Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2

Average Error: 29.6 → 9.8

Time: 2.0min

Precision: binary64

Cost: 8712

Math

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

↓

\[\begin{array}{l} t_1 := z + y \cdot x\\ t_2 := c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\\ \mathbf{if}\;y \leq -1.3 \cdot 10^{+98}:\\ \;\;\;\;\frac{z}{y} + \left(x - a \cdot \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -6.7 \cdot 10^{+19}:\\ \;\;\;\;230661.510616 \cdot \frac{1}{t_2} + \left(i \cdot \left(-\left(27464.7644705 \cdot \frac{1}{t_2 \cdot t_2} + \left(230661.510616 \cdot \frac{\frac{\frac{1}{y}}{t_2}}{t_2} + y \cdot \frac{\frac{t_1}{t_2}}{t_2}\right)\right)\right) + y \cdot \frac{27464.7644705 + y \cdot t_1}{t_2}\right)\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+50}:\\ \;\;\;\;\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+159}:\\ \;\;\;\;\frac{4}{4 \cdot \left(\frac{1}{x} + \frac{\frac{a}{x} - \frac{z}{{x}^{2}}}{y}\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - x \cdot \frac{a}{y}\\ \end{array} \]

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)))

↓

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ z (* y x))) (t_2 (+ c (* y (+ b (* y (+ y a)))))))
   (if (<= y -1.3e+98)
     (+ (/ z y) (- x (* a (/ x y))))
     (if (<= y -6.7e+19)
       (+
        (* 230661.510616 (/ 1.0 t_2))
        (+
         (*
          i
          (-
           (+
            (* 27464.7644705 (/ 1.0 (* t_2 t_2)))
            (+
             (* 230661.510616 (/ (/ (/ 1.0 y) t_2) t_2))
             (* y (/ (/ t_1 t_2) t_2))))))
         (* y (/ (+ 27464.7644705 (* y t_1)) t_2))))
       (if (<= y 1.7e+50)
         (/
          (+
           (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y)
           t)
          (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i))
         (if (<= y 5e+159)
           (/ 4.0 (* 4.0 (+ (/ 1.0 x) (/ (- (/ a x) (/ z (pow x 2.0))) y))))
           (- (+ 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) {
	return ((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i);
}

↓

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = z + (y * x);
	double t_2 = c + (y * (b + (y * (y + a))));
	double tmp;
	if (y <= -1.3e+98) {
		tmp = (z / y) + (x - (a * (x / y)));
	} else if (y <= -6.7e+19) {
		tmp = (230661.510616 * (1.0 / t_2)) + ((i * -((27464.7644705 * (1.0 / (t_2 * t_2))) + ((230661.510616 * (((1.0 / y) / t_2) / t_2)) + (y * ((t_1 / t_2) / t_2))))) + (y * ((27464.7644705 + (y * t_1)) / t_2)));
	} else if (y <= 1.7e+50) {
		tmp = ((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i);
	} else if (y <= 5e+159) {
		tmp = 4.0 / (4.0 * ((1.0 / x) + (((a / x) - (z / pow(x, 2.0))) / y)));
	} 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
    code = ((((((((x * y) + z) * y) + 27464.7644705d0) * y) + 230661.510616d0) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i)
end function

↓

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z + (y * x)
    t_2 = c + (y * (b + (y * (y + a))))
    if (y <= (-1.3d+98)) then
        tmp = (z / y) + (x - (a * (x / y)))
    else if (y <= (-6.7d+19)) then
        tmp = (230661.510616d0 * (1.0d0 / t_2)) + ((i * -((27464.7644705d0 * (1.0d0 / (t_2 * t_2))) + ((230661.510616d0 * (((1.0d0 / y) / t_2) / t_2)) + (y * ((t_1 / t_2) / t_2))))) + (y * ((27464.7644705d0 + (y * t_1)) / t_2)))
    else if (y <= 1.7d+50) then
        tmp = ((((((((x * y) + z) * y) + 27464.7644705d0) * y) + 230661.510616d0) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i)
    else if (y <= 5d+159) then
        tmp = 4.0d0 / (4.0d0 * ((1.0d0 / x) + (((a / x) - (z / (x ** 2.0d0))) / y)))
    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) {
	return ((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i);
}

