?

Average Error: 41.96% → 1.6%
Time: 32.8s
Precision: binary64
Cost: 47048

?

\[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
↓
\[\begin{array}{l} \mathbf{if}\;x \leq -8.2 \cdot 10^{+39}:\\ \;\;\;\;\mathsf{fma}\left(x, 4.16438922228, \frac{3655.1204654076414}{x}\right) + \left(-110.1139242984811 + \frac{y + -130977.50649958357}{x \cdot x}\right)\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{+65}:\\ \;\;\;\;\left(x + -2\right) \cdot \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \frac{\left(x \cdot x\right) \cdot 17.342137594641823 + -6193.6101064416025}{\mathsf{fma}\left(x, 4.16438922228, -78.6994924154\right)}, 137.519416416\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + 43.3400022514, 263.505074721\right), 313.399215894\right), 47.066876606\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \end{array} \]
(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 -8.2e+39)
   (+
    (fma x 4.16438922228 (/ 3655.1204654076414 x))
    (+ -110.1139242984811 (/ (+ y -130977.50649958357) (* x x))))
   (if (<= x 3.3e+65)
     (*
      (+ x -2.0)
      (/
       (fma
        x
        (fma
         x
         (fma
          x
          (/
           (+ (* (* x x) 17.342137594641823) -6193.6101064416025)
           (fma x 4.16438922228 -78.6994924154))
          137.519416416)
         y)
        z)
       (fma
        x
        (fma x (fma x (+ x 43.3400022514) 263.505074721) 313.399215894)
        47.066876606)))
     (/ (+ x -2.0) 0.24013125253755718))))
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 <= -8.2e+39) {
		tmp = fma(x, 4.16438922228, (3655.1204654076414 / x)) + (-110.1139242984811 + ((y + -130977.50649958357) / (x * x)));
	} else if (x <= 3.3e+65) {
		tmp = (x + -2.0) * (fma(x, fma(x, fma(x, ((((x * x) * 17.342137594641823) + -6193.6101064416025) / fma(x, 4.16438922228, -78.6994924154)), 137.519416416), y), z) / fma(x, fma(x, fma(x, (x + 43.3400022514), 263.505074721), 313.399215894), 47.066876606));
	} else {
		tmp = (x + -2.0) / 0.24013125253755718;
	}
	return tmp;
}

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 <= -8.2e+39)
		tmp = Float64(fma(x, 4.16438922228, Float64(3655.1204654076414 / x)) + Float64(-110.1139242984811 + Float64(Float64(y + -130977.50649958357) / Float64(x * x))));
	elseif (x <= 3.3e+65)
		tmp = Float64(Float64(x + -2.0) * Float64(fma(x, fma(x, fma(x, Float64(Float64(Float64(Float64(x * x) * 17.342137594641823) + -6193.6101064416025) / fma(x, 4.16438922228, -78.6994924154)), 137.519416416), y), z) / fma(x, fma(x, fma(x, Float64(x + 43.3400022514), 263.505074721), 313.399215894), 47.066876606)));
	else
		tmp = Float64(Float64(x + -2.0) / 0.24013125253755718);
	end
	return tmp
end

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, -8.2e+39], N[(N[(x * 4.16438922228 + N[(3655.1204654076414 / x), $MachinePrecision]), $MachinePrecision] + N[(-110.1139242984811 + N[(N[(y + -130977.50649958357), $MachinePrecision] / N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.3e+65], N[(N[(x + -2.0), $MachinePrecision] * N[(N[(x * N[(x * N[(x * N[(N[(N[(N[(x * x), $MachinePrecision] * 17.342137594641823), $MachinePrecision] + -6193.6101064416025), $MachinePrecision] / N[(x * 4.16438922228 + -78.6994924154), $MachinePrecision]), $MachinePrecision] + 137.519416416), $MachinePrecision] + y), $MachinePrecision] + z), $MachinePrecision] / N[(x * N[(x * N[(x * N[(x + 43.3400022514), $MachinePrecision] + 263.505074721), $MachinePrecision] + 313.399215894), $MachinePrecision] + 47.066876606), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + -2.0), $MachinePrecision] / 0.24013125253755718), $MachinePrecision]]]

