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

Average Error: 41.56% → 2.27%

Time: 26.3s

Precision: binary64

Cost: 2760

Math

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

↓

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

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
 (if (<= x -1.15e+17)
   (+
    (+ (/ 3655.1204654076414 x) (* x 4.16438922228))
    (+ -110.1139242984811 (* (- 130977.50649958357 y) (/ -1.0 (* x x)))))
   (if (<= x 3.2e+16)
     (/
      (*
       (+
        (*
         x
         (+
          y
          (*
           x
           (- 137.519416416 (* x (- -78.6994924154 (* x 4.16438922228)))))))
        z)
       (+ x -2.0))
      (+
       (*
        x
        (+
         (+ (* x (* x (+ x 43.3400022514))) (* x 263.505074721))
         313.399215894))
       47.066876606))
     (-
      (* x 4.16438922228)
      (+ (/ (- 130977.50649958357 y) (* x x)) 110.1139242984811)))))

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 tmp;
	if (x <= -1.15e+17) {
		tmp = ((3655.1204654076414 / x) + (x * 4.16438922228)) + (-110.1139242984811 + ((130977.50649958357 - y) * (-1.0 / (x * x))));
	} else if (x <= 3.2e+16) {
		tmp = (((x * (y + (x * (137.519416416 - (x * (-78.6994924154 - (x * 4.16438922228))))))) + z) * (x + -2.0)) / ((x * (((x * (x * (x + 43.3400022514))) + (x * 263.505074721)) + 313.399215894)) + 47.066876606);
	} else {
		tmp = (x * 4.16438922228) - (((130977.50649958357 - y) / (x * x)) + 110.1139242984811);
	}
	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) :: tmp
    if (x <= (-1.15d+17)) then
        tmp = ((3655.1204654076414d0 / x) + (x * 4.16438922228d0)) + ((-110.1139242984811d0) + ((130977.50649958357d0 - y) * ((-1.0d0) / (x * x))))
    else if (x <= 3.2d+16) then
        tmp = (((x * (y + (x * (137.519416416d0 - (x * ((-78.6994924154d0) - (x * 4.16438922228d0))))))) + z) * (x + (-2.0d0))) / ((x * (((x * (x * (x + 43.3400022514d0))) + (x * 263.505074721d0)) + 313.399215894d0)) + 47.066876606d0)
    else
        tmp = (x * 4.16438922228d0) - (((130977.50649958357d0 - y) / (x * x)) + 110.1139242984811d0)
    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 tmp;
	if (x <= -1.15e+17) {
		tmp = ((3655.1204654076414 / x) + (x * 4.16438922228)) + (-110.1139242984811 + ((130977.50649958357 - y) * (-1.0 / (x * x))));
	} else if (x <= 3.2e+16) {
		tmp = (((x * (y + (x * (137.519416416 - (x * (-78.6994924154 - (x * 4.16438922228))))))) + z) * (x + -2.0)) / ((x * (((x * (x * (x + 43.3400022514))) + (x * 263.505074721)) + 313.399215894)) + 47.066876606);
	} else {
		tmp = (x * 4.16438922228) - (((130977.50649958357 - y) / (x * x)) + 110.1139242984811);
	}
	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):
	tmp = 0
	if x <= -1.15e+17:
		tmp = ((3655.1204654076414 / x) + (x * 4.16438922228)) + (-110.1139242984811 + ((130977.50649958357 - y) * (-1.0 / (x * x))))
	elif x <= 3.2e+16:
		tmp = (((x * (y + (x * (137.519416416 - (x * (-78.6994924154 - (x * 4.16438922228))))))) + z) * (x + -2.0)) / ((x * (((x * (x * (x + 43.3400022514))) + (x * 263.505074721)) + 313.399215894)) + 47.066876606)
	else:
		tmp = (x * 4.16438922228) - (((130977.50649958357 - y) / (x * x)) + 110.1139242984811)
	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)
	tmp = 0.0
	if (x <= -1.15e+17)
		tmp = Float64(Float64(Float64(3655.1204654076414 / x) + Float64(x * 4.16438922228)) + Float64(-110.1139242984811 + Float64(Float64(130977.50649958357 - y) * Float64(-1.0 / Float64(x * x)))));
	elseif (x <= 3.2e+16)
		tmp = Float64(Float64(Float64(Float64(x * Float64(y + Float64(x * Float64(137.519416416 - Float64(x * Float64(-78.6994924154 - Float64(x * 4.16438922228))))))) + z) * Float64(x + -2.0)) / Float64(Float64(x * Float64(Float64(Float64(x * Float64(x * Float64(x + 43.3400022514))) + Float64(x * 263.505074721)) + 313.399215894)) + 47.066876606));
	else
		tmp = Float64(Float64(x * 4.16438922228) - Float64(Float64(Float64(130977.50649958357 - y) / Float64(x * x)) + 110.1139242984811));
	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)
	tmp = 0.0;
	if (x <= -1.15e+17)
		tmp = ((3655.1204654076414 / x) + (x * 4.16438922228)) + (-110.1139242984811 + ((130977.50649958357 - y) * (-1.0 / (x * x))));
	elseif (x <= 3.2e+16)
		tmp = (((x * (y + (x * (137.519416416 - (x * (-78.6994924154 - (x * 4.16438922228))))))) + z) * (x + -2.0)) / ((x * (((x * (x * (x + 43.3400022514))) + (x * 263.505074721)) + 313.399215894)) + 47.066876606);
	else
		tmp = (x * 4.16438922228) - (((130977.50649958357 - y) / (x * x)) + 110.1139242984811);
	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_] := If[LessEqual[x, -1.15e+17], N[(N[(N[(3655.1204654076414 / x), $MachinePrecision] + N[(x * 4.16438922228), $MachinePrecision]), $MachinePrecision] + N[(-110.1139242984811 + N[(N[(130977.50649958357 - y), $MachinePrecision] * N[(-1.0 / N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.2e+16], N[(N[(N[(N[(x * N[(y + N[(x * N[(137.519416416 - N[(x * N[(-78.6994924154 - N[(x * 4.16438922228), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision] * N[(x + -2.0), $MachinePrecision]), $MachinePrecision] / N[(N[(x * N[(N[(N[(x * N[(x * N[(x + 43.3400022514), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * 263.505074721), $MachinePrecision]), $MachinePrecision] + 313.399215894), $MachinePrecision]), $MachinePrecision] + 47.066876606), $MachinePrecision]), $MachinePrecision], N[(N[(x * 4.16438922228), $MachinePrecision] - N[(N[(N[(130977.50649958357 - y), $MachinePrecision] / N[(x * x), $MachinePrecision]), $MachinePrecision] + 110.1139242984811), $MachinePrecision]), $MachinePrecision]]]

