Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2

Average Accuracy: 54.5% → 85.7%

Time: 52.7s

Precision: binary64

Cost: 50376

Math

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

↓

\[\begin{array}{l} t_1 := \frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ t_2 := \mathsf{fma}\left(\mathsf{fma}\left(y + a, y, b\right), y, c\right)\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;x \cdot \frac{{y}^{4}}{\mathsf{fma}\left(y, t_2, i\right)}\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+288}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\mathsf{fma}\left(t_2, y, i\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - x \cdot \frac{a}{y}\right)\\ \end{array} \]

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
         (/
          (+
           t
           (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ z (* y x))))))))
          (+ i (* y (+ c (* y (+ b (* y (+ y a)))))))))
        (t_2 (fma (fma (+ y a) y b) y c)))
   (if (<= t_1 (- INFINITY))
     (* x (/ (pow y 4.0) (fma y t_2 i)))
     (if (<= t_1 2e+288)
       (/
        (fma (fma (fma (fma x y z) y 27464.7644705) y 230661.510616) y t)
        (fma t_2 y i))
       (+ x (- (/ z y) (* x (/ a y))))))))

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 = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / (i + (y * (c + (y * (b + (y * (y + a)))))));
	double t_2 = fma(fma((y + a), y, b), y, c);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = x * (pow(y, 4.0) / fma(y, t_2, i));
	} else if (t_1 <= 2e+288) {
		tmp = fma(fma(fma(fma(x, y, z), y, 27464.7644705), y, 230661.510616), y, t) / fma(t_2, y, i);
	} else {
		tmp = x + ((z / y) - (x * (a / y)));
	}
	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(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(z + Float64(y * x)))))))) / Float64(i + Float64(y * Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a))))))))
	t_2 = fma(fma(Float64(y + a), y, b), y, c)
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(x * Float64((y ^ 4.0) / fma(y, t_2, i)));
	elseif (t_1 <= 2e+288)
		tmp = Float64(fma(fma(fma(fma(x, y, z), y, 27464.7644705), y, 230661.510616), y, t) / fma(t_2, y, i));
	else
		tmp = Float64(x + Float64(Float64(z / y) - Float64(x * Float64(a / y))));
	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[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(y + a), $MachinePrecision] * y + b), $MachinePrecision] * y + c), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(x * N[(N[Power[y, 4.0], $MachinePrecision] / N[(y * t$95$2 + i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+288], N[(N[(N[(N[(N[(x * y + z), $MachinePrecision] * y + 27464.7644705), $MachinePrecision] * y + 230661.510616), $MachinePrecision] * y + t), $MachinePrecision] / N[(t$95$2 * y + i), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z / y), $MachinePrecision] - N[(x * N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 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 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 x around inf 0.8%

      \[\leadsto \color{blue}{\frac{{y}^{4} \cdot x}{y \cdot \left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) + i}} \]

   3. Simplified 65.6%

      \[\leadsto \color{blue}{\frac{{y}^{4}}{\mathsf{fma}\left(y, \mathsf{fma}\left(\mathsf{fma}\left(y + a, y, b\right), y, c\right), i\right)} \cdot x} \]
      Proof

