (i + (y * (c + (y * (b + (y * y))))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x + (z / y)) - ((x * a) / y);
	double tmp;
	if (y <= -1.35e+103) {
		tmp = t_1;
	} else if (y <= -3.3e+16) {
		tmp = 1.0 / ((1.0 / x) - (((z / (x * x)) - (a / x)) / y));
	} else if (y <= 4.2e+24) {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * (c + (y * (b + (y * y))))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x + (z / y)) - ((x * a) / y)
	tmp = 0
	if y <= -1.35e+103:
		tmp = t_1
	elif y <= -3.3e+16:
		tmp = 1.0 / ((1.0 / x) - (((z / (x * x)) - (a / x)) / y))
	elif y <= 4.2e+24:
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * (c + (y * (b + (y * y))))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x + Float64(z / y)) - Float64(Float64(x * a) / y))
	tmp = 0.0
	if (y <= -1.35e+103)
		tmp = t_1;
	elseif (y <= -3.3e+16)
		tmp = Float64(1.0 / Float64(Float64(1.0 / x) - Float64(Float64(Float64(z / Float64(x * x)) - Float64(a / x)) / y)));
	elseif (y <= 4.2e+24)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * 27464.7644705)))) / Float64(i + Float64(y * Float64(c + Float64(y * Float64(b + Float64(y * y)))))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x + (z / y)) - ((x * a) / y);
	tmp = 0.0;
	if (y <= -1.35e+103)
		tmp = t_1;
	elseif (y <= -3.3e+16)
		tmp = 1.0 / ((1.0 / x) - (((z / (x * x)) - (a / x)) / y));
	elseif (y <= 4.2e+24)
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * (c + (y * (b + (y * y))))));
	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[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(N[(x * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.35e+103], t$95$1, If[LessEqual[y, -3.3e+16], N[(1.0 / N[(N[(1.0 / x), $MachinePrecision] - N[(N[(N[(z / N[(x * x), $MachinePrecision]), $MachinePrecision] - N[(a / x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.2e+24], N[(N[(t + N[(y * N[(230661.510616 + N[(y * 27464.7644705), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * N[(b + N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.34999999999999996e103 or 4.2000000000000003e24 < y

   1. Initial program 1.4%

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

   2. Taylor expanded in y around inf 71.8%

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

   if -1.34999999999999996e103 < y < -3.3e16

   1. Initial program 19.7%

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

      1. clear-num 19.6%

         \[\leadsto \color{blue}{\frac{1}{\frac{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}}} \]

      2. inv-pow 19.6%

         \[\leadsto \color{blue}{{\left(\frac{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}\right)}^{-1}} \]

   3. Applied egg-rr 19.7%

      \[\leadsto \color{blue}{{\left(\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right), 230661.510616\right), t\right)}\right)}^{-1}} \]
   4. Step-by-step derivation

      1. unpow-1 19.7%

         \[\leadsto \color{blue}{\frac{1}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right), 230661.510616\right), t\right)}}} \]

      2. fma-udef 19.7%

         \[\leadsto \frac{1}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{x \cdot y + z}, 27464.7644705\right), 230661.510616\right), t\right)}} \]

      3. *-commutative 19.7%

         \[\leadsto \frac{1}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{y \cdot x} + z, 27464.7644705\right), 230661.510616\right), t\right)}} \]

      4. fma-def 19.7%

         \[\leadsto \frac{1}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(y, x, z\right)}, 27464.7644705\right), 230661.510616\right), t\right)}} \]

   5. Simplified 19.7%

      \[\leadsto \color{blue}{\frac{1}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), 27464.7644705\right), 230661.510616\right), t\right)}}} \]

   6. Taylor expanded in y around -inf 52.0%

      \[\leadsto \frac{1}{\color{blue}{\frac{1}{x} + -1 \cdot \frac{-1 \cdot \frac{a}{x} - -1 \cdot \frac{z}{{x}^{2}}}{y}}} \]
   7. Step-by-step derivation

      1. mul-1-neg 52.0%

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

      2. distribute-lft-out-- 52.0%

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

      3. unpow2 52.0%

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

   8. Simplified 52.0%

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

   if -3.3e16 < y < 4.2000000000000003e24

   1. Initial program 97.6%

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

   2. Taylor expanded in y around 0 84.0%

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

      1. *-commutative 84.0%

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

   4. Simplified 84.0%

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

   5. Taylor expanded in a around 0 81.9%

      \[\leadsto \frac{\left(y \cdot 27464.7644705 + 230661.510616\right) \cdot y + t}{\left(\color{blue}{\left({y}^{2} + b\right) \cdot y} + c\right) \cdot y + i} \]
   6. Step-by-step derivation

      1. *-commutative 81.9%

         \[\leadsto \frac{\left(y \cdot 27464.7644705 + 230661.510616\right) \cdot y + t}{\left(\color{blue}{y \cdot \left({y}^{2} + b\right)} + c\right) \cdot y + i} \]

      2. +-commutative 81.9%

         \[\leadsto \frac{\left(y \cdot 27464.7644705 + 230661.510616\right) \cdot y + t}{\left(y \cdot \color{blue}{\left(b + {y}^{2}\right)} + c\right) \cdot y + i} \]

      3. unpow2 81.9%

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

   7. Simplified 81.9%

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

4. Final simplification 75.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{+103}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{elif}\;y \leq -3.3 \cdot 10^{+16}:\\ \;\;\;\;\frac{1}{\frac{1}{x} - \frac{\frac{z}{x \cdot x} - \frac{a}{x}}{y}}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+24}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot y\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \end{array} \]

Alternative 11: 76.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{if}\;y \leq -3.7 \cdot 10^{+102}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -9.2 \cdot 10^{+17}:\\ \;\;\;\;\frac{1}{\frac{1}{x} - \frac{\frac{z}{x \cdot x} - \frac{a}{x}}{y}}\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{+24}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (- (+ x (/ z y)) (/ (* x a) y))))
   (if (<= y -3.7e+102)
     t_1
     (if (<= y -9.2e+17)
       (/ 1.0 (- (/ 1.0 x) (/ (- (/ z (* x x)) (/ a x)) y)))
       (if (<= y 4.6e+24)
         (/
          (+ t (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y z))))))
          (+ i (* y (+ c (* y b)))))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x + (z / y)) - ((x * a) / y);
	double tmp;
	if (y <= -3.7e+102) {
		tmp = t_1;
	} else if (y <= -9.2e+17) {
		tmp = 1.0 / ((1.0 / x) - (((z / (x * x)) - (a / x)) / y));
	} else if (y <= 4.6e+24) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * b))));
	} 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 = (x + (z / y)) - ((x * a) / y)
    if (y <= (-3.7d+102)) then
        tmp = t_1
    else if (y <= (-9.2d+17)) then
        tmp = 1.0d0 / ((1.0d0 / x) - (((z / (x * x)) - (a / x)) / y))
    else if (y <= 4.6d+24) then
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * z)))))) / (i + (y * (c + (y * b))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x + (z / y)) - ((x * a) / y);
	double tmp;
	if (y <= -3.7e+102) {
		tmp = t_1;
	} else if (y <= -9.2e+17) {
		tmp = 1.0 / ((1.0 / x) - (((z / (x * x)) - (a / x)) / y));
	} else if (y <= 4.6e+24) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * b))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x + (z / y)) - ((x * a) / y)
	tmp = 0
	if y <= -3.7e+102:
		tmp = t_1
	elif y <= -9.2e+17:
		tmp = 1.0 / ((1.0 / x) - (((z / (x * x)) - (a / x)) / y))
	elif y <= 4.6e+24:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * b))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x + Float64(z / y)) - Float64(Float64(x * a) / y))
	tmp = 0.0
	if (y <= -3.7e+102)
		tmp = t_1;
	elseif (y <= -9.2e+17)
		tmp = Float64(1.0 / Float64(Float64(1.0 / x) - Float64(Float64(Float64(z / Float64(x * x)) - Float64(a / x)) / y)));
	elseif (y <= 4.6e+24)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * z)))))) / Float64(i + Float64(y * Float64(c + Float64(y * b)))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x + (z / y)) - ((x * a) / y);
	tmp = 0.0;
	if (y <= -3.7e+102)
		tmp = t_1;
	elseif (y <= -9.2e+17)
		tmp = 1.0 / ((1.0 / x) - (((z / (x * x)) - (a / x)) / y));
	elseif (y <= 4.6e+24)
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * b))));
	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[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(N[(x * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.7e+102], t$95$1, If[LessEqual[y, -9.2e+17], N[(1.0 / N[(N[(1.0 / x), $MachinePrecision] - N[(N[(N[(z / N[(x * x), $MachinePrecision]), $MachinePrecision] - N[(a / x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.6e+24], N[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.70000000000000023e102 or 4.5999999999999998e24 < y

   1. Initial program 1.4%

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

   2. Taylor expanded in y around inf 71.8%

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

   if -3.70000000000000023e102 < y < -9.2e17

   1. Initial program 20.3%

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

      1. clear-num 20.2%

         \[\leadsto \color{blue}{\frac{1}{\frac{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}}} \]

      2. inv-pow 20.2%

         \[\leadsto \color{blue}{{\left(\frac{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}\right)}^{-1}} \]

