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

Average Error: 26.9 → 0.7

Time: 17.3s

Precision: binary64

Math

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

↓

\[\begin{array}{l} t_0 := \mathsf{fma}\left(x \cdot x, 263.505074721, \mathsf{fma}\left({x}^{3}, 43.3400022514, x \cdot 313.399215894\right)\right)\\ t_1 := {x}^{4} + \left(47.066876606 + t_0\right)\\ t_2 := x \cdot \frac{y}{t_1}\\ \mathbf{if}\;x \leq -4.5 \cdot 10^{+61}:\\ \;\;\;\;\frac{3655.1204654076414}{x} + \mathsf{fma}\left(x, 4.16438922228, -110.1139242984811\right)\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{+61}:\\ \;\;\;\;\mathsf{fma}\left(\frac{{x}^{4}}{t_1}, 70.37071397084, \mathsf{fma}\left(4.16438922228, \frac{{x}^{5}}{t_1}, x \cdot t_2\right) + \mathsf{fma}\left(\frac{z}{{x}^{4} + \left(47.066876606 + {\left(\sqrt[3]{t_0}\right)}^{3}\right)}, x, -2 \cdot \left(t_2 + \frac{z}{t_1}\right) - \mathsf{fma}\left(x \cdot \frac{x}{t_1}, 275.038832832, \frac{19.8795684148}{\frac{t_1}{{x}^{3}}}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, 4.16438922228, \frac{3655.1204654076414}{x}\right) + \left(\frac{y}{x \cdot x} + \left(-110.1139242984811 + \frac{-130977.50649958357}{x \cdot x}\right)\right)\\ \end{array} \]

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
         (fma
          (* x x)
          263.505074721
          (fma (pow x 3.0) 43.3400022514 (* x 313.399215894))))
        (t_1 (+ (pow x 4.0) (+ 47.066876606 t_0)))
        (t_2 (* x (/ y t_1))))
   (if (<= x -4.5e+61)
     (+ (/ 3655.1204654076414 x) (fma x 4.16438922228 -110.1139242984811))
     (if (<= x 4.5e+61)
       (fma
        (/ (pow x 4.0) t_1)
        70.37071397084
        (+
         (fma 4.16438922228 (/ (pow x 5.0) t_1) (* x t_2))
         (fma
          (/ z (+ (pow x 4.0) (+ 47.066876606 (pow (cbrt t_0) 3.0))))
          x
          (-
           (* -2.0 (+ t_2 (/ z t_1)))
           (fma
            (* x (/ x t_1))
            275.038832832
            (/ 19.8795684148 (/ t_1 (pow x 3.0))))))))
       (+
        (fma x 4.16438922228 (/ 3655.1204654076414 x))
        (+
         (/ y (* x x))
         (+ -110.1139242984811 (/ -130977.50649958357 (* x x)))))))))