      [Start] 0.8	\[ \frac{{y}^{4} \cdot x}{y \cdot \left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) + i} \]
      associate-/l* [=>] 65.7	\[ \color{blue}{\frac{{y}^{4}}{\frac{y \cdot \left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) + i}{x}}} \]
      *-commutative [=>] 65.7	\[ \frac{{y}^{4}}{\frac{\color{blue}{\left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) \cdot y} + i}{x}} \]
      +-commutative [=>] 65.7	\[ \frac{{y}^{4}}{\frac{\color{blue}{\left(y \cdot \left(\left(y + a\right) \cdot y + b\right) + c\right)} \cdot y + i}{x}} \]
      *-commutative [=>] 65.7	\[ \frac{{y}^{4}}{\frac{\left(\color{blue}{\left(\left(y + a\right) \cdot y + b\right) \cdot y} + c\right) \cdot y + i}{x}} \]
      fma-udef [<=] 65.7	\[ \frac{{y}^{4}}{\frac{\color{blue}{\mathsf{fma}\left(\left(y + a\right) \cdot y + b, y, c\right)} \cdot y + i}{x}} \]
      fma-def [=>] 65.7	\[ \frac{{y}^{4}}{\frac{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(y + a, y, b\right)}, y, c\right) \cdot y + i}{x}} \]
      fma-udef [<=] 65.7	\[ \frac{{y}^{4}}{\frac{\color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y + a, y, b\right), y, c\right), y, i\right)}}{x}} \]
      associate-/r/ [=>] 65.6	\[ \color{blue}{\frac{{y}^{4}}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y + a, y, b\right), y, c\right), y, i\right)} \cdot x} \]

   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)) < 2e288

   1. Initial program 94.0%

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

   2. Simplified 94.0%

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

      [Start] 94.0	\[ \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
      fma-def [=>] 94.0	\[ \frac{\color{blue}{\mathsf{fma}\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616, y, t\right)}}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
      fma-def [=>] 94.0	\[ \frac{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705, y, 230661.510616\right)}, y, t\right)}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
      fma-def [=>] 94.0	\[ \frac{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x \cdot y + z, y, 27464.7644705\right)}, y, 230661.510616\right), y, t\right)}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
      fma-def [=>] 94.0	\[ \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x, y, z\right)}, y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
      fma-def [=>] 94.0	\[ \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\color{blue}{\mathsf{fma}\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c, y, i\right)}} \]
      fma-def [=>] 94.0	\[ \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(y + a\right) \cdot y + b, y, c\right)}, y, i\right)} \]
      fma-def [=>] 94.0	\[ \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(y + a, y, b\right)}, y, c\right), y, i\right)} \]

   if 2e288 < (/.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 0.6%

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

   2. Simplified 0.6%

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

      [Start] 0.6	\[ \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
      fma-def [=>] 0.6	\[ \frac{\color{blue}{\mathsf{fma}\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616, y, t\right)}}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
      fma-def [=>] 0.6	\[ \frac{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705, y, 230661.510616\right)}, y, t\right)}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
      fma-def [=>] 0.6	\[ \frac{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x \cdot y + z, y, 27464.7644705\right)}, y, 230661.510616\right), y, t\right)}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
      fma-def [=>] 0.6	\[ \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x, y, z\right)}, y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
      fma-def [=>] 0.6	\[ \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\color{blue}{\mathsf{fma}\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c, y, i\right)}} \]
      fma-def [=>] 0.6	\[ \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(y + a\right) \cdot y + b, y, c\right)}, y, i\right)} \]
      fma-def [=>] 0.6	\[ \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(y + a, y, b\right)}, y, c\right), y, i\right)} \]

   3. Taylor expanded in y around inf 69.4%

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

   4. Simplified 74.6%

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

      [Start] 69.4	\[ \left(\frac{z}{y} + x\right) - \frac{a \cdot x}{y} \]
      +-commutative [=>] 69.4	\[ \color{blue}{\left(x + \frac{z}{y}\right)} - \frac{a \cdot x}{y} \]
      associate--l+ [=>] 69.4	\[ \color{blue}{x + \left(\frac{z}{y} - \frac{a \cdot x}{y}\right)} \]
      associate-/l* [=>] 74.6	\[ x + \left(\frac{z}{y} - \color{blue}{\frac{a}{\frac{y}{x}}}\right) \]
      associate-/r/ [=>] 74.6	\[ x + \left(\frac{z}{y} - \color{blue}{\frac{a}{y} \cdot x}\right) \]

