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

Average Accuracy: 54.5% → 97.8%

Time: 39.5s

Precision: binary64

Cost: 46537

Math

\[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]

↓

\[\begin{array}{l} \mathbf{if}\;z \leq -7.6 \cdot 10^{+45} \lor \neg \left(z \leq 1.15 \cdot 10^{+66}\right):\\ \;\;\;\;x + \left(\left(\frac{y}{z \cdot z} \cdot t + \left(y \cdot 3.13060547623 + \frac{y \cdot -36.52704169880642}{z}\right)\right) - \frac{y \cdot -457.9610022158428}{z \cdot z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687407, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), z, t\right), z, a\right), z, b\right)}}\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (+
  x
  (/
   (*
    y
    (+ (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z) b))
   (+
    (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z)
    0.607771387771))))

↓

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -7.6e+45) (not (<= z 1.15e+66)))
   (+
    x
    (-
     (+
      (* (/ y (* z z)) t)
      (+ (* y 3.13060547623) (/ (* y -36.52704169880642) z)))
     (/ (* y -457.9610022158428) (* z z))))
   (+
    x
    (/
     y
     (/
      (fma
       (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721)
       z
       0.607771387771)
      (fma (fma (fma (fma z 3.13060547623 11.1667541262) z t) z a) z b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	return x + ((y * ((((((((z * 3.13060547623) + 11.1667541262) * z) + t) * z) + a) * z) + b)) / (((((((z + 15.234687407) * z) + 31.4690115749) * z) + 11.9400905721) * z) + 0.607771387771));
}

↓

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -7.6e+45) || !(z <= 1.15e+66)) {
		tmp = x + ((((y / (z * z)) * t) + ((y * 3.13060547623) + ((y * -36.52704169880642) / z))) - ((y * -457.9610022158428) / (z * z)));
	} else {
		tmp = x + (y / (fma(fma(fma((z + 15.234687407), z, 31.4690115749), z, 11.9400905721), z, 0.607771387771) / fma(fma(fma(fma(z, 3.13060547623, 11.1667541262), z, t), z, a), z, b)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	return Float64(x + Float64(Float64(y * Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(z * 3.13060547623) + 11.1667541262) * z) + t) * z) + a) * z) + b)) / Float64(Float64(Float64(Float64(Float64(Float64(Float64(z + 15.234687407) * z) + 31.4690115749) * z) + 11.9400905721) * z) + 0.607771387771)))
end

↓

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -7.6e+45) || !(z <= 1.15e+66))
		tmp = Float64(x + Float64(Float64(Float64(Float64(y / Float64(z * z)) * t) + Float64(Float64(y * 3.13060547623) + Float64(Float64(y * -36.52704169880642) / z))) - Float64(Float64(y * -457.9610022158428) / Float64(z * z))));
	else
		tmp = Float64(x + Float64(y / Float64(fma(fma(fma(Float64(z + 15.234687407), z, 31.4690115749), z, 11.9400905721), z, 0.607771387771) / fma(fma(fma(fma(z, 3.13060547623, 11.1667541262), z, t), z, a), z, b))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(x + N[(N[(y * N[(N[(N[(N[(N[(N[(N[(N[(z * 3.13060547623), $MachinePrecision] + 11.1667541262), $MachinePrecision] * z), $MachinePrecision] + t), $MachinePrecision] * z), $MachinePrecision] + a), $MachinePrecision] * z), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(N[(N[(N[(N[(z + 15.234687407), $MachinePrecision] * z), $MachinePrecision] + 31.4690115749), $MachinePrecision] * z), $MachinePrecision] + 11.9400905721), $MachinePrecision] * z), $MachinePrecision] + 0.607771387771), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -7.6e+45], N[Not[LessEqual[z, 1.15e+66]], $MachinePrecision]], N[(x + N[(N[(N[(N[(y / N[(z * z), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision] + N[(N[(y * 3.13060547623), $MachinePrecision] + N[(N[(y * -36.52704169880642), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y * -457.9610022158428), $MachinePrecision] / N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(N[(N[(N[(N[(z + 15.234687407), $MachinePrecision] * z + 31.4690115749), $MachinePrecision] * z + 11.9400905721), $MachinePrecision] * z + 0.607771387771), $MachinePrecision] / N[(N[(N[(N[(z * 3.13060547623 + 11.1667541262), $MachinePrecision] * z + t), $MachinePrecision] * z + a), $MachinePrecision] * z + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Target

