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

Average Error: 41.27% → 1.21%

Time: 25.7s

Precision: binary64

Cost: 16200

Math

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

↓

\[\begin{array}{l} t_0 := 313.399215894 + x \cdot \left(263.505074721 + x \cdot \left(x + 43.3400022514\right)\right)\\ \mathbf{if}\;x \leq -2.9 \cdot 10^{+54}:\\ \;\;\;\;\left(\frac{4752.4581585918595}{x} + \left(x \cdot 4.16438922228 + \frac{y}{x \cdot x}\right)\right) + \left(-110.1139242984811 + \frac{-207551.7024428275}{x \cdot x}\right)\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{+59}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(x \cdot \frac{\mathsf{fma}\left(137.519416416 + x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right), x, y\right)}{\mathsf{fma}\left(t_0, x, 47.066876606\right)} + \frac{z}{47.066876606 + x \cdot t_0}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \end{array} \]

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
         (+ 313.399215894 (* x (+ 263.505074721 (* x (+ x 43.3400022514)))))))
   (if (<= x -2.9e+54)
     (+
      (+ (/ 4752.4581585918595 x) (+ (* x 4.16438922228) (/ y (* x x))))
      (+ -110.1139242984811 (/ -207551.7024428275 (* x x))))
     (if (<= x 1.4e+59)
       (*
        (+ x -2.0)
        (+
         (*
          x
          (/
           (fma
            (+ 137.519416416 (* x (+ (* x 4.16438922228) 78.6994924154)))
            x
            y)
           (fma t_0 x 47.066876606)))
         (/ z (+ 47.066876606 (* x t_0)))))
       (/ (+ x -2.0) 0.24013125253755718)))))

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 = 313.399215894 + (x * (263.505074721 + (x * (x + 43.3400022514))));
	double tmp;
	if (x <= -2.9e+54) {
		tmp = ((4752.4581585918595 / x) + ((x * 4.16438922228) + (y / (x * x)))) + (-110.1139242984811 + (-207551.7024428275 / (x * x)));
	} else if (x <= 1.4e+59) {
		tmp = (x + -2.0) * ((x * (fma((137.519416416 + (x * ((x * 4.16438922228) + 78.6994924154))), x, y) / fma(t_0, x, 47.066876606))) + (z / (47.066876606 + (x * t_0))));
	} else {
		tmp = (x + -2.0) / 0.24013125253755718;
	}
	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(313.399215894 + Float64(x * Float64(263.505074721 + Float64(x * Float64(x + 43.3400022514)))))
	tmp = 0.0
	if (x <= -2.9e+54)
		tmp = Float64(Float64(Float64(4752.4581585918595 / x) + Float64(Float64(x * 4.16438922228) + Float64(y / Float64(x * x)))) + Float64(-110.1139242984811 + Float64(-207551.7024428275 / Float64(x * x))));
	elseif (x <= 1.4e+59)
		tmp = Float64(Float64(x + -2.0) * Float64(Float64(x * Float64(fma(Float64(137.519416416 + Float64(x * Float64(Float64(x * 4.16438922228) + 78.6994924154))), x, y) / fma(t_0, x, 47.066876606))) + Float64(z / Float64(47.066876606 + Float64(x * t_0)))));
	else
		tmp = Float64(Float64(x + -2.0) / 0.24013125253755718);
	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[(313.399215894 + N[(x * N[(263.505074721 + N[(x * N[(x + 43.3400022514), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.9e+54], N[(N[(N[(4752.4581585918595 / x), $MachinePrecision] + N[(N[(x * 4.16438922228), $MachinePrecision] + N[(y / N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-110.1139242984811 + N[(-207551.7024428275 / N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.4e+59], N[(N[(x + -2.0), $MachinePrecision] * N[(N[(x * N[(N[(N[(137.519416416 + N[(x * N[(N[(x * 4.16438922228), $MachinePrecision] + 78.6994924154), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * x + y), $MachinePrecision] / N[(t$95$0 * x + 47.066876606), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z / N[(47.066876606 + N[(x * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + -2.0), $MachinePrecision] / 0.24013125253755718), $MachinePrecision]]]]

