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

Average Accuracy: 57.8% → 97.4%

Time: 29.2s

Precision: binary64

Cost: 37256

Math

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

↓

\[\begin{array}{l} t_0 := \left(\left({x}^{2} + 4\right) - x \cdot -2\right) \cdot \left(47.066876606 + x \cdot \left(313.399215894 + x \cdot \left(263.505074721 + x \cdot \left(x + 43.3400022514\right)\right)\right)\right)\\ t_1 := {x}^{3} - 8\\ \mathbf{if}\;x \leq -2.95 \cdot 10^{+38}:\\ \;\;\;\;x \cdot 4.16438922228 + \left(\frac{3655.1204654076414}{x} + \frac{y - 130977.50649958357}{x \cdot x}\right)\\ \mathbf{elif}\;x \leq 8.6 \cdot 10^{+22}:\\ \;\;\;\;\frac{t_1 \cdot \left({x}^{2} \cdot \left(137.519416416 + x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right)\right) + z\right)}{t_0} + \frac{t_1 \cdot \left(x \cdot y\right)}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{4752.4581585918595}{x} + \left(\mathsf{fma}\left(4.16438922228, x, \frac{y - 207551.7024428275}{x \cdot x}\right) - 110.1139242984811\right)\\ \end{array} \]

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
         (*
          (- (+ (pow x 2.0) 4.0) (* x -2.0))
          (+
           47.066876606
           (*
            x
            (+
             313.399215894
             (* x (+ 263.505074721 (* x (+ x 43.3400022514)))))))))
        (t_1 (- (pow x 3.0) 8.0)))
   (if (<= x -2.95e+38)
     (+
      (* x 4.16438922228)
      (+ (/ 3655.1204654076414 x) (/ (- y 130977.50649958357) (* x x))))
     (if (<= x 8.6e+22)
       (+
        (/
         (*
          t_1
          (+
           (*
            (pow x 2.0)
            (+ 137.519416416 (* x (+ (* x 4.16438922228) 78.6994924154))))
           z))
         t_0)
        (/ (* t_1 (* x y)) t_0))
       (+
        (/ 4752.4581585918595 x)
        (-
         (fma 4.16438922228 x (/ (- y 207551.7024428275) (* x x)))
         110.1139242984811))))))

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 = ((pow(x, 2.0) + 4.0) - (x * -2.0)) * (47.066876606 + (x * (313.399215894 + (x * (263.505074721 + (x * (x + 43.3400022514)))))));
	double t_1 = pow(x, 3.0) - 8.0;
	double tmp;
	if (x <= -2.95e+38) {
		tmp = (x * 4.16438922228) + ((3655.1204654076414 / x) + ((y - 130977.50649958357) / (x * x)));
	} else if (x <= 8.6e+22) {
		tmp = ((t_1 * ((pow(x, 2.0) * (137.519416416 + (x * ((x * 4.16438922228) + 78.6994924154)))) + z)) / t_0) + ((t_1 * (x * y)) / t_0);
	} else {
		tmp = (4752.4581585918595 / x) + (fma(4.16438922228, x, ((y - 207551.7024428275) / (x * x))) - 110.1139242984811);
	}
	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(Float64((x ^ 2.0) + 4.0) - Float64(x * -2.0)) * Float64(47.066876606 + Float64(x * Float64(313.399215894 + Float64(x * Float64(263.505074721 + Float64(x * Float64(x + 43.3400022514))))))))
	t_1 = Float64((x ^ 3.0) - 8.0)
	tmp = 0.0
	if (x <= -2.95e+38)
		tmp = Float64(Float64(x * 4.16438922228) + Float64(Float64(3655.1204654076414 / x) + Float64(Float64(y - 130977.50649958357) / Float64(x * x))));
	elseif (x <= 8.6e+22)
		tmp = Float64(Float64(Float64(t_1 * Float64(Float64((x ^ 2.0) * Float64(137.519416416 + Float64(x * Float64(Float64(x * 4.16438922228) + 78.6994924154)))) + z)) / t_0) + Float64(Float64(t_1 * Float64(x * y)) / t_0));
	else
		tmp = Float64(Float64(4752.4581585918595 / x) + Float64(fma(4.16438922228, x, Float64(Float64(y - 207551.7024428275) / Float64(x * x))) - 110.1139242984811));
	end
	return 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[(N[(N[Power[x, 2.0], $MachinePrecision] + 4.0), $MachinePrecision] - N[(x * -2.0), $MachinePrecision]), $MachinePrecision] * N[(47.066876606 + N[(x * N[(313.399215894 + N[(x * N[(263.505074721 + N[(x * N[(x + 43.3400022514), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[Power[x, 3.0], $MachinePrecision] - 8.0), $MachinePrecision]}, If[LessEqual[x, -2.95e+38], N[(N[(x * 4.16438922228), $MachinePrecision] + N[(N[(3655.1204654076414 / x), $MachinePrecision] + N[(N[(y - 130977.50649958357), $MachinePrecision] / N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 8.6e+22], N[(N[(N[(t$95$1 * N[(N[(N[Power[x, 2.0], $MachinePrecision] * N[(137.519416416 + N[(x * N[(N[(x * 4.16438922228), $MachinePrecision] + 78.6994924154), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] / t$95$0), $MachinePrecision] + N[(N[(t$95$1 * N[(x * y), $MachinePrecision]), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision], N[(N[(4752.4581585918595 / x), $MachinePrecision] + N[(N[(4.16438922228 * x + N[(N[(y - 207551.7024428275), $MachinePrecision] / N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 110.1139242984811), $MachinePrecision]), $MachinePrecision]]]]]

