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

Average Error: 29.7 → 0.7

Time: 30.3s

Precision: binary64

Cost: 14985

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+15} \lor \neg \left(z \leq 1.1 \cdot 10^{+17}\right):\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547623 + \left(\frac{457.9610022158428}{z \cdot z} + \left(\left(\frac{t}{z \cdot z} + \frac{a + \left(-5864.8025282699045 + t \cdot -15.234687407\right)}{{z}^{3}}\right) + \frac{-36.52704169880642}{z}\right)\right), x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 - z \cdot -3.13060547623\right)\right)\right) + b\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}\\ \end{array} \]

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 -5.2e+15) (not (<= z 1.1e+17)))
   (fma
    y
    (+
     3.13060547623
     (+
      (/ 457.9610022158428 (* z z))
      (+
       (+
        (/ t (* z z))
        (/ (+ a (+ -5864.8025282699045 (* t -15.234687407))) (pow z 3.0)))
       (/ -36.52704169880642 z))))
    x)
   (+
    x
    (/
     (*
      y
      (+
       (* z (+ a (* z (+ t (* z (- 11.1667541262 (* z -3.13060547623)))))))
       b))
     (+
      (* z (+ (* z (+ (* z (+ z 15.234687407)) 31.4690115749)) 11.9400905721))
      0.607771387771)))))

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 <= -5.2e+15) || !(z <= 1.1e+17)) {
		tmp = fma(y, (3.13060547623 + ((457.9610022158428 / (z * z)) + (((t / (z * z)) + ((a + (-5864.8025282699045 + (t * -15.234687407))) / pow(z, 3.0))) + (-36.52704169880642 / z)))), x);
	} else {
		tmp = x + ((y * ((z * (a + (z * (t + (z * (11.1667541262 - (z * -3.13060547623))))))) + b)) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771));
	}
	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 <= -5.2e+15) || !(z <= 1.1e+17))
		tmp = fma(y, Float64(3.13060547623 + Float64(Float64(457.9610022158428 / Float64(z * z)) + Float64(Float64(Float64(t / Float64(z * z)) + Float64(Float64(a + Float64(-5864.8025282699045 + Float64(t * -15.234687407))) / (z ^ 3.0))) + Float64(-36.52704169880642 / z)))), x);
	else
		tmp = Float64(x + Float64(Float64(y * Float64(Float64(z * Float64(a + Float64(z * Float64(t + Float64(z * Float64(11.1667541262 - Float64(z * -3.13060547623))))))) + b)) / Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)));
	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, -5.2e+15], N[Not[LessEqual[z, 1.1e+17]], $MachinePrecision]], N[(y * N[(3.13060547623 + N[(N[(457.9610022158428 / N[(z * z), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(t / N[(z * z), $MachinePrecision]), $MachinePrecision] + N[(N[(a + N[(-5864.8025282699045 + N[(t * -15.234687407), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[Power[z, 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-36.52704169880642 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(x + N[(N[(y * N[(N[(z * N[(a + N[(z * N[(t + N[(z * N[(11.1667541262 - N[(z * -3.13060547623), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / N[(N[(z * N[(N[(z * N[(N[(z * N[(z + 15.234687407), $MachinePrecision]), $MachinePrecision] + 31.4690115749), $MachinePrecision]), $MachinePrecision] + 11.9400905721), $MachinePrecision]), $MachinePrecision] + 0.607771387771), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Target

Original	29.7
Target	1.0
Herbie	0.7

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

Derivation

1. Split input into 2 regimes

2. if z < -5.2e15 or 1.1e17 < z

   1. Initial program 57.6

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

   2. Simplified 54.8

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

      [Start] 57.6	\[ x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
      +-commutative [=>] 57.6	\[ \color{blue}{\frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} + x} \]
      associate-*r/ [<=] 54.8	\[ \color{blue}{y \cdot \frac{\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771}} + x \]
      fma-def [=>] 54.8	\[ \color{blue}{\mathsf{fma}\left(y, \frac{\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771}, x\right)} \]

