Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2

Average Accuracy: 54.9% → 82.9%

Time: 44.7s

Precision: binary64

Cost: 46412

Math

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

↓

\[\begin{array}{l} t_1 := \frac{z}{y} + x\\ \mathbf{if}\;y \leq -4.5 \cdot 10^{+84}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -3.3 \cdot 10^{+27}:\\ \;\;\;\;\frac{z}{a + \left(y + \left(\frac{c}{y \cdot y} + \frac{b}{y}\right)\right)}\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+31}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y + a, y, b\right), y, c\right), y, i\right)}\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{+137}:\\ \;\;\;\;\frac{27464.7644705}{y \cdot a} + \left(\frac{z}{a} + \frac{y}{\frac{a}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

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 (+ (/ z y) x)))
   (if (<= y -4.5e+84)
     t_1
     (if (<= y -3.3e+27)
       (/ z (+ a (+ y (+ (/ c (* y y)) (/ b y)))))
       (if (<= y 6.5e+31)
         (/
          (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))
         (if (<= y 4.4e+137)
           (+ (/ 27464.7644705 (* y a)) (+ (/ z a) (/ y (/ a x))))
           t_1))))))

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 = (z / y) + x;
	double tmp;
	if (y <= -4.5e+84) {
		tmp = t_1;
	} else if (y <= -3.3e+27) {
		tmp = z / (a + (y + ((c / (y * y)) + (b / y))));
	} else if (y <= 6.5e+31) {
		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 if (y <= 4.4e+137) {
		tmp = (27464.7644705 / (y * a)) + ((z / a) + (y / (a / x)));
	} else {
		tmp = t_1;
	}
	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(z / y) + x)
	tmp = 0.0
	if (y <= -4.5e+84)
		tmp = t_1;
	elseif (y <= -3.3e+27)
		tmp = Float64(z / Float64(a + Float64(y + Float64(Float64(c / Float64(y * y)) + Float64(b / y)))));
	elseif (y <= 6.5e+31)
		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));
	elseif (y <= 4.4e+137)
		tmp = Float64(Float64(27464.7644705 / Float64(y * a)) + Float64(Float64(z / a) + Float64(y / Float64(a / x))));
	else
		tmp = t_1;
	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[(z / y), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[y, -4.5e+84], t$95$1, If[LessEqual[y, -3.3e+27], N[(z / N[(a + N[(y + N[(N[(c / N[(y * y), $MachinePrecision]), $MachinePrecision] + N[(b / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.5e+31], 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], If[LessEqual[y, 4.4e+137], N[(N[(27464.7644705 / N[(y * a), $MachinePrecision]), $MachinePrecision] + N[(N[(z / a), $MachinePrecision] + N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.4999999999999997e84 or 4.40000000000000031e137 < y

   1. Initial program 0.4%

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

   2. Taylor expanded in y around inf 74.5%

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

   3. Simplified 80.5%

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

      [Start] 74.5	\[ \left(\frac{z}{y} + x\right) - \frac{a \cdot x}{y} \]
      associate--l+ [=>] 74.5	\[ \color{blue}{\frac{z}{y} + \left(x - \frac{a \cdot x}{y}\right)} \]
      associate-/l* [=>] 80.5	\[ \frac{z}{y} + \left(x - \color{blue}{\frac{a}{\frac{y}{x}}}\right) \]

   4. Taylor expanded in a around 0 80.4%

      \[\leadsto \color{blue}{\frac{z}{y} + x} \]

   if -4.4999999999999997e84 < y < -3.2999999999999998e27

   1. Initial program 27.9%

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

   2. Simplified 27.9%

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

      [Start] 27.9	\[ \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
      fma-def [=>] 27.9	\[ \frac{\color{blue}{\mathsf{fma}\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616, y, t\right)}}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
      fma-def [=>] 27.9	\[ \frac{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705, y, 230661.510616\right)}, y, t\right)}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
      fma-def [=>] 27.9	\[ \frac{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x \cdot y + z, y, 27464.7644705\right)}, y, 230661.510616\right), y, t\right)}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
      fma-def [=>] 27.9	\[ \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x, y, z\right)}, y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
      fma-def [=>] 27.9	\[ \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\color{blue}{\mathsf{fma}\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c, y, i\right)}} \]
      fma-def [=>] 27.9	\[ \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(y + a\right) \cdot y + b, y, c\right)}, y, i\right)} \]
      fma-def [=>] 27.9	\[ \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(y + a, y, b\right)}, y, c\right), y, i\right)} \]

