Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2

Percentage Accurate: 56.4% → 83.8%

Time: 39.3s

Precision: binary64

Cost: 90568

Math

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

↓

\[\begin{array}{l} t_1 := \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), 27464.7644705\right), 230661.510616\right), t\right)\\ t_2 := \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y + a, y, b\right), y, c\right), y, i\right)}\\ t_3 := \frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + x \cdot y\right)\right)\right)}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)}\\ \mathbf{if}\;t_3 \leq -2 \cdot 10^{-288}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_3 \leq 0:\\ \;\;\;\;\frac{1}{\frac{i}{t_1} + \left(\frac{c}{\frac{t_1}{y}} + \frac{y \cdot y}{\frac{t_1}{\mathsf{fma}\left(y, y + a, b\right)}}\right)}\\ \mathbf{elif}\;t_3 \leq 2 \cdot 10^{+304}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \end{array} \]

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 (fma y (fma y (fma y (fma y x z) 27464.7644705) 230661.510616) t))
        (t_2
         (/
          (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_3
         (/
          (+
           t
           (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ z (* x y))))))))
          (+ i (* y (+ c (* y (+ (* y (+ y a)) b))))))))
   (if (<= t_3 -2e-288)
     t_2
     (if (<= t_3 0.0)
       (/
        1.0
        (+
         (/ i t_1)
         (+ (/ c (/ t_1 y)) (/ (* y y) (/ t_1 (fma y (+ y a) b))))))
       (if (<= t_3 2e+304) t_2 (- (+ x (/ z y)) (/ (* x a) y)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return ((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i);
}

↓

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = fma(y, fma(y, fma(y, fma(y, x, z), 27464.7644705), 230661.510616), t);
	double t_2 = 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);
	double t_3 = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (x * y)))))))) / (i + (y * (c + (y * ((y * (y + a)) + b)))));
	double tmp;
	if (t_3 <= -2e-288) {
		tmp = t_2;
	} else if (t_3 <= 0.0) {
		tmp = 1.0 / ((i / t_1) + ((c / (t_1 / y)) + ((y * y) / (t_1 / fma(y, (y + a), b)))));
	} else if (t_3 <= 2e+304) {
		tmp = t_2;
	} else {
		tmp = (x + (z / y)) - ((x * a) / y);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	return Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / Float64(Float64(Float64(Float64(Float64(Float64(Float64(y + a) * y) + b) * y) + c) * y) + i))
end

↓

function code(x, y, z, t, a, b, c, i)
	t_1 = fma(y, fma(y, fma(y, fma(y, x, z), 27464.7644705), 230661.510616), t)
	t_2 = 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))
	t_3 = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(z + Float64(x * y)))))))) / Float64(i + Float64(y * Float64(c + Float64(y * Float64(Float64(y * Float64(y + a)) + b))))))
	tmp = 0.0
	if (t_3 <= -2e-288)
		tmp = t_2;
	elseif (t_3 <= 0.0)
		tmp = Float64(1.0 / Float64(Float64(i / t_1) + Float64(Float64(c / Float64(t_1 / y)) + Float64(Float64(y * y) / Float64(t_1 / fma(y, Float64(y + a), b))))));
	elseif (t_3 <= 2e+304)
		tmp = t_2;
	else
		tmp = Float64(Float64(x + Float64(z / y)) - Float64(Float64(x * a) / y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(N[(N[(N[(N[(N[(N[(N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision] * y), $MachinePrecision] + 27464.7644705), $MachinePrecision] * y), $MachinePrecision] + 230661.510616), $MachinePrecision] * y), $MachinePrecision] + t), $MachinePrecision] / N[(N[(N[(N[(N[(N[(N[(y + a), $MachinePrecision] * y), $MachinePrecision] + b), $MachinePrecision] * y), $MachinePrecision] + c), $MachinePrecision] * y), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(y * N[(y * N[(y * N[(y * x + z), $MachinePrecision] + 27464.7644705), $MachinePrecision] + 230661.510616), $MachinePrecision] + t), $MachinePrecision]}, Block[{t$95$2 = 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]}, Block[{t$95$3 = N[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * N[(z + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, -2e-288], t$95$2, If[LessEqual[t$95$3, 0.0], N[(1.0 / N[(N[(i / t$95$1), $MachinePrecision] + N[(N[(c / N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision] + N[(N[(y * y), $MachinePrecision] / N[(t$95$1 / N[(y * N[(y + a), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 2e+304], t$95$2, N[(N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(N[(x * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) 54929528941/2000000) y) 28832688827/125000) y) t) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c) y) i)) < -2.00000000000000012e-288 or 0.0 < (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) 54929528941/2000000) y) 28832688827/125000) y) t) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c) y) i)) < 1.9999999999999999e304