Target

Original	41.56%
Target	1.44%
Herbie	2.27%

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

Derivation

1. Split input into 3 regimes

2. if x < -1.15e17

   1. Initial program 86.84

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

   2. Simplified 79.96

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

      [Start] 86.84	\[ \frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
      associate-*l/ [<=] 79.96	\[ \color{blue}{\frac{x - 2}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)} \]
      *-commutative [=>] 79.96	\[ \color{blue}{\left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right) \cdot \frac{x - 2}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}} \]
      *-commutative [=>] 79.96	\[ \left(\color{blue}{x \cdot \left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right)} + z\right) \cdot \frac{x - 2}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
      fma-def [=>] 79.96	\[ \color{blue}{\mathsf{fma}\left(x, \left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y, z\right)} \cdot \frac{x - 2}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
      *-commutative [=>] 79.96	\[ \mathsf{fma}\left(x, \color{blue}{x \cdot \left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right)} + y, z\right) \cdot \frac{x - 2}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
      fma-def [=>] 79.96	\[ \mathsf{fma}\left(x, \color{blue}{\mathsf{fma}\left(x, \left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416, y\right)}, z\right) \cdot \frac{x - 2}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
      *-commutative [=>] 79.96	\[ \mathsf{fma}\left(x, \mathsf{fma}\left(x, \color{blue}{x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right)} + 137.519416416, y\right), z\right) \cdot \frac{x - 2}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
      fma-def [=>] 79.96	\[ \mathsf{fma}\left(x, \mathsf{fma}\left(x, \color{blue}{\mathsf{fma}\left(x, x \cdot 4.16438922228 + 78.6994924154, 137.519416416\right)}, y\right), z\right) \cdot \frac{x - 2}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
      fma-def [=>] 79.96	\[ \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \color{blue}{\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right)}, 137.519416416\right), y\right), z\right) \cdot \frac{x - 2}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
      sub-neg [=>] 79.96	\[ \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right) \cdot \frac{\color{blue}{x + \left(-2\right)}}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
      metadata-eval [=>] 79.96	\[ \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right) \cdot \frac{x + \color{blue}{-2}}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

   3. Taylor expanded in x around -inf 4.41

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

   4. Simplified 4.41

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, 4.16438922228, \frac{3655.1204654076414}{x}\right) - \left(\frac{130977.50649958357 - y}{x \cdot x} - -110.1139242984811\right)} \]
      Proof

      [Start] 4.41	\[ \left(-1 \cdot \frac{130977.50649958357 + -1 \cdot y}{{x}^{2}} + \left(4.16438922228 \cdot x + 3655.1204654076414 \cdot \frac{1}{x}\right)\right) - 110.1139242984811 \]
      sub-neg [=>] 4.41	\[ \color{blue}{\left(-1 \cdot \frac{130977.50649958357 + -1 \cdot y}{{x}^{2}} + \left(4.16438922228 \cdot x + 3655.1204654076414 \cdot \frac{1}{x}\right)\right) + \left(-110.1139242984811\right)} \]
      +-commutative [=>] 4.41	\[ \color{blue}{\left(\left(4.16438922228 \cdot x + 3655.1204654076414 \cdot \frac{1}{x}\right) + -1 \cdot \frac{130977.50649958357 + -1 \cdot y}{{x}^{2}}\right)} + \left(-110.1139242984811\right) \]
      mul-1-neg [=>] 4.41	\[ \left(\left(4.16438922228 \cdot x + 3655.1204654076414 \cdot \frac{1}{x}\right) + \color{blue}{\left(-\frac{130977.50649958357 + -1 \cdot y}{{x}^{2}}\right)}\right) + \left(-110.1139242984811\right) \]
      unsub-neg [=>] 4.41	\[ \color{blue}{\left(\left(4.16438922228 \cdot x + 3655.1204654076414 \cdot \frac{1}{x}\right) - \frac{130977.50649958357 + -1 \cdot y}{{x}^{2}}\right)} + \left(-110.1139242984811\right) \]
      associate-+l- [=>] 4.41	\[ \color{blue}{\left(4.16438922228 \cdot x + 3655.1204654076414 \cdot \frac{1}{x}\right) - \left(\frac{130977.50649958357 + -1 \cdot y}{{x}^{2}} - \left(-110.1139242984811\right)\right)} \]
      *-commutative [=>] 4.41	\[ \left(\color{blue}{x \cdot 4.16438922228} + 3655.1204654076414 \cdot \frac{1}{x}\right) - \left(\frac{130977.50649958357 + -1 \cdot y}{{x}^{2}} - \left(-110.1139242984811\right)\right) \]
      fma-def [=>] 4.41	\[ \color{blue}{\mathsf{fma}\left(x, 4.16438922228, 3655.1204654076414 \cdot \frac{1}{x}\right)} - \left(\frac{130977.50649958357 + -1 \cdot y}{{x}^{2}} - \left(-110.1139242984811\right)\right) \]
      associate-*r/ [=>] 4.41	\[ \mathsf{fma}\left(x, 4.16438922228, \color{blue}{\frac{3655.1204654076414 \cdot 1}{x}}\right) - \left(\frac{130977.50649958357 + -1 \cdot y}{{x}^{2}} - \left(-110.1139242984811\right)\right) \]
      metadata-eval [=>] 4.41	\[ \mathsf{fma}\left(x, 4.16438922228, \frac{\color{blue}{3655.1204654076414}}{x}\right) - \left(\frac{130977.50649958357 + -1 \cdot y}{{x}^{2}} - \left(-110.1139242984811\right)\right) \]
      mul-1-neg [=>] 4.41	\[ \mathsf{fma}\left(x, 4.16438922228, \frac{3655.1204654076414}{x}\right) - \left(\frac{130977.50649958357 + \color{blue}{\left(-y\right)}}{{x}^{2}} - \left(-110.1139242984811\right)\right) \]
      unsub-neg [=>] 4.41	\[ \mathsf{fma}\left(x, 4.16438922228, \frac{3655.1204654076414}{x}\right) - \left(\frac{\color{blue}{130977.50649958357 - y}}{{x}^{2}} - \left(-110.1139242984811\right)\right) \]
      unpow2 [=>] 4.41	\[ \mathsf{fma}\left(x, 4.16438922228, \frac{3655.1204654076414}{x}\right) - \left(\frac{130977.50649958357 - y}{\color{blue}{x \cdot x}} - \left(-110.1139242984811\right)\right) \]
      metadata-eval [=>] 4.41	\[ \mathsf{fma}\left(x, 4.16438922228, \frac{3655.1204654076414}{x}\right) - \left(\frac{130977.50649958357 - y}{x \cdot x} - \color{blue}{-110.1139242984811}\right) \]