Original	54.5%
Target	98.1%
Herbie	97.8%

\[\begin{array}{l} \mathbf{if}\;z < -6.499344996252632 \cdot 10^{+53}:\\ \;\;\;\;x + \left(\left(3.13060547623 - \frac{36.527041698806414}{z}\right) + \frac{t}{z \cdot z}\right) \cdot \frac{y}{1}\\ \mathbf{elif}\;z < 7.066965436914287 \cdot 10^{+59}:\\ \;\;\;\;x + \frac{y}{\frac{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771}{\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(3.13060547623 - \frac{36.527041698806414}{z}\right) + \frac{t}{z \cdot z}\right) \cdot \frac{y}{1}\\ \end{array} \]

Derivation

1. Split input into 2 regimes

2. if z < -7.6000000000000004e45 or 1.15e66 < z

   1. Initial program 3.8%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]

   2. Simplified 5.8%

      \[\leadsto \color{blue}{x + \frac{y}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)} \cdot \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), t\right), a\right), b\right)} \]
      Proof

      [Start] 3.8	\[ x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
      associate-*l/ [<=] 5.8	\[ x + \color{blue}{\frac{y}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)} \]
      *-commutative [=>] 5.8	\[ x + \frac{y}{\color{blue}{z \cdot \left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right)} + 0.607771387771} \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right) \]
      fma-def [=>] 5.8	\[ x + \frac{y}{\color{blue}{\mathsf{fma}\left(z, \left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721, 0.607771387771\right)}} \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right) \]
      *-commutative [=>] 5.8	\[ x + \frac{y}{\mathsf{fma}\left(z, \color{blue}{z \cdot \left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right)} + 11.9400905721, 0.607771387771\right)} \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right) \]
      fma-def [=>] 5.8	\[ x + \frac{y}{\mathsf{fma}\left(z, \color{blue}{\mathsf{fma}\left(z, \left(z + 15.234687407\right) \cdot z + 31.4690115749, 11.9400905721\right)}, 0.607771387771\right)} \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right) \]
      *-commutative [=>] 5.8	\[ x + \frac{y}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \color{blue}{z \cdot \left(z + 15.234687407\right)} + 31.4690115749, 11.9400905721\right), 0.607771387771\right)} \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right) \]
      fma-def [=>] 5.8	\[ x + \frac{y}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \color{blue}{\mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right)}, 11.9400905721\right), 0.607771387771\right)} \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right) \]
      *-commutative [=>] 5.8	\[ x + \frac{y}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)} \cdot \left(\color{blue}{z \cdot \left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right)} + b\right) \]
      fma-def [=>] 5.8	\[ x + \frac{y}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)} \cdot \color{blue}{\mathsf{fma}\left(z, \left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a, b\right)} \]

   3. Taylor expanded in z around inf 86.5%

      \[\leadsto x + \color{blue}{\left(\left(\frac{y \cdot t}{{z}^{2}} + \left(11.1667541262 \cdot \frac{y}{z} + 3.13060547623 \cdot y\right)\right) - \left(47.69379582500642 \cdot \frac{y}{z} + \left(98.5170599679272 \cdot \frac{y}{{z}^{2}} + 15.234687407 \cdot \frac{11.1667541262 \cdot y - 47.69379582500642 \cdot y}{{z}^{2}}\right)\right)\right)} \]

   4. Simplified 97.5%

      \[\leadsto x + \color{blue}{\left(\left(\frac{y}{z \cdot z} \cdot t + \left(y \cdot 3.13060547623 + \frac{y \cdot -36.52704169880642}{z}\right)\right) - \mathsf{fma}\left(98.5170599679272, \frac{y}{z \cdot z}, \frac{y \cdot -556.47806218377}{z \cdot z}\right)\right)} \]
      Proof

