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

Average Accuracy: 58.2% → 99.0%

Time: 34.3s

Precision: binary64

Cost: 9929

Math

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

↓

\[\begin{array}{l} t_0 := x \cdot \left(263.505074721 + x \cdot \left(x + 43.3400022514\right)\right)\\ \mathbf{if}\;x \leq -3.9 \cdot 10^{+75} \lor \neg \left(x \leq 1.6 \cdot 10^{+65}\right):\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(x \cdot \frac{y + x \cdot \left(137.519416416 + x \cdot \left(78.6994924154 + x \cdot 4.16438922228\right)\right)}{\mathsf{fma}\left(313.399215894 + t_0, x, 47.066876606\right)} + \frac{z}{47.066876606 - x \cdot \left(-313.399215894 - t_0\right)}\right)\\ \end{array} \]

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 (+ 263.505074721 (* x (+ x 43.3400022514))))))
   (if (or (<= x -3.9e+75) (not (<= x 1.6e+65)))
     (/ (+ x -2.0) 0.24013125253755718)
     (*
      (+ x -2.0)
      (+
       (*
        x
        (/
         (+
          y
          (* x (+ 137.519416416 (* x (+ 78.6994924154 (* x 4.16438922228))))))
         (fma (+ 313.399215894 t_0) x 47.066876606)))
       (/ z (- 47.066876606 (* x (- -313.399215894 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 * (263.505074721 + (x * (x + 43.3400022514)));
	double tmp;
	if ((x <= -3.9e+75) || !(x <= 1.6e+65)) {
		tmp = (x + -2.0) / 0.24013125253755718;
	} else {
		tmp = (x + -2.0) * ((x * ((y + (x * (137.519416416 + (x * (78.6994924154 + (x * 4.16438922228)))))) / fma((313.399215894 + t_0), x, 47.066876606))) + (z / (47.066876606 - (x * (-313.399215894 - 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(x * Float64(263.505074721 + Float64(x * Float64(x + 43.3400022514))))
	tmp = 0.0
	if ((x <= -3.9e+75) || !(x <= 1.6e+65))
		tmp = Float64(Float64(x + -2.0) / 0.24013125253755718);
	else
		tmp = Float64(Float64(x + -2.0) * Float64(Float64(x * Float64(Float64(y + Float64(x * Float64(137.519416416 + Float64(x * Float64(78.6994924154 + Float64(x * 4.16438922228)))))) / fma(Float64(313.399215894 + t_0), x, 47.066876606))) + Float64(z / Float64(47.066876606 - Float64(x * Float64(-313.399215894 - t_0))))));
	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[(x * N[(263.505074721 + N[(x * N[(x + 43.3400022514), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[x, -3.9e+75], N[Not[LessEqual[x, 1.6e+65]], $MachinePrecision]], N[(N[(x + -2.0), $MachinePrecision] / 0.24013125253755718), $MachinePrecision], N[(N[(x + -2.0), $MachinePrecision] * N[(N[(x * N[(N[(y + N[(x * N[(137.519416416 + N[(x * N[(78.6994924154 + N[(x * 4.16438922228), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(313.399215894 + t$95$0), $MachinePrecision] * x + 47.066876606), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z / N[(47.066876606 - N[(x * N[(-313.399215894 - t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Target

