Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2

Average Error: 29.3 → 10.2

Time: 50.3s

Precision: binary64

Cost: 46280

Math

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

↓

\[\begin{array}{l} t_1 := y \cdot \left(z + y \cdot x\right)\\ t_2 := x + \left(\frac{z}{y} - x \cdot \frac{a}{y}\right)\\ t_3 := c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\\ t_4 := t_3 \cdot t_3\\ \mathbf{if}\;y \leq -4.3 \cdot 10^{+32}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 51000000:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y + a, y, b\right), y, c\right), y, i\right)}\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+81}:\\ \;\;\;\;\frac{t}{y \cdot t_3} + \left(i \cdot \left(\left(230661.510616 \cdot \frac{-1}{y \cdot t_4} + \left(27464.7644705 \cdot \frac{-1}{t_4} - \frac{t_1}{t_4}\right)\right) - \frac{t}{{y}^{2} \cdot t_4}\right) + \frac{230661.510616 + y \cdot \left(27464.7644705 + t_1\right)}{t_3}\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

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 (* y (+ z (* y x))))
        (t_2 (+ x (- (/ z y) (* x (/ a y)))))
        (t_3 (+ c (* y (+ b (* y (+ y a))))))
        (t_4 (* t_3 t_3)))
   (if (<= y -4.3e+32)
     t_2
     (if (<= y 51000000.0)
       (/
        (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 3.3e+81)
         (+
          (/ t (* y t_3))
          (+
           (*
            i
            (-
             (+
              (* 230661.510616 (/ -1.0 (* y t_4)))
              (- (* 27464.7644705 (/ -1.0 t_4)) (/ t_1 t_4)))
             (/ t (* (pow y 2.0) t_4))))
           (/ (+ 230661.510616 (* y (+ 27464.7644705 t_1))) t_3)))
         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 = y * (z + (y * x));
	double t_2 = x + ((z / y) - (x * (a / y)));
	double t_3 = c + (y * (b + (y * (y + a))));
	double t_4 = t_3 * t_3;
	double tmp;
	if (y <= -4.3e+32) {
		tmp = t_2;
	} else if (y <= 51000000.0) {
		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 <= 3.3e+81) {
		tmp = (t / (y * t_3)) + ((i * (((230661.510616 * (-1.0 / (y * t_4))) + ((27464.7644705 * (-1.0 / t_4)) - (t_1 / t_4))) - (t / (pow(y, 2.0) * t_4)))) + ((230661.510616 + (y * (27464.7644705 + t_1))) / t_3));
	} 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(y * Float64(z + Float64(y * x)))
	t_2 = Float64(x + Float64(Float64(z / y) - Float64(x * Float64(a / y))))
	t_3 = Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a)))))
	t_4 = Float64(t_3 * t_3)
	tmp = 0.0
	if (y <= -4.3e+32)
		tmp = t_2;
	elseif (y <= 51000000.0)
		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 <= 3.3e+81)
		tmp = Float64(Float64(t / Float64(y * t_3)) + Float64(Float64(i * Float64(Float64(Float64(230661.510616 * Float64(-1.0 / Float64(y * t_4))) + Float64(Float64(27464.7644705 * Float64(-1.0 / t_4)) - Float64(t_1 / t_4))) - Float64(t / Float64((y ^ 2.0) * t_4)))) + Float64(Float64(230661.510616 + Float64(y * Float64(27464.7644705 + t_1))) / t_3)));
	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[(y * N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(z / y), $MachinePrecision] - N[(x * N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(c + N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$3 * t$95$3), $MachinePrecision]}, If[LessEqual[y, -4.3e+32], t$95$2, If[LessEqual[y, 51000000.0], 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, 3.3e+81], N[(N[(t / N[(y * t$95$3), $MachinePrecision]), $MachinePrecision] + N[(N[(i * N[(N[(N[(230661.510616 * N[(-1.0 / N[(y * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(27464.7644705 * N[(-1.0 / t$95$4), $MachinePrecision]), $MachinePrecision] - N[(t$95$1 / t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t / N[(N[Power[y, 2.0], $MachinePrecision] * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(230661.510616 + N[(y * N[(27464.7644705 + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.2999999999999997e32 or 3.3e81 < y

