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

Average Error: 29.3 → 1.1

Time: 48.7s

Precision: binary64

Cost: 46664

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+31}:\\ \;\;\;\;x + \left(y \cdot \left(\frac{t}{z \cdot z} + 3.13060547623\right) - \frac{y}{z} \cdot \left(47.69379582500642 - 11.1667541262\right)\right)\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+43}:\\ \;\;\;\;x + \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(\mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), z, t\right), a\right), b\right) \cdot \left(y \cdot \frac{1}{\mathsf{fma}\left(\mathsf{fma}\left(z, \mathsf{fma}\left(z + 15.234687407, z, 31.4690115749\right), 11.9400905721\right), z, 0.607771387771\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{y}{z} \cdot \left(\frac{t}{z} + -47.69379582500642\right) + y \cdot \left(\frac{11.1667541262}{z} + 3.13060547623\right)\right)\\ \end{array} \]

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 (<= z -2.4e+31)
   (+
    x
    (-
     (* y (+ (/ t (* z z)) 3.13060547623))
     (* (/ y z) (- 47.69379582500642 11.1667541262))))
   (if (<= z 5e+43)
     (+
      x
      (*
       (fma z (fma z (fma (fma z 3.13060547623 11.1667541262) z t) a) b)
       (*
        y
        (/
         1.0
         (fma
          (fma z (fma (+ z 15.234687407) z 31.4690115749) 11.9400905721)
          z
          0.607771387771)))))
     (+
      x
      (+
       (* (/ y z) (+ (/ t z) -47.69379582500642))
       (* y (+ (/ 11.1667541262 z) 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 <= -2.4e+31) {
		tmp = x + ((y * ((t / (z * z)) + 3.13060547623)) - ((y / z) * (47.69379582500642 - 11.1667541262)));
	} else if (z <= 5e+43) {
		tmp = x + (fma(z, fma(z, fma(fma(z, 3.13060547623, 11.1667541262), z, t), a), b) * (y * (1.0 / fma(fma(z, fma((z + 15.234687407), z, 31.4690115749), 11.9400905721), z, 0.607771387771))));
	} else {
		tmp = x + (((y / z) * ((t / z) + -47.69379582500642)) + (y * ((11.1667541262 / z) + 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 <= -2.4e+31)
		tmp = Float64(x + Float64(Float64(y * Float64(Float64(t / Float64(z * z)) + 3.13060547623)) - Float64(Float64(y / z) * Float64(47.69379582500642 - 11.1667541262))));
	elseif (z <= 5e+43)
		tmp = Float64(x + Float64(fma(z, fma(z, fma(fma(z, 3.13060547623, 11.1667541262), z, t), a), b) * Float64(y * Float64(1.0 / fma(fma(z, fma(Float64(z + 15.234687407), z, 31.4690115749), 11.9400905721), z, 0.607771387771)))));
	else
		tmp = Float64(x + Float64(Float64(Float64(y / z) * Float64(Float64(t / z) + -47.69379582500642)) + Float64(y * Float64(Float64(11.1667541262 / z) + 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, -2.4e+31], N[(x + N[(N[(y * N[(N[(t / N[(z * z), $MachinePrecision]), $MachinePrecision] + 3.13060547623), $MachinePrecision]), $MachinePrecision] - N[(N[(y / z), $MachinePrecision] * N[(47.69379582500642 - 11.1667541262), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5e+43], N[(x + N[(N[(z * N[(z * N[(N[(z * 3.13060547623 + 11.1667541262), $MachinePrecision] * z + t), $MachinePrecision] + a), $MachinePrecision] + b), $MachinePrecision] * N[(y * N[(1.0 / N[(N[(z * N[(N[(z + 15.234687407), $MachinePrecision] * z + 31.4690115749), $MachinePrecision] + 11.9400905721), $MachinePrecision] * z + 0.607771387771), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(N[(y / z), $MachinePrecision] * N[(N[(t / z), $MachinePrecision] + -47.69379582500642), $MachinePrecision]), $MachinePrecision] + N[(y * N[(N[(11.1667541262 / z), $MachinePrecision] + 3.13060547623), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Target

