Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2

Average Accuracy: 55.8% → 84.9%

Time: 1.1min

Precision: binary64

Cost: 46280

Math

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

↓

\[\begin{array}{l} t_1 := \frac{z}{x \cdot x}\\ t_2 := \frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ t_3 := b + y \cdot \left(y + a\right)\\ t_4 := y \cdot t_3\\ t_5 := t_3 \cdot t_3\\ \mathbf{if}\;y \leq -6 \cdot 10^{+36}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+19}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y + a, y, b\right), y, c\right), y, i\right)}\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+94}:\\ \;\;\;\;\frac{27464.7644705 + y \cdot \left(z + y \cdot x\right)}{t_3} + \left(230661.510616 \cdot \frac{1}{t_4} - c \cdot \left(\frac{z}{t_5} + \left(27464.7644705 \cdot \frac{1}{t_3 \cdot t_4} + \left(230661.510616 \cdot \frac{1}{t_3 \cdot \left(t_3 \cdot {y}^{2}\right)} + \frac{y \cdot x}{t_5}\right)\right)\right)\right)\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{+157}:\\ \;\;\;\;\frac{y}{\left(\left(\frac{a}{x} + \left(\frac{y}{x} + \frac{b}{y \cdot x}\right)\right) - \frac{z}{x} \cdot \frac{\frac{a}{x} - t_1}{y}\right) - \left(t_1 + \frac{27464.7644705}{y \cdot \left(x \cdot x\right)}\right)}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

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 (* x x)))
        (t_2 (+ (/ z y) (- x (/ a (/ y x)))))
        (t_3 (+ b (* y (+ y a))))
        (t_4 (* y t_3))
        (t_5 (* t_3 t_3)))
   (if (<= y -6e+36)
     t_2
     (if (<= y 9.5e+19)
       (/
        (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 2.7e+94)
         (+
          (/ (+ 27464.7644705 (* y (+ z (* y x)))) t_3)
          (-
           (* 230661.510616 (/ 1.0 t_4))
           (*
            c
            (+
             (/ z t_5)
             (+
              (* 27464.7644705 (/ 1.0 (* t_3 t_4)))
              (+
               (* 230661.510616 (/ 1.0 (* t_3 (* t_3 (pow y 2.0)))))
               (/ (* y x) t_5)))))))
         (if (<= y 8.2e+157)
           (/
            y
            (-
             (-
              (+ (/ a x) (+ (/ y x) (/ b (* y x))))
              (* (/ z x) (/ (- (/ a x) t_1) y)))
             (+ t_1 (/ 27464.7644705 (* y (* x x))))))
           t_2))))))