      [Start] 86.5	\[ x + \left(\left(\frac{y \cdot t}{{z}^{2}} + \left(11.1667541262 \cdot \frac{y}{z} + 3.13060547623 \cdot y\right)\right) - \left(47.69379582500642 \cdot \frac{y}{z} + \left(98.5170599679272 \cdot \frac{y}{{z}^{2}} + 15.234687407 \cdot \frac{11.1667541262 \cdot y - 47.69379582500642 \cdot y}{{z}^{2}}\right)\right)\right) \]
      associate--r+ [=>] 86.5	\[ x + \color{blue}{\left(\left(\left(\frac{y \cdot t}{{z}^{2}} + \left(11.1667541262 \cdot \frac{y}{z} + 3.13060547623 \cdot y\right)\right) - 47.69379582500642 \cdot \frac{y}{z}\right) - \left(98.5170599679272 \cdot \frac{y}{{z}^{2}} + 15.234687407 \cdot \frac{11.1667541262 \cdot y - 47.69379582500642 \cdot y}{{z}^{2}}\right)\right)} \]

   5. Taylor expanded in y around 0 97.7%

      \[\leadsto x + \left(\left(\frac{y}{z \cdot z} \cdot t + \left(y \cdot 3.13060547623 + \frac{y \cdot -36.52704169880642}{z}\right)\right) - \color{blue}{-457.9610022158428 \cdot \frac{y}{{z}^{2}}}\right) \]

   6. Simplified 97.5%

      \[\leadsto x + \left(\left(\frac{y}{z \cdot z} \cdot t + \left(y \cdot 3.13060547623 + \frac{y \cdot -36.52704169880642}{z}\right)\right) - \color{blue}{\frac{-457.9610022158428 \cdot y}{z \cdot z}}\right) \]
      Proof

      [Start] 97.7	\[ x + \left(\left(\frac{y}{z \cdot z} \cdot t + \left(y \cdot 3.13060547623 + \frac{y \cdot -36.52704169880642}{z}\right)\right) - -457.9610022158428 \cdot \frac{y}{{z}^{2}}\right) \]
      unpow2 [=>] 97.7	\[ x + \left(\left(\frac{y}{z \cdot z} \cdot t + \left(y \cdot 3.13060547623 + \frac{y \cdot -36.52704169880642}{z}\right)\right) - -457.9610022158428 \cdot \frac{y}{\color{blue}{z \cdot z}}\right) \]
      associate-*r/ [=>] 97.5	\[ x + \left(\left(\frac{y}{z \cdot z} \cdot t + \left(y \cdot 3.13060547623 + \frac{y \cdot -36.52704169880642}{z}\right)\right) - \color{blue}{\frac{-457.9610022158428 \cdot y}{z \cdot z}}\right) \]

   if -7.6000000000000004e45 < z < 1.15e66

   1. Initial program 95.0%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]

   2. Simplified 97.9%

      \[\leadsto \color{blue}{x + \frac{y}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687407, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), z, t\right), z, a\right), z, b\right)}}} \]
      Proof

      [Start] 95.0	\[ x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
      associate-/l* [=>] 97.9	\[ x + \color{blue}{\frac{y}{\frac{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771}{\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}} \]
      fma-def [=>] 97.9	\[ x + \frac{y}{\frac{\color{blue}{\mathsf{fma}\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721, z, 0.607771387771\right)}}{\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}} \]
      fma-def [=>] 97.9	\[ x + \frac{y}{\frac{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749, z, 11.9400905721\right)}, z, 0.607771387771\right)}{\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}} \]
      fma-def [=>] 97.9	\[ x + \frac{y}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(z + 15.234687407, z, 31.4690115749\right)}, z, 11.9400905721\right), z, 0.607771387771\right)}{\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}} \]
      fma-def [=>] 97.9	\[ x + \frac{y}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687407, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}{\color{blue}{\mathsf{fma}\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a, z, b\right)}}} \]
      fma-def [=>] 97.9	\[ x + \frac{y}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687407, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t, z, a\right)}, z, b\right)}} \]
      fma-def [=>] 97.9	\[ x + \frac{y}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687407, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(z \cdot 3.13060547623 + 11.1667541262, z, t\right)}, z, a\right), z, b\right)}} \]
      fma-def [=>] 97.9	\[ x + \frac{y}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687407, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right)}, z, t\right), z, a\right), z, b\right)}} \]

