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

Average Error: 27.4 → 1.3

Time: 23.6s

Precision: binary64

Cost: 7944

Math

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

↓

\[\begin{array}{l} t_0 := \left(313.399215894 + \left(263.505074721 + x \cdot \left(43.3400022514 + x\right)\right) \cdot x\right) \cdot x + 47.066876606\\ t_1 := \left(\left(3655.1204654076414 \cdot \frac{1}{x} + x \cdot 4.16438922228\right) + \left(-\frac{130977.50649958357 + \left(-y\right)}{{x}^{2}}\right)\right) - 110.1139242984811\\ \mathbf{if}\;x \leq -2.6 \cdot 10^{+45}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{+29}:\\ \;\;\;\;z \cdot \left(\frac{x}{t_0} - 2 \cdot \frac{1}{t_0}\right) + \frac{\left(\left(137.519416416 + \left(78.6994924154 + 4.16438922228 \cdot x\right) \cdot x\right) \cdot x + y\right) \cdot \left(x \cdot \left(x - 2\right)\right)}{t_0}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

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 (* (+ 263.505074721 (* x (+ 43.3400022514 x))) x))
           x)
          47.066876606))
        (t_1
         (-
          (+
           (+ (* 3655.1204654076414 (/ 1.0 x)) (* x 4.16438922228))
           (- (/ (+ 130977.50649958357 (- y)) (pow x 2.0))))
          110.1139242984811)))
   (if (<= x -2.6e+45)
     t_1
     (if (<= x 1.8e+29)
       (+
        (* z (- (/ x t_0) (* 2.0 (/ 1.0 t_0))))
        (/
         (*
          (+
           (* (+ 137.519416416 (* (+ 78.6994924154 (* 4.16438922228 x)) x)) x)
           y)
          (* x (- x 2.0)))
         t_0))
       t_1))))