\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 -8.2 \cdot 10^{+39}:\\
\;\;\;\;\mathsf{fma}\left(x, 4.16438922228, \frac{3655.1204654076414}{x}\right) + \left(-110.1139242984811 + \frac{y + -130977.50649958357}{x \cdot x}\right)\\

\mathbf{elif}\;x \leq 3.3 \cdot 10^{+65}:\\
\;\;\;\;\left(x + -2\right) \cdot \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \frac{\left(x \cdot x\right) \cdot 17.342137594641823 + -6193.6101064416025}{\mathsf{fma}\left(x, 4.16438922228, -78.6994924154\right)}, 137.519416416\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + 43.3400022514, 263.505074721\right), 313.399215894\right), 47.066876606\right)}\\

\mathbf{else}:\\
\;\;\;\;\frac{x + -2}{0.24013125253755718}\\


\end{array}

Error?

Target

Original41.96%
Target1.12%
Herbie1.6%
\[\begin{array}{l} \mathbf{if}\;x < -3.326128725870005 \cdot 10^{+62}:\\ \;\;\;\;\left(\frac{y}{x \cdot x} + 4.16438922228 \cdot x\right) - 110.1139242984811\\ \mathbf{elif}\;x < 9.429991714554673 \cdot 10^{+55}:\\ \;\;\;\;\frac{x - 2}{1} \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(263.505074721 \cdot x + \left(43.3400022514 \cdot \left(x \cdot x\right) + x \cdot \left(x \cdot x\right)\right)\right) + 313.399215894\right) \cdot x + 47.066876606}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{y}{x \cdot x} + 4.16438922228 \cdot x\right) - 110.1139242984811\\ \end{array} \]

Derivation?

  1. Split input into 3 regimes

  2. if x < -8.20000000000000008e39

    1. Initial program 93.14

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

    2. Simplified87.05

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

      [Start]93.14

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

      associate-*l/ [<=]87.05

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

      *-commutative [=>]87.05

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

      *-commutative [=>]87.05

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

      fma-def [=>]87.05

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

      *-commutative [=>]87.05

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

      fma-def [=>]87.05

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

      *-commutative [=>]87.05

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

      fma-def [=>]87.05

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

      fma-def [=>]87.05

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

      sub-neg [=>]87.05

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

      metadata-eval [=>]87.05

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

    3. Taylor expanded in x around -inf 2.73

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

    4. Simplified2.73

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

      [Start]2.73

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

      sub-neg [=>]2.73

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

      +-commutative [=>]2.73

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

      mul-1-neg [=>]2.73

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

      unsub-neg [=>]2.73

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

      associate-+l- [=>]2.73

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

      *-commutative [=>]2.73

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

      fma-def [=>]2.73

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

      associate-*r/ [=>]2.73

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

      metadata-eval [=>]2.73

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

      mul-1-neg [=>]2.73

      \[ \mathsf{fma}\left(x, 4.16438922228, \frac{3655.1204654076414}{x}\right) - \left(\frac{130977.50649958357 + \color{blue}{\left(-y\right)}}{{x}^{2}} - \left(-110.1139242984811\right)\right) \]

      unsub-neg [=>]2.73

      \[ \mathsf{fma}\left(x, 4.16438922228, \frac{3655.1204654076414}{x}\right) - \left(\frac{\color{blue}{130977.50649958357 - y}}{{x}^{2}} - \left(-110.1139242984811\right)\right) \]

