Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2

Average Error: 29.3 → 10.9

Time: 59.5s

Precision: binary64

Cost: 15436

Math

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

↓

\[\begin{array}{l} t_1 := b + y \cdot \left(y + a\right)\\ t_2 := t_1 \cdot t_1\\ t_3 := y \cdot \left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) + i\\ t_4 := \frac{t}{t_3}\\ t_5 := \left(\frac{z}{y} + x\right) - \frac{a \cdot x}{y}\\ \mathbf{if}\;y \leq -2.2 \cdot 10^{+57}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+30}:\\ \;\;\;\;t_4 + \frac{\left(230661.510616 + y \cdot \left(27464.7644705 + \left(y \cdot x + z\right) \cdot y\right)\right) \cdot y}{t_3}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+113}:\\ \;\;\;\;t_4 + \left(\frac{27464.7644705 + y \cdot \left(z + y \cdot x\right)}{t_1} + \left(230661.510616 \cdot \frac{1}{y \cdot t_1} + c \cdot \left(-\left(\frac{z}{t_2} + \left(27464.7644705 \cdot \frac{1}{y \cdot t_2} + \left(230661.510616 \cdot \frac{1}{{y}^{2} \cdot t_2} + \frac{y \cdot x}{t_2}\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_5\\ \end{array} \]

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 (+ b (* y (+ y a))))
        (t_2 (* t_1 t_1))
        (t_3 (+ (* y (+ c (* y (+ (* (+ y a) y) b)))) i))
        (t_4 (/ t t_3))
        (t_5 (- (+ (/ z y) x) (/ (* a x) y))))
   (if (<= y -2.2e+57)
     t_5
     (if (<= y 1.05e+30)
       (+
        t_4
        (/
         (* (+ 230661.510616 (* y (+ 27464.7644705 (* (+ (* y x) z) y)))) y)
         t_3))
       (if (<= y 1.2e+113)
         (+
          t_4
          (+
           (/ (+ 27464.7644705 (* y (+ z (* y x)))) t_1)
           (+
            (* 230661.510616 (/ 1.0 (* y t_1)))
            (*
             c
             (-
              (+
               (/ z t_2)
               (+
                (* 27464.7644705 (/ 1.0 (* y t_2)))
                (+
                 (* 230661.510616 (/ 1.0 (* (pow y 2.0) t_2)))
                 (/ (* y x) t_2)))))))))
         t_5)))))