Original	58.2%
Target	98.7%
Herbie	99.0%

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

Derivation

1. Split input into 2 regimes

2. if x < -3.90000000000000038e75 or 1.60000000000000003e65 < x

   1. Initial program 0.0%

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

   2. Simplified 2.3%

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

      [Start] 0.0	\[ \frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
      associate-/l* [=>] 2.3	\[ \color{blue}{\frac{x - 2}{\frac{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}}} \]
      sub-neg [=>] 2.3	\[ \frac{\color{blue}{x + \left(-2\right)}}{\frac{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}} \]
      metadata-eval [=>] 2.3	\[ \frac{x + \color{blue}{-2}}{\frac{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}} \]
      fma-def [=>] 2.3	\[ \frac{x + -2}{\frac{\color{blue}{\mathsf{fma}\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894, x, 47.066876606\right)}}{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}} \]
      fma-def [=>] 2.3	\[ \frac{x + -2}{\frac{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721, x, 313.399215894\right)}, x, 47.066876606\right)}{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}} \]
      fma-def [=>] 2.3	\[ \frac{x + -2}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right)}, x, 313.399215894\right), x, 47.066876606\right)}{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}} \]
      fma-def [=>] 2.3	\[ \frac{x + -2}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}{\color{blue}{\mathsf{fma}\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y, x, z\right)}}} \]
      fma-def [=>] 2.3	\[ \frac{x + -2}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416, x, y\right)}, x, z\right)}} \]
      fma-def [=>] 2.3	\[ \frac{x + -2}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x \cdot 4.16438922228 + 78.6994924154, x, 137.519416416\right)}, x, y\right), x, z\right)}} \]
      fma-def [=>] 2.3	\[ \frac{x + -2}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right)}, x, 137.519416416\right), x, y\right), x, z\right)}} \]

   3. Taylor expanded in x around inf 98.3%

      \[\leadsto \frac{x + -2}{\color{blue}{0.24013125253755718}} \]

   if -3.90000000000000038e75 < x < 1.60000000000000003e65

   1. Initial program 94.9%

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

   2. Simplified 98.5%

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

      [Start] 94.9	\[ \frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
      associate-*r/ [<=] 98.5	\[ \color{blue}{\left(x - 2\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}} \]
      sub-neg [=>] 98.5	\[ \color{blue}{\left(x + \left(-2\right)\right)} \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
      metadata-eval [=>] 98.5	\[ \left(x + \color{blue}{-2}\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
      *-commutative [=>] 98.5	\[ \left(x + -2\right) \cdot \frac{\color{blue}{x \cdot \left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right)} + z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
      fma-def [=>] 98.5	\[ \left(x + -2\right) \cdot \frac{\color{blue}{\mathsf{fma}\left(x, \left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y, z\right)}}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
      *-commutative [=>] 98.5	\[ \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(x, \color{blue}{x \cdot \left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right)} + y, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
      fma-def [=>] 98.5	\[ \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(x, \color{blue}{\mathsf{fma}\left(x, \left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416, y\right)}, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
      *-commutative [=>] 98.5	\[ \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \color{blue}{x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right)} + 137.519416416, y\right), z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
      fma-def [=>] 98.5	\[ \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \color{blue}{\mathsf{fma}\left(x, x \cdot 4.16438922228 + 78.6994924154, 137.519416416\right)}, y\right), z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
      fma-def [=>] 98.5	\[ \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \color{blue}{\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right)}, 137.519416416\right), y\right), z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
      *-commutative [=>] 98.5	\[ \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right)}{\color{blue}{x \cdot \left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right)} + 47.066876606} \]