      unpow2 [=>]2.73

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

      metadata-eval [=>]2.73

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

    if -8.20000000000000008e39 < x < 3.30000000000000023e65

    1. Initial program 2.75

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

    2. Simplified1.04

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

      [Start]2.75

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

      associate-*r/ [<=]1.05

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

      sub-neg [=>]1.05

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

      metadata-eval [=>]1.05

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

      *-commutative [=>]1.05

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

      fma-def [=>]1.05

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

      *-commutative [=>]1.05

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

      fma-def [=>]1.04

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

      *-commutative [=>]1.04

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

      fma-def [=>]1.04

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

      fma-def [=>]1.04

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

      *-commutative [=>]1.04

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

    3. Applied egg-rr1.03

      \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \color{blue}{\frac{\left(x \cdot 4.16438922228\right) \cdot \left(x \cdot 4.16438922228\right) - 6193.6101064416025}{x \cdot 4.16438922228 - 78.6994924154}}, 137.519416416\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + 43.3400022514, 263.505074721\right), 313.399215894\right), 47.066876606\right)} \]

    4. Simplified1.03

      \[\leadsto \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \color{blue}{\frac{\left(x \cdot x\right) \cdot 17.342137594641823 + -6193.6101064416025}{\mathsf{fma}\left(x, 4.16438922228, -78.6994924154\right)}}, 137.519416416\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + 43.3400022514, 263.505074721\right), 313.399215894\right), 47.066876606\right)} \]
      Proof

      [Start]1.03

      \[ \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \frac{\left(x \cdot 4.16438922228\right) \cdot \left(x \cdot 4.16438922228\right) - 6193.6101064416025}{x \cdot 4.16438922228 - 78.6994924154}, 137.519416416\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + 43.3400022514, 263.505074721\right), 313.399215894\right), 47.066876606\right)} \]

      sub-neg [=>]1.03

      \[ \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \frac{\color{blue}{\left(x \cdot 4.16438922228\right) \cdot \left(x \cdot 4.16438922228\right) + \left(-6193.6101064416025\right)}}{x \cdot 4.16438922228 - 78.6994924154}, 137.519416416\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + 43.3400022514, 263.505074721\right), 313.399215894\right), 47.066876606\right)} \]

      swap-sqr [=>]1.04

      \[ \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \frac{\color{blue}{\left(x \cdot x\right) \cdot \left(4.16438922228 \cdot 4.16438922228\right)} + \left(-6193.6101064416025\right)}{x \cdot 4.16438922228 - 78.6994924154}, 137.519416416\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + 43.3400022514, 263.505074721\right), 313.399215894\right), 47.066876606\right)} \]

      metadata-eval [=>]1.03

      \[ \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \frac{\left(x \cdot x\right) \cdot \color{blue}{17.342137594641823} + \left(-6193.6101064416025\right)}{x \cdot 4.16438922228 - 78.6994924154}, 137.519416416\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + 43.3400022514, 263.505074721\right), 313.399215894\right), 47.066876606\right)} \]

      metadata-eval [=>]1.03

      \[ \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \frac{\left(x \cdot x\right) \cdot 17.342137594641823 + \color{blue}{-6193.6101064416025}}{x \cdot 4.16438922228 - 78.6994924154}, 137.519416416\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + 43.3400022514, 263.505074721\right), 313.399215894\right), 47.066876606\right)} \]

      fma-neg [=>]1.03

      \[ \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \frac{\left(x \cdot x\right) \cdot 17.342137594641823 + -6193.6101064416025}{\color{blue}{\mathsf{fma}\left(x, 4.16438922228, -78.6994924154\right)}}, 137.519416416\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + 43.3400022514, 263.505074721\right), 313.399215894\right), 47.066876606\right)} \]

      metadata-eval [=>]1.03

      \[ \left(x + -2\right) \cdot \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \frac{\left(x \cdot x\right) \cdot 17.342137594641823 + -6193.6101064416025}{\mathsf{fma}\left(x, 4.16438922228, \color{blue}{-78.6994924154}\right)}, 137.519416416\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + 43.3400022514, 263.505074721\right), 313.399215894\right), 47.066876606\right)} \]

    if 3.30000000000000023e65 < x

    1. Initial program 100

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

    2. Simplified95.55

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

      [Start]100

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

      associate-/l* [=>]95.55

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

      sub-neg [=>]95.55

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

      metadata-eval [=>]95.55

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

      fma-def [=>]95.55

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

      fma-def [=>]95.55

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

      fma-def [=>]95.55

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

      fma-def [=>]95.55

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

      fma-def [=>]95.55

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

      fma-def [=>]95.55

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

      fma-def [=>]95.55

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

    3. Taylor expanded in x around inf 1.99

      \[\leadsto \frac{x + -2}{\color{blue}{0.24013125253755718}} \]
  3. Recombined 3 regimes into one program.