   3. Applied egg-rr 20.3%

      \[\leadsto \color{blue}{{\left(\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right), 230661.510616\right), t\right)}\right)}^{-1}} \]
   4. Step-by-step derivation

      1. unpow-1 20.3%

         \[\leadsto \color{blue}{\frac{1}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right), 230661.510616\right), t\right)}}} \]

      2. fma-udef 20.3%

         \[\leadsto \frac{1}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{x \cdot y + z}, 27464.7644705\right), 230661.510616\right), t\right)}} \]

      3. *-commutative 20.3%

         \[\leadsto \frac{1}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{y \cdot x} + z, 27464.7644705\right), 230661.510616\right), t\right)}} \]

      4. fma-def 20.3%

         \[\leadsto \frac{1}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(y, x, z\right)}, 27464.7644705\right), 230661.510616\right), t\right)}} \]

   5. Simplified 20.3%

      \[\leadsto \color{blue}{\frac{1}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), 27464.7644705\right), 230661.510616\right), t\right)}}} \]

   6. Taylor expanded in y around -inf 54.3%

      \[\leadsto \frac{1}{\color{blue}{\frac{1}{x} + -1 \cdot \frac{-1 \cdot \frac{a}{x} - -1 \cdot \frac{z}{{x}^{2}}}{y}}} \]
   7. Step-by-step derivation

      1. mul-1-neg 54.3%

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

      2. distribute-lft-out-- 54.3%

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

      3. unpow2 54.3%

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

   8. Simplified 54.3%

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

   if -9.2e17 < y < 4.5999999999999998e24

   1. Initial program 96.9%

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

   2. Taylor expanded in y around 0 90.3%

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

   3. Taylor expanded in x around 0 86.1%

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

4. Final simplification 78.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{+102}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{elif}\;y \leq -9.2 \cdot 10^{+17}:\\ \;\;\;\;\frac{1}{\frac{1}{x} - \frac{\frac{z}{x \cdot x} - \frac{a}{x}}{y}}\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{+24}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \end{array} \]

Alternative 12: 74.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{if}\;y \leq -1.15 \cdot 10^{+104}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -0.00305:\\ \;\;\;\;\frac{1}{\frac{1}{x} - \frac{\frac{z}{x \cdot x} - \frac{a}{x}}{y}}\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+24}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (- (+ x (/ z y)) (/ (* x a) y))))
   (if (<= y -1.15e+104)
     t_1
     (if (<= y -0.00305)
       (/ 1.0 (- (/ 1.0 x) (/ (- (/ z (* x x)) (/ a x)) y)))
       (if (<= y 2.4e+24)
         (/
          (+ t (* y 230661.510616))
          (+ i (* y (+ c (* y (+ b (* y (+ 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 = (x + (z / y)) - ((x * a) / y);
	double tmp;
	if (y <= -1.15e+104) {
		tmp = t_1;
	} else if (y <= -0.00305) {
		tmp = 1.0 / ((1.0 / x) - (((z / (x * x)) - (a / x)) / y));
	} else if (y <= 2.4e+24) {
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * (b + (y * (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 = (x + (z / y)) - ((x * a) / y)
    if (y <= (-1.15d+104)) then
        tmp = t_1
    else if (y <= (-0.00305d0)) then
        tmp = 1.0d0 / ((1.0d0 / x) - (((z / (x * x)) - (a / x)) / y))
    else if (y <= 2.4d+24) then
        tmp = (t + (y * 230661.510616d0)) / (i + (y * (c + (y * (b + (y * (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 = (x + (z / y)) - ((x * a) / y);
	double tmp;
	if (y <= -1.15e+104) {
		tmp = t_1;
	} else if (y <= -0.00305) {
		tmp = 1.0 / ((1.0 / x) - (((z / (x * x)) - (a / x)) / y));
	} else if (y <= 2.4e+24) {
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * (b + (y * (y + a)))))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x + (z / y)) - ((x * a) / y)
	tmp = 0
	if y <= -1.15e+104:
		tmp = t_1
	elif y <= -0.00305:
		tmp = 1.0 / ((1.0 / x) - (((z / (x * x)) - (a / x)) / y))
	elif y <= 2.4e+24:
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * (b + (y * (y + a)))))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x + Float64(z / y)) - Float64(Float64(x * a) / y))
	tmp = 0.0
	if (y <= -1.15e+104)
		tmp = t_1;
	elseif (y <= -0.00305)
		tmp = Float64(1.0 / Float64(Float64(1.0 / x) - Float64(Float64(Float64(z / Float64(x * x)) - Float64(a / x)) / y)));
	elseif (y <= 2.4e+24)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(i + Float64(y * Float64(c + Float64(y * Float64(b + Float64(y * Float64(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 = (x + (z / y)) - ((x * a) / y);
	tmp = 0.0;
	if (y <= -1.15e+104)
		tmp = t_1;
	elseif (y <= -0.00305)
		tmp = 1.0 / ((1.0 / x) - (((z / (x * x)) - (a / x)) / y));
	elseif (y <= 2.4e+24)
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * (b + (y * (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[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(N[(x * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.15e+104], t$95$1, If[LessEqual[y, -0.00305], N[(1.0 / N[(N[(1.0 / x), $MachinePrecision] - N[(N[(N[(z / N[(x * x), $MachinePrecision]), $MachinePrecision] - N[(a / x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.4e+24], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.14999999999999992e104 or 2.4000000000000001e24 < y

   1. Initial program 1.4%

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

   2. Taylor expanded in y around inf 71.8%

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

   if -1.14999999999999992e104 < y < -0.00305000000000000019

   1. Initial program 33.9%

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

      1. clear-num 33.9%

         \[\leadsto \color{blue}{\frac{1}{\frac{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}}} \]

      2. inv-pow 33.9%

         \[\leadsto \color{blue}{{\left(\frac{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}\right)}^{-1}} \]

   3. Applied egg-rr 33.9%

      \[\leadsto \color{blue}{{\left(\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right), 230661.510616\right), t\right)}\right)}^{-1}} \]
   4. Step-by-step derivation

      1. unpow-1 33.9%

         \[\leadsto \color{blue}{\frac{1}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right), 230661.510616\right), t\right)}}} \]

      2. fma-udef 33.9%

         \[\leadsto \frac{1}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{x \cdot y + z}, 27464.7644705\right), 230661.510616\right), t\right)}} \]

      3. *-commutative 33.9%

         \[\leadsto \frac{1}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{y \cdot x} + z, 27464.7644705\right), 230661.510616\right), t\right)}} \]

      4. fma-def 33.9%

         \[\leadsto \frac{1}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(y, x, z\right)}, 27464.7644705\right), 230661.510616\right), t\right)}} \]

   5. Simplified 33.9%

      \[\leadsto \color{blue}{\frac{1}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), 27464.7644705\right), 230661.510616\right), t\right)}}} \]

   6. Taylor expanded in y around -inf 46.8%

      \[\leadsto \frac{1}{\color{blue}{\frac{1}{x} + -1 \cdot \frac{-1 \cdot \frac{a}{x} - -1 \cdot \frac{z}{{x}^{2}}}{y}}} \]
   7. Step-by-step derivation

      1. mul-1-neg 46.8%

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

      2. distribute-lft-out-- 46.8%

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

      3. unpow2 46.8%

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

   8. Simplified 46.8%

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

   if -0.00305000000000000019 < y < 2.4000000000000001e24

   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 83.6%

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

      1. *-commutative 83.6%

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

   4. Simplified 83.6%

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

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+104}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{elif}\;y \leq -0.00305:\\ \;\;\;\;\frac{1}{\frac{1}{x} - \frac{\frac{z}{x \cdot x} - \frac{a}{x}}{y}}\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+24}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \end{array} \]