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 = b + (y * (y + a));
	double t_2 = t_1 * t_1;
	double t_3 = (y * (c + (y * (((y + a) * y) + b)))) + i;
	double t_4 = t / t_3;
	double t_5 = ((z / y) + x) - ((a * x) / y);
	double tmp;
	if (y <= -2.2e+57) {
		tmp = t_5;
	} else if (y <= 1.05e+30) {
		tmp = t_4 + (((230661.510616 + (y * (27464.7644705 + (((y * x) + z) * y)))) * y) / t_3);
	} else if (y <= 1.2e+113) {
		tmp = t_4 + (((27464.7644705 + (y * (z + (y * x)))) / t_1) + ((230661.510616 * (1.0 / (y * t_1))) + (c * -((z / t_2) + ((27464.7644705 * (1.0 / (y * t_2))) + ((230661.510616 * (1.0 / (pow(y, 2.0) * t_2))) + ((y * x) / t_2)))))));
	} else {
		tmp = t_5;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    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) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_1 = b + (y * (y + a))
    t_2 = t_1 * t_1
    t_3 = (y * (c + (y * (((y + a) * y) + b)))) + i
    t_4 = t / t_3
    t_5 = ((z / y) + x) - ((a * x) / y)
    if (y <= (-2.2d+57)) then
        tmp = t_5
    else if (y <= 1.05d+30) then
        tmp = t_4 + (((230661.510616d0 + (y * (27464.7644705d0 + (((y * x) + z) * y)))) * y) / t_3)
    else if (y <= 1.2d+113) then
        tmp = t_4 + (((27464.7644705d0 + (y * (z + (y * x)))) / t_1) + ((230661.510616d0 * (1.0d0 / (y * t_1))) + (c * -((z / t_2) + ((27464.7644705d0 * (1.0d0 / (y * t_2))) + ((230661.510616d0 * (1.0d0 / ((y ** 2.0d0) * t_2))) + ((y * x) / t_2)))))))
    else
        tmp = t_5
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	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 = b + (y * (y + a));
	double t_2 = t_1 * t_1;
	double t_3 = (y * (c + (y * (((y + a) * y) + b)))) + i;
	double t_4 = t / t_3;
	double t_5 = ((z / y) + x) - ((a * x) / y);
	double tmp;
	if (y <= -2.2e+57) {
		tmp = t_5;
	} else if (y <= 1.05e+30) {
		tmp = t_4 + (((230661.510616 + (y * (27464.7644705 + (((y * x) + z) * y)))) * y) / t_3);
	} else if (y <= 1.2e+113) {
		tmp = t_4 + (((27464.7644705 + (y * (z + (y * x)))) / t_1) + ((230661.510616 * (1.0 / (y * t_1))) + (c * -((z / t_2) + ((27464.7644705 * (1.0 / (y * t_2))) + ((230661.510616 * (1.0 / (Math.pow(y, 2.0) * t_2))) + ((y * x) / t_2)))))));
	} else {
		tmp = t_5;
	}
	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 = b + (y * (y + a))
	t_2 = t_1 * t_1
	t_3 = (y * (c + (y * (((y + a) * y) + b)))) + i
	t_4 = t / t_3
	t_5 = ((z / y) + x) - ((a * x) / y)
	tmp = 0
	if y <= -2.2e+57:
		tmp = t_5
	elif y <= 1.05e+30:
		tmp = t_4 + (((230661.510616 + (y * (27464.7644705 + (((y * x) + z) * y)))) * y) / t_3)
	elif y <= 1.2e+113:
		tmp = t_4 + (((27464.7644705 + (y * (z + (y * x)))) / t_1) + ((230661.510616 * (1.0 / (y * t_1))) + (c * -((z / t_2) + ((27464.7644705 * (1.0 / (y * t_2))) + ((230661.510616 * (1.0 / (math.pow(y, 2.0) * t_2))) + ((y * x) / t_2)))))))
	else:
		tmp = t_5
	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(b + Float64(y * Float64(y + a)))