  4. Final simplification1.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.2 \cdot 10^{+39}:\\ \;\;\;\;\mathsf{fma}\left(x, 4.16438922228, \frac{3655.1204654076414}{x}\right) + \left(-110.1139242984811 + \frac{y + -130977.50649958357}{x \cdot x}\right)\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{+65}:\\ \;\;\;\;\left(x + -2\right) \cdot \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \frac{\left(x \cdot x\right) \cdot 17.342137594641823 + -6193.6101064416025}{\mathsf{fma}\left(x, 4.16438922228, -78.6994924154\right)}, 137.519416416\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + 43.3400022514, 263.505074721\right), 313.399215894\right), 47.066876606\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \end{array} \]

Alternatives

Alternative 1
Error1.66%
Cost46536
\[\begin{array}{l} \mathbf{if}\;x \leq -3.2 \cdot 10^{+38}:\\ \;\;\;\;\mathsf{fma}\left(x, 4.16438922228, \frac{3655.1204654076414}{x}\right) + \left(-110.1139242984811 + \frac{y + -130977.50649958357}{x \cdot x}\right)\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{+63}:\\ \;\;\;\;\left(x + -2\right) \cdot \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + 43.3400022514, 263.505074721\right), 313.399215894\right), 47.066876606\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \end{array} \]
Alternative 2
Error1.38%
Cost20105
\[\begin{array}{l} t_0 := \left(x + -2\right) \cdot \left(z + x \cdot \left(y + x \cdot \left(137.519416416 + x \cdot \left(78.6994924154 + x \cdot 4.16438922228\right)\right)\right)\right)\\ t_1 := \frac{t_0}{47.066876606 + x \cdot \left(313.399215894 + x \cdot \left(263.505074721 + x \cdot \left(x + 43.3400022514\right)\right)\right)}\\ \mathbf{if}\;t_1 \leq -\infty \lor \neg \left(t_1 \leq 5 \cdot 10^{+304}\right):\\ \;\;\;\;\mathsf{fma}\left(x, 4.16438922228, \frac{3655.1204654076414}{x}\right) + \left(-110.1139242984811 + \frac{y + -130977.50649958357}{x \cdot x}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t_0}{47.066876606 + x \cdot \left(313.399215894 + \mathsf{fma}\left(43.3400022514, x \cdot x, {x}^{3} + x \cdot 263.505074721\right)\right)}\\ \end{array} \]
Alternative 3
Error1.38%
Cost13641
\[\begin{array}{l} t_0 := \left(x + -2\right) \cdot \left(z + x \cdot \left(y + x \cdot \left(137.519416416 + x \cdot \left(78.6994924154 + x \cdot 4.16438922228\right)\right)\right)\right)\\ t_1 := \frac{t_0}{47.066876606 + x \cdot \left(313.399215894 + x \cdot \left(263.505074721 + x \cdot \left(x + 43.3400022514\right)\right)\right)}\\ \mathbf{if}\;t_1 \leq -\infty \lor \neg \left(t_1 \leq 5 \cdot 10^{+304}\right):\\ \;\;\;\;\mathsf{fma}\left(x, 4.16438922228, \frac{3655.1204654076414}{x}\right) + \left(-110.1139242984811 + \frac{y + -130977.50649958357}{x \cdot x}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t_0}{47.066876606 + x \cdot \left(313.399215894 + \mathsf{fma}\left(x, 263.505074721, \left(x \cdot x\right) \cdot \left(x + 43.3400022514\right)\right)\right)}\\ \end{array} \]
Alternative 4
Error1.39%
Cost12233