   3. Taylor expanded in z around -inf 0.9

      \[\leadsto \mathsf{fma}\left(y, \color{blue}{\left(3.13060547623 + \left(457.9610022158428 \cdot \frac{1}{{z}^{2}} + \left(\frac{t}{{z}^{2}} + -1 \cdot \frac{-1 \cdot a - \left(1112.0901850848957 + -15.234687407 \cdot \left(457.9610022158428 + t\right)\right)}{{z}^{3}}\right)\right)\right) - 36.52704169880642 \cdot \frac{1}{z}}, x\right) \]

   4. Simplified 0.9

      \[\leadsto \mathsf{fma}\left(y, \color{blue}{3.13060547623 + \left(\frac{457.9610022158428}{z \cdot z} + \left(\left(\frac{t}{z \cdot z} - \frac{\left(-a\right) - \left(-5864.8025282699045 + t \cdot -15.234687407\right)}{{z}^{3}}\right) - \frac{36.52704169880642}{z}\right)\right)}, x\right) \]
      Proof

      [Start] 0.9	\[ \mathsf{fma}\left(y, \left(3.13060547623 + \left(457.9610022158428 \cdot \frac{1}{{z}^{2}} + \left(\frac{t}{{z}^{2}} + -1 \cdot \frac{-1 \cdot a - \left(1112.0901850848957 + -15.234687407 \cdot \left(457.9610022158428 + t\right)\right)}{{z}^{3}}\right)\right)\right) - 36.52704169880642 \cdot \frac{1}{z}, x\right) \]
      associate--l+ [=>] 0.9	\[ \mathsf{fma}\left(y, \color{blue}{3.13060547623 + \left(\left(457.9610022158428 \cdot \frac{1}{{z}^{2}} + \left(\frac{t}{{z}^{2}} + -1 \cdot \frac{-1 \cdot a - \left(1112.0901850848957 + -15.234687407 \cdot \left(457.9610022158428 + t\right)\right)}{{z}^{3}}\right)\right) - 36.52704169880642 \cdot \frac{1}{z}\right)}, x\right) \]
      associate--l+ [=>] 0.9	\[ \mathsf{fma}\left(y, 3.13060547623 + \color{blue}{\left(457.9610022158428 \cdot \frac{1}{{z}^{2}} + \left(\left(\frac{t}{{z}^{2}} + -1 \cdot \frac{-1 \cdot a - \left(1112.0901850848957 + -15.234687407 \cdot \left(457.9610022158428 + t\right)\right)}{{z}^{3}}\right) - 36.52704169880642 \cdot \frac{1}{z}\right)\right)}, x\right) \]
      associate-*r/ [=>] 0.9	\[ \mathsf{fma}\left(y, 3.13060547623 + \left(\color{blue}{\frac{457.9610022158428 \cdot 1}{{z}^{2}}} + \left(\left(\frac{t}{{z}^{2}} + -1 \cdot \frac{-1 \cdot a - \left(1112.0901850848957 + -15.234687407 \cdot \left(457.9610022158428 + t\right)\right)}{{z}^{3}}\right) - 36.52704169880642 \cdot \frac{1}{z}\right)\right), x\right) \]
      metadata-eval [=>] 0.9	\[ \mathsf{fma}\left(y, 3.13060547623 + \left(\frac{\color{blue}{457.9610022158428}}{{z}^{2}} + \left(\left(\frac{t}{{z}^{2}} + -1 \cdot \frac{-1 \cdot a - \left(1112.0901850848957 + -15.234687407 \cdot \left(457.9610022158428 + t\right)\right)}{{z}^{3}}\right) - 36.52704169880642 \cdot \frac{1}{z}\right)\right), x\right) \]
      unpow2 [=>] 0.9	\[ \mathsf{fma}\left(y, 3.13060547623 + \left(\frac{457.9610022158428}{\color{blue}{z \cdot z}} + \left(\left(\frac{t}{{z}^{2}} + -1 \cdot \frac{-1 \cdot a - \left(1112.0901850848957 + -15.234687407 \cdot \left(457.9610022158428 + t\right)\right)}{{z}^{3}}\right) - 36.52704169880642 \cdot \frac{1}{z}\right)\right), x\right) \]

   if -5.2e15 < z < 1.1e17

   1. Initial program 0.5

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
3. Recombined 2 regimes into one program.