Alternative 13: 73.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{if}\;y \leq -5.5 \cdot 10^{+100}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -3.3 \cdot 10^{+16}:\\ \;\;\;\;\frac{1}{\frac{a}{y \cdot x} + \left(\frac{1}{x} - \frac{z}{y \cdot \left(x \cdot x\right)}\right)}\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+24}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (- (+ x (/ z y)) (/ (* x a) y))))
   (if (<= y -5.5e+100)
     t_1
     (if (<= y -3.3e+16)
       (/ 1.0 (+ (/ a (* y x)) (- (/ 1.0 x) (/ z (* y (* x x))))))
       (if (<= y 4.5e+24)
         (/
          (+ t (* y (+ 230661.510616 (* y 27464.7644705))))
          (+ i (* y (+ c (* y b)))))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x + (z / y)) - ((x * a) / y);
	double tmp;
	if (y <= -5.5e+100) {
		tmp = t_1;
	} else if (y <= -3.3e+16) {
		tmp = 1.0 / ((a / (y * x)) + ((1.0 / x) - (z / (y * (x * x)))));
	} else if (y <= 4.5e+24) {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * (c + (y * b))));
	} 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 = (x + (z / y)) - ((x * a) / y)
    if (y <= (-5.5d+100)) then
        tmp = t_1
    else if (y <= (-3.3d+16)) then
        tmp = 1.0d0 / ((a / (y * x)) + ((1.0d0 / x) - (z / (y * (x * x)))))
    else if (y <= 4.5d+24) then
        tmp = (t + (y * (230661.510616d0 + (y * 27464.7644705d0)))) / (i + (y * (c + (y * b))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x + (z / y)) - ((x * a) / y);
	double tmp;
	if (y <= -5.5e+100) {
		tmp = t_1;
	} else if (y <= -3.3e+16) {
		tmp = 1.0 / ((a / (y * x)) + ((1.0 / x) - (z / (y * (x * x)))));
	} else if (y <= 4.5e+24) {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * (c + (y * b))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x + (z / y)) - ((x * a) / y)
	tmp = 0
	if y <= -5.5e+100:
		tmp = t_1
	elif y <= -3.3e+16:
		tmp = 1.0 / ((a / (y * x)) + ((1.0 / x) - (z / (y * (x * x)))))
	elif y <= 4.5e+24:
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * (c + (y * b))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x + Float64(z / y)) - Float64(Float64(x * a) / y))
	tmp = 0.0
	if (y <= -5.5e+100)
		tmp = t_1;
	elseif (y <= -3.3e+16)
		tmp = Float64(1.0 / Float64(Float64(a / Float64(y * x)) + Float64(Float64(1.0 / x) - Float64(z / Float64(y * Float64(x * x))))));
	elseif (y <= 4.5e+24)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * 27464.7644705)))) / Float64(i + Float64(y * Float64(c + Float64(y * b)))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x + (z / y)) - ((x * a) / y);
	tmp = 0.0;
	if (y <= -5.5e+100)
		tmp = t_1;
	elseif (y <= -3.3e+16)
		tmp = 1.0 / ((a / (y * x)) + ((1.0 / x) - (z / (y * (x * x)))));
	elseif (y <= 4.5e+24)
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * (c + (y * b))));
	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[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(N[(x * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.5e+100], t$95$1, If[LessEqual[y, -3.3e+16], N[(1.0 / N[(N[(a / N[(y * x), $MachinePrecision]), $MachinePrecision] + N[(N[(1.0 / x), $MachinePrecision] - N[(z / N[(y * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.5e+24], N[(N[(t + N[(y * N[(230661.510616 + N[(y * 27464.7644705), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.5000000000000002e100 or 4.50000000000000019e24 < y

   1. Initial program 1.4%

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

   2. Taylor expanded in y around inf 71.8%

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

   if -5.5000000000000002e100 < y < -3.3e16

   1. Initial program 19.7%

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

      1. clear-num 19.6%

         \[\leadsto \color{blue}{\frac{1}{\frac{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}}} \]

      2. inv-pow 19.6%

         \[\leadsto \color{blue}{{\left(\frac{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}\right)}^{-1}} \]

   3. Applied egg-rr 19.7%

      \[\leadsto \color{blue}{{\left(\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right), 230661.510616\right), t\right)}\right)}^{-1}} \]
   4. Step-by-step derivation

      1. unpow-1 19.7%

         \[\leadsto \color{blue}{\frac{1}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right), 230661.510616\right), t\right)}}} \]

      2. fma-udef 19.7%

         \[\leadsto \frac{1}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{x \cdot y + z}, 27464.7644705\right), 230661.510616\right), t\right)}} \]

      3. *-commutative 19.7%

         \[\leadsto \frac{1}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{y \cdot x} + z, 27464.7644705\right), 230661.510616\right), t\right)}} \]

      4. fma-def 19.7%

         \[\leadsto \frac{1}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(y, x, z\right)}, 27464.7644705\right), 230661.510616\right), t\right)}} \]

   5. Simplified 19.7%

      \[\leadsto \color{blue}{\frac{1}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), 27464.7644705\right), 230661.510616\right), t\right)}}} \]

   6. Taylor expanded in y around inf 52.0%

      \[\leadsto \frac{1}{\color{blue}{\left(\frac{a}{y \cdot x} + \frac{1}{x}\right) - \frac{z}{y \cdot {x}^{2}}}} \]
   7. Step-by-step derivation

      1. associate--l+ 52.0%

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

      2. unpow2 52.0%

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

   8. Simplified 52.0%

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

   if -3.3e16 < y < 4.50000000000000019e24

   1. Initial program 97.6%

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

   2. Taylor expanded in y around 0 84.0%

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

      1. *-commutative 84.0%

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

   4. Simplified 84.0%

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

   5. Taylor expanded in y around 0 80.8%

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

4. Final simplification 74.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+100}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{elif}\;y \leq -3.3 \cdot 10^{+16}:\\ \;\;\;\;\frac{1}{\frac{a}{y \cdot x} + \left(\frac{1}{x} - \frac{z}{y \cdot \left(x \cdot x\right)}\right)}\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+24}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \end{array} \]

Alternative 14: 73.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{if}\;y \leq -5 \cdot 10^{+101}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -8.8 \cdot 10^{+15}:\\ \;\;\;\;\frac{1}{\frac{1}{x} - \frac{\frac{z}{x \cdot x} - \frac{a}{x}}{y}}\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+24}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (- (+ x (/ z y)) (/ (* x a) y))))
   (if (<= y -5e+101)
     t_1
     (if (<= y -8.8e+15)
       (/ 1.0 (- (/ 1.0 x) (/ (- (/ z (* x x)) (/ a x)) y)))
       (if (<= y 2.7e+24)
         (/
          (+ t (* y (+ 230661.510616 (* y 27464.7644705))))
          (+ i (* y (+ c (* y b)))))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x + (z / y)) - ((x * a) / y);
	double tmp;
	if (y <= -5e+101) {
		tmp = t_1;
	} else if (y <= -8.8e+15) {
		tmp = 1.0 / ((1.0 / x) - (((z / (x * x)) - (a / x)) / y));
	} else if (y <= 2.7e+24) {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * (c + (y * b))));
	} 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 = (x + (z / y)) - ((x * a) / y)
    if (y <= (-5d+101)) then
        tmp = t_1
    else if (y <= (-8.8d+15)) then
        tmp = 1.0d0 / ((1.0d0 / x) - (((z / (x * x)) - (a / x)) / y))
    else if (y <= 2.7d+24) then
        tmp = (t + (y * (230661.510616d0 + (y * 27464.7644705d0)))) / (i + (y * (c + (y * b))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x + (z / y)) - ((x * a) / y);
	double tmp;
	if (y <= -5e+101) {
		tmp = t_1;
	} else if (y <= -8.8e+15) {
		tmp = 1.0 / ((1.0 / x) - (((z / (x * x)) - (a / x)) / y));
	} else if (y <= 2.7e+24) {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * (c + (y * b))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x + (z / y)) - ((x * a) / y)
	tmp = 0
	if y <= -5e+101:
		tmp = t_1
	elif y <= -8.8e+15:
		tmp = 1.0 / ((1.0 / x) - (((z / (x * x)) - (a / x)) / y))
	elif y <= 2.7e+24:
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * (c + (y * b))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x + Float64(z / y)) - Float64(Float64(x * a) / y))
	tmp = 0.0
	if (y <= -5e+101)
		tmp = t_1;
	elseif (y <= -8.8e+15)
		tmp = Float64(1.0 / Float64(Float64(1.0 / x) - Float64(Float64(Float64(z / Float64(x * x)) - Float64(a / x)) / y)));
	elseif (y <= 2.7e+24)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * 27464.7644705)))) / Float64(i + Float64(y * Float64(c + Float64(y * b)))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x + (z / y)) - ((x * a) / y);
	tmp = 0.0;
	if (y <= -5e+101)
		tmp = t_1;
	elseif (y <= -8.8e+15)
		tmp = 1.0 / ((1.0 / x) - (((z / (x * x)) - (a / x)) / y));
	elseif (y <= 2.7e+24)
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * (c + (y * b))));
	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[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(N[(x * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5e+101], t$95$1, If[LessEqual[y, -8.8e+15], N[(1.0 / N[(N[(1.0 / x), $MachinePrecision] - N[(N[(N[(z / N[(x * x), $MachinePrecision]), $MachinePrecision] - N[(a / x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.7e+24], N[(N[(t + N[(y * N[(230661.510616 + N[(y * 27464.7644705), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.99999999999999989e101 or 2.7e24 < y

   1. Initial program 1.4%

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

   2. Taylor expanded in y around inf 71.8%

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

   if -4.99999999999999989e101 < y < -8.8e15

   1. Initial program 19.7%

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

      1. clear-num 19.6%

         \[\leadsto \color{blue}{\frac{1}{\frac{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}}} \]

      2. inv-pow 19.6%

         \[\leadsto \color{blue}{{\left(\frac{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}\right)}^{-1}} \]

   3. Applied egg-rr 19.7%

      \[\leadsto \color{blue}{{\left(\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right), 230661.510616\right), t\right)}\right)}^{-1}} \]
   4. Step-by-step derivation

      1. unpow-1 19.7%

         \[\leadsto \color{blue}{\frac{1}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right), 230661.510616\right), t\right)}}} \]

      2. fma-udef 19.7%

         \[\leadsto \frac{1}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{x \cdot y + z}, 27464.7644705\right), 230661.510616\right), t\right)}} \]

      3. *-commutative 19.7%

         \[\leadsto \frac{1}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{y \cdot x} + z, 27464.7644705\right), 230661.510616\right), t\right)}} \]