   5. Applied egg-rr 4.41

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

   6. Applied egg-rr 4.42

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

   7. Applied egg-rr 4.42

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

   if -1.15e17 < x < 3.2e16

   1. Initial program 0.65

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

   2. Applied egg-rr 0.65

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

   if 3.2e16 < x

   1. Initial program 86.89

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

   2. Simplified 79.72

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

      [Start] 86.89	\[ \frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
      associate-*l/ [<=] 79.72	\[ \color{blue}{\frac{x - 2}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)} \]
      *-commutative [=>] 79.72	\[ \color{blue}{\left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right) \cdot \frac{x - 2}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}} \]
      *-commutative [=>] 79.72	\[ \left(\color{blue}{x \cdot \left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right)} + z\right) \cdot \frac{x - 2}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
      fma-def [=>] 79.72	\[ \color{blue}{\mathsf{fma}\left(x, \left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y, z\right)} \cdot \frac{x - 2}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
      *-commutative [=>] 79.72	\[ \mathsf{fma}\left(x, \color{blue}{x \cdot \left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right)} + y, z\right) \cdot \frac{x - 2}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
      fma-def [=>] 79.72	\[ \mathsf{fma}\left(x, \color{blue}{\mathsf{fma}\left(x, \left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416, y\right)}, z\right) \cdot \frac{x - 2}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
      *-commutative [=>] 79.72	\[ \mathsf{fma}\left(x, \mathsf{fma}\left(x, \color{blue}{x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right)} + 137.519416416, y\right), z\right) \cdot \frac{x - 2}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
      fma-def [=>] 79.72	\[ \mathsf{fma}\left(x, \mathsf{fma}\left(x, \color{blue}{\mathsf{fma}\left(x, x \cdot 4.16438922228 + 78.6994924154, 137.519416416\right)}, y\right), z\right) \cdot \frac{x - 2}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
      fma-def [=>] 79.72	\[ \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \color{blue}{\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right)}, 137.519416416\right), y\right), z\right) \cdot \frac{x - 2}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
      sub-neg [=>] 79.72	\[ \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right) \cdot \frac{\color{blue}{x + \left(-2\right)}}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
      metadata-eval [=>] 79.72	\[ \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right) \cdot \frac{x + \color{blue}{-2}}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