Target

Original	41.27%
Target	1.26%
Herbie	1.21%

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

Derivation

1. Split input into 3 regimes

2. if x < -2.8999999999999999e54

   1. Initial program 97.88

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

   2. Simplified 92

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

      [Start] 97.88	\[ \frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
      associate-/l* [=>] 92	\[ \color{blue}{\frac{x - 2}{\frac{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}}} \]
      sub-neg [=>] 92	\[ \frac{\color{blue}{x + \left(-2\right)}}{\frac{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}} \]
      metadata-eval [=>] 92	\[ \frac{x + \color{blue}{-2}}{\frac{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}} \]
      fma-def [=>] 92	\[ \frac{x + -2}{\frac{\color{blue}{\mathsf{fma}\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894, x, 47.066876606\right)}}{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}} \]
      fma-def [=>] 92	\[ \frac{x + -2}{\frac{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721, x, 313.399215894\right)}, x, 47.066876606\right)}{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}} \]
      fma-def [=>] 92	\[ \frac{x + -2}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right)}, x, 313.399215894\right), x, 47.066876606\right)}{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}} \]
      fma-def [=>] 92	\[ \frac{x + -2}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}{\color{blue}{\mathsf{fma}\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y, x, z\right)}}} \]
      fma-def [=>] 92	\[ \frac{x + -2}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416, x, y\right)}, x, z\right)}} \]
      fma-def [=>] 92	\[ \frac{x + -2}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x \cdot 4.16438922228 + 78.6994924154, x, 137.519416416\right)}, x, y\right), x, z\right)}} \]
      fma-def [=>] 92	\[ \frac{x + -2}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right)}, x, 137.519416416\right), x, y\right), x, z\right)}} \]

   3. Taylor expanded in z around 0 92.49

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

   4. Taylor expanded in x around inf 92.49

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

   5. Simplified 92.49

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

      [Start] 92.49	\[ \frac{x + -2}{\frac{47.066876606 + \left(313.399215894 + \left(43.3400022514 \cdot {x}^{2} + {x}^{3}\right)\right) \cdot x}{\left(\left(137.519416416 + \left(78.6994924154 + 4.16438922228 \cdot x\right) \cdot x\right) \cdot x + y\right) \cdot x}} \]
      unpow2 [=>] 92.49	\[ \frac{x + -2}{\frac{47.066876606 + \left(313.399215894 + \left(43.3400022514 \cdot \color{blue}{\left(x \cdot x\right)} + {x}^{3}\right)\right) \cdot x}{\left(\left(137.519416416 + \left(78.6994924154 + 4.16438922228 \cdot x\right) \cdot x\right) \cdot x + y\right) \cdot x}} \]
      cube-mult [=>] 92.49	\[ \frac{x + -2}{\frac{47.066876606 + \left(313.399215894 + \left(43.3400022514 \cdot \left(x \cdot x\right) + \color{blue}{x \cdot \left(x \cdot x\right)}\right)\right) \cdot x}{\left(\left(137.519416416 + \left(78.6994924154 + 4.16438922228 \cdot x\right) \cdot x\right) \cdot x + y\right) \cdot x}} \]
      distribute-rgt-in [<=] 92.49	\[ \frac{x + -2}{\frac{47.066876606 + \left(313.399215894 + \color{blue}{\left(x \cdot x\right) \cdot \left(43.3400022514 + x\right)}\right) \cdot x}{\left(\left(137.519416416 + \left(78.6994924154 + 4.16438922228 \cdot x\right) \cdot x\right) \cdot x + y\right) \cdot x}} \]
      +-commutative [=>] 92.49	\[ \frac{x + -2}{\frac{47.066876606 + \left(313.399215894 + \left(x \cdot x\right) \cdot \color{blue}{\left(x + 43.3400022514\right)}\right) \cdot x}{\left(\left(137.519416416 + \left(78.6994924154 + 4.16438922228 \cdot x\right) \cdot x\right) \cdot x + y\right) \cdot x}} \]
      *-commutative [=>] 92.49	\[ \frac{x + -2}{\frac{47.066876606 + \left(313.399215894 + \color{blue}{\left(x + 43.3400022514\right) \cdot \left(x \cdot x\right)}\right) \cdot x}{\left(\left(137.519416416 + \left(78.6994924154 + 4.16438922228 \cdot x\right) \cdot x\right) \cdot x + y\right) \cdot x}} \]