Target

Original	57.8%
Target	98.8%
Herbie	97.4%

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

Derivation

1. Split input into 3 regimes

2. if x < -2.94999999999999991e38

   1. Initial program 6.6%

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

   2. Simplified 12.2%

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

      [Start] 6.6	\[ \frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
      *-commutative [=>] 6.6	\[ \frac{\color{blue}{\left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right) \cdot \left(x - 2\right)}}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
      associate-*r/ [<=] 12.2	\[ \color{blue}{\left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right) \cdot \frac{x - 2}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}} \]
      *-commutative [=>] 12.2	\[ \left(\color{blue}{x \cdot \left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right)} + z\right) \cdot \frac{x - 2}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
      fma-def [=>] 12.2	\[ \color{blue}{\mathsf{fma}\left(x, \left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y, z\right)} \cdot \frac{x - 2}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
      *-commutative [=>] 12.2	\[ \mathsf{fma}\left(x, \color{blue}{x \cdot \left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right)} + y, z\right) \cdot \frac{x - 2}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
      fma-def [=>] 12.2	\[ \mathsf{fma}\left(x, \color{blue}{\mathsf{fma}\left(x, \left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416, y\right)}, z\right) \cdot \frac{x - 2}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
      *-commutative [=>] 12.2	\[ \mathsf{fma}\left(x, \mathsf{fma}\left(x, \color{blue}{x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right)} + 137.519416416, y\right), z\right) \cdot \frac{x - 2}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
      fma-def [=>] 12.2	\[ \mathsf{fma}\left(x, \mathsf{fma}\left(x, \color{blue}{\mathsf{fma}\left(x, x \cdot 4.16438922228 + 78.6994924154, 137.519416416\right)}, y\right), z\right) \cdot \frac{x - 2}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
      fma-def [=>] 12.2	\[ \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \color{blue}{\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right)}, 137.519416416\right), y\right), z\right) \cdot \frac{x - 2}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

   3. Taylor expanded in x around inf 97.4%

      \[\leadsto \color{blue}{\left(\frac{y}{{x}^{2}} + \left(4.16438922228 \cdot x + 3655.1204654076414 \cdot \frac{1}{x}\right)\right) - \left(110.1139242984811 + 130977.50649958357 \cdot \frac{1}{{x}^{2}}\right)} \]

   4. Simplified 97.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, 4.16438922228, -110.1139242984811\right) + \left(\frac{3655.1204654076414}{x} - \frac{130977.50649958357 - y}{x \cdot x}\right)} \]
      Proof