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 + ((263.505074721 + (x * (43.3400022514 + x))) * x)) * x) + 47.066876606;
	double t_1 = (((3655.1204654076414 * (1.0 / x)) + (x * 4.16438922228)) + -((130977.50649958357 + -y) / pow(x, 2.0))) - 110.1139242984811;
	double tmp;
	if (x <= -2.6e+45) {
		tmp = t_1;
	} else if (x <= 1.8e+29) {
		tmp = (z * ((x / t_0) - (2.0 * (1.0 / t_0)))) + (((((137.519416416 + ((78.6994924154 + (4.16438922228 * x)) * x)) * x) + y) * (x * (x - 2.0))) / t_0);
	} else {
		tmp = t_1;
	}
	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) :: t_1
    real(8) :: tmp
    t_0 = ((313.399215894d0 + ((263.505074721d0 + (x * (43.3400022514d0 + x))) * x)) * x) + 47.066876606d0
    t_1 = (((3655.1204654076414d0 * (1.0d0 / x)) + (x * 4.16438922228d0)) + -((130977.50649958357d0 + -y) / (x ** 2.0d0))) - 110.1139242984811d0
    if (x <= (-2.6d+45)) then
        tmp = t_1
    else if (x <= 1.8d+29) then
        tmp = (z * ((x / t_0) - (2.0d0 * (1.0d0 / t_0)))) + (((((137.519416416d0 + ((78.6994924154d0 + (4.16438922228d0 * x)) * x)) * x) + y) * (x * (x - 2.0d0))) / t_0)
    else
        tmp = t_1
    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 = ((313.399215894 + ((263.505074721 + (x * (43.3400022514 + x))) * x)) * x) + 47.066876606;
	double t_1 = (((3655.1204654076414 * (1.0 / x)) + (x * 4.16438922228)) + -((130977.50649958357 + -y) / Math.pow(x, 2.0))) - 110.1139242984811;
	double tmp;
	if (x <= -2.6e+45) {
		tmp = t_1;
	} else if (x <= 1.8e+29) {
		tmp = (z * ((x / t_0) - (2.0 * (1.0 / t_0)))) + (((((137.519416416 + ((78.6994924154 + (4.16438922228 * x)) * x)) * x) + y) * (x * (x - 2.0))) / t_0);
	} else {
		tmp = t_1;
	}
	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 = ((313.399215894 + ((263.505074721 + (x * (43.3400022514 + x))) * x)) * x) + 47.066876606
	t_1 = (((3655.1204654076414 * (1.0 / x)) + (x * 4.16438922228)) + -((130977.50649958357 + -y) / math.pow(x, 2.0))) - 110.1139242984811
	tmp = 0
	if x <= -2.6e+45:
		tmp = t_1
	elif x <= 1.8e+29:
		tmp = (z * ((x / t_0) - (2.0 * (1.0 / t_0)))) + (((((137.519416416 + ((78.6994924154 + (4.16438922228 * x)) * x)) * x) + y) * (x * (x - 2.0))) / t_0)
	else:
		tmp = t_1
	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(313.399215894 + Float64(Float64(263.505074721 + Float64(x * Float64(43.3400022514 + x))) * x)) * x) + 47.066876606)
	t_1 = Float64(Float64(Float64(Float64(3655.1204654076414 * Float64(1.0 / x)) + Float64(x * 4.16438922228)) + Float64(-Float64(Float64(130977.50649958357 + Float64(-y)) / (x ^ 2.0)))) - 110.1139242984811)
	tmp = 0.0
	if (x <= -2.6e+45)
		tmp = t_1;
	elseif (x <= 1.8e+29)
		tmp = Float64(Float64(z * Float64(Float64(x / t_0) - Float64(2.0 * Float64(1.0 / t_0)))) + Float64(Float64(Float64(Float64(Float64(137.519416416 + Float64(Float64(78.6994924154 + Float64(4.16438922228 * x)) * x)) * x) + y) * Float64(x * Float64(x - 2.0))) / t_0));
	else
		tmp = t_1;
	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 = ((313.399215894 + ((263.505074721 + (x * (43.3400022514 + x))) * x)) * x) + 47.066876606;
	t_1 = (((3655.1204654076414 * (1.0 / x)) + (x * 4.16438922228)) + -((130977.50649958357 + -y) / (x ^ 2.0))) - 110.1139242984811;
	tmp = 0.0;
	if (x <= -2.6e+45)
		tmp = t_1;
	elseif (x <= 1.8e+29)
		tmp = (z * ((x / t_0) - (2.0 * (1.0 / t_0)))) + (((((137.519416416 + ((78.6994924154 + (4.16438922228 * x)) * x)) * x) + y) * (x * (x - 2.0))) / t_0);
	else
		tmp = t_1;
	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[(313.399215894 + N[(N[(263.505074721 + N[(x * N[(43.3400022514 + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision] + 47.066876606), $MachinePrecision]}, Block[{t$95$1 = N[(N[(N[(N[(3655.1204654076414 * N[(1.0 / x), $MachinePrecision]), $MachinePrecision] + N[(x * 4.16438922228), $MachinePrecision]), $MachinePrecision] + (-N[(N[(130977.50649958357 + (-y)), $MachinePrecision] / N[Power[x, 2.0], $MachinePrecision]), $MachinePrecision])), $MachinePrecision] - 110.1139242984811), $MachinePrecision]}, If[LessEqual[x, -2.6e+45], t$95$1, If[LessEqual[x, 1.8e+29], N[(N[(z * N[(N[(x / t$95$0), $MachinePrecision] - N[(2.0 * N[(1.0 / t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(N[(N[(137.519416416 + N[(N[(78.6994924154 + N[(4.16438922228 * x), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision] + y), $MachinePrecision] * N[(x * N[(x - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Target