   3. Taylor expanded in x around -inf 3.7

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

   4. Simplified 3.7

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, 4.16438922228, \frac{3655.1204654076414}{x}\right) - \left(\frac{130977.50649958357 - y}{x \cdot x} - -110.1139242984811\right)} \]
      Proof

      [Start] 3.7	\[ \left(-1 \cdot \frac{130977.50649958357 + -1 \cdot y}{{x}^{2}} + \left(4.16438922228 \cdot x + 3655.1204654076414 \cdot \frac{1}{x}\right)\right) - 110.1139242984811 \]
      sub-neg [=>] 3.7	\[ \color{blue}{\left(-1 \cdot \frac{130977.50649958357 + -1 \cdot y}{{x}^{2}} + \left(4.16438922228 \cdot x + 3655.1204654076414 \cdot \frac{1}{x}\right)\right) + \left(-110.1139242984811\right)} \]
      +-commutative [=>] 3.7	\[ \color{blue}{\left(\left(4.16438922228 \cdot x + 3655.1204654076414 \cdot \frac{1}{x}\right) + -1 \cdot \frac{130977.50649958357 + -1 \cdot y}{{x}^{2}}\right)} + \left(-110.1139242984811\right) \]
      mul-1-neg [=>] 3.7	\[ \left(\left(4.16438922228 \cdot x + 3655.1204654076414 \cdot \frac{1}{x}\right) + \color{blue}{\left(-\frac{130977.50649958357 + -1 \cdot y}{{x}^{2}}\right)}\right) + \left(-110.1139242984811\right) \]
      unsub-neg [=>] 3.7	\[ \color{blue}{\left(\left(4.16438922228 \cdot x + 3655.1204654076414 \cdot \frac{1}{x}\right) - \frac{130977.50649958357 + -1 \cdot y}{{x}^{2}}\right)} + \left(-110.1139242984811\right) \]
      associate-+l- [=>] 3.7	\[ \color{blue}{\left(4.16438922228 \cdot x + 3655.1204654076414 \cdot \frac{1}{x}\right) - \left(\frac{130977.50649958357 + -1 \cdot y}{{x}^{2}} - \left(-110.1139242984811\right)\right)} \]
      *-commutative [=>] 3.7	\[ \left(\color{blue}{x \cdot 4.16438922228} + 3655.1204654076414 \cdot \frac{1}{x}\right) - \left(\frac{130977.50649958357 + -1 \cdot y}{{x}^{2}} - \left(-110.1139242984811\right)\right) \]
      fma-def [=>] 3.7	\[ \color{blue}{\mathsf{fma}\left(x, 4.16438922228, 3655.1204654076414 \cdot \frac{1}{x}\right)} - \left(\frac{130977.50649958357 + -1 \cdot y}{{x}^{2}} - \left(-110.1139242984811\right)\right) \]
      associate-*r/ [=>] 3.7	\[ \mathsf{fma}\left(x, 4.16438922228, \color{blue}{\frac{3655.1204654076414 \cdot 1}{x}}\right) - \left(\frac{130977.50649958357 + -1 \cdot y}{{x}^{2}} - \left(-110.1139242984811\right)\right) \]
      metadata-eval [=>] 3.7	\[ \mathsf{fma}\left(x, 4.16438922228, \frac{\color{blue}{3655.1204654076414}}{x}\right) - \left(\frac{130977.50649958357 + -1 \cdot y}{{x}^{2}} - \left(-110.1139242984811\right)\right) \]
      mul-1-neg [=>] 3.7	\[ \mathsf{fma}\left(x, 4.16438922228, \frac{3655.1204654076414}{x}\right) - \left(\frac{130977.50649958357 + \color{blue}{\left(-y\right)}}{{x}^{2}} - \left(-110.1139242984811\right)\right) \]
      unsub-neg [=>] 3.7	\[ \mathsf{fma}\left(x, 4.16438922228, \frac{3655.1204654076414}{x}\right) - \left(\frac{\color{blue}{130977.50649958357 - y}}{{x}^{2}} - \left(-110.1139242984811\right)\right) \]
      unpow2 [=>] 3.7	\[ \mathsf{fma}\left(x, 4.16438922228, \frac{3655.1204654076414}{x}\right) - \left(\frac{130977.50649958357 - y}{\color{blue}{x \cdot x}} - \left(-110.1139242984811\right)\right) \]
      metadata-eval [=>] 3.7	\[ \mathsf{fma}\left(x, 4.16438922228, \frac{3655.1204654076414}{x}\right) - \left(\frac{130977.50649958357 - y}{x \cdot x} - \color{blue}{-110.1139242984811}\right) \]