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 / (x * x);
	double t_2 = (z / y) + (x - (a / (y / x)));
	double t_3 = b + (y * (y + a));
	double t_4 = y * t_3;
	double t_5 = t_3 * t_3;
	double tmp;
	if (y <= -6e+36) {
		tmp = t_2;
	} else if (y <= 9.5e+19) {
		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 <= 2.7e+94) {
		tmp = ((27464.7644705 + (y * (z + (y * x)))) / t_3) + ((230661.510616 * (1.0 / t_4)) - (c * ((z / t_5) + ((27464.7644705 * (1.0 / (t_3 * t_4))) + ((230661.510616 * (1.0 / (t_3 * (t_3 * pow(y, 2.0))))) + ((y * x) / t_5))))));
	} else if (y <= 8.2e+157) {
		tmp = y / ((((a / x) + ((y / x) + (b / (y * x)))) - ((z / x) * (((a / x) - t_1) / y))) - (t_1 + (27464.7644705 / (y * (x * x)))));
	} else {
		tmp = t_2;
	}
	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(z / Float64(x * x))
	t_2 = Float64(Float64(z / y) + Float64(x - Float64(a / Float64(y / x))))
	t_3 = Float64(b + Float64(y * Float64(y + a)))
	t_4 = Float64(y * t_3)
	t_5 = Float64(t_3 * t_3)
	tmp = 0.0
	if (y <= -6e+36)
		tmp = t_2;
	elseif (y <= 9.5e+19)
		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 <= 2.7e+94)
		tmp = Float64(Float64(Float64(27464.7644705 + Float64(y * Float64(z + Float64(y * x)))) / t_3) + Float64(Float64(230661.510616 * Float64(1.0 / t_4)) - Float64(c * Float64(Float64(z / t_5) + Float64(Float64(27464.7644705 * Float64(1.0 / Float64(t_3 * t_4))) + Float64(Float64(230661.510616 * Float64(1.0 / Float64(t_3 * Float64(t_3 * (y ^ 2.0))))) + Float64(Float64(y * x) / t_5)))))));
	elseif (y <= 8.2e+157)
		tmp = Float64(y / Float64(Float64(Float64(Float64(a / x) + Float64(Float64(y / x) + Float64(b / Float64(y * x)))) - Float64(Float64(z / x) * Float64(Float64(Float64(a / x) - t_1) / y))) - Float64(t_1 + Float64(27464.7644705 / Float64(y * Float64(x * x))))));
	else
		tmp = t_2;
	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[(z / N[(x * x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z / y), $MachinePrecision] + N[(x - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(y * t$95$3), $MachinePrecision]}, Block[{t$95$5 = N[(t$95$3 * t$95$3), $MachinePrecision]}, If[LessEqual[y, -6e+36], t$95$2, If[LessEqual[y, 9.5e+19], 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, 2.7e+94], N[(N[(N[(27464.7644705 + N[(y * N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$3), $MachinePrecision] + N[(N[(230661.510616 * N[(1.0 / t$95$4), $MachinePrecision]), $MachinePrecision] - N[(c * N[(N[(z / t$95$5), $MachinePrecision] + N[(N[(27464.7644705 * N[(1.0 / N[(t$95$3 * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(230661.510616 * N[(1.0 / N[(t$95$3 * N[(t$95$3 * N[Power[y, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y * x), $MachinePrecision] / t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.2e+157], N[(y / N[(N[(N[(N[(a / x), $MachinePrecision] + N[(N[(y / x), $MachinePrecision] + N[(b / N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(z / x), $MachinePrecision] * N[(N[(N[(a / x), $MachinePrecision] - t$95$1), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t$95$1 + N[(27464.7644705 / N[(y * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -6e36 or 8.20000000000000032e157 < y

   1. Initial program 2.5%

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

   2. Simplified 2.5%

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

      [Start] 2.5	\[ \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
      fma-def [=>] 2.5	\[ \frac{\color{blue}{\mathsf{fma}\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616, y, t\right)}}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
      fma-def [=>] 2.5	\[ \frac{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705, y, 230661.510616\right)}, y, t\right)}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
      fma-def [=>] 2.5	\[ \frac{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x \cdot y + z, y, 27464.7644705\right)}, y, 230661.510616\right), y, t\right)}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
      fma-def [=>] 2.5	\[ \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x, y, z\right)}, y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
      fma-def [=>] 2.5	\[ \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\color{blue}{\mathsf{fma}\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c, y, i\right)}} \]
      fma-def [=>] 2.5	\[ \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(y + a\right) \cdot y + b, y, c\right)}, y, i\right)} \]
      fma-def [=>] 2.5	\[ \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(y + a, y, b\right)}, y, c\right), y, i\right)} \]