   1. Initial program 96.8%

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

   2. Simplified 96.8%

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

      [Start] 96.8%	\[ \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
      fma-def [=>] 96.8%	\[ \frac{\color{blue}{\mathsf{fma}\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616, y, t\right)}}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
      fma-def [=>] 96.8%	\[ \frac{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705, y, 230661.510616\right)}, y, t\right)}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
      fma-def [=>] 96.8%	\[ \frac{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x \cdot y + z, y, 27464.7644705\right)}, y, 230661.510616\right), y, t\right)}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
      fma-def [=>] 96.8%	\[ \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x, y, z\right)}, y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
      fma-def [=>] 96.8%	\[ \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\color{blue}{\mathsf{fma}\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c, y, i\right)}} \]
      fma-def [=>] 96.8%	\[ \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(y + a\right) \cdot y + b, y, c\right)}, y, i\right)} \]
      fma-def [=>] 96.8%	\[ \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(y + a, y, b\right)}, y, c\right), y, i\right)} \]

   if -2.00000000000000012e-288 < (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) 54929528941/2000000) y) 28832688827/125000) y) t) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c) y) i)) < 0.0

   1. Initial program 40.3%

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

   2. Applied egg-rr 40.3%

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

      [Start] 40.3%	\[ \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
      clear-num [=>] 40.3%	\[ \color{blue}{\frac{1}{\frac{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}}} \]
      inv-pow [=>] 40.3%	\[ \color{blue}{{\left(\frac{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}\right)}^{-1}} \]

   3. Simplified 40.3%

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

      [Start] 40.3%	\[ {\left(\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right), 230661.510616\right), t\right)}\right)}^{-1} \]
      unpow-1 [=>] 40.3%	\[ \color{blue}{\frac{1}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right), 230661.510616\right), t\right)}}} \]
      fma-udef [=>] 40.3%	\[ \frac{1}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{x \cdot y + z}, 27464.7644705\right), 230661.510616\right), t\right)}} \]
      *-commutative [<=] 40.3%	\[ \frac{1}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{y \cdot x} + z, 27464.7644705\right), 230661.510616\right), t\right)}} \]
      fma-def [=>] 40.3%	\[ \frac{1}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(y, x, z\right)}, 27464.7644705\right), 230661.510616\right), t\right)}} \]