   1. Initial program 62.2

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

   2. Simplified 62.2

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y + a, y, b\right), y, c\right), y, i\right)}} \]
      Proof
      (/.f64 (fma.f64 (fma.f64 (fma.f64 (fma.f64 x y z) y 54929528941/2000000) y 28832688827/125000) y t) (fma.f64 (fma.f64 (fma.f64 (+.f64 y a) y b) y c) y i)): 0 points increase in error, 0 points decrease in error
      (/.f64 (fma.f64 (fma.f64 (fma.f64 (Rewrite<= fma-def_binary64 (+.f64 (*.f64 x y) z)) y 54929528941/2000000) y 28832688827/125000) y t) (fma.f64 (fma.f64 (fma.f64 (+.f64 y a) y b) y c) y i)): 0 points increase in error, 0 points decrease in error
      (/.f64 (fma.f64 (fma.f64 (Rewrite<= fma-def_binary64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) 54929528941/2000000)) y 28832688827/125000) y t) (fma.f64 (fma.f64 (fma.f64 (+.f64 y a) y b) y c) y i)): 0 points increase in error, 0 points decrease in error
      (/.f64 (fma.f64 (Rewrite<= fma-def_binary64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) 54929528941/2000000) y) 28832688827/125000)) y t) (fma.f64 (fma.f64 (fma.f64 (+.f64 y a) y b) y c) y i)): 0 points increase in error, 0 points decrease in error
      (/.f64 (Rewrite<= fma-def_binary64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) 54929528941/2000000) y) 28832688827/125000) y) t)) (fma.f64 (fma.f64 (fma.f64 (+.f64 y a) y b) y c) y i)): 0 points increase in error, 8 points decrease in error
      (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) 54929528941/2000000) y) 28832688827/125000) y) t) (fma.f64 (fma.f64 (Rewrite<= fma-def_binary64 (+.f64 (*.f64 (+.f64 y a) y) b)) y c) y i)): 0 points increase in error, 0 points decrease in error
      (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) 54929528941/2000000) y) 28832688827/125000) y) t) (fma.f64 (Rewrite<= fma-def_binary64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c)) y i)): 8 points increase in error, 0 points decrease in error
      (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) 54929528941/2000000) y) 28832688827/125000) y) t) (Rewrite<= fma-def_binary64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c) y) i))): 0 points increase in error, 0 points decrease in error

   3. Taylor expanded in y around inf 20.4

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

   4. Simplified 17.4

      \[\leadsto \color{blue}{x + \left(\frac{z}{y} - \frac{a}{y} \cdot x\right)} \]
      Proof
      (+.f64 x (-.f64 (/.f64 z y) (*.f64 (/.f64 a y) x))): 0 points increase in error, 0 points decrease in error
      (+.f64 x (-.f64 (/.f64 z y) (Rewrite<= associate-/r/_binary64 (/.f64 a (/.f64 y x))))): 0 points increase in error, 0 points decrease in error
      (+.f64 x (-.f64 (/.f64 z y) (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 a x) y)))): 5 points increase in error, 0 points decrease in error
      (Rewrite<= associate--l+_binary64 (-.f64 (+.f64 x (/.f64 z y)) (/.f64 (*.f64 a x) y))): 0 points increase in error, 5 points decrease in error
      (-.f64 (Rewrite<= +-commutative_binary64 (+.f64 (/.f64 z y) x)) (/.f64 (*.f64 a x) y)): 5 points increase in error, 0 points decrease in error