↓

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = z + (y * x);
	double t_2 = c + (y * (b + (y * (y + a))));
	double tmp;
	if (y <= -1.3e+98) {
		tmp = (z / y) + (x - (a * (x / y)));
	} else if (y <= -6.7e+19) {
		tmp = (230661.510616 * (1.0 / t_2)) + ((i * -((27464.7644705 * (1.0 / (t_2 * t_2))) + ((230661.510616 * (((1.0 / y) / t_2) / t_2)) + (y * ((t_1 / t_2) / t_2))))) + (y * ((27464.7644705 + (y * t_1)) / t_2)));
	} else if (y <= 1.7e+50) {
		tmp = ((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i);
	} else if (y <= 5e+159) {
		tmp = 4.0 / (4.0 * ((1.0 / x) + (((a / x) - (z / Math.pow(x, 2.0))) / y)));
	} else {
		tmp = (x + (z / y)) - (x * (a / y));
	}
	return tmp;
}

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)

↓

def code(x, y, z, t, a, b, c, i):
	t_1 = z + (y * x)
	t_2 = c + (y * (b + (y * (y + a))))
	tmp = 0
	if y <= -1.3e+98:
		tmp = (z / y) + (x - (a * (x / y)))
	elif y <= -6.7e+19:
		tmp = (230661.510616 * (1.0 / t_2)) + ((i * -((27464.7644705 * (1.0 / (t_2 * t_2))) + ((230661.510616 * (((1.0 / y) / t_2) / t_2)) + (y * ((t_1 / t_2) / t_2))))) + (y * ((27464.7644705 + (y * t_1)) / t_2)))
	elif y <= 1.7e+50:
		tmp = ((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i)
	elif y <= 5e+159:
		tmp = 4.0 / (4.0 * ((1.0 / x) + (((a / x) - (z / math.pow(x, 2.0))) / y)))
	else:
		tmp = (x + (z / y)) - (x * (a / y))
	return tmp

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

↓

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(z + Float64(y * x))
	t_2 = Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a)))))
	tmp = 0.0
	if (y <= -1.3e+98)
		tmp = Float64(Float64(z / y) + Float64(x - Float64(a * Float64(x / y))));
	elseif (y <= -6.7e+19)
		tmp = Float64(Float64(230661.510616 * Float64(1.0 / t_2)) + Float64(Float64(i * Float64(-Float64(Float64(27464.7644705 * Float64(1.0 / Float64(t_2 * t_2))) + Float64(Float64(230661.510616 * Float64(Float64(Float64(1.0 / y) / t_2) / t_2)) + Float64(y * Float64(Float64(t_1 / t_2) / t_2)))))) + Float64(y * Float64(Float64(27464.7644705 + Float64(y * t_1)) / t_2))));
	elseif (y <= 1.7e+50)
		tmp = 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));
	elseif (y <= 5e+159)
		tmp = Float64(4.0 / Float64(4.0 * Float64(Float64(1.0 / x) + Float64(Float64(Float64(a / x) - Float64(z / (x ^ 2.0))) / y))));
	else
		tmp = Float64(Float64(x + Float64(z / y)) - Float64(x * Float64(a / y)));
	end
	return tmp
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

↓

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = z + (y * x);
	t_2 = c + (y * (b + (y * (y + a))));
	tmp = 0.0;
	if (y <= -1.3e+98)
		tmp = (z / y) + (x - (a * (x / y)));
	elseif (y <= -6.7e+19)
		tmp = (230661.510616 * (1.0 / t_2)) + ((i * -((27464.7644705 * (1.0 / (t_2 * t_2))) + ((230661.510616 * (((1.0 / y) / t_2) / t_2)) + (y * ((t_1 / t_2) / t_2))))) + (y * ((27464.7644705 + (y * t_1)) / t_2)));
	elseif (y <= 1.7e+50)
		tmp = ((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i);
	elseif (y <= 5e+159)
		tmp = 4.0 / (4.0 * ((1.0 / x) + (((a / x) - (z / (x ^ 2.0))) / y)));
	else
		tmp = (x + (z / y)) - (x * (a / y));
	end
	tmp_2 = tmp;
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]