\[\begin{array}{l} t_0 := \frac{\left(x + -2\right) \cdot \left(z + x \cdot \left(y + x \cdot \left(137.519416416 + x \cdot \left(78.6994924154 + x \cdot 4.16438922228\right)\right)\right)\right)}{47.066876606 + x \cdot \left(313.399215894 + x \cdot \left(263.505074721 + x \cdot \left(x + 43.3400022514\right)\right)\right)}\\ \mathbf{if}\;t_0 \leq -\infty \lor \neg \left(t_0 \leq 5 \cdot 10^{+304}\right):\\ \;\;\;\;\mathsf{fma}\left(x, 4.16438922228, \frac{3655.1204654076414}{x}\right) + \left(-110.1139242984811 + \frac{y + -130977.50649958357}{x \cdot x}\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]
Alternative 5
Error2.49%
Cost7240
\[\begin{array}{l} t_0 := x \cdot \left(y + x \cdot \left(137.519416416 + x \cdot \left(78.6994924154 + x \cdot 4.16438922228\right)\right)\right)\\ t_1 := \frac{\left(x + -2\right) \cdot \left(z + t_0\right)}{47.066876606 + x \cdot \left(313.399215894 + x \cdot \left(263.505074721 + x \cdot \left(x + 43.3400022514\right)\right)\right)}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\frac{x + -2}{\frac{47.066876606 + x \cdot \left(313.399215894 + \left(x \cdot x\right) \cdot \left(x + 43.3400022514\right)\right)}{t_0}}\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+304}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \end{array} \]
Alternative 6
Error3.62%
Cost2768
\[\begin{array}{l} t_0 := 47.066876606 + x \cdot \left(313.399215894 + x \cdot \left(263.505074721 + x \cdot \left(x + 43.3400022514\right)\right)\right)\\ t_1 := \frac{x + -2}{0.24013125253755718}\\ t_2 := x \cdot \left(y + x \cdot \left(137.519416416 + x \cdot \left(78.6994924154 + x \cdot 4.16438922228\right)\right)\right)\\ \mathbf{if}\;x \leq -1.2 \cdot 10^{+63}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -950:\\ \;\;\;\;\frac{x + -2}{\frac{t_0}{t_2}}\\ \mathbf{elif}\;x \leq 1400000:\\ \;\;\;\;\frac{\left(x + -2\right) \cdot \left(z + x \cdot \left(y + x \cdot \left(137.519416416 + x \cdot 78.6994924154\right)\right)\right)}{t_0}\\ \mathbf{elif}\;x \leq 3.45 \cdot 10^{+55}:\\ \;\;\;\;\frac{\left(x + -2\right) \cdot \left(z + t_2\right)}{47.066876606 + x \cdot \left(313.399215894 + \left(x \cdot x\right) \cdot \left(x + 43.3400022514\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 7
Error3.93%
Cost2505
\[\begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{+59} \lor \neg \left(x \leq 1.2 \cdot 10^{+59}\right):\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x + -2\right) \cdot \left(z + x \cdot \left(y + x \cdot \left(137.519416416 + x \cdot \left(78.6994924154 + x \cdot 4.16438922228\right)\right)\right)\right)}{47.066876606 + x \cdot \left(313.399215894 + \left(x \cdot x\right) \cdot \left(x + 43.3400022514\right)\right)}\\ \end{array} \]
Alternative 8
Error5.68%
Cost2376
\[\begin{array}{l} \mathbf{if}\;x \leq -135000:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718 + \left(\frac{5.86923874282773}{x} + \frac{-55.572073733743466}{x \cdot x}\right)}\\ \mathbf{elif}\;x \leq 7 \cdot 10^{+23}:\\ \;\;\;\;\frac{\left(x + -2\right) \cdot \left(z + x \cdot \left(y + x \cdot \left(137.519416416 + x \cdot 78.6994924154\right)\right)\right)}{47.066876606 + x \cdot \left(313.399215894 + x \cdot \left(263.505074721 + x \cdot \left(x + 43.3400022514\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \end{array} \]
Alternative 9
Error5.85%
Cost2120
