Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2

Average Error: 28.9 → 10.0

Time: 48.8s

Precision: binary64

Cost: 29256

Math

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

↓

\[\begin{array}{l} t_1 := y \cdot \left(z + y \cdot x\right)\\ t_2 := b + y \cdot \left(y + a\right)\\ t_3 := x + \left(\frac{z}{y} - x \cdot \frac{a}{y}\right)\\ t_4 := 27464.7644705 + t_1\\ t_5 := y \cdot t_2\\ t_6 := c + t_5\\ t_7 := y \cdot t_6\\ t_8 := t_6 \cdot t_6\\ t_9 := t_2 \cdot t_2\\ \mathbf{if}\;y \leq -1.22 \cdot 10^{+89}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -480000000:\\ \;\;\;\;\frac{t}{t_7} + \left(i \cdot \left(\left(230661.510616 \cdot \frac{-1}{y \cdot t_8} - \left(27464.7644705 \cdot \frac{1}{t_8} + \frac{t_1}{t_8}\right)\right) - \frac{t}{{y}^{2} \cdot t_8}\right) + \left(\frac{t_4}{t_2} + \left(230661.510616 \cdot \frac{1}{t_5} + c \cdot \left(\left(\frac{1}{t_5 \cdot t_2} \cdot -27464.7644705 - \left(230661.510616 \cdot \frac{1}{t_2 \cdot \left({y}^{2} \cdot t_2\right)} + \frac{y \cdot x}{t_9}\right)\right) - \frac{z}{t_9}\right)\right)\right)\right)\\ \mathbf{elif}\;y \leq 1.38 \cdot 10^{+42}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot t_4\right)}{t_7 + i}\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

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 (* y (+ z (* y x))))
        (t_2 (+ b (* y (+ y a))))
        (t_3 (+ x (- (/ z y) (* x (/ a y)))))
        (t_4 (+ 27464.7644705 t_1))
        (t_5 (* y t_2))
        (t_6 (+ c t_5))
        (t_7 (* y t_6))
        (t_8 (* t_6 t_6))
        (t_9 (* t_2 t_2)))
   (if (<= y -1.22e+89)
     t_3
     (if (<= y -480000000.0)
       (+
        (/ t t_7)
        (+
         (*
          i
          (-
           (-
            (* 230661.510616 (/ -1.0 (* y t_8)))
            (+ (* 27464.7644705 (/ 1.0 t_8)) (/ t_1 t_8)))
           (/ t (* (pow y 2.0) t_8))))
         (+
          (/ t_4 t_2)
          (+
           (* 230661.510616 (/ 1.0 t_5))
           (*
            c
            (-
             (-
              (* (/ 1.0 (* t_5 t_2)) -27464.7644705)
              (+
               (* 230661.510616 (/ 1.0 (* t_2 (* (pow y 2.0) t_2))))
               (/ (* y x) t_9)))
             (/ z t_9)))))))
       (if (<= y 1.38e+42)
         (/ (+ t (* y (+ 230661.510616 (* y t_4)))) (+ t_7 i))
         t_3)))))