   6. Taylor expanded in x around inf 1.39

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

   7. Simplified 1.39

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

      [Start] 1.39	\[ \left(4752.4581585918595 \cdot \frac{1}{x} + \left(\frac{y}{{x}^{2}} + 4.16438922228 \cdot x\right)\right) - \left(110.1139242984811 + 207551.7024428275 \cdot \frac{1}{{x}^{2}}\right) \]
      associate-*r/ [=>] 1.39	\[ \left(\color{blue}{\frac{4752.4581585918595 \cdot 1}{x}} + \left(\frac{y}{{x}^{2}} + 4.16438922228 \cdot x\right)\right) - \left(110.1139242984811 + 207551.7024428275 \cdot \frac{1}{{x}^{2}}\right) \]
      metadata-eval [=>] 1.39	\[ \left(\frac{\color{blue}{4752.4581585918595}}{x} + \left(\frac{y}{{x}^{2}} + 4.16438922228 \cdot x\right)\right) - \left(110.1139242984811 + 207551.7024428275 \cdot \frac{1}{{x}^{2}}\right) \]
      +-commutative [=>] 1.39	\[ \left(\frac{4752.4581585918595}{x} + \color{blue}{\left(4.16438922228 \cdot x + \frac{y}{{x}^{2}}\right)}\right) - \left(110.1139242984811 + 207551.7024428275 \cdot \frac{1}{{x}^{2}}\right) \]
      *-commutative [<=] 1.39	\[ \left(\frac{4752.4581585918595}{x} + \left(\color{blue}{x \cdot 4.16438922228} + \frac{y}{{x}^{2}}\right)\right) - \left(110.1139242984811 + 207551.7024428275 \cdot \frac{1}{{x}^{2}}\right) \]
      unpow2 [=>] 1.39	\[ \left(\frac{4752.4581585918595}{x} + \left(x \cdot 4.16438922228 + \frac{y}{\color{blue}{x \cdot x}}\right)\right) - \left(110.1139242984811 + 207551.7024428275 \cdot \frac{1}{{x}^{2}}\right) \]
      associate-*r/ [=>] 1.39	\[ \left(\frac{4752.4581585918595}{x} + \left(x \cdot 4.16438922228 + \frac{y}{x \cdot x}\right)\right) - \left(110.1139242984811 + \color{blue}{\frac{207551.7024428275 \cdot 1}{{x}^{2}}}\right) \]
      metadata-eval [=>] 1.39	\[ \left(\frac{4752.4581585918595}{x} + \left(x \cdot 4.16438922228 + \frac{y}{x \cdot x}\right)\right) - \left(110.1139242984811 + \frac{\color{blue}{207551.7024428275}}{{x}^{2}}\right) \]
      unpow2 [=>] 1.39	\[ \left(\frac{4752.4581585918595}{x} + \left(x \cdot 4.16438922228 + \frac{y}{x \cdot x}\right)\right) - \left(110.1139242984811 + \frac{207551.7024428275}{\color{blue}{x \cdot x}}\right) \]