   3. Taylor expanded in z around 0 98.5%

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

   4. Applied egg-rr 98.5%

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

      [Start] 98.5	\[ \left(x + -2\right) \cdot \left(\frac{\left(\left(137.519416416 + \left(78.6994924154 + 4.16438922228 \cdot x\right) \cdot x\right) \cdot x + y\right) \cdot x}{\left(313.399215894 + \left(263.505074721 + x \cdot \left(43.3400022514 + x\right)\right) \cdot x\right) \cdot x + 47.066876606} + \frac{z}{\left(313.399215894 + \left(263.505074721 + x \cdot \left(43.3400022514 + x\right)\right) \cdot x\right) \cdot x + 47.066876606}\right) \]
      *-commutative [=>] 98.5	\[ \left(x + -2\right) \cdot \left(\frac{\left(\color{blue}{x \cdot \left(137.519416416 + \left(78.6994924154 + 4.16438922228 \cdot x\right) \cdot x\right)} + y\right) \cdot x}{\left(313.399215894 + \left(263.505074721 + x \cdot \left(43.3400022514 + x\right)\right) \cdot x\right) \cdot x + 47.066876606} + \frac{z}{\left(313.399215894 + \left(263.505074721 + x \cdot \left(43.3400022514 + x\right)\right) \cdot x\right) \cdot x + 47.066876606}\right) \]
      +-commutative [=>] 98.5	\[ \left(x + -2\right) \cdot \left(\frac{\left(x \cdot \color{blue}{\left(\left(78.6994924154 + 4.16438922228 \cdot x\right) \cdot x + 137.519416416\right)} + y\right) \cdot x}{\left(313.399215894 + \left(263.505074721 + x \cdot \left(43.3400022514 + x\right)\right) \cdot x\right) \cdot x + 47.066876606} + \frac{z}{\left(313.399215894 + \left(263.505074721 + x \cdot \left(43.3400022514 + x\right)\right) \cdot x\right) \cdot x + 47.066876606}\right) \]
      distribute-rgt-in [=>] 98.5	\[ \left(x + -2\right) \cdot \left(\frac{\left(\color{blue}{\left(\left(\left(78.6994924154 + 4.16438922228 \cdot x\right) \cdot x\right) \cdot x + 137.519416416 \cdot x\right)} + y\right) \cdot x}{\left(313.399215894 + \left(263.505074721 + x \cdot \left(43.3400022514 + x\right)\right) \cdot x\right) \cdot x + 47.066876606} + \frac{z}{\left(313.399215894 + \left(263.505074721 + x \cdot \left(43.3400022514 + x\right)\right) \cdot x\right) \cdot x + 47.066876606}\right) \]
      *-commutative [=>] 98.5	\[ \left(x + -2\right) \cdot \left(\frac{\left(\left(\color{blue}{\left(x \cdot \left(78.6994924154 + 4.16438922228 \cdot x\right)\right)} \cdot x + 137.519416416 \cdot x\right) + y\right) \cdot x}{\left(313.399215894 + \left(263.505074721 + x \cdot \left(43.3400022514 + x\right)\right) \cdot x\right) \cdot x + 47.066876606} + \frac{z}{\left(313.399215894 + \left(263.505074721 + x \cdot \left(43.3400022514 + x\right)\right) \cdot x\right) \cdot x + 47.066876606}\right) \]

