Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2

Average Error: 45.32% → 17.35%

Time: 57.3s

Precision: binary64

Cost: 46412

Math

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

↓

\[\begin{array}{l} t_1 := \left(\frac{z}{y} + x\right) - \frac{x \cdot a}{y}\\ t_2 := \frac{z}{x \cdot x}\\ t_3 := \frac{a}{x} - t_2\\ t_4 := t_2 - \frac{a}{x}\\ \mathbf{if}\;y \leq -1.75 \cdot 10^{+99}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{+35}:\\ \;\;\;\;\frac{1}{\mathsf{fma}\left(-1, \frac{\left(\left(\frac{230661.510616}{x \cdot x} - \frac{c}{x}\right) + \frac{27464.7644705 \cdot t_3}{x}\right) - \frac{z \cdot \left(\frac{z \cdot t_3}{x} + \left(\frac{27464.7644705}{x \cdot x} - \frac{b}{x}\right)\right)}{x}}{{y}^{3}}, \frac{1}{x} - \left(\frac{t_4}{y} - \frac{\frac{b}{x}}{y \cdot y}\right)\right) + \left(\frac{-27464.7644705}{\left(x \cdot x\right) \cdot \left(y \cdot y\right)} + \frac{t_4}{\frac{y \cdot \left(y \cdot x\right)}{z}}\right)}\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{+50}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y + a, y, b\right), y, c\right), y, i\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

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) (/ (* x a) y)))
        (t_2 (/ z (* x x)))
        (t_3 (- (/ a x) t_2))
        (t_4 (- t_2 (/ a x))))
   (if (<= y -1.75e+99)
     t_1
     (if (<= y -6.2e+35)
       (/
        1.0
        (+
         (fma
          -1.0
          (/
           (-
            (+
             (- (/ 230661.510616 (* x x)) (/ c x))
             (/ (* 27464.7644705 t_3) x))
            (/
             (* z (+ (/ (* z t_3) x) (- (/ 27464.7644705 (* x x)) (/ b x))))
             x))
           (pow y 3.0))
          (- (/ 1.0 x) (- (/ t_4 y) (/ (/ b x) (* y y)))))
         (+
          (/ -27464.7644705 (* (* x x) (* y y)))
          (/ t_4 (/ (* y (* y x)) z)))))
       (if (<= y 1.65e+50)
         (/
          (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))
         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) - ((x * a) / y);
	double t_2 = z / (x * x);
	double t_3 = (a / x) - t_2;
	double t_4 = t_2 - (a / x);
	double tmp;
	if (y <= -1.75e+99) {
		tmp = t_1;
	} else if (y <= -6.2e+35) {
		tmp = 1.0 / (fma(-1.0, (((((230661.510616 / (x * x)) - (c / x)) + ((27464.7644705 * t_3) / x)) - ((z * (((z * t_3) / x) + ((27464.7644705 / (x * x)) - (b / x)))) / x)) / pow(y, 3.0)), ((1.0 / x) - ((t_4 / y) - ((b / x) / (y * y))))) + ((-27464.7644705 / ((x * x) * (y * y))) + (t_4 / ((y * (y * x)) / z))));
	} else if (y <= 1.65e+50) {
		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 = 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(Float64(z / y) + x) - Float64(Float64(x * a) / y))
	t_2 = Float64(z / Float64(x * x))
	t_3 = Float64(Float64(a / x) - t_2)
	t_4 = Float64(t_2 - Float64(a / x))
	tmp = 0.0
	if (y <= -1.75e+99)
		tmp = t_1;
	elseif (y <= -6.2e+35)
		tmp = Float64(1.0 / Float64(fma(-1.0, Float64(Float64(Float64(Float64(Float64(230661.510616 / Float64(x * x)) - Float64(c / x)) + Float64(Float64(27464.7644705 * t_3) / x)) - Float64(Float64(z * Float64(Float64(Float64(z * t_3) / x) + Float64(Float64(27464.7644705 / Float64(x * x)) - Float64(b / x)))) / x)) / (y ^ 3.0)), Float64(Float64(1.0 / x) - Float64(Float64(t_4 / y) - Float64(Float64(b / x) / Float64(y * y))))) + Float64(Float64(-27464.7644705 / Float64(Float64(x * x) * Float64(y * y))) + Float64(t_4 / Float64(Float64(y * Float64(y * x)) / z)))));
	elseif (y <= 1.65e+50)
		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 = 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[(N[(z / y), $MachinePrecision] + x), $MachinePrecision] - N[(N[(x * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z / N[(x * x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(a / x), $MachinePrecision] - t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$2 - N[(a / x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.75e+99], t$95$1, If[LessEqual[y, -6.2e+35], N[(1.0 / N[(N[(-1.0 * N[(N[(N[(N[(N[(230661.510616 / N[(x * x), $MachinePrecision]), $MachinePrecision] - N[(c / x), $MachinePrecision]), $MachinePrecision] + N[(N[(27464.7644705 * t$95$3), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] - N[(N[(z * N[(N[(N[(z * t$95$3), $MachinePrecision] / x), $MachinePrecision] + N[(N[(27464.7644705 / N[(x * x), $MachinePrecision]), $MachinePrecision] - N[(b / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / N[Power[y, 3.0], $MachinePrecision]), $MachinePrecision] + N[(N[(1.0 / x), $MachinePrecision] - N[(N[(t$95$4 / y), $MachinePrecision] - N[(N[(b / x), $MachinePrecision] / N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(-27464.7644705 / N[(N[(x * x), $MachinePrecision] * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$4 / N[(N[(y * N[(y * x), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.65e+50], 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], t$95$1]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.7499999999999999e99 or 1.65e50 < y