3. Recombined 3 regimes into one program.

4. Final simplification 85.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)} \leq -\infty:\\ \;\;\;\;x \cdot \frac{{y}^{4}}{\mathsf{fma}\left(y, \mathsf{fma}\left(\mathsf{fma}\left(y + a, y, b\right), y, c\right), i\right)}\\ \mathbf{elif}\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)} \leq 2 \cdot 10^{+288}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y + a, y, b\right), y, c\right), y, i\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - x \cdot \frac{a}{y}\right)\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	85.0%
Cost	73801

\[\begin{array}{l} t_1 := \mathsf{fma}\left(y, \mathsf{fma}\left(\mathsf{fma}\left(y + a, y, b\right), y, c\right), i\right)\\ \mathbf{if}\;y \leq -5.5 \cdot 10^{+67} \lor \neg \left(y \leq 5.5 \cdot 10^{+48}\right):\\ \;\;\;\;\frac{z}{y} + \left(\left(\frac{27464.7644705}{y \cdot y} + x\right) - \frac{x}{y} \cdot \frac{b}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{\left(230661.510616 + y \cdot 27464.7644705\right) + x \cdot {y}^{3}}{t_1} + \left(\frac{z \cdot {y}^{3}}{t_1} + \frac{t}{t_1}\right)\\ \end{array} \]

Alternative 2
Accuracy	85.7%
Cost	28676

\[\begin{array}{l} t_1 := \frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;x \cdot \frac{{y}^{4}}{\mathsf{fma}\left(y, \mathsf{fma}\left(\mathsf{fma}\left(y + a, y, b\right), y, c\right), i\right)}\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+288}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - x \cdot \frac{a}{y}\right)\\ \end{array} \]

Alternative 3
Accuracy	85.0%
Cost	2377

\[\begin{array}{l} \mathbf{if}\;y \leq -1.95 \cdot 10^{+54} \lor \neg \left(y \leq 2.35 \cdot 10^{+48}\right):\\ \;\;\;\;\frac{z}{y} + \left(\left(\frac{27464.7644705}{y \cdot y} + x\right) - \frac{x}{y} \cdot \frac{b}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \end{array} \]

Alternative 4
Accuracy	76.4%
Cost	2128

\[\begin{array}{l} t_1 := \frac{27464.7644705}{y \cdot y}\\ t_2 := \frac{z}{y} + \left(\left(t_1 + x\right) - \frac{x}{y} \cdot \frac{b}{y}\right)\\ \mathbf{if}\;y \leq -5.5 \cdot 10^{+38}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 72000000000:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+84}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+159}:\\ \;\;\;\;x + \left(\left(\frac{z}{y} + t_1\right) + \frac{a}{y} \cdot \left(\frac{x \cdot a - z}{y} - x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 5
Accuracy	76.8%
Cost	2128

\[\begin{array}{l} t_1 := \frac{27464.7644705}{y \cdot y}\\ t_2 := \frac{z}{y} + \left(\left(t_1 + x\right) - \frac{x}{y} \cdot \frac{b}{y}\right)\\ \mathbf{if}\;y \leq -2 \cdot 10^{+39}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 340000000000:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+86}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+159}:\\ \;\;\;\;x + \left(\left(\frac{z}{y} + t_1\right) + \frac{a}{y} \cdot \left(\frac{x \cdot a - z}{y} - x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 6
Accuracy	80.1%
Cost	2128

\[\begin{array}{l} t_1 := \frac{27464.7644705}{y \cdot y}\\ t_2 := \frac{z}{y} + \left(\left(t_1 + x\right) - \frac{x}{y} \cdot \frac{b}{y}\right)\\ \mathbf{if}\;y \leq -1.95 \cdot 10^{+39}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 45000000000:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + z \cdot \left(y \cdot y\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{+84}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;y \leq 2.55 \cdot 10^{+160}:\\ \;\;\;\;x + \left(\left(\frac{z}{y} + t_1\right) + \frac{a}{y} \cdot \left(\frac{x \cdot a - z}{y} - x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 7
Accuracy	80.5%
Cost	2128

