Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2

Average Error: 46.36% → 15.56%

Time: 46.0s

Precision: binary64

Cost: 8900

Math

\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

↓

\[\begin{array}{l} t_1 := i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)\\ t_2 := \frac{t}{t_1}\\ \mathbf{if}\;y \leq -1.72 \cdot 10^{+71}:\\ \;\;\;\;\frac{z}{y} + \left(\mathsf{fma}\left(1 + \left(\left(\frac{a}{y} \cdot \frac{a}{y} - \frac{b}{y \cdot y}\right) - \frac{a}{y}\right), x, \frac{27464.7644705}{y \cdot y}\right) - a \cdot \frac{z}{y \cdot y}\right)\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{+56}:\\ \;\;\;\;t_2 + \frac{y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{t_1}\\ \mathbf{else}:\\ \;\;\;\;t_2 + \left(x + \left(\frac{z}{y} - \frac{x}{\frac{y}{a}}\right)\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (/
  (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t)
  (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)))

↓

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ i (* y (+ c (* y (+ b (* y (+ y a)))))))) (t_2 (/ t t_1)))
   (if (<= y -1.72e+71)
     (+
      (/ z y)
      (-
       (fma
        (+ 1.0 (- (- (* (/ a y) (/ a y)) (/ b (* y y))) (/ a y)))
        x
        (/ 27464.7644705 (* y y)))
       (* a (/ z (* y y)))))
     (if (<= y 2.65e+56)
       (+
        t_2
        (/
         (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ z (* y x)))))))
         t_1))
       (+ t_2 (+ x (- (/ z y) (/ x (/ y a)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return ((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i);
}

↓

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = i + (y * (c + (y * (b + (y * (y + a))))));
	double t_2 = t / t_1;
	double tmp;
	if (y <= -1.72e+71) {
		tmp = (z / y) + (fma((1.0 + ((((a / y) * (a / y)) - (b / (y * y))) - (a / y))), x, (27464.7644705 / (y * y))) - (a * (z / (y * y))));
	} else if (y <= 2.65e+56) {
		tmp = t_2 + ((y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x))))))) / t_1);
	} else {
		tmp = t_2 + (x + ((z / y) - (x / (y / a))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	return Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / Float64(Float64(Float64(Float64(Float64(Float64(Float64(y + a) * y) + b) * y) + c) * y) + i))
end

↓

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(i + Float64(y * Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a)))))))
	t_2 = Float64(t / t_1)
	tmp = 0.0
	if (y <= -1.72e+71)
		tmp = Float64(Float64(z / y) + Float64(fma(Float64(1.0 + Float64(Float64(Float64(Float64(a / y) * Float64(a / y)) - Float64(b / Float64(y * y))) - Float64(a / y))), x, Float64(27464.7644705 / Float64(y * y))) - Float64(a * Float64(z / Float64(y * y)))));
	elseif (y <= 2.65e+56)
		tmp = Float64(t_2 + Float64(Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(z + Float64(y * x))))))) / t_1));
	else
		tmp = Float64(t_2 + Float64(x + Float64(Float64(z / y) - Float64(x / Float64(y / a)))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(N[(N[(N[(N[(N[(N[(N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision] * y), $MachinePrecision] + 27464.7644705), $MachinePrecision] * y), $MachinePrecision] + 230661.510616), $MachinePrecision] * y), $MachinePrecision] + t), $MachinePrecision] / N[(N[(N[(N[(N[(N[(N[(y + a), $MachinePrecision] * y), $MachinePrecision] + b), $MachinePrecision] * y), $MachinePrecision] + c), $MachinePrecision] * y), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(i + N[(y * N[(c + N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t / t$95$1), $MachinePrecision]}, If[LessEqual[y, -1.72e+71], N[(N[(z / y), $MachinePrecision] + N[(N[(N[(1.0 + N[(N[(N[(N[(a / y), $MachinePrecision] * N[(a / y), $MachinePrecision]), $MachinePrecision] - N[(b / N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * x + N[(27464.7644705 / N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * N[(z / N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.65e+56], N[(t$95$2 + N[(N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], N[(t$95$2 + N[(x + N[(N[(z / y), $MachinePrecision] - N[(x / N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.72e71

   1. Initial program 98.81

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   2. Taylor expanded in y around inf 41.45

      \[\leadsto \color{blue}{\left(\frac{z}{y} + \left(27464.7644705 \cdot \frac{1}{{y}^{2}} + x\right)\right) - \left(\frac{\left(z - a \cdot x\right) \cdot a}{{y}^{2}} + \left(\frac{a \cdot x}{y} + \frac{b \cdot x}{{y}^{2}}\right)\right)} \]

