Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, C

Average Accuracy: 58.2% → 98.2%

Time: 27.3s

Precision: binary64

Cost: 11145

Math

\[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

↓

\[\begin{array}{l} t_0 := x \cdot \left(313.399215894 + x \cdot \left(263.505074721 + x \cdot \left(x + 43.3400022514\right)\right)\right) + 47.066876606\\ \mathbf{if}\;x \leq -1.7 \cdot 10^{+38} \lor \neg \left(x \leq 1000000000000\right):\\ \;\;\;\;\left(x + -2\right) \cdot \left(\frac{-101.7851458539211}{x} - \left(\frac{124074.40615218398 - y}{{x}^{3}} + \left(-4.16438922228 - \frac{\frac{3451.550173699799}{x}}{x}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(\frac{x \cdot y}{t_0} - \left(\frac{{x}^{2} \cdot \left(x \cdot \left(x \cdot -4.16438922228 + -78.6994924154\right) + -137.519416416\right)}{t_0} - \frac{z}{t_0}\right)\right)\\ \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (/
  (*
   (- x 2.0)
   (+
    (*
     (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y)
     x)
    z))
  (+
   (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x)
   47.066876606)))

↓

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (+
          (*
           x
           (+ 313.399215894 (* x (+ 263.505074721 (* x (+ x 43.3400022514))))))
          47.066876606)))
   (if (or (<= x -1.7e+38) (not (<= x 1000000000000.0)))
     (*
      (+ x -2.0)
      (-
       (/ -101.7851458539211 x)
       (+
        (/ (- 124074.40615218398 y) (pow x 3.0))
        (- -4.16438922228 (/ (/ 3451.550173699799 x) x)))))
     (*
      (+ x -2.0)
      (-
       (/ (* x y) t_0)
       (-
        (/
         (*
          (pow x 2.0)
          (+ (* x (+ (* x -4.16438922228) -78.6994924154)) -137.519416416))
         t_0)
        (/ z t_0)))))))

C

double code(double x, double y, double z) {
	return ((x - 2.0) * ((((((((x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z)) / (((((((x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606);
}

↓

double code(double x, double y, double z) {
	double t_0 = (x * (313.399215894 + (x * (263.505074721 + (x * (x + 43.3400022514)))))) + 47.066876606;
	double tmp;
	if ((x <= -1.7e+38) || !(x <= 1000000000000.0)) {
		tmp = (x + -2.0) * ((-101.7851458539211 / x) - (((124074.40615218398 - y) / pow(x, 3.0)) + (-4.16438922228 - ((3451.550173699799 / x) / x))));
	} else {
		tmp = (x + -2.0) * (((x * y) / t_0) - (((pow(x, 2.0) * ((x * ((x * -4.16438922228) + -78.6994924154)) + -137.519416416)) / t_0) - (z / t_0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = ((x - 2.0d0) * ((((((((x * 4.16438922228d0) + 78.6994924154d0) * x) + 137.519416416d0) * x) + y) * x) + z)) / (((((((x + 43.3400022514d0) * x) + 263.505074721d0) * x) + 313.399215894d0) * x) + 47.066876606d0)
end function

↓

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (x * (313.399215894d0 + (x * (263.505074721d0 + (x * (x + 43.3400022514d0)))))) + 47.066876606d0
    if ((x <= (-1.7d+38)) .or. (.not. (x <= 1000000000000.0d0))) then
        tmp = (x + (-2.0d0)) * (((-101.7851458539211d0) / x) - (((124074.40615218398d0 - y) / (x ** 3.0d0)) + ((-4.16438922228d0) - ((3451.550173699799d0 / x) / x))))
    else
        tmp = (x + (-2.0d0)) * (((x * y) / t_0) - ((((x ** 2.0d0) * ((x * ((x * (-4.16438922228d0)) + (-78.6994924154d0))) + (-137.519416416d0))) / t_0) - (z / t_0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	return ((x - 2.0) * ((((((((x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z)) / (((((((x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606);
}