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 = y * (z + (y * x));
	double t_2 = b + (y * (y + a));
	double t_3 = x + ((z / y) - (x * (a / y)));
	double t_4 = 27464.7644705 + t_1;
	double t_5 = y * t_2;
	double t_6 = c + t_5;
	double t_7 = y * t_6;
	double t_8 = t_6 * t_6;
	double t_9 = t_2 * t_2;
	double tmp;
	if (y <= -1.22e+89) {
		tmp = t_3;
	} else if (y <= -480000000.0) {
		tmp = (t / t_7) + ((i * (((230661.510616 * (-1.0 / (y * t_8))) - ((27464.7644705 * (1.0 / t_8)) + (t_1 / t_8))) - (t / (pow(y, 2.0) * t_8)))) + ((t_4 / t_2) + ((230661.510616 * (1.0 / t_5)) + (c * ((((1.0 / (t_5 * t_2)) * -27464.7644705) - ((230661.510616 * (1.0 / (t_2 * (pow(y, 2.0) * t_2)))) + ((y * x) / t_9))) - (z / t_9))))));
	} else if (y <= 1.38e+42) {
		tmp = (t + (y * (230661.510616 + (y * t_4)))) / (t_7 + i);
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    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) :: t_6
    real(8) :: t_7
    real(8) :: t_8
    real(8) :: t_9
    real(8) :: tmp
    t_1 = y * (z + (y * x))
    t_2 = b + (y * (y + a))
    t_3 = x + ((z / y) - (x * (a / y)))
    t_4 = 27464.7644705d0 + t_1
    t_5 = y * t_2
    t_6 = c + t_5
    t_7 = y * t_6
    t_8 = t_6 * t_6
    t_9 = t_2 * t_2
    if (y <= (-1.22d+89)) then
        tmp = t_3
    else if (y <= (-480000000.0d0)) then
        tmp = (t / t_7) + ((i * (((230661.510616d0 * ((-1.0d0) / (y * t_8))) - ((27464.7644705d0 * (1.0d0 / t_8)) + (t_1 / t_8))) - (t / ((y ** 2.0d0) * t_8)))) + ((t_4 / t_2) + ((230661.510616d0 * (1.0d0 / t_5)) + (c * ((((1.0d0 / (t_5 * t_2)) * (-27464.7644705d0)) - ((230661.510616d0 * (1.0d0 / (t_2 * ((y ** 2.0d0) * t_2)))) + ((y * x) / t_9))) - (z / t_9))))))
    else if (y <= 1.38d+42) then
        tmp = (t + (y * (230661.510616d0 + (y * t_4)))) / (t_7 + i)
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	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 = y * (z + (y * x));
	double t_2 = b + (y * (y + a));
	double t_3 = x + ((z / y) - (x * (a / y)));
	double t_4 = 27464.7644705 + t_1;
	double t_5 = y * t_2;
	double t_6 = c + t_5;
	double t_7 = y * t_6;
	double t_8 = t_6 * t_6;
	double t_9 = t_2 * t_2;
	double tmp;
	if (y <= -1.22e+89) {
		tmp = t_3;
	} else if (y <= -480000000.0) {
		tmp = (t / t_7) + ((i * (((230661.510616 * (-1.0 / (y * t_8))) - ((27464.7644705 * (1.0 / t_8)) + (t_1 / t_8))) - (t / (Math.pow(y, 2.0) * t_8)))) + ((t_4 / t_2) + ((230661.510616 * (1.0 / t_5)) + (c * ((((1.0 / (t_5 * t_2)) * -27464.7644705) - ((230661.510616 * (1.0 / (t_2 * (Math.pow(y, 2.0) * t_2)))) + ((y * x) / t_9))) - (z / t_9))))));
	} else if (y <= 1.38e+42) {
		tmp = (t + (y * (230661.510616 + (y * t_4)))) / (t_7 + i);
	} else {
		tmp = t_3;
	}
	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 = y * (z + (y * x))
	t_2 = b + (y * (y + a))
	t_3 = x + ((z / y) - (x * (a / y)))
	t_4 = 27464.7644705 + t_1
	t_5 = y * t_2
	t_6 = c + t_5
	t_7 = y * t_6
	t_8 = t_6 * t_6
	t_9 = t_2 * t_2
	tmp = 0
	if y <= -1.22e+89:
		tmp = t_3
	elif y <= -480000000.0:
		tmp = (t / t_7) + ((i * (((230661.510616 * (-1.0 / (y * t_8))) - ((27464.7644705 * (1.0 / t_8)) + (t_1 / t_8))) - (t / (math.pow(y, 2.0) * t_8)))) + ((t_4 / t_2) + ((230661.510616 * (1.0 / t_5)) + (c * ((((1.0 / (t_5 * t_2)) * -27464.7644705) - ((230661.510616 * (1.0 / (t_2 * (math.pow(y, 2.0) * t_2)))) + ((y * x) / t_9))) - (z / t_9))))))