Original	29.3
Target	1.1
Herbie	1.1

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

Derivation

1. Split input into 3 regimes

2. if z < -2.39999999999999982e31

   1. Initial program 59.6

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

   2. Taylor expanded in z around inf 9.7

      \[\leadsto x + \color{blue}{\left(\left(11.1667541262 \cdot \frac{y}{z} + \left(3.13060547623 \cdot y + \left(y \cdot t - \left(15.234687407 \cdot \left(11.1667541262 \cdot y - 47.69379582500642 \cdot y\right) + 98.5170599679272 \cdot y\right)\right) \cdot {\left(\frac{1}{z}\right)}^{2}\right)\right) - 47.69379582500642 \cdot \frac{y}{z}\right)} \]

   3. Taylor expanded in t around inf 9.5

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

   4. Simplified 9.5

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

   5. Applied egg-rr 1.6

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

   if -2.39999999999999982e31 < z < 5.0000000000000004e43

   1. Initial program 1.9

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

   2. Applied egg-rr 0.9

      \[\leadsto x + \color{blue}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(\mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), z, t\right), a\right), b\right) \cdot \left(y \cdot \frac{1}{\mathsf{fma}\left(\mathsf{fma}\left(z, \mathsf{fma}\left(z + 15.234687407, z, 31.4690115749\right), 11.9400905721\right), z, 0.607771387771\right)}\right)} \]

   if 5.0000000000000004e43 < z

   1. Initial program 60.3

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

   2. Taylor expanded in z around inf 8.3

      \[\leadsto x + \color{blue}{\left(\left(11.1667541262 \cdot \frac{y}{z} + \left(3.13060547623 \cdot y + \left(y \cdot t - \left(15.234687407 \cdot \left(11.1667541262 \cdot y - 47.69379582500642 \cdot y\right) + 98.5170599679272 \cdot y\right)\right) \cdot {\left(\frac{1}{z}\right)}^{2}\right)\right) - 47.69379582500642 \cdot \frac{y}{z}\right)} \]

   3. Taylor expanded in t around inf 8.1

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

   4. Simplified 8.1

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

   5. Applied egg-rr 1.5

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

   6. Applied egg-rr 1.3

      \[\leadsto x + \color{blue}{\left(\frac{y}{z} \cdot \left(\frac{t}{z} + -47.69379582500642\right) + y \cdot \left(\frac{11.1667541262}{z} + 3.13060547623\right)\right)} \]
3. Recombined 3 regimes into one program.

Alternatives

Alternative 1
Error	1.2
Cost	46664

\[\begin{array}{l} t_1 := x + \left(\frac{y}{z} \cdot \left(\frac{t}{z} + -47.69379582500642\right) + y \cdot \left(\frac{11.1667541262}{z} + 3.13060547623\right)\right)\\ \mathbf{if}\;z \leq -1.9 \cdot 10^{+67}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+38}:\\ \;\;\;\;x + y \cdot \left(\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(\mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), z, t\right), a\right), b\right) \cdot \frac{1}{\mathsf{fma}\left(\mathsf{fma}\left(z, \mathsf{fma}\left(z + 15.234687407, z, 31.4690115749\right), 11.9400905721\right), z, 0.607771387771\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Error	1.3
Cost	46536

\[\begin{array}{l} t_1 := x + \left(\frac{y}{z} \cdot \left(\frac{t}{z} + -47.69379582500642\right) + y \cdot \left(\frac{11.1667541262}{z} + 3.13060547623\right)\right)\\ \mathbf{if}\;z \leq -2.4 \cdot 10^{+67}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+39}:\\ \;\;\;\;x + \frac{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(\mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), z, t\right), a\right), b\right)}{\mathsf{fma}\left(z, \mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687407, z, 31.4690115749\right), z, 11.9400905721\right), 0.607771387771\right)} \cdot y\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 3
Error	1.2
Cost	46536