   5. Taylor expanded in x around inf 3.7

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

   6. Simplified 3.7

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

      [Start] 3.7	\[ 4.16438922228 \cdot x - \left(\frac{130977.50649958357 - y}{x \cdot x} - -110.1139242984811\right) \]
      *-commutative [=>] 3.7	\[ \color{blue}{x \cdot 4.16438922228} - \left(\frac{130977.50649958357 - y}{x \cdot x} - -110.1139242984811\right) \]

3. Recombined 3 regimes into one program.

4. Final simplification 2.27

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

Alternatives

Alternative 1
Error	2.27%
Cost	2632

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

Alternative 2
Error	3.36%
Cost	2248

\[\begin{array}{l} t_0 := \frac{3655.1204654076414}{x} + x \cdot 4.16438922228\\ \mathbf{if}\;x \leq -3600000000000:\\ \;\;\;\;t_0 + \left(-110.1139242984811 + \left(130977.50649958357 - y\right) \cdot \frac{-1}{x \cdot x}\right)\\ \mathbf{elif}\;x \leq 18000:\\ \;\;\;\;\frac{\left(z + x \cdot \left(y + x \cdot 137.519416416\right)\right) \cdot \left(x + -2\right)}{x \cdot \left(\left(x \cdot \left(x \cdot \left(x + 43.3400022514\right)\right) + x \cdot 263.505074721\right) + 313.399215894\right) + 47.066876606}\\ \mathbf{else}:\\ \;\;\;\;t_0 + \left(-110.1139242984811 + \frac{y + -130977.50649958357}{x \cdot x}\right)\\ \end{array} \]

Alternative 3
Error	3.34%
Cost	2120

\[\begin{array}{l} t_0 := \frac{3655.1204654076414}{x} + x \cdot 4.16438922228\\ \mathbf{if}\;x \leq -1.1 \cdot 10^{+14}:\\ \;\;\;\;t_0 + \left(-110.1139242984811 + \left(130977.50649958357 - y\right) \cdot \frac{-1}{x \cdot x}\right)\\ \mathbf{elif}\;x \leq 18000:\\ \;\;\;\;\frac{\left(z + x \cdot \left(y + x \cdot 137.519416416\right)\right) \cdot \left(x + -2\right)}{47.066876606 + x \cdot \left(313.399215894 + x \cdot \left(263.505074721 + x \cdot \left(x + 43.3400022514\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t_0 + \left(-110.1139242984811 + \frac{y + -130977.50649958357}{x \cdot x}\right)\\ \end{array} \]

Alternative 4
Error	19.76%
Cost	1356

\[\begin{array}{l} t_0 := x \cdot 4.16438922228 - \left(\frac{130977.50649958357 - y}{x \cdot x} + 110.1139242984811\right)\\ \mathbf{if}\;x \leq -37:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -2.45 \cdot 10^{-40}:\\ \;\;\;\;y \cdot \frac{x + -2}{313.399215894 + \frac{47.066876606}{x}}\\ \mathbf{elif}\;x \leq 15:\\ \;\;\;\;\frac{z \cdot \left(x + -2\right)}{47.066876606 + x \cdot \left(x \cdot 263.505074721 + 313.399215894\right)}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 5
Error	7.01%
Cost	1353

\[\begin{array}{l} \mathbf{if}\;x \leq -5.5 \lor \neg \left(x \leq 15\right):\\ \;\;\;\;x \cdot 4.16438922228 - \left(\frac{130977.50649958357 - y}{x \cdot x} + 110.1139242984811\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(z \cdot 0.0212463641547976 + x \cdot \left(y \cdot 0.0212463641547976 + z \cdot -0.14147091005106402\right)\right)\\ \end{array} \]