↓

public static double code(double x, double y, double z) {
	double t_0 = (x * (313.399215894 + (x * (263.505074721 + (x * (x + 43.3400022514)))))) + 47.066876606;
	double tmp;
	if ((x <= -1.7e+38) || !(x <= 1000000000000.0)) {
		tmp = (x + -2.0) * ((-101.7851458539211 / x) - (((124074.40615218398 - y) / Math.pow(x, 3.0)) + (-4.16438922228 - ((3451.550173699799 / x) / x))));
	} else {
		tmp = (x + -2.0) * (((x * y) / t_0) - (((Math.pow(x, 2.0) * ((x * ((x * -4.16438922228) + -78.6994924154)) + -137.519416416)) / t_0) - (z / t_0)));
	}
	return tmp;
}

Python

def code(x, y, z):
	return ((x - 2.0) * ((((((((x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z)) / (((((((x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606)

↓

def code(x, y, z):
	t_0 = (x * (313.399215894 + (x * (263.505074721 + (x * (x + 43.3400022514)))))) + 47.066876606
	tmp = 0
	if (x <= -1.7e+38) or not (x <= 1000000000000.0):
		tmp = (x + -2.0) * ((-101.7851458539211 / x) - (((124074.40615218398 - y) / math.pow(x, 3.0)) + (-4.16438922228 - ((3451.550173699799 / x) / x))))
	else:
		tmp = (x + -2.0) * (((x * y) / t_0) - (((math.pow(x, 2.0) * ((x * ((x * -4.16438922228) + -78.6994924154)) + -137.519416416)) / t_0) - (z / t_0)))
	return tmp

Julia

function code(x, y, z)
	return Float64(Float64(Float64(x - 2.0) * Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z)) / Float64(Float64(Float64(Float64(Float64(Float64(Float64(x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606))
end

↓

function code(x, y, z)
	t_0 = Float64(Float64(x * Float64(313.399215894 + Float64(x * Float64(263.505074721 + Float64(x * Float64(x + 43.3400022514)))))) + 47.066876606)
	tmp = 0.0
	if ((x <= -1.7e+38) || !(x <= 1000000000000.0))
		tmp = Float64(Float64(x + -2.0) * Float64(Float64(-101.7851458539211 / x) - Float64(Float64(Float64(124074.40615218398 - y) / (x ^ 3.0)) + Float64(-4.16438922228 - Float64(Float64(3451.550173699799 / x) / x)))));
	else
		tmp = Float64(Float64(x + -2.0) * Float64(Float64(Float64(x * y) / t_0) - Float64(Float64(Float64((x ^ 2.0) * Float64(Float64(x * Float64(Float64(x * -4.16438922228) + -78.6994924154)) + -137.519416416)) / t_0) - Float64(z / t_0))));
	end
	return tmp
end

MATLAB

function tmp = code(x, y, z)
	tmp = ((x - 2.0) * ((((((((x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z)) / (((((((x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606);
end

↓

function tmp_2 = code(x, y, z)
	t_0 = (x * (313.399215894 + (x * (263.505074721 + (x * (x + 43.3400022514)))))) + 47.066876606;
	tmp = 0.0;
	if ((x <= -1.7e+38) || ~((x <= 1000000000000.0)))
		tmp = (x + -2.0) * ((-101.7851458539211 / x) - (((124074.40615218398 - y) / (x ^ 3.0)) + (-4.16438922228 - ((3451.550173699799 / x) / x))));
	else
		tmp = (x + -2.0) * (((x * y) / t_0) - ((((x ^ 2.0) * ((x * ((x * -4.16438922228) + -78.6994924154)) + -137.519416416)) / t_0) - (z / t_0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := N[(N[(N[(x - 2.0), $MachinePrecision] * N[(N[(N[(N[(N[(N[(N[(N[(x * 4.16438922228), $MachinePrecision] + 78.6994924154), $MachinePrecision] * x), $MachinePrecision] + 137.519416416), $MachinePrecision] * x), $MachinePrecision] + y), $MachinePrecision] * x), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(N[(N[(N[(N[(x + 43.3400022514), $MachinePrecision] * x), $MachinePrecision] + 263.505074721), $MachinePrecision] * x), $MachinePrecision] + 313.399215894), $MachinePrecision] * x), $MachinePrecision] + 47.066876606), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x * N[(313.399215894 + N[(x * N[(263.505074721 + N[(x * N[(x + 43.3400022514), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 47.066876606), $MachinePrecision]}, If[Or[LessEqual[x, -1.7e+38], N[Not[LessEqual[x, 1000000000000.0]], $MachinePrecision]], N[(N[(x + -2.0), $MachinePrecision] * N[(N[(-101.7851458539211 / x), $MachinePrecision] - N[(N[(N[(124074.40615218398 - y), $MachinePrecision] / N[Power[x, 3.0], $MachinePrecision]), $MachinePrecision] + N[(-4.16438922228 - N[(N[(3451.550173699799 / x), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + -2.0), $MachinePrecision] * N[(N[(N[(x * y), $MachinePrecision] / t$95$0), $MachinePrecision] - N[(N[(N[(N[Power[x, 2.0], $MachinePrecision] * N[(N[(x * N[(N[(x * -4.16438922228), $MachinePrecision] + -78.6994924154), $MachinePrecision]), $MachinePrecision] + -137.519416416), $MachinePrecision]), $MachinePrecision] / t$95$0), $MachinePrecision] - N[(z / t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Target