   5. Applied egg-rr 99.5%

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

      [Start] 98.5	\[ \left(x + -2\right) \cdot \left(\frac{\left(\left(\left(x \cdot \left(78.6994924154 + 4.16438922228 \cdot x\right)\right) \cdot x + 137.519416416 \cdot x\right) + y\right) \cdot x}{\left(313.399215894 + \left(263.505074721 + x \cdot \left(43.3400022514 + x\right)\right) \cdot x\right) \cdot x + 47.066876606} + \frac{z}{\left(313.399215894 + \left(263.505074721 + x \cdot \left(43.3400022514 + x\right)\right) \cdot x\right) \cdot x + 47.066876606}\right) \]
      associate-/l* [=>] 99.5	\[ \left(x + -2\right) \cdot \left(\color{blue}{\frac{\left(\left(x \cdot \left(78.6994924154 + 4.16438922228 \cdot x\right)\right) \cdot x + 137.519416416 \cdot x\right) + y}{\frac{\left(313.399215894 + \left(263.505074721 + x \cdot \left(43.3400022514 + x\right)\right) \cdot x\right) \cdot x + 47.066876606}{x}}} + \frac{z}{\left(313.399215894 + \left(263.505074721 + x \cdot \left(43.3400022514 + x\right)\right) \cdot x\right) \cdot x + 47.066876606}\right) \]
      associate-/r/ [=>] 99.5	\[ \left(x + -2\right) \cdot \left(\color{blue}{\frac{\left(\left(x \cdot \left(78.6994924154 + 4.16438922228 \cdot x\right)\right) \cdot x + 137.519416416 \cdot x\right) + y}{\left(313.399215894 + \left(263.505074721 + x \cdot \left(43.3400022514 + x\right)\right) \cdot x\right) \cdot x + 47.066876606} \cdot x} + \frac{z}{\left(313.399215894 + \left(263.505074721 + x \cdot \left(43.3400022514 + x\right)\right) \cdot x\right) \cdot x + 47.066876606}\right) \]
      distribute-rgt-out [=>] 99.5	\[ \left(x + -2\right) \cdot \left(\frac{\color{blue}{x \cdot \left(x \cdot \left(78.6994924154 + 4.16438922228 \cdot x\right) + 137.519416416\right)} + y}{\left(313.399215894 + \left(263.505074721 + x \cdot \left(43.3400022514 + x\right)\right) \cdot x\right) \cdot x + 47.066876606} \cdot x + \frac{z}{\left(313.399215894 + \left(263.505074721 + x \cdot \left(43.3400022514 + x\right)\right) \cdot x\right) \cdot x + 47.066876606}\right) \]
      *-commutative [=>] 99.5	\[ \left(x + -2\right) \cdot \left(\frac{x \cdot \left(x \cdot \left(78.6994924154 + \color{blue}{x \cdot 4.16438922228}\right) + 137.519416416\right) + y}{\left(313.399215894 + \left(263.505074721 + x \cdot \left(43.3400022514 + x\right)\right) \cdot x\right) \cdot x + 47.066876606} \cdot x + \frac{z}{\left(313.399215894 + \left(263.505074721 + x \cdot \left(43.3400022514 + x\right)\right) \cdot x\right) \cdot x + 47.066876606}\right) \]
      fma-def [=>] 99.5	\[ \left(x + -2\right) \cdot \left(\frac{x \cdot \left(x \cdot \left(78.6994924154 + x \cdot 4.16438922228\right) + 137.519416416\right) + y}{\color{blue}{\mathsf{fma}\left(313.399215894 + \left(263.505074721 + x \cdot \left(43.3400022514 + x\right)\right) \cdot x, x, 47.066876606\right)}} \cdot x + \frac{z}{\left(313.399215894 + \left(263.505074721 + x \cdot \left(43.3400022514 + x\right)\right) \cdot x\right) \cdot x + 47.066876606}\right) \]
      *-commutative [=>] 99.5	\[ \left(x + -2\right) \cdot \left(\frac{x \cdot \left(x \cdot \left(78.6994924154 + x \cdot 4.16438922228\right) + 137.519416416\right) + y}{\mathsf{fma}\left(313.399215894 + \color{blue}{x \cdot \left(263.505074721 + x \cdot \left(43.3400022514 + x\right)\right)}, x, 47.066876606\right)} \cdot x + \frac{z}{\left(313.399215894 + \left(263.505074721 + x \cdot \left(43.3400022514 + x\right)\right) \cdot x\right) \cdot x + 47.066876606}\right) \]
      +-commutative [=>] 99.5	\[ \left(x + -2\right) \cdot \left(\frac{x \cdot \left(x \cdot \left(78.6994924154 + x \cdot 4.16438922228\right) + 137.519416416\right) + y}{\mathsf{fma}\left(313.399215894 + x \cdot \left(263.505074721 + x \cdot \color{blue}{\left(x + 43.3400022514\right)}\right), x, 47.066876606\right)} \cdot x + \frac{z}{\left(313.399215894 + \left(263.505074721 + x \cdot \left(43.3400022514 + x\right)\right) \cdot x\right) \cdot x + 47.066876606}\right) \]

3. Recombined 2 regimes into one program.

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.9 \cdot 10^{+75} \lor \neg \left(x \leq 1.6 \cdot 10^{+65}\right):\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(x \cdot \frac{y + x \cdot \left(137.519416416 + x \cdot \left(78.6994924154 + x \cdot 4.16438922228\right)\right)}{\mathsf{fma}\left(313.399215894 + x \cdot \left(263.505074721 + x \cdot \left(x + 43.3400022514\right)\right), x, 47.066876606\right)} + \frac{z}{47.066876606 - x \cdot \left(-313.399215894 - x \cdot \left(263.505074721 + x \cdot \left(x + 43.3400022514\right)\right)\right)}\right)\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	98.5%
Cost	8072