   1. Initial program 98.21

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

   2. Taylor expanded in y around inf 30.07

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

   if -1.7499999999999999e99 < y < -6.19999999999999973e35

   1. Initial program 81.36

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

   2. Applied egg-rr 81.38

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, 27464.7644705\right), y, 230661.510616\right), y, t\right) \cdot \frac{1}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y + a, y, b\right), y, c\right), y, i\right)}} \]

   3. Applied egg-rr 81.36

      \[\leadsto \color{blue}{\frac{1}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y + a, y, b\right), y, c\right), y, i\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}}} \]

   4. Taylor expanded in y around -inf 57.46

      \[\leadsto \frac{1}{\color{blue}{\left(-1 \cdot \frac{\left(230661.510616 \cdot \frac{1}{{x}^{2}} + -1 \cdot \frac{c}{x}\right) - \left(27464.7644705 \cdot \frac{-1 \cdot \frac{a}{x} - -1 \cdot \frac{z}{{x}^{2}}}{x} + -1 \cdot \frac{\left(\frac{b}{x} - \left(27464.7644705 \cdot \frac{1}{{x}^{2}} + -1 \cdot \frac{\left(-1 \cdot \frac{a}{x} - -1 \cdot \frac{z}{{x}^{2}}\right) \cdot z}{x}\right)\right) \cdot z}{x}\right)}{{y}^{3}} + \left(\frac{1}{x} + \left(\frac{b}{{y}^{2} \cdot x} + -1 \cdot \frac{-1 \cdot \frac{a}{x} - -1 \cdot \frac{z}{{x}^{2}}}{y}\right)\right)\right) - \left(-1 \cdot \frac{\left(-1 \cdot \frac{a}{x} - -1 \cdot \frac{z}{{x}^{2}}\right) \cdot z}{{y}^{2} \cdot x} + 27464.7644705 \cdot \frac{1}{{y}^{2} \cdot {x}^{2}}\right)}} \]

   5. Simplified 54.15

      \[\leadsto \frac{1}{\color{blue}{\mathsf{fma}\left(-1, \frac{\left(\left(\frac{230661.510616}{x \cdot x} + \left(-\frac{c}{x}\right)\right) - \frac{-27464.7644705 \cdot \left(\frac{a}{x} - \frac{z}{x \cdot x}\right)}{x}\right) - \frac{\left(-z\right) \cdot \left(\left(\frac{b}{x} - \frac{27464.7644705}{x \cdot x}\right) - \frac{\left(1 \cdot \left(\frac{a}{x} - \frac{z}{x \cdot x}\right)\right) \cdot z}{x}\right)}{x}}{{y}^{3}}, \frac{1}{x} + \left(\frac{\frac{b}{x}}{y \cdot y} + \frac{1 \cdot \left(\frac{a}{x} - \frac{z}{x \cdot x}\right)}{y}\right)\right) - \left(\frac{27464.7644705}{\left(y \cdot y\right) \cdot \left(x \cdot x\right)} + \frac{1 \cdot \left(\frac{a}{x} - \frac{z}{x \cdot x}\right)}{\frac{y \cdot \left(y \cdot x\right)}{z}}\right)}} \]
      Proof

      [Start] 57.46

      \[ \frac{1}{\left(-1 \cdot \frac{\left(230661.510616 \cdot \frac{1}{{x}^{2}} + -1 \cdot \frac{c}{x}\right) - \left(27464.7644705 \cdot \frac{-1 \cdot \frac{a}{x} - -1 \cdot \frac{z}{{x}^{2}}}{x} + -1 \cdot \frac{\left(\frac{b}{x} - \left(27464.7644705 \cdot \frac{1}{{x}^{2}} + -1 \cdot \frac{\left(-1 \cdot \frac{a}{x} - -1 \cdot \frac{z}{{x}^{2}}\right) \cdot z}{x}\right)\right) \cdot z}{x}\right)}{{y}^{3}} + \left(\frac{1}{x} + \left(\frac{b}{{y}^{2} \cdot x} + -1 \cdot \frac{-1 \cdot \frac{a}{x} - -1 \cdot \frac{z}{{x}^{2}}}{y}\right)\right)\right) - \left(-1 \cdot \frac{\left(-1 \cdot \frac{a}{x} - -1 \cdot \frac{z}{{x}^{2}}\right) \cdot z}{{y}^{2} \cdot x} + 27464.7644705 \cdot \frac{1}{{y}^{2} \cdot {x}^{2}}\right)} \]

