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

Average Error: 26.3 → 1.3

Time: 30.0s

Precision: binary64

Cost: 7944

Math

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

↓

\[\begin{array}{l} t_0 := 47.066876606 + \left(313.399215894 + \left(\left(43.3400022514 + x\right) \cdot x + 263.505074721\right) \cdot x\right) \cdot x\\ t_1 := \left(4.16438922228 \cdot x + \left(\left(y - 130977.50649958357\right) \cdot {\left(\frac{1}{x}\right)}^{2} + 3655.1204654076414 \cdot \frac{1}{x}\right)\right) - 110.1139242984811\\ \mathbf{if}\;x \leq -8.2 \cdot 10^{+29}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{+17}:\\ \;\;\;\;\left(\frac{\left(\left(137.519416416 + \left(78.6994924154 + 4.16438922228 \cdot x\right) \cdot x\right) \cdot x + y\right) \cdot x}{t_0} + \frac{z}{t_0}\right) \cdot \left(x + -2\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

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
         (+
          47.066876606
          (*
           (+ 313.399215894 (* (+ (* (+ 43.3400022514 x) x) 263.505074721) x))
           x)))
        (t_1
         (-
          (+
           (* 4.16438922228 x)
           (+
            (* (- y 130977.50649958357) (pow (/ 1.0 x) 2.0))
            (* 3655.1204654076414 (/ 1.0 x))))
          110.1139242984811)))
   (if (<= x -8.2e+29)
     t_1
     (if (<= x 3.8e+17)
       (*
        (+
         (/
          (*
           (+
            (* (+ 137.519416416 (* (+ 78.6994924154 (* 4.16438922228 x)) x)) x)
            y)
           x)
          t_0)
         (/ z t_0))
        (+ x -2.0))
       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 = 47.066876606 + ((313.399215894 + ((((43.3400022514 + x) * x) + 263.505074721) * x)) * x);
	double t_1 = ((4.16438922228 * x) + (((y - 130977.50649958357) * pow((1.0 / x), 2.0)) + (3655.1204654076414 * (1.0 / x)))) - 110.1139242984811;
	double tmp;
	if (x <= -8.2e+29) {
		tmp = t_1;
	} else if (x <= 3.8e+17) {
		tmp = ((((((137.519416416 + ((78.6994924154 + (4.16438922228 * x)) * x)) * x) + y) * x) / t_0) + (z / t_0)) * (x + -2.0);
	} 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 = 47.066876606d0 + ((313.399215894d0 + ((((43.3400022514d0 + x) * x) + 263.505074721d0) * x)) * x)
    t_1 = ((4.16438922228d0 * x) + (((y - 130977.50649958357d0) * ((1.0d0 / x) ** 2.0d0)) + (3655.1204654076414d0 * (1.0d0 / x)))) - 110.1139242984811d0
    if (x <= (-8.2d+29)) then
        tmp = t_1
    else if (x <= 3.8d+17) then
        tmp = ((((((137.519416416d0 + ((78.6994924154d0 + (4.16438922228d0 * x)) * x)) * x) + y) * x) / t_0) + (z / t_0)) * (x + (-2.0d0))
    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 = 47.066876606 + ((313.399215894 + ((((43.3400022514 + x) * x) + 263.505074721) * x)) * x);
	double t_1 = ((4.16438922228 * x) + (((y - 130977.50649958357) * Math.pow((1.0 / x), 2.0)) + (3655.1204654076414 * (1.0 / x)))) - 110.1139242984811;
	double tmp;
	if (x <= -8.2e+29) {
		tmp = t_1;
	} else if (x <= 3.8e+17) {
		tmp = ((((((137.519416416 + ((78.6994924154 + (4.16438922228 * x)) * x)) * x) + y) * x) / t_0) + (z / t_0)) * (x + -2.0);
	} 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 = 47.066876606 + ((313.399215894 + ((((43.3400022514 + x) * x) + 263.505074721) * x)) * x)
	t_1 = ((4.16438922228 * x) + (((y - 130977.50649958357) * math.pow((1.0 / x), 2.0)) + (3655.1204654076414 * (1.0 / x)))) - 110.1139242984811
	tmp = 0
	if x <= -8.2e+29:
		tmp = t_1
	elif x <= 3.8e+17:
		tmp = ((((((137.519416416 + ((78.6994924154 + (4.16438922228 * x)) * x)) * x) + y) * x) / t_0) + (z / t_0)) * (x + -2.0)
	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(47.066876606 + Float64(Float64(313.399215894 + Float64(Float64(Float64(Float64(43.3400022514 + x) * x) + 263.505074721) * x)) * x))
	t_1 = Float64(Float64(Float64(4.16438922228 * x) + Float64(Float64(Float64(y - 130977.50649958357) * (Float64(1.0 / x) ^ 2.0)) + Float64(3655.1204654076414 * Float64(1.0 / x)))) - 110.1139242984811)
	tmp = 0.0
	if (x <= -8.2e+29)
		tmp = t_1;
	elseif (x <= 3.8e+17)
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(137.519416416 + Float64(Float64(78.6994924154 + Float64(4.16438922228 * x)) * x)) * x) + y) * x) / t_0) + Float64(z / t_0)) * Float64(x + -2.0));
	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 = 47.066876606 + ((313.399215894 + ((((43.3400022514 + x) * x) + 263.505074721) * x)) * x);
	t_1 = ((4.16438922228 * x) + (((y - 130977.50649958357) * ((1.0 / x) ^ 2.0)) + (3655.1204654076414 * (1.0 / x)))) - 110.1139242984811;
	tmp = 0.0;
	if (x <= -8.2e+29)
		tmp = t_1;
	elseif (x <= 3.8e+17)
		tmp = ((((((137.519416416 + ((78.6994924154 + (4.16438922228 * x)) * x)) * x) + y) * x) / t_0) + (z / t_0)) * (x + -2.0);
	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[(47.066876606 + N[(N[(313.399215894 + N[(N[(N[(N[(43.3400022514 + x), $MachinePrecision] * x), $MachinePrecision] + 263.505074721), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(N[(4.16438922228 * x), $MachinePrecision] + N[(N[(N[(y - 130977.50649958357), $MachinePrecision] * N[Power[N[(1.0 / x), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] + N[(3655.1204654076414 * N[(1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 110.1139242984811), $MachinePrecision]}, If[LessEqual[x, -8.2e+29], t$95$1, If[LessEqual[x, 3.8e+17], N[(N[(N[(N[(N[(N[(N[(137.519416416 + N[(N[(78.6994924154 + N[(4.16438922228 * x), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision] + y), $MachinePrecision] * x), $MachinePrecision] / t$95$0), $MachinePrecision] + N[(z / t$95$0), $MachinePrecision]), $MachinePrecision] * N[(x + -2.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Target