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 = fma((x * x), 263.505074721, fma(pow(x, 3.0), 43.3400022514, (x * 313.399215894)));
	double t_1 = pow(x, 4.0) + (47.066876606 + t_0);
	double t_2 = x * (y / t_1);
	double tmp;
	if (x <= -4.5e+61) {
		tmp = (3655.1204654076414 / x) + fma(x, 4.16438922228, -110.1139242984811);
	} else if (x <= 4.5e+61) {
		tmp = fma((pow(x, 4.0) / t_1), 70.37071397084, (fma(4.16438922228, (pow(x, 5.0) / t_1), (x * t_2)) + fma((z / (pow(x, 4.0) + (47.066876606 + pow(cbrt(t_0), 3.0)))), x, ((-2.0 * (t_2 + (z / t_1))) - fma((x * (x / t_1)), 275.038832832, (19.8795684148 / (t_1 / pow(x, 3.0))))))));
	} else {
		tmp = fma(x, 4.16438922228, (3655.1204654076414 / x)) + ((y / (x * x)) + (-110.1139242984811 + (-130977.50649958357 / (x * x))));
	}
	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 = fma(Float64(x * x), 263.505074721, fma((x ^ 3.0), 43.3400022514, Float64(x * 313.399215894)))
	t_1 = Float64((x ^ 4.0) + Float64(47.066876606 + t_0))
	t_2 = Float64(x * Float64(y / t_1))
	tmp = 0.0
	if (x <= -4.5e+61)
		tmp = Float64(Float64(3655.1204654076414 / x) + fma(x, 4.16438922228, -110.1139242984811));
	elseif (x <= 4.5e+61)
		tmp = fma(Float64((x ^ 4.0) / t_1), 70.37071397084, Float64(fma(4.16438922228, Float64((x ^ 5.0) / t_1), Float64(x * t_2)) + fma(Float64(z / Float64((x ^ 4.0) + Float64(47.066876606 + (cbrt(t_0) ^ 3.0)))), x, Float64(Float64(-2.0 * Float64(t_2 + Float64(z / t_1))) - fma(Float64(x * Float64(x / t_1)), 275.038832832, Float64(19.8795684148 / Float64(t_1 / (x ^ 3.0))))))));
	else
		tmp = Float64(fma(x, 4.16438922228, Float64(3655.1204654076414 / x)) + Float64(Float64(y / Float64(x * x)) + Float64(-110.1139242984811 + Float64(-130977.50649958357 / Float64(x * x)))));
	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[(x * x), $MachinePrecision] * 263.505074721 + N[(N[Power[x, 3.0], $MachinePrecision] * 43.3400022514 + N[(x * 313.399215894), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[Power[x, 4.0], $MachinePrecision] + N[(47.066876606 + t$95$0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(y / t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.5e+61], N[(N[(3655.1204654076414 / x), $MachinePrecision] + N[(x * 4.16438922228 + -110.1139242984811), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.5e+61], N[(N[(N[Power[x, 4.0], $MachinePrecision] / t$95$1), $MachinePrecision] * 70.37071397084 + N[(N[(4.16438922228 * N[(N[Power[x, 5.0], $MachinePrecision] / t$95$1), $MachinePrecision] + N[(x * t$95$2), $MachinePrecision]), $MachinePrecision] + N[(N[(z / N[(N[Power[x, 4.0], $MachinePrecision] + N[(47.066876606 + N[Power[N[Power[t$95$0, 1/3], $MachinePrecision], 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * x + N[(N[(-2.0 * N[(t$95$2 + N[(z / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x * N[(x / t$95$1), $MachinePrecision]), $MachinePrecision] * 275.038832832 + N[(19.8795684148 / N[(t$95$1 / N[Power[x, 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * 4.16438922228 + N[(3655.1204654076414 / x), $MachinePrecision]), $MachinePrecision] + N[(N[(y / N[(x * x), $MachinePrecision]), $MachinePrecision] + N[(-110.1139242984811 + N[(-130977.50649958357 / N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original	26.9
Target	0.9
Herbie	0.7

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

Derivation

1. Split input into 3 regimes

2. if x < -4.5e61

   1. Initial program 64.0

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

   2. Simplified 60.3

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

   3. Applied egg-rr 60.3

      \[\leadsto \left(x + -2\right) \cdot \color{blue}{\left(\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right) \cdot \frac{1}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + 43.3400022514, 263.505074721\right), 313.399215894\right), 47.066876606\right)}\right)} \]

   4. Taylor expanded in x around inf 1.8

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

   5. Simplified 1.8

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

   if -4.5e61 < x < 4.5e61

   1. Initial program 1.9

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

   2. Simplified 0.9

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

   3. Applied egg-rr 1.0

      \[\leadsto \left(x + -2\right) \cdot \color{blue}{\left(\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right) \cdot \frac{1}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + 43.3400022514, 263.505074721\right), 313.399215894\right), 47.066876606\right)}\right)} \]

   4. Taylor expanded in y around 0 1.9

      \[\leadsto \color{blue}{\left(70.37071397084 \cdot \frac{{x}^{4}}{{x}^{4} + \left(47.066876606 + \left(263.505074721 \cdot {x}^{2} + \left(43.3400022514 \cdot {x}^{3} + 313.399215894 \cdot x\right)\right)\right)} + \left(\frac{y \cdot {x}^{2}}{{x}^{4} + \left(47.066876606 + \left(263.505074721 \cdot {x}^{2} + \left(43.3400022514 \cdot {x}^{3} + 313.399215894 \cdot x\right)\right)\right)} + \left(4.16438922228 \cdot \frac{{x}^{5}}{{x}^{4} + \left(47.066876606 + \left(263.505074721 \cdot {x}^{2} + \left(43.3400022514 \cdot {x}^{3} + 313.399215894 \cdot x\right)\right)\right)} + \frac{z \cdot x}{{x}^{4} + \left(47.066876606 + \left(263.505074721 \cdot {x}^{2} + \left(43.3400022514 \cdot {x}^{3} + 313.399215894 \cdot x\right)\right)\right)}\right)\right)\right) - \left(2 \cdot \frac{y \cdot x}{{x}^{4} + \left(47.066876606 + \left(263.505074721 \cdot {x}^{2} + \left(43.3400022514 \cdot {x}^{3} + 313.399215894 \cdot x\right)\right)\right)} + \left(2 \cdot \frac{z}{{x}^{4} + \left(47.066876606 + \left(263.505074721 \cdot {x}^{2} + \left(43.3400022514 \cdot {x}^{3} + 313.399215894 \cdot x\right)\right)\right)} + \left(275.038832832 \cdot \frac{{x}^{2}}{{x}^{4} + \left(47.066876606 + \left(263.505074721 \cdot {x}^{2} + \left(43.3400022514 \cdot {x}^{3} + 313.399215894 \cdot x\right)\right)\right)} + 19.8795684148 \cdot \frac{{x}^{3}}{{x}^{4} + \left(47.066876606 + \left(263.505074721 \cdot {x}^{2} + \left(43.3400022514 \cdot {x}^{3} + 313.399215894 \cdot x\right)\right)\right)}\right)\right)\right)} \]