\[\begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{+32}:\\ \;\;\;\;x + \left(y \cdot \left(\frac{t}{z \cdot z} + 3.13060547623\right) - \frac{y}{z} \cdot \left(47.69379582500642 - 11.1667541262\right)\right)\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+46}:\\ \;\;\;\;x + \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(\mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), z, t\right), a\right), b\right) \cdot \frac{y}{\mathsf{fma}\left(z, \mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687407, z, 31.4690115749\right), z, 11.9400905721\right), 0.607771387771\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{y}{z} \cdot \left(\frac{t}{z} + -47.69379582500642\right) + y \cdot \left(\frac{11.1667541262}{z} + 3.13060547623\right)\right)\\ \end{array} \]

Alternative 4
Error	1.4
Cost	6984

\[\begin{array}{l} t_1 := \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;x + \left(\left(11.1667541262 \cdot \frac{y}{z} + \left(3.13060547623 \cdot y + \frac{y}{z \cdot z} \cdot t\right)\right) - 47.69379582500642 \cdot \frac{y}{z}\right)\\ \mathbf{elif}\;t_1 \leq 10^{+288}:\\ \;\;\;\;x + t_1\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot \left(\frac{t}{z \cdot z} + 3.13060547623\right) - \frac{y}{z} \cdot \left(47.69379582500642 - 11.1667541262\right)\right)\\ \end{array} \]

Alternative 5
Error	6.3
Cost	1992

\[\begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{+32}:\\ \;\;\;\;x + \left(\frac{y}{z} \cdot \left(\frac{t}{z} + -47.69379582500642\right) + y \cdot \left(\frac{11.1667541262}{z} + 3.13060547623\right)\right)\\ \mathbf{elif}\;z \leq 11200000000:\\ \;\;\;\;x + \frac{y \cdot \left(\left(z \cdot z\right) \cdot t + b\right)}{0.607771387771 + \left(11.9400905721 + z \cdot \left(31.4690115749 + \left(15.234687407 + z\right) \cdot z\right)\right) \cdot z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(\frac{y}{z} \cdot \left(11.1667541262 + \frac{t}{z}\right) + 3.13060547623 \cdot y\right) - 47.69379582500642 \cdot \frac{y}{z}\right)\\ \end{array} \]

Alternative 6
Error	2.2
Cost	1992

\[\begin{array}{l} \mathbf{if}\;z \leq -5.3 \cdot 10^{+17}:\\ \;\;\;\;x + \left(y \cdot \left(\frac{t}{z \cdot z} + 3.13060547623\right) - \frac{y}{z} \cdot \left(47.69379582500642 - 11.1667541262\right)\right)\\ \mathbf{elif}\;z \leq 330000:\\ \;\;\;\;x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{11.9400905721 \cdot z + 0.607771387771}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(\frac{y}{z} \cdot \left(11.1667541262 + \frac{t}{z}\right) + 3.13060547623 \cdot y\right) - 47.69379582500642 \cdot \frac{y}{z}\right)\\ \end{array} \]

Alternative 7
Error	34.3
Cost	1644

\[\begin{array}{l} t_1 := 1.6453555072203998 \cdot \left(y \cdot b\right)\\ \mathbf{if}\;z \leq -3.9 \cdot 10^{+211}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{+152}:\\ \;\;\;\;y \cdot 3.13060547623\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-100}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -3.15 \cdot 10^{-204}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-273}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-249}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 7.1 \cdot 10^{-187}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.62 \cdot 10^{-137}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 8.4 \cdot 10^{+76}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 10^{+97}:\\ \;\;\;\;y \cdot 3.13060547623\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+236}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot 3.13060547623\\ \end{array} \]