\[\begin{array}{l} \mathbf{if}\;x \leq -150000:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718 + \left(\frac{5.86923874282773}{x} + \frac{-55.572073733743466}{x \cdot x}\right)}\\ \mathbf{elif}\;x \leq 9 \cdot 10^{+23}:\\ \;\;\;\;\frac{\left(x + -2\right) \cdot \left(z + x \cdot \left(y + x \cdot 137.519416416\right)\right)}{47.066876606 + x \cdot \left(313.399215894 + x \cdot \left(263.505074721 + x \cdot \left(x + 43.3400022514\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \end{array} \]
Alternative 10
Error7.48%
Cost1992
\[\begin{array}{l} \mathbf{if}\;x \leq -16.5:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718 + \left(\frac{5.86923874282773}{x} + \frac{-55.572073733743466}{x \cdot x}\right)}\\ \mathbf{elif}\;x \leq 980:\\ \;\;\;\;\left(x + -2\right) \cdot \left(x \cdot \left(x \cdot \left(2.9217875995295866 + y \cdot -0.14147091005106402\right)\right) + \left(z \cdot 0.0212463641547976 + x \cdot \left(y \cdot 0.0212463641547976 + z \cdot -0.14147091005106402\right)\right)\right)\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{+23}:\\ \;\;\;\;\frac{y}{x \cdot x}\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{+33} \lor \neg \left(x \leq 7.6 \cdot 10^{+38}\right):\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \frac{z}{47.066876606 + x \cdot \left(313.399215894 + x \cdot \left(x \cdot x\right)\right)}\\ \end{array} \]
Alternative 11
Error22.25%
Cost1748
\[\begin{array}{l} t_0 := \left(x + -2\right) \cdot \left(x \cdot \left(y \cdot 0.0212463641547976 + x \cdot \left(2.9217875995295866 + y \cdot -0.14147091005106402\right)\right)\right)\\ t_1 := \frac{x + -2}{0.24013125253755718 + \left(\frac{5.86923874282773}{x} + \frac{-55.572073733743466}{x \cdot x}\right)}\\ \mathbf{if}\;x \leq -7.6:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -3.7 \cdot 10^{-44}:\\ \;\;\;\;\left(x + -2\right) \cdot \frac{z}{47.066876606 + x \cdot \left(313.399215894 + x \cdot 263.505074721\right)}\\ \mathbf{elif}\;x \leq -7.2 \cdot 10^{-113}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-62}:\\ \;\;\;\;\left(x + -2\right) \cdot \frac{z}{47.066876606 + x \cdot 313.399215894}\\ \mathbf{elif}\;x \leq 2.6:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 12
Error10.1%
Cost1353
\[\begin{array}{l} \mathbf{if}\;x \leq -12.2 \lor \neg \left(x \leq 15\right):\\ \;\;\;\;\frac{x + -2}{0.24013125253755718 + \left(\frac{5.86923874282773}{x} + \frac{-55.572073733743466}{x \cdot x}\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(0.0212463641547976 \cdot \left(z + y \cdot -2\right) + z \cdot 0.28294182010212804\right) + z \cdot -0.0424927283095952\\ \end{array} \]
Alternative 13
Error10.2%
Cost1352
\[\begin{array}{l} \mathbf{if}\;x \leq -5.5:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718 + \left(\frac{5.86923874282773}{x} + \frac{-55.572073733743466}{x \cdot x}\right)}\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{-7}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(z \cdot 0.0212463641547976 + x \cdot \left(y \cdot 0.0212463641547976 + z \cdot -0.14147091005106402\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718 + \frac{5.86923874282773}{x}}\\ \end{array} \]
Alternative 14
Error22.18%
Cost1225
\[\begin{array}{l} \mathbf{if}\;x \leq -50 \lor \neg \left(x \leq 2.3 \cdot 10^{-7}\right):\\ \;\;\;\;\frac{x + -2}{0.24013125253755718 + \frac{5.86923874282773}{x}}\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(z \cdot \left(0.0212463641547976 + x \cdot \left(-0.14147091005106402 + x \cdot 0.8230490379027244\right)\right)\right)\\ \end{array} \]