   5. Simplified 0.3

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{{x}^{4}}{{x}^{4} + \left(47.066876606 + \mathsf{fma}\left(x \cdot x, 263.505074721, \mathsf{fma}\left({x}^{3}, 43.3400022514, x \cdot 313.399215894\right)\right)\right)}, 70.37071397084, \mathsf{fma}\left(4.16438922228, \frac{{x}^{5}}{{x}^{4} + \left(47.066876606 + \mathsf{fma}\left(x \cdot x, 263.505074721, \mathsf{fma}\left({x}^{3}, 43.3400022514, x \cdot 313.399215894\right)\right)\right)}, \left(\frac{y}{{x}^{4} + \left(47.066876606 + \mathsf{fma}\left(x \cdot x, 263.505074721, \mathsf{fma}\left({x}^{3}, 43.3400022514, x \cdot 313.399215894\right)\right)\right)} \cdot x\right) \cdot x\right) + \mathsf{fma}\left(\frac{z}{{x}^{4} + \left(47.066876606 + \mathsf{fma}\left(x \cdot x, 263.505074721, \mathsf{fma}\left({x}^{3}, 43.3400022514, x \cdot 313.399215894\right)\right)\right)}, x, -2 \cdot \left(\frac{y}{{x}^{4} + \left(47.066876606 + \mathsf{fma}\left(x \cdot x, 263.505074721, \mathsf{fma}\left({x}^{3}, 43.3400022514, x \cdot 313.399215894\right)\right)\right)} \cdot x + \frac{z}{{x}^{4} + \left(47.066876606 + \mathsf{fma}\left(x \cdot x, 263.505074721, \mathsf{fma}\left({x}^{3}, 43.3400022514, x \cdot 313.399215894\right)\right)\right)}\right) - \mathsf{fma}\left(\frac{x}{{x}^{4} + \left(47.066876606 + \mathsf{fma}\left(x \cdot x, 263.505074721, \mathsf{fma}\left({x}^{3}, 43.3400022514, x \cdot 313.399215894\right)\right)\right)} \cdot x, 275.038832832, \frac{19.8795684148}{\frac{{x}^{4} + \left(47.066876606 + \mathsf{fma}\left(x \cdot x, 263.505074721, \mathsf{fma}\left({x}^{3}, 43.3400022514, x \cdot 313.399215894\right)\right)\right)}{{x}^{3}}}\right)\right)\right)} \]

   6. Applied egg-rr 0.3

      \[\leadsto \mathsf{fma}\left(\frac{{x}^{4}}{{x}^{4} + \left(47.066876606 + \mathsf{fma}\left(x \cdot x, 263.505074721, \mathsf{fma}\left({x}^{3}, 43.3400022514, x \cdot 313.399215894\right)\right)\right)}, 70.37071397084, \mathsf{fma}\left(4.16438922228, \frac{{x}^{5}}{{x}^{4} + \left(47.066876606 + \mathsf{fma}\left(x \cdot x, 263.505074721, \mathsf{fma}\left({x}^{3}, 43.3400022514, x \cdot 313.399215894\right)\right)\right)}, \left(\frac{y}{{x}^{4} + \left(47.066876606 + \mathsf{fma}\left(x \cdot x, 263.505074721, \mathsf{fma}\left({x}^{3}, 43.3400022514, x \cdot 313.399215894\right)\right)\right)} \cdot x\right) \cdot x\right) + \mathsf{fma}\left(\frac{z}{{x}^{4} + \left(47.066876606 + \color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(x \cdot x, 263.505074721, \mathsf{fma}\left({x}^{3}, 43.3400022514, x \cdot 313.399215894\right)\right)}\right)}^{3}}\right)}, x, -2 \cdot \left(\frac{y}{{x}^{4} + \left(47.066876606 + \mathsf{fma}\left(x \cdot x, 263.505074721, \mathsf{fma}\left({x}^{3}, 43.3400022514, x \cdot 313.399215894\right)\right)\right)} \cdot x + \frac{z}{{x}^{4} + \left(47.066876606 + \mathsf{fma}\left(x \cdot x, 263.505074721, \mathsf{fma}\left({x}^{3}, 43.3400022514, x \cdot 313.399215894\right)\right)\right)}\right) - \mathsf{fma}\left(\frac{x}{{x}^{4} + \left(47.066876606 + \mathsf{fma}\left(x \cdot x, 263.505074721, \mathsf{fma}\left({x}^{3}, 43.3400022514, x \cdot 313.399215894\right)\right)\right)} \cdot x, 275.038832832, \frac{19.8795684148}{\frac{{x}^{4} + \left(47.066876606 + \mathsf{fma}\left(x \cdot x, 263.505074721, \mathsf{fma}\left({x}^{3}, 43.3400022514, x \cdot 313.399215894\right)\right)\right)}{{x}^{3}}}\right)\right)\right) \]