Original	58.2%
Target	98.8%
Herbie	98.2%

\[\begin{array}{l} \mathbf{if}\;x < -3.326128725870005 \cdot 10^{+62}:\\ \;\;\;\;\left(\frac{y}{x \cdot x} + 4.16438922228 \cdot x\right) - 110.1139242984811\\ \mathbf{elif}\;x < 9.429991714554673 \cdot 10^{+55}:\\ \;\;\;\;\frac{x - 2}{1} \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(263.505074721 \cdot x + \left(43.3400022514 \cdot \left(x \cdot x\right) + x \cdot \left(x \cdot x\right)\right)\right) + 313.399215894\right) \cdot x + 47.066876606}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{y}{x \cdot x} + 4.16438922228 \cdot x\right) - 110.1139242984811\\ \end{array} \]

Derivation

1. Split input into 2 regimes

2. if x < -1.69999999999999998e38 or 1e12 < x

   1. Initial program 9.8%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

   2. Simplified 16.7%

      \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + 43.3400022514, 263.505074721\right), 313.399215894\right), 47.066876606\right)}} \]
      Proof

      [Start] 9.8	\[ \frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
      associate-*r/ [<=] 16.7	\[ \color{blue}{\left(x - 2\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}} \]
      sub-neg [=>] 16.7	\[ \color{blue}{\left(x + \left(-2\right)\right)} \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
      metadata-eval [=>] 16.7	\[ \left(x + \color{blue}{-2}\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
      *-commutative [=>] 16.7	\[ \left(x + -2\right) \cdot \frac{\color{blue}{x \cdot \left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right)} + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
      fma-def [=>] 16.7	\[ \left(x + -2\right) \cdot \frac{\color{blue}{\mathsf{fma}\left(x, \left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y, z\right)}}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
      *-commutative [=>] 16.7	\[ \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(x, \color{blue}{x \cdot \left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right)} + y, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
      fma-def [=>] 16.7	\[ \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(x, \color{blue}{\mathsf{fma}\left(x, \left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416, y\right)}, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
      *-commutative [=>] 16.7	\[ \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \color{blue}{x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right)} + 137.519416416, y\right), z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
      fma-def [=>] 16.7	\[ \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \color{blue}{\mathsf{fma}\left(x, x \cdot 4.16438922228 + 78.6994924154, 137.519416416\right)}, y\right), z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
      fma-def [=>] 16.7	\[ \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \color{blue}{\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right)}, 137.519416416\right), y\right), z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
      *-commutative [=>] 16.7	\[ \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right)}{\color{blue}{x \cdot \left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right)} + 47.066876606} \]

   3. Taylor expanded in x around -inf 96.6%

      \[\leadsto \left(x + -2\right) \cdot \color{blue}{\left(\left(-1 \cdot \frac{124074.40615218398 + -1 \cdot y}{{x}^{3}} + \left(4.16438922228 + 3451.550173699799 \cdot \frac{1}{{x}^{2}}\right)\right) - 101.7851458539211 \cdot \frac{1}{x}\right)} \]

   4. Simplified 96.6%

      \[\leadsto \left(x + -2\right) \cdot \color{blue}{\left(\left(\left(4.16438922228 + \frac{\frac{3451.550173699799}{x}}{x}\right) - \frac{124074.40615218398 - y}{{x}^{3}}\right) + \frac{-101.7851458539211}{x}\right)} \]
      Proof