      [Start] 97.4	\[ \left(\frac{y}{{x}^{2}} + \left(4.16438922228 \cdot x + 3655.1204654076414 \cdot \frac{1}{x}\right)\right) - \left(110.1139242984811 + 130977.50649958357 \cdot \frac{1}{{x}^{2}}\right) \]
      associate--l+ [=>] 97.4	\[ \color{blue}{\frac{y}{{x}^{2}} + \left(\left(4.16438922228 \cdot x + 3655.1204654076414 \cdot \frac{1}{x}\right) - \left(110.1139242984811 + 130977.50649958357 \cdot \frac{1}{{x}^{2}}\right)\right)} \]
      +-commutative [=>] 97.4	\[ \color{blue}{\left(\left(4.16438922228 \cdot x + 3655.1204654076414 \cdot \frac{1}{x}\right) - \left(110.1139242984811 + 130977.50649958357 \cdot \frac{1}{{x}^{2}}\right)\right) + \frac{y}{{x}^{2}}} \]
      associate--r+ [=>] 97.4	\[ \color{blue}{\left(\left(\left(4.16438922228 \cdot x + 3655.1204654076414 \cdot \frac{1}{x}\right) - 110.1139242984811\right) - 130977.50649958357 \cdot \frac{1}{{x}^{2}}\right)} + \frac{y}{{x}^{2}} \]
      associate-+l- [=>] 97.4	\[ \color{blue}{\left(\left(4.16438922228 \cdot x + 3655.1204654076414 \cdot \frac{1}{x}\right) - 110.1139242984811\right) - \left(130977.50649958357 \cdot \frac{1}{{x}^{2}} - \frac{y}{{x}^{2}}\right)} \]
      associate-*r/ [=>] 97.4	\[ \left(\left(4.16438922228 \cdot x + 3655.1204654076414 \cdot \frac{1}{x}\right) - 110.1139242984811\right) - \left(\color{blue}{\frac{130977.50649958357 \cdot 1}{{x}^{2}}} - \frac{y}{{x}^{2}}\right) \]
      metadata-eval [=>] 97.4	\[ \left(\left(4.16438922228 \cdot x + 3655.1204654076414 \cdot \frac{1}{x}\right) - 110.1139242984811\right) - \left(\frac{\color{blue}{130977.50649958357}}{{x}^{2}} - \frac{y}{{x}^{2}}\right) \]
      div-sub [<=] 97.4	\[ \left(\left(4.16438922228 \cdot x + 3655.1204654076414 \cdot \frac{1}{x}\right) - 110.1139242984811\right) - \color{blue}{\frac{130977.50649958357 - y}{{x}^{2}}} \]
      unsub-neg [<=] 97.4	\[ \left(\left(4.16438922228 \cdot x + 3655.1204654076414 \cdot \frac{1}{x}\right) - 110.1139242984811\right) - \frac{\color{blue}{130977.50649958357 + \left(-y\right)}}{{x}^{2}} \]
      mul-1-neg [<=] 97.4	\[ \left(\left(4.16438922228 \cdot x + 3655.1204654076414 \cdot \frac{1}{x}\right) - 110.1139242984811\right) - \frac{130977.50649958357 + \color{blue}{-1 \cdot y}}{{x}^{2}} \]
      sub-neg [=>] 97.4	\[ \color{blue}{\left(\left(4.16438922228 \cdot x + 3655.1204654076414 \cdot \frac{1}{x}\right) + \left(-110.1139242984811\right)\right)} - \frac{130977.50649958357 + -1 \cdot y}{{x}^{2}} \]
      +-commutative [=>] 97.4	\[ \color{blue}{\left(\left(-110.1139242984811\right) + \left(4.16438922228 \cdot x + 3655.1204654076414 \cdot \frac{1}{x}\right)\right)} - \frac{130977.50649958357 + -1 \cdot y}{{x}^{2}} \]
      associate-+r- [<=] 97.4	\[ \color{blue}{\left(-110.1139242984811\right) + \left(\left(4.16438922228 \cdot x + 3655.1204654076414 \cdot \frac{1}{x}\right) - \frac{130977.50649958357 + -1 \cdot y}{{x}^{2}}\right)} \]
      unsub-neg [<=] 97.4	\[ \left(-110.1139242984811\right) + \color{blue}{\left(\left(4.16438922228 \cdot x + 3655.1204654076414 \cdot \frac{1}{x}\right) + \left(-\frac{130977.50649958357 + -1 \cdot y}{{x}^{2}}\right)\right)} \]

   5. Taylor expanded in x around inf 97.4%

      \[\leadsto \color{blue}{4.16438922228 \cdot x} + \left(\frac{3655.1204654076414}{x} - \frac{130977.50649958357 - y}{x \cdot x}\right) \]

   6. Simplified 97.4%

      \[\leadsto \color{blue}{x \cdot 4.16438922228} + \left(\frac{3655.1204654076414}{x} - \frac{130977.50649958357 - y}{x \cdot x}\right) \]
      Proof