Alternative 6
Error	7.06%
Cost	1353

\[\begin{array}{l} \mathbf{if}\;x \leq -5.5 \lor \neg \left(x \leq 12.5\right):\\ \;\;\;\;x \cdot 4.16438922228 - \left(\frac{130977.50649958357 - y}{x \cdot x} + 110.1139242984811\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot -0.0424927283095952 - x \cdot \left(z \cdot -0.28294182010212804 + 0.0212463641547976 \cdot \left(y \cdot 2 - z\right)\right)\\ \end{array} \]

Alternative 7
Error	7.04%
Cost	1352

\[\begin{array}{l} \mathbf{if}\;x \leq -5.5:\\ \;\;\;\;x \cdot 4.16438922228 - \left(\frac{130977.50649958357 - y}{x \cdot x} + 110.1139242984811\right)\\ \mathbf{elif}\;x \leq 13:\\ \;\;\;\;z \cdot -0.0424927283095952 - x \cdot \left(z \cdot -0.28294182010212804 + 0.0212463641547976 \cdot \left(y \cdot 2 - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{3655.1204654076414}{x} + x \cdot 4.16438922228\right) + \left(-110.1139242984811 + \frac{y + -130977.50649958357}{x \cdot x}\right)\\ \end{array} \]

Alternative 8
Error	7.01%
Cost	1352

\[\begin{array}{l} t_0 := \frac{3655.1204654076414}{x} + x \cdot 4.16438922228\\ \mathbf{if}\;x \leq -5.5:\\ \;\;\;\;t_0 + \left(-110.1139242984811 + \left(130977.50649958357 - y\right) \cdot \frac{-1}{x \cdot x}\right)\\ \mathbf{elif}\;x \leq 12.6:\\ \;\;\;\;z \cdot -0.0424927283095952 - x \cdot \left(z \cdot -0.28294182010212804 + 0.0212463641547976 \cdot \left(y \cdot 2 - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0 + \left(-110.1139242984811 + \frac{y + -130977.50649958357}{x \cdot x}\right)\\ \end{array} \]

Alternative 9
Error	23.43%
Cost	1232

\[\begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{+47}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \mathbf{elif}\;x \leq -37:\\ \;\;\;\;\frac{y}{x \cdot x}\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{-41}:\\ \;\;\;\;y \cdot \frac{x + -2}{313.399215894 + \frac{47.066876606}{x}}\\ \mathbf{elif}\;x \leq 1.7:\\ \;\;\;\;\frac{z \cdot \left(x + -2\right)}{47.066876606 + x \cdot 313.399215894}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718 + \frac{5.86923874282773}{x}}\\ \end{array} \]

Alternative 10
Error	19.81%
Cost	1228

\[\begin{array}{l} t_0 := x \cdot 4.16438922228 - \left(\frac{130977.50649958357 - y}{x \cdot x} + 110.1139242984811\right)\\ \mathbf{if}\;x \leq -37:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -3.6 \cdot 10^{-40}:\\ \;\;\;\;y \cdot \frac{x + -2}{313.399215894 + \frac{47.066876606}{x}}\\ \mathbf{elif}\;x \leq 30.5:\\ \;\;\;\;\frac{z \cdot \left(x + -2\right)}{47.066876606 + x \cdot 313.399215894}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 11
Error	23.78%
Cost	1104

\[\begin{array}{l} \mathbf{if}\;x \leq -1.36 \cdot 10^{+48}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \mathbf{elif}\;x \leq -21:\\ \;\;\;\;\frac{y}{x \cdot x}\\ \mathbf{elif}\;x \leq -1.22 \cdot 10^{-39}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(0.0212463641547976 \cdot \left(x \cdot y\right)\right)\\ \mathbf{elif}\;x \leq 0.14:\\ \;\;\;\;z \cdot \left(-0.0424927283095952 + x \cdot 0.3041881842569256\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718 + \frac{5.86923874282773}{x}}\\ \end{array} \]

