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

Average Accuracy: 53.2% → 96.8%

Time: 34.2s

Precision: binary64

Cost: 52808

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+43}:\\ \;\;\;\;\mathsf{fma}\left(-36.52704169880642, \frac{y}{z}, \mathsf{fma}\left(3.13060547623, y, x + \frac{y}{\frac{z \cdot z}{t + 457.9610022158428}}\right)\right)\\ \mathbf{elif}\;z \leq 190000000000:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), t\right), a\right), b\right)}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)}, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \]

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 (<= z -1.5e+43)
   (fma
    -36.52704169880642
    (/ y z)
    (fma 3.13060547623 y (+ x (/ y (/ (* z z) (+ t 457.9610022158428))))))
   (if (<= z 190000000000.0)
     (fma
      y
      (/
       (fma z (fma z (fma z (fma z 3.13060547623 11.1667541262) t) a) b)
       (fma
        z
        (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721)
        0.607771387771))
      x)
     (+ x (* y 3.13060547623)))))

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 <= -1.5e+43) {
		tmp = fma(-36.52704169880642, (y / z), fma(3.13060547623, y, (x + (y / ((z * z) / (t + 457.9610022158428))))));
	} else if (z <= 190000000000.0) {
		tmp = fma(y, (fma(z, fma(z, fma(z, fma(z, 3.13060547623, 11.1667541262), t), a), b) / fma(z, fma(z, fma(z, (z + 15.234687407), 31.4690115749), 11.9400905721), 0.607771387771)), x);
	} else {
		tmp = x + (y * 3.13060547623);
	}
	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 <= -1.5e+43)
		tmp = fma(-36.52704169880642, Float64(y / z), fma(3.13060547623, y, Float64(x + Float64(y / Float64(Float64(z * z) / Float64(t + 457.9610022158428))))));
	elseif (z <= 190000000000.0)
		tmp = fma(y, Float64(fma(z, fma(z, fma(z, fma(z, 3.13060547623, 11.1667541262), t), a), b) / fma(z, fma(z, fma(z, Float64(z + 15.234687407), 31.4690115749), 11.9400905721), 0.607771387771)), x);
	else
		tmp = Float64(x + Float64(y * 3.13060547623));
	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[LessEqual[z, -1.5e+43], N[(-36.52704169880642 * N[(y / z), $MachinePrecision] + N[(3.13060547623 * y + N[(x + N[(y / N[(N[(z * z), $MachinePrecision] / N[(t + 457.9610022158428), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 190000000000.0], N[(y * N[(N[(z * N[(z * N[(z * N[(z * 3.13060547623 + 11.1667541262), $MachinePrecision] + t), $MachinePrecision] + a), $MachinePrecision] + b), $MachinePrecision] / N[(z * N[(z * N[(z * N[(z + 15.234687407), $MachinePrecision] + 31.4690115749), $MachinePrecision] + 11.9400905721), $MachinePrecision] + 0.607771387771), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision]]]

Target

Original	53.2%
Target	98.4%
Herbie	96.8%

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

Derivation

1. Split input into 3 regimes

2. if z < -1.50000000000000008e43

   1. Initial program 5.0%

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

   2. Simplified 8.4%

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

      [Start] 5.0	\[ x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
      +-commutative [=>] 5.0	\[ \color{blue}{\frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} + x} \]
      associate-*r/ [<=] 8.4	\[ \color{blue}{y \cdot \frac{\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771}} + x \]
      fma-def [=>] 8.4	\[ \color{blue}{\mathsf{fma}\left(y, \frac{\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771}, x\right)} \]