      [Start] 97.4	\[ 4.16438922228 \cdot x + \left(\frac{3655.1204654076414}{x} - \frac{130977.50649958357 - y}{x \cdot x}\right) \]
      *-commutative [<=] 97.4	\[ \color{blue}{x \cdot 4.16438922228} + \left(\frac{3655.1204654076414}{x} - \frac{130977.50649958357 - y}{x \cdot x}\right) \]

   if -2.94999999999999991e38 < x < 8.6000000000000004e22

   1. Initial program 98.9%

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

   2. Simplified 99.4%

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

      [Start] 98.9	\[ \frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
      associate-*r/ [<=] 99.4	\[ \color{blue}{\left(x - 2\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}} \]
      sub-neg [=>] 99.4	\[ \color{blue}{\left(x + \left(-2\right)\right)} \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
      metadata-eval [=>] 99.4	\[ \left(x + \color{blue}{-2}\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
      *-commutative [=>] 99.4	\[ \left(x + -2\right) \cdot \frac{\color{blue}{x \cdot \left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right)} + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
      fma-def [=>] 99.4	\[ \left(x + -2\right) \cdot \frac{\color{blue}{\mathsf{fma}\left(x, \left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y, z\right)}}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
      *-commutative [=>] 99.4	\[ \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(x, \color{blue}{x \cdot \left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right)} + y, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
      fma-def [=>] 99.4	\[ \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(x, \color{blue}{\mathsf{fma}\left(x, \left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416, y\right)}, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
      *-commutative [=>] 99.4	\[ \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \color{blue}{x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right)} + 137.519416416, y\right), z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
      fma-def [=>] 99.4	\[ \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \color{blue}{\mathsf{fma}\left(x, x \cdot 4.16438922228 + 78.6994924154, 137.519416416\right)}, y\right), z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
      fma-def [=>] 99.4	\[ \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \color{blue}{\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right)}, 137.519416416\right), y\right), z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
      *-commutative [=>] 99.4	\[ \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right)}{\color{blue}{x \cdot \left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right)} + 47.066876606} \]

   3. Applied egg-rr 99.4%

      \[\leadsto \color{blue}{\frac{\frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + 43.3400022514, 263.505074721\right), 313.399215894\right), 47.066876606\right)} \cdot \left(-8 + {x}^{3}\right)}{\mathsf{fma}\left(x, x, 4 - x \cdot -2\right)}} \]
      Proof

      [Start] 99.4	\[ \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + 43.3400022514, 263.505074721\right), 313.399215894\right), 47.066876606\right)} \]
      *-commutative [=>] 99.4	\[ \color{blue}{\frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + 43.3400022514, 263.505074721\right), 313.399215894\right), 47.066876606\right)} \cdot \left(x + -2\right)} \]
      flip3-+ [=>] 99.4	\[ \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + 43.3400022514, 263.505074721\right), 313.399215894\right), 47.066876606\right)} \cdot \color{blue}{\frac{{x}^{3} + {-2}^{3}}{x \cdot x + \left(-2 \cdot -2 - x \cdot -2\right)}} \]
      associate-*r/ [=>] 99.4	\[ \color{blue}{\frac{\frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + 43.3400022514, 263.505074721\right), 313.399215894\right), 47.066876606\right)} \cdot \left({x}^{3} + {-2}^{3}\right)}{x \cdot x + \left(-2 \cdot -2 - x \cdot -2\right)}} \]
      metadata-eval [=>] 99.4	\[ \frac{\frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + 43.3400022514, 263.505074721\right), 313.399215894\right), 47.066876606\right)} \cdot \left({x}^{3} + \color{blue}{-8}\right)}{x \cdot x + \left(-2 \cdot -2 - x \cdot -2\right)} \]
      metadata-eval [<=] 99.4	\[ \frac{\frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + 43.3400022514, 263.505074721\right), 313.399215894\right), 47.066876606\right)} \cdot \left({x}^{3} + \color{blue}{4 \cdot -2}\right)}{x \cdot x + \left(-2 \cdot -2 - x \cdot -2\right)} \]
      metadata-eval [<=] 99.4	\[ \frac{\frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + 43.3400022514, 263.505074721\right), 313.399215894\right), 47.066876606\right)} \cdot \left({x}^{3} + \color{blue}{\left(-2 \cdot -2\right)} \cdot -2\right)}{x \cdot x + \left(-2 \cdot -2 - x \cdot -2\right)} \]
      +-commutative [=>] 99.4	\[ \frac{\frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + 43.3400022514, 263.505074721\right), 313.399215894\right), 47.066876606\right)} \cdot \color{blue}{\left(\left(-2 \cdot -2\right) \cdot -2 + {x}^{3}\right)}}{x \cdot x + \left(-2 \cdot -2 - x \cdot -2\right)} \]
      metadata-eval [=>] 99.4	\[ \frac{\frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + 43.3400022514, 263.505074721\right), 313.399215894\right), 47.066876606\right)} \cdot \left(\color{blue}{4} \cdot -2 + {x}^{3}\right)}{x \cdot x + \left(-2 \cdot -2 - x \cdot -2\right)} \]
      metadata-eval [=>] 99.4	\[ \frac{\frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + 43.3400022514, 263.505074721\right), 313.399215894\right), 47.066876606\right)} \cdot \left(\color{blue}{-8} + {x}^{3}\right)}{x \cdot x + \left(-2 \cdot -2 - x \cdot -2\right)} \]
      fma-def [=>] 99.4	\[ \frac{\frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + 43.3400022514, 263.505074721\right), 313.399215894\right), 47.066876606\right)} \cdot \left(-8 + {x}^{3}\right)}{\color{blue}{\mathsf{fma}\left(x, x, -2 \cdot -2 - x \cdot -2\right)}} \]
      metadata-eval [=>] 99.4	\[ \frac{\frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + 43.3400022514, 263.505074721\right), 313.399215894\right), 47.066876606\right)} \cdot \left(-8 + {x}^{3}\right)}{\mathsf{fma}\left(x, x, \color{blue}{4} - x \cdot -2\right)} \]