	t_2 = Float64(t_1 * t_1)
	t_3 = Float64(Float64(y * Float64(c + Float64(y * Float64(Float64(Float64(y + a) * y) + b)))) + i)
	t_4 = Float64(t / t_3)
	t_5 = Float64(Float64(Float64(z / y) + x) - Float64(Float64(a * x) / y))
	tmp = 0.0
	if (y <= -2.2e+57)
		tmp = t_5;
	elseif (y <= 1.05e+30)
		tmp = Float64(t_4 + Float64(Float64(Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(Float64(Float64(y * x) + z) * y)))) * y) / t_3));
	elseif (y <= 1.2e+113)
		tmp = Float64(t_4 + Float64(Float64(Float64(27464.7644705 + Float64(y * Float64(z + Float64(y * x)))) / t_1) + Float64(Float64(230661.510616 * Float64(1.0 / Float64(y * t_1))) + Float64(c * Float64(-Float64(Float64(z / t_2) + Float64(Float64(27464.7644705 * Float64(1.0 / Float64(y * t_2))) + Float64(Float64(230661.510616 * Float64(1.0 / Float64((y ^ 2.0) * t_2))) + Float64(Float64(y * x) / t_2)))))))));
	else
		tmp = t_5;
	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 = b + (y * (y + a));
	t_2 = t_1 * t_1;
	t_3 = (y * (c + (y * (((y + a) * y) + b)))) + i;
	t_4 = t / t_3;
	t_5 = ((z / y) + x) - ((a * x) / y);
	tmp = 0.0;
	if (y <= -2.2e+57)
		tmp = t_5;
	elseif (y <= 1.05e+30)
		tmp = t_4 + (((230661.510616 + (y * (27464.7644705 + (((y * x) + z) * y)))) * y) / t_3);
	elseif (y <= 1.2e+113)
		tmp = t_4 + (((27464.7644705 + (y * (z + (y * x)))) / t_1) + ((230661.510616 * (1.0 / (y * t_1))) + (c * -((z / t_2) + ((27464.7644705 * (1.0 / (y * t_2))) + ((230661.510616 * (1.0 / ((y ^ 2.0) * t_2))) + ((y * x) / t_2)))))));
	else
		tmp = t_5;
	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[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 * t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y * N[(c + N[(y * N[(N[(N[(y + a), $MachinePrecision] * y), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]}, Block[{t$95$4 = N[(t / t$95$3), $MachinePrecision]}, Block[{t$95$5 = N[(N[(N[(z / y), $MachinePrecision] + x), $MachinePrecision] - N[(N[(a * x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.2e+57], t$95$5, If[LessEqual[y, 1.05e+30], N[(t$95$4 + N[(N[(N[(230661.510616 + N[(y * N[(27464.7644705 + N[(N[(N[(y * x), $MachinePrecision] + z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision] / t$95$3), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.2e+113], N[(t$95$4 + N[(N[(N[(27464.7644705 + N[(y * N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision] + N[(N[(230661.510616 * N[(1.0 / N[(y * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * (-N[(N[(z / t$95$2), $MachinePrecision] + N[(N[(27464.7644705 * N[(1.0 / N[(y * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(230661.510616 * N[(1.0 / N[(N[Power[y, 2.0], $MachinePrecision] * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y * x), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision])), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$5]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.2000000000000001e57 or 1.19999999999999992e113 < y

