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

Average Accuracy: 54.0% → 98.5%

Time: 29.7s

Precision: binary64

Cost: 46536

Math

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

↓

\[\begin{array}{l} t_1 := \frac{457.9610022158428}{z \cdot z}\\ t_2 := \frac{t}{z \cdot z}\\ \mathbf{if}\;z \leq -1.08 \cdot 10^{+40}:\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547623 + \left(\left(t_1 + t_2\right) + \frac{-36.52704169880642}{z}\right), x\right)\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+17}:\\ \;\;\;\;x + \frac{y}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687407, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), z, t\right), z, a\right), z, b\right)}}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547623 + \left(t_1 + \left(\left(t_2 + \frac{a - \left(5864.8025282699045 - t \cdot -15.234687407\right)}{{z}^{3}}\right) + \frac{-36.52704169880642}{z}\right)\right), x\right)\\ \end{array} \]

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
 (let* ((t_1 (/ 457.9610022158428 (* z z))) (t_2 (/ t (* z z))))
   (if (<= z -1.08e+40)
     (fma y (+ 3.13060547623 (+ (+ t_1 t_2) (/ -36.52704169880642 z))) x)
     (if (<= z 1.8e+17)
       (+
        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))))
       (fma
        y
        (+
         3.13060547623
         (+
          t_1
          (+
           (+
            t_2
            (/ (- a (- 5864.8025282699045 (* t -15.234687407))) (pow z 3.0)))
           (/ -36.52704169880642 z))))
        x)))))

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 t_1 = 457.9610022158428 / (z * z);
	double t_2 = t / (z * z);
	double tmp;
	if (z <= -1.08e+40) {
		tmp = fma(y, (3.13060547623 + ((t_1 + t_2) + (-36.52704169880642 / z))), x);
	} else if (z <= 1.8e+17) {
		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)));
	} else {
		tmp = fma(y, (3.13060547623 + (t_1 + ((t_2 + ((a - (5864.8025282699045 - (t * -15.234687407))) / pow(z, 3.0))) + (-36.52704169880642 / z)))), x);
	}
	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)
	t_1 = Float64(457.9610022158428 / Float64(z * z))
	t_2 = Float64(t / Float64(z * z))
	tmp = 0.0
	if (z <= -1.08e+40)
		tmp = fma(y, Float64(3.13060547623 + Float64(Float64(t_1 + t_2) + Float64(-36.52704169880642 / z))), x);
	elseif (z <= 1.8e+17)
		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))));
	else
		tmp = fma(y, Float64(3.13060547623 + Float64(t_1 + Float64(Float64(t_2 + Float64(Float64(a - Float64(5864.8025282699045 - Float64(t * -15.234687407))) / (z ^ 3.0))) + Float64(-36.52704169880642 / z)))), x);
	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_] := Block[{t$95$1 = N[(457.9610022158428 / N[(z * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t / N[(z * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.08e+40], N[(y * N[(3.13060547623 + N[(N[(t$95$1 + t$95$2), $MachinePrecision] + N[(-36.52704169880642 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[z, 1.8e+17], 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], N[(y * N[(3.13060547623 + N[(t$95$1 + N[(N[(t$95$2 + 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]]]]]

Target

Original	54.0%
Target	98.3%
Herbie	98.5%

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

Derivation

1. Split input into 3 regimes

2. if z < -1.08000000000000001e40

   1. Initial program 6.6%

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

   2. Simplified 10.3%

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

      [Start] 6.6	\[ x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
      +-commutative [=>] 6.6	\[ \color{blue}{\frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} + x} \]
      associate-*r/ [<=] 10.3	\[ \color{blue}{y \cdot \frac{\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771}} + x \]
      fma-def [=>] 10.3	\[ \color{blue}{\mathsf{fma}\left(y, \frac{\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771}, x\right)} \]