   4. Taylor expanded in y around inf 97.9%

      \[\leadsto \color{blue}{\frac{\left({x}^{3} - 8\right) \cdot \left(\left(137.519416416 + \left(78.6994924154 + 4.16438922228 \cdot x\right) \cdot x\right) \cdot {x}^{2} + z\right)}{\left(\left(4 + {x}^{2}\right) - -2 \cdot x\right) \cdot \left(47.066876606 + \left(313.399215894 + \left(\left(43.3400022514 + x\right) \cdot x + 263.505074721\right) \cdot x\right) \cdot x\right)} + \frac{\left({x}^{3} - 8\right) \cdot \left(y \cdot x\right)}{\left(\left(4 + {x}^{2}\right) - -2 \cdot x\right) \cdot \left(47.066876606 + \left(313.399215894 + \left(\left(43.3400022514 + x\right) \cdot x + 263.505074721\right) \cdot x\right) \cdot x\right)}} \]

   if 8.6000000000000004e22 < x

   1. Initial program 10.1%

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

   2. Taylor expanded in x around inf 10.1%

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

   3. Simplified 10.1%

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

      [Start] 10.1	\[ \frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(43.3400022514 \cdot {x}^{2} + {x}^{3}\right) + 313.399215894\right) \cdot x + 47.066876606} \]
      +-commutative [=>] 10.1	\[ \frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\color{blue}{\left({x}^{3} + 43.3400022514 \cdot {x}^{2}\right)} + 313.399215894\right) \cdot x + 47.066876606} \]
      cube-mult [=>] 10.1	\[ \frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\color{blue}{x \cdot \left(x \cdot x\right)} + 43.3400022514 \cdot {x}^{2}\right) + 313.399215894\right) \cdot x + 47.066876606} \]
      unpow2 [<=] 10.1	\[ \frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(x \cdot \color{blue}{{x}^{2}} + 43.3400022514 \cdot {x}^{2}\right) + 313.399215894\right) \cdot x + 47.066876606} \]
      distribute-rgt-out [=>] 10.1	\[ \frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\color{blue}{{x}^{2} \cdot \left(x + 43.3400022514\right)} + 313.399215894\right) \cdot x + 47.066876606} \]
      unpow2 [=>] 10.1	\[ \frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\color{blue}{\left(x \cdot x\right)} \cdot \left(x + 43.3400022514\right) + 313.399215894\right) \cdot x + 47.066876606} \]

   4. Taylor expanded in x around -inf 96.5%

      \[\leadsto \color{blue}{\left(4752.4581585918595 \cdot \frac{1}{x} + \left(4.16438922228 \cdot x + -1 \cdot \frac{207551.7024428275 + -1 \cdot y}{{x}^{2}}\right)\right) - 110.1139242984811} \]