   3. Taylor expanded in z around inf 8.1%

      \[\leadsto \color{blue}{\frac{{y}^{3} \cdot z}{y \cdot \left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) + i}} \]

   4. Simplified 19.1%

      \[\leadsto \color{blue}{\frac{z}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(\mathsf{fma}\left(y + a, y, b\right), y, c\right), i\right)}{{y}^{3}}}} \]
      Proof

      [Start] 8.1	\[ \frac{{y}^{3} \cdot z}{y \cdot \left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) + i} \]
      *-commutative [=>] 8.1	\[ \frac{\color{blue}{z \cdot {y}^{3}}}{y \cdot \left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) + i} \]
      *-commutative [=>] 8.1	\[ \frac{z \cdot {y}^{3}}{\color{blue}{\left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) \cdot y} + i} \]
      +-commutative [=>] 8.1	\[ \frac{z \cdot {y}^{3}}{\color{blue}{\left(y \cdot \left(\left(y + a\right) \cdot y + b\right) + c\right)} \cdot y + i} \]
      *-commutative [=>] 8.1	\[ \frac{z \cdot {y}^{3}}{\left(\color{blue}{\left(\left(y + a\right) \cdot y + b\right) \cdot y} + c\right) \cdot y + i} \]
      fma-udef [<=] 8.1	\[ \frac{z \cdot {y}^{3}}{\color{blue}{\mathsf{fma}\left(\left(y + a\right) \cdot y + b, y, c\right)} \cdot y + i} \]
      fma-def [=>] 8.1	\[ \frac{z \cdot {y}^{3}}{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(y + a, y, b\right)}, y, c\right) \cdot y + i} \]
      fma-udef [<=] 8.1	\[ \frac{z \cdot {y}^{3}}{\color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y + a, y, b\right), y, c\right), y, i\right)}} \]
      associate-/l* [=>] 19.1	\[ \color{blue}{\frac{z}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y + a, y, b\right), y, c\right), y, i\right)}{{y}^{3}}}} \]

   5. Taylor expanded in y around inf 32.6%

      \[\leadsto \frac{z}{\color{blue}{a + \left(y + \left(\frac{b}{y} + \frac{c}{{y}^{2}}\right)\right)}} \]

   6. Simplified 32.6%

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

      [Start] 32.6	\[ \frac{z}{a + \left(y + \left(\frac{b}{y} + \frac{c}{{y}^{2}}\right)\right)} \]
      +-commutative [=>] 32.6	\[ \frac{z}{a + \left(y + \color{blue}{\left(\frac{c}{{y}^{2}} + \frac{b}{y}\right)}\right)} \]
      unpow2 [=>] 32.6	\[ \frac{z}{a + \left(y + \left(\frac{c}{\color{blue}{y \cdot y}} + \frac{b}{y}\right)\right)} \]

   if -3.2999999999999998e27 < y < 6.5000000000000004e31

   1. Initial program 97.8%

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

   2. Simplified 97.8%

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

      [Start] 97.8	\[ \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
      fma-def [=>] 97.8	\[ \frac{\color{blue}{\mathsf{fma}\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616, y, t\right)}}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
      fma-def [=>] 97.8	\[ \frac{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705, y, 230661.510616\right)}, y, t\right)}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
      fma-def [=>] 97.8	\[ \frac{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x \cdot y + z, y, 27464.7644705\right)}, y, 230661.510616\right), y, t\right)}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
      fma-def [=>] 97.8	\[ \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x, y, z\right)}, y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
      fma-def [=>] 97.8	\[ \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\color{blue}{\mathsf{fma}\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c, y, i\right)}} \]
      fma-def [=>] 97.8	\[ \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(y + a\right) \cdot y + b, y, c\right)}, y, i\right)} \]
      fma-def [=>] 97.8	\[ \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(y + a, y, b\right)}, y, c\right), y, i\right)} \]

   if 6.5000000000000004e31 < y < 4.40000000000000031e137

   1. Initial program 14.2%

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

   2. Taylor expanded in a around inf 4.2%

      \[\leadsto \color{blue}{\frac{y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + \left(y \cdot x + z\right) \cdot y\right)\right) + t}{a \cdot {y}^{3}}} \]