   if -2.8999999999999999e54 < x < 1.3999999999999999e59

   1. Initial program 2.78

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

   2. Simplified 1.35

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

      [Start] 2.78	\[ \frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
      associate-*r/ [<=] 1.35	\[ \color{blue}{\left(x - 2\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}} \]
      sub-neg [=>] 1.35	\[ \color{blue}{\left(x + \left(-2\right)\right)} \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
      metadata-eval [=>] 1.35	\[ \left(x + \color{blue}{-2}\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
      *-commutative [=>] 1.35	\[ \left(x + -2\right) \cdot \frac{\color{blue}{x \cdot \left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right)} + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
      fma-def [=>] 1.35	\[ \left(x + -2\right) \cdot \frac{\color{blue}{\mathsf{fma}\left(x, \left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y, z\right)}}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
      *-commutative [=>] 1.35	\[ \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(x, \color{blue}{x \cdot \left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right)} + y, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
      fma-def [=>] 1.35	\[ \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(x, \color{blue}{\mathsf{fma}\left(x, \left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416, y\right)}, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
      *-commutative [=>] 1.35	\[ \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \color{blue}{x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right)} + 137.519416416, y\right), z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
      fma-def [=>] 1.35	\[ \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \color{blue}{\mathsf{fma}\left(x, x \cdot 4.16438922228 + 78.6994924154, 137.519416416\right)}, y\right), z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
      fma-def [=>] 1.35	\[ \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \color{blue}{\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right)}, 137.519416416\right), y\right), z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
      *-commutative [=>] 1.35	\[ \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right)}{\color{blue}{x \cdot \left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right)} + 47.066876606} \]

   3. Taylor expanded in z around 0 1.35

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

   4. Applied egg-rr 0.45

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

   if 1.3999999999999999e59 < x

   1. Initial program 99.19

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

   2. Simplified 94.63

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

      [Start] 99.19	\[ \frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
      associate-/l* [=>] 94.63	\[ \color{blue}{\frac{x - 2}{\frac{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}}} \]
      sub-neg [=>] 94.63	\[ \frac{\color{blue}{x + \left(-2\right)}}{\frac{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}} \]
      metadata-eval [=>] 94.63	\[ \frac{x + \color{blue}{-2}}{\frac{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}} \]
      fma-def [=>] 94.63	\[ \frac{x + -2}{\frac{\color{blue}{\mathsf{fma}\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894, x, 47.066876606\right)}}{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}} \]
      fma-def [=>] 94.63	\[ \frac{x + -2}{\frac{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721, x, 313.399215894\right)}, x, 47.066876606\right)}{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}} \]
      fma-def [=>] 94.63	\[ \frac{x + -2}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right)}, x, 313.399215894\right), x, 47.066876606\right)}{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}} \]
      fma-def [=>] 94.63	\[ \frac{x + -2}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}{\color{blue}{\mathsf{fma}\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y, x, z\right)}}} \]
      fma-def [=>] 94.63	\[ \frac{x + -2}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416, x, y\right)}, x, z\right)}} \]
      fma-def [=>] 94.63	\[ \frac{x + -2}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x \cdot 4.16438922228 + 78.6994924154, x, 137.519416416\right)}, x, y\right), x, z\right)}} \]
      fma-def [=>] 94.63	\[ \frac{x + -2}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right)}, x, 137.519416416\right), x, y\right), x, z\right)}} \]

   3. Taylor expanded in x around inf 3.32

      \[\leadsto \frac{x + -2}{\color{blue}{0.24013125253755718}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 1.21

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.9 \cdot 10^{+54}:\\ \;\;\;\;\left(\frac{4752.4581585918595}{x} + \left(x \cdot 4.16438922228 + \frac{y}{x \cdot x}\right)\right) + \left(-110.1139242984811 + \frac{-207551.7024428275}{x \cdot x}\right)\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{+59}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(x \cdot \frac{\mathsf{fma}\left(137.519416416 + x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right), x, y\right)}{\mathsf{fma}\left(313.399215894 + x \cdot \left(263.505074721 + x \cdot \left(x + 43.3400022514\right)\right), x, 47.066876606\right)} + \frac{z}{47.066876606 + x \cdot \left(313.399215894 + x \cdot \left(263.505074721 + x \cdot \left(x + 43.3400022514\right)\right)\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \end{array} \]