      [Start] 96.6	\[ \left(x + -2\right) \cdot \left(\left(-1 \cdot \frac{124074.40615218398 + -1 \cdot y}{{x}^{3}} + \left(4.16438922228 + 3451.550173699799 \cdot \frac{1}{{x}^{2}}\right)\right) - 101.7851458539211 \cdot \frac{1}{x}\right) \]
      cancel-sign-sub-inv [=>] 96.6	\[ \left(x + -2\right) \cdot \color{blue}{\left(\left(-1 \cdot \frac{124074.40615218398 + -1 \cdot y}{{x}^{3}} + \left(4.16438922228 + 3451.550173699799 \cdot \frac{1}{{x}^{2}}\right)\right) + \left(-101.7851458539211\right) \cdot \frac{1}{x}\right)} \]
      +-commutative [=>] 96.6	\[ \left(x + -2\right) \cdot \left(\color{blue}{\left(\left(4.16438922228 + 3451.550173699799 \cdot \frac{1}{{x}^{2}}\right) + -1 \cdot \frac{124074.40615218398 + -1 \cdot y}{{x}^{3}}\right)} + \left(-101.7851458539211\right) \cdot \frac{1}{x}\right) \]
      mul-1-neg [=>] 96.6	\[ \left(x + -2\right) \cdot \left(\left(\left(4.16438922228 + 3451.550173699799 \cdot \frac{1}{{x}^{2}}\right) + \color{blue}{\left(-\frac{124074.40615218398 + -1 \cdot y}{{x}^{3}}\right)}\right) + \left(-101.7851458539211\right) \cdot \frac{1}{x}\right) \]
      unsub-neg [=>] 96.6	\[ \left(x + -2\right) \cdot \left(\color{blue}{\left(\left(4.16438922228 + 3451.550173699799 \cdot \frac{1}{{x}^{2}}\right) - \frac{124074.40615218398 + -1 \cdot y}{{x}^{3}}\right)} + \left(-101.7851458539211\right) \cdot \frac{1}{x}\right) \]
      associate-*r/ [=>] 96.6	\[ \left(x + -2\right) \cdot \left(\left(\left(4.16438922228 + \color{blue}{\frac{3451.550173699799 \cdot 1}{{x}^{2}}}\right) - \frac{124074.40615218398 + -1 \cdot y}{{x}^{3}}\right) + \left(-101.7851458539211\right) \cdot \frac{1}{x}\right) \]
      metadata-eval [=>] 96.6	\[ \left(x + -2\right) \cdot \left(\left(\left(4.16438922228 + \frac{\color{blue}{3451.550173699799}}{{x}^{2}}\right) - \frac{124074.40615218398 + -1 \cdot y}{{x}^{3}}\right) + \left(-101.7851458539211\right) \cdot \frac{1}{x}\right) \]
      unpow2 [=>] 96.6	\[ \left(x + -2\right) \cdot \left(\left(\left(4.16438922228 + \frac{3451.550173699799}{\color{blue}{x \cdot x}}\right) - \frac{124074.40615218398 + -1 \cdot y}{{x}^{3}}\right) + \left(-101.7851458539211\right) \cdot \frac{1}{x}\right) \]
      associate-/r* [=>] 96.6	\[ \left(x + -2\right) \cdot \left(\left(\left(4.16438922228 + \color{blue}{\frac{\frac{3451.550173699799}{x}}{x}}\right) - \frac{124074.40615218398 + -1 \cdot y}{{x}^{3}}\right) + \left(-101.7851458539211\right) \cdot \frac{1}{x}\right) \]
      mul-1-neg [=>] 96.6	\[ \left(x + -2\right) \cdot \left(\left(\left(4.16438922228 + \frac{\frac{3451.550173699799}{x}}{x}\right) - \frac{124074.40615218398 + \color{blue}{\left(-y\right)}}{{x}^{3}}\right) + \left(-101.7851458539211\right) \cdot \frac{1}{x}\right) \]
      unsub-neg [=>] 96.6	\[ \left(x + -2\right) \cdot \left(\left(\left(4.16438922228 + \frac{\frac{3451.550173699799}{x}}{x}\right) - \frac{\color{blue}{124074.40615218398 - y}}{{x}^{3}}\right) + \left(-101.7851458539211\right) \cdot \frac{1}{x}\right) \]
      associate-*r/ [=>] 96.6	\[ \left(x + -2\right) \cdot \left(\left(\left(4.16438922228 + \frac{\frac{3451.550173699799}{x}}{x}\right) - \frac{124074.40615218398 - y}{{x}^{3}}\right) + \color{blue}{\frac{\left(-101.7851458539211\right) \cdot 1}{x}}\right) \]
      metadata-eval [=>] 96.6	\[ \left(x + -2\right) \cdot \left(\left(\left(4.16438922228 + \frac{\frac{3451.550173699799}{x}}{x}\right) - \frac{124074.40615218398 - y}{{x}^{3}}\right) + \frac{\color{blue}{-101.7851458539211} \cdot 1}{x}\right) \]
      metadata-eval [=>] 96.6	\[ \left(x + -2\right) \cdot \left(\left(\left(4.16438922228 + \frac{\frac{3451.550173699799}{x}}{x}\right) - \frac{124074.40615218398 - y}{{x}^{3}}\right) + \frac{\color{blue}{-101.7851458539211}}{x}\right) \]