	elif y <= 1.38e+42:
		tmp = (t + (y * (230661.510616 + (y * t_4)))) / (t_7 + i)
	else:
		tmp = t_3
	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(y * Float64(z + Float64(y * x)))
	t_2 = Float64(b + Float64(y * Float64(y + a)))
	t_3 = Float64(x + Float64(Float64(z / y) - Float64(x * Float64(a / y))))
	t_4 = Float64(27464.7644705 + t_1)
	t_5 = Float64(y * t_2)
	t_6 = Float64(c + t_5)
	t_7 = Float64(y * t_6)
	t_8 = Float64(t_6 * t_6)
	t_9 = Float64(t_2 * t_2)
	tmp = 0.0
	if (y <= -1.22e+89)
		tmp = t_3;
	elseif (y <= -480000000.0)
		tmp = Float64(Float64(t / t_7) + 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_1 / t_8))) - Float64(t / Float64((y ^ 2.0) * t_8)))) + Float64(Float64(t_4 / t_2) + Float64(Float64(230661.510616 * Float64(1.0 / t_5)) + Float64(c * Float64(Float64(Float64(Float64(1.0 / Float64(t_5 * t_2)) * -27464.7644705) - Float64(Float64(230661.510616 * Float64(1.0 / Float64(t_2 * Float64((y ^ 2.0) * t_2)))) + Float64(Float64(y * x) / t_9))) - Float64(z / t_9)))))));
	elseif (y <= 1.38e+42)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * t_4)))) / Float64(t_7 + i));
	else
		tmp = t_3;
	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 = y * (z + (y * x));
	t_2 = b + (y * (y + a));
	t_3 = x + ((z / y) - (x * (a / y)));
	t_4 = 27464.7644705 + t_1;
	t_5 = y * t_2;
	t_6 = c + t_5;
	t_7 = y * t_6;
	t_8 = t_6 * t_6;
	t_9 = t_2 * t_2;
	tmp = 0.0;
	if (y <= -1.22e+89)
		tmp = t_3;
	elseif (y <= -480000000.0)
		tmp = (t / t_7) + ((i * (((230661.510616 * (-1.0 / (y * t_8))) - ((27464.7644705 * (1.0 / t_8)) + (t_1 / t_8))) - (t / ((y ^ 2.0) * t_8)))) + ((t_4 / t_2) + ((230661.510616 * (1.0 / t_5)) + (c * ((((1.0 / (t_5 * t_2)) * -27464.7644705) - ((230661.510616 * (1.0 / (t_2 * ((y ^ 2.0) * t_2)))) + ((y * x) / t_9))) - (z / t_9))))));
	elseif (y <= 1.38e+42)
		tmp = (t + (y * (230661.510616 + (y * t_4)))) / (t_7 + i);
	else
		tmp = t_3;
	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[(y * N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x + N[(N[(z / y), $MachinePrecision] - N[(x * N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(27464.7644705 + t$95$1), $MachinePrecision]}, Block[{t$95$5 = N[(y * t$95$2), $MachinePrecision]}, Block[{t$95$6 = N[(c + t$95$5), $MachinePrecision]}, Block[{t$95$7 = N[(y * t$95$6), $MachinePrecision]}, Block[{t$95$8 = N[(t$95$6 * t$95$6), $MachinePrecision]}, Block[{t$95$9 = N[(t$95$2 * t$95$2), $MachinePrecision]}, If[LessEqual[y, -1.22e+89], t$95$3, If[LessEqual[y, -480000000.0], N[(N[(t / t$95$7), $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$1 / 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$2), $MachinePrecision] + N[(N[(230661.510616 * N[(1.0 / t$95$5), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(N[(N[(1.0 / N[(t$95$5 * t$95$2), $MachinePrecision]), $MachinePrecision] * -27464.7644705), $MachinePrecision] - N[(N[(230661.510616 * N[(1.0 / N[(t$95$2 * N[(N[Power[y, 2.0], $MachinePrecision] * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y * x), $MachinePrecision] / t$95$9), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z / t$95$9), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.38e+42], N[(N[(t + N[(y * N[(230661.510616 + N[(y * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t$95$7 + i), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.22e89 or 1.3800000000000001e42 < y