Original	26.3
Target	0.9
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 < -8.2000000000000007e29 or 3.8e17 < x

   1. Initial program 57.1

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

   2. Simplified 57.1

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

   3. Taylor expanded in x around inf 2.3

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

   if -8.2000000000000007e29 < x < 3.8e17

   1. Initial program 0.6

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

   2. Simplified 0.6

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

   3. Applied egg-rr 0.4

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

   4. Taylor expanded in z around 0 0.4

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

Alternatives

Alternative 1
Error	1.5
Cost	3656

\[\begin{array}{l} t_0 := 47.066876606 + \left(313.399215894 + \left(\left(43.3400022514 + x\right) \cdot x + 263.505074721\right) \cdot x\right) \cdot x\\ \mathbf{if}\;x \leq -3.9 \cdot 10^{+44}:\\ \;\;\;\;4.16438922228 \cdot x\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{+58}:\\ \;\;\;\;\left(\frac{\left(\left(137.519416416 + \left(78.6994924154 + 4.16438922228 \cdot x\right) \cdot x\right) \cdot x + y\right) \cdot x}{t_0} + \frac{z}{t_0}\right) \cdot \left(x + -2\right)\\ \mathbf{else}:\\ \;\;\;\;4.16438922228 \cdot x\\ \end{array} \]

Alternative 2
Error	2.0
Cost	2632

\[\begin{array}{l} \mathbf{if}\;x \leq -3.9 \cdot 10^{+44}:\\ \;\;\;\;4.16438922228 \cdot x\\ \mathbf{elif}\;x \leq 5.7 \cdot 10^{+57}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}\\ \mathbf{else}:\\ \;\;\;\;4.16438922228 \cdot x\\ \end{array} \]

Alternative 3
Error	3.2
Cost	2120

\[\begin{array}{l} t_0 := \left(4.16438922228 + \frac{z}{47.066876606 + \left(313.399215894 + \left(\left(43.3400022514 + x\right) \cdot x + 263.505074721\right) \cdot x\right) \cdot x}\right) \cdot \left(x + -2\right)\\ \mathbf{if}\;x \leq -3.2 \cdot 10^{+26}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 0.94:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(\left(137.519416416 \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 4
Error	5.4
Cost	1736

\[\begin{array}{l} t_0 := \left(4.16438922228 + \frac{z}{47.066876606 + \left(313.399215894 + \left(\left(43.3400022514 + x\right) \cdot x + 263.505074721\right) \cdot x\right) \cdot x}\right) \cdot \left(x + -2\right)\\ \mathbf{if}\;x \leq -4 \cdot 10^{-17}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{-6}:\\ \;\;\;\;\left(0.0212463641547976 \cdot \left(-2 \cdot y + z\right) - -0.28294182010212804 \cdot z\right) \cdot x + \frac{z}{-23.533438303}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 5
Error	6.9
Cost	1608

\[\begin{array}{l} \mathbf{if}\;x \leq -8.8 \cdot 10^{+36}:\\ \;\;\;\;4.16438922228 \cdot x\\ \mathbf{elif}\;x \leq -7 \cdot 10^{-6}:\\ \;\;\;\;\frac{z}{47.066876606 + \left(313.399215894 + \left(\left(43.3400022514 + x\right) \cdot x + 263.505074721\right) \cdot x\right) \cdot x} \cdot \left(x + -2\right)\\ \mathbf{elif}\;x \leq 0.94:\\ \;\;\;\;\left(0.0212463641547976 \cdot \left(-2 \cdot y + z\right) - -0.28294182010212804 \cdot z\right) \cdot x + \frac{z}{-23.533438303}\\ \mathbf{else}:\\ \;\;\;\;4.16438922228 \cdot x\\ \end{array} \]