   3. Taylor expanded in y around inf 70.7%

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

   4. Simplified 76.2%

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

      [Start] 70.7	\[ \left(\frac{z}{y} + x\right) - \frac{a \cdot x}{y} \]
      associate--l+ [=>] 70.7	\[ \color{blue}{\frac{z}{y} + \left(x - \frac{a \cdot x}{y}\right)} \]
      associate-/l* [=>] 76.2	\[ \frac{z}{y} + \left(x - \color{blue}{\frac{a}{\frac{y}{x}}}\right) \]

   if -6e36 < y < 9.5e19

   1. Initial program 97.3%

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

   2. Simplified 97.3%

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

      [Start] 97.3	\[ \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
      fma-def [=>] 97.3	\[ \frac{\color{blue}{\mathsf{fma}\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616, y, t\right)}}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
      fma-def [=>] 97.3	\[ \frac{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705, y, 230661.510616\right)}, y, t\right)}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
      fma-def [=>] 97.3	\[ \frac{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x \cdot y + z, y, 27464.7644705\right)}, y, 230661.510616\right), y, t\right)}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
      fma-def [=>] 97.3	\[ \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x, y, z\right)}, y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
      fma-def [=>] 97.3	\[ \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\color{blue}{\mathsf{fma}\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c, y, i\right)}} \]
      fma-def [=>] 97.3	\[ \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(y + a\right) \cdot y + b, y, c\right)}, y, i\right)} \]
      fma-def [=>] 97.3	\[ \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(y + a, y, b\right)}, y, c\right), y, i\right)} \]

   if 9.5e19 < y < 2.7000000000000001e94

   1. Initial program 29.9%

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

   2. Taylor expanded in t around 0 24.0%

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

   3. Simplified 31.0%

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

      [Start] 24.0	\[ \frac{\left(230661.510616 + y \cdot \left(27464.7644705 + \left(y \cdot x + z\right) \cdot y\right)\right) \cdot y}{y \cdot \left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) + i} \]
      *-commutative [=>] 24.0	\[ \frac{\color{blue}{y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + \left(y \cdot x + z\right) \cdot y\right)\right)}}{y \cdot \left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) + i} \]
      associate-/l* [=>] 31.0	\[ \color{blue}{\frac{y}{\frac{y \cdot \left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) + i}{230661.510616 + y \cdot \left(27464.7644705 + \left(y \cdot x + z\right) \cdot y\right)}}} \]
      fma-def [=>] 31.0	\[ \frac{y}{\frac{\color{blue}{\mathsf{fma}\left(y, c + y \cdot \left(\left(y + a\right) \cdot y + b\right), i\right)}}{230661.510616 + y \cdot \left(27464.7644705 + \left(y \cdot x + z\right) \cdot y\right)}} \]
      +-commutative [=>] 31.0	\[ \frac{y}{\frac{\mathsf{fma}\left(y, \color{blue}{y \cdot \left(\left(y + a\right) \cdot y + b\right) + c}, i\right)}{230661.510616 + y \cdot \left(27464.7644705 + \left(y \cdot x + z\right) \cdot y\right)}} \]
      *-commutative [=>] 31.0	\[ \frac{y}{\frac{\mathsf{fma}\left(y, \color{blue}{\left(\left(y + a\right) \cdot y + b\right) \cdot y} + c, i\right)}{230661.510616 + y \cdot \left(27464.7644705 + \left(y \cdot x + z\right) \cdot y\right)}} \]
      fma-def [=>] 31.0	\[ \frac{y}{\frac{\mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(y + a, y, b\right)} \cdot y + c, i\right)}{230661.510616 + y \cdot \left(27464.7644705 + \left(y \cdot x + z\right) \cdot y\right)}} \]
      fma-udef [<=] 31.0	\[ \frac{y}{\frac{\mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y + a, y, b\right), y, c\right)}, i\right)}{230661.510616 + y \cdot \left(27464.7644705 + \left(y \cdot x + z\right) \cdot y\right)}} \]
      +-commutative [=>] 31.0	\[ \frac{y}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(\mathsf{fma}\left(y + a, y, b\right), y, c\right), i\right)}{\color{blue}{y \cdot \left(27464.7644705 + \left(y \cdot x + z\right) \cdot y\right) + 230661.510616}}} \]