   if -4.2999999999999997e32 < y < 5.1e7

   1. Initial program 1.4

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

   2. Simplified 1.4

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y + a, y, b\right), y, c\right), y, i\right)}} \]
      Proof
      (/.f64 (fma.f64 (fma.f64 (fma.f64 (fma.f64 x y z) y 54929528941/2000000) y 28832688827/125000) y t) (fma.f64 (fma.f64 (fma.f64 (+.f64 y a) y b) y c) y i)): 0 points increase in error, 0 points decrease in error
      (/.f64 (fma.f64 (fma.f64 (fma.f64 (Rewrite<= fma-def_binary64 (+.f64 (*.f64 x y) z)) y 54929528941/2000000) y 28832688827/125000) y t) (fma.f64 (fma.f64 (fma.f64 (+.f64 y a) y b) y c) y i)): 0 points increase in error, 0 points decrease in error
      (/.f64 (fma.f64 (fma.f64 (Rewrite<= fma-def_binary64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) 54929528941/2000000)) y 28832688827/125000) y t) (fma.f64 (fma.f64 (fma.f64 (+.f64 y a) y b) y c) y i)): 0 points increase in error, 0 points decrease in error
      (/.f64 (fma.f64 (Rewrite<= fma-def_binary64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) 54929528941/2000000) y) 28832688827/125000)) y t) (fma.f64 (fma.f64 (fma.f64 (+.f64 y a) y b) y c) y i)): 0 points increase in error, 0 points decrease in error
      (/.f64 (Rewrite<= fma-def_binary64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) 54929528941/2000000) y) 28832688827/125000) y) t)) (fma.f64 (fma.f64 (fma.f64 (+.f64 y a) y b) y c) y i)): 0 points increase in error, 8 points decrease in error
      (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) 54929528941/2000000) y) 28832688827/125000) y) t) (fma.f64 (fma.f64 (Rewrite<= fma-def_binary64 (+.f64 (*.f64 (+.f64 y a) y) b)) y c) y i)): 0 points increase in error, 0 points decrease in error
      (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) 54929528941/2000000) y) 28832688827/125000) y) t) (fma.f64 (Rewrite<= fma-def_binary64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c)) y i)): 8 points increase in error, 0 points decrease in error
      (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) 54929528941/2000000) y) 28832688827/125000) y) t) (Rewrite<= fma-def_binary64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c) y) i))): 0 points increase in error, 0 points decrease in error

   if 5.1e7 < y < 3.3e81

   1. Initial program 39.4

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

   2. Taylor expanded in i around 0 34.8

      \[\leadsto \color{blue}{\frac{t}{y \cdot \left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right)} + \left(-1 \cdot \left(i \cdot \left(\frac{t}{{y}^{2} \cdot \left(\left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) \cdot \left(c + \left(b + y \cdot \left(a + y\right)\right) \cdot y\right)\right)} + \left(230661.510616 \cdot \frac{1}{y \cdot \left(\left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) \cdot \left(c + \left(b + y \cdot \left(a + y\right)\right) \cdot y\right)\right)} + \left(27464.7644705 \cdot \frac{1}{\left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) \cdot \left(c + \left(b + y \cdot \left(a + y\right)\right) \cdot y\right)} + \frac{\left(y \cdot x + z\right) \cdot y}{\left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) \cdot \left(c + \left(b + y \cdot \left(a + y\right)\right) \cdot y\right)}\right)\right)\right)\right) + \frac{230661.510616 + y \cdot \left(27464.7644705 + \left(y \cdot x + z\right) \cdot y\right)}{c + y \cdot \left(\left(y + a\right) \cdot y + b\right)}\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 10.2

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.3 \cdot 10^{+32}:\\ \;\;\;\;x + \left(\frac{z}{y} - x \cdot \frac{a}{y}\right)\\ \mathbf{elif}\;y \leq 51000000:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y + a, y, b\right), y, c\right), y, i\right)}\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+81}:\\ \;\;\;\;\frac{t}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)} + \left(i \cdot \left(\left(230661.510616 \cdot \frac{-1}{y \cdot \left(\left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)\right)} + \left(27464.7644705 \cdot \frac{-1}{\left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)} - \frac{y \cdot \left(z + y \cdot x\right)}{\left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\right)\right) - \frac{t}{{y}^{2} \cdot \left(\left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)\right)}\right) + \frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)}{c + y \cdot \left(b + y \cdot \left(y + a\right)\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - x \cdot \frac{a}{y}\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	10.2
Cost	17164

\[\begin{array}{l} t_1 := y \cdot \left(z + y \cdot x\right)\\ t_2 := c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\\ t_3 := y \cdot t_2\\ t_4 := t_2 \cdot t_2\\ t_5 := 230661.510616 + y \cdot \left(27464.7644705 + t_1\right)\\ t_6 := x + \left(\frac{z}{y} - x \cdot \frac{a}{y}\right)\\ \mathbf{if}\;y \leq -4.3 \cdot 10^{+32}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;y \leq 10000000:\\ \;\;\;\;\frac{t + y \cdot t_5}{i + t_3}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+81}:\\ \;\;\;\;\frac{t}{t_3} + \left(i \cdot \left(\left(230661.510616 \cdot \frac{-1}{y \cdot t_4} + \left(27464.7644705 \cdot \frac{-1}{t_4} - \frac{t_1}{t_4}\right)\right) - \frac{t}{{y}^{2} \cdot t_4}\right) + \frac{t_5}{t_2}\right)\\ \mathbf{else}:\\ \;\;\;\;t_6\\ \end{array} \]