   if 4.5e61 < x

   1. Initial program 64.0

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

   2. Simplified 60.5

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

   3. Taylor expanded in x around inf 0.7

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

   4. Simplified 0.7

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, 4.16438922228, \frac{3655.1204654076414}{x}\right) + \left(\frac{y}{x \cdot x} + \left(-110.1139242984811 + \frac{-130977.50649958357}{x \cdot x}\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 0.7

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{+61}:\\ \;\;\;\;\frac{3655.1204654076414}{x} + \mathsf{fma}\left(x, 4.16438922228, -110.1139242984811\right)\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{+61}:\\ \;\;\;\;\mathsf{fma}\left(\frac{{x}^{4}}{{x}^{4} + \left(47.066876606 + \mathsf{fma}\left(x \cdot x, 263.505074721, \mathsf{fma}\left({x}^{3}, 43.3400022514, x \cdot 313.399215894\right)\right)\right)}, 70.37071397084, \mathsf{fma}\left(4.16438922228, \frac{{x}^{5}}{{x}^{4} + \left(47.066876606 + \mathsf{fma}\left(x \cdot x, 263.505074721, \mathsf{fma}\left({x}^{3}, 43.3400022514, x \cdot 313.399215894\right)\right)\right)}, x \cdot \left(x \cdot \frac{y}{{x}^{4} + \left(47.066876606 + \mathsf{fma}\left(x \cdot x, 263.505074721, \mathsf{fma}\left({x}^{3}, 43.3400022514, x \cdot 313.399215894\right)\right)\right)}\right)\right) + \mathsf{fma}\left(\frac{z}{{x}^{4} + \left(47.066876606 + {\left(\sqrt[3]{\mathsf{fma}\left(x \cdot x, 263.505074721, \mathsf{fma}\left({x}^{3}, 43.3400022514, x \cdot 313.399215894\right)\right)}\right)}^{3}\right)}, x, -2 \cdot \left(x \cdot \frac{y}{{x}^{4} + \left(47.066876606 + \mathsf{fma}\left(x \cdot x, 263.505074721, \mathsf{fma}\left({x}^{3}, 43.3400022514, x \cdot 313.399215894\right)\right)\right)} + \frac{z}{{x}^{4} + \left(47.066876606 + \mathsf{fma}\left(x \cdot x, 263.505074721, \mathsf{fma}\left({x}^{3}, 43.3400022514, x \cdot 313.399215894\right)\right)\right)}\right) - \mathsf{fma}\left(x \cdot \frac{x}{{x}^{4} + \left(47.066876606 + \mathsf{fma}\left(x \cdot x, 263.505074721, \mathsf{fma}\left({x}^{3}, 43.3400022514, x \cdot 313.399215894\right)\right)\right)}, 275.038832832, \frac{19.8795684148}{\frac{{x}^{4} + \left(47.066876606 + \mathsf{fma}\left(x \cdot x, 263.505074721, \mathsf{fma}\left({x}^{3}, 43.3400022514, x \cdot 313.399215894\right)\right)\right)}{{x}^{3}}}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, 4.16438922228, \frac{3655.1204654076414}{x}\right) + \left(\frac{y}{x \cdot x} + \left(-110.1139242984811 + \frac{-130977.50649958357}{x \cdot x}\right)\right)\\ \end{array} \]

Reproduce

herbie shell --seed 2022166 
(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)))