   1. Initial program 63.4

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

   2. Taylor expanded in y around inf 18.2

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

   if -2.2000000000000001e57 < y < 1.05e30

   1. Initial program 3.1

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

   2. Taylor expanded in t around inf 3.1

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

   if 1.05e30 < y < 1.19999999999999992e113

   1. Initial program 52.3

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

   2. Taylor expanded in t around inf 52.3

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

   3. Taylor expanded in i around 0 44.0

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

   4. Taylor expanded in c around 0 32.0

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

   5. Simplified 32.0

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

      [Start] 32.0	\[ \frac{t}{y \cdot \left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) + i} + \left(\frac{27464.7644705 + \left(y \cdot x + z\right) \cdot y}{\left(y + a\right) \cdot y + b} + \left(230661.510616 \cdot \frac{1}{y \cdot \left(\left(y + a\right) \cdot y + b\right)} + -1 \cdot \left(c \cdot \left(\frac{z}{\left(b + y \cdot \left(a + y\right)\right) \cdot \left(\left(y + a\right) \cdot y + b\right)} + \left(27464.7644705 \cdot \frac{1}{\left(b + y \cdot \left(a + y\right)\right) \cdot \left(y \cdot \left(\left(y + a\right) \cdot y + b\right)\right)} + \left(230661.510616 \cdot \frac{1}{\left(b + y \cdot \left(a + y\right)\right) \cdot \left({y}^{2} \cdot \left(\left(y + a\right) \cdot y + b\right)\right)} + \frac{y \cdot x}{\left(b + y \cdot \left(a + y\right)\right) \cdot \left(\left(y + a\right) \cdot y + b\right)}\right)\right)\right)\right)\right)\right) \]
      rational.json-simplify-2 [=>] 32.0	\[ \frac{t}{y \cdot \left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) + i} + \left(\frac{27464.7644705 + \color{blue}{y \cdot \left(y \cdot x + z\right)}}{\left(y + a\right) \cdot y + b} + \left(230661.510616 \cdot \frac{1}{y \cdot \left(\left(y + a\right) \cdot y + b\right)} + -1 \cdot \left(c \cdot \left(\frac{z}{\left(b + y \cdot \left(a + y\right)\right) \cdot \left(\left(y + a\right) \cdot y + b\right)} + \left(27464.7644705 \cdot \frac{1}{\left(b + y \cdot \left(a + y\right)\right) \cdot \left(y \cdot \left(\left(y + a\right) \cdot y + b\right)\right)} + \left(230661.510616 \cdot \frac{1}{\left(b + y \cdot \left(a + y\right)\right) \cdot \left({y}^{2} \cdot \left(\left(y + a\right) \cdot y + b\right)\right)} + \frac{y \cdot x}{\left(b + y \cdot \left(a + y\right)\right) \cdot \left(\left(y + a\right) \cdot y + b\right)}\right)\right)\right)\right)\right)\right) \]
      rational.json-simplify-1 [=>] 32.0	\[ \frac{t}{y \cdot \left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) + i} + \left(\frac{27464.7644705 + y \cdot \color{blue}{\left(z + y \cdot x\right)}}{\left(y + a\right) \cdot y + b} + \left(230661.510616 \cdot \frac{1}{y \cdot \left(\left(y + a\right) \cdot y + b\right)} + -1 \cdot \left(c \cdot \left(\frac{z}{\left(b + y \cdot \left(a + y\right)\right) \cdot \left(\left(y + a\right) \cdot y + b\right)} + \left(27464.7644705 \cdot \frac{1}{\left(b + y \cdot \left(a + y\right)\right) \cdot \left(y \cdot \left(\left(y + a\right) \cdot y + b\right)\right)} + \left(230661.510616 \cdot \frac{1}{\left(b + y \cdot \left(a + y\right)\right) \cdot \left({y}^{2} \cdot \left(\left(y + a\right) \cdot y + b\right)\right)} + \frac{y \cdot x}{\left(b + y \cdot \left(a + y\right)\right) \cdot \left(\left(y + a\right) \cdot y + b\right)}\right)\right)\right)\right)\right)\right) \]
      rational.json-simplify-1 [=>] 32.0	\[ \frac{t}{y \cdot \left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) + i} + \left(\frac{27464.7644705 + y \cdot \left(z + y \cdot x\right)}{\color{blue}{b + \left(y + a\right) \cdot y}} + \left(230661.510616 \cdot \frac{1}{y \cdot \left(\left(y + a\right) \cdot y + b\right)} + -1 \cdot \left(c \cdot \left(\frac{z}{\left(b + y \cdot \left(a + y\right)\right) \cdot \left(\left(y + a\right) \cdot y + b\right)} + \left(27464.7644705 \cdot \frac{1}{\left(b + y \cdot \left(a + y\right)\right) \cdot \left(y \cdot \left(\left(y + a\right) \cdot y + b\right)\right)} + \left(230661.510616 \cdot \frac{1}{\left(b + y \cdot \left(a + y\right)\right) \cdot \left({y}^{2} \cdot \left(\left(y + a\right) \cdot y + b\right)\right)} + \frac{y \cdot x}{\left(b + y \cdot \left(a + y\right)\right) \cdot \left(\left(y + a\right) \cdot y + b\right)}\right)\right)\right)\right)\right)\right) \]
      rational.json-simplify-2 [<=] 32.0	\[ \frac{t}{y \cdot \left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) + i} + \left(\frac{27464.7644705 + y \cdot \left(z + y \cdot x\right)}{b + \color{blue}{y \cdot \left(y + a\right)}} + \left(230661.510616 \cdot \frac{1}{y \cdot \left(\left(y + a\right) \cdot y + b\right)} + -1 \cdot \left(c \cdot \left(\frac{z}{\left(b + y \cdot \left(a + y\right)\right) \cdot \left(\left(y + a\right) \cdot y + b\right)} + \left(27464.7644705 \cdot \frac{1}{\left(b + y \cdot \left(a + y\right)\right) \cdot \left(y \cdot \left(\left(y + a\right) \cdot y + b\right)\right)} + \left(230661.510616 \cdot \frac{1}{\left(b + y \cdot \left(a + y\right)\right) \cdot \left({y}^{2} \cdot \left(\left(y + a\right) \cdot y + b\right)\right)} + \frac{y \cdot x}{\left(b + y \cdot \left(a + y\right)\right) \cdot \left(\left(y + a\right) \cdot y + b\right)}\right)\right)\right)\right)\right)\right) \]