   3. Taylor expanded in y around inf 26.3%

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

   4. Simplified 28.1%

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

      [Start] 26.3	\[ \frac{z}{a} + \left(27464.7644705 \cdot \frac{1}{a \cdot y} + \frac{y \cdot x}{a}\right) \]
      +-commutative [=>] 26.3	\[ \color{blue}{\left(27464.7644705 \cdot \frac{1}{a \cdot y} + \frac{y \cdot x}{a}\right) + \frac{z}{a}} \]
      associate-+r+ [<=] 26.3	\[ \color{blue}{27464.7644705 \cdot \frac{1}{a \cdot y} + \left(\frac{y \cdot x}{a} + \frac{z}{a}\right)} \]
      associate-*r/ [=>] 26.3	\[ \color{blue}{\frac{27464.7644705 \cdot 1}{a \cdot y}} + \left(\frac{y \cdot x}{a} + \frac{z}{a}\right) \]
      metadata-eval [=>] 26.3	\[ \frac{\color{blue}{27464.7644705}}{a \cdot y} + \left(\frac{y \cdot x}{a} + \frac{z}{a}\right) \]
      *-commutative [<=] 26.3	\[ \frac{27464.7644705}{\color{blue}{y \cdot a}} + \left(\frac{y \cdot x}{a} + \frac{z}{a}\right) \]
      +-commutative [<=] 26.3	\[ \frac{27464.7644705}{y \cdot a} + \color{blue}{\left(\frac{z}{a} + \frac{y \cdot x}{a}\right)} \]
      associate-/l* [=>] 28.1	\[ \frac{27464.7644705}{y \cdot a} + \left(\frac{z}{a} + \color{blue}{\frac{y}{\frac{a}{x}}}\right) \]

3. Recombined 4 regimes into one program.

4. Final simplification 82.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+84}:\\ \;\;\;\;\frac{z}{y} + x\\ \mathbf{elif}\;y \leq -3.3 \cdot 10^{+27}:\\ \;\;\;\;\frac{z}{a + \left(y + \left(\frac{c}{y \cdot y} + \frac{b}{y}\right)\right)}\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+31}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y + a, y, b\right), y, c\right), y, i\right)}\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{+137}:\\ \;\;\;\;\frac{27464.7644705}{y \cdot a} + \left(\frac{z}{a} + \frac{y}{\frac{a}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{y} + x\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	82.8%
Cost	2508

\[\begin{array}{l} t_1 := \frac{z}{y} + x\\ \mathbf{if}\;y \leq -1.65 \cdot 10^{+84}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -3.4 \cdot 10^{+27}:\\ \;\;\;\;\frac{z}{a + \left(y + \left(\frac{c}{y \cdot y} + \frac{b}{y}\right)\right)}\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+31}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{+140}:\\ \;\;\;\;\frac{27464.7644705}{y \cdot a} + \left(\frac{z}{a} + \frac{y}{\frac{a}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Accuracy	79.3%
Cost	2252

\[\begin{array}{l} t_1 := \frac{z}{y} + x\\ \mathbf{if}\;y \leq -5.4 \cdot 10^{+85}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -3.45 \cdot 10^{+16}:\\ \;\;\;\;\frac{z}{a + \left(y + \left(\frac{c}{y \cdot y} + \frac{b}{y}\right)\right)}\\ \mathbf{elif}\;y \leq 1.06 \cdot 10^{+30}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{+137}:\\ \;\;\;\;\frac{27464.7644705}{y \cdot a} + \left(\frac{z}{a} + \frac{y}{\frac{a}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 3
Accuracy	78.8%
Cost	2124

\[\begin{array}{l} t_1 := \frac{z}{y} + x\\ \mathbf{if}\;y \leq -2.2 \cdot 10^{+84}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -6 \cdot 10^{+15}:\\ \;\;\;\;\frac{z}{a + \left(y + \left(\frac{c}{y \cdot y} + \frac{b}{y}\right)\right)}\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{+31}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + z \cdot \left(y \cdot y\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{+137}:\\ \;\;\;\;\frac{27464.7644705}{y \cdot a} + \left(\frac{z}{a} + \frac{y}{\frac{a}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Accuracy	75.1%
Cost	1996