   3. Simplified 27.31

      \[\leadsto \color{blue}{\frac{z}{y} + \left(\left(\left(x + \frac{27464.7644705}{y \cdot y}\right) - \frac{a}{y \cdot y} \cdot \left(z - a \cdot x\right)\right) - \left(\frac{a}{y} \cdot x + \frac{x}{\frac{y \cdot y}{b}}\right)\right)} \]
      Proof

      [Start] 41.45	\[ \left(\frac{z}{y} + \left(27464.7644705 \cdot \frac{1}{{y}^{2}} + x\right)\right) - \left(\frac{\left(z - a \cdot x\right) \cdot a}{{y}^{2}} + \left(\frac{a \cdot x}{y} + \frac{b \cdot x}{{y}^{2}}\right)\right) \]
      associate--l+ [=>] 41.45	\[ \color{blue}{\frac{z}{y} + \left(\left(27464.7644705 \cdot \frac{1}{{y}^{2}} + x\right) - \left(\frac{\left(z - a \cdot x\right) \cdot a}{{y}^{2}} + \left(\frac{a \cdot x}{y} + \frac{b \cdot x}{{y}^{2}}\right)\right)\right)} \]
      associate--r+ [=>] 41.45	\[ \frac{z}{y} + \color{blue}{\left(\left(\left(27464.7644705 \cdot \frac{1}{{y}^{2}} + x\right) - \frac{\left(z - a \cdot x\right) \cdot a}{{y}^{2}}\right) - \left(\frac{a \cdot x}{y} + \frac{b \cdot x}{{y}^{2}}\right)\right)} \]
      +-commutative [=>] 41.45	\[ \frac{z}{y} + \left(\left(\color{blue}{\left(x + 27464.7644705 \cdot \frac{1}{{y}^{2}}\right)} - \frac{\left(z - a \cdot x\right) \cdot a}{{y}^{2}}\right) - \left(\frac{a \cdot x}{y} + \frac{b \cdot x}{{y}^{2}}\right)\right) \]
      associate-*r/ [=>] 41.45	\[ \frac{z}{y} + \left(\left(\left(x + \color{blue}{\frac{27464.7644705 \cdot 1}{{y}^{2}}}\right) - \frac{\left(z - a \cdot x\right) \cdot a}{{y}^{2}}\right) - \left(\frac{a \cdot x}{y} + \frac{b \cdot x}{{y}^{2}}\right)\right) \]
      metadata-eval [=>] 41.45	\[ \frac{z}{y} + \left(\left(\left(x + \frac{\color{blue}{27464.7644705}}{{y}^{2}}\right) - \frac{\left(z - a \cdot x\right) \cdot a}{{y}^{2}}\right) - \left(\frac{a \cdot x}{y} + \frac{b \cdot x}{{y}^{2}}\right)\right) \]
      unpow2 [=>] 41.45	\[ \frac{z}{y} + \left(\left(\left(x + \frac{27464.7644705}{\color{blue}{y \cdot y}}\right) - \frac{\left(z - a \cdot x\right) \cdot a}{{y}^{2}}\right) - \left(\frac{a \cdot x}{y} + \frac{b \cdot x}{{y}^{2}}\right)\right) \]
      *-commutative [=>] 41.45	\[ \frac{z}{y} + \left(\left(\left(x + \frac{27464.7644705}{y \cdot y}\right) - \frac{\color{blue}{a \cdot \left(z - a \cdot x\right)}}{{y}^{2}}\right) - \left(\frac{a \cdot x}{y} + \frac{b \cdot x}{{y}^{2}}\right)\right) \]
      associate-/l* [=>] 34.36	\[ \frac{z}{y} + \left(\left(\left(x + \frac{27464.7644705}{y \cdot y}\right) - \color{blue}{\frac{a}{\frac{{y}^{2}}{z - a \cdot x}}}\right) - \left(\frac{a \cdot x}{y} + \frac{b \cdot x}{{y}^{2}}\right)\right) \]
      associate-/r/ [=>] 34.36	\[ \frac{z}{y} + \left(\left(\left(x + \frac{27464.7644705}{y \cdot y}\right) - \color{blue}{\frac{a}{{y}^{2}} \cdot \left(z - a \cdot x\right)}\right) - \left(\frac{a \cdot x}{y} + \frac{b \cdot x}{{y}^{2}}\right)\right) \]
      unpow2 [=>] 34.36	\[ \frac{z}{y} + \left(\left(\left(x + \frac{27464.7644705}{y \cdot y}\right) - \frac{a}{\color{blue}{y \cdot y}} \cdot \left(z - a \cdot x\right)\right) - \left(\frac{a \cdot x}{y} + \frac{b \cdot x}{{y}^{2}}\right)\right) \]