   4. Taylor expanded in i around 0 40.0%

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

   5. Taylor expanded in c around 0 47.2%

      \[\leadsto \color{blue}{\frac{27464.7644705 + \left(y \cdot x + z\right) \cdot y}{\left(y + a\right) \cdot y + b} + \left(230661.510616 \cdot \frac{1}{y \cdot \left(\left(y + a\right) \cdot y + b\right)} + -1 \cdot \left(c \cdot \left(\frac{z}{\left(b + y \cdot \left(a + y\right)\right) \cdot \left(\left(y + a\right) \cdot y + b\right)} + \left(27464.7644705 \cdot \frac{1}{\left(b + y \cdot \left(a + y\right)\right) \cdot \left(y \cdot \left(\left(y + a\right) \cdot y + b\right)\right)} + \left(230661.510616 \cdot \frac{1}{\left(b + y \cdot \left(a + y\right)\right) \cdot \left({y}^{2} \cdot \left(\left(y + a\right) \cdot y + b\right)\right)} + \frac{y \cdot x}{\left(b + y \cdot \left(a + y\right)\right) \cdot \left(\left(y + a\right) \cdot y + b\right)}\right)\right)\right)\right)\right)} \]

   if 2.7000000000000001e94 < y < 8.20000000000000032e157

   1. Initial program 1.1%

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

   2. Taylor expanded in t around 0 1.1%

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

   3. Simplified 2.1%

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

      [Start] 1.1	\[ \frac{\left(230661.510616 + y \cdot \left(27464.7644705 + \left(y \cdot x + z\right) \cdot y\right)\right) \cdot y}{y \cdot \left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) + i} \]
      *-commutative [=>] 1.1	\[ \frac{\color{blue}{y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + \left(y \cdot x + z\right) \cdot y\right)\right)}}{y \cdot \left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) + i} \]
      associate-/l* [=>] 2.1	\[ \color{blue}{\frac{y}{\frac{y \cdot \left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) + i}{230661.510616 + y \cdot \left(27464.7644705 + \left(y \cdot x + z\right) \cdot y\right)}}} \]
      fma-def [=>] 2.1	\[ \frac{y}{\frac{\color{blue}{\mathsf{fma}\left(y, c + y \cdot \left(\left(y + a\right) \cdot y + b\right), i\right)}}{230661.510616 + y \cdot \left(27464.7644705 + \left(y \cdot x + z\right) \cdot y\right)}} \]
      +-commutative [=>] 2.1	\[ \frac{y}{\frac{\mathsf{fma}\left(y, \color{blue}{y \cdot \left(\left(y + a\right) \cdot y + b\right) + c}, i\right)}{230661.510616 + y \cdot \left(27464.7644705 + \left(y \cdot x + z\right) \cdot y\right)}} \]
      *-commutative [=>] 2.1	\[ \frac{y}{\frac{\mathsf{fma}\left(y, \color{blue}{\left(\left(y + a\right) \cdot y + b\right) \cdot y} + c, i\right)}{230661.510616 + y \cdot \left(27464.7644705 + \left(y \cdot x + z\right) \cdot y\right)}} \]
      fma-def [=>] 2.1	\[ \frac{y}{\frac{\mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(y + a, y, b\right)} \cdot y + c, i\right)}{230661.510616 + y \cdot \left(27464.7644705 + \left(y \cdot x + z\right) \cdot y\right)}} \]
      fma-udef [<=] 2.1	\[ \frac{y}{\frac{\mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y + a, y, b\right), y, c\right)}, i\right)}{230661.510616 + y \cdot \left(27464.7644705 + \left(y \cdot x + z\right) \cdot y\right)}} \]
      +-commutative [=>] 2.1	\[ \frac{y}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(\mathsf{fma}\left(y + a, y, b\right), y, c\right), i\right)}{\color{blue}{y \cdot \left(27464.7644705 + \left(y \cdot x + z\right) \cdot y\right) + 230661.510616}}} \]