   3. Taylor expanded in z around inf 97.4%

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

   4. Simplified 97.4%

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

      [Start] 97.4	\[ \mathsf{fma}\left(y, \left(3.13060547623 + \left(457.9610022158428 \cdot \frac{1}{{z}^{2}} + \frac{t}{{z}^{2}}\right)\right) - 36.52704169880642 \cdot \frac{1}{z}, x\right) \]
      associate--l+ [=>] 97.4	\[ \mathsf{fma}\left(y, \color{blue}{3.13060547623 + \left(\left(457.9610022158428 \cdot \frac{1}{{z}^{2}} + \frac{t}{{z}^{2}}\right) - 36.52704169880642 \cdot \frac{1}{z}\right)}, x\right) \]
      associate-*r/ [=>] 97.4	\[ \mathsf{fma}\left(y, 3.13060547623 + \left(\left(\color{blue}{\frac{457.9610022158428 \cdot 1}{{z}^{2}}} + \frac{t}{{z}^{2}}\right) - 36.52704169880642 \cdot \frac{1}{z}\right), x\right) \]
      metadata-eval [=>] 97.4	\[ \mathsf{fma}\left(y, 3.13060547623 + \left(\left(\frac{\color{blue}{457.9610022158428}}{{z}^{2}} + \frac{t}{{z}^{2}}\right) - 36.52704169880642 \cdot \frac{1}{z}\right), x\right) \]
      unpow2 [=>] 97.4	\[ \mathsf{fma}\left(y, 3.13060547623 + \left(\left(\frac{457.9610022158428}{\color{blue}{z \cdot z}} + \frac{t}{{z}^{2}}\right) - 36.52704169880642 \cdot \frac{1}{z}\right), x\right) \]
      unpow2 [=>] 97.4	\[ \mathsf{fma}\left(y, 3.13060547623 + \left(\left(\frac{457.9610022158428}{z \cdot z} + \frac{t}{\color{blue}{z \cdot z}}\right) - 36.52704169880642 \cdot \frac{1}{z}\right), x\right) \]
      associate-*r/ [=>] 97.4	\[ \mathsf{fma}\left(y, 3.13060547623 + \left(\left(\frac{457.9610022158428}{z \cdot z} + \frac{t}{z \cdot z}\right) - \color{blue}{\frac{36.52704169880642 \cdot 1}{z}}\right), x\right) \]
      metadata-eval [=>] 97.4	\[ \mathsf{fma}\left(y, 3.13060547623 + \left(\left(\frac{457.9610022158428}{z \cdot z} + \frac{t}{z \cdot z}\right) - \frac{\color{blue}{36.52704169880642}}{z}\right), x\right) \]

   if -1.08000000000000001e40 < z < 1.8e17

   1. Initial program 98.1%

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

   2. Simplified 99.0%

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

      [Start] 98.1	\[ x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
      associate-/l* [=>] 99.0	\[ x + \color{blue}{\frac{y}{\frac{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771}{\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}} \]
      fma-def [=>] 99.0	\[ x + \frac{y}{\frac{\color{blue}{\mathsf{fma}\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721, z, 0.607771387771\right)}}{\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}} \]
      fma-def [=>] 99.0	\[ x + \frac{y}{\frac{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749, z, 11.9400905721\right)}, z, 0.607771387771\right)}{\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}} \]
      fma-def [=>] 99.0	\[ x + \frac{y}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(z + 15.234687407, z, 31.4690115749\right)}, z, 11.9400905721\right), z, 0.607771387771\right)}{\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}} \]
      fma-def [=>] 99.0	\[ x + \frac{y}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687407, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}{\color{blue}{\mathsf{fma}\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a, z, b\right)}}} \]
      fma-def [=>] 99.0	\[ x + \frac{y}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687407, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t, z, a\right)}, z, b\right)}} \]
      fma-def [=>] 99.0	\[ x + \frac{y}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687407, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(z \cdot 3.13060547623 + 11.1667541262, z, t\right)}, z, a\right), z, b\right)}} \]
      fma-def [=>] 99.0	\[ x + \frac{y}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687407, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right)}, z, t\right), z, a\right), z, b\right)}} \]

   if 1.8e17 < z

   1. Initial program 11.4%

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

   2. Simplified 16.9%

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

      [Start] 11.4	\[ x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
      +-commutative [=>] 11.4	\[ \color{blue}{\frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} + x} \]
      associate-*r/ [<=] 16.9	\[ \color{blue}{y \cdot \frac{\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771}} + x \]
      fma-def [=>] 16.9	\[ \color{blue}{\mathsf{fma}\left(y, \frac{\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771}, x\right)} \]

