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

Average Error: 26.6 → 1.5

Time: 18.3s

Precision: binary64

Cost: 15560

Math

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

↓

\[\begin{array}{l} t_0 := \left(3655.1204654076414 \cdot \frac{1}{x} + x \cdot 4.16438922228\right) + \left(\left(-\frac{130977.50649958357 + \left(-y\right)}{{x}^{2}}\right) - 110.1139242984811\right)\\ \mathbf{if}\;x \leq -1.15 \cdot 10^{+17}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{+16}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left({x}^{3} + \left(x \cdot 263.505074721 + {x}^{2} \cdot 43.3400022514\right)\right) + 313.399215894\right) \cdot x + 47.066876606}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

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
         (+
          (+ (* 3655.1204654076414 (/ 1.0 x)) (* x 4.16438922228))
          (-
           (- (/ (+ 130977.50649958357 (- y)) (pow x 2.0)))
           110.1139242984811))))
   (if (<= x -1.15e+17)
     t_0
     (if (<= x 3.2e+16)
       (/
        (*
         (- x 2.0)
         (+
          (*
           (+
            (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x)
            y)
           x)
          z))
        (+
         (*
          (+
           (+
            (pow x 3.0)
            (+ (* x 263.505074721) (* (pow x 2.0) 43.3400022514)))
           313.399215894)
          x)
         47.066876606))
       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 = ((3655.1204654076414 * (1.0 / x)) + (x * 4.16438922228)) + (-((130977.50649958357 + -y) / pow(x, 2.0)) - 110.1139242984811);
	double tmp;
	if (x <= -1.15e+17) {
		tmp = t_0;
	} else if (x <= 3.2e+16) {
		tmp = ((x - 2.0) * ((((((((x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z)) / ((((pow(x, 3.0) + ((x * 263.505074721) + (pow(x, 2.0) * 43.3400022514))) + 313.399215894) * x) + 47.066876606);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

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

↓

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = ((3655.1204654076414d0 * (1.0d0 / x)) + (x * 4.16438922228d0)) + (-((130977.50649958357d0 + -y) / (x ** 2.0d0)) - 110.1139242984811d0)
    if (x <= (-1.15d+17)) then
        tmp = t_0
    else if (x <= 3.2d+16) then
        tmp = ((x - 2.0d0) * ((((((((x * 4.16438922228d0) + 78.6994924154d0) * x) + 137.519416416d0) * x) + y) * x) + z)) / (((((x ** 3.0d0) + ((x * 263.505074721d0) + ((x ** 2.0d0) * 43.3400022514d0))) + 313.399215894d0) * x) + 47.066876606d0)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

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

↓

public static double code(double x, double y, double z) {
	double t_0 = ((3655.1204654076414 * (1.0 / x)) + (x * 4.16438922228)) + (-((130977.50649958357 + -y) / Math.pow(x, 2.0)) - 110.1139242984811);
	double tmp;
	if (x <= -1.15e+17) {
		tmp = t_0;
	} else if (x <= 3.2e+16) {
		tmp = ((x - 2.0) * ((((((((x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z)) / ((((Math.pow(x, 3.0) + ((x * 263.505074721) + (Math.pow(x, 2.0) * 43.3400022514))) + 313.399215894) * x) + 47.066876606);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

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

↓

def code(x, y, z):
	t_0 = ((3655.1204654076414 * (1.0 / x)) + (x * 4.16438922228)) + (-((130977.50649958357 + -y) / math.pow(x, 2.0)) - 110.1139242984811)
	tmp = 0
	if x <= -1.15e+17:
		tmp = t_0
	elif x <= 3.2e+16:
		tmp = ((x - 2.0) * ((((((((x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z)) / ((((math.pow(x, 3.0) + ((x * 263.505074721) + (math.pow(x, 2.0) * 43.3400022514))) + 313.399215894) * x) + 47.066876606)
	else:
		tmp = t_0
	return tmp

Julia

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

↓

function code(x, y, z)
	t_0 = Float64(Float64(Float64(3655.1204654076414 * Float64(1.0 / x)) + Float64(x * 4.16438922228)) + Float64(Float64(-Float64(Float64(130977.50649958357 + Float64(-y)) / (x ^ 2.0))) - 110.1139242984811))
	tmp = 0.0
	if (x <= -1.15e+17)
		tmp = t_0;
	elseif (x <= 3.2e+16)
		tmp = 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((x ^ 3.0) + Float64(Float64(x * 263.505074721) + Float64((x ^ 2.0) * 43.3400022514))) + 313.399215894) * x) + 47.066876606));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