Alternatives

Alternative 1
Error	3.41%
Cost	7240

\[\begin{array}{l} t_0 := \frac{\left(x + -2\right) \cdot \left(z + x \cdot \left(y + x \cdot \left(137.519416416 + x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right)\right)\right)\right)}{47.066876606 + x \cdot \left(313.399215894 + x \cdot \left(263.505074721 + x \cdot \left(x + 43.3400022514\right)\right)\right)}\\ \mathbf{if}\;t_0 \leq -\infty:\\ \;\;\;\;\left(\frac{4752.4581585918595}{x} + \left(x \cdot 4.16438922228 + \frac{y}{x \cdot x}\right)\right) + \left(-110.1139242984811 + \frac{-207551.7024428275}{x \cdot x}\right)\\ \mathbf{elif}\;t_0 \leq 10^{+172}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{z}{47.066876606 + x \cdot \left(313.399215894 + \left(x \cdot x\right) \cdot \left(x + 43.3400022514\right)\right)}\right)\\ \end{array} \]

Alternative 2
Error	1.4%
Cost	3657

\[\begin{array}{l} t_0 := 47.066876606 + x \cdot \left(313.399215894 + x \cdot \left(263.505074721 + x \cdot \left(x + 43.3400022514\right)\right)\right)\\ \mathbf{if}\;x \leq -3.6 \cdot 10^{+58} \lor \neg \left(x \leq 2.05 \cdot 10^{+32}\right):\\ \;\;\;\;\left(\frac{4752.4581585918595}{x} + \left(x \cdot 4.16438922228 + \frac{y}{x \cdot x}\right)\right) + \left(-110.1139242984811 + \frac{-207551.7024428275}{x \cdot x}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(\frac{z}{t_0} + \frac{x \cdot \left(y + x \cdot \left(137.519416416 + x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right)\right)\right)}{t_0}\right)\\ \end{array} \]

Alternative 3
Error	2.92%
Cost	2377

\[\begin{array}{l} \mathbf{if}\;x \leq -7500000000000 \lor \neg \left(x \leq 950000000000\right):\\ \;\;\;\;\left(\frac{4752.4581585918595}{x} + \left(x \cdot 4.16438922228 + \frac{y}{x \cdot x}\right)\right) + \left(-110.1139242984811 + \frac{-207551.7024428275}{x \cdot x}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x + -2\right) \cdot \left(z + x \cdot \left(y + x \cdot \left(137.519416416 + x \cdot 78.6994924154\right)\right)\right)}{47.066876606 + x \cdot \left(313.399215894 + x \cdot \left(263.505074721 + x \cdot \left(x + 43.3400022514\right)\right)\right)}\\ \end{array} \]

Alternative 4
Error	2.99%
Cost	2121

\[\begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{+15} \lor \neg \left(x \leq 850000000000\right):\\ \;\;\;\;\left(\frac{4752.4581585918595}{x} + \left(x \cdot 4.16438922228 + \frac{y}{x \cdot x}\right)\right) + \left(-110.1139242984811 + \frac{-207551.7024428275}{x \cdot x}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x + -2\right) \cdot \left(z + x \cdot \left(y + x \cdot 137.519416416\right)\right)}{47.066876606 + x \cdot \left(313.399215894 + x \cdot \left(263.505074721 + x \cdot \left(x + 43.3400022514\right)\right)\right)}\\ \end{array} \]