Alternative 15
Error22.03%
Cost1225
\[\begin{array}{l} \mathbf{if}\;x \leq -75 \lor \neg \left(x \leq 2.3 \cdot 10^{-7}\right):\\ \;\;\;\;\frac{x + -2}{0.24013125253755718 + \frac{5.86923874282773}{x}}\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \frac{z}{47.066876606 + x \cdot \left(313.399215894 + x \cdot 263.505074721\right)}\\ \end{array} \]
Alternative 16
Error21.89%
Cost1225
\[\begin{array}{l} \mathbf{if}\;x \leq -9.6 \lor \neg \left(x \leq 50\right):\\ \;\;\;\;\frac{x + -2}{0.24013125253755718 + \left(\frac{5.86923874282773}{x} + \frac{-55.572073733743466}{x \cdot x}\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \frac{z}{47.066876606 + x \cdot \left(313.399215894 + x \cdot 263.505074721\right)}\\ \end{array} \]
Alternative 17
Error22.1%
Cost969
\[\begin{array}{l} \mathbf{if}\;x \leq -0.85 \lor \neg \left(x \leq 2.3 \cdot 10^{-7}\right):\\ \;\;\;\;\frac{x + -2}{0.24013125253755718 + \frac{5.86923874282773}{x}}\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \frac{z}{47.066876606 + x \cdot 313.399215894}\\ \end{array} \]
Alternative 18
Error22.38%
Cost841
\[\begin{array}{l} \mathbf{if}\;x \leq -36 \lor \neg \left(x \leq 2.3 \cdot 10^{-7}\right):\\ \;\;\;\;\frac{x + -2}{0.24013125253755718 + \frac{5.86923874282773}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + -2}{\frac{47.066876606}{z}}\\ \end{array} \]
Alternative 19
Error22.59%
Cost712
\[\begin{array}{l} \mathbf{if}\;x \leq -85:\\ \;\;\;\;-110.1139242984811 + x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{-7}:\\ \;\;\;\;\frac{x + -2}{\frac{47.066876606}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \end{array} \]
Alternative 20
Error22.6%
Cost712
\[\begin{array}{l} \mathbf{if}\;x \leq -36:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{-101.7851458539211}{x}\right)\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{-7}:\\ \;\;\;\;\frac{x + -2}{\frac{47.066876606}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \end{array} \]
Alternative 21
Error22.57%
Cost712
\[\begin{array}{l} \mathbf{if}\;x \leq -36:\\ \;\;\;\;x \cdot 4.16438922228 + \left(\frac{3655.1204654076414}{x} + -110.1139242984811\right)\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{-7}:\\ \;\;\;\;\frac{x + -2}{\frac{47.066876606}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \end{array} \]
Alternative 22
Error22.68%
Cost585
\[\begin{array}{l} \mathbf{if}\;x \leq -35 \lor \neg \left(x \leq 2.3 \cdot 10^{-7}\right):\\ \;\;\;\;-110.1139242984811 + x \cdot 4.16438922228\\ \mathbf{else}:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \end{array} \]
Alternative 23
Error22.62%
Cost584
\[\begin{array}{l} \mathbf{if}\;x \leq -50:\\ \;\;\;\;-110.1139242984811 + x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{-7}:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \mathbf{else}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \end{array} \]
Alternative 24
Error22.77%
Cost456
\[\begin{array}{l} \mathbf{if}\;x \leq -80:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq 2:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228\\ \end{array} \]
Alternative 25
Error54.69%
Cost192
\[x \cdot 4.16438922228 \]

Error

Reproduce?

herbie shell --seed 2023121 
(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)))