   1. Initial program 62.2

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

   2. Applied egg-rr 62.2

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

   3. Taylor expanded in y around inf 20.2

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

   4. Simplified 16.9

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

      [Start] 20.2	\[ \left(\frac{z}{y} + x\right) - \frac{a \cdot x}{y} \]
      +-commutative [=>] 20.2	\[ \color{blue}{\left(x + \frac{z}{y}\right)} - \frac{a \cdot x}{y} \]
      associate--l+ [=>] 20.2	\[ \color{blue}{x + \left(\frac{z}{y} - \frac{a \cdot x}{y}\right)} \]
      associate-/l* [=>] 16.9	\[ x + \left(\frac{z}{y} - \color{blue}{\frac{a}{\frac{y}{x}}}\right) \]
      associate-/r/ [=>] 16.9	\[ x + \left(\frac{z}{y} - \color{blue}{\frac{a}{y} \cdot x}\right) \]

   if -1.22e89 < y < -4.8e8

   1. Initial program 41.5

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

   2. Taylor expanded in i around 0 35.9

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

   3. Taylor expanded in c around 0 32.1

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

   if -4.8e8 < y < 1.3800000000000001e42

   1. Initial program 2.0

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

4. Final simplification 10.0

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.22 \cdot 10^{+89}:\\ \;\;\;\;x + \left(\frac{z}{y} - x \cdot \frac{a}{y}\right)\\ \mathbf{elif}\;y \leq -480000000:\\ \;\;\;\;\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(\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)} \cdot -27464.7644705 - \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 1.38 \cdot 10^{+42}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) + i}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - x \cdot \frac{a}{y}\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	10.6
Cost	15880

\[\begin{array}{l} t_1 := 27464.7644705 + y \cdot \left(z + y \cdot x\right)\\ t_2 := x + \left(\frac{z}{y} - x \cdot \frac{a}{y}\right)\\ t_3 := b + y \cdot \left(y + a\right)\\ t_4 := y \cdot t_3\\ t_5 := y \cdot \left(c + t_4\right)\\ t_6 := t_3 \cdot t_3\\ \mathbf{if}\;y \leq -4.9 \cdot 10^{+86}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -8.2 \cdot 10^{+24}:\\ \;\;\;\;\frac{t}{t_5} + \left(\left(\frac{t_1}{t_3} + \left(230661.510616 \cdot \frac{1}{t_4} + c \cdot \left(\left(\frac{1}{t_4 \cdot t_3} \cdot -27464.7644705 - \left(230661.510616 \cdot \frac{1}{t_3 \cdot \left({y}^{2} \cdot t_3\right)} + \frac{y \cdot x}{t_6}\right)\right) - \frac{z}{t_6}\right)\right)\right) - \frac{\frac{t \cdot i}{c \cdot c}}{y \cdot y}\right)\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+43}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot t_1\right)}{t_5 + i}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 2
Error	10.3
Cost	4808

\[\begin{array}{l} t_1 := 230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\\ t_2 := c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\\ t_3 := y \cdot t_2\\ t_4 := x + \left(\frac{z}{y} - x \cdot \frac{a}{y}\right)\\ \mathbf{if}\;y \leq -4.9 \cdot 10^{+86}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{+20}:\\ \;\;\;\;\frac{t}{t_3} + \left(\frac{t_1}{t_2} - \frac{y \cdot \left(z \cdot i\right)}{t_2 \cdot t_2}\right)\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+42}:\\ \;\;\;\;\frac{t + y \cdot t_1}{t_3 + i}\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 3
Error	10.3
Cost	4292

\[\begin{array}{l} t_1 := \frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) + i}\\ \mathbf{if}\;t_1 \leq 4 \cdot 10^{+290}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - x \cdot \frac{a}{y}\right)\\ \end{array} \]