   if -1.69999999999999998e38 < x < 1e12

   1. Initial program 99.0%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

   2. Simplified 99.5%

      \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + 43.3400022514, 263.505074721\right), 313.399215894\right), 47.066876606\right)}} \]
      Proof

      [Start] 99.0	\[ \frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
      associate-*r/ [<=] 99.5	\[ \color{blue}{\left(x - 2\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}} \]
      sub-neg [=>] 99.5	\[ \color{blue}{\left(x + \left(-2\right)\right)} \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
      metadata-eval [=>] 99.5	\[ \left(x + \color{blue}{-2}\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
      *-commutative [=>] 99.5	\[ \left(x + -2\right) \cdot \frac{\color{blue}{x \cdot \left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right)} + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
      fma-def [=>] 99.5	\[ \left(x + -2\right) \cdot \frac{\color{blue}{\mathsf{fma}\left(x, \left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y, z\right)}}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
      *-commutative [=>] 99.5	\[ \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(x, \color{blue}{x \cdot \left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right)} + y, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
      fma-def [=>] 99.5	\[ \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(x, \color{blue}{\mathsf{fma}\left(x, \left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416, y\right)}, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
      *-commutative [=>] 99.5	\[ \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \color{blue}{x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right)} + 137.519416416, y\right), z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
      fma-def [=>] 99.5	\[ \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \color{blue}{\mathsf{fma}\left(x, x \cdot 4.16438922228 + 78.6994924154, 137.519416416\right)}, y\right), z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
      fma-def [=>] 99.5	\[ \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \color{blue}{\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right)}, 137.519416416\right), y\right), z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
      *-commutative [=>] 99.5	\[ \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right)}{\color{blue}{x \cdot \left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right)} + 47.066876606} \]

   3. Taylor expanded in y around 0 99.5%

      \[\leadsto \left(x + -2\right) \cdot \color{blue}{\left(\frac{y \cdot x}{\left(313.399215894 + \left(263.505074721 + x \cdot \left(43.3400022514 + x\right)\right) \cdot x\right) \cdot x + 47.066876606} + \left(\frac{\left(137.519416416 + \left(78.6994924154 + 4.16438922228 \cdot x\right) \cdot x\right) \cdot {x}^{2}}{\left(313.399215894 + \left(263.505074721 + x \cdot \left(43.3400022514 + x\right)\right) \cdot x\right) \cdot x + 47.066876606} + \frac{z}{\left(313.399215894 + \left(263.505074721 + x \cdot \left(43.3400022514 + x\right)\right) \cdot x\right) \cdot x + 47.066876606}\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{+38} \lor \neg \left(x \leq 1000000000000\right):\\ \;\;\;\;\left(x + -2\right) \cdot \left(\frac{-101.7851458539211}{x} - \left(\frac{124074.40615218398 - y}{{x}^{3}} + \left(-4.16438922228 - \frac{\frac{3451.550173699799}{x}}{x}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(\frac{x \cdot y}{x \cdot \left(313.399215894 + x \cdot \left(263.505074721 + x \cdot \left(x + 43.3400022514\right)\right)\right) + 47.066876606} - \left(\frac{{x}^{2} \cdot \left(x \cdot \left(x \cdot -4.16438922228 + -78.6994924154\right) + -137.519416416\right)}{x \cdot \left(313.399215894 + x \cdot \left(263.505074721 + x \cdot \left(x + 43.3400022514\right)\right)\right) + 47.066876606} - \frac{z}{x \cdot \left(313.399215894 + x \cdot \left(263.505074721 + x \cdot \left(x + 43.3400022514\right)\right)\right) + 47.066876606}\right)\right)\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	98.2%
Cost	8073