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

↓

function tmp_2 = code(x, y, z)
	t_0 = ((3655.1204654076414 * (1.0 / x)) + (x * 4.16438922228)) + (-((130977.50649958357 + -y) / (x ^ 2.0)) - 110.1139242984811);
	tmp = 0.0;
	if (x <= -1.15e+17)
		tmp = t_0;
	elseif (x <= 3.2e+16)
		tmp = ((x - 2.0) * ((((((((x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z)) / (((((x ^ 3.0) + ((x * 263.505074721) + ((x ^ 2.0) * 43.3400022514))) + 313.399215894) * x) + 47.066876606);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

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

↓

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(3655.1204654076414 * N[(1.0 / x), $MachinePrecision]), $MachinePrecision] + N[(x * 4.16438922228), $MachinePrecision]), $MachinePrecision] + N[((-N[(N[(130977.50649958357 + (-y)), $MachinePrecision] / N[Power[x, 2.0], $MachinePrecision]), $MachinePrecision]) - 110.1139242984811), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.15e+17], t$95$0, If[LessEqual[x, 3.2e+16], 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[Power[x, 3.0], $MachinePrecision] + N[(N[(x * 263.505074721), $MachinePrecision] + N[(N[Power[x, 2.0], $MachinePrecision] * 43.3400022514), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 313.399215894), $MachinePrecision] * x), $MachinePrecision] + 47.066876606), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Target

Original	26.6
Target	0.9
Herbie	1.5

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

Derivation

1. Split input into 2 regimes

2. if x < -1.15e17 or 3.2e16 < x

   1. Initial program 55.6

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

   2. Taylor expanded in x around -inf 2.6

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

   3. Simplified 2.6

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

      [Start] 2.6	\[ \left(-1 \cdot \frac{130977.50649958357 + -1 \cdot y}{{x}^{2}} + \left(4.16438922228 \cdot x + 3655.1204654076414 \cdot \frac{1}{x}\right)\right) - 110.1139242984811 \]
      rational_best_oopsla_all_46_json_45_simplify-107 [=>] 2.6	\[ \color{blue}{\left(4.16438922228 \cdot x + 3655.1204654076414 \cdot \frac{1}{x}\right) + \left(-1 \cdot \frac{130977.50649958357 + -1 \cdot y}{{x}^{2}} - 110.1139242984811\right)} \]
      rational_best_oopsla_all_46_json_45_simplify-35 [=>] 2.6	\[ \color{blue}{\left(3655.1204654076414 \cdot \frac{1}{x} + 4.16438922228 \cdot x\right)} + \left(-1 \cdot \frac{130977.50649958357 + -1 \cdot y}{{x}^{2}} - 110.1139242984811\right) \]
      rational_best_oopsla_all_46_json_45_simplify-74 [<=] 2.6	\[ \left(3655.1204654076414 \cdot \frac{1}{x} + \color{blue}{x \cdot 4.16438922228}\right) + \left(-1 \cdot \frac{130977.50649958357 + -1 \cdot y}{{x}^{2}} - 110.1139242984811\right) \]
      rational_best_oopsla_all_46_json_45_simplify-74 [=>] 2.6	\[ \left(3655.1204654076414 \cdot \frac{1}{x} + x \cdot 4.16438922228\right) + \left(\color{blue}{\frac{130977.50649958357 + -1 \cdot y}{{x}^{2}} \cdot -1} - 110.1139242984811\right) \]
      rational_best_oopsla_all_46_json_45_simplify-92 [=>] 2.6	\[ \left(3655.1204654076414 \cdot \frac{1}{x} + x \cdot 4.16438922228\right) + \left(\color{blue}{\left(-\frac{130977.50649958357 + -1 \cdot y}{{x}^{2}}\right)} - 110.1139242984811\right) \]
      rational_best_oopsla_all_46_json_45_simplify-74 [=>] 2.6	\[ \left(3655.1204654076414 \cdot \frac{1}{x} + x \cdot 4.16438922228\right) + \left(\left(-\frac{130977.50649958357 + \color{blue}{y \cdot -1}}{{x}^{2}}\right) - 110.1139242984811\right) \]
      rational_best_oopsla_all_46_json_45_simplify-92 [=>] 2.6	\[ \left(3655.1204654076414 \cdot \frac{1}{x} + x \cdot 4.16438922228\right) + \left(\left(-\frac{130977.50649958357 + \color{blue}{\left(-y\right)}}{{x}^{2}}\right) - 110.1139242984811\right) \]