3. Recombined 3 regimes into one program.

4. Final simplification 10.9

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{+57}:\\ \;\;\;\;\left(\frac{z}{y} + x\right) - \frac{a \cdot x}{y}\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+30}:\\ \;\;\;\;\frac{t}{y \cdot \left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) + i} + \frac{\left(230661.510616 + y \cdot \left(27464.7644705 + \left(y \cdot x + z\right) \cdot y\right)\right) \cdot y}{y \cdot \left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) + i}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+113}:\\ \;\;\;\;\frac{t}{y \cdot \left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) + i} + \left(\frac{27464.7644705 + y \cdot \left(z + y \cdot x\right)}{b + y \cdot \left(y + a\right)} + \left(230661.510616 \cdot \frac{1}{y \cdot \left(b + y \cdot \left(y + a\right)\right)} + c \cdot \left(-\left(\frac{z}{\left(b + y \cdot \left(y + a\right)\right) \cdot \left(b + y \cdot \left(y + a\right)\right)} + \left(27464.7644705 \cdot \frac{1}{y \cdot \left(\left(b + y \cdot \left(y + a\right)\right) \cdot \left(b + y \cdot \left(y + a\right)\right)\right)} + \left(230661.510616 \cdot \frac{1}{{y}^{2} \cdot \left(\left(b + y \cdot \left(y + a\right)\right) \cdot \left(b + y \cdot \left(y + a\right)\right)\right)} + \frac{y \cdot x}{\left(b + y \cdot \left(y + a\right)\right) \cdot \left(b + y \cdot \left(y + a\right)\right)}\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{z}{y} + x\right) - \frac{a \cdot x}{y}\\ \end{array} \]

Alternatives

Alternative 1
Error	11.3
Cost	5316

\[\begin{array}{l} t_1 := \left(y + a\right) \cdot y + b\\ t_2 := y \cdot \left(c + y \cdot t_1\right) + i\\ \mathbf{if}\;\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(t_1 \cdot y + c\right) \cdot y + i} \leq 5 \cdot 10^{+296}:\\ \;\;\;\;\frac{t}{t_2} + \frac{\left(230661.510616 + y \cdot \left(27464.7644705 + \left(y \cdot x + z\right) \cdot y\right)\right) \cdot y}{t_2}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{z}{y} + x\right) - \frac{a \cdot x}{y}\\ \end{array} \]

Alternative 2
Error	11.3
Cost	4292

\[\begin{array}{l} t_1 := \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\\ \mathbf{if}\;t_1 \leq 5 \cdot 10^{+296}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{z}{y} + x\right) - \frac{a \cdot x}{y}\\ \end{array} \]