Original	27.4
Target	0.8
Herbie	1.3

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

Derivation

1. Split input into 2 regimes

2. if x < -2.60000000000000007e45 or 1.79999999999999988e29 < x

   1. Initial program 59.4

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

   2. Taylor expanded in x around -inf 1.8

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

   3. Simplified 1.8

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

      [Start] 1.8	\[ \left(-1 \cdot \frac{130977.50649958357 + -1 \cdot y}{{x}^{2}} + \left(4.16438922228 \cdot x + 3655.1204654076414 \cdot \frac{1}{x}\right)\right) - 110.1139242984811 \]
      rational.json-simplify-1 [=>] 1.8	\[ \color{blue}{\left(\left(4.16438922228 \cdot x + 3655.1204654076414 \cdot \frac{1}{x}\right) + -1 \cdot \frac{130977.50649958357 + -1 \cdot y}{{x}^{2}}\right)} - 110.1139242984811 \]
      rational.json-simplify-1 [=>] 1.8	\[ \left(\color{blue}{\left(3655.1204654076414 \cdot \frac{1}{x} + 4.16438922228 \cdot x\right)} + -1 \cdot \frac{130977.50649958357 + -1 \cdot y}{{x}^{2}}\right) - 110.1139242984811 \]
      rational.json-simplify-2 [<=] 1.8	\[ \left(\left(3655.1204654076414 \cdot \frac{1}{x} + \color{blue}{x \cdot 4.16438922228}\right) + -1 \cdot \frac{130977.50649958357 + -1 \cdot y}{{x}^{2}}\right) - 110.1139242984811 \]
      rational.json-simplify-2 [=>] 1.8	\[ \left(\left(3655.1204654076414 \cdot \frac{1}{x} + x \cdot 4.16438922228\right) + \color{blue}{\frac{130977.50649958357 + -1 \cdot y}{{x}^{2}} \cdot -1}\right) - 110.1139242984811 \]
      rational.json-simplify-9 [=>] 1.8	\[ \left(\left(3655.1204654076414 \cdot \frac{1}{x} + x \cdot 4.16438922228\right) + \color{blue}{\left(-\frac{130977.50649958357 + -1 \cdot y}{{x}^{2}}\right)}\right) - 110.1139242984811 \]
      rational.json-simplify-2 [=>] 1.8	\[ \left(\left(3655.1204654076414 \cdot \frac{1}{x} + x \cdot 4.16438922228\right) + \left(-\frac{130977.50649958357 + \color{blue}{y \cdot -1}}{{x}^{2}}\right)\right) - 110.1139242984811 \]
      rational.json-simplify-9 [=>] 1.8	\[ \left(\left(3655.1204654076414 \cdot \frac{1}{x} + x \cdot 4.16438922228\right) + \left(-\frac{130977.50649958357 + \color{blue}{\left(-y\right)}}{{x}^{2}}\right)\right) - 110.1139242984811 \]

   if -2.60000000000000007e45 < x < 1.79999999999999988e29

   1. Initial program 1.0

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

   2. Taylor expanded in z around 0 0.9

      \[\leadsto \color{blue}{z \cdot \left(\frac{x}{\left(313.399215894 + \left(263.505074721 + x \cdot \left(43.3400022514 + x\right)\right) \cdot x\right) \cdot x + 47.066876606} - 2 \cdot \frac{1}{\left(313.399215894 + \left(263.505074721 + x \cdot \left(43.3400022514 + x\right)\right) \cdot x\right) \cdot x + 47.066876606}\right) + \frac{\left(\left(137.519416416 + \left(78.6994924154 + 4.16438922228 \cdot x\right) \cdot x\right) \cdot x + y\right) \cdot \left(x \cdot \left(x - 2\right)\right)}{\left(313.399215894 + \left(263.505074721 + x \cdot \left(43.3400022514 + x\right)\right) \cdot x\right) \cdot x + 47.066876606}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 1.3

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{+45}:\\ \;\;\;\;\left(\left(3655.1204654076414 \cdot \frac{1}{x} + x \cdot 4.16438922228\right) + \left(-\frac{130977.50649958357 + \left(-y\right)}{{x}^{2}}\right)\right) - 110.1139242984811\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{+29}:\\ \;\;\;\;z \cdot \left(\frac{x}{\left(313.399215894 + \left(263.505074721 + x \cdot \left(43.3400022514 + x\right)\right) \cdot x\right) \cdot x + 47.066876606} - 2 \cdot \frac{1}{\left(313.399215894 + \left(263.505074721 + x \cdot \left(43.3400022514 + x\right)\right) \cdot x\right) \cdot x + 47.066876606}\right) + \frac{\left(\left(137.519416416 + \left(78.6994924154 + 4.16438922228 \cdot x\right) \cdot x\right) \cdot x + y\right) \cdot \left(x \cdot \left(x - 2\right)\right)}{\left(313.399215894 + \left(263.505074721 + x \cdot \left(43.3400022514 + x\right)\right) \cdot x\right) \cdot x + 47.066876606}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(3655.1204654076414 \cdot \frac{1}{x} + x \cdot 4.16438922228\right) + \left(-\frac{130977.50649958357 + \left(-y\right)}{{x}^{2}}\right)\right) - 110.1139242984811\\ \end{array} \]

Alternatives

Alternative 1
Error	2.1
Cost	3016

\[\begin{array}{l} t_0 := \left(313.399215894 + \left(263.505074721 + x \cdot \left(43.3400022514 + x\right)\right) \cdot x\right) \cdot x + 47.066876606\\ \mathbf{if}\;x \leq -3.7 \cdot 10^{+55}:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{+27}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\frac{x}{t_0} - 2 \cdot \frac{1}{t_0}\right) + x \cdot 4.16438922228\\ \end{array} \]

Alternative 2
Error	1.9
Cost	2632

\[\begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{+60}:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq 10^{+53}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228\\ \end{array} \]

