Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2

Percentage Accurate: 56.3% → 84.9%

Time: 37.4s

Precision: binary64

Cost: 48196

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616\right) + t}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)} \leq \infty:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y + a, y, b\right), y, c\right), y, i\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{y} - \left(\frac{a}{\frac{y}{x}} - x\right)\\ \end{array} \]

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
 (if (<=
      (/
       (+
        (* y (+ (* y (+ (* y (+ (* x y) z)) 27464.7644705)) 230661.510616))
        t)
       (+ i (* y (+ c (* y (+ (* y (+ y a)) b))))))
      INFINITY)
   (/
    (fma (fma (fma (fma x y z) y 27464.7644705) y 230661.510616) y t)
    (fma (fma (fma (+ y a) y b) y c) y i))
   (- (/ z y) (- (/ a (/ y x)) x))))

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 tmp;
	if ((((y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616)) + t) / (i + (y * (c + (y * ((y * (y + a)) + b)))))) <= ((double) INFINITY)) {
		tmp = fma(fma(fma(fma(x, y, z), y, 27464.7644705), y, 230661.510616), y, t) / fma(fma(fma((y + a), y, b), y, c), y, i);
	} else {
		tmp = (z / y) - ((a / (y / x)) - x);
	}
	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)
	tmp = 0.0
	if (Float64(Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(Float64(x * y) + z)) + 27464.7644705)) + 230661.510616)) + t) / Float64(i + Float64(y * Float64(c + Float64(y * Float64(Float64(y * Float64(y + a)) + b)))))) <= Inf)
		tmp = Float64(fma(fma(fma(fma(x, y, z), y, 27464.7644705), y, 230661.510616), y, t) / fma(fma(fma(Float64(y + a), y, b), y, c), y, i));
	else
		tmp = Float64(Float64(z / y) - Float64(Float64(a / Float64(y / x)) - x));
	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_] := If[LessEqual[N[(N[(N[(y * N[(N[(y * N[(N[(y * N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] + 27464.7644705), $MachinePrecision]), $MachinePrecision] + 230661.510616), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[(N[(N[(N[(x * y + z), $MachinePrecision] * y + 27464.7644705), $MachinePrecision] * y + 230661.510616), $MachinePrecision] * y + t), $MachinePrecision] / N[(N[(N[(N[(y + a), $MachinePrecision] * y + b), $MachinePrecision] * y + c), $MachinePrecision] * y + i), $MachinePrecision]), $MachinePrecision], N[(N[(z / y), $MachinePrecision] - N[(N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) 54929528941/2000000) y) 28832688827/125000) y) t) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c) y) i)) < +inf.0

   1. Initial program 90.3%

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

   2. Simplified 90.3%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y + a, y, b\right), y, c\right), y, i\right)}} \]
      Step-by-step derivation

      [Start] 90.3%	\[ \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
      fma-def [=>] 90.3%	\[ \frac{\color{blue}{\mathsf{fma}\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616, y, t\right)}}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
      fma-def [=>] 90.3%	\[ \frac{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705, y, 230661.510616\right)}, y, t\right)}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
      fma-def [=>] 90.3%	\[ \frac{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x \cdot y + z, y, 27464.7644705\right)}, y, 230661.510616\right), y, t\right)}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
      fma-def [=>] 90.3%	\[ \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x, y, z\right)}, y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
      fma-def [=>] 90.3%	\[ \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\color{blue}{\mathsf{fma}\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c, y, i\right)}} \]
      fma-def [=>] 90.3%	\[ \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(y + a\right) \cdot y + b, y, c\right)}, y, i\right)} \]
      fma-def [=>] 90.3%	\[ \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(y + a, y, b\right)}, y, c\right), y, i\right)} \]

   if +inf.0 < (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) 54929528941/2000000) y) 28832688827/125000) y) t) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c) y) i))

   1. Initial program 0.0%

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

   2. Taylor expanded in y around inf 71.1%

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

   3. Simplified 77.0%

      \[\leadsto \color{blue}{\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)} \]
      Step-by-step derivation

      [Start] 71.1%	\[ \left(\frac{z}{y} + x\right) - \frac{a \cdot x}{y} \]
      associate--l+ [=>] 71.1%	\[ \color{blue}{\frac{z}{y} + \left(x - \frac{a \cdot x}{y}\right)} \]
      associate-/l* [=>] 77.0%	\[ \frac{z}{y} + \left(x - \color{blue}{\frac{a}{\frac{y}{x}}}\right) \]