   3. Taylor expanded in z around inf 86.3%

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

   4. Simplified 98.3%

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

      [Start] 86.3	\[ -36.52704169880642 \cdot \frac{y}{z} + \left(3.13060547623 \cdot y + \left(\frac{y \cdot \left(457.9610022158428 + t\right)}{{z}^{2}} + x\right)\right) \]
      fma-def [=>] 86.3	\[ \color{blue}{\mathsf{fma}\left(-36.52704169880642, \frac{y}{z}, 3.13060547623 \cdot y + \left(\frac{y \cdot \left(457.9610022158428 + t\right)}{{z}^{2}} + x\right)\right)} \]
      fma-def [=>] 86.3	\[ \mathsf{fma}\left(-36.52704169880642, \frac{y}{z}, \color{blue}{\mathsf{fma}\left(3.13060547623, y, \frac{y \cdot \left(457.9610022158428 + t\right)}{{z}^{2}} + x\right)}\right) \]
      +-commutative [=>] 86.3	\[ \mathsf{fma}\left(-36.52704169880642, \frac{y}{z}, \mathsf{fma}\left(3.13060547623, y, \color{blue}{x + \frac{y \cdot \left(457.9610022158428 + t\right)}{{z}^{2}}}\right)\right) \]
      associate-/l* [=>] 98.3	\[ \mathsf{fma}\left(-36.52704169880642, \frac{y}{z}, \mathsf{fma}\left(3.13060547623, y, x + \color{blue}{\frac{y}{\frac{{z}^{2}}{457.9610022158428 + t}}}\right)\right) \]
      unpow2 [=>] 98.3	\[ \mathsf{fma}\left(-36.52704169880642, \frac{y}{z}, \mathsf{fma}\left(3.13060547623, y, x + \frac{y}{\frac{\color{blue}{z \cdot z}}{457.9610022158428 + t}}\right)\right) \]
      +-commutative [=>] 98.3	\[ \mathsf{fma}\left(-36.52704169880642, \frac{y}{z}, \mathsf{fma}\left(3.13060547623, y, x + \frac{y}{\frac{z \cdot z}{\color{blue}{t + 457.9610022158428}}}\right)\right) \]

   if -1.50000000000000008e43 < z < 1.9e11

   1. Initial program 98.2%

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

   2. Simplified 99.1%

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

      [Start] 98.2	\[ x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
      +-commutative [=>] 98.2	\[ \color{blue}{\frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} + x} \]
      associate-*r/ [<=] 99.1	\[ \color{blue}{y \cdot \frac{\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771}} + x \]
      fma-def [=>] 99.1	\[ \color{blue}{\mathsf{fma}\left(y, \frac{\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771}, x\right)} \]

   if 1.9e11 < z

   1. Initial program 10.8%

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

   2. Simplified 16.5%

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

      [Start] 10.8	\[ x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
      +-commutative [=>] 10.8	\[ \color{blue}{\frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} + x} \]
      associate-*r/ [<=] 16.5	\[ \color{blue}{y \cdot \frac{\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771}} + x \]
      fma-def [=>] 16.5	\[ \color{blue}{\mathsf{fma}\left(y, \frac{\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771}, x\right)} \]

   3. Taylor expanded in z around inf 91.3%

      \[\leadsto \color{blue}{3.13060547623 \cdot y + x} \]
3. Recombined 3 regimes into one program.

4. Final simplification 96.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+43}:\\ \;\;\;\;\mathsf{fma}\left(-36.52704169880642, \frac{y}{z}, \mathsf{fma}\left(3.13060547623, y, x + \frac{y}{\frac{z \cdot z}{t + 457.9610022158428}}\right)\right)\\ \mathbf{elif}\;z \leq 190000000000:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), t\right), a\right), b\right)}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)}, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	96.9%
Cost	46536

\[\begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+38}:\\ \;\;\;\;\mathsf{fma}\left(-36.52704169880642, \frac{y}{z}, \mathsf{fma}\left(3.13060547623, y, x + \frac{y}{\frac{z \cdot z}{t + 457.9610022158428}}\right)\right)\\ \mathbf{elif}\;z \leq 190000000000:\\ \;\;\;\;x + \frac{y}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687407, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), z, t\right), z, a\right), z, b\right)}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \]