↓

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c + N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.3e+98], N[(N[(z / y), $MachinePrecision] + N[(x - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -6.7e+19], N[(N[(230661.510616 * N[(1.0 / t$95$2), $MachinePrecision]), $MachinePrecision] + N[(N[(i * (-N[(N[(27464.7644705 * N[(1.0 / N[(t$95$2 * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(230661.510616 * N[(N[(N[(1.0 / y), $MachinePrecision] / t$95$2), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision] + N[(y * N[(N[(t$95$1 / t$95$2), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision])), $MachinePrecision] + N[(y * N[(N[(27464.7644705 + N[(y * t$95$1), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.7e+50], 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], If[LessEqual[y, 5e+159], N[(4.0 / N[(4.0 * N[(N[(1.0 / x), $MachinePrecision] + N[(N[(N[(a / x), $MachinePrecision] - N[(z / N[Power[x, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(x * N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.3e98

   1. Initial program 63.9

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

   2. Taylor expanded in y around inf 15.0

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

   3. Simplified 11.2

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

      [Start] 15.0	\[ \left(\frac{z}{y} + x\right) - \frac{a \cdot x}{y} \]
      rational.json-simplify-1 [=>] 15.0	\[ \color{blue}{\left(x + \frac{z}{y}\right)} - \frac{a \cdot x}{y} \]
      rational.json-simplify-48 [=>] 15.0	\[ \color{blue}{\frac{z}{y} + \left(x - \frac{a \cdot x}{y}\right)} \]
      rational.json-simplify-2 [=>] 15.0	\[ \frac{z}{y} + \left(x - \frac{\color{blue}{x \cdot a}}{y}\right) \]
      rational.json-simplify-49 [=>] 11.2	\[ \frac{z}{y} + \left(x - \color{blue}{a \cdot \frac{x}{y}}\right) \]

   if -1.3e98 < y < -6.7e19

   1. Initial program 47.1

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

   2. Taylor expanded in t around 0 50.8

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

   3. Simplified 48.1

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

      [Start] 50.8	\[ \frac{\left(230661.510616 + y \cdot \left(27464.7644705 + \left(y \cdot x + z\right) \cdot y\right)\right) \cdot y}{y \cdot \left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) + i} \]
      rational.json-simplify-49 [=>] 48.1	\[ \color{blue}{y \cdot \frac{230661.510616 + y \cdot \left(27464.7644705 + \left(y \cdot x + z\right) \cdot y\right)}{y \cdot \left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) + i}} \]
      rational.json-simplify-2 [<=] 48.1	\[ y \cdot \frac{230661.510616 + y \cdot \left(27464.7644705 + \left(\color{blue}{x \cdot y} + z\right) \cdot y\right)}{y \cdot \left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) + i} \]
      rational.json-simplify-2 [<=] 48.1	\[ y \cdot \frac{230661.510616 + y \cdot \left(27464.7644705 + \color{blue}{y \cdot \left(x \cdot y + z\right)}\right)}{y \cdot \left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) + i} \]
      rational.json-simplify-1 [=>] 48.1	\[ y \cdot \frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \color{blue}{\left(z + x \cdot y\right)}\right)}{y \cdot \left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) + i} \]
      rational.json-simplify-2 [=>] 48.1	\[ y \cdot \frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + \color{blue}{y \cdot x}\right)\right)}{y \cdot \left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) + i} \]
      rational.json-simplify-2 [=>] 48.1	\[ y \cdot \frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)}{y \cdot \left(c + y \cdot \left(\color{blue}{y \cdot \left(y + a\right)} + b\right)\right) + i} \]