\[\begin{array}{l} t_0 := 47.066876606 - x \cdot \left(-313.399215894 - x \cdot \left(263.505074721 + x \cdot \left(x + 43.3400022514\right)\right)\right)\\ \mathbf{if}\;x \leq -2 \cdot 10^{+72}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \mathbf{elif}\;x \leq 3.55 \cdot 10^{+49}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(\frac{z}{t_0} + \frac{x \cdot \left(y + \left(x \cdot \left(x \cdot \left(78.6994924154 + x \cdot 4.16438922228\right)\right) + x \cdot 137.519416416\right)\right)}{t_0}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(\frac{-101.7851458539211}{x} - \left(\frac{124074.40615218398 - y}{{x}^{3}} - \left(4.16438922228 - \frac{\frac{-3451.550173699799}{x}}{x}\right)\right)\right)\\ \end{array} \]

Alternative 2
Accuracy	98.6%
Cost	7624

\[\begin{array}{l} t_0 := 47.066876606 - x \cdot \left(-313.399215894 - x \cdot \left(263.505074721 + x \cdot \left(x + 43.3400022514\right)\right)\right)\\ \mathbf{if}\;x \leq -3.2 \cdot 10^{+75}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{+49}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(\frac{z}{t_0} + \frac{x \cdot \left(y + \left(x \cdot \left(x \cdot \left(78.6994924154 + x \cdot 4.16438922228\right)\right) + x \cdot 137.519416416\right)\right)}{t_0}\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, 4.16438922228, \frac{3655.1204654076414}{x}\right) + \left(-110.1139242984811 + \frac{y + -130977.50649958357}{x \cdot x}\right)\\ \end{array} \]

Alternative 3
Accuracy	98.2%
Cost	3785

\[\begin{array}{l} t_0 := 47.066876606 - x \cdot \left(-313.399215894 - x \cdot \left(263.505074721 + x \cdot \left(x + 43.3400022514\right)\right)\right)\\ \mathbf{if}\;x \leq -1.52 \cdot 10^{+75} \lor \neg \left(x \leq 8.5 \cdot 10^{+50}\right):\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(\frac{z}{t_0} + \frac{x \cdot \left(y + \left(x \cdot \left(x \cdot \left(78.6994924154 + x \cdot 4.16438922228\right)\right) + x \cdot 137.519416416\right)\right)}{t_0}\right)\\ \end{array} \]

Alternative 4
Accuracy	98.2%
Cost	3657

\[\begin{array}{l} t_0 := 47.066876606 - x \cdot \left(-313.399215894 - x \cdot \left(263.505074721 + x \cdot \left(x + 43.3400022514\right)\right)\right)\\ \mathbf{if}\;x \leq -2 \cdot 10^{+75} \lor \neg \left(x \leq 8.5 \cdot 10^{+50}\right):\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(\frac{z}{t_0} - \frac{x \cdot \left(x \cdot \left(x \cdot \left(-78.6994924154 - x \cdot 4.16438922228\right) + -137.519416416\right) - y\right)}{t_0}\right)\\ \end{array} \]

Alternative 5
Accuracy	96.7%
Cost	2761

\[\begin{array}{l} \mathbf{if}\;x \leq -1.85 \cdot 10^{+61} \lor \neg \left(x \leq 5.5 \cdot 10^{+29}\right):\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(2 - x\right) \cdot \left(x \cdot \left(x \cdot \left(x \cdot \left(-78.6994924154 - x \cdot 4.16438922228\right) + -137.519416416\right) - y\right) - z\right)}{47.066876606 - x \cdot \left(-313.399215894 + \left(x \cdot -263.505074721 - x \cdot \left(x \cdot \left(x + 43.3400022514\right)\right)\right)\right)}\\ \end{array} \]

Alternative 6
Accuracy	96.7%
Cost	2633

\[\begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{+60} \lor \neg \left(x \leq 5.5 \cdot 10^{+29}\right):\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(2 - x\right) \cdot \left(x \cdot \left(x \cdot \left(x \cdot \left(-78.6994924154 - x \cdot 4.16438922228\right) + -137.519416416\right) - y\right) - z\right)}{47.066876606 - x \cdot \left(-313.399215894 - x \cdot \left(263.505074721 + x \cdot \left(x + 43.3400022514\right)\right)\right)}\\ \end{array} \]