   4. Taylor expanded in c around inf 39.3%

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

   5. Simplified 94.7%

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

      [Start] 39.3%	\[ \frac{1}{\frac{i}{y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + \left(y \cdot x + z\right) \cdot y\right)\right) + t} + \left(\frac{c \cdot y}{y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + \left(y \cdot x + z\right) \cdot y\right)\right) + t} + \frac{{y}^{2} \cdot \left(\left(y + a\right) \cdot y + b\right)}{y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + \left(y \cdot x + z\right) \cdot y\right)\right) + t}\right)} \]
      fma-def [=>] 39.3%	\[ \frac{1}{\frac{i}{\color{blue}{\mathsf{fma}\left(y, 230661.510616 + y \cdot \left(27464.7644705 + \left(y \cdot x + z\right) \cdot y\right), t\right)}} + \left(\frac{c \cdot y}{y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + \left(y \cdot x + z\right) \cdot y\right)\right) + t} + \frac{{y}^{2} \cdot \left(\left(y + a\right) \cdot y + b\right)}{y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + \left(y \cdot x + z\right) \cdot y\right)\right) + t}\right)} \]
      fma-def [=>] 39.3%	\[ \frac{1}{\frac{i}{\mathsf{fma}\left(y, 230661.510616 + y \cdot \left(27464.7644705 + \color{blue}{\mathsf{fma}\left(y, x, z\right)} \cdot y\right), t\right)} + \left(\frac{c \cdot y}{y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + \left(y \cdot x + z\right) \cdot y\right)\right) + t} + \frac{{y}^{2} \cdot \left(\left(y + a\right) \cdot y + b\right)}{y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + \left(y \cdot x + z\right) \cdot y\right)\right) + t}\right)} \]
      *-commutative [<=] 39.3%	\[ \frac{1}{\frac{i}{\mathsf{fma}\left(y, 230661.510616 + y \cdot \left(27464.7644705 + \color{blue}{y \cdot \mathsf{fma}\left(y, x, z\right)}\right), t\right)} + \left(\frac{c \cdot y}{y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + \left(y \cdot x + z\right) \cdot y\right)\right) + t} + \frac{{y}^{2} \cdot \left(\left(y + a\right) \cdot y + b\right)}{y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + \left(y \cdot x + z\right) \cdot y\right)\right) + t}\right)} \]
      +-commutative [<=] 39.3%	\[ \frac{1}{\frac{i}{\mathsf{fma}\left(y, 230661.510616 + y \cdot \color{blue}{\left(y \cdot \mathsf{fma}\left(y, x, z\right) + 27464.7644705\right)}, t\right)} + \left(\frac{c \cdot y}{y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + \left(y \cdot x + z\right) \cdot y\right)\right) + t} + \frac{{y}^{2} \cdot \left(\left(y + a\right) \cdot y + b\right)}{y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + \left(y \cdot x + z\right) \cdot y\right)\right) + t}\right)} \]
      fma-def [=>] 39.3%	\[ \frac{1}{\frac{i}{\mathsf{fma}\left(y, 230661.510616 + y \cdot \color{blue}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), 27464.7644705\right)}, t\right)} + \left(\frac{c \cdot y}{y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + \left(y \cdot x + z\right) \cdot y\right)\right) + t} + \frac{{y}^{2} \cdot \left(\left(y + a\right) \cdot y + b\right)}{y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + \left(y \cdot x + z\right) \cdot y\right)\right) + t}\right)} \]
      +-commutative [<=] 39.3%	\[ \frac{1}{\frac{i}{\mathsf{fma}\left(y, \color{blue}{y \cdot \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), 27464.7644705\right) + 230661.510616}, t\right)} + \left(\frac{c \cdot y}{y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + \left(y \cdot x + z\right) \cdot y\right)\right) + t} + \frac{{y}^{2} \cdot \left(\left(y + a\right) \cdot y + b\right)}{y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + \left(y \cdot x + z\right) \cdot y\right)\right) + t}\right)} \]
      fma-def [=>] 39.3%	\[ \frac{1}{\frac{i}{\mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), 27464.7644705\right), 230661.510616\right)}, t\right)} + \left(\frac{c \cdot y}{y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + \left(y \cdot x + z\right) \cdot y\right)\right) + t} + \frac{{y}^{2} \cdot \left(\left(y + a\right) \cdot y + b\right)}{y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + \left(y \cdot x + z\right) \cdot y\right)\right) + t}\right)} \]

   if 1.9999999999999999e304 < (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) 54929528941/2000000) y) 28832688827/125000) y) t) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c) y) i))

   1. Initial program 1.3%

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

   2. Taylor expanded in y around inf 72.3%

      \[\leadsto \color{blue}{\left(\frac{z}{y} + x\right) - \frac{a \cdot x}{y}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 87.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + x \cdot y\right)\right)\right)}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)} \leq -2 \cdot 10^{-288}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y + a, y, b\right), y, c\right), y, i\right)}\\ \mathbf{elif}\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + x \cdot y\right)\right)\right)}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)} \leq 0:\\ \;\;\;\;\frac{1}{\frac{i}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), 27464.7644705\right), 230661.510616\right), t\right)} + \left(\frac{c}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), 27464.7644705\right), 230661.510616\right), t\right)}{y}} + \frac{y \cdot y}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), 27464.7644705\right), 230661.510616\right), t\right)}{\mathsf{fma}\left(y, y + a, b\right)}}\right)}\\ \mathbf{elif}\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + x \cdot y\right)\right)\right)}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)} \leq 2 \cdot 10^{+304}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y + a, y, b\right), y, c\right), y, i\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	83.8%
Cost	90568

\[\begin{array}{l} t_1 := \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), 27464.7644705\right), 230661.510616\right), t\right)\\ t_2 := \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y + a, y, b\right), y, c\right), y, i\right)}\\ t_3 := \frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + x \cdot y\right)\right)\right)}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)}\\ \mathbf{if}\;t_3 \leq -2 \cdot 10^{-288}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_3 \leq 0:\\ \;\;\;\;\frac{1}{\frac{i}{t_1} + \left(\frac{c}{\frac{t_1}{y}} + \frac{y \cdot y}{\frac{t_1}{\mathsf{fma}\left(y, y + a, b\right)}}\right)}\\ \mathbf{elif}\;t_3 \leq 2 \cdot 10^{+304}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \end{array} \]