\[\begin{array}{l} t_0 := x \cdot \left(313.399215894 + x \cdot \left(263.505074721 + x \cdot \left(x + 43.3400022514\right)\right)\right) + 47.066876606\\ \mathbf{if}\;x \leq -1.9 \cdot 10^{+38} \lor \neg \left(x \leq 1000000000000\right):\\ \;\;\;\;\left(x + -2\right) \cdot \left(\frac{-101.7851458539211}{x} - \left(\frac{124074.40615218398 - y}{{x}^{3}} + \left(-4.16438922228 - \frac{\frac{3451.550173699799}{x}}{x}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(\frac{z}{t_0} + \frac{x \cdot \left(y + x \cdot \left(137.519416416 + x \cdot \left(78.6994924154 + x \cdot 4.16438922228\right)\right)\right)}{t_0}\right)\\ \end{array} \]

Alternative 2
Accuracy	98.3%
Cost	7241

\[\begin{array}{l} t_0 := x \cdot \left(313.399215894 + x \cdot \left(263.505074721 + x \cdot \left(x + 43.3400022514\right)\right)\right) + 47.066876606\\ \mathbf{if}\;x \leq -1.8 \cdot 10^{+38} \lor \neg \left(x \leq 3.4 \cdot 10^{+18}\right):\\ \;\;\;\;\frac{y}{x \cdot x} + \mathsf{fma}\left(4.16438922228, x, -8.32877844456\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(\frac{z}{t_0} + \frac{x \cdot \left(y + x \cdot \left(137.519416416 + x \cdot \left(78.6994924154 + x \cdot 4.16438922228\right)\right)\right)}{t_0}\right)\\ \end{array} \]

Alternative 3
Accuracy	97.9%
Cost	3657

\[\begin{array}{l} t_0 := x \cdot \left(313.399215894 + x \cdot \left(263.505074721 + x \cdot \left(x + 43.3400022514\right)\right)\right) + 47.066876606\\ \mathbf{if}\;x \leq -1.9 \cdot 10^{+38} \lor \neg \left(x \leq 9 \cdot 10^{+74}\right):\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(\frac{z}{t_0} + \frac{x \cdot \left(y + x \cdot \left(137.519416416 + x \cdot \left(78.6994924154 + x \cdot 4.16438922228\right)\right)\right)}{t_0}\right)\\ \end{array} \]

Alternative 4
Accuracy	96.9%
Cost	2633

\[\begin{array}{l} \mathbf{if}\;x \leq -3.7 \cdot 10^{+37} \lor \neg \left(x \leq 3.1 \cdot 10^{+41}\right):\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x + -2\right) \cdot \left(z + x \cdot \left(y + x \cdot \left(137.519416416 + x \cdot \left(78.6994924154 + x \cdot 4.16438922228\right)\right)\right)\right)}{x \cdot \left(313.399215894 + x \cdot \left(263.505074721 + x \cdot \left(x + 43.3400022514\right)\right)\right) + 47.066876606}\\ \end{array} \]

Alternative 5
Accuracy	94.3%
Cost	2120

\[\begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{+25}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \mathbf{elif}\;x \leq 1000000000000:\\ \;\;\;\;\frac{\left(x + -2\right) \cdot \left(z - x \cdot \left(x \cdot -137.519416416 - y\right)\right)}{x \cdot \left(313.399215894 + x \cdot \left(263.505074721 + x \cdot \left(x + 43.3400022514\right)\right)\right) + 47.066876606}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718 + \frac{5.86923874282773}{x}}\\ \end{array} \]

Alternative 6
Accuracy	91.3%
Cost	1996

\[\begin{array}{l} \mathbf{if}\;x \leq -50000000:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718 + \frac{5.86923874282773}{x}}\\ \mathbf{elif}\;x \leq 4.9 \cdot 10^{-6}:\\ \;\;\;\;z \cdot -0.0424927283095952 - x \cdot \left(z \cdot -0.28294182010212804 + 0.0212463641547976 \cdot \left(y \cdot 2 - z\right)\right)\\ \mathbf{elif}\;x \leq 7 \cdot 10^{+75}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{x \cdot y}{x \cdot \left(313.399215894 + x \cdot \left(263.505074721 + x \cdot \left(x + 43.3400022514\right)\right)\right) + 47.066876606}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \end{array} \]