Alternative 8
Error	34.3
Cost	1644

\[\begin{array}{l} t_1 := 1.6453555072203998 \cdot \left(y \cdot b\right)\\ \mathbf{if}\;z \leq -1.3 \cdot 10^{+205}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.46 \cdot 10^{+152}:\\ \;\;\;\;y \cdot 3.13060547623\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-101}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-203}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-273}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-249}:\\ \;\;\;\;\left(1.6453555072203998 \cdot b\right) \cdot y\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-190}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{-138}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+78}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+96}:\\ \;\;\;\;y \cdot 3.13060547623\\ \mathbf{elif}\;z \leq 10^{+236}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot 3.13060547623\\ \end{array} \]

Alternative 9
Error	34.2
Cost	1644

\[\begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+208}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{+152}:\\ \;\;\;\;y \cdot 3.13060547623\\ \mathbf{elif}\;z \leq -1.08 \cdot 10^{-100}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{-207}:\\ \;\;\;\;\left(1.6453555072203998 \cdot y\right) \cdot b\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-275}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-252}:\\ \;\;\;\;\left(1.6453555072203998 \cdot b\right) \cdot y\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-186}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.12 \cdot 10^{-134}:\\ \;\;\;\;1.6453555072203998 \cdot \left(y \cdot b\right)\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{+78}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+94}:\\ \;\;\;\;y \cdot 3.13060547623\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+236}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot 3.13060547623\\ \end{array} \]

Alternative 10
Error	5.8
Cost	1608

\[\begin{array}{l} \mathbf{if}\;z \leq -0.005:\\ \;\;\;\;x + \left(y \cdot \left(\frac{t}{z \cdot z} + 3.13060547623\right) - \frac{y}{z} \cdot \left(47.69379582500642 - 11.1667541262\right)\right)\\ \mathbf{elif}\;z \leq 0.058:\\ \;\;\;\;x + \left(\left(1.6453555072203998 \cdot \left(a \cdot y\right) - 32.324150453290734 \cdot \left(y \cdot b\right)\right) \cdot z + 1.6453555072203998 \cdot \left(y \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{y}{z} \cdot \left(\frac{t}{z} + -47.69379582500642\right) + y \cdot \left(\frac{11.1667541262}{z} + 3.13060547623\right)\right)\\ \end{array} \]

Alternative 11
Error	5.8
Cost	1608

\[\begin{array}{l} \mathbf{if}\;z \leq -0.005:\\ \;\;\;\;x + \left(y \cdot \left(\frac{t}{z \cdot z} + 3.13060547623\right) - \frac{y}{z} \cdot \left(47.69379582500642 - 11.1667541262\right)\right)\\ \mathbf{elif}\;z \leq 0.06:\\ \;\;\;\;x + \left(\left(1.6453555072203998 \cdot \left(a \cdot y\right) - 32.324150453290734 \cdot \left(y \cdot b\right)\right) \cdot z + 1.6453555072203998 \cdot \left(y \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(\frac{y}{z} \cdot \left(11.1667541262 + \frac{t}{z}\right) + 3.13060547623 \cdot y\right) - 47.69379582500642 \cdot \frac{y}{z}\right)\\ \end{array} \]

Alternative 12
Error	7.6
Cost	1480

\[\begin{array}{l} t_1 := x + \left(\frac{y}{z} \cdot \left(\frac{t}{z} + -47.69379582500642\right) + y \cdot \left(\frac{11.1667541262}{z} + 3.13060547623\right)\right)\\ \mathbf{if}\;z \leq -0.0045:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 0.051:\\ \;\;\;\;x + \left(1.6453555072203998 \cdot b + -32.324150453290734 \cdot \left(b \cdot z\right)\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 13
Error	7.6
Cost	1480

\[\begin{array}{l} \mathbf{if}\;z \leq -0.005:\\ \;\;\;\;x + \left(y \cdot \left(\frac{t}{z \cdot z} + 3.13060547623\right) - \frac{y}{z} \cdot \left(47.69379582500642 - 11.1667541262\right)\right)\\ \mathbf{elif}\;z \leq 0.08:\\ \;\;\;\;x + \left(1.6453555072203998 \cdot b + -32.324150453290734 \cdot \left(b \cdot z\right)\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{y}{z} \cdot \left(\frac{t}{z} + -47.69379582500642\right) + y \cdot \left(\frac{11.1667541262}{z} + 3.13060547623\right)\right)\\ \end{array} \]