4. Final simplification 0.7

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+15} \lor \neg \left(z \leq 1.1 \cdot 10^{+17}\right):\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547623 + \left(\frac{457.9610022158428}{z \cdot z} + \left(\left(\frac{t}{z \cdot z} + \frac{a + \left(-5864.8025282699045 + t \cdot -15.234687407\right)}{{z}^{3}}\right) + \frac{-36.52704169880642}{z}\right)\right), x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 - z \cdot -3.13060547623\right)\right)\right) + b\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}\\ \end{array} \]

Alternatives

Alternative 1
Error	1.3
Cost	2632

\[\begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+21}:\\ \;\;\;\;x - y \cdot \left(\left(-3.13060547623 - \frac{-36.52704169880642}{z}\right) - \frac{\frac{t}{z}}{z}\right)\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{+16}:\\ \;\;\;\;x + \frac{y \cdot \left(z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 - z \cdot -3.13060547623\right)\right)\right) + b\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(\left(3.13060547623 + \frac{-36.52704169880642}{z}\right) + \frac{457.9610022158428 + t}{z \cdot z}\right)\\ \end{array} \]

Alternative 2
Error	3.3
Cost	2380

\[\begin{array}{l} t_1 := x + y \cdot \left(\left(3.13060547623 + \frac{-36.52704169880642}{z}\right) + \frac{457.9610022158428 + t}{z \cdot z}\right)\\ t_2 := x + \frac{y \cdot b + a \cdot \left(z \cdot y\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}\\ \mathbf{if}\;z \leq -28000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-119}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-23}:\\ \;\;\;\;1.6453555072203998 \cdot \left(t \cdot \left(z \cdot \left(z \cdot y\right)\right)\right) + \left(\left(x + \left(y \cdot b\right) \cdot 1.6453555072203998\right) - z \cdot \left(\left(y \cdot b\right) \cdot 32.324150453290734 - 1.6453555072203998 \cdot \left(y \cdot a\right)\right)\right)\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{+22}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 3
Error	1.5
Cost	2377

\[\begin{array}{l} \mathbf{if}\;z \leq -430000000 \lor \neg \left(z \leq 6.8 \cdot 10^{+16}\right):\\ \;\;\;\;x + y \cdot \left(\left(3.13060547623 + \frac{-36.52704169880642}{z}\right) + \frac{457.9610022158428 + t}{z \cdot z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot 11.1667541262\right)\right)\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}\\ \end{array} \]

Alternative 4
Error	3.7
Cost	1993

\[\begin{array}{l} \mathbf{if}\;z \leq -120000000 \lor \neg \left(z \leq 6.4 \cdot 10^{+21}\right):\\ \;\;\;\;x + y \cdot \left(\left(3.13060547623 + \frac{-36.52704169880642}{z}\right) + \frac{457.9610022158428 + t}{z \cdot z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot b + a \cdot \left(z \cdot y\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}\\ \end{array} \]