Alternative 12
Error	23.51%
Cost	1104

\[\begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{+46}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \mathbf{elif}\;x \leq -37:\\ \;\;\;\;\frac{y}{x \cdot x}\\ \mathbf{elif}\;x \leq -1.1 \cdot 10^{-39}:\\ \;\;\;\;y \cdot \frac{x + -2}{313.399215894 + \frac{47.066876606}{x}}\\ \mathbf{elif}\;x \leq 0.08:\\ \;\;\;\;z \cdot \left(-0.0424927283095952 + x \cdot 0.3041881842569256\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718 + \frac{5.86923874282773}{x}}\\ \end{array} \]

Alternative 13
Error	23.73%
Cost	976

\[\begin{array}{l} t_0 := \frac{x + -2}{0.24013125253755718}\\ \mathbf{if}\;x \leq -8.2 \cdot 10^{+46}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -19:\\ \;\;\;\;\frac{y}{x \cdot x}\\ \mathbf{elif}\;x \leq -5.4 \cdot 10^{-41}:\\ \;\;\;\;-0.0424927283095952 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \leq 0.14:\\ \;\;\;\;z \cdot \left(-0.0424927283095952 + x \cdot 0.3041881842569256\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 14
Error	23.73%
Cost	976

\[\begin{array}{l} t_0 := \frac{x + -2}{0.24013125253755718}\\ \mathbf{if}\;x \leq -7.5 \cdot 10^{+46}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -11.5:\\ \;\;\;\;\frac{y}{x \cdot x}\\ \mathbf{elif}\;x \leq -6.2 \cdot 10^{-40}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(0.0212463641547976 \cdot \left(x \cdot y\right)\right)\\ \mathbf{elif}\;x \leq 0.125:\\ \;\;\;\;z \cdot \left(-0.0424927283095952 + x \cdot 0.3041881842569256\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 15
Error	24.08%
Cost	848

\[\begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{+47}:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq -15.6:\\ \;\;\;\;\frac{y}{x \cdot x}\\ \mathbf{elif}\;x \leq -2.45 \cdot 10^{-40}:\\ \;\;\;\;-0.0424927283095952 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \leq 0.7:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \mathbf{else}:\\ \;\;\;\;4.16438922228 \cdot \left(x + -2\right)\\ \end{array} \]

Alternative 16
Error	23.84%
Cost	848

\[\begin{array}{l} t_0 := \frac{x + -2}{0.24013125253755718}\\ \mathbf{if}\;x \leq -7.5 \cdot 10^{+46}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -11.5:\\ \;\;\;\;\frac{y}{x \cdot x}\\ \mathbf{elif}\;x \leq -1.25 \cdot 10^{-39}:\\ \;\;\;\;-0.0424927283095952 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \leq 0.112:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 17
Error	24.28%
Cost	716

\[\begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{+25}:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq -5.5 \cdot 10^{-40}:\\ \;\;\;\;-0.0424927283095952 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \leq 0.1:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \mathbf{else}:\\ \;\;\;\;4.16438922228 \cdot \left(x + -2\right)\\ \end{array} \]

Alternative 18
Error	24.28%
Cost	588

\[\begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{+25}:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq -2.8 \cdot 10^{-40}:\\ \;\;\;\;-0.0424927283095952 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \leq 2:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228\\ \end{array} \]

Alternative 19
Error	24.15%
Cost	456

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

Alternative 20
Error	97.74%
Cost	192

\[x \cdot -0.3407596943375357 \]

Alternative 21
Error	55.31%
Cost	192

\[x \cdot 4.16438922228 \]

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)))