Alternative 14
Error	20.3
Cost	1244

\[\begin{array}{l} t_1 := x + 3.13060547623 \cdot y\\ \mathbf{if}\;z \leq -5.2 \cdot 10^{-98}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.05 \cdot 10^{-203}:\\ \;\;\;\;\left(1.6453555072203998 \cdot y\right) \cdot b\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-273}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.66 \cdot 10^{-251}:\\ \;\;\;\;\left(1.6453555072203998 \cdot b\right) \cdot y\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-186}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-133}:\\ \;\;\;\;1.6453555072203998 \cdot \left(y \cdot b\right)\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-78}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 15
Error	9.4
Cost	1096

\[\begin{array}{l} \mathbf{if}\;z \leq -0.005:\\ \;\;\;\;x + 3.13060547623 \cdot y\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-5}:\\ \;\;\;\;x + b \cdot \left(\left(-32.324150453290734 \cdot y\right) \cdot z + 1.6453555072203998 \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(3.13060547623 - \frac{36.52704169880642}{z}\right)\\ \end{array} \]

Alternative 16
Error	9.3
Cost	1096

\[\begin{array}{l} \mathbf{if}\;z \leq -0.005:\\ \;\;\;\;x + 3.13060547623 \cdot y\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-5}:\\ \;\;\;\;x + \left(1.6453555072203998 \cdot b + -32.324150453290734 \cdot \left(b \cdot z\right)\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(3.13060547623 - \frac{36.52704169880642}{z}\right)\\ \end{array} \]

Alternative 17
Error	9.3
Cost	968

\[\begin{array}{l} \mathbf{if}\;z \leq -0.005:\\ \;\;\;\;x + 3.13060547623 \cdot y\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-5}:\\ \;\;\;\;x + \left(y \cdot b\right) \cdot \left(z \cdot -32.324150453290734 + 1.6453555072203998\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(3.13060547623 - \frac{36.52704169880642}{z}\right)\\ \end{array} \]

Alternative 18
Error	9.4
Cost	840

\[\begin{array}{l} \mathbf{if}\;z \leq -0.005:\\ \;\;\;\;x + 3.13060547623 \cdot y\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-5}:\\ \;\;\;\;x + \left(1.6453555072203998 \cdot y\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(3.13060547623 - \frac{36.52704169880642}{z}\right)\\ \end{array} \]

Alternative 19
Error	9.4
Cost	712

\[\begin{array}{l} t_1 := x + 3.13060547623 \cdot y\\ \mathbf{if}\;z \leq -0.005:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-16}:\\ \;\;\;\;x + 1.6453555072203998 \cdot \left(y \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 20
Error	9.4
Cost	712

\[\begin{array}{l} t_1 := x + 3.13060547623 \cdot y\\ \mathbf{if}\;z \leq -0.005:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-16}:\\ \;\;\;\;x + \left(1.6453555072203998 \cdot b\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 21
Error	9.4
Cost	712

\[\begin{array}{l} t_1 := x + 3.13060547623 \cdot y\\ \mathbf{if}\;z \leq -0.005:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-16}:\\ \;\;\;\;x + \left(1.6453555072203998 \cdot y\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 22
Error	28.4
Cost	456

\[\begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{-117}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{-193}:\\ \;\;\;\;y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 23
Error	32.3
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023010 
(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))))