\[\begin{array}{l} t_1 := \frac{z}{y} + x\\ \mathbf{if}\;y \leq -1.55 \cdot 10^{+85}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -9000000000:\\ \;\;\;\;\frac{z}{a + \left(y + \left(\frac{c}{y \cdot y} + \frac{b}{y}\right)\right)}\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{+29}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+137}:\\ \;\;\;\;\frac{27464.7644705}{y \cdot a} + \left(\frac{z}{a} + \frac{y}{\frac{a}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 5
Accuracy	58.5%
Cost	1884

\[\begin{array}{l} t_1 := \frac{t + y \cdot 230661.510616}{y \cdot c}\\ t_2 := \frac{27464.7644705}{y \cdot a} + \left(\frac{z}{a} + \frac{y}{\frac{a}{x}}\right)\\ t_3 := \frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{i}\\ \mathbf{if}\;y \leq -5 \cdot 10^{+105}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{+16}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{-77}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-137}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{-112}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-31}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{+137}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{y} + x\\ \end{array} \]

Alternative 6
Accuracy	59.8%
Cost	1884

\[\begin{array}{l} t_1 := \frac{t + y \cdot 230661.510616}{y \cdot c}\\ t_2 := \frac{z}{a + \left(y + \left(\frac{c}{y \cdot y} + \frac{b}{y}\right)\right)}\\ t_3 := \frac{z}{y} + x\\ \mathbf{if}\;y \leq -1.55 \cdot 10^{+85}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -12500000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{-74}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{-137}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{i}\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{-111}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{-70}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{+121}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 7
Accuracy	74.7%
Cost	1740

\[\begin{array}{l} t_1 := \frac{z}{y} + x\\ \mathbf{if}\;y \leq -3.8 \cdot 10^{+85}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -9500000000:\\ \;\;\;\;\frac{z}{a + \left(y + \left(\frac{c}{y \cdot y} + \frac{b}{y}\right)\right)}\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{+28}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{+137}:\\ \;\;\;\;\frac{27464.7644705}{y \cdot a} + \left(\frac{z}{a} + \frac{y}{\frac{a}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 8
Accuracy	73.2%
Cost	1612

\[\begin{array}{l} t_1 := \frac{z}{y} + x\\ \mathbf{if}\;y \leq -8.5 \cdot 10^{+83}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -460000000:\\ \;\;\;\;\frac{z}{a + \left(y + \left(\frac{c}{y \cdot y} + \frac{b}{y}\right)\right)}\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{+18}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{+137}:\\ \;\;\;\;\frac{27464.7644705}{y \cdot a} + \left(\frac{z}{a} + \frac{y}{\frac{a}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 9
Accuracy	55.6%
Cost	1500

\[\begin{array}{l} t_1 := \frac{z}{a} + \frac{y \cdot x}{a}\\ t_2 := \frac{t}{y \cdot c}\\ t_3 := \frac{z}{y} + x\\ \mathbf{if}\;y \leq -5.2 \cdot 10^{+84}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{+16}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{-74}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{-137}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-109}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{-70}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+94}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 10
Accuracy	56.1%
Cost	1500

\[\begin{array}{l} t_1 := \frac{z}{a} + \frac{y \cdot x}{a}\\ t_2 := \frac{t + y \cdot 230661.510616}{y \cdot c}\\ t_3 := \frac{z}{y} + x\\ \mathbf{if}\;y \leq -2.3 \cdot 10^{+83}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{+16}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.02 \cdot 10^{-79}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-138}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{elif}\;y \leq 7.7 \cdot 10^{-112}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{-70}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+94}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 11
Accuracy	55.8%
Cost	1500

\[\begin{array}{l} t_1 := \frac{z}{a} + \frac{y \cdot x}{a}\\ t_2 := \frac{t + y \cdot 230661.510616}{y \cdot c}\\ \mathbf{if}\;y \leq -6.6 \cdot 10^{+105}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{+16}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -3.15 \cdot 10^{-78}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{-137}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{-111}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{-70}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+96}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{y} + x\\ \end{array} \]