   4. Taylor expanded in i around 0 41.8

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

   5. Simplified 35.2

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

      [Start] 41.8

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

   if -6.7e19 < y < 1.6999999999999999e50

   1. Initial program 2.8

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

   if 1.6999999999999999e50 < y < 5.00000000000000003e159

   1. Initial program 60.6

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

   2. Applied egg-rr 60.6

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

   3. Applied egg-rr 60.6

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

   4. Taylor expanded in y around inf 32.3

      \[\leadsto \frac{4}{\color{blue}{4 \cdot \frac{\frac{a}{x} - \frac{z}{{x}^{2}}}{y} + 4 \cdot \frac{1}{x}}} \]

   5. Simplified 32.3

      \[\leadsto \frac{4}{\color{blue}{4 \cdot \left(\frac{1}{x} + \frac{\frac{a}{x} - \frac{z}{{x}^{2}}}{y}\right)}} \]
      Proof

      [Start] 32.3	\[ \frac{4}{4 \cdot \frac{\frac{a}{x} - \frac{z}{{x}^{2}}}{y} + 4 \cdot \frac{1}{x}} \]
      rational.json-simplify-2 [=>] 32.3	\[ \frac{4}{4 \cdot \frac{\frac{a}{x} - \frac{z}{{x}^{2}}}{y} + \color{blue}{\frac{1}{x} \cdot 4}} \]
      rational.json-simplify-51 [=>] 32.3	\[ \frac{4}{\color{blue}{4 \cdot \left(\frac{1}{x} + \frac{\frac{a}{x} - \frac{z}{{x}^{2}}}{y}\right)}} \]

   if 5.00000000000000003e159 < y

   1. Initial program 64.0

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

   2. Taylor expanded in t around 0 64.0

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

   3. Simplified 63.8

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

      [Start] 64.0	\[ \frac{\left(230661.510616 + y \cdot \left(27464.7644705 + \left(y \cdot x + z\right) \cdot y\right)\right) \cdot y}{y \cdot \left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) + i} \]
      rational.json-simplify-49 [=>] 63.8	\[ \color{blue}{y \cdot \frac{230661.510616 + y \cdot \left(27464.7644705 + \left(y \cdot x + z\right) \cdot y\right)}{y \cdot \left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) + i}} \]
      rational.json-simplify-2 [<=] 63.8	\[ y \cdot \frac{230661.510616 + y \cdot \left(27464.7644705 + \left(\color{blue}{x \cdot y} + z\right) \cdot y\right)}{y \cdot \left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) + i} \]
      rational.json-simplify-2 [<=] 63.8	\[ y \cdot \frac{230661.510616 + y \cdot \left(27464.7644705 + \color{blue}{y \cdot \left(x \cdot y + z\right)}\right)}{y \cdot \left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) + i} \]
      rational.json-simplify-1 [=>] 63.8	\[ y \cdot \frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \color{blue}{\left(z + x \cdot y\right)}\right)}{y \cdot \left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) + i} \]
      rational.json-simplify-2 [=>] 63.8	\[ y \cdot \frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + \color{blue}{y \cdot x}\right)\right)}{y \cdot \left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) + i} \]
      rational.json-simplify-2 [=>] 63.8	\[ y \cdot \frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)}{y \cdot \left(c + y \cdot \left(\color{blue}{y \cdot \left(y + a\right)} + b\right)\right) + i} \]

   4. Taylor expanded in y around inf 11.9

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

   5. Simplified 6.8

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

      [Start] 11.9	\[ \left(\frac{z}{y} + x\right) - \frac{a \cdot x}{y} \]
      rational.json-simplify-1 [=>] 11.9	\[ \color{blue}{\left(x + \frac{z}{y}\right)} - \frac{a \cdot x}{y} \]
      rational.json-simplify-49 [=>] 6.8	\[ \left(x + \frac{z}{y}\right) - \color{blue}{x \cdot \frac{a}{y}} \]