      4. fma-def 19.7%

         \[\leadsto \frac{1}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(y, x, z\right)}, 27464.7644705\right), 230661.510616\right), t\right)}} \]

   5. Simplified 19.7%

      \[\leadsto \color{blue}{\frac{1}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), 27464.7644705\right), 230661.510616\right), t\right)}}} \]

   6. Taylor expanded in y around -inf 52.0%

      \[\leadsto \frac{1}{\color{blue}{\frac{1}{x} + -1 \cdot \frac{-1 \cdot \frac{a}{x} - -1 \cdot \frac{z}{{x}^{2}}}{y}}} \]
   7. Step-by-step derivation

      1. mul-1-neg 52.0%

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

      2. distribute-lft-out-- 52.0%

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

      3. unpow2 52.0%

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

   8. Simplified 52.0%

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

   if -8.8e15 < y < 2.7e24

   1. Initial program 97.6%

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

   2. Taylor expanded in y around 0 84.0%

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

      1. *-commutative 84.0%

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

   4. Simplified 84.0%

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

   5. Taylor expanded in y around 0 80.8%

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

4. Final simplification 74.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+101}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{elif}\;y \leq -8.8 \cdot 10^{+15}:\\ \;\;\;\;\frac{1}{\frac{1}{x} - \frac{\frac{z}{x \cdot x} - \frac{a}{x}}{y}}\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+24}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \end{array} \]

Alternative 15: 59.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{if}\;y \leq -6.5 \cdot 10^{+99}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -0.00055:\\ \;\;\;\;\frac{y \cdot x}{a}\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{-101}:\\ \;\;\;\;\frac{t}{b \cdot \left(y \cdot y\right)}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-131}:\\ \;\;\;\;\frac{t}{i + y \cdot c}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-31}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{elif}\;y \leq 5.1 \cdot 10^{+70}:\\ \;\;\;\;\frac{y \cdot y}{\frac{b}{x}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (- (+ x (/ z y)) (/ (* x a) y))))
   (if (<= y -6.5e+99)
     t_1
     (if (<= y -0.00055)
       (/ (* y x) a)
       (if (<= y -2.2e-101)
         (/ t (* b (* y y)))
         (if (<= y 1.6e-131)
           (/ t (+ i (* y c)))
           (if (<= y 3.2e-31)
             (/ (+ t (* y 230661.510616)) i)
             (if (<= y 5.1e+70) (/ (* y y) (/ b x)) t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x + (z / y)) - ((x * a) / y);
	double tmp;
	if (y <= -6.5e+99) {
		tmp = t_1;
	} else if (y <= -0.00055) {
		tmp = (y * x) / a;
	} else if (y <= -2.2e-101) {
		tmp = t / (b * (y * y));
	} else if (y <= 1.6e-131) {
		tmp = t / (i + (y * c));
	} else if (y <= 3.2e-31) {
		tmp = (t + (y * 230661.510616)) / i;
	} else if (y <= 5.1e+70) {
		tmp = (y * y) / (b / x);
	} 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 = (x + (z / y)) - ((x * a) / y)
    if (y <= (-6.5d+99)) then
        tmp = t_1
    else if (y <= (-0.00055d0)) then
        tmp = (y * x) / a
    else if (y <= (-2.2d-101)) then
        tmp = t / (b * (y * y))
    else if (y <= 1.6d-131) then
        tmp = t / (i + (y * c))
    else if (y <= 3.2d-31) then
        tmp = (t + (y * 230661.510616d0)) / i
    else if (y <= 5.1d+70) then
        tmp = (y * y) / (b / x)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x + (z / y)) - ((x * a) / y);
	double tmp;
	if (y <= -6.5e+99) {
		tmp = t_1;
	} else if (y <= -0.00055) {
		tmp = (y * x) / a;
	} else if (y <= -2.2e-101) {
		tmp = t / (b * (y * y));
	} else if (y <= 1.6e-131) {
		tmp = t / (i + (y * c));
	} else if (y <= 3.2e-31) {
		tmp = (t + (y * 230661.510616)) / i;
	} else if (y <= 5.1e+70) {
		tmp = (y * y) / (b / x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x + (z / y)) - ((x * a) / y)
	tmp = 0
	if y <= -6.5e+99:
		tmp = t_1
	elif y <= -0.00055:
		tmp = (y * x) / a
	elif y <= -2.2e-101:
		tmp = t / (b * (y * y))
	elif y <= 1.6e-131:
		tmp = t / (i + (y * c))
	elif y <= 3.2e-31:
		tmp = (t + (y * 230661.510616)) / i
	elif y <= 5.1e+70:
		tmp = (y * y) / (b / x)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x + Float64(z / y)) - Float64(Float64(x * a) / y))
	tmp = 0.0
	if (y <= -6.5e+99)
		tmp = t_1;
	elseif (y <= -0.00055)
		tmp = Float64(Float64(y * x) / a);
	elseif (y <= -2.2e-101)
		tmp = Float64(t / Float64(b * Float64(y * y)));
	elseif (y <= 1.6e-131)
		tmp = Float64(t / Float64(i + Float64(y * c)));
	elseif (y <= 3.2e-31)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / i);
	elseif (y <= 5.1e+70)
		tmp = Float64(Float64(y * y) / Float64(b / x));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x + (z / y)) - ((x * a) / y);
	tmp = 0.0;
	if (y <= -6.5e+99)
		tmp = t_1;
	elseif (y <= -0.00055)
		tmp = (y * x) / a;
	elseif (y <= -2.2e-101)
		tmp = t / (b * (y * y));
	elseif (y <= 1.6e-131)
		tmp = t / (i + (y * c));
	elseif (y <= 3.2e-31)
		tmp = (t + (y * 230661.510616)) / i;
	elseif (y <= 5.1e+70)
		tmp = (y * y) / (b / x);
	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[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(N[(x * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.5e+99], t$95$1, If[LessEqual[y, -0.00055], N[(N[(y * x), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[y, -2.2e-101], N[(t / N[(b * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.6e-131], N[(t / N[(i + N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.2e-31], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / i), $MachinePrecision], If[LessEqual[y, 5.1e+70], N[(N[(y * y), $MachinePrecision] / N[(b / x), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -6.5000000000000004e99 or 5.10000000000000014e70 < y

   1. Initial program 0.3%

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

   2. Taylor expanded in y around inf 77.5%

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

   if -6.5000000000000004e99 < y < -5.50000000000000033e-4

   1. Initial program 35.2%

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

   2. Taylor expanded in x around inf 17.1%

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

   3. Taylor expanded in a around inf 34.4%

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

   if -5.50000000000000033e-4 < y < -2.1999999999999999e-101

   1. Initial program 99.4%

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

      1. fma-def 99.4%

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

      2. fma-def 99.4%

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

      3. fma-def 99.4%

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

      4. fma-def 99.4%

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

      5. fma-def 99.3%

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

      6. fma-def 99.3%

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

      7. fma-def 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in y around 0 55.8%

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

   5. Taylor expanded in b around inf 33.7%

      \[\leadsto \color{blue}{\frac{t}{{y}^{2} \cdot b}} \]
   6. Step-by-step derivation

      1. *-commutative 33.7%

         \[\leadsto \frac{t}{\color{blue}{b \cdot {y}^{2}}} \]

      2. unpow2 33.7%

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

   7. Simplified 33.7%

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

   if -2.1999999999999999e-101 < y < 1.6e-131

   1. Initial program 99.8%

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

      1. fma-def 99.8%

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

      2. fma-def 99.8%

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

      3. fma-def 99.8%

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

      4. fma-def 99.8%

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

      5. fma-def 99.8%

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

      6. fma-def 99.8%

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

      7. fma-def 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around 0 88.3%

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

   5. Taylor expanded in y around 0 87.1%

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

   if 1.6e-131 < y < 3.20000000000000018e-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 75.8%

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

      1. *-commutative 75.8%

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

   4. Simplified 75.8%

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

   5. Taylor expanded in i around inf 41.3%

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

   if 3.20000000000000018e-31 < y < 5.10000000000000014e70

   1. Initial program 57.5%

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

   2. Taylor expanded in x around inf 20.4%

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

   3. Taylor expanded in b around inf 17.7%

      \[\leadsto \color{blue}{\frac{{y}^{2} \cdot x}{b}} \]
   4. Step-by-step derivation

      1. associate-/l* 21.9%

         \[\leadsto \color{blue}{\frac{{y}^{2}}{\frac{b}{x}}} \]

      2. unpow2 21.9%

         \[\leadsto \frac{\color{blue}{y \cdot y}}{\frac{b}{x}} \]

   5. Simplified 21.9%

      \[\leadsto \color{blue}{\frac{y \cdot y}{\frac{b}{x}}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 65.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+99}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{elif}\;y \leq -0.00055:\\ \;\;\;\;\frac{y \cdot x}{a}\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{-101}:\\ \;\;\;\;\frac{t}{b \cdot \left(y \cdot y\right)}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-131}:\\ \;\;\;\;\frac{t}{i + y \cdot c}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-31}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{elif}\;y \leq 5.1 \cdot 10^{+70}:\\ \;\;\;\;\frac{y \cdot y}{\frac{b}{x}}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \end{array} \]