   5. Simplified 96.5%

      \[\leadsto \color{blue}{\frac{4752.4581585918595}{x} + \left(\mathsf{fma}\left(4.16438922228, x, -\frac{207551.7024428275 + \left(-y\right)}{x \cdot x}\right) - 110.1139242984811\right)} \]
      Proof

      [Start] 96.5	\[ \left(4752.4581585918595 \cdot \frac{1}{x} + \left(4.16438922228 \cdot x + -1 \cdot \frac{207551.7024428275 + -1 \cdot y}{{x}^{2}}\right)\right) - 110.1139242984811 \]
      associate--l+ [=>] 96.5	\[ \color{blue}{4752.4581585918595 \cdot \frac{1}{x} + \left(\left(4.16438922228 \cdot x + -1 \cdot \frac{207551.7024428275 + -1 \cdot y}{{x}^{2}}\right) - 110.1139242984811\right)} \]
      associate-*r/ [=>] 96.5	\[ \color{blue}{\frac{4752.4581585918595 \cdot 1}{x}} + \left(\left(4.16438922228 \cdot x + -1 \cdot \frac{207551.7024428275 + -1 \cdot y}{{x}^{2}}\right) - 110.1139242984811\right) \]
      metadata-eval [=>] 96.5	\[ \frac{\color{blue}{4752.4581585918595}}{x} + \left(\left(4.16438922228 \cdot x + -1 \cdot \frac{207551.7024428275 + -1 \cdot y}{{x}^{2}}\right) - 110.1139242984811\right) \]
      fma-def [=>] 96.5	\[ \frac{4752.4581585918595}{x} + \left(\color{blue}{\mathsf{fma}\left(4.16438922228, x, -1 \cdot \frac{207551.7024428275 + -1 \cdot y}{{x}^{2}}\right)} - 110.1139242984811\right) \]
      mul-1-neg [=>] 96.5	\[ \frac{4752.4581585918595}{x} + \left(\mathsf{fma}\left(4.16438922228, x, \color{blue}{-\frac{207551.7024428275 + -1 \cdot y}{{x}^{2}}}\right) - 110.1139242984811\right) \]
      mul-1-neg [=>] 96.5	\[ \frac{4752.4581585918595}{x} + \left(\mathsf{fma}\left(4.16438922228, x, -\frac{207551.7024428275 + \color{blue}{\left(-y\right)}}{{x}^{2}}\right) - 110.1139242984811\right) \]
      unpow2 [=>] 96.5	\[ \frac{4752.4581585918595}{x} + \left(\mathsf{fma}\left(4.16438922228, x, -\frac{207551.7024428275 + \left(-y\right)}{\color{blue}{x \cdot x}}\right) - 110.1139242984811\right) \]

3. Recombined 3 regimes into one program.

4. Final simplification 97.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.95 \cdot 10^{+38}:\\ \;\;\;\;x \cdot 4.16438922228 + \left(\frac{3655.1204654076414}{x} + \frac{y - 130977.50649958357}{x \cdot x}\right)\\ \mathbf{elif}\;x \leq 8.6 \cdot 10^{+22}:\\ \;\;\;\;\frac{\left({x}^{3} - 8\right) \cdot \left({x}^{2} \cdot \left(137.519416416 + x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right)\right) + z\right)}{\left(\left({x}^{2} + 4\right) - x \cdot -2\right) \cdot \left(47.066876606 + x \cdot \left(313.399215894 + x \cdot \left(263.505074721 + x \cdot \left(x + 43.3400022514\right)\right)\right)\right)} + \frac{\left({x}^{3} - 8\right) \cdot \left(x \cdot y\right)}{\left(\left({x}^{2} + 4\right) - x \cdot -2\right) \cdot \left(47.066876606 + x \cdot \left(313.399215894 + x \cdot \left(263.505074721 + x \cdot \left(x + 43.3400022514\right)\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{4752.4581585918595}{x} + \left(\mathsf{fma}\left(4.16438922228, x, \frac{y - 207551.7024428275}{x \cdot x}\right) - 110.1139242984811\right)\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	98.0%
Cost	7624

\[\begin{array}{l} \mathbf{if}\;x \leq -6.2 \cdot 10^{+41}:\\ \;\;\;\;x \cdot 4.16438922228 + \left(\frac{3655.1204654076414}{x} + \frac{y - 130977.50649958357}{x \cdot x}\right)\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{+29}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(z + x \cdot \left(y + x \cdot \left(137.519416416 + x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right)\right)\right)\right)}{47.066876606 + x \cdot \left(313.399215894 + x \cdot \left(263.505074721 + x \cdot \left(x + 43.3400022514\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{4752.4581585918595}{x} + \left(\mathsf{fma}\left(4.16438922228, x, \frac{y - 207551.7024428275}{x \cdot x}\right) - 110.1139242984811\right)\\ \end{array} \]