Alternative 3
Error	14.5
Cost	1992

\[\begin{array}{l} t_1 := \left(\frac{z}{y} + x\right) - \frac{a \cdot x}{y}\\ \mathbf{if}\;y \leq -1.15 \cdot 10^{+52}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+27}:\\ \;\;\;\;\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(y \cdot b + c\right) \cdot y + i}\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{+115}:\\ \;\;\;\;\frac{z}{a} + \left(27464.7644705 \cdot \frac{1}{a \cdot y} + \frac{y \cdot x}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Error	16.3
Cost	1864

\[\begin{array}{l} t_1 := \left(\frac{z}{y} + x\right) - \frac{a \cdot x}{y}\\ \mathbf{if}\;y \leq -1.75 \cdot 10^{+61}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{+37}:\\ \;\;\;\;\frac{\left(y \cdot 27464.7644705 + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 5
Error	18.4
Cost	1484

\[\begin{array}{l} t_1 := \left(\frac{z}{y} + x\right) - \frac{a \cdot x}{y}\\ \mathbf{if}\;y \leq -4 \cdot 10^{+33}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-27}:\\ \;\;\;\;\frac{y \cdot 230661.510616 + t}{\left(y \cdot b + c\right) \cdot y + i}\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{+115}:\\ \;\;\;\;\frac{z}{a} + \left(27464.7644705 \cdot \frac{1}{a \cdot y} + \frac{y \cdot x}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Error	18.3
Cost	1484

\[\begin{array}{l} t_1 := \left(\frac{z}{y} + x\right) - \frac{a \cdot x}{y}\\ \mathbf{if}\;y \leq -1.2 \cdot 10^{+52}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-27}:\\ \;\;\;\;\frac{\left(y \cdot 27464.7644705 + 230661.510616\right) \cdot y + t}{\left(y \cdot b + c\right) \cdot y + i}\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{+115}:\\ \;\;\;\;\frac{z}{a} + \left(27464.7644705 \cdot \frac{1}{a \cdot y} + \frac{y \cdot x}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 7
Error	17.9
Cost	1224

\[\begin{array}{l} t_1 := \left(\frac{z}{y} + x\right) - \frac{a \cdot x}{y}\\ \mathbf{if}\;y \leq -1.8 \cdot 10^{+34}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+33}:\\ \;\;\;\;\frac{y \cdot 230661.510616 + t}{\left(y \cdot b + c\right) \cdot y + i}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 8
Error	26.4
Cost	968

\[\begin{array}{l} t_1 := \left(\frac{z}{y} + x\right) - \frac{a \cdot x}{y}\\ \mathbf{if}\;y \leq -3.8 \cdot 10^{+17}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+34}:\\ \;\;\;\;\frac{t + 230661.510616 \cdot y}{i}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 9
Error	22.1
Cost	968

\[\begin{array}{l} t_1 := \left(\frac{z}{y} + x\right) - \frac{a \cdot x}{y}\\ \mathbf{if}\;y \leq -1.2 \cdot 10^{+33}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+33}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(y \cdot b + c\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 10
Error	20.2
Cost	968

\[\begin{array}{l} t_1 := \left(\frac{z}{y} + x\right) - \frac{a \cdot x}{y}\\ \mathbf{if}\;y \leq -4.6 \cdot 10^{+14}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.52 \cdot 10^{+34}:\\ \;\;\;\;\frac{y \cdot 230661.510616 + t}{c \cdot y + i}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 11
Error	32.3
Cost	848

\[\begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{+119}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -9 \cdot 10^{+17}:\\ \;\;\;\;\frac{z}{y}\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{+15}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{+115}:\\ \;\;\;\;\frac{y \cdot x}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 12
Error	30.3
Cost	848

\[\begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{+119}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.85 \cdot 10^{+17}:\\ \;\;\;\;\frac{z}{y}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-27}:\\ \;\;\;\;\frac{t + 230661.510616 \cdot y}{i}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+117}:\\ \;\;\;\;\frac{y \cdot x}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 13
Error	32.1
Cost	588

\[\begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{+119}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -26500000000000:\\ \;\;\;\;\frac{z}{y}\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-7}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 14
Error	32.0
Cost	456

\[\begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+81}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-7}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 15
Error	46.8
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023077 
(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)))