Alternative 16: 71.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{if}\;y \leq -7.9 \cdot 10^{+99}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{+16}:\\ \;\;\;\;\frac{y \cdot x}{a}\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{+14} \lor \neg \left(y \leq 8.5 \cdot 10^{+23}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (- (+ x (/ z y)) (/ (* x a) y))))
   (if (<= y -7.9e+99)
     t_1
     (if (<= y -4.2e+16)
       (/ (* y x) a)
       (if (or (<= y -8.5e+14) (not (<= y 8.5e+23)))
         t_1
         (/ (+ t (* y 230661.510616)) (+ i (* y (+ c (* y b))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x + (z / y)) - ((x * a) / y);
	double tmp;
	if (y <= -7.9e+99) {
		tmp = t_1;
	} else if (y <= -4.2e+16) {
		tmp = (y * x) / a;
	} else if ((y <= -8.5e+14) || !(y <= 8.5e+23)) {
		tmp = t_1;
	} else {
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * b))));
	}
	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 = (x + (z / y)) - ((x * a) / y)
    if (y <= (-7.9d+99)) then
        tmp = t_1
    else if (y <= (-4.2d+16)) then
        tmp = (y * x) / a
    else if ((y <= (-8.5d+14)) .or. (.not. (y <= 8.5d+23))) then
        tmp = t_1
    else
        tmp = (t + (y * 230661.510616d0)) / (i + (y * (c + (y * b))))
    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 = (x + (z / y)) - ((x * a) / y);
	double tmp;
	if (y <= -7.9e+99) {
		tmp = t_1;
	} else if (y <= -4.2e+16) {
		tmp = (y * x) / a;
	} else if ((y <= -8.5e+14) || !(y <= 8.5e+23)) {
		tmp = t_1;
	} else {
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * b))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x + (z / y)) - ((x * a) / y)
	tmp = 0
	if y <= -7.9e+99:
		tmp = t_1
	elif y <= -4.2e+16:
		tmp = (y * x) / a
	elif (y <= -8.5e+14) or not (y <= 8.5e+23):
		tmp = t_1
	else:
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * b))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x + Float64(z / y)) - Float64(Float64(x * a) / y))
	tmp = 0.0
	if (y <= -7.9e+99)
		tmp = t_1;
	elseif (y <= -4.2e+16)
		tmp = Float64(Float64(y * x) / a);
	elseif ((y <= -8.5e+14) || !(y <= 8.5e+23))
		tmp = t_1;
	else
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(i + Float64(y * Float64(c + Float64(y * b)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x + (z / y)) - ((x * a) / y);
	tmp = 0.0;
	if (y <= -7.9e+99)
		tmp = t_1;
	elseif (y <= -4.2e+16)
		tmp = (y * x) / a;
	elseif ((y <= -8.5e+14) || ~((y <= 8.5e+23)))
		tmp = t_1;
	else
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * b))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(N[(x * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7.9e+99], t$95$1, If[LessEqual[y, -4.2e+16], N[(N[(y * x), $MachinePrecision] / a), $MachinePrecision], If[Or[LessEqual[y, -8.5e+14], N[Not[LessEqual[y, 8.5e+23]], $MachinePrecision]], t$95$1, N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.9000000000000003e99 or -4.2e16 < y < -8.5e14 or 8.5000000000000001e23 < 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 71.1%

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

   if -7.9000000000000003e99 < y < -4.2e16

   1. Initial program 21.3%

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

   2. Taylor expanded in x around inf 11.9%

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

   3. Taylor expanded in a around inf 38.1%

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

   if -8.5e14 < y < 8.5000000000000001e23

   1. Initial program 97.6%

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

   2. Taylor expanded in y around 0 82.0%

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

      1. *-commutative 82.0%

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

   4. Simplified 82.0%

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

   5. Taylor expanded in y around 0 79.3%

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

4. Final simplification 72.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.9 \cdot 10^{+99}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{+16}:\\ \;\;\;\;\frac{y \cdot x}{a}\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{+14} \lor \neg \left(y \leq 8.5 \cdot 10^{+23}\right):\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot b\right)}\\ \end{array} \]

Alternative 17: 72.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{if}\;y \leq -9 \cdot 10^{+103}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -3.4 \cdot 10^{-8}:\\ \;\;\;\;\frac{1}{\frac{a}{y \cdot x} + \left(\frac{1}{x} - \frac{z}{y \cdot \left(x \cdot x\right)}\right)}\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+23}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (- (+ x (/ z y)) (/ (* x a) y))))
   (if (<= y -9e+103)
     t_1
     (if (<= y -3.4e-8)
       (/ 1.0 (+ (/ a (* y x)) (- (/ 1.0 x) (/ z (* y (* x x))))))
       (if (<= y 5.2e+23)
         (/ (+ t (* y 230661.510616)) (+ i (* y (+ c (* y b)))))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x + (z / y)) - ((x * a) / y);
	double tmp;
	if (y <= -9e+103) {
		tmp = t_1;
	} else if (y <= -3.4e-8) {
		tmp = 1.0 / ((a / (y * x)) + ((1.0 / x) - (z / (y * (x * x)))));
	} else if (y <= 5.2e+23) {
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * b))));
	} 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 = (x + (z / y)) - ((x * a) / y)
    if (y <= (-9d+103)) then
        tmp = t_1
    else if (y <= (-3.4d-8)) then
        tmp = 1.0d0 / ((a / (y * x)) + ((1.0d0 / x) - (z / (y * (x * x)))))
    else if (y <= 5.2d+23) then
        tmp = (t + (y * 230661.510616d0)) / (i + (y * (c + (y * b))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x + (z / y)) - ((x * a) / y);
	double tmp;
	if (y <= -9e+103) {
		tmp = t_1;
	} else if (y <= -3.4e-8) {
		tmp = 1.0 / ((a / (y * x)) + ((1.0 / x) - (z / (y * (x * x)))));
	} else if (y <= 5.2e+23) {
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * b))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x + (z / y)) - ((x * a) / y)
	tmp = 0
	if y <= -9e+103:
		tmp = t_1
	elif y <= -3.4e-8:
		tmp = 1.0 / ((a / (y * x)) + ((1.0 / x) - (z / (y * (x * x)))))
	elif y <= 5.2e+23:
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * b))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x + Float64(z / y)) - Float64(Float64(x * a) / y))
	tmp = 0.0
	if (y <= -9e+103)
		tmp = t_1;
	elseif (y <= -3.4e-8)
		tmp = Float64(1.0 / Float64(Float64(a / Float64(y * x)) + Float64(Float64(1.0 / x) - Float64(z / Float64(y * Float64(x * x))))));
	elseif (y <= 5.2e+23)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(i + Float64(y * Float64(c + Float64(y * b)))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x + (z / y)) - ((x * a) / y);
	tmp = 0.0;
	if (y <= -9e+103)
		tmp = t_1;
	elseif (y <= -3.4e-8)
		tmp = 1.0 / ((a / (y * x)) + ((1.0 / x) - (z / (y * (x * x)))));
	elseif (y <= 5.2e+23)
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * b))));
	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[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(N[(x * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9e+103], t$95$1, If[LessEqual[y, -3.4e-8], N[(1.0 / N[(N[(a / N[(y * x), $MachinePrecision]), $MachinePrecision] + N[(N[(1.0 / x), $MachinePrecision] - N[(z / N[(y * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.2e+23], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.00000000000000002e103 or 5.19999999999999983e23 < y

   1. Initial program 1.4%

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

   2. Taylor expanded in y around inf 71.8%

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

   if -9.00000000000000002e103 < y < -3.4e-8

   1. Initial program 36.2%

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

      1. clear-num 36.2%

         \[\leadsto \color{blue}{\frac{1}{\frac{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}}} \]

      2. inv-pow 36.2%

         \[\leadsto \color{blue}{{\left(\frac{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}\right)}^{-1}} \]

   3. Applied egg-rr 36.2%

      \[\leadsto \color{blue}{{\left(\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right), 230661.510616\right), t\right)}\right)}^{-1}} \]
   4. Step-by-step derivation

      1. unpow-1 36.2%

         \[\leadsto \color{blue}{\frac{1}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right), 230661.510616\right), t\right)}}} \]

      2. fma-udef 36.2%

         \[\leadsto \frac{1}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{x \cdot y + z}, 27464.7644705\right), 230661.510616\right), t\right)}} \]

      3. *-commutative 36.2%

         \[\leadsto \frac{1}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{y \cdot x} + z, 27464.7644705\right), 230661.510616\right), t\right)}} \]

      4. fma-def 36.2%

         \[\leadsto \frac{1}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(y, x, z\right)}, 27464.7644705\right), 230661.510616\right), t\right)}} \]

   5. Simplified 36.2%

      \[\leadsto \color{blue}{\frac{1}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), 27464.7644705\right), 230661.510616\right), t\right)}}} \]

   6. Taylor expanded in y around inf 45.3%

      \[\leadsto \frac{1}{\color{blue}{\left(\frac{a}{y \cdot x} + \frac{1}{x}\right) - \frac{z}{y \cdot {x}^{2}}}} \]
   7. Step-by-step derivation