Alternative 4
Error	10.6
Cost	3784

\[\begin{array}{l} t_1 := 230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\\ t_2 := c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\\ t_3 := y \cdot t_2\\ t_4 := \frac{t}{t_3}\\ t_5 := x + \left(\frac{z}{y} - x \cdot \frac{a}{y}\right)\\ \mathbf{if}\;y \leq -7.5 \cdot 10^{+86}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{+42}:\\ \;\;\;\;t_4 + \left(\frac{t_1}{t_2} + \frac{\frac{t}{\frac{c}{i}} \cdot \frac{-1}{c}}{y \cdot y}\right)\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{+42}:\\ \;\;\;\;t_4 + \left(x - \frac{\frac{t \cdot i}{c \cdot c}}{y \cdot y}\right)\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{+43}:\\ \;\;\;\;\frac{t + y \cdot t_1}{t_3 + i}\\ \mathbf{else}:\\ \;\;\;\;t_5\\ \end{array} \]

Alternative 5
Error	10.6
Cost	3656

\[\begin{array}{l} t_1 := 230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\\ t_2 := c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\\ t_3 := y \cdot t_2\\ t_4 := \frac{t}{t_3}\\ t_5 := x + \left(\frac{z}{y} - x \cdot \frac{a}{y}\right)\\ t_6 := \frac{\frac{t \cdot i}{c \cdot c}}{y \cdot y}\\ \mathbf{if}\;y \leq -4.9 \cdot 10^{+86}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{+42}:\\ \;\;\;\;t_4 + \left(\frac{t_1}{t_2} - t_6\right)\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{+42}:\\ \;\;\;\;t_4 + \left(x - t_6\right)\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+43}:\\ \;\;\;\;\frac{t + y \cdot t_1}{t_3 + i}\\ \mathbf{else}:\\ \;\;\;\;t_5\\ \end{array} \]

Alternative 6
Error	13.4
Cost	2249

\[\begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+75} \lor \neg \left(y \leq 7 \cdot 10^{+42}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - x \cdot \frac{a}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + x \cdot \left(y \cdot y\right)\right)\right)}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) + i}\\ \end{array} \]

Alternative 7
Error	16.3
Cost	1996

\[\begin{array}{l} t_1 := x + \left(\frac{z}{y} - x \cdot \frac{a}{y}\right)\\ \mathbf{if}\;y \leq -6 \cdot 10^{+89}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -0.72:\\ \;\;\;\;\frac{z}{a} + \frac{y \cdot x}{a}\\ \mathbf{elif}\;y \leq 0.054:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) + i}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 8
Error	13.0
Cost	1993

\[\begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+35} \lor \neg \left(y \leq 1.5 \cdot 10^{+39}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - x \cdot \frac{a}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + z \cdot \left(y \cdot y\right)\right)}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) + i}\\ \end{array} \]

Alternative 9
Error	18.8
Cost	1876

\[\begin{array}{l} t_1 := x + \left(\frac{z}{y} - x \cdot \frac{a}{y}\right)\\ \mathbf{if}\;y \leq -3.3 \cdot 10^{+87}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -0.00036:\\ \;\;\;\;\frac{z}{a} + \frac{y \cdot x}{a}\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{-139}:\\ \;\;\;\;\frac{t}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) + i}\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+35}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + z \cdot \left(y \cdot y\right)\right)}{i + y \cdot c}\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+148}:\\ \;\;\;\;\frac{z}{y} + \left(\left(x + \frac{27464.7644705}{y \cdot y}\right) - \frac{x \cdot b}{y \cdot y}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 10
Error	16.3
Cost	1740

\[\begin{array}{l} t_1 := x + \left(\frac{z}{y} - x \cdot \frac{a}{y}\right)\\ \mathbf{if}\;y \leq -4.8 \cdot 10^{+87}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -0.72:\\ \;\;\;\;\frac{z}{a} + \frac{y \cdot x}{a}\\ \mathbf{elif}\;y \leq 0.054:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) + i}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 11
Error	16.2
Cost	1740