\[\begin{array}{l} t_1 := \frac{27464.7644705}{y \cdot y}\\ t_2 := \frac{z}{y} + \left(\left(t_1 + x\right) - \frac{x}{y} \cdot \frac{b}{y}\right)\\ \mathbf{if}\;y \leq -2.35 \cdot 10^{+39}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 14000000000:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+86}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+159}:\\ \;\;\;\;x + \left(\left(\frac{z}{y} + t_1\right) + \frac{a}{y} \cdot \left(\frac{x \cdot a - z}{y} - x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 8
Accuracy	71.8%
Cost	1612

\[\begin{array}{l} t_1 := \frac{z}{y} + \left(\left(\frac{27464.7644705}{y \cdot y} + x\right) - \frac{x}{y} \cdot \frac{b}{y}\right)\\ \mathbf{if}\;y \leq -24000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-116}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{i + y \cdot c}\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+35}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 9
Accuracy	77.0%
Cost	1609

\[\begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+39} \lor \neg \left(y \leq 9.5 \cdot 10^{+35}\right):\\ \;\;\;\;\frac{z}{y} + \left(\left(\frac{27464.7644705}{y \cdot y} + x\right) - \frac{x}{y} \cdot \frac{b}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \end{array} \]

Alternative 10
Accuracy	70.9%
Cost	1484

\[\begin{array}{l} t_1 := x + \left(\frac{z}{y} - x \cdot \frac{a}{y}\right)\\ \mathbf{if}\;y \leq -0.0015:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-116}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot c}\\ \mathbf{elif}\;y \leq 340000000000:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+67}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 11
Accuracy	62.8%
Cost	1104

\[\begin{array}{l} t_1 := x - \frac{x \cdot a - z}{y}\\ \mathbf{if}\;y \leq -7.1 \cdot 10^{+227}:\\ \;\;\;\;x \cdot \left(1 - \frac{a}{y}\right)\\ \mathbf{elif}\;y \leq -0.0015:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 75000000000:\\ \;\;\;\;\frac{t}{i + y \cdot c}\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+66}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 12
Accuracy	65.3%
Cost	1100

\[\begin{array}{l} t_1 := x + \left(\frac{z}{y} - x \cdot \frac{a}{y}\right)\\ \mathbf{if}\;y \leq -0.0015:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 125000000000:\\ \;\;\;\;\frac{t}{i + y \cdot c}\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+65}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 13
Accuracy	70.9%
Cost	1100

\[\begin{array}{l} t_1 := x + \left(\frac{z}{y} - x \cdot \frac{a}{y}\right)\\ \mathbf{if}\;y \leq -0.0015:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-24}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot c}\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+65}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 14
Accuracy	50.6%
Cost	716

\[\begin{array}{l} \mathbf{if}\;y \leq -125000:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 52000000000:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+84}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 15
Accuracy	50.6%
Cost	716

\[\begin{array}{l} \mathbf{if}\;y \leq -1400:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 85000000000:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{+85}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 16
Accuracy	58.2%
Cost	716

\[\begin{array}{l} \mathbf{if}\;y \leq -52:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 48000000000:\\ \;\;\;\;\frac{t}{i + y \cdot c}\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+84}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 17
Accuracy	58.1%
Cost	716

\[\begin{array}{l} \mathbf{if}\;y \leq -0.0015:\\ \;\;\;\;x \cdot \left(1 - \frac{a}{y}\right)\\ \mathbf{elif}\;y \leq 245000000000:\\ \;\;\;\;\frac{t}{i + y \cdot c}\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+86}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 18
Accuracy	50.4%
Cost	456

\[\begin{array}{l} \mathbf{if}\;y \leq -52:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3800000000000:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 19
Accuracy	26.8%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023133 
(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)))