Alternative 2
Accuracy	82.1%
Cost	46412

\[\begin{array}{l} t_1 := x \cdot \left(y \cdot y\right)\\ t_2 := \left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{if}\;y \leq -2.2 \cdot 10^{+63}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{+25}:\\ \;\;\;\;\frac{1}{\left(\frac{a}{x \cdot y} + \left(\frac{1}{x} + \frac{b}{t_1}\right)\right) + \left(\frac{\frac{z}{x \cdot x} - \frac{a}{x}}{\frac{t_1}{z}} - \left(\frac{z}{y \cdot \left(x \cdot x\right)} + \frac{27464.7644705}{\left(y \cdot y\right) \cdot \left(x \cdot x\right)}\right)\right)}\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+71}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y + a, y, b\right), y, c\right), y, i\right)}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 3
Accuracy	81.3%
Cost	5316

\[\begin{array}{l} t_1 := i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)\\ t_2 := y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + x \cdot y\right)\right)\right)\\ \mathbf{if}\;\frac{t + t_2}{t_1} \leq 2 \cdot 10^{+304}:\\ \;\;\;\;\frac{t}{t_1} + \frac{t_2}{t_1}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \end{array} \]

Alternative 4
Accuracy	81.3%
Cost	4292

\[\begin{array}{l} t_1 := \frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + x \cdot y\right)\right)\right)}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)}\\ \mathbf{if}\;t_1 \leq 2 \cdot 10^{+304}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \end{array} \]

Alternative 5
Accuracy	82.1%
Cost	3784

\[\begin{array}{l} t_1 := x \cdot \left(y \cdot y\right)\\ t_2 := i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)\\ t_3 := \left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{if}\;y \leq -3.1 \cdot 10^{+63}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{+25}:\\ \;\;\;\;\frac{1}{\left(\frac{a}{x \cdot y} + \left(\frac{1}{x} + \frac{b}{t_1}\right)\right) + \left(\frac{\frac{z}{x \cdot x} - \frac{a}{x}}{\frac{t_1}{z}} - \left(\frac{z}{y \cdot \left(x \cdot x\right)} + \frac{27464.7644705}{\left(y \cdot y\right) \cdot \left(x \cdot x\right)}\right)\right)}\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+71}:\\ \;\;\;\;\frac{t}{t_2} + \frac{y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + x \cdot y\right)\right)\right)}{t_2}\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 6
Accuracy	78.1%
Cost	2380

\[\begin{array}{l} t_1 := \left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{if}\;y \leq -5.5 \cdot 10^{+63}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{+25}:\\ \;\;\;\;\frac{1}{\frac{a}{x \cdot y} + \left(\frac{1}{x} - \frac{z}{y \cdot \left(x \cdot x\right)}\right)}\\ \mathbf{elif}\;y \leq 10^{+34}:\\ \;\;\;\;\frac{1}{\frac{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)}{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 7
Accuracy	65.0%
Cost	2268

\[\begin{array}{l} t_1 := 230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + x \cdot y\right)\right)\\ t_2 := \left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ t_3 := \frac{\frac{t}{c}}{y} + \frac{t_1}{c}\\ t_4 := \frac{t}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)}\\ \mathbf{if}\;y \leq -1.05 \cdot 10^{+64}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{+30}:\\ \;\;\;\;\frac{1}{\frac{a}{x \cdot y} + \left(\frac{1}{x} - \frac{z}{y \cdot \left(x \cdot x\right)}\right)}\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{-7}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-198}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{-17}:\\ \;\;\;\;\frac{t + y \cdot t_1}{i}\\ \mathbf{elif}\;y \leq 190000:\\ \;\;\;\;t_4 + \frac{230661.510616}{c}\\ \mathbf{elif}\;y \leq 7.4 \cdot 10^{+35}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 8
Accuracy	74.0%
Cost	2128

\[\begin{array}{l} t_1 := i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)\\ t_2 := \left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{if}\;y \leq -9 \cdot 10^{+63}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -5.3 \cdot 10^{+28}:\\ \;\;\;\;\frac{1}{\frac{a}{x \cdot y} + \left(\frac{1}{x} - \frac{z}{y \cdot \left(x \cdot x\right)}\right)}\\ \mathbf{elif}\;y \leq -0.062:\\ \;\;\;\;\frac{t}{t_1} + \frac{y \cdot y}{\frac{c}{z}}\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+64}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{t_1}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 9
Accuracy	77.8%
Cost	2124