   4. Taylor expanded in y around inf 55.1%

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

   5. Simplified 55.7%

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

      [Start] 55.1	\[ \frac{y}{\left(\frac{y}{x} + \left(\frac{b}{y \cdot x} + \frac{a}{x}\right)\right) - \left(\frac{\left(\frac{a}{x} - \frac{z}{{x}^{2}}\right) \cdot z}{y \cdot x} + \left(27464.7644705 \cdot \frac{1}{y \cdot {x}^{2}} + \frac{z}{{x}^{2}}\right)\right)} \]
      associate--r+ [=>] 55.1	\[ \frac{y}{\color{blue}{\left(\left(\frac{y}{x} + \left(\frac{b}{y \cdot x} + \frac{a}{x}\right)\right) - \frac{\left(\frac{a}{x} - \frac{z}{{x}^{2}}\right) \cdot z}{y \cdot x}\right) - \left(27464.7644705 \cdot \frac{1}{y \cdot {x}^{2}} + \frac{z}{{x}^{2}}\right)}} \]
      associate-+r+ [=>] 55.1	\[ \frac{y}{\left(\color{blue}{\left(\left(\frac{y}{x} + \frac{b}{y \cdot x}\right) + \frac{a}{x}\right)} - \frac{\left(\frac{a}{x} - \frac{z}{{x}^{2}}\right) \cdot z}{y \cdot x}\right) - \left(27464.7644705 \cdot \frac{1}{y \cdot {x}^{2}} + \frac{z}{{x}^{2}}\right)} \]
      +-commutative [=>] 55.1	\[ \frac{y}{\left(\color{blue}{\left(\frac{a}{x} + \left(\frac{y}{x} + \frac{b}{y \cdot x}\right)\right)} - \frac{\left(\frac{a}{x} - \frac{z}{{x}^{2}}\right) \cdot z}{y \cdot x}\right) - \left(27464.7644705 \cdot \frac{1}{y \cdot {x}^{2}} + \frac{z}{{x}^{2}}\right)} \]
      times-frac [=>] 55.7	\[ \frac{y}{\left(\left(\frac{a}{x} + \left(\frac{y}{x} + \frac{b}{y \cdot x}\right)\right) - \color{blue}{\frac{\frac{a}{x} - \frac{z}{{x}^{2}}}{y} \cdot \frac{z}{x}}\right) - \left(27464.7644705 \cdot \frac{1}{y \cdot {x}^{2}} + \frac{z}{{x}^{2}}\right)} \]
      *-commutative [=>] 55.7	\[ \frac{y}{\left(\left(\frac{a}{x} + \left(\frac{y}{x} + \frac{b}{y \cdot x}\right)\right) - \color{blue}{\frac{z}{x} \cdot \frac{\frac{a}{x} - \frac{z}{{x}^{2}}}{y}}\right) - \left(27464.7644705 \cdot \frac{1}{y \cdot {x}^{2}} + \frac{z}{{x}^{2}}\right)} \]
      unpow2 [=>] 55.7	\[ \frac{y}{\left(\left(\frac{a}{x} + \left(\frac{y}{x} + \frac{b}{y \cdot x}\right)\right) - \frac{z}{x} \cdot \frac{\frac{a}{x} - \frac{z}{\color{blue}{x \cdot x}}}{y}\right) - \left(27464.7644705 \cdot \frac{1}{y \cdot {x}^{2}} + \frac{z}{{x}^{2}}\right)} \]
      +-commutative [=>] 55.7	\[ \frac{y}{\left(\left(\frac{a}{x} + \left(\frac{y}{x} + \frac{b}{y \cdot x}\right)\right) - \frac{z}{x} \cdot \frac{\frac{a}{x} - \frac{z}{x \cdot x}}{y}\right) - \color{blue}{\left(\frac{z}{{x}^{2}} + 27464.7644705 \cdot \frac{1}{y \cdot {x}^{2}}\right)}} \]
      unpow2 [=>] 55.7	\[ \frac{y}{\left(\left(\frac{a}{x} + \left(\frac{y}{x} + \frac{b}{y \cdot x}\right)\right) - \frac{z}{x} \cdot \frac{\frac{a}{x} - \frac{z}{x \cdot x}}{y}\right) - \left(\frac{z}{\color{blue}{x \cdot x}} + 27464.7644705 \cdot \frac{1}{y \cdot {x}^{2}}\right)} \]
      associate-*r/ [=>] 55.7	\[ \frac{y}{\left(\left(\frac{a}{x} + \left(\frac{y}{x} + \frac{b}{y \cdot x}\right)\right) - \frac{z}{x} \cdot \frac{\frac{a}{x} - \frac{z}{x \cdot x}}{y}\right) - \left(\frac{z}{x \cdot x} + \color{blue}{\frac{27464.7644705 \cdot 1}{y \cdot {x}^{2}}}\right)} \]
      metadata-eval [=>] 55.7	\[ \frac{y}{\left(\left(\frac{a}{x} + \left(\frac{y}{x} + \frac{b}{y \cdot x}\right)\right) - \frac{z}{x} \cdot \frac{\frac{a}{x} - \frac{z}{x \cdot x}}{y}\right) - \left(\frac{z}{x \cdot x} + \frac{\color{blue}{27464.7644705}}{y \cdot {x}^{2}}\right)} \]
      unpow2 [=>] 55.7	\[ \frac{y}{\left(\left(\frac{a}{x} + \left(\frac{y}{x} + \frac{b}{y \cdot x}\right)\right) - \frac{z}{x} \cdot \frac{\frac{a}{x} - \frac{z}{x \cdot x}}{y}\right) - \left(\frac{z}{x \cdot x} + \frac{27464.7644705}{y \cdot \color{blue}{\left(x \cdot x\right)}}\right)} \]