   if -6.19999999999999973e35 < y < 1.65e50

   1. Initial program 4.74

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

   2. Simplified 4.73

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

      [Start] 4.74	\[ \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
      fma-def [=>] 4.74	\[ \frac{\color{blue}{\mathsf{fma}\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616, y, t\right)}}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
      fma-def [=>] 4.74	\[ \frac{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705, y, 230661.510616\right)}, y, t\right)}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
      fma-def [=>] 4.74	\[ \frac{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x \cdot y + z, y, 27464.7644705\right)}, y, 230661.510616\right), y, t\right)}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
      fma-def [=>] 4.74	\[ \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x, y, z\right)}, y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
      fma-def [=>] 4.73	\[ \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\color{blue}{\mathsf{fma}\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c, y, i\right)}} \]
      fma-def [=>] 4.73	\[ \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(y + a\right) \cdot y + b, y, c\right)}, y, i\right)} \]
      fma-def [=>] 4.73	\[ \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(y + a, y, b\right)}, y, c\right), y, i\right)} \]

3. Recombined 3 regimes into one program.

4. Final simplification 17.35

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{+99}:\\ \;\;\;\;\left(\frac{z}{y} + x\right) - \frac{x \cdot a}{y}\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{+35}:\\ \;\;\;\;\frac{1}{\mathsf{fma}\left(-1, \frac{\left(\left(\frac{230661.510616}{x \cdot x} - \frac{c}{x}\right) + \frac{27464.7644705 \cdot \left(\frac{a}{x} - \frac{z}{x \cdot x}\right)}{x}\right) - \frac{z \cdot \left(\frac{z \cdot \left(\frac{a}{x} - \frac{z}{x \cdot x}\right)}{x} + \left(\frac{27464.7644705}{x \cdot x} - \frac{b}{x}\right)\right)}{x}}{{y}^{3}}, \frac{1}{x} - \left(\frac{\frac{z}{x \cdot x} - \frac{a}{x}}{y} - \frac{\frac{b}{x}}{y \cdot y}\right)\right) + \left(\frac{-27464.7644705}{\left(x \cdot x\right) \cdot \left(y \cdot y\right)} + \frac{\frac{z}{x \cdot x} - \frac{a}{x}}{\frac{y \cdot \left(y \cdot x\right)}{z}}\right)}\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{+50}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y + a, y, b\right), y, c\right), y, i\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{z}{y} + x\right) - \frac{x \cdot a}{y}\\ \end{array} \]

Alternatives

Alternative 1
Error	17.32%
Cost	19976

\[\begin{array}{l} t_1 := \left(\frac{z}{y} + x\right) - \frac{x \cdot a}{y}\\ t_2 := \frac{z}{x \cdot x}\\ t_3 := \frac{a}{x} - t_2\\ t_4 := t_2 - \frac{a}{x}\\ \mathbf{if}\;y \leq -8 \cdot 10^{+98}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{+34}:\\ \;\;\;\;\frac{1}{\mathsf{fma}\left(-1, \frac{\left(\left(\frac{230661.510616}{x \cdot x} - \frac{c}{x}\right) + \frac{27464.7644705 \cdot t_3}{x}\right) - \frac{z \cdot \left(\frac{z \cdot t_3}{x} + \left(\frac{27464.7644705}{x \cdot x} - \frac{b}{x}\right)\right)}{x}}{{y}^{3}}, \frac{1}{x} - \left(\frac{t_4}{y} - \frac{\frac{b}{x}}{y \cdot y}\right)\right) + \left(\frac{-27464.7644705}{\left(x \cdot x\right) \cdot \left(y \cdot y\right)} + \frac{t_4}{\frac{y \cdot \left(y \cdot x\right)}{z}}\right)}\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{+51}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 - y \cdot \left(-27464.7644705 - y \cdot \left(z + y \cdot x\right)\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Error	18.11%
Cost	4292

\[\begin{array}{l} t_1 := \frac{t + y \cdot \left(230661.510616 - y \cdot \left(-27464.7644705 - y \cdot \left(z + y \cdot x\right)\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{if}\;t_1 \leq 2 \cdot 10^{+298}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{z}{y} + x\right) - \frac{x \cdot a}{y}\\ \end{array} \]