Alternative 12
Accuracy	59.1%
Cost	1500

\[\begin{array}{l} t_1 := \frac{z}{a} + \frac{y \cdot x}{a}\\ t_2 := \frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{i}\\ t_3 := \frac{t + y \cdot 230661.510616}{y \cdot c}\\ \mathbf{if}\;y \leq -4 \cdot 10^{+105}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq -4 \cdot 10^{+16}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{-76}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-137}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{-112}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-29}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+95}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{y} + x\\ \end{array} \]

Alternative 13
Accuracy	69.4%
Cost	1488

\[\begin{array}{l} t_1 := \frac{z}{y} + x\\ \mathbf{if}\;y \leq -6.5 \cdot 10^{+84}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -3300000000:\\ \;\;\;\;\frac{z}{a + \left(y + \left(\frac{c}{y \cdot y} + \frac{b}{y}\right)\right)}\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-28}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{i + y \cdot c}\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{+137}:\\ \;\;\;\;\frac{27464.7644705}{y \cdot a} + \left(\frac{z}{a} + \frac{y}{\frac{a}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 14
Accuracy	71.1%
Cost	1488

\[\begin{array}{l} t_1 := \frac{z}{y} + x\\ \mathbf{if}\;y \leq -2 \cdot 10^{+85}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -220000000:\\ \;\;\;\;\frac{z}{a + \left(y + \left(\frac{c}{y \cdot y} + \frac{b}{y}\right)\right)}\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-10}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + a \cdot \left(y \cdot y\right)\right)}\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{+137}:\\ \;\;\;\;\frac{27464.7644705}{y \cdot a} + \left(\frac{z}{a} + \frac{y}{\frac{a}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 15
Accuracy	54.3%
Cost	1376

\[\begin{array}{l} t_1 := \frac{z}{y} + x\\ t_2 := \frac{t}{y \cdot c}\\ \mathbf{if}\;y \leq -3.2 \cdot 10^{+83}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -6.9 \cdot 10^{+36}:\\ \;\;\;\;\frac{z}{a}\\ \mathbf{elif}\;y \leq -7.2 \cdot 10^{+17}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{-74}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{-137}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{elif}\;y \leq 7.7 \cdot 10^{-112}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{-70}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+95}:\\ \;\;\;\;\frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 16
Accuracy	54.2%
Cost	1376

\[\begin{array}{l} t_1 := \frac{z}{y} + x\\ t_2 := \frac{t}{y \cdot c}\\ \mathbf{if}\;y \leq -3.5 \cdot 10^{+84}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -5.25 \cdot 10^{+36}:\\ \;\;\;\;\frac{z}{a}\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{+17}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;y \leq -4.1 \cdot 10^{-76}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{-137}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{elif}\;y \leq 7.7 \cdot 10^{-112}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{-70}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{+94}:\\ \;\;\;\;\frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 17
Accuracy	55.0%
Cost	1244

\[\begin{array}{l} t_1 := \frac{z}{y + a}\\ t_2 := \frac{t}{y \cdot c}\\ t_3 := \frac{z}{y} + x\\ \mathbf{if}\;y \leq -7.5 \cdot 10^{+84}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{+22}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -6.4 \cdot 10^{-75}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{-137}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{elif}\;y \leq 7.7 \cdot 10^{-112}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-79}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{+121}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 18
Accuracy	55.1%
Cost	980

\[\begin{array}{l} t_1 := \frac{z}{y} + x\\ \mathbf{if}\;y \leq -4.4 \cdot 10^{+83}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.12 \cdot 10^{+36}:\\ \;\;\;\;\frac{z}{a}\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-27}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{-70}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{+94}:\\ \;\;\;\;\frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 19
Accuracy	48.5%
Cost	852

\[\begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{+85}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{+36}:\\ \;\;\;\;\frac{z}{a}\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-28}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{-70}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{+121}:\\ \;\;\;\;\frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 20
Accuracy	48.7%
Cost	852

\[\begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+85}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -6 \cdot 10^{+35}:\\ \;\;\;\;\frac{z}{a}\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-28}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{-70}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{elif}\;y \leq 10^{+122}:\\ \;\;\;\;\frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 21
Accuracy	49.7%
Cost	456

\[\begin{array}{l} \mathbf{if}\;y \leq -2.05 \cdot 10^{-27}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 125000000000:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 22
Accuracy	26.5%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023141 
(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)))