3. Recombined 2 regimes into one program.

4. Final simplification 85.3%

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

Alternatives

Alternative 1
Accuracy	84.9%
Cost	48196

\[\begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616\right) + t}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)} \leq \infty:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y + a, y, b\right), y, c\right), y, i\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{y} - \left(\frac{a}{\frac{y}{x}} - x\right)\\ \end{array} \]

Alternative 2
Accuracy	84.9%
Cost	4292

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

Alternative 3
Accuracy	78.1%
Cost	2380

\[\begin{array}{l} t_1 := i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)\\ \mathbf{if}\;y \leq -1.5 \cdot 10^{+21}:\\ \;\;\;\;\frac{z}{y} - \left(\frac{a}{\frac{y}{x}} - x\right)\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{-16}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + z \cdot \left(y \cdot y\right)\right)}{t_1}\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+36}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + x \cdot \left(y \cdot y\right)\right)\right)}{t_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{1}{x} - \frac{\frac{z}{x \cdot x} - \frac{a}{x}}{y}}\\ \end{array} \]

Alternative 4
Accuracy	79.7%
Cost	2252

\[\begin{array}{l} t_1 := \frac{z}{y} - \left(\frac{a}{\frac{y}{x}} - x\right)\\ \mathbf{if}\;y \leq -1.6 \cdot 10^{+21}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-17}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + z \cdot \left(y \cdot y\right)\right)}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)}\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+46}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + x \cdot \left(y \cdot y\right)\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot y\right)\right)}\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{+117}:\\ \;\;\;\;\frac{z}{a} + \frac{x \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 5
Accuracy	77.1%
Cost	2252

\[\begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+21}:\\ \;\;\;\;\frac{z}{y} - \left(\frac{a}{\frac{y}{x}} - x\right)\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-105}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + z \cdot \left(y \cdot y\right)\right)}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+37}:\\ \;\;\;\;\frac{y \cdot \left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616\right) + t}{i + y \cdot \left(c + a \cdot \left(y \cdot y\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{1}{x} - \frac{\frac{z}{x \cdot x} - \frac{a}{x}}{y}}\\ \end{array} \]

Alternative 6
Accuracy	77.4%
Cost	1992

\[\begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+21}:\\ \;\;\;\;\frac{z}{y} - \left(\frac{a}{\frac{y}{x}} - x\right)\\ \mathbf{elif}\;y \leq 450000000:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + z \cdot \left(y \cdot y\right)\right)}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{1}{x} - \frac{\frac{z}{x \cdot x} - \frac{a}{x}}{y}}\\ \end{array} \]

Alternative 7
Accuracy	74.1%
Cost	1864

\[\begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+21}:\\ \;\;\;\;\frac{z}{y} - \left(\frac{a}{\frac{y}{x}} - x\right)\\ \mathbf{elif}\;y \leq 440000000:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{1}{x} - \frac{\frac{z}{x \cdot x} - \frac{a}{x}}{y}}\\ \end{array} \]

Alternative 8
Accuracy	73.6%
Cost	1608

\[\begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+21}:\\ \;\;\;\;\frac{z}{y} - \left(\frac{a}{\frac{y}{x}} - x\right)\\ \mathbf{elif}\;y \leq 450000000:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{1}{x} - \frac{\frac{z}{x \cdot x} - \frac{a}{x}}{y}}\\ \end{array} \]

Alternative 9
Accuracy	58.8%
Cost	1496

\[\begin{array}{l} t_1 := \frac{z}{y} - \left(\frac{a}{\frac{y}{x}} - x\right)\\ \mathbf{if}\;y \leq -9.5 \cdot 10^{+120}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -9.6 \cdot 10^{-22}:\\ \;\;\;\;\frac{z}{a} + \frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-42}:\\ \;\;\;\;x + \frac{t}{b \cdot \left(y \cdot y\right)}\\ \mathbf{elif}\;y \leq -3.3 \cdot 10^{-100}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{-27}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+147}:\\ \;\;\;\;\frac{z}{a} + \frac{x \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 10
Accuracy	60.9%
Cost	1484

\[\begin{array}{l} t_1 := \frac{z}{y} - \left(\frac{a}{\frac{y}{x}} - x\right)\\ \mathbf{if}\;y \leq -1.65 \cdot 10^{+20}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-27}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i}\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+147}:\\ \;\;\;\;\frac{z}{a} + \left(\frac{x \cdot y}{a} + 27464.7644705 \cdot \frac{1}{y \cdot a}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 11
Accuracy	67.9%
Cost	1484