      1. associate--l+ 45.3%

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

      2. unpow2 45.3%

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

   8. Simplified 45.3%

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

   if -3.4e-8 < y < 5.19999999999999983e23

   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 83.8%

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

      1. *-commutative 83.8%

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

   4. Simplified 83.8%

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

   5. Taylor expanded in y around 0 81.5%

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

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+103}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{elif}\;y \leq -3.4 \cdot 10^{-8}:\\ \;\;\;\;\frac{1}{\frac{a}{y \cdot x} + \left(\frac{1}{x} - \frac{z}{y \cdot \left(x \cdot x\right)}\right)}\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+23}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \end{array} \]

Alternative 18: 65.3% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{if}\;y \leq -5.9 \cdot 10^{+99}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{+17}:\\ \;\;\;\;\frac{y \cdot x}{a}\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{+16} \lor \neg \left(y \leq 3.4 \cdot 10^{+24}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (- (+ x (/ z y)) (/ (* x a) y))))
   (if (<= y -5.9e+99)
     t_1
     (if (<= y -9.5e+17)
       (/ (* y x) a)
       (if (or (<= y -1.35e+16) (not (<= y 3.4e+24)))
         t_1
         (/ t (+ i (* y (+ c (* y b))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x + (z / y)) - ((x * a) / y);
	double tmp;
	if (y <= -5.9e+99) {
		tmp = t_1;
	} else if (y <= -9.5e+17) {
		tmp = (y * x) / a;
	} else if ((y <= -1.35e+16) || !(y <= 3.4e+24)) {
		tmp = t_1;
	} else {
		tmp = t / (i + (y * (c + (y * b))));
	}
	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 = (x + (z / y)) - ((x * a) / y)
    if (y <= (-5.9d+99)) then
        tmp = t_1
    else if (y <= (-9.5d+17)) then
        tmp = (y * x) / a
    else if ((y <= (-1.35d+16)) .or. (.not. (y <= 3.4d+24))) then
        tmp = t_1
    else
        tmp = t / (i + (y * (c + (y * b))))
    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 = (x + (z / y)) - ((x * a) / y);
	double tmp;
	if (y <= -5.9e+99) {
		tmp = t_1;
	} else if (y <= -9.5e+17) {
		tmp = (y * x) / a;
	} else if ((y <= -1.35e+16) || !(y <= 3.4e+24)) {
		tmp = t_1;
	} else {
		tmp = t / (i + (y * (c + (y * b))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x + (z / y)) - ((x * a) / y)
	tmp = 0
	if y <= -5.9e+99:
		tmp = t_1
	elif y <= -9.5e+17:
		tmp = (y * x) / a
	elif (y <= -1.35e+16) or not (y <= 3.4e+24):
		tmp = t_1
	else:
		tmp = t / (i + (y * (c + (y * b))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x + Float64(z / y)) - Float64(Float64(x * a) / y))
	tmp = 0.0
	if (y <= -5.9e+99)
		tmp = t_1;
	elseif (y <= -9.5e+17)
		tmp = Float64(Float64(y * x) / a);
	elseif ((y <= -1.35e+16) || !(y <= 3.4e+24))
		tmp = t_1;
	else
		tmp = Float64(t / Float64(i + Float64(y * Float64(c + Float64(y * b)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x + (z / y)) - ((x * a) / y);
	tmp = 0.0;
	if (y <= -5.9e+99)
		tmp = t_1;
	elseif (y <= -9.5e+17)
		tmp = (y * x) / a;
	elseif ((y <= -1.35e+16) || ~((y <= 3.4e+24)))
		tmp = t_1;
	else
		tmp = t / (i + (y * (c + (y * b))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(N[(x * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.9e+99], t$95$1, If[LessEqual[y, -9.5e+17], N[(N[(y * x), $MachinePrecision] / a), $MachinePrecision], If[Or[LessEqual[y, -1.35e+16], N[Not[LessEqual[y, 3.4e+24]], $MachinePrecision]], t$95$1, N[(t / N[(i + N[(y * N[(c + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.8999999999999999e99 or -9.5e17 < y < -1.35e16 or 3.4000000000000001e24 < y

   1. Initial program 1.5%

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

   2. Taylor expanded in y around inf 71.8%

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

   if -5.8999999999999999e99 < y < -9.5e17

   1. Initial program 21.3%

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

   2. Taylor expanded in x around inf 11.9%

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

   3. Taylor expanded in a around inf 38.1%

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

   if -1.35e16 < y < 3.4000000000000001e24

   1. Initial program 97.6%

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

   2. Taylor expanded in y around 0 90.9%

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

   3. Taylor expanded in t around inf 64.3%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.9 \cdot 10^{+99}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{+17}:\\ \;\;\;\;\frac{y \cdot x}{a}\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{+16} \lor \neg \left(y \leq 3.4 \cdot 10^{+24}\right):\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot b\right)}\\ \end{array} \]

Alternative 19: 68.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{if}\;y \leq -5.5 \cdot 10^{+99}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -6.8 \cdot 10^{+16}:\\ \;\;\;\;\frac{y \cdot x}{a}\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{+14} \lor \neg \left(y \leq 200000000000\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot c}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (- (+ x (/ z y)) (/ (* x a) y))))
   (if (<= y -5.5e+99)
     t_1
     (if (<= y -6.8e+16)
       (/ (* y x) a)
       (if (or (<= y -5.5e+14) (not (<= y 200000000000.0)))
         t_1
         (/ (+ t (* y 230661.510616)) (+ i (* y c))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x + (z / y)) - ((x * a) / y);
	double tmp;
	if (y <= -5.5e+99) {
		tmp = t_1;
	} else if (y <= -6.8e+16) {
		tmp = (y * x) / a;
	} else if ((y <= -5.5e+14) || !(y <= 200000000000.0)) {
		tmp = t_1;
	} else {
		tmp = (t + (y * 230661.510616)) / (i + (y * c));
	}
	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 = (x + (z / y)) - ((x * a) / y)
    if (y <= (-5.5d+99)) then
        tmp = t_1
    else if (y <= (-6.8d+16)) then
        tmp = (y * x) / a
    else if ((y <= (-5.5d+14)) .or. (.not. (y <= 200000000000.0d0))) then
        tmp = t_1
    else
        tmp = (t + (y * 230661.510616d0)) / (i + (y * c))
    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 = (x + (z / y)) - ((x * a) / y);
	double tmp;
	if (y <= -5.5e+99) {
		tmp = t_1;
	} else if (y <= -6.8e+16) {
		tmp = (y * x) / a;
	} else if ((y <= -5.5e+14) || !(y <= 200000000000.0)) {
		tmp = t_1;
	} else {
		tmp = (t + (y * 230661.510616)) / (i + (y * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x + (z / y)) - ((x * a) / y)
	tmp = 0
	if y <= -5.5e+99:
		tmp = t_1
	elif y <= -6.8e+16:
		tmp = (y * x) / a
	elif (y <= -5.5e+14) or not (y <= 200000000000.0):
		tmp = t_1
	else:
		tmp = (t + (y * 230661.510616)) / (i + (y * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x + Float64(z / y)) - Float64(Float64(x * a) / y))
	tmp = 0.0
	if (y <= -5.5e+99)
		tmp = t_1;
	elseif (y <= -6.8e+16)
		tmp = Float64(Float64(y * x) / a);
	elseif ((y <= -5.5e+14) || !(y <= 200000000000.0))
		tmp = t_1;
	else
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(i + Float64(y * c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x + (z / y)) - ((x * a) / y);
	tmp = 0.0;
	if (y <= -5.5e+99)
		tmp = t_1;
	elseif (y <= -6.8e+16)
		tmp = (y * x) / a;
	elseif ((y <= -5.5e+14) || ~((y <= 200000000000.0)))
		tmp = t_1;
	else
		tmp = (t + (y * 230661.510616)) / (i + (y * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(N[(x * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.5e+99], t$95$1, If[LessEqual[y, -6.8e+16], N[(N[(y * x), $MachinePrecision] / a), $MachinePrecision], If[Or[LessEqual[y, -5.5e+14], N[Not[LessEqual[y, 200000000000.0]], $MachinePrecision]], t$95$1, N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.5000000000000002e99 or -6.8e16 < y < -5.5e14 or 2e11 < y

   1. Initial program 5.3%

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

   2. Taylor expanded in y around inf 67.2%

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

   if -5.5000000000000002e99 < y < -6.8e16

   1. Initial program 21.3%

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

   2. Taylor expanded in x around inf 11.9%

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

   3. Taylor expanded in a around inf 38.1%

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

   if -5.5e14 < y < 2e11

   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 85.4%

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

      1. *-commutative 85.4%

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

   4. Simplified 85.4%

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

   5. Taylor expanded in y around 0 75.9%

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

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+99}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{elif}\;y \leq -6.8 \cdot 10^{+16}:\\ \;\;\;\;\frac{y \cdot x}{a}\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{+14} \lor \neg \left(y \leq 200000000000\right):\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot c}\\ \end{array} \]