Alternative 2
Accuracy	98.1%
Cost	18504

\[\begin{array}{l} t_1 := y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + z \cdot 3.13060547623\right)\right)\right)\right)\\ t_2 := \frac{t_1}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547623 + \left(\left(\frac{457.9610022158428}{z \cdot z} + \frac{t}{z \cdot z}\right) + \frac{-36.52704169880642}{z}\right), x\right)\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{+286}:\\ \;\;\;\;x + \frac{t_1}{0.607771387771 + \left(z \cdot \left(z \cdot \mathsf{fma}\left(z + 15.234687407, z, 31.4690115749\right)\right) + z \cdot 11.9400905721\right)}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-36.52704169880642, \frac{y}{z}, \mathsf{fma}\left(3.13060547623, y, x + \frac{y}{\frac{z \cdot z}{t + 457.9610022158428}}\right)\right)\\ \end{array} \]

Alternative 3
Accuracy	98.1%
Cost	13385

\[\begin{array}{l} t_1 := y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + z \cdot 3.13060547623\right)\right)\right)\right)\\ t_2 := \frac{t_1}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)}\\ \mathbf{if}\;t_2 \leq -\infty \lor \neg \left(t_2 \leq 2 \cdot 10^{+286}\right):\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547623 + \left(\left(\frac{457.9610022158428}{z \cdot z} + \frac{t}{z \cdot z}\right) + \frac{-36.52704169880642}{z}\right), x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t_1}{0.607771387771 + \left(z \cdot \left(z \cdot \mathsf{fma}\left(z + 15.234687407, z, 31.4690115749\right)\right) + z \cdot 11.9400905721\right)}\\ \end{array} \]

Alternative 4
Accuracy	98.1%
Cost	12233

\[\begin{array}{l} t_1 := \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + z \cdot 3.13060547623\right)\right)\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)}\\ \mathbf{if}\;t_1 \leq -\infty \lor \neg \left(t_1 \leq 2 \cdot 10^{+286}\right):\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547623 + \left(\left(\frac{457.9610022158428}{z \cdot z} + \frac{t}{z \cdot z}\right) + \frac{-36.52704169880642}{z}\right), x\right)\\ \mathbf{else}:\\ \;\;\;\;x + t_1\\ \end{array} \]

Alternative 5
Accuracy	96.0%
Cost	6984

\[\begin{array}{l} t_1 := \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + z \cdot 3.13060547623\right)\right)\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+286}:\\ \;\;\;\;x + t_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{0.31942702700572795 + \left(\frac{t}{z \cdot z} \cdot -0.10203362558171805 + \frac{3.7269864963038164}{z}\right)}\\ \end{array} \]

Alternative 6
Accuracy	95.4%
Cost	2376

\[\begin{array}{l} \mathbf{if}\;z \leq -2.45 \cdot 10^{+25}:\\ \;\;\;\;x + \frac{y}{0.31942702700572795 + \left(\frac{t}{z \cdot z} \cdot -0.10203362558171805 + \frac{3.7269864963038164}{z}\right)}\\ \mathbf{elif}\;z \leq 190000000000:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot 11.1667541262\right)\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \]

Alternative 7
Accuracy	94.2%
Cost	1992

\[\begin{array}{l} \mathbf{if}\;z \leq -13:\\ \;\;\;\;x + \frac{y}{0.31942702700572795 + \left(\frac{3.7269864963038164}{z} + \frac{-3.241970391368047 + t \cdot -0.10203362558171805}{z \cdot z}\right)}\\ \mathbf{elif}\;z \leq 3800000000:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + z \cdot 3.13060547623\right)\right)\right)\right)}{0.607771387771 + z \cdot 11.9400905721}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \]

Alternative 8
Accuracy	94.2%
Cost	1736

\[\begin{array}{l} \mathbf{if}\;z \leq -13:\\ \;\;\;\;x + \frac{y}{0.31942702700572795 + \left(\frac{3.7269864963038164}{z} + \frac{-3.241970391368047 + t \cdot -0.10203362558171805}{z \cdot z}\right)}\\ \mathbf{elif}\;z \leq 3800000000:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot 11.1667541262\right)\right)\right)}{0.607771387771 + z \cdot 11.9400905721}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \]