\[\begin{array}{l} t_1 := \frac{z}{y} - \left(\frac{a}{\frac{y}{x}} - x\right)\\ \mathbf{if}\;y \leq -2.3 \cdot 10^{+20}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-27}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)}\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+147}:\\ \;\;\;\;\frac{z}{a} + \left(\frac{x \cdot y}{a} + 27464.7644705 \cdot \frac{1}{y \cdot a}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 12
Accuracy	66.3%
Cost	1480

\[\begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+21}:\\ \;\;\;\;\frac{z}{y} - \left(\frac{a}{\frac{y}{x}} - x\right)\\ \mathbf{elif}\;y \leq 450000000:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{a}{x \cdot y} + \left(\frac{1}{x} - \frac{z}{y \cdot \left(x \cdot x\right)}\right)}\\ \end{array} \]

Alternative 13
Accuracy	71.7%
Cost	1480

\[\begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+21}:\\ \;\;\;\;\frac{z}{y} - \left(\frac{a}{\frac{y}{x}} - x\right)\\ \mathbf{elif}\;y \leq 400000000:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{a}{x \cdot y} + \left(\frac{1}{x} - \frac{z}{y \cdot \left(x \cdot x\right)}\right)}\\ \end{array} \]

Alternative 14
Accuracy	72.3%
Cost	1480

\[\begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+19}:\\ \;\;\;\;\frac{z}{y} - \left(\frac{a}{\frac{y}{x}} - x\right)\\ \mathbf{elif}\;y \leq 450000000:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{1}{x} - \frac{\frac{z}{x \cdot x} - \frac{a}{x}}{y}}\\ \end{array} \]

Alternative 15
Accuracy	60.8%
Cost	1224

\[\begin{array}{l} t_1 := \frac{z}{y} - \left(\frac{a}{\frac{y}{x}} - x\right)\\ \mathbf{if}\;y \leq -3 \cdot 10^{+20}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-27}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i}\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+147}:\\ \;\;\;\;\frac{z}{a} + \frac{x \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 16
Accuracy	54.9%
Cost	1104

\[\begin{array}{l} t_1 := \frac{z}{a} + \frac{y}{\frac{a}{x}}\\ \mathbf{if}\;y \leq -1.1 \cdot 10^{+136}:\\ \;\;\;\;x - \frac{a}{\frac{y}{x}}\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-28}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{+120}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 17
Accuracy	54.3%
Cost	1104

\[\begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+136}:\\ \;\;\;\;x - \frac{a}{\frac{y}{x}}\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{-18}:\\ \;\;\;\;\frac{z}{a} + \frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{-27}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+147}:\\ \;\;\;\;\frac{z}{a} + \frac{x \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 18
Accuracy	60.8%
Cost	1100

\[\begin{array}{l} t_1 := \frac{z}{y} - \left(\frac{a}{\frac{y}{x}} - x\right)\\ \mathbf{if}\;y \leq -6.4 \cdot 10^{+19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 7.4 \cdot 10^{-27}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + z \cdot \left(y \cdot y\right)\right)}{i}\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+147}:\\ \;\;\;\;\frac{z}{a} + \frac{x \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 19
Accuracy	53.8%
Cost	844

\[\begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+93}:\\ \;\;\;\;x - \frac{a}{\frac{y}{x}}\\ \mathbf{elif}\;y \leq -9.6 \cdot 10^{-17}:\\ \;\;\;\;\frac{z}{a}\\ \mathbf{elif}\;y \leq 7500000000000:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 20
Accuracy	50.6%
Cost	588

\[\begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{+94}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{-20}:\\ \;\;\;\;\frac{z}{a}\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+19}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 21
Accuracy	50.4%
Cost	588

\[\begin{array}{l} \mathbf{if}\;y \leq -9.4 \cdot 10^{+104}:\\ \;\;\;\;x - \frac{a}{\frac{y}{x}}\\ \mathbf{elif}\;y \leq -6.8 \cdot 10^{-19}:\\ \;\;\;\;\frac{z}{a}\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{+15}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 22
Accuracy	50.6%
Cost	456

\[\begin{array}{l} \mathbf{if}\;y \leq -8.6 \cdot 10^{-7}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+16}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 23
Accuracy	25.8%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023263 
(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)))