Alternative 20: 57.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.85 \cdot 10^{+48}:\\ \;\;\;\;x - \frac{a}{\frac{y}{x}}\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-15}:\\ \;\;\;\;\frac{y \cdot x}{a}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-131}:\\ \;\;\;\;\frac{t}{i + y \cdot c}\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-31}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{elif}\;y \leq 5.3 \cdot 10^{+69}:\\ \;\;\;\;\frac{y \cdot y}{\frac{b}{x}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -2.85e+48)
   (- x (/ a (/ y x)))
   (if (<= y -6e-15)
     (/ (* y x) a)
     (if (<= y 3.2e-131)
       (/ t (+ i (* y c)))
       (if (<= y 3.1e-31)
         (/ (+ t (* y 230661.510616)) i)
         (if (<= y 5.3e+69) (/ (* y y) (/ b x)) x))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -2.85e+48) {
		tmp = x - (a / (y / x));
	} else if (y <= -6e-15) {
		tmp = (y * x) / a;
	} else if (y <= 3.2e-131) {
		tmp = t / (i + (y * c));
	} else if (y <= 3.1e-31) {
		tmp = (t + (y * 230661.510616)) / i;
	} else if (y <= 5.3e+69) {
		tmp = (y * y) / (b / x);
	} 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 <= (-2.85d+48)) then
        tmp = x - (a / (y / x))
    else if (y <= (-6d-15)) then
        tmp = (y * x) / a
    else if (y <= 3.2d-131) then
        tmp = t / (i + (y * c))
    else if (y <= 3.1d-31) then
        tmp = (t + (y * 230661.510616d0)) / i
    else if (y <= 5.3d+69) then
        tmp = (y * y) / (b / x)
    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 <= -2.85e+48) {
		tmp = x - (a / (y / x));
	} else if (y <= -6e-15) {
		tmp = (y * x) / a;
	} else if (y <= 3.2e-131) {
		tmp = t / (i + (y * c));
	} else if (y <= 3.1e-31) {
		tmp = (t + (y * 230661.510616)) / i;
	} else if (y <= 5.3e+69) {
		tmp = (y * y) / (b / x);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -2.85e+48:
		tmp = x - (a / (y / x))
	elif y <= -6e-15:
		tmp = (y * x) / a
	elif y <= 3.2e-131:
		tmp = t / (i + (y * c))
	elif y <= 3.1e-31:
		tmp = (t + (y * 230661.510616)) / i
	elif y <= 5.3e+69:
		tmp = (y * y) / (b / x)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -2.85e+48)
		tmp = Float64(x - Float64(a / Float64(y / x)));
	elseif (y <= -6e-15)
		tmp = Float64(Float64(y * x) / a);
	elseif (y <= 3.2e-131)
		tmp = Float64(t / Float64(i + Float64(y * c)));
	elseif (y <= 3.1e-31)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / i);
	elseif (y <= 5.3e+69)
		tmp = Float64(Float64(y * y) / Float64(b / x));
	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 <= -2.85e+48)
		tmp = x - (a / (y / x));
	elseif (y <= -6e-15)
		tmp = (y * x) / a;
	elseif (y <= 3.2e-131)
		tmp = t / (i + (y * c));
	elseif (y <= 3.1e-31)
		tmp = (t + (y * 230661.510616)) / i;
	elseif (y <= 5.3e+69)
		tmp = (y * y) / (b / x);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -2.85e+48], N[(x - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -6e-15], N[(N[(y * x), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[y, 3.2e-131], N[(t / N[(i + N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.1e-31], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / i), $MachinePrecision], If[LessEqual[y, 5.3e+69], N[(N[(y * y), $MachinePrecision] / N[(b / x), $MachinePrecision]), $MachinePrecision], x]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -2.84999999999999984e48

   1. Initial program 5.5%

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

   2. Taylor expanded in x around inf 2.0%

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

   3. Taylor expanded in i around 0 7.3%

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

   4. Taylor expanded in y around inf 53.2%

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

      1. +-commutative 53.2%

         \[\leadsto \color{blue}{x + -1 \cdot \frac{a \cdot x}{y}} \]

      2. mul-1-neg 53.2%

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

      3. sub-neg 53.2%

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

      4. associate-/l* 58.0%

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

   6. Simplified 58.0%

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

   if -2.84999999999999984e48 < y < -6e-15

   1. Initial program 45.5%

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

   2. Taylor expanded in x around inf 21.7%

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

   3. Taylor expanded in a around inf 37.8%

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

   if -6e-15 < y < 3.2e-131

   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. Step-by-step derivation

      1. fma-def 99.7%

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

      2. fma-def 99.7%

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

      3. fma-def 99.7%

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

      4. fma-def 99.7%

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

      5. fma-def 99.7%

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

      6. fma-def 99.7%

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

      7. fma-def 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around 0 84.7%

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

   5. Taylor expanded in y around 0 79.4%

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

   if 3.2e-131 < y < 3.1e-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 75.8%

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

      1. *-commutative 75.8%

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

   4. Simplified 75.8%

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

   5. Taylor expanded in i around inf 41.3%

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

   if 3.1e-31 < y < 5.3e69

   1. Initial program 57.5%

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

   2. Taylor expanded in x around inf 20.4%

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

   3. Taylor expanded in b around inf 17.7%

      \[\leadsto \color{blue}{\frac{{y}^{2} \cdot x}{b}} \]
   4. Step-by-step derivation

      1. associate-/l* 21.9%

         \[\leadsto \color{blue}{\frac{{y}^{2}}{\frac{b}{x}}} \]

      2. unpow2 21.9%

         \[\leadsto \frac{\color{blue}{y \cdot y}}{\frac{b}{x}} \]

   5. Simplified 21.9%

      \[\leadsto \color{blue}{\frac{y \cdot y}{\frac{b}{x}}} \]

   if 5.3e69 < y

   1. Initial program 0.7%

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

   2. Taylor expanded in y around inf 59.4%

      \[\leadsto \color{blue}{x} \]
3. Recombined 6 regimes into one program.

4. Final simplification 59.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.85 \cdot 10^{+48}:\\ \;\;\;\;x - \frac{a}{\frac{y}{x}}\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-15}:\\ \;\;\;\;\frac{y \cdot x}{a}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-131}:\\ \;\;\;\;\frac{t}{i + y \cdot c}\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-31}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{elif}\;y \leq 5.3 \cdot 10^{+69}:\\ \;\;\;\;\frac{y \cdot y}{\frac{b}{x}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 21: 58.6% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+48}:\\ \;\;\;\;x - \frac{a}{\frac{y}{x}}\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-11}:\\ \;\;\;\;\frac{y \cdot x}{a}\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{+14}:\\ \;\;\;\;\frac{t}{i + y \cdot c}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -5e+48)
   (- x (/ a (/ y x)))
   (if (<= y -1.4e-11)
     (/ (* y x) a)
     (if (<= y 1.12e+14) (/ t (+ i (* y c))) x))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -5e+48) {
		tmp = x - (a / (y / x));
	} else if (y <= -1.4e-11) {
		tmp = (y * x) / a;
	} else if (y <= 1.12e+14) {
		tmp = t / (i + (y * c));
	} 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 <= (-5d+48)) then
        tmp = x - (a / (y / x))
    else if (y <= (-1.4d-11)) then
        tmp = (y * x) / a
    else if (y <= 1.12d+14) then
        tmp = t / (i + (y * c))
    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 <= -5e+48) {
		tmp = x - (a / (y / x));
	} else if (y <= -1.4e-11) {
		tmp = (y * x) / a;
	} else if (y <= 1.12e+14) {
		tmp = t / (i + (y * c));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -5e+48:
		tmp = x - (a / (y / x))
	elif y <= -1.4e-11:
		tmp = (y * x) / a
	elif y <= 1.12e+14:
		tmp = t / (i + (y * c))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -5e+48)
		tmp = Float64(x - Float64(a / Float64(y / x)));
	elseif (y <= -1.4e-11)
		tmp = Float64(Float64(y * x) / a);
	elseif (y <= 1.12e+14)
		tmp = Float64(t / Float64(i + Float64(y * c)));
	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 <= -5e+48)
		tmp = x - (a / (y / x));
	elseif (y <= -1.4e-11)
		tmp = (y * x) / a;
	elseif (y <= 1.12e+14)
		tmp = t / (i + (y * c));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -5e+48], N[(x - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.4e-11], N[(N[(y * x), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[y, 1.12e+14], N[(t / N[(i + N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.99999999999999973e48

   1. Initial program 5.5%

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

   2. Taylor expanded in x around inf 2.0%

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

   3. Taylor expanded in i around 0 7.3%

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

   4. Taylor expanded in y around inf 53.2%

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

      1. +-commutative 53.2%

         \[\leadsto \color{blue}{x + -1 \cdot \frac{a \cdot x}{y}} \]