Alternative 5
Error	6.28%
Cost	1993

\[\begin{array}{l} \mathbf{if}\;x \leq -2800000 \lor \neg \left(x \leq 23000\right):\\ \;\;\;\;\left(\frac{4752.4581585918595}{x} + \left(x \cdot 4.16438922228 + \frac{y}{x \cdot x}\right)\right) + \left(-110.1139242984811 + \frac{-207551.7024428275}{x \cdot x}\right)\\ \mathbf{else}:\\ \;\;\;\;-0.0424927283095952 \cdot \left(x \cdot y\right) + \frac{\left(x + -2\right) \cdot z}{47.066876606 + x \cdot \left(313.399215894 + x \cdot \left(263.505074721 + x \cdot \left(x + 43.3400022514\right)\right)\right)}\\ \end{array} \]

Alternative 6
Error	8.69%
Cost	1609

\[\begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{-16} \lor \neg \left(x \leq 0.0028\right):\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{z}{47.066876606 + x \cdot \left(313.399215894 + \left(x \cdot x\right) \cdot \left(x + 43.3400022514\right)\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(z \cdot 0.0212463641547976 + x \cdot \left(y \cdot 0.0212463641547976 + z \cdot -0.14147091005106402\right)\right)\\ \end{array} \]

Alternative 7
Error	6.76%
Cost	1609

\[\begin{array}{l} \mathbf{if}\;x \leq -0.65 \lor \neg \left(x \leq 2.5\right):\\ \;\;\;\;\left(\frac{4752.4581585918595}{x} + \left(x \cdot 4.16438922228 + \frac{y}{x \cdot x}\right)\right) + \left(-110.1139242984811 + \frac{-207551.7024428275}{x \cdot x}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(z \cdot 0.0212463641547976 + x \cdot \left(y \cdot 0.0212463641547976 + z \cdot -0.14147091005106402\right)\right)\\ \end{array} \]

Alternative 8
Error	10.13%
Cost	1352

\[\begin{array}{l} \mathbf{if}\;x \leq -0.175:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \mathbf{elif}\;x \leq 11:\\ \;\;\;\;\left(x + -2\right) \cdot \left(z \cdot 0.0212463641547976 + x \cdot \left(y \cdot 0.0212463641547976 + z \cdot -0.14147091005106402\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718 + \left(\frac{5.86923874282773}{x} + \frac{-55.572073733743466}{x \cdot x}\right)}\\ \end{array} \]

Alternative 9
Error	23.72%
Cost	1232

\[\begin{array}{l} t_0 := \frac{\left(x + -2\right) \cdot z}{47.066876606 + x \cdot 313.399215894}\\ \mathbf{if}\;x \leq -1.35:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \mathbf{elif}\;x \leq -5.2 \cdot 10^{-107}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -6.5 \cdot 10^{-133}:\\ \;\;\;\;y \cdot \left(x \cdot -0.0424927283095952\right)\\ \mathbf{elif}\;x \leq 2.8:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718 + \frac{5.86923874282773}{x}}\\ \end{array} \]

Alternative 10
Error	22.75%
Cost	1224

\[\begin{array}{l} \mathbf{if}\;x \leq -1.35:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \mathbf{elif}\;x \leq 7.4:\\ \;\;\;\;\frac{\left(x + -2\right) \cdot z}{47.066876606 + x \cdot 313.399215894}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718 + \left(\frac{5.86923874282773}{x} + \frac{-55.572073733743466}{x \cdot x}\right)}\\ \end{array} \]

Alternative 11
Error	23.97%
Cost	1104

\[\begin{array}{l} t_0 := \frac{x + -2}{\frac{47.066876606}{z}}\\ \mathbf{if}\;x \leq -0.135:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \mathbf{elif}\;x \leq -1.3 \cdot 10^{-106}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -6.3 \cdot 10^{-133}:\\ \;\;\;\;y \cdot \left(x \cdot -0.0424927283095952\right)\\ \mathbf{elif}\;x \leq 0.036:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718 + \frac{5.86923874282773}{x}}\\ \end{array} \]