   4. Taylor expanded in x around 0 32.44

      \[\leadsto \frac{z}{y} + \color{blue}{\left(\left(27464.7644705 \cdot \frac{1}{{y}^{2}} + \left(1 - \left(\frac{b}{{y}^{2}} + \left(\frac{a}{y} + -1 \cdot \frac{{a}^{2}}{{y}^{2}}\right)\right)\right) \cdot x\right) - \frac{a \cdot z}{{y}^{2}}\right)} \]

   5. Simplified 22.68

      \[\leadsto \frac{z}{y} + \color{blue}{\left(\mathsf{fma}\left(1 + \left(\left(\frac{a}{y} \cdot \frac{a}{y} - \frac{b}{y \cdot y}\right) - \frac{a}{y}\right), x, \frac{27464.7644705}{y \cdot y}\right) - a \cdot \frac{z}{y \cdot y}\right)} \]
      Proof

      [Start] 32.44	\[ \frac{z}{y} + \left(\left(27464.7644705 \cdot \frac{1}{{y}^{2}} + \left(1 - \left(\frac{b}{{y}^{2}} + \left(\frac{a}{y} + -1 \cdot \frac{{a}^{2}}{{y}^{2}}\right)\right)\right) \cdot x\right) - \frac{a \cdot z}{{y}^{2}}\right) \]
      +-commutative [=>] 32.44	\[ \frac{z}{y} + \left(\color{blue}{\left(\left(1 - \left(\frac{b}{{y}^{2}} + \left(\frac{a}{y} + -1 \cdot \frac{{a}^{2}}{{y}^{2}}\right)\right)\right) \cdot x + 27464.7644705 \cdot \frac{1}{{y}^{2}}\right)} - \frac{a \cdot z}{{y}^{2}}\right) \]
      associate--l+ [=>] 32.44	\[ \frac{z}{y} + \color{blue}{\left(\left(1 - \left(\frac{b}{{y}^{2}} + \left(\frac{a}{y} + -1 \cdot \frac{{a}^{2}}{{y}^{2}}\right)\right)\right) \cdot x + \left(27464.7644705 \cdot \frac{1}{{y}^{2}} - \frac{a \cdot z}{{y}^{2}}\right)\right)} \]

   if -1.72e71 < y < 2.6500000000000001e56

   1. Initial program 9.34

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   2. Taylor expanded in t around inf 9.35

      \[\leadsto \color{blue}{\frac{t}{y \cdot \left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) + i} + \frac{\left(230661.510616 + y \cdot \left(27464.7644705 + \left(y \cdot x + z\right) \cdot y\right)\right) \cdot y}{y \cdot \left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) + i}} \]

   if 2.6500000000000001e56 < y

   1. Initial program 97.9

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   2. Taylor expanded in t around inf 97.9

      \[\leadsto \color{blue}{\frac{t}{y \cdot \left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) + i} + \frac{\left(230661.510616 + y \cdot \left(27464.7644705 + \left(y \cdot x + z\right) \cdot y\right)\right) \cdot y}{y \cdot \left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) + i}} \]

   3. Taylor expanded in y around inf 30.56

      \[\leadsto \frac{t}{y \cdot \left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) + i} + \color{blue}{\left(\left(\frac{z}{y} + x\right) - \frac{a \cdot x}{y}\right)} \]

   4. Simplified 25.84

      \[\leadsto \frac{t}{y \cdot \left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) + i} + \color{blue}{\left(x + \left(\frac{z}{y} - \frac{x}{\frac{y}{a}}\right)\right)} \]
      Proof

      [Start] 30.56	\[ \frac{t}{y \cdot \left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) + i} + \left(\left(\frac{z}{y} + x\right) - \frac{a \cdot x}{y}\right) \]
      +-commutative [=>] 30.56	\[ \frac{t}{y \cdot \left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) + i} + \left(\color{blue}{\left(x + \frac{z}{y}\right)} - \frac{a \cdot x}{y}\right) \]
      associate--l+ [=>] 30.56	\[ \frac{t}{y \cdot \left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) + i} + \color{blue}{\left(x + \left(\frac{z}{y} - \frac{a \cdot x}{y}\right)\right)} \]
      *-commutative [=>] 30.56	\[ \frac{t}{y \cdot \left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) + i} + \left(x + \left(\frac{z}{y} - \frac{\color{blue}{x \cdot a}}{y}\right)\right) \]
      associate-/l* [=>] 25.84	\[ \frac{t}{y \cdot \left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) + i} + \left(x + \left(\frac{z}{y} - \color{blue}{\frac{x}{\frac{y}{a}}}\right)\right) \]