\[\begin{array}{l} t_1 := x + \left(\frac{z}{y} - x \cdot \frac{a}{y}\right)\\ \mathbf{if}\;y \leq -2.4 \cdot 10^{+86}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-13}:\\ \;\;\;\;\frac{\frac{230661.510616}{a}}{y \cdot y} + \left(\frac{27464.7644705}{y \cdot a} + \left(\frac{z}{a} + \frac{y}{\frac{a}{x}}\right)\right)\\ \mathbf{elif}\;y \leq 0.054:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) + i}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 12
Error	19.6
Cost	1484

\[\begin{array}{l} t_1 := x + \left(\frac{z}{y} - x \cdot \frac{a}{y}\right)\\ \mathbf{if}\;y \leq -4.8 \cdot 10^{+87}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -0.00036:\\ \;\;\;\;\frac{z}{a} + \frac{y \cdot x}{a}\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{-139}:\\ \;\;\;\;\frac{t}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) + i}\\ \mathbf{elif}\;y \leq 0.0125:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 13
Error	18.6
Cost	1484

\[\begin{array}{l} t_1 := x + \left(\frac{z}{y} - x \cdot \frac{a}{y}\right)\\ \mathbf{if}\;y \leq -1.12 \cdot 10^{+92}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -3.35 \cdot 10^{-12}:\\ \;\;\;\;\frac{z}{a} + \frac{y \cdot x}{a}\\ \mathbf{elif}\;y \leq 0.054:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot \left(y \cdot a\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 14
Error	18.6
Cost	1484

\[\begin{array}{l} t_1 := x + \left(\frac{z}{y} - x \cdot \frac{a}{y}\right)\\ \mathbf{if}\;y \leq -3.15 \cdot 10^{+87}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.62 \cdot 10^{-12}:\\ \;\;\;\;\frac{z}{a} + \frac{y \cdot x}{a}\\ \mathbf{elif}\;y \leq 0.029:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + a \cdot \left(y \cdot y\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 15
Error	25.9
Cost	1100

\[\begin{array}{l} t_1 := x + \left(\frac{z}{y} - x \cdot \frac{a}{y}\right)\\ \mathbf{if}\;y \leq -8 \cdot 10^{+91}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -3.3 \cdot 10^{-12}:\\ \;\;\;\;\frac{z}{a} + \frac{y \cdot x}{a}\\ \mathbf{elif}\;y \leq 0.0005:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 16
Error	19.4
Cost	1100

\[\begin{array}{l} t_1 := x + \left(\frac{z}{y} - x \cdot \frac{a}{y}\right)\\ \mathbf{if}\;y \leq -5.2 \cdot 10^{+86}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -8 \cdot 10^{-13}:\\ \;\;\;\;\frac{z}{a} + \frac{y \cdot x}{a}\\ \mathbf{elif}\;y \leq 0.05:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 17
Error	27.1
Cost	972

\[\begin{array}{l} t_1 := x + \frac{z - x \cdot a}{y}\\ \mathbf{if}\;y \leq -1.95 \cdot 10^{+98}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{-14}:\\ \;\;\;\;\frac{z}{a} + \frac{y \cdot x}{a}\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-5}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 18
Error	27.0
Cost	841

\[\begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{-6} \lor \neg \left(y \leq 0.022\right):\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \end{array} \]

Alternative 19
Error	32.4
Cost	716

\[\begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{-7}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.66 \cdot 10^{-18}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+97}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 20
Error	32.4
Cost	716

\[\begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{-6}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-18}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{+94}:\\ \;\;\;\;\frac{y \cdot x}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 21
Error	30.3
Cost	716

\[\begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{-12}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-16}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+93}:\\ \;\;\;\;\frac{y \cdot x}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 22
Error	32.4
Cost	456

\[\begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{-10}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.35 \cdot 10^{-8}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 23
Error	47.1
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023016 
(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)))