Alternative 2
Accuracy	98.1%
Cost	2633

\[\begin{array}{l} \mathbf{if}\;x \leq -9.8 \cdot 10^{+38} \lor \neg \left(x \leq 1.3 \cdot 10^{+37}\right):\\ \;\;\;\;x \cdot 4.16438922228 + \left(\frac{3655.1204654076414}{x} + \frac{y - 130977.50649958357}{x \cdot x}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(z + x \cdot \left(y + x \cdot \left(137.519416416 + x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right)\right)\right)\right)}{47.066876606 + x \cdot \left(313.399215894 + x \cdot \left(263.505074721 + x \cdot \left(x + 43.3400022514\right)\right)\right)}\\ \end{array} \]

Alternative 3
Accuracy	96.7%
Cost	2505

\[\begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{+39} \lor \neg \left(x \leq 2.9 \cdot 10^{+45}\right):\\ \;\;\;\;x \cdot 4.16438922228 + \left(\frac{3655.1204654076414}{x} + \frac{y - 130977.50649958357}{x \cdot x}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(z + x \cdot \left(y + x \cdot \left(137.519416416 + x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right)\right)\right)\right)}{47.066876606 + x \cdot \left(313.399215894 + \left(x \cdot x\right) \cdot \left(x + 43.3400022514\right)\right)}\\ \end{array} \]

Alternative 4
Accuracy	96.6%
Cost	2376

\[\begin{array}{l} t_0 := \frac{3655.1204654076414}{x} + \frac{y - 130977.50649958357}{x \cdot x}\\ \mathbf{if}\;x \leq -34000000:\\ \;\;\;\;t_0 + \left(x \cdot 4.16438922228 - 110.1139242984811\right)\\ \mathbf{elif}\;x \leq 5.7 \cdot 10^{+20}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(z + x \cdot \left(y + x \cdot \left(137.519416416 + x \cdot 78.6994924154\right)\right)\right)}{47.066876606 + x \cdot \left(313.399215894 + x \cdot \left(263.505074721 + x \cdot \left(x + 43.3400022514\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228 + t_0\\ \end{array} \]

Alternative 5
Accuracy	96.5%
Cost	2120

\[\begin{array}{l} t_0 := \frac{3655.1204654076414}{x} + \frac{y - 130977.50649958357}{x \cdot x}\\ \mathbf{if}\;x \leq -820000000:\\ \;\;\;\;t_0 + \left(x \cdot 4.16438922228 - 110.1139242984811\right)\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{+19}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(z + x \cdot \left(y + x \cdot 137.519416416\right)\right)}{47.066876606 + x \cdot \left(313.399215894 + x \cdot \left(263.505074721 + x \cdot \left(x + 43.3400022514\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228 + t_0\\ \end{array} \]

Alternative 6
Accuracy	95.5%
Cost	1992

\[\begin{array}{l} t_0 := \frac{3655.1204654076414}{x} + \frac{y - 130977.50649958357}{x \cdot x}\\ \mathbf{if}\;x \leq -1050000000:\\ \;\;\;\;t_0 + \left(x \cdot 4.16438922228 - 110.1139242984811\right)\\ \mathbf{elif}\;x \leq 8.8 \cdot 10^{+21}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(z + x \cdot \left(y + x \cdot 137.519416416\right)\right)}{47.066876606 + x \cdot \left(313.399215894 + \left(x \cdot x\right) \cdot \left(x + 43.3400022514\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228 + t_0\\ \end{array} \]

Alternative 7
Accuracy	92.5%
Cost	1353

\[\begin{array}{l} \mathbf{if}\;x \leq -0.245 \lor \neg \left(x \leq 3.5\right):\\ \;\;\;\;\left(\frac{3655.1204654076414}{x} + \frac{y - 130977.50649958357}{x \cdot x}\right) + \left(x \cdot 4.16438922228 - 110.1139242984811\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(z \cdot 0.0212463641547976 + x \cdot \left(y \cdot 0.0212463641547976 - z \cdot 0.14147091005106402\right)\right)\\ \end{array} \]