Alternative 2
Error	12.7
Cost	2380

\[\begin{array}{l} t_1 := y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)\\ t_2 := x + \left(\frac{z}{y} - x \cdot \frac{a}{y}\right)\\ \mathbf{if}\;y \leq -4 \cdot 10^{+32}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-21}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + z \cdot \left(y \cdot y\right)\right)}{i + t_1}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+59}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{t_1}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 3
Error	13.3
Cost	2380

\[\begin{array}{l} t_1 := y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)\\ t_2 := x + \left(\frac{z}{y} - x \cdot \frac{a}{y}\right)\\ \mathbf{if}\;y \leq -3.8 \cdot 10^{+21}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-25}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + x \cdot \left(y \cdot y\right)\right)\right)}{i + t_1}\\ \mathbf{elif}\;y \leq 3.05 \cdot 10^{+59}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{t_1}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 4
Error	10.3
Cost	2377

\[\begin{array}{l} \mathbf{if}\;y \leq -4.3 \cdot 10^{+32} \lor \neg \left(y \leq 9 \cdot 10^{+58}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - x \cdot \frac{a}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \end{array} \]

Alternative 5
Error	13.2
Cost	1993

\[\begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+29} \lor \neg \left(y \leq 7.5 \cdot 10^{+58}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - x \cdot \frac{a}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \end{array} \]

Alternative 6
Error	13.2
Cost	1993

\[\begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+32} \lor \neg \left(y \leq 1.9 \cdot 10^{+59}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - x \cdot \frac{a}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + z \cdot \left(y \cdot y\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \end{array} \]

Alternative 7
Error	16.2
Cost	1865

\[\begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+21} \lor \neg \left(y \leq 5.8 \cdot 10^{+96}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - x \cdot \frac{a}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \end{array} \]

Alternative 8
Error	14.7
Cost	1865

\[\begin{array}{l} \mathbf{if}\;y \leq -1.22 \cdot 10^{+27} \lor \neg \left(y \leq 1.85 \cdot 10^{+59}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - x \cdot \frac{a}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot y\right)\right)}\\ \end{array} \]

Alternative 9
Error	16.7
Cost	1609

\[\begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+19} \lor \neg \left(y \leq 5.8 \cdot 10^{+96}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - x \cdot \frac{a}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \end{array} \]

Alternative 10
Error	17.8
Cost	1484

\[\begin{array}{l} t_1 := t + y \cdot \left(230661.510616 + y \cdot \left(y \cdot z\right)\right)\\ t_2 := x + \left(\frac{z}{y} - x \cdot \frac{a}{y}\right)\\ \mathbf{if}\;y \leq -1.8 \cdot 10^{+28}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-35}:\\ \;\;\;\;\frac{t_1}{i + b \cdot \left(y \cdot y\right)}\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+58}:\\ \;\;\;\;\frac{t_1}{i + y \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 11
Error	17.6
Cost	1353

\[\begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+17} \lor \neg \left(y \leq 7.5 \cdot 10^{+58}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - x \cdot \frac{a}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(y \cdot z\right)\right)}{i + y \cdot c}\\ \end{array} \]

Alternative 12
Error	23.5
Cost	969

\[\begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{-28} \lor \neg \left(y \leq 7.5 \cdot 10^{+58}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - x \cdot \frac{a}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i + y \cdot c}\\ \end{array} \]

Alternative 13
Error	19.4
Cost	969

\[\begin{array}{l} \mathbf{if}\;y \leq -6600000000000 \lor \neg \left(y \leq 7.5 \cdot 10^{+58}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - x \cdot \frac{a}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot c}\\ \end{array} \]

Alternative 14
Error	33.3
Cost	712

\[\begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{-28}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+111}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \frac{a}{y}\\ \end{array} \]

Alternative 15
Error	27.9
Cost	712

\[\begin{array}{l} \mathbf{if}\;y \leq -170000:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+100}:\\ \;\;\;\;\frac{t}{i + y \cdot c}\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \frac{a}{y}\\ \end{array} \]

Alternative 16
Error	33.3
Cost	456

\[\begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{-28}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+111}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 17
Error	46.7
Cost	64

\[x \]

Reproduce

herbie shell --seed 2022343 
(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)))