3. Recombined 5 regimes into one program.

4. Final simplification 9.8

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+98}:\\ \;\;\;\;\frac{z}{y} + \left(x - a \cdot \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -6.7 \cdot 10^{+19}:\\ \;\;\;\;230661.510616 \cdot \frac{1}{c + y \cdot \left(b + y \cdot \left(y + a\right)\right)} + \left(i \cdot \left(-\left(27464.7644705 \cdot \frac{1}{\left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)} + \left(230661.510616 \cdot \frac{\frac{\frac{1}{y}}{c + y \cdot \left(b + y \cdot \left(y + a\right)\right)}}{c + y \cdot \left(b + y \cdot \left(y + a\right)\right)} + y \cdot \frac{\frac{z + y \cdot x}{c + y \cdot \left(b + y \cdot \left(y + a\right)\right)}}{c + y \cdot \left(b + y \cdot \left(y + a\right)\right)}\right)\right)\right) + y \cdot \frac{27464.7644705 + y \cdot \left(z + y \cdot x\right)}{c + y \cdot \left(b + y \cdot \left(y + a\right)\right)}\right)\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+50}:\\ \;\;\;\;\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+159}:\\ \;\;\;\;\frac{4}{4 \cdot \left(\frac{1}{x} + \frac{\frac{a}{x} - \frac{z}{{x}^{2}}}{y}\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - x \cdot \frac{a}{y}\\ \end{array} \]

Alternatives

Alternative 1
Error	10.5
Cost	8328

\[\begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+116}:\\ \;\;\;\;\frac{z}{y} + \left(x - a \cdot \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -4.1 \cdot 10^{+58}:\\ \;\;\;\;\left(27464.7644705 \cdot \frac{1}{y \cdot a} + \left(x \cdot \frac{y}{a} + \frac{z}{a}\right)\right) - x \cdot \frac{c}{y \cdot {a}^{2}}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+51}:\\ \;\;\;\;\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\\ \mathbf{elif}\;y \leq 2.45 \cdot 10^{+160}:\\ \;\;\;\;\frac{4}{4 \cdot \left(\frac{1}{x} + \frac{\frac{a}{x} - \frac{z}{{x}^{2}}}{y}\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - x \cdot \frac{a}{y}\\ \end{array} \]

Alternative 2
Error	10.5
Cost	8200

\[\begin{array}{l} \mathbf{if}\;y \leq -6.4 \cdot 10^{+115}:\\ \;\;\;\;\frac{z}{y} + \left(x - a \cdot \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -6 \cdot 10^{+58}:\\ \;\;\;\;\frac{z}{a} + \left(27464.7644705 \cdot \frac{1}{y \cdot a} + x \cdot \left(\frac{y}{a} - \frac{\frac{c}{y}}{{a}^{2}}\right)\right)\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+52}:\\ \;\;\;\;\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{+160}:\\ \;\;\;\;\frac{4}{4 \cdot \left(\frac{1}{x} + \frac{\frac{a}{x} - \frac{z}{{x}^{2}}}{y}\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - x \cdot \frac{a}{y}\\ \end{array} \]

Alternative 3
Error	10.2
Cost	7948

\[\begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+76}:\\ \;\;\;\;\frac{z}{y} + \left(x - a \cdot \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+50}:\\ \;\;\;\;\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\\ \mathbf{elif}\;y \leq 6.7 \cdot 10^{+159}:\\ \;\;\;\;\frac{4}{4 \cdot \left(\frac{1}{x} + \frac{\frac{a}{x} - \frac{z}{{x}^{2}}}{y}\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - x \cdot \frac{a}{y}\\ \end{array} \]

Alternative 4
Error	13.8
Cost	2524

\[\begin{array}{l} t_1 := \left(y + a\right) \cdot y + b\\ t_2 := 230661.510616 + y \cdot \left(27464.7644705 + \left(y \cdot x + z\right) \cdot y\right)\\ t_3 := \frac{t_2}{c + y \cdot t_1}\\ t_4 := \frac{y \cdot t_2 + t}{i + c \cdot y}\\ \mathbf{if}\;y \leq -4.6 \cdot 10^{+97}:\\ \;\;\;\;\frac{z}{y} + \left(x - a \cdot \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -60000000000000:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{-36}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y \leq -1.16 \cdot 10^{-40}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-73}:\\ \;\;\;\;\frac{y \cdot 230661.510616 + t}{\left(t_1 \cdot y + c\right) \cdot y + i}\\ \mathbf{elif}\;y \leq 3.55 \cdot 10^{-16}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{+48}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+91}:\\ \;\;\;\;y \cdot \frac{x}{a} + \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - x \cdot \frac{a}{y}\\ \end{array} \]