Alternative 7
Accuracy	94.3%
Cost	2121

\[\begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{+33} \lor \neg \left(x \leq 2.2 \cdot 10^{+28}\right):\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x + -2\right) \cdot \left(z + x \cdot \left(y + x \cdot 137.519416416\right)\right)}{47.066876606 - x \cdot \left(-313.399215894 - x \cdot \left(263.505074721 + x \cdot \left(x + 43.3400022514\right)\right)\right)}\\ \end{array} \]

Alternative 8
Accuracy	92.7%
Cost	1993

\[\begin{array}{l} \mathbf{if}\;x \leq -5.5 \lor \neg \left(x \leq 15500\right):\\ \;\;\;\;\frac{x + -2}{0.24013125253755718 + \left(\frac{5.86923874282773}{x} + \frac{-55.572073733743466}{x \cdot x}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(2 - x\right) \cdot \left(x \cdot \left(x \cdot \left(x \cdot -78.6994924154 + -137.519416416\right) - y\right) - z\right)}{47.066876606 - x \cdot \left(-313.399215894 - x \cdot 263.505074721\right)}\\ \end{array} \]

Alternative 9
Accuracy	92.6%
Cost	1737

\[\begin{array}{l} \mathbf{if}\;x \leq -16.5 \lor \neg \left(x \leq 9000\right):\\ \;\;\;\;\frac{x + -2}{0.24013125253755718 + \left(\frac{5.86923874282773}{x} + \frac{-55.572073733743466}{x \cdot x}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x + -2\right) \cdot \left(z + x \cdot \left(y + x \cdot 137.519416416\right)\right)}{47.066876606 - x \cdot \left(-313.399215894 - x \cdot 263.505074721\right)}\\ \end{array} \]

Alternative 10
Accuracy	89.0%
Cost	1616

\[\begin{array}{l} t_0 := \frac{x + -2}{0.24013125253755718 + \left(\frac{5.86923874282773}{x} + \frac{-55.572073733743466}{x \cdot x}\right)}\\ \mathbf{if}\;x \leq -6.5:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{-56}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(z \cdot 0.0212463641547976 - x \cdot \left(y \cdot -0.0212463641547976 - z \cdot -0.14147091005106402\right)\right)\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{-12}:\\ \;\;\;\;z \cdot \left(-0.0424927283095952 + x \cdot 0.3041881842569256\right) + \left(x \cdot x\right) \cdot \left(-5.843575199059173 + z \cdot -1.787568985856513\right)\\ \mathbf{elif}\;x \leq 8:\\ \;\;\;\;\left(x + -2\right) \cdot \frac{x \cdot y}{47.066876606 - x \cdot \left(-313.399215894 - x \cdot 263.505074721\right)}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 11
Accuracy	92.5%
Cost	1481

\[\begin{array}{l} \mathbf{if}\;x \leq -36 \lor \neg \left(x \leq 8500\right):\\ \;\;\;\;\frac{x + -2}{0.24013125253755718 + \left(\frac{5.86923874282773}{x} + \frac{-55.572073733743466}{x \cdot x}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x + -2\right) \cdot \left(z + x \cdot \left(y + x \cdot 137.519416416\right)\right)}{47.066876606 - x \cdot -313.399215894}\\ \end{array} \]

Alternative 12
Accuracy	89.6%
Cost	1353

\[\begin{array}{l} \mathbf{if}\;x \leq -5.5 \lor \neg \left(x \leq 8.5\right):\\ \;\;\;\;\frac{x + -2}{0.24013125253755718 + \left(\frac{5.86923874282773}{x} + \frac{-55.572073733743466}{x \cdot x}\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(z \cdot 0.0212463641547976 - x \cdot \left(y \cdot -0.0212463641547976 - z \cdot -0.14147091005106402\right)\right)\\ \end{array} \]