   3. Taylor expanded in z around -inf 98.4%

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

   4. Simplified 98.4%

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

      [Start] 98.4	\[ \mathsf{fma}\left(y, \left(3.13060547623 + \left(457.9610022158428 \cdot \frac{1}{{z}^{2}} + \left(\frac{t}{{z}^{2}} + -1 \cdot \frac{-1 \cdot a - \left(1112.0901850848957 + -15.234687407 \cdot \left(457.9610022158428 + t\right)\right)}{{z}^{3}}\right)\right)\right) - 36.52704169880642 \cdot \frac{1}{z}, x\right) \]
      associate--l+ [=>] 98.4	\[ \mathsf{fma}\left(y, \color{blue}{3.13060547623 + \left(\left(457.9610022158428 \cdot \frac{1}{{z}^{2}} + \left(\frac{t}{{z}^{2}} + -1 \cdot \frac{-1 \cdot a - \left(1112.0901850848957 + -15.234687407 \cdot \left(457.9610022158428 + t\right)\right)}{{z}^{3}}\right)\right) - 36.52704169880642 \cdot \frac{1}{z}\right)}, x\right) \]
      associate--l+ [=>] 98.4	\[ \mathsf{fma}\left(y, 3.13060547623 + \color{blue}{\left(457.9610022158428 \cdot \frac{1}{{z}^{2}} + \left(\left(\frac{t}{{z}^{2}} + -1 \cdot \frac{-1 \cdot a - \left(1112.0901850848957 + -15.234687407 \cdot \left(457.9610022158428 + t\right)\right)}{{z}^{3}}\right) - 36.52704169880642 \cdot \frac{1}{z}\right)\right)}, x\right) \]
      associate-*r/ [=>] 98.4	\[ \mathsf{fma}\left(y, 3.13060547623 + \left(\color{blue}{\frac{457.9610022158428 \cdot 1}{{z}^{2}}} + \left(\left(\frac{t}{{z}^{2}} + -1 \cdot \frac{-1 \cdot a - \left(1112.0901850848957 + -15.234687407 \cdot \left(457.9610022158428 + t\right)\right)}{{z}^{3}}\right) - 36.52704169880642 \cdot \frac{1}{z}\right)\right), x\right) \]
      metadata-eval [=>] 98.4	\[ \mathsf{fma}\left(y, 3.13060547623 + \left(\frac{\color{blue}{457.9610022158428}}{{z}^{2}} + \left(\left(\frac{t}{{z}^{2}} + -1 \cdot \frac{-1 \cdot a - \left(1112.0901850848957 + -15.234687407 \cdot \left(457.9610022158428 + t\right)\right)}{{z}^{3}}\right) - 36.52704169880642 \cdot \frac{1}{z}\right)\right), x\right) \]
      unpow2 [=>] 98.4	\[ \mathsf{fma}\left(y, 3.13060547623 + \left(\frac{457.9610022158428}{\color{blue}{z \cdot z}} + \left(\left(\frac{t}{{z}^{2}} + -1 \cdot \frac{-1 \cdot a - \left(1112.0901850848957 + -15.234687407 \cdot \left(457.9610022158428 + t\right)\right)}{{z}^{3}}\right) - 36.52704169880642 \cdot \frac{1}{z}\right)\right), x\right) \]

3. Recombined 3 regimes into one program.

4. Final simplification 98.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.08 \cdot 10^{+40}:\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547623 + \left(\left(\frac{457.9610022158428}{z \cdot z} + \frac{t}{z \cdot z}\right) + \frac{-36.52704169880642}{z}\right), x\right)\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+17}:\\ \;\;\;\;x + \frac{y}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687407, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), z, t\right), z, a\right), z, b\right)}}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547623 + \left(\frac{457.9610022158428}{z \cdot z} + \left(\left(\frac{t}{z \cdot z} + \frac{a - \left(5864.8025282699045 - t \cdot -15.234687407\right)}{{z}^{3}}\right) + \frac{-36.52704169880642}{z}\right)\right), x\right)\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	98.1%
Cost	14984