Alternative 5
Error	10.1
Cost	2376

\[\begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+76}:\\ \;\;\;\;\frac{z}{y} + \left(x - a \cdot \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+50}:\\ \;\;\;\;\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+95}:\\ \;\;\;\;y \cdot \frac{x}{a} + \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - x \cdot \frac{a}{y}\\ \end{array} \]

Alternative 6
Error	14.7
Cost	2260

\[\begin{array}{l} t_1 := \frac{y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + \left(y \cdot x + z\right) \cdot y\right)\right) + t}{i + c \cdot y}\\ \mathbf{if}\;y \leq -6.7 \cdot 10^{+19}:\\ \;\;\;\;\frac{z}{y} + \left(x - a \cdot \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -3.7 \cdot 10^{-31}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-75}:\\ \;\;\;\;\frac{y \cdot 230661.510616 + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-16}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+45}:\\ \;\;\;\;y \cdot \frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)}{y \cdot \left(c + y \cdot b\right) + i}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+95}:\\ \;\;\;\;y \cdot \frac{x}{a} + \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - x \cdot \frac{a}{y}\\ \end{array} \]

Alternative 7
Error	11.9
Cost	2252

\[\begin{array}{l} t_1 := \left(y + a\right) \cdot y + b\\ \mathbf{if}\;y \leq -4.8 \cdot 10^{+97}:\\ \;\;\;\;\frac{z}{y} + \left(x - a \cdot \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{+15}:\\ \;\;\;\;\frac{230661.510616 + y \cdot \left(27464.7644705 + \left(y \cdot x + z\right) \cdot y\right)}{c + y \cdot t_1}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+49}:\\ \;\;\;\;\frac{\left(y \cdot \left(y \cdot z + 27464.7644705\right) + 230661.510616\right) \cdot y + t}{\left(t_1 \cdot y + c\right) \cdot y + i}\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+91}:\\ \;\;\;\;y \cdot \frac{x}{a} + \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - x \cdot \frac{a}{y}\\ \end{array} \]

Alternative 8
Error	12.4
Cost	2124

\[\begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+98}:\\ \;\;\;\;\frac{z}{y} + \left(x - a \cdot \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -7 \cdot 10^{+14}:\\ \;\;\;\;\frac{230661.510616 + y \cdot \left(27464.7644705 + \left(y \cdot x + z\right) \cdot y\right)}{c + y \cdot \left(\left(y + a\right) \cdot y + b\right)}\\ \mathbf{elif}\;y \leq 1.62 \cdot 10^{+47}:\\ \;\;\;\;\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(y \cdot b + c\right) \cdot y + i}\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{+95}:\\ \;\;\;\;y \cdot \frac{x}{a} + \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - x \cdot \frac{a}{y}\\ \end{array} \]

Alternative 9
Error	15.0
Cost	2004

\[\begin{array}{l} t_1 := \frac{y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + \left(y \cdot x + z\right) \cdot y\right)\right) + t}{i + c \cdot y}\\ \mathbf{if}\;y \leq -6.7 \cdot 10^{+19}:\\ \;\;\;\;\frac{z}{y} + \left(x - a \cdot \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -4.4 \cdot 10^{-33}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 10^{-72}:\\ \;\;\;\;\frac{y \cdot 230661.510616 + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{-14}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{+45}:\\ \;\;\;\;\frac{4}{4 \cdot \frac{i + y \cdot \left(c + \left(b + y \cdot \left(a + y\right)\right) \cdot y\right)}{t}}\\ \mathbf{elif}\;y \leq 5.7 \cdot 10^{+94}:\\ \;\;\;\;y \cdot \frac{x}{a} + \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - x \cdot \frac{a}{y}\\ \end{array} \]