   if -1.15e17 < x < 3.2e16

   1. Initial program 0.4

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

   2. Taylor expanded in x around 0 0.4

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

   3. Simplified 0.4

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

      [Start] 0.4	\[ \frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(43.3400022514 \cdot {x}^{2} + \left(263.505074721 \cdot x + {x}^{3}\right)\right) + 313.399215894\right) \cdot x + 47.066876606} \]
      rational_best_oopsla_all_46_json_45_simplify-82 [=>] 0.4	\[ \frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\color{blue}{\left(263.505074721 \cdot x + \left(43.3400022514 \cdot {x}^{2} + {x}^{3}\right)\right)} + 313.399215894\right) \cdot x + 47.066876606} \]
      rational_best_oopsla_all_46_json_45_simplify-35 [=>] 0.4	\[ \frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(263.505074721 \cdot x + \color{blue}{\left({x}^{3} + 43.3400022514 \cdot {x}^{2}\right)}\right) + 313.399215894\right) \cdot x + 47.066876606} \]
      rational_best_oopsla_all_46_json_45_simplify-82 [=>] 0.4	\[ \frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\color{blue}{\left({x}^{3} + \left(263.505074721 \cdot x + 43.3400022514 \cdot {x}^{2}\right)\right)} + 313.399215894\right) \cdot x + 47.066876606} \]
      rational_best_oopsla_all_46_json_45_simplify-74 [<=] 0.4	\[ \frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left({x}^{3} + \left(\color{blue}{x \cdot 263.505074721} + 43.3400022514 \cdot {x}^{2}\right)\right) + 313.399215894\right) \cdot x + 47.066876606} \]
      rational_best_oopsla_all_46_json_45_simplify-74 [=>] 0.4	\[ \frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left({x}^{3} + \left(x \cdot 263.505074721 + \color{blue}{{x}^{2} \cdot 43.3400022514}\right)\right) + 313.399215894\right) \cdot x + 47.066876606} \]

3. Recombined 2 regimes into one program.

4. Final simplification 1.5

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{+17}:\\ \;\;\;\;\left(3655.1204654076414 \cdot \frac{1}{x} + x \cdot 4.16438922228\right) + \left(\left(-\frac{130977.50649958357 + \left(-y\right)}{{x}^{2}}\right) - 110.1139242984811\right)\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{+16}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left({x}^{3} + \left(x \cdot 263.505074721 + {x}^{2} \cdot 43.3400022514\right)\right) + 313.399215894\right) \cdot x + 47.066876606}\\ \mathbf{else}:\\ \;\;\;\;\left(3655.1204654076414 \cdot \frac{1}{x} + x \cdot 4.16438922228\right) + \left(\left(-\frac{130977.50649958357 + \left(-y\right)}{{x}^{2}}\right) - 110.1139242984811\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	1.5
Cost	7944

\[\begin{array}{l} t_0 := \left(3655.1204654076414 \cdot \frac{1}{x} + x \cdot 4.16438922228\right) + \left(\left(-\frac{130977.50649958357 + \left(-y\right)}{{x}^{2}}\right) - 110.1139242984811\right)\\ \mathbf{if}\;x \leq -1.15 \cdot 10^{+17}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{+17}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(x \cdot \left(x \cdot \left(x + 43.3400022514\right)\right) + x \cdot 263.505074721\right) + 313.399215894\right) \cdot x + 47.066876606}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Error	1.9
Cost	5064

\[\begin{array}{l} t_0 := \left(313.399215894 + \left(263.505074721 + x \cdot \left(43.3400022514 + x\right)\right) \cdot x\right) \cdot x + 47.066876606\\ \mathbf{if}\;x \leq -3.4 \cdot 10^{+61}:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{+45}:\\ \;\;\;\;z \cdot \left(\frac{x}{t_0} - 2 \cdot \frac{1}{t_0}\right) + \frac{\left(\left(137.519416416 + \left(78.6994924154 + 4.16438922228 \cdot x\right) \cdot x\right) \cdot x + y\right) \cdot \left(x \cdot \left(x - 2\right)\right)}{t_0}\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228\\ \end{array} \]

Alternative 3
Error	2.1
Cost	2760

\[\begin{array}{l} \mathbf{if}\;x \leq -1.85 \cdot 10^{+61}:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{+45}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(x \cdot \left(x \cdot \left(x + 43.3400022514\right)\right) + x \cdot 263.505074721\right) + 313.399215894\right) \cdot x + 47.066876606}\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228\\ \end{array} \]