Alternative 3
Error	3.9
Cost	2120

\[\begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{+22}:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq 6 \cdot 10^{+19}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(\left(x \cdot 137.519416416 + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228\\ \end{array} \]

Alternative 4
Error	4.7
Cost	1736

\[\begin{array}{l} t_0 := \left(x \cdot 4.16438922228 + \frac{3655.1204654076414}{x}\right) - 110.1139242984811\\ \mathbf{if}\;x \leq -20000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 940:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(\left(x \cdot 137.519416416 + y\right) \cdot x + z\right)}{\left(x \cdot 263.505074721 + 313.399215894\right) \cdot x + 47.066876606}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 5
Error	6.4
Cost	1352

\[\begin{array}{l} t_0 := \left(x \cdot 4.16438922228 + \frac{3655.1204654076414}{x}\right) - 110.1139242984811\\ \mathbf{if}\;x \leq -20000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 6.3:\\ \;\;\;\;\left(0.0212463641547976 \cdot \left(-2 \cdot y + z\right) - -0.28294182010212804 \cdot z\right) \cdot x + -0.0424927283095952 \cdot z\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 6
Error	15.1
Cost	1240

\[\begin{array}{l} t_0 := z \cdot \left(-0.0424927283095952 + x \cdot 0.3041881842569256\right)\\ t_1 := x \cdot 4.16438922228 - 110.1139242984811\\ t_2 := -0.0424927283095952 \cdot \left(y \cdot x\right)\\ \mathbf{if}\;x \leq -9.2 \cdot 10^{-8}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.06 \cdot 10^{-56}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -2.5 \cdot 10^{-93}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{-89}:\\ \;\;\;\;-0.0424927283095952 \cdot z\\ \mathbf{elif}\;x \leq 1.02 \cdot 10^{-47}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 166:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 7
Error	6.5
Cost	1096

\[\begin{array}{l} t_0 := \left(x \cdot 4.16438922228 + \frac{3655.1204654076414}{x}\right) - 110.1139242984811\\ \mathbf{if}\;x \leq -20000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 14.5:\\ \;\;\;\;\left(-0.0424927283095952 \cdot y - -0.28294182010212804 \cdot z\right) \cdot x + -0.0424927283095952 \cdot z\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 8
Error	15.0
Cost	848

\[\begin{array}{l} t_0 := x \cdot 4.16438922228 - 110.1139242984811\\ \mathbf{if}\;x \leq -9.2 \cdot 10^{-8}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 4.1 \cdot 10^{-89}:\\ \;\;\;\;-0.0424927283095952 \cdot z\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{-48}:\\ \;\;\;\;-0.0424927283095952 \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{-10}:\\ \;\;\;\;-0.0424927283095952 \cdot z\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 9
Error	6.7
Cost	840

\[\begin{array}{l} t_0 := x \cdot 4.16438922228 - 110.1139242984811\\ \mathbf{if}\;x \leq -20000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{-10}:\\ \;\;\;\;-0.0424927283095952 \cdot \left(y \cdot x\right) + -0.0424927283095952 \cdot z\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 10
Error	6.7
Cost	840

\[\begin{array}{l} t_0 := x \cdot 4.16438922228 - 110.1139242984811\\ \mathbf{if}\;x \leq -20000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{-10}:\\ \;\;\;\;x \cdot \left(-0.0424927283095952 \cdot y\right) + -0.0424927283095952 \cdot z\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 11
Error	6.5
Cost	840

\[\begin{array}{l} t_0 := \left(x \cdot 4.16438922228 + \frac{3655.1204654076414}{x}\right) - 110.1139242984811\\ \mathbf{if}\;x \leq -20000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 2:\\ \;\;\;\;x \cdot \left(-0.0424927283095952 \cdot y\right) + -0.0424927283095952 \cdot z\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 12
Error	15.1
Cost	720

\[\begin{array}{l} \mathbf{if}\;x \leq -9.2 \cdot 10^{-8}:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{-89}:\\ \;\;\;\;-0.0424927283095952 \cdot z\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{-47}:\\ \;\;\;\;-0.0424927283095952 \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;x \leq 2:\\ \;\;\;\;-0.0424927283095952 \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228\\ \end{array} \]

Alternative 13
Error	14.8
Cost	456

\[\begin{array}{l} \mathbf{if}\;x \leq -9.2 \cdot 10^{-8}:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq 2:\\ \;\;\;\;-0.0424927283095952 \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228\\ \end{array} \]

Alternative 14
Error	42.0
Cost	192

\[-0.0424927283095952 \cdot z \]

Reproduce

herbie shell --seed 2023077 
(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)))