3. Recombined 2 regimes into one program.

4. Final simplification 97.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.6 \cdot 10^{+45} \lor \neg \left(z \leq 1.15 \cdot 10^{+66}\right):\\ \;\;\;\;x + \left(\left(\frac{y}{z \cdot z} \cdot t + \left(y \cdot 3.13060547623 + \frac{y \cdot -36.52704169880642}{z}\right)\right) - \frac{y \cdot -457.9610022158428}{z \cdot z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687407, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), z, t\right), z, a\right), z, b\right)}}\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	97.5%
Cost	27721

\[\begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+45} \lor \neg \left(z \leq 6.8 \cdot 10^{+65}\right):\\ \;\;\;\;x + \left(\left(\frac{y}{z \cdot z} \cdot t + \left(y \cdot 3.13060547623 + \frac{y \cdot -36.52704169880642}{z}\right)\right) - \frac{y \cdot -457.9610022158428}{z \cdot z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)} \cdot \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), t\right), a\right), b\right)\\ \end{array} \]

Alternative 2
Accuracy	96.8%
Cost	2633

\[\begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{+45} \lor \neg \left(z \leq 180000000\right):\\ \;\;\;\;x + \left(\left(\frac{y}{z \cdot z} \cdot t + \left(y \cdot 3.13060547623 + \frac{y \cdot -36.52704169880642}{z}\right)\right) - \frac{y \cdot -457.9610022158428}{z \cdot z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + z \cdot 3.13060547623\right)\right)\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)}\\ \end{array} \]

Alternative 3
Accuracy	96.1%
Cost	2249

\[\begin{array}{l} \mathbf{if}\;z \leq -80 \lor \neg \left(z \leq 86\right):\\ \;\;\;\;x + \left(\left(\frac{y}{z \cdot z} \cdot t + \left(y \cdot 3.13060547623 + \frac{y \cdot -36.52704169880642}{z}\right)\right) - \frac{y \cdot -457.9610022158428}{z \cdot z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + z \cdot 3.13060547623\right)\right)\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot 31.4690115749\right)}\\ \end{array} \]

Alternative 4
Accuracy	93.2%
Cost	1993

\[\begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+45} \lor \neg \left(z \leq 23500\right):\\ \;\;\;\;x + \left(\left(\frac{y}{z \cdot z} \cdot t + \left(y \cdot 3.13060547623 + \frac{y \cdot -36.52704169880642}{z}\right)\right) - \frac{y \cdot -457.9610022158428}{z \cdot z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot a\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)}\\ \end{array} \]

Alternative 5
Accuracy	91.5%
Cost	1864

\[\begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+45}:\\ \;\;\;\;x + \frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 - \frac{t \cdot 0.10203362558171805}{z \cdot z}\right)}\\ \mathbf{elif}\;z \leq 24000:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot a\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 - \frac{t \cdot 0.10203362558171805 + 3.241970391368047}{z \cdot z}\right)}\\ \end{array} \]

Alternative 6
Accuracy	91.2%
Cost	1481

\[\begin{array}{l} \mathbf{if}\;z \leq -6500 \lor \neg \left(z \leq 3200\right):\\ \;\;\;\;x + \frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 - \frac{t \cdot 0.10203362558171805}{z \cdot z}\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot a\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot 31.4690115749\right)}\\ \end{array} \]

Alternative 7
Accuracy	91.2%
Cost	1480

\[\begin{array}{l} \mathbf{if}\;z \leq -2050:\\ \;\;\;\;x + \frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 - \frac{t \cdot 0.10203362558171805}{z \cdot z}\right)}\\ \mathbf{elif}\;z \leq 15500:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot a\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot 31.4690115749\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 - \frac{t \cdot 0.10203362558171805 + 3.241970391368047}{z \cdot z}\right)}\\ \end{array} \]