Alternative 4
Error	3.8
Cost	2636

\[\begin{array}{l} t_0 := x \cdot \left(x + 43.3400022514\right)\\ \mathbf{if}\;x \leq -7.5 \cdot 10^{+46}:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq 11:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(\left(x \cdot 137.519416416 + y\right) \cdot x + z\right)}{\left(\left(x \cdot t_0 + x \cdot 263.505074721\right) + 313.399215894\right) \cdot x + 47.066876606}\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{+45}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(x \cdot \left(y + x \cdot \left(137.519416416 + x \cdot \left(78.6994924154 + x \cdot 4.16438922228\right)\right)\right)\right)}{x \cdot \left(313.399215894 + x \cdot \left(263.505074721 + t_0\right)\right) + 47.066876606}\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228\\ \end{array} \]

Alternative 5
Error	2.1
Cost	2632

\[\begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{+56}:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{+45}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228\\ \end{array} \]

Alternative 6
Error	4.2
Cost	2248

\[\begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{+46}:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq 4.3 \cdot 10^{+40}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(\left(x \cdot 137.519416416 + y\right) \cdot x + z\right)}{\left(\left(x \cdot \left(x \cdot \left(x + 43.3400022514\right)\right) + x \cdot 263.505074721\right) + 313.399215894\right) \cdot x + 47.066876606}\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228\\ \end{array} \]

Alternative 7
Error	4.1
Cost	2120

\[\begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{+46}:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{+39}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(\left(x \cdot 137.519416416 + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228\\ \end{array} \]

Alternative 8
Error	5.4
Cost	1736

\[\begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{+46}:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{-6}:\\ \;\;\;\;\frac{y \cdot \left(\left(x - 2\right) \cdot x\right)}{\left(313.399215894 + \left(263.505074721 + x \cdot \left(43.3400022514 + x\right)\right) \cdot x\right) \cdot x + 47.066876606}\\ \mathbf{elif}\;x \leq 280:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(\left(x \cdot 137.519416416 + y\right) \cdot x + z\right)}{x \cdot 313.399215894 + 47.066876606}\\ \mathbf{else}:\\ \;\;\;\;\left(4.16438922228 \cdot x + 3655.1204654076414 \cdot \frac{1}{x}\right) - 110.1139242984811\\ \end{array} \]

Alternative 9
Error	5.1
Cost	1480

\[\begin{array}{l} \mathbf{if}\;x \leq -37:\\ \;\;\;\;70.37071397084 + x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq 650:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(\left(x \cdot 137.519416416 + y\right) \cdot x + z\right)}{x \cdot 313.399215894 + 47.066876606}\\ \mathbf{else}:\\ \;\;\;\;\left(4.16438922228 \cdot x + 3655.1204654076414 \cdot \frac{1}{x}\right) - 110.1139242984811\\ \end{array} \]

Alternative 10
Error	7.1
Cost	1352

\[\begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{+25}:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq 2:\\ \;\;\;\;\left(0.0212463641547976 \cdot \left(-2 \cdot y + z\right) - -0.28294182010212804 \cdot z\right) \cdot x + -0.0424927283095952 \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(4.16438922228 \cdot x + 3655.1204654076414 \cdot \frac{1}{x}\right) - 110.1139242984811\\ \end{array} \]

Alternative 11
Error	7.2
Cost	968

\[\begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{+25}:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq 2:\\ \;\;\;\;-0.0424927283095952 \cdot \left(y \cdot x\right) + -0.0424927283095952 \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(4.16438922228 \cdot x + 3655.1204654076414 \cdot \frac{1}{x}\right) - 110.1139242984811\\ \end{array} \]

Alternative 12
Error	15.4
Cost	844

\[\begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{+25}:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq -1.02 \cdot 10^{-39}:\\ \;\;\;\;-0.0424927283095952 \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;x \leq 195:\\ \;\;\;\;\left(x \cdot 0.3041881842569256 + -0.0424927283095952\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228 - 110.1139242984811\\ \end{array} \]

Alternative 13
Error	7.2
Cost	840

\[\begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{+25}:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq 12.6:\\ \;\;\;\;-0.0424927283095952 \cdot \left(y \cdot x\right) + -0.0424927283095952 \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228 - 110.1139242984811\\ \end{array} \]

Alternative 14
Error	15.5
Cost	588

\[\begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{+25}:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq -1.6 \cdot 10^{-40}:\\ \;\;\;\;-0.0424927283095952 \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;x \leq 2:\\ \;\;\;\;-0.0424927283095952 \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228\\ \end{array} \]

Alternative 15
Error	15.5
Cost	456

\[\begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{+25}:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq 2:\\ \;\;\;\;-0.0424927283095952 \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228\\ \end{array} \]

Alternative 16
Error	41.7
Cost	192

\[-0.0424927283095952 \cdot z \]

Reproduce

herbie shell --seed 2023090 
(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)))