3. Recombined 3 regimes into one program.

4. Final simplification 15.56

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.72 \cdot 10^{+71}:\\ \;\;\;\;\frac{z}{y} + \left(\mathsf{fma}\left(1 + \left(\left(\frac{a}{y} \cdot \frac{a}{y} - \frac{b}{y \cdot y}\right) - \frac{a}{y}\right), x, \frac{27464.7644705}{y \cdot y}\right) - a \cdot \frac{z}{y \cdot y}\right)\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{+56}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)} + \frac{y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)} + \left(x + \left(\frac{z}{y} - \frac{x}{\frac{y}{a}}\right)\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	15.75%
Cost	3400

\[\begin{array}{l} t_1 := i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)\\ t_2 := \frac{t}{t_1}\\ \mathbf{if}\;y \leq -2.15 \cdot 10^{+38}:\\ \;\;\;\;\frac{z}{y} + x\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{+56}:\\ \;\;\;\;t_2 + \frac{y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{t_1}\\ \mathbf{else}:\\ \;\;\;\;t_2 + \left(x + \left(\frac{z}{y} - \frac{x}{\frac{y}{a}}\right)\right)\\ \end{array} \]

Alternative 2
Error	15.72%
Cost	2376

\[\begin{array}{l} t_1 := i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)\\ \mathbf{if}\;y \leq -1.42 \cdot 10^{+38}:\\ \;\;\;\;\frac{z}{y} + x\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+58}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{t_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{t_1} + \left(x + \left(\frac{z}{y} - \frac{x}{\frac{y}{a}}\right)\right)\\ \end{array} \]

Alternative 3
Error	20.05%
Cost	2120

\[\begin{array}{l} t_1 := i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)\\ \mathbf{if}\;y \leq -1.65 \cdot 10^{+38}:\\ \;\;\;\;\frac{z}{y} + x\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+56}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + z \cdot \left(y \cdot y\right)\right)}{t_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{t_1} + \left(x + \left(\frac{z}{y} - \frac{x}{\frac{y}{a}}\right)\right)\\ \end{array} \]

Alternative 4
Error	20.08%
Cost	1993

\[\begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+37} \lor \neg \left(y \leq 3.45 \cdot 10^{+56}\right):\\ \;\;\;\;\frac{z}{y} + x\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + z \cdot \left(y \cdot y\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \end{array} \]

Alternative 5
Error	24.89%
Cost	1609

\[\begin{array}{l} \mathbf{if}\;y \leq -0.0013 \lor \neg \left(y \leq 8.8 \cdot 10^{+35}\right):\\ \;\;\;\;\frac{z}{y} + x\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \end{array} \]

Alternative 6
Error	23.07%
Cost	1609

\[\begin{array}{l} \mathbf{if}\;y \leq -3500000000000 \lor \neg \left(y \leq 4.2 \cdot 10^{+37}\right):\\ \;\;\;\;\frac{z}{y} + x\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + z \cdot \left(y \cdot y\right)\right)}{i + y \cdot \left(c + y \cdot b\right)}\\ \end{array} \]

Alternative 7
Error	26.1%
Cost	1481

\[\begin{array}{l} \mathbf{if}\;y \leq -3000000 \lor \neg \left(y \leq 2.9 \cdot 10^{+32}\right):\\ \;\;\;\;\frac{z}{y} + x\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{i + y \cdot \left(c + y \cdot b\right)}\\ \end{array} \]

Alternative 8
Error	26.35%
Cost	1225

\[\begin{array}{l} \mathbf{if}\;y \leq -980000 \lor \neg \left(y \leq 2.1 \cdot 10^{+31}\right):\\ \;\;\;\;\frac{z}{y} + x\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot b\right)}\\ \end{array} \]

Alternative 9
Error	33.36%
Cost	969

\[\begin{array}{l} \mathbf{if}\;y \leq -1750000 \lor \neg \left(y \leq 2.95 \cdot 10^{+34}\right):\\ \;\;\;\;\frac{z}{y} + x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot b\right)}\\ \end{array} \]

Alternative 10
Error	35.51%
Cost	713

\[\begin{array}{l} \mathbf{if}\;y \leq -1750000 \lor \neg \left(y \leq 1.16 \cdot 10^{+30}\right):\\ \;\;\;\;\frac{z}{y} + x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i + y \cdot c}\\ \end{array} \]

Alternative 11
Error	42.92%
Cost	585

\[\begin{array}{l} \mathbf{if}\;y \leq -2800000 \lor \neg \left(y \leq 5.8 \cdot 10^{+29}\right):\\ \;\;\;\;\frac{z}{y} + x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i}\\ \end{array} \]

Alternative 12
Error	50.02%
Cost	456

\[\begin{array}{l} \mathbf{if}\;y \leq -1020000:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{+24}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 13
Error	72.38%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023088 
(FPCore (x y z t a b c i)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2"
  :precision binary64
  (/ (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)))