Alternative 8
Accuracy	91.0%
Cost	1352

\[\begin{array}{l} \mathbf{if}\;x \leq -26.5:\\ \;\;\;\;x \cdot 4.16438922228 + \left(\frac{3655.1204654076414}{x} + \frac{y - 130977.50649958357}{x \cdot x}\right)\\ \mathbf{elif}\;x \leq 0.3:\\ \;\;\;\;\left(x + -2\right) \cdot \left(z \cdot 0.0212463641547976 + x \cdot \left(y \cdot 0.0212463641547976 - z \cdot 0.14147091005106402\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{\frac{3451.550173699799}{x} - 101.7851458539211}{x}\right)\\ \end{array} \]

Alternative 9
Accuracy	76.9%
Cost	1097

\[\begin{array}{l} \mathbf{if}\;x \leq -36 \lor \neg \left(x \leq 4.4\right):\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{\frac{3451.550173699799}{x} - 101.7851458539211}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(x - 2\right)}{47.066876606 + x \cdot 313.399215894}\\ \end{array} \]

Alternative 10
Accuracy	89.5%
Cost	1097

\[\begin{array}{l} \mathbf{if}\;x \leq -0.175 \lor \neg \left(x \leq 28\right):\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{\frac{3451.550173699799}{x} - 101.7851458539211}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot -0.0424927283095952 - z \cdot -0.3041881842569256\right) + z \cdot -0.0424927283095952\\ \end{array} \]

Alternative 11
Accuracy	91.0%
Cost	1096

\[\begin{array}{l} \mathbf{if}\;x \leq -5.5:\\ \;\;\;\;x \cdot 4.16438922228 + \left(\frac{3655.1204654076414}{x} + \frac{y - 130977.50649958357}{x \cdot x}\right)\\ \mathbf{elif}\;x \leq 0.75:\\ \;\;\;\;x \cdot \left(y \cdot -0.0424927283095952 - z \cdot -0.3041881842569256\right) + z \cdot -0.0424927283095952\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{\frac{3451.550173699799}{x} - 101.7851458539211}{x}\right)\\ \end{array} \]

Alternative 12
Accuracy	76.9%
Cost	969

\[\begin{array}{l} \mathbf{if}\;x \leq -36 \lor \neg \left(x \leq 13.5\right):\\ \;\;\;\;x \cdot 4.16438922228 + \left(\frac{3655.1204654076414}{x} + -110.1139242984811\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(x - 2\right)}{47.066876606 + x \cdot 313.399215894}\\ \end{array} \]

Alternative 13
Accuracy	76.7%
Cost	841

\[\begin{array}{l} \mathbf{if}\;x \leq -5.5 \lor \neg \left(x \leq 24.5\right):\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-0.0424927283095952 + x \cdot 0.3041881842569256\right)\\ \end{array} \]

Alternative 14
Accuracy	76.8%
Cost	841

\[\begin{array}{l} \mathbf{if}\;x \leq -0.165 \lor \neg \left(x \leq 0.175\right):\\ \;\;\;\;x \cdot 4.16438922228 + \left(\frac{3655.1204654076414}{x} + -110.1139242984811\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-0.0424927283095952 + x \cdot 0.3041881842569256\right)\\ \end{array} \]

Alternative 15
Accuracy	76.7%
Cost	713

\[\begin{array}{l} \mathbf{if}\;x \leq -0.175 \lor \neg \left(x \leq 0.14\right):\\ \;\;\;\;x \cdot 4.16438922228 - 110.1139242984811\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-0.0424927283095952 + x \cdot 0.3041881842569256\right)\\ \end{array} \]

Alternative 16
Accuracy	76.4%
Cost	585

\[\begin{array}{l} \mathbf{if}\;x \leq -12000 \lor \neg \left(x \leq 2\right):\\ \;\;\;\;4.16438922228 \cdot \left(x + -2\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \end{array} \]

Alternative 17
Accuracy	76.5%
Cost	585

\[\begin{array}{l} \mathbf{if}\;x \leq -0.175 \lor \neg \left(x \leq 0.7\right):\\ \;\;\;\;x \cdot 4.16438922228 - 110.1139242984811\\ \mathbf{else}:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \end{array} \]

Alternative 18
Accuracy	76.4%
Cost	456

\[\begin{array}{l} \mathbf{if}\;x \leq -0.18:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq 2:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228\\ \end{array} \]

Alternative 19
Accuracy	45.5%
Cost	192

\[x \cdot 4.16438922228 \]

Reproduce

herbie shell --seed 2023151 
(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)))