\[\begin{array}{l} t_1 := \frac{457.9610022158428}{z \cdot z}\\ t_2 := \frac{t}{z \cdot z}\\ \mathbf{if}\;z \leq -7.5 \cdot 10^{+38}:\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547623 + \left(\left(t_1 + t_2\right) + \frac{-36.52704169880642}{z}\right), x\right)\\ \mathbf{elif}\;z \leq 10800000000000:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 - z \cdot -3.13060547623\right)\right)\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547623 + \left(t_1 + \left(\left(t_2 + \frac{a - \left(5864.8025282699045 - t \cdot -15.234687407\right)}{{z}^{3}}\right) + \frac{-36.52704169880642}{z}\right)\right), x\right)\\ \end{array} \]

Alternative 2
Accuracy	95.7%
Cost	11208

\[\begin{array}{l} t_1 := \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 - z \cdot -3.13060547623\right)\right)\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+284}:\\ \;\;\;\;x + t_1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547623, x\right)\\ \end{array} \]

Alternative 3
Accuracy	97.6%
Cost	7881

\[\begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+38} \lor \neg \left(z \leq 2.1 \cdot 10^{+22}\right):\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547623 + \left(\left(\frac{457.9610022158428}{z \cdot z} + \frac{t}{z \cdot z}\right) + \frac{-36.52704169880642}{z}\right), x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 - z \cdot -3.13060547623\right)\right)\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)}\\ \end{array} \]

Alternative 4
Accuracy	95.7%
Cost	6985

\[\begin{array}{l} t_1 := \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 - z \cdot -3.13060547623\right)\right)\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)}\\ \mathbf{if}\;t_1 \leq -\infty \lor \neg \left(t_1 \leq 5 \cdot 10^{+284}\right):\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x + t_1\\ \end{array} \]

Alternative 5
Accuracy	93.9%
Cost	1737

\[\begin{array}{l} \mathbf{if}\;z \leq -12.6 \lor \neg \left(z \leq 3000000\right):\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot 11.1667541262\right)\right)\right)}{0.607771387771 + z \cdot 11.9400905721}\\ \end{array} \]

Alternative 6
Accuracy	91.3%
Cost	1225

\[\begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{-7} \lor \neg \left(z \leq 8100\right):\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot a\right)}{0.607771387771 + z \cdot 11.9400905721}\\ \end{array} \]

Alternative 7
Accuracy	85.7%
Cost	969

\[\begin{array}{l} \mathbf{if}\;z \leq -0.016 \lor \neg \left(z \leq 10\right):\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot b\right) \cdot \left(1.6453555072203998 + z \cdot -32.324150453290734\right)\\ \end{array} \]

Alternative 8
Accuracy	85.7%
Cost	840

\[\begin{array}{l} \mathbf{if}\;z \leq -0.065:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{elif}\;z \leq 0.33:\\ \;\;\;\;x + y \cdot \left(b \cdot 1.6453555072203998\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{0.31942702700572795 + \frac{3.7269864963038164}{z}}\\ \end{array} \]

Alternative 9
Accuracy	85.6%
Cost	713

\[\begin{array}{l} \mathbf{if}\;z \leq -1750 \lor \neg \left(z \leq 0.106\right):\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot \left(y \cdot 1.6453555072203998\right)\\ \end{array} \]

Alternative 10
Accuracy	85.6%
Cost	713

\[\begin{array}{l} \mathbf{if}\;z \leq -0.06 \lor \neg \left(z \leq 0.42\right):\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(b \cdot 1.6453555072203998\right)\\ \end{array} \]

Alternative 11
Accuracy	71.2%
Cost	585

\[\begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{-76} \lor \neg \left(z \leq 5.2 \cdot 10^{-133}\right):\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 12
Accuracy	57.4%
Cost	456

\[\begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+79}:\\ \;\;\;\;y \cdot 3.13060547623\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{+78}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot 3.13060547623\\ \end{array} \]

Alternative 13
Accuracy	50.4%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023137 
(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))))