Alternative 6
Error	6.8
Cost	1352

\[\begin{array}{l} \mathbf{if}\;x \leq -0.175:\\ \;\;\;\;4.16438922228 \cdot \left(x + -2\right)\\ \mathbf{elif}\;x \leq 0.94:\\ \;\;\;\;\left(0.0212463641547976 \cdot z + \left(0.0212463641547976 \cdot y - 0.14147091005106402 \cdot z\right) \cdot x\right) \cdot \left(x + -2\right)\\ \mathbf{else}:\\ \;\;\;\;4.16438922228 \cdot x\\ \end{array} \]

Alternative 7
Error	6.8
Cost	1352

\[\begin{array}{l} \mathbf{if}\;x \leq -5.5:\\ \;\;\;\;4.16438922228 \cdot \left(x + -2\right)\\ \mathbf{elif}\;x \leq 0.94:\\ \;\;\;\;\left(0.0212463641547976 \cdot \left(-2 \cdot y + z\right) - -0.28294182010212804 \cdot z\right) \cdot x + \frac{z}{-23.533438303}\\ \mathbf{else}:\\ \;\;\;\;4.16438922228 \cdot x\\ \end{array} \]

Alternative 8
Error	7.0
Cost	1096

\[\begin{array}{l} t_0 := 4.16438922228 \cdot \left(x + -2\right)\\ \mathbf{if}\;x \leq -0.175:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 26:\\ \;\;\;\;\left(0.0212463641547976 \cdot z + 0.0212463641547976 \cdot \left(y \cdot x\right)\right) \cdot \left(x + -2\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 9
Error	6.9
Cost	1096

\[\begin{array}{l} \mathbf{if}\;x \leq -0.175:\\ \;\;\;\;4.16438922228 \cdot \left(x + -2\right)\\ \mathbf{elif}\;x \leq 0.94:\\ \;\;\;\;\left(-0.0424927283095952 \cdot y - -0.28294182010212804 \cdot z\right) \cdot x + -0.0424927283095952 \cdot z\\ \mathbf{else}:\\ \;\;\;\;4.16438922228 \cdot x\\ \end{array} \]

Alternative 10
Error	15.3
Cost	840

\[\begin{array}{l} \mathbf{if}\;x \leq -0.21:\\ \;\;\;\;4.16438922228 \cdot \left(x + -2\right)\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{-7}:\\ \;\;\;\;z \cdot \left(0.3041881842569256 \cdot x\right) + -0.0424927283095952 \cdot z\\ \mathbf{else}:\\ \;\;\;\;4.16438922228 \cdot x\\ \end{array} \]

Alternative 11
Error	7.0
Cost	840

\[\begin{array}{l} t_0 := 4.16438922228 \cdot \left(x + -2\right)\\ \mathbf{if}\;x \leq -0.175:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 2:\\ \;\;\;\;\left(x \cdot -0.0424927283095952\right) \cdot y + -0.0424927283095952 \cdot z\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 12
Error	15.3
Cost	584

\[\begin{array}{l} t_0 := 4.16438922228 \cdot \left(x + -2\right)\\ \mathbf{if}\;x \leq -0.195:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 1.7:\\ \;\;\;\;\frac{z}{-23.533438303}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 13
Error	15.4
Cost	456

\[\begin{array}{l} \mathbf{if}\;x \leq -0.155:\\ \;\;\;\;4.16438922228 \cdot x\\ \mathbf{elif}\;x \leq 2:\\ \;\;\;\;-0.0424927283095952 \cdot z\\ \mathbf{else}:\\ \;\;\;\;4.16438922228 \cdot x\\ \end{array} \]

Alternative 14
Error	15.3
Cost	456

\[\begin{array}{l} \mathbf{if}\;x \leq -0.175:\\ \;\;\;\;4.16438922228 \cdot x\\ \mathbf{elif}\;x \leq 2:\\ \;\;\;\;\frac{z}{-23.533438303}\\ \mathbf{else}:\\ \;\;\;\;4.16438922228 \cdot x\\ \end{array} \]

Alternative 15
Error	41.7
Cost	192

\[-0.0424927283095952 \cdot z \]

Reproduce

herbie shell --seed 2023010 
(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)))