Alternative 7
Accuracy	74.7%
Cost	1616

\[\begin{array}{l} t_0 := \frac{x + -2}{0.24013125253755718 + \frac{5.86923874282773}{x}}\\ \mathbf{if}\;x \leq -1950:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -2.7 \cdot 10^{-119}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(x \cdot \left(y \cdot 0.0212463641547976 + \left(x \cdot y\right) \cdot -0.14147091005106402\right)\right)\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{-103}:\\ \;\;\;\;\frac{x + -2}{\frac{47.066876606}{z}}\\ \mathbf{elif}\;x \leq 19000000:\\ \;\;\;\;\left(x + -2\right) \cdot \left(x \cdot \frac{y}{47.066876606 + x \cdot \left(313.399215894 - x \cdot -263.505074721\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 8
Accuracy	74.6%
Cost	1360

\[\begin{array}{l} t_0 := \left(x + -2\right) \cdot \frac{x \cdot y}{47.066876606 - x \cdot -313.399215894}\\ t_1 := \frac{x + -2}{0.24013125253755718 + \frac{5.86923874282773}{x}}\\ \mathbf{if}\;x \leq -1900:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -2.4 \cdot 10^{-119}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{-103}:\\ \;\;\;\;\frac{x + -2}{\frac{47.066876606}{z}}\\ \mathbf{elif}\;x \leq 19000000:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 9
Accuracy	74.7%
Cost	1360

\[\begin{array}{l} t_0 := \frac{x + -2}{0.24013125253755718 + \frac{5.86923874282773}{x}}\\ \mathbf{if}\;x \leq -1900:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -4.9 \cdot 10^{-119}:\\ \;\;\;\;\left(x + -2\right) \cdot \frac{y}{\frac{-47.066876606 + x \cdot -313.399215894}{-x}}\\ \mathbf{elif}\;x \leq 10^{-103}:\\ \;\;\;\;\frac{x + -2}{\frac{47.066876606}{z}}\\ \mathbf{elif}\;x \leq 19000000:\\ \;\;\;\;\left(x + -2\right) \cdot \frac{x \cdot y}{47.066876606 - x \cdot -313.399215894}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 10
Accuracy	74.6%
Cost	1360

\[\begin{array}{l} t_0 := \frac{x + -2}{0.24013125253755718 + \frac{5.86923874282773}{x}}\\ \mathbf{if}\;x \leq -1900:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -5.6 \cdot 10^{-119}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(x \cdot \left(y \cdot 0.0212463641547976 + \left(x \cdot y\right) \cdot -0.14147091005106402\right)\right)\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{-103}:\\ \;\;\;\;\frac{x + -2}{\frac{47.066876606}{z}}\\ \mathbf{elif}\;x \leq 19000000:\\ \;\;\;\;\left(x + -2\right) \cdot \frac{x \cdot y}{47.066876606 - x \cdot -313.399215894}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 11
Accuracy	90.1%
Cost	1353

\[\begin{array}{l} \mathbf{if}\;x \leq -1900 \lor \neg \left(x \leq 19000000\right):\\ \;\;\;\;\frac{x + -2}{0.24013125253755718 + \frac{5.86923874282773}{x}}\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(z \cdot 0.0212463641547976 - x \cdot \left(z \cdot 0.14147091005106402 + y \cdot -0.0212463641547976\right)\right)\\ \end{array} \]

Alternative 12
Accuracy	90.1%
Cost	1353

\[\begin{array}{l} \mathbf{if}\;x \leq -50000000 \lor \neg \left(x \leq 10.2\right):\\ \;\;\;\;\frac{x + -2}{0.24013125253755718 + \frac{5.86923874282773}{x}}\\ \mathbf{else}:\\ \;\;\;\;z \cdot -0.0424927283095952 - x \cdot \left(z \cdot -0.28294182010212804 + 0.0212463641547976 \cdot \left(y \cdot 2 - z\right)\right)\\ \end{array} \]