Alternative 9
Accuracy	91.4%
Cost	1348

\[\begin{array}{l} \mathbf{if}\;z \leq -13:\\ \;\;\;\;x + \frac{y}{0.31942702700572795 + \left(\frac{3.7269864963038164}{z} + \frac{-3.241970391368047 + t \cdot -0.10203362558171805}{z \cdot z}\right)}\\ \mathbf{elif}\;z \leq 4000000000:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot a\right)}{0.607771387771 + z \cdot 11.9400905721}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \]

Alternative 10
Accuracy	91.4%
Cost	1224

\[\begin{array}{l} \mathbf{if}\;z \leq -13.2:\\ \;\;\;\;x + \frac{y}{0.31942702700572795 + \left(\frac{3.7269864963038164}{z} + \frac{\frac{-3.241970391368047}{z}}{z}\right)}\\ \mathbf{elif}\;z \leq 10200000000:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot a\right)}{0.607771387771 + z \cdot 11.9400905721}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \]

Alternative 11
Accuracy	91.4%
Cost	1224

\[\begin{array}{l} \mathbf{if}\;z \leq -13.5:\\ \;\;\;\;x + \frac{y}{0.31942702700572795 + \left(\frac{t}{z \cdot z} \cdot -0.10203362558171805 + \frac{3.7269864963038164}{z}\right)}\\ \mathbf{elif}\;z \leq 3800000000:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot a\right)}{0.607771387771 + z \cdot 11.9400905721}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \]

Alternative 12
Accuracy	86.1%
Cost	1092

\[\begin{array}{l} \mathbf{if}\;z \leq -0.06:\\ \;\;\;\;x + \frac{y}{0.31942702700572795 + \left(\frac{3.7269864963038164}{z} + \frac{\frac{-3.241970391368047}{z}}{z}\right)}\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-18}:\\ \;\;\;\;x + 1.6453555072203998 \cdot \left(y \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y \cdot 3.13060547623\right) + -36.52704169880642 \cdot \frac{y}{z}\\ \end{array} \]

Alternative 13
Accuracy	86.1%
Cost	968

\[\begin{array}{l} \mathbf{if}\;z \leq -0.06:\\ \;\;\;\;x + \frac{y}{0.31942702700572795 + \frac{3.7269864963038164}{z}}\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-18}:\\ \;\;\;\;x + 1.6453555072203998 \cdot \left(y \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y \cdot 3.13060547623\right) + -36.52704169880642 \cdot \frac{y}{z}\\ \end{array} \]

Alternative 14
Accuracy	86.2%
Cost	713

\[\begin{array}{l} \mathbf{if}\;z \leq -1.9 \lor \neg \left(z \leq 3800000000\right):\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(b \cdot 1.6453555072203998\right)\\ \end{array} \]

Alternative 15
Accuracy	86.2%
Cost	713

\[\begin{array}{l} \mathbf{if}\;z \leq -1.9 \lor \neg \left(z \leq 3800000000\right):\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x + 1.6453555072203998 \cdot \left(y \cdot b\right)\\ \end{array} \]

Alternative 16
Accuracy	86.2%
Cost	712

\[\begin{array}{l} \mathbf{if}\;z \leq -0.08:\\ \;\;\;\;x + \frac{y}{0.31942702700572795 + \frac{3.7269864963038164}{z}}\\ \mathbf{elif}\;z \leq 3800000000:\\ \;\;\;\;x + 1.6453555072203998 \cdot \left(y \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \]

Alternative 17
Accuracy	72.0%
Cost	585

\[\begin{array}{l} \mathbf{if}\;z \leq -0.78 \lor \neg \left(z \leq 2.3 \cdot 10^{-190}\right):\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 18
Accuracy	56.4%
Cost	456

\[\begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{+78}:\\ \;\;\;\;y \cdot 3.13060547623\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+203}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot 3.13060547623\\ \end{array} \]

Alternative 19
Accuracy	51.0%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023141 
(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))))