Alternative 10
Error	16.1
Cost	1608

\[\begin{array}{l} \mathbf{if}\;y \leq -6.7 \cdot 10^{+19}:\\ \;\;\;\;\frac{z}{y} + \left(x - a \cdot \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{-29}:\\ \;\;\;\;\left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right) \cdot \frac{y}{i + c \cdot y}\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+45}:\\ \;\;\;\;\frac{y \cdot 230661.510616 + t}{\left(y \cdot b + c\right) \cdot y + i}\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+102}:\\ \;\;\;\;y \cdot \frac{x}{a} + \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - x \cdot \frac{a}{y}\\ \end{array} \]

Alternative 11
Error	15.3
Cost	1608

\[\begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+34}:\\ \;\;\;\;\frac{z}{y} + \left(x - a \cdot \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+45}:\\ \;\;\;\;\frac{y \cdot 230661.510616 + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+93}:\\ \;\;\;\;y \cdot \frac{x}{a} + \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - x \cdot \frac{a}{y}\\ \end{array} \]

Alternative 12
Error	16.4
Cost	1224

\[\begin{array}{l} \mathbf{if}\;y \leq -7.6 \cdot 10^{+34}:\\ \;\;\;\;\frac{z}{y} + \left(x - a \cdot \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+45}:\\ \;\;\;\;\frac{y \cdot 230661.510616 + t}{\left(y \cdot b + c\right) \cdot y + i}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+95}:\\ \;\;\;\;y \cdot \frac{x}{a} + \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - x \cdot \frac{a}{y}\\ \end{array} \]

Alternative 13
Error	26.8
Cost	1104

\[\begin{array}{l} t_1 := y \cdot \frac{x}{a} + \frac{z}{a}\\ \mathbf{if}\;y \leq -6.8 \cdot 10^{+155}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -15000000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+45}:\\ \;\;\;\;\frac{t}{i + y \cdot c}\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+95}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 14
Error	22.1
Cost	1100

\[\begin{array}{l} t_1 := \frac{z}{y} + \left(x - a \cdot \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -1.75 \cdot 10^{+25}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+45}:\\ \;\;\;\;\frac{t}{i + y \cdot c}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+91}:\\ \;\;\;\;y \cdot \frac{x}{a} + \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 15
Error	22.1
Cost	1100

\[\begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{+28}:\\ \;\;\;\;\frac{z}{y} + \left(x - a \cdot \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+45}:\\ \;\;\;\;\frac{t}{i + y \cdot c}\\ \mathbf{elif}\;y \leq 6.1 \cdot 10^{+91}:\\ \;\;\;\;y \cdot \frac{x}{a} + \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - x \cdot \frac{a}{y}\\ \end{array} \]

Alternative 16
Error	20.7
Cost	1100

\[\begin{array}{l} \mathbf{if}\;y \leq -2.55 \cdot 10^{+33}:\\ \;\;\;\;\frac{z}{y} + \left(x - a \cdot \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+45}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(y \cdot b + c\right)}\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{+95}:\\ \;\;\;\;y \cdot \frac{x}{a} + \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - x \cdot \frac{a}{y}\\ \end{array} \]

Alternative 17
Error	18.4
Cost	1100

\[\begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{+30}:\\ \;\;\;\;\frac{z}{y} + \left(x - a \cdot \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+45}:\\ \;\;\;\;\frac{y \cdot 230661.510616 + t}{c \cdot y + i}\\ \mathbf{elif}\;y \leq 10^{+100}:\\ \;\;\;\;y \cdot \frac{x}{a} + \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - x \cdot \frac{a}{y}\\ \end{array} \]

Alternative 18
Error	26.6
Cost	712

\[\begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{-9}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+26}:\\ \;\;\;\;\frac{t}{i + y \cdot c}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 19
Error	31.6
Cost	456

\[\begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{-9}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{+52}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 20
Error	46.5
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023074 
(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)))