Alternative 3
Error	25.62%
Cost	2256

\[\begin{array}{l} t_1 := t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)\\ t_2 := \left(\frac{z}{y} + x\right) - \frac{x \cdot a}{y}\\ \mathbf{if}\;y \leq -3.2 \cdot 10^{+44}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.55 \cdot 10^{-33}:\\ \;\;\;\;\frac{t_1}{i + y \cdot \left(c + \left(y \cdot y\right) \cdot \left(y + a\right)\right)}\\ \mathbf{elif}\;y \leq -1 \cdot 10^{-89}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 - y \cdot \left(-27464.7644705 - y \cdot \left(z + y \cdot x\right)\right)\right)}{i + b \cdot \left(y \cdot y\right)}\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+56}:\\ \;\;\;\;\frac{t_1}{i + y \cdot \left(c + y \cdot \left(b + y \cdot y\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 4
Error	23.02%
Cost	2249

\[\begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+45} \lor \neg \left(y \leq 1.25 \cdot 10^{+39}\right):\\ \;\;\;\;\left(\frac{z}{y} + x\right) - \frac{x \cdot a}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + x \cdot \left(y \cdot y\right)\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \end{array} \]

Alternative 5
Error	21.33%
Cost	2121

\[\begin{array}{l} \mathbf{if}\;y \leq -7.6 \cdot 10^{+49} \lor \neg \left(y \leq 4.8 \cdot 10^{+55}\right):\\ \;\;\;\;\left(\frac{z}{y} + x\right) - \frac{x \cdot a}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \end{array} \]

Alternative 6
Error	24.45%
Cost	1993

\[\begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+50} \lor \neg \left(y \leq 6.2 \cdot 10^{+57}\right):\\ \;\;\;\;\left(\frac{z}{y} + x\right) - \frac{x \cdot a}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot y\right)\right)}\\ \end{array} \]

Alternative 7
Error	22.29%
Cost	1993

\[\begin{array}{l} \mathbf{if}\;y \leq -6.4 \cdot 10^{+49} \lor \neg \left(y \leq 1.05 \cdot 10^{+56}\right):\\ \;\;\;\;\left(\frac{z}{y} + x\right) - \frac{x \cdot a}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - y \cdot \left(-230661.510616 - z \cdot \left(y \cdot y\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \end{array} \]

Alternative 8
Error	26.23%
Cost	1865

\[\begin{array}{l} \mathbf{if}\;y \leq -4.3 \cdot 10^{+45} \lor \neg \left(y \leq 4.1 \cdot 10^{+37}\right):\\ \;\;\;\;\left(\frac{z}{y} + x\right) - \frac{x \cdot a}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \end{array} \]

Alternative 9
Error	30.38%
Cost	1744

\[\begin{array}{l} t_1 := \left(\frac{z}{y} + x\right) - \frac{x \cdot a}{y}\\ \mathbf{if}\;y \leq -2.2 \cdot 10^{+36}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{-98}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot c}\\ \mathbf{elif}\;y \leq 3600000000000:\\ \;\;\;\;\frac{1}{\frac{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}{t}}\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+61}:\\ \;\;\;\;\frac{1}{\left(\frac{1}{x} + \frac{a}{y \cdot x}\right) - \frac{z}{y \cdot \left(x \cdot x\right)}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 10
Error	27.03%
Cost	1609

\[\begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+41} \lor \neg \left(y \leq 8.5 \cdot 10^{+35}\right):\\ \;\;\;\;\left(\frac{z}{y} + x\right) - \frac{x \cdot a}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \end{array} \]

Alternative 11
Error	34.61%
Cost	1353

\[\begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+42} \lor \neg \left(y \leq 5 \cdot 10^{+36}\right):\\ \;\;\;\;\left(\frac{z}{y} + x\right) - \frac{x \cdot a}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \end{array} \]

Alternative 12
Error	43.86%
Cost	969

\[\begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+25} \lor \neg \left(y \leq 2 \cdot 10^{+35}\right):\\ \;\;\;\;\left(\frac{z}{y} + x\right) - \frac{x \cdot a}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i + b \cdot \left(y \cdot y\right)}\\ \end{array} \]

Alternative 13
Error	36%
Cost	969

\[\begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{+37} \lor \neg \left(y \leq 3.2 \cdot 10^{+35}\right):\\ \;\;\;\;\left(\frac{z}{y} + x\right) - \frac{x \cdot a}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot b\right)}\\ \end{array} \]

Alternative 14
Error	48.78%
Cost	840

\[\begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+21}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+14}:\\ \;\;\;\;\frac{t}{i + b \cdot \left(y \cdot y\right)}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 15
Error	48.28%
Cost	712

\[\begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{-44}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-40}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 16
Error	51.7%
Cost	456

\[\begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{-44}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-40}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 17
Error	73.74%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023121 
(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)))