Alternative 13
Accuracy	74.3%
Cost	1104

\[\begin{array}{l} t_0 := \left(x + -2\right) \cdot \left(\left(x \cdot y\right) \cdot 0.0212463641547976\right)\\ \mathbf{if}\;x \leq -1900:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \mathbf{elif}\;x \leq -5.6 \cdot 10^{-119}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 2.75 \cdot 10^{-104}:\\ \;\;\;\;\frac{x + -2}{\frac{47.066876606}{z}}\\ \mathbf{elif}\;x \leq 19000000:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228 + -110.1139242984811\\ \end{array} \]

Alternative 14
Accuracy	74.2%
Cost	1104

\[\begin{array}{l} \mathbf{if}\;x \leq -1900:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \mathbf{elif}\;x \leq -4.4 \cdot 10^{-119}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(\left(x \cdot y\right) \cdot 0.0212463641547976\right)\\ \mathbf{elif}\;x \leq 2.05 \cdot 10^{-103}:\\ \;\;\;\;\frac{x + -2}{\frac{47.066876606}{z}}\\ \mathbf{elif}\;x \leq 19000000:\\ \;\;\;\;\left(x + -2\right) \cdot \frac{x \cdot y}{47.066876606}\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228 + -110.1139242984811\\ \end{array} \]

Alternative 15
Accuracy	74.5%
Cost	1104

\[\begin{array}{l} t_0 := \frac{x + -2}{0.24013125253755718 + \frac{5.86923874282773}{x}}\\ \mathbf{if}\;x \leq -1900:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -6 \cdot 10^{-119}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(\left(x \cdot y\right) \cdot 0.0212463641547976\right)\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{-103}:\\ \;\;\;\;\frac{x + -2}{\frac{47.066876606}{z}}\\ \mathbf{elif}\;x \leq 19000000:\\ \;\;\;\;\left(x + -2\right) \cdot \frac{x \cdot y}{47.066876606}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 16
Accuracy	74.2%
Cost	848

\[\begin{array}{l} t_0 := x \cdot 4.16438922228 + -110.1139242984811\\ t_1 := \left(x \cdot y\right) \cdot -0.0424927283095952\\ \mathbf{if}\;x \leq -2200:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -7 \cdot 10^{-119}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.15 \cdot 10^{-103}:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \mathbf{elif}\;x \leq 0.118:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 17
Accuracy	74.3%
Cost	848

\[\begin{array}{l} t_0 := \left(x \cdot y\right) \cdot -0.0424927283095952\\ \mathbf{if}\;x \leq -1900:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \mathbf{elif}\;x \leq -7.4 \cdot 10^{-119}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{-103}:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \mathbf{elif}\;x \leq 0.66:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228 + -110.1139242984811\\ \end{array} \]

Alternative 18
Accuracy	74.3%
Cost	848

\[\begin{array}{l} t_0 := \left(x \cdot y\right) \cdot -0.0424927283095952\\ \mathbf{if}\;x \leq -1900:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \mathbf{elif}\;x \leq -7.4 \cdot 10^{-119}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 1.08 \cdot 10^{-103}:\\ \;\;\;\;\frac{x + -2}{\frac{47.066876606}{z}}\\ \mathbf{elif}\;x \leq 0.54:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228 + -110.1139242984811\\ \end{array} \]

Alternative 19
Accuracy	75.3%
Cost	716

\[\begin{array}{l} \mathbf{if}\;x \leq -6.2 \cdot 10^{-12}:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{-103}:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \mathbf{elif}\;x \leq 2:\\ \;\;\;\;\left(x \cdot y\right) \cdot -0.0424927283095952\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228\\ \end{array} \]

Alternative 20
Accuracy	76.4%
Cost	456

\[\begin{array}{l} \mathbf{if}\;x \leq -6.2 \cdot 10^{-12}:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{-5}:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228\\ \end{array} \]

Alternative 21
Accuracy	44.9%
Cost	192

\[x \cdot 4.16438922228 \]

Reproduce

herbie shell --seed 2023141 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, C"
  :precision binary64

  :herbie-target
  (if (< x -3.326128725870005e+62) (- (+ (/ y (* x x)) (* 4.16438922228 x)) 110.1139242984811) (if (< x 9.429991714554673e+55) (* (/ (- x 2.0) 1.0) (/ (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (+ (* (+ (+ (* 263.505074721 x) (+ (* 43.3400022514 (* x x)) (* x (* x x)))) 313.399215894) x) 47.066876606))) (- (+ (/ y (* x x)) (* 4.16438922228 x)) 110.1139242984811)))

  (/ (* (- x 2.0) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)) (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))