\[\begin{array}{l} t_1 := \left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{if}\;y \leq -6.4 \cdot 10^{+63}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -8 \cdot 10^{+24}:\\ \;\;\;\;\frac{1}{\frac{a}{x \cdot y} + \left(\frac{1}{x} - \frac{z}{y \cdot \left(x \cdot x\right)}\right)}\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{+32}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + z \cdot \left(y \cdot y\right)\right)}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 10
Accuracy	73.8%
Cost	2004

\[\begin{array}{l} t_1 := \frac{\frac{t}{c}}{y} + \frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + x \cdot y\right)\right)}{c}\\ t_2 := \left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{if}\;y \leq -2.4 \cdot 10^{+63}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -4.9 \cdot 10^{+35}:\\ \;\;\;\;\frac{1}{\frac{a}{x \cdot y} + \left(\frac{1}{x} - \frac{z}{y \cdot \left(x \cdot x\right)}\right)}\\ \mathbf{elif}\;y \leq -0.04:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 115000:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)}\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+35}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 11
Accuracy	73.7%
Cost	2004

\[\begin{array}{l} t_1 := i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)\\ t_2 := \left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{if}\;y \leq -1.6 \cdot 10^{+63}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{+29}:\\ \;\;\;\;\frac{1}{\frac{a}{x \cdot y} + \left(\frac{1}{x} - \frac{z}{y \cdot \left(x \cdot x\right)}\right)}\\ \mathbf{elif}\;y \leq -0.0245:\\ \;\;\;\;\frac{t}{t_1} + \frac{y \cdot y}{\frac{c}{z}}\\ \mathbf{elif}\;y \leq 122000:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{t_1}\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+36}:\\ \;\;\;\;\frac{\frac{t}{c}}{y} + \frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + x \cdot y\right)\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 12
Accuracy	64.2%
Cost	1876

\[\begin{array}{l} t_1 := 230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + x \cdot y\right)\right)\\ t_2 := \left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{if}\;y \leq -7.6 \cdot 10^{+63}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{+28}:\\ \;\;\;\;\frac{1}{\frac{a}{x \cdot y} + \left(\frac{1}{x} - \frac{z}{y \cdot \left(x \cdot x\right)}\right)}\\ \mathbf{elif}\;y \leq -0.065:\\ \;\;\;\;\frac{t_1}{c} + \frac{t}{i}\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{-199}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)}\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-15}:\\ \;\;\;\;\frac{t + y \cdot t_1}{i}\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+28}:\\ \;\;\;\;\frac{t}{b \cdot \left(y \cdot y\right)} + \frac{230661.510616 + y \cdot 27464.7644705}{c}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 13
Accuracy	66.2%
Cost	1616

\[\begin{array}{l} t_1 := \left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{if}\;y \leq -4.4 \cdot 10^{+63}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -5.6 \cdot 10^{+27}:\\ \;\;\;\;\frac{1}{\frac{a}{x \cdot y} + \left(\frac{1}{x} - \frac{z}{y \cdot \left(x \cdot x\right)}\right)}\\ \mathbf{elif}\;y \leq -0.065:\\ \;\;\;\;\frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + x \cdot y\right)\right)}{c} + \frac{t}{i}\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+53}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 14
Accuracy	52.0%
Cost	1360

\[\begin{array}{l} t_1 := \frac{230661.510616 + y \cdot 27464.7644705}{c} + \frac{t}{y \cdot c}\\ t_2 := \left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{if}\;y \leq -2.4 \cdot 10^{+21}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{-200}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-128}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+28}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 15
Accuracy	66.3%
Cost	1353

\[\begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+21} \lor \neg \left(y \leq 3.8 \cdot 10^{+51}\right):\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)}\\ \end{array} \]

Alternative 16
Accuracy	55.2%
Cost	969

\[\begin{array}{l} \mathbf{if}\;y \leq -6.4 \cdot 10^{+19} \lor \neg \left(y \leq 1.8 \cdot 10^{-15}\right):\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i}\\ \end{array} \]

Alternative 17
Accuracy	50.2%
Cost	456

\[\begin{array}{l} \mathbf{if}\;y \leq -5.6 \cdot 10^{+27}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 34000:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 18
Accuracy	24.8%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023272 
(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)))