3. Recombined 4 regimes into one program.

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+36}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+19}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y + a, y, b\right), y, c\right), y, i\right)}\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+94}:\\ \;\;\;\;\frac{27464.7644705 + y \cdot \left(z + y \cdot x\right)}{b + y \cdot \left(y + a\right)} + \left(230661.510616 \cdot \frac{1}{y \cdot \left(b + y \cdot \left(y + a\right)\right)} - c \cdot \left(\frac{z}{\left(b + y \cdot \left(y + a\right)\right) \cdot \left(b + y \cdot \left(y + a\right)\right)} + \left(27464.7644705 \cdot \frac{1}{\left(b + y \cdot \left(y + a\right)\right) \cdot \left(y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)} + \left(230661.510616 \cdot \frac{1}{\left(b + y \cdot \left(y + a\right)\right) \cdot \left(\left(b + y \cdot \left(y + a\right)\right) \cdot {y}^{2}\right)} + \frac{y \cdot x}{\left(b + y \cdot \left(y + a\right)\right) \cdot \left(b + y \cdot \left(y + a\right)\right)}\right)\right)\right)\right)\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{+157}:\\ \;\;\;\;\frac{y}{\left(\left(\frac{a}{x} + \left(\frac{y}{x} + \frac{b}{y \cdot x}\right)\right) - \frac{z}{x} \cdot \frac{\frac{a}{x} - \frac{z}{x \cdot x}}{y}\right) - \left(\frac{z}{x \cdot x} + \frac{27464.7644705}{y \cdot \left(x \cdot x\right)}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	84.9%
Cost	14220