Alternative 12
Error	24.04%
Cost	976

\[\begin{array}{l} t_0 := \frac{x + -2}{0.24013125253755718}\\ t_1 := \left(x + -2\right) \cdot \left(z \cdot 0.0212463641547976\right)\\ \mathbf{if}\;x \leq -0.16:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -5.2 \cdot 10^{-107}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -6.5 \cdot 10^{-133}:\\ \;\;\;\;y \cdot \left(x \cdot -0.0424927283095952\right)\\ \mathbf{elif}\;x \leq 0.65:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 13
Error	24.04%
Cost	976

\[\begin{array}{l} t_0 := \frac{x + -2}{0.24013125253755718}\\ t_1 := \frac{x + -2}{\frac{47.066876606}{z}}\\ \mathbf{if}\;x \leq -0.17:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -5.2 \cdot 10^{-107}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -6.5 \cdot 10^{-133}:\\ \;\;\;\;y \cdot \left(x \cdot -0.0424927283095952\right)\\ \mathbf{elif}\;x \leq 140:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 14
Error	24.28%
Cost	848

\[\begin{array}{l} t_0 := 4.16438922228 \cdot \left(x + -2\right)\\ \mathbf{if}\;x \leq -0.048:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -5.2 \cdot 10^{-107}:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \mathbf{elif}\;x \leq -6.5 \cdot 10^{-133}:\\ \;\;\;\;y \cdot \left(x \cdot -0.0424927283095952\right)\\ \mathbf{elif}\;x \leq 2:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 15
Error	24.23%
Cost	848

\[\begin{array}{l} \mathbf{if}\;x \leq -0.04:\\ \;\;\;\;4.16438922228 \cdot \left(x + -2\right)\\ \mathbf{elif}\;x \leq -3.95 \cdot 10^{-106}:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \mathbf{elif}\;x \leq -6.5 \cdot 10^{-133}:\\ \;\;\;\;y \cdot \left(x \cdot -0.0424927283095952\right)\\ \mathbf{elif}\;x \leq 0.55:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228 + -110.1139242984811\\ \end{array} \]

Alternative 16
Error	24.04%
Cost	848

\[\begin{array}{l} t_0 := \frac{x + -2}{0.24013125253755718}\\ \mathbf{if}\;x \leq -0.11:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -5.4 \cdot 10^{-107}:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \mathbf{elif}\;x \leq -6.5 \cdot 10^{-133}:\\ \;\;\;\;y \cdot \left(x \cdot -0.0424927283095952\right)\\ \mathbf{elif}\;x \leq 0.8:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 17
Error	24.27%
Cost	720

\[\begin{array}{l} \mathbf{if}\;x \leq -0.105:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq -5.3 \cdot 10^{-106}:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \mathbf{elif}\;x \leq -6.5 \cdot 10^{-133}:\\ \;\;\;\;x \cdot \left(y \cdot -0.0424927283095952\right)\\ \mathbf{elif}\;x \leq 2:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228\\ \end{array} \]

Alternative 18
Error	24.28%
Cost	720

\[\begin{array}{l} \mathbf{if}\;x \leq -1.3:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq -5.4 \cdot 10^{-107}:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \mathbf{elif}\;x \leq -6.5 \cdot 10^{-133}:\\ \;\;\;\;y \cdot \left(x \cdot -0.0424927283095952\right)\\ \mathbf{elif}\;x \leq 2:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228\\ \end{array} \]

Alternative 19
Error	23.34%
Cost	456

\[\begin{array}{l} \mathbf{if}\;x \leq -0.33:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq 2:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228\\ \end{array} \]

Alternative 20
Error	97.73%
Cost	192

\[x \cdot -0.3407596943375357 \]

Alternative 21
Error	55.8%
Cost	192

\[x \cdot 4.16438922228 \]

Reproduce

herbie shell --seed 2023089 
(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)))