Alternative 8
Accuracy	91.1%
Cost	1353

\[\begin{array}{l} \mathbf{if}\;z \leq -42 \lor \neg \left(z \leq 3900\right):\\ \;\;\;\;x + \frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 - \frac{t \cdot 0.10203362558171805}{z \cdot z}\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot a\right)}{0.607771387771 + z \cdot 11.9400905721}\\ \end{array} \]

Alternative 9
Accuracy	90.9%
Cost	1224

\[\begin{array}{l} \mathbf{if}\;z \leq -75:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{elif}\;z \leq 58:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot a\right)}{0.607771387771}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{1}{0.31942702700572795 + \frac{3.7269864963038164 - \frac{3.241970391368047}{z}}{z}}\\ \end{array} \]

Alternative 10
Accuracy	91.1%
Cost	1224

\[\begin{array}{l} \mathbf{if}\;z \leq -42:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{elif}\;z \leq 1.2:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot a\right)}{0.607771387771 + z \cdot 11.9400905721}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{1}{0.31942702700572795 + \frac{3.7269864963038164 - \frac{3.241970391368047}{z}}{z}}\\ \end{array} \]

Alternative 11
Accuracy	90.9%
Cost	1096

\[\begin{array}{l} \mathbf{if}\;z \leq -8500:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{elif}\;z \leq 72:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot a\right)}{0.607771387771}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{0.31942702700572795 + \frac{3.7269864963038164 + \frac{-3.241970391368047}{z}}{z}}\\ \end{array} \]

Alternative 12
Accuracy	85.2%
Cost	968

\[\begin{array}{l} \mathbf{if}\;z \leq -7400000:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{elif}\;z \leq 5800:\\ \;\;\;\;x + \frac{y \cdot b}{0.607771387771 + z \cdot 11.9400905721}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{3.7269864963038164}{z} + 0.31942702700572795}\\ \end{array} \]

Alternative 13
Accuracy	90.9%
Cost	968

\[\begin{array}{l} \mathbf{if}\;z \leq -115:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{elif}\;z \leq 2050:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot a\right)}{0.607771387771}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{3.7269864963038164}{z} + 0.31942702700572795}\\ \end{array} \]

Alternative 14
Accuracy	85.2%
Cost	840

\[\begin{array}{l} \mathbf{if}\;z \leq -7400000:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{elif}\;z \leq 960:\\ \;\;\;\;x + \left(y \cdot b\right) \cdot 1.6453555072203998\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(3.13060547623 - \frac{36.52704169880642}{z}\right)\\ \end{array} \]

Alternative 15
Accuracy	85.2%
Cost	840

\[\begin{array}{l} \mathbf{if}\;z \leq -7600000000:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x + \left(y \cdot b\right) \cdot 1.6453555072203998\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{3.7269864963038164}{z} + 0.31942702700572795}\\ \end{array} \]

Alternative 16
Accuracy	85.2%
Cost	713

\[\begin{array}{l} \mathbf{if}\;z \leq -7400000 \lor \neg \left(z \leq 350\right):\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot b\right) \cdot 1.6453555072203998\\ \end{array} \]

Alternative 17
Accuracy	70.1%
Cost	585

\[\begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{-26} \lor \neg \left(z \leq 5.1 \cdot 10^{-89}\right):\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 18
Accuracy	48.6%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023151 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, D"
  :precision binary64

  :herbie-target
  (if (< z -6.499344996252632e+53) (+ x (* (+ (- 3.13060547623 (/ 36.527041698806414 z)) (/ t (* z z))) (/ y 1.0))) (if (< z 7.066965436914287e+59) (+ x (/ y (/ (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771) (+ (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z) b)))) (+ x (* (+ (- 3.13060547623 (/ 36.527041698806414 z)) (/ t (* z z))) (/ y 1.0)))))

  (+ x (/ (* y (+ (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z) b)) (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771))))