\[\begin{array}{l} t_1 := \frac{z}{x \cdot x}\\ t_2 := \frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ t_3 := 27464.7644705 + y \cdot \left(z + y \cdot x\right)\\ t_4 := b + y \cdot \left(y + a\right)\\ t_5 := y \cdot t_4\\ t_6 := t_4 \cdot t_4\\ \mathbf{if}\;y \leq -6 \cdot 10^{+36}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+19}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot t_3\right)}{i + y \cdot \left(c + t_5\right)}\\ \mathbf{elif}\;y \leq 2.75 \cdot 10^{+94}:\\ \;\;\;\;\frac{t_3}{t_4} + \left(230661.510616 \cdot \frac{1}{t_5} - c \cdot \left(\frac{z}{t_6} + \left(27464.7644705 \cdot \frac{1}{t_4 \cdot t_5} + \left(230661.510616 \cdot \frac{1}{t_4 \cdot \left(t_4 \cdot {y}^{2}\right)} + \frac{y \cdot x}{t_6}\right)\right)\right)\right)\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{+157}:\\ \;\;\;\;\frac{y}{\left(\left(\frac{a}{x} + \left(\frac{y}{x} + \frac{b}{y \cdot x}\right)\right) - \frac{z}{x} \cdot \frac{\frac{a}{x} - t_1}{y}\right) - \left(t_1 + \frac{27464.7644705}{y \cdot \left(x \cdot x\right)}\right)}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 2
Accuracy	84.7%
Cost	3276

\[\begin{array}{l} t_1 := \frac{z}{x \cdot x}\\ t_2 := \frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{if}\;y \leq -6 \cdot 10^{+36}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{+68}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{+157}:\\ \;\;\;\;\frac{y}{\left(\left(\frac{a}{x} + \left(\frac{y}{x} + \frac{b}{y \cdot x}\right)\right) - \frac{z}{x} \cdot \frac{\frac{a}{x} - t_1}{y}\right) - \left(t_1 + \frac{27464.7644705}{y \cdot \left(x \cdot x\right)}\right)}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 3
Accuracy	84.5%
Cost	2376

\[\begin{array}{l} t_1 := \frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{if}\;y \leq -6 \cdot 10^{+36}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 9.6 \cdot 10^{+58}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+158}:\\ \;\;\;\;\frac{y}{\frac{y}{x} + \left(\frac{a}{x} - \frac{z}{x \cdot x}\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Accuracy	77.8%
Cost	1996

\[\begin{array}{l} t_1 := \frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{if}\;y \leq -2.3 \cdot 10^{+36}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-41}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + z \cdot \left(y \cdot y\right)\right)}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+94}:\\ \;\;\;\;\frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)}{c + y \cdot \left(b + y \cdot \left(y + a\right)\right)}\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{+158}:\\ \;\;\;\;\frac{y}{\frac{y}{x} + \left(\frac{a}{x} - \frac{z}{x \cdot x}\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 5
Accuracy	80.6%
Cost	1996

\[\begin{array}{l} t_1 := c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\\ t_2 := \frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{if}\;y \leq -6 \cdot 10^{+36}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-19}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + z \cdot \left(y \cdot y\right)\right)}{i + y \cdot t_1}\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+94}:\\ \;\;\;\;\frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)}{t_1}\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{+157}:\\ \;\;\;\;\frac{y}{\frac{y}{x} + \left(\frac{a}{x} - \frac{z}{x \cdot x}\right)}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 6
Accuracy	74.0%
Cost	1740

\[\begin{array}{l} t_1 := \frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{if}\;y \leq -9 \cdot 10^{+35}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-41}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+58}:\\ \;\;\;\;\frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)}{c + a \cdot \left(y \cdot y\right)}\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{+157}:\\ \;\;\;\;\frac{y}{\frac{y}{x} + \left(\frac{a}{x} - \frac{z}{x \cdot x}\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 7
Accuracy	75.5%
Cost	1740

\[\begin{array}{l} t_1 := \frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{if}\;y \leq -1.12 \cdot 10^{+36}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-41}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+58}:\\ \;\;\;\;\frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)}{c + a \cdot \left(y \cdot y\right)}\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{+157}:\\ \;\;\;\;\frac{y}{\frac{y}{x} + \left(\frac{a}{x} - \frac{z}{x \cdot x}\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 8
Accuracy	76.4%
Cost	1740