      2. mul-1-neg 53.2%

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

      3. sub-neg 53.2%

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

      4. associate-/l* 58.0%

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

   6. Simplified 58.0%

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

   if -4.99999999999999973e48 < y < -1.4e-11

   1. Initial program 45.5%

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

   2. Taylor expanded in x around inf 21.7%

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

   3. Taylor expanded in a around inf 37.8%

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

   if -1.4e-11 < y < 1.12e14

   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. Step-by-step derivation

      1. fma-def 99.7%

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

      2. fma-def 99.7%

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

      3. fma-def 99.7%

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

      4. fma-def 99.7%

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

      5. fma-def 99.7%

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

      6. fma-def 99.7%

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

      7. fma-def 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around 0 69.1%

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

   5. Taylor expanded in y around 0 62.9%

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

   if 1.12e14 < y

   1. Initial program 4.7%

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

   2. Taylor expanded in y around inf 47.6%

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

4. Final simplification 56.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+48}:\\ \;\;\;\;x - \frac{a}{\frac{y}{x}}\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-11}:\\ \;\;\;\;\frac{y \cdot x}{a}\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{+14}:\\ \;\;\;\;\frac{t}{i + y \cdot c}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 22: 51.0% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.3 \cdot 10^{+48}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -4.7 \cdot 10^{-7}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-31}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -5.3e+48)
   x
   (if (<= y -4.7e-7) (/ y (/ a x)) (if (<= y 1.1e-31) (/ 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 <= -5.3e+48) {
		tmp = x;
	} else if (y <= -4.7e-7) {
		tmp = y / (a / x);
	} else if (y <= 1.1e-31) {
		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 <= (-5.3d+48)) then
        tmp = x
    else if (y <= (-4.7d-7)) then
        tmp = y / (a / x)
    else if (y <= 1.1d-31) 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 <= -5.3e+48) {
		tmp = x;
	} else if (y <= -4.7e-7) {
		tmp = y / (a / x);
	} else if (y <= 1.1e-31) {
		tmp = t / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -5.3e+48:
		tmp = x
	elif y <= -4.7e-7:
		tmp = y / (a / x)
	elif y <= 1.1e-31:
		tmp = t / i
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -5.3e+48)
		tmp = x;
	elseif (y <= -4.7e-7)
		tmp = Float64(y / Float64(a / x));
	elseif (y <= 1.1e-31)
		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 <= -5.3e+48)
		tmp = x;
	elseif (y <= -4.7e-7)
		tmp = y / (a / x);
	elseif (y <= 1.1e-31)
		tmp = t / i;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -5.3e+48], x, If[LessEqual[y, -4.7e-7], N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.1e-31], N[(t / i), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.3e48 or 1.10000000000000005e-31 < y

   1. Initial program 13.4%

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

   2. Taylor expanded in y around inf 48.6%

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

   if -5.3e48 < y < -4.7e-7

   1. Initial program 41.8%

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

   2. Taylor expanded in x around inf 22.9%

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

   3. Taylor expanded in a around inf 40.1%

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

      1. associate-/l* 39.9%

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

   5. Simplified 39.9%

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

   if -4.7e-7 < y < 1.10000000000000005e-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 57.7%

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

4. Final simplification 52.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.3 \cdot 10^{+48}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -4.7 \cdot 10^{-7}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-31}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 23: 51.0% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{+48}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -0.000125:\\ \;\;\;\;\frac{y \cdot x}{a}\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-31}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -1.45e+48)
   x
   (if (<= y -0.000125) (/ (* y x) a) (if (<= y 2.7e-31) (/ 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 <= -1.45e+48) {
		tmp = x;
	} else if (y <= -0.000125) {
		tmp = (y * x) / a;
	} else if (y <= 2.7e-31) {
		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 <= (-1.45d+48)) then
        tmp = x
    else if (y <= (-0.000125d0)) then
        tmp = (y * x) / a
    else if (y <= 2.7d-31) 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 <= -1.45e+48) {
		tmp = x;
	} else if (y <= -0.000125) {
		tmp = (y * x) / a;
	} else if (y <= 2.7e-31) {
		tmp = t / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -1.45e+48:
		tmp = x
	elif y <= -0.000125:
		tmp = (y * x) / a
	elif y <= 2.7e-31:
		tmp = t / i
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -1.45e+48)
		tmp = x;
	elseif (y <= -0.000125)
		tmp = Float64(Float64(y * x) / a);
	elseif (y <= 2.7e-31)
		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 <= -1.45e+48)
		tmp = x;
	elseif (y <= -0.000125)
		tmp = (y * x) / a;
	elseif (y <= 2.7e-31)
		tmp = t / i;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -1.45e+48], x, If[LessEqual[y, -0.000125], N[(N[(y * x), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[y, 2.7e-31], N[(t / i), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.4499999999999999e48 or 2.70000000000000014e-31 < y

   1. Initial program 13.4%

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

   2. Taylor expanded in y around inf 48.6%

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

   if -1.4499999999999999e48 < y < -1.25e-4

   1. Initial program 41.8%

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

   2. Taylor expanded in x around inf 22.9%

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

   3. Taylor expanded in a around inf 40.1%

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

   if -1.25e-4 < y < 2.70000000000000014e-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 57.7%

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

4. Final simplification 52.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{+48}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -0.000125:\\ \;\;\;\;\frac{y \cdot x}{a}\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-31}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 24: 51.0% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+48}:\\ \;\;\;\;x - \frac{a}{\frac{y}{x}}\\ \mathbf{elif}\;y \leq -6.8 \cdot 10^{-6}:\\ \;\;\;\;\frac{y \cdot x}{a}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-31}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -7e+48)
   (- x (/ a (/ y x)))
   (if (<= y -6.8e-6) (/ (* y x) a) (if (<= y 3.2e-31) (/ 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 <= -7e+48) {
		tmp = x - (a / (y / x));
	} else if (y <= -6.8e-6) {
		tmp = (y * x) / a;
	} else if (y <= 3.2e-31) {
		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 <= (-7d+48)) then
        tmp = x - (a / (y / x))
    else if (y <= (-6.8d-6)) then
        tmp = (y * x) / a
    else if (y <= 3.2d-31) 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 <= -7e+48) {
		tmp = x - (a / (y / x));
	} else if (y <= -6.8e-6) {
		tmp = (y * x) / a;
	} else if (y <= 3.2e-31) {
		tmp = t / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -7e+48:
		tmp = x - (a / (y / x))
	elif y <= -6.8e-6:
		tmp = (y * x) / a
	elif y <= 3.2e-31:
		tmp = t / i
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -7e+48)
		tmp = Float64(x - Float64(a / Float64(y / x)));
	elseif (y <= -6.8e-6)
		tmp = Float64(Float64(y * x) / a);
	elseif (y <= 3.2e-31)
		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 <= -7e+48)
		tmp = x - (a / (y / x));
	elseif (y <= -6.8e-6)
		tmp = (y * x) / a;
	elseif (y <= 3.2e-31)
		tmp = t / i;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -7e+48], N[(x - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -6.8e-6], N[(N[(y * x), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[y, 3.2e-31], N[(t / i), $MachinePrecision], x]]]

Derivation

1. Split input into 4 regimes

2. if y < -6.9999999999999995e48

   1. Initial program 5.5%

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

   2. Taylor expanded in x around inf 2.0%

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

   3. Taylor expanded in i around 0 7.3%

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

   4. Taylor expanded in y around inf 53.2%

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

      1. +-commutative 53.2%

         \[\leadsto \color{blue}{x + -1 \cdot \frac{a \cdot x}{y}} \]

      2. mul-1-neg 53.2%

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

      3. sub-neg 53.2%

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

      4. associate-/l* 58.0%

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

   6. Simplified 58.0%

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

   if -6.9999999999999995e48 < y < -6.80000000000000012e-6

   1. Initial program 41.8%

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

   2. Taylor expanded in x around inf 22.9%

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

   3. Taylor expanded in a around inf 40.1%

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

   if -6.80000000000000012e-6 < y < 3.20000000000000018e-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 57.7%

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

   if 3.20000000000000018e-31 < y

   1. Initial program 20.5%

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

   2. Taylor expanded in y around inf 40.3%

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

4. Final simplification 52.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+48}:\\ \;\;\;\;x - \frac{a}{\frac{y}{x}}\\ \mathbf{elif}\;y \leq -6.8 \cdot 10^{-6}:\\ \;\;\;\;\frac{y \cdot x}{a}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-31}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 25: 50.8% accurate, 4.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.02 \cdot 10^{+21}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-31}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -1.02e+21) x (if (<= y 3.1e-31) (/ 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 <= -1.02e+21) {
		tmp = x;
	} else if (y <= 3.1e-31) {
		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 <= (-1.02d+21)) then
        tmp = x
    else if (y <= 3.1d-31) 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 <= -1.02e+21) {
		tmp = x;
	} else if (y <= 3.1e-31) {
		tmp = t / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -1.02e+21:
		tmp = x
	elif y <= 3.1e-31:
		tmp = t / i
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -1.02e+21)
		tmp = x;
	elseif (y <= 3.1e-31)
		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 <= -1.02e+21)
		tmp = x;
	elseif (y <= 3.1e-31)
		tmp = t / i;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -1.02e+21], x, If[LessEqual[y, 3.1e-31], N[(t / i), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -1.02e21 or 3.1e-31 < y

   1. Initial program 12.8%

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

   2. Taylor expanded in y around inf 45.9%

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

   if -1.02e21 < y < 3.1e-31

   1. Initial program 98.9%

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

   2. Taylor expanded in y around 0 55.4%

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

4. Final simplification 50.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.02 \cdot 10^{+21}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-31}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 26: 26.0% 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 54.2%

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

2. Taylor expanded in y around inf 25.5%

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

3. Final simplification 25.5%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023268 
(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)))