Alternative 13
Accuracy	76.9%
Cost	1225

\[\begin{array}{l} \mathbf{if}\;x \leq -0.108 \lor \neg \left(x \leq 4.5 \cdot 10^{-16}\right):\\ \;\;\;\;\frac{x + -2}{0.24013125253755718 + \frac{5.86923874282773}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x + -2\right) \cdot z}{47.066876606 - x \cdot \left(-313.399215894 - x \cdot 263.505074721\right)}\\ \end{array} \]

Alternative 14
Accuracy	77.3%
Cost	1225

\[\begin{array}{l} \mathbf{if}\;x \leq -0.108 \lor \neg \left(x \leq 5.6\right):\\ \;\;\;\;\frac{x + -2}{0.24013125253755718 + \left(\frac{5.86923874282773}{x} + \frac{-55.572073733743466}{x \cdot x}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x + -2\right) \cdot z}{47.066876606 - x \cdot \left(-313.399215894 - x \cdot 263.505074721\right)}\\ \end{array} \]

Alternative 15
Accuracy	76.8%
Cost	969

\[\begin{array}{l} \mathbf{if}\;x \leq -0.108 \lor \neg \left(x \leq 4.5 \cdot 10^{-16}\right):\\ \;\;\;\;\frac{x + -2}{0.24013125253755718 + \frac{5.86923874282773}{x}}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-0.0424927283095952 + x \cdot \left(0.3041881842569256 + x \cdot -1.787568985856513\right)\right)\\ \end{array} \]

Alternative 16
Accuracy	76.7%
Cost	841

\[\begin{array}{l} \mathbf{if}\;x \leq -0.108 \lor \neg \left(x \leq 4.5 \cdot 10^{-16}\right):\\ \;\;\;\;\frac{x + -2}{0.24013125253755718 + \frac{5.86923874282773}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + -2}{\frac{47.066876606}{z}}\\ \end{array} \]

Alternative 17
Accuracy	76.8%
Cost	840

\[\begin{array}{l} \mathbf{if}\;x \leq -45:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \mathbf{elif}\;x \leq 6.8:\\ \;\;\;\;\frac{x + -2}{\frac{47.066876606}{z}}\\ \mathbf{else}:\\ \;\;\;\;-110.1139242984811 + \left(x \cdot 4.16438922228 + \frac{3655.1204654076414}{x}\right)\\ \end{array} \]

Alternative 18
Accuracy	76.7%
Cost	713

\[\begin{array}{l} \mathbf{if}\;x \leq -5.5 \lor \neg \left(x \leq 9.5 \cdot 10^{-12}\right):\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \mathbf{else}:\\ \;\;\;\;\left(2 - x\right) \cdot \left(z \cdot -0.0212463641547976\right)\\ \end{array} \]

Alternative 19
Accuracy	76.7%
Cost	713

\[\begin{array}{l} \mathbf{if}\;x \leq -5.5 \lor \neg \left(x \leq 9.5 \cdot 10^{-12}\right):\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + -2}{\frac{47.066876606}{z}}\\ \end{array} \]

Alternative 20
Accuracy	76.5%
Cost	585

\[\begin{array}{l} \mathbf{if}\;x \leq -44 \lor \neg \left(x \leq 9.5 \cdot 10^{-12}\right):\\ \;\;\;\;x \cdot 4.16438922228 + -110.1139242984811\\ \mathbf{else}:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \end{array} \]

Alternative 21
Accuracy	76.7%
Cost	585

\[\begin{array}{l} \mathbf{if}\;x \leq -56 \lor \neg \left(x \leq 9.5 \cdot 10^{-12}\right):\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \mathbf{else}:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \end{array} \]

Alternative 22
Accuracy	76.5%
Cost	456

\[\begin{array}{l} \mathbf{if}\;x \leq -5.5:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq 5.8:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228\\ \end{array} \]

Alternative 23
Accuracy	9.2%
Cost	192

\[x \cdot 0.5218852675289308 \]

Alternative 24
Accuracy	45.3%
Cost	192

\[x \cdot 4.16438922228 \]

Reproduce

herbie shell --seed 2023138 
(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)))