\[\begin{array}{l} t_1 := \frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{if}\;y \leq -1.15 \cdot 10^{+36}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-41}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + z \cdot \left(y \cdot y\right)\right)}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+58}:\\ \;\;\;\;\frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)}{c + a \cdot \left(y \cdot y\right)}\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{+163}:\\ \;\;\;\;\frac{y}{\frac{y}{x} + \left(\frac{a}{x} - \frac{z}{x \cdot x}\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 9
Accuracy	66.7%
Cost	1488

\[\begin{array}{l} t_1 := \frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{if}\;y \leq -2.4 \cdot 10^{+36}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-41}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+68}:\\ \;\;\;\;\frac{27464.7644705}{y \cdot a} + \left(\frac{z}{a} + \frac{y \cdot x}{a}\right)\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{+159}:\\ \;\;\;\;\frac{y}{\frac{y}{x} + \left(\frac{a}{x} - \frac{z}{x \cdot x}\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 10
Accuracy	73.0%
Cost	1488

\[\begin{array}{l} t_1 := \frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{if}\;y \leq -4.5 \cdot 10^{+35}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-41}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{elif}\;y \leq 7.4 \cdot 10^{+67}:\\ \;\;\;\;\frac{27464.7644705}{y \cdot a} + \left(\frac{z}{a} + \frac{y \cdot x}{a}\right)\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{+158}:\\ \;\;\;\;\frac{y}{\frac{y}{x} + \left(\frac{a}{x} - \frac{z}{x \cdot x}\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 11
Accuracy	65.6%
Cost	1356

\[\begin{array}{l} t_1 := \frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{if}\;y \leq -2.1 \cdot 10^{+36}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-41}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+138}:\\ \;\;\;\;\frac{27464.7644705}{y \cdot a} + \left(\frac{z}{a} + \frac{y \cdot x}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 12
Accuracy	58.9%
Cost	1100

\[\begin{array}{l} t_1 := \frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{if}\;y \leq -4.2 \cdot 10^{+35}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-41}:\\ \;\;\;\;230661.510616 \cdot \frac{y}{i} + \frac{t}{i}\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+138}:\\ \;\;\;\;\frac{z}{a} + \frac{y \cdot x}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 13
Accuracy	65.4%
Cost	1100

\[\begin{array}{l} t_1 := \frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{if}\;y \leq -4.2 \cdot 10^{+35}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-41}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{+139}:\\ \;\;\;\;\frac{z}{a} + \frac{y \cdot x}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 14
Accuracy	53.0%
Cost	972

\[\begin{array}{l} \mathbf{if}\;y \leq -2.75 \cdot 10^{-17}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-45}:\\ \;\;\;\;230661.510616 \cdot \frac{y}{i} + \frac{t}{i}\\ \mathbf{elif}\;y \leq 1.42 \cdot 10^{+139}:\\ \;\;\;\;\frac{z}{a} + \frac{y \cdot x}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 15
Accuracy	52.2%
Cost	840

\[\begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{-17}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.06 \cdot 10^{+18}:\\ \;\;\;\;230661.510616 \cdot \frac{y}{i} + \frac{t}{i}\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{+158}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 16
Accuracy	48.8%
Cost	716

\[\begin{array}{l} \mathbf{if}\;y \leq -9.6 \cdot 10^{-18}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+14}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{+157}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 17
Accuracy	27.8%
Cost	456

\[\begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{-42}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-20}:\\ \;\;\;\;\frac{230661.510616}{c}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 18
Accuracy	50.0%
Cost	456

\[\begin{array}{l} \mathbf{if}\;y \leq -2.65 \cdot 10^{-17}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+14}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 19
Accuracy	25.9%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023138 
(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)))