Alternative 5
Error	7.4
Cost	1484

\[\begin{array}{l} t_1 := x + y \cdot \left(\left(3.13060547623 + \frac{-36.52704169880642}{z}\right) + \frac{457.9610022158428 + t}{z \cdot z}\right)\\ \mathbf{if}\;z \leq -14500:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.08 \cdot 10^{-56}:\\ \;\;\;\;x + \frac{y}{\frac{0.607771387771}{b}}\\ \mathbf{elif}\;z \leq 70000:\\ \;\;\;\;x + 1.6453555072203998 \cdot \left(t \cdot \left(y \cdot \left(z \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Error	3.8
Cost	1481

\[\begin{array}{l} \mathbf{if}\;z \leq -14500 \lor \neg \left(z \leq 5.1 \cdot 10^{-17}\right):\\ \;\;\;\;x + y \cdot \left(\left(3.13060547623 + \frac{-36.52704169880642}{z}\right) + \frac{457.9610022158428 + t}{z \cdot z}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + \left(y \cdot b\right) \cdot 1.6453555072203998\right) + y \cdot \left(z \cdot \left(a \cdot 1.6453555072203998 + b \cdot -32.324150453290734\right)\right)\\ \end{array} \]

Alternative 7
Error	7.4
Cost	1356

\[\begin{array}{l} t_1 := x - y \cdot \left(\left(-3.13060547623 - \frac{-36.52704169880642}{z}\right) - \frac{\frac{t}{z}}{z}\right)\\ \mathbf{if}\;z \leq -14500:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-54}:\\ \;\;\;\;x + \frac{y}{\frac{0.607771387771}{b}}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-20}:\\ \;\;\;\;x + 1.6453555072203998 \cdot \left(t \cdot \left(y \cdot \left(z \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 8
Error	9.8
Cost	1100

\[\begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{-73}:\\ \;\;\;\;x + \frac{y}{0.31942702700572795 + \frac{3.7269864963038164}{z}}\\ \mathbf{elif}\;z \leq 1.52 \cdot 10^{-58}:\\ \;\;\;\;x + \frac{y}{\frac{0.607771387771}{b}}\\ \mathbf{elif}\;z \leq 430000000:\\ \;\;\;\;x + 1.6453555072203998 \cdot \left(t \cdot \left(y \cdot \left(z \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \]

Alternative 9
Error	9.9
Cost	1100

\[\begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{-73}:\\ \;\;\;\;x + \frac{y}{0.31942702700572795 + \frac{3.7269864963038164}{z}}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-56}:\\ \;\;\;\;x + \frac{y}{\frac{0.607771387771}{b}}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-23}:\\ \;\;\;\;x + 1.6453555072203998 \cdot \left(t \cdot \left(y \cdot \left(z \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 - \frac{y}{\frac{z}{36.52704169880642}}\right)\\ \end{array} \]

Alternative 10
Error	9.9
Cost	1100

\[\begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{-73}:\\ \;\;\;\;x + \frac{y}{0.31942702700572795 + \frac{3.7269864963038164 + \frac{-3.241970391368047}{z}}{z}}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-56}:\\ \;\;\;\;x + \frac{y}{\frac{0.607771387771}{b}}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-23}:\\ \;\;\;\;x + 1.6453555072203998 \cdot \left(t \cdot \left(y \cdot \left(z \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 - \frac{y}{\frac{z}{36.52704169880642}}\right)\\ \end{array} \]

Alternative 11
Error	8.9
Cost	713

\[\begin{array}{l} \mathbf{if}\;z \leq -14500 \lor \neg \left(z \leq 6.2 \cdot 10^{+16}\right):\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(b \cdot 1.6453555072203998\right)\\ \end{array} \]

Alternative 12
Error	9.7
Cost	712

\[\begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{-73}:\\ \;\;\;\;x + \frac{y}{0.31942702700572795 + \frac{3.7269864963038164}{z}}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+16}:\\ \;\;\;\;x + y \cdot \left(b \cdot 1.6453555072203998\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \]

Alternative 13
Error	18.7
Cost	585

\[\begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{-176} \lor \neg \left(z \leq 1.6 \cdot 10^{-123}\right):\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 14
Error	30.0
Cost	456

\[\begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{+35}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{+42}:\\ \;\;\;\;y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 15
Error	32.4
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023066 
(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))))