Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2

Average Error: 28.9 → 12.1

Time: 46.0s

Precision: binary64

Cost: 2376

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+61}:\\ \;\;\;\;\frac{y}{\frac{y}{x} + \left(\frac{a}{x} - \frac{z}{x \cdot x}\right)}\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+40}:\\ \;\;\;\;\frac{y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right) + t}{i + y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]

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
 (if (<= y -1.25e+61)
   (/ y (+ (/ y x) (- (/ a x) (/ z (* x x)))))
   (if (<= y 8e+40)
     (/
      (+ (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ z (* y x))))))) t)
      (+ i (* y (+ (* y (+ (* y (+ y a)) b)) c))))
     (+ (/ z y) (- x (/ a (/ y x)))))))

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 tmp;
	if (y <= -1.25e+61) {
		tmp = y / ((y / x) + ((a / x) - (z / (x * x))));
	} else if (y <= 8e+40) {
		tmp = ((y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x))))))) + t) / (i + (y * ((y * ((y * (y + a)) + b)) + c)));
	} else {
		tmp = (z / y) + (x - (a / (y / x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    code = ((((((((x * y) + z) * y) + 27464.7644705d0) * y) + 230661.510616d0) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i)
end function

↓

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= (-1.25d+61)) then
        tmp = y / ((y / x) + ((a / x) - (z / (x * x))))
    else if (y <= 8d+40) then
        tmp = ((y * (230661.510616d0 + (y * (27464.7644705d0 + (y * (z + (y * x))))))) + t) / (i + (y * ((y * ((y * (y + a)) + b)) + c)))
    else
        tmp = (z / y) + (x - (a / (y / x)))
    end if
    code = tmp
end function

Java

public static 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);
}

↓

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -1.25e+61) {
		tmp = y / ((y / x) + ((a / x) - (z / (x * x))));
	} else if (y <= 8e+40) {
		tmp = ((y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x))))))) + t) / (i + (y * ((y * ((y * (y + a)) + b)) + c)));
	} else {
		tmp = (z / y) + (x - (a / (y / x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	return ((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i)

↓

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -1.25e+61:
		tmp = y / ((y / x) + ((a / x) - (z / (x * x))))
	elif y <= 8e+40:
		tmp = ((y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x))))))) + t) / (i + (y * ((y * ((y * (y + a)) + b)) + c)))
	else:
		tmp = (z / y) + (x - (a / (y / x)))
	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)
	tmp = 0.0
	if (y <= -1.25e+61)
		tmp = Float64(y / Float64(Float64(y / x) + Float64(Float64(a / x) - Float64(z / Float64(x * x)))));
	elseif (y <= 8e+40)
		tmp = Float64(Float64(Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(z + Float64(y * x))))))) + t) / Float64(i + Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c))));
	else
		tmp = Float64(Float64(z / y) + Float64(x - Float64(a / Float64(y / x))));
	end
	return tmp
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i)
	tmp = ((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i);
end

↓

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -1.25e+61)
		tmp = y / ((y / x) + ((a / x) - (z / (x * x))));
	elseif (y <= 8e+40)
		tmp = ((y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x))))))) + t) / (i + (y * ((y * ((y * (y + a)) + b)) + c)));
	else
		tmp = (z / y) + (x - (a / (y / x)));
	end
	tmp_2 = 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_] := If[LessEqual[y, -1.25e+61], N[(y / N[(N[(y / x), $MachinePrecision] + N[(N[(a / x), $MachinePrecision] - N[(z / N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8e+40], N[(N[(N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision] / N[(i + N[(y * N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z / y), $MachinePrecision] + N[(x - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.25000000000000004e61

   1. Initial program 63.0

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

   2. Taylor expanded in t around 0 63.1

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

   3. Simplified 62.5

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

      [Start] 63.1	\[ \frac{\left(230661.510616 + y \cdot \left(27464.7644705 + \left(y \cdot x + z\right) \cdot y\right)\right) \cdot y}{y \cdot \left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) + i} \]
      *-commutative [<=] 63.1	\[ \frac{\color{blue}{y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + \left(y \cdot x + z\right) \cdot y\right)\right)}}{y \cdot \left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) + i} \]
      associate-/l* [=>] 62.5	\[ \color{blue}{\frac{y}{\frac{y \cdot \left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) + i}{230661.510616 + y \cdot \left(27464.7644705 + \left(y \cdot x + z\right) \cdot y\right)}}} \]
      fma-def [=>] 62.5	\[ \frac{y}{\frac{\color{blue}{\mathsf{fma}\left(y, c + y \cdot \left(\left(y + a\right) \cdot y + b\right), i\right)}}{230661.510616 + y \cdot \left(27464.7644705 + \left(y \cdot x + z\right) \cdot y\right)}} \]
      +-commutative [=>] 62.5	\[ \frac{y}{\frac{\mathsf{fma}\left(y, \color{blue}{y \cdot \left(\left(y + a\right) \cdot y + b\right) + c}, i\right)}{230661.510616 + y \cdot \left(27464.7644705 + \left(y \cdot x + z\right) \cdot y\right)}} \]
      *-commutative [=>] 62.5	\[ \frac{y}{\frac{\mathsf{fma}\left(y, \color{blue}{\left(\left(y + a\right) \cdot y + b\right) \cdot y} + c, i\right)}{230661.510616 + y \cdot \left(27464.7644705 + \left(y \cdot x + z\right) \cdot y\right)}} \]
      fma-udef [<=] 62.5	\[ \frac{y}{\frac{\mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(\left(y + a\right) \cdot y + b, y, c\right)}, i\right)}{230661.510616 + y \cdot \left(27464.7644705 + \left(y \cdot x + z\right) \cdot y\right)}} \]
      fma-def [=>] 62.5	\[ \frac{y}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(y + a, y, b\right)}, y, c\right), i\right)}{230661.510616 + y \cdot \left(27464.7644705 + \left(y \cdot x + z\right) \cdot y\right)}} \]
      +-commutative [=>] 62.5	\[ \frac{y}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(\mathsf{fma}\left(y + a, y, b\right), y, c\right), i\right)}{\color{blue}{y \cdot \left(27464.7644705 + \left(y \cdot x + z\right) \cdot y\right) + 230661.510616}}} \]

   4. Taylor expanded in y around inf 27.1

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

   5. Simplified 27.1

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

      [Start] 27.1	\[ \frac{y}{\left(\frac{y}{x} + \frac{a}{x}\right) - \frac{z}{{x}^{2}}} \]
      associate--l+ [=>] 27.1	\[ \frac{y}{\color{blue}{\frac{y}{x} + \left(\frac{a}{x} - \frac{z}{{x}^{2}}\right)}} \]
      unpow2 [=>] 27.1	\[ \frac{y}{\frac{y}{x} + \left(\frac{a}{x} - \frac{z}{\color{blue}{x \cdot x}}\right)} \]

   if -1.25000000000000004e61 < y < 8.00000000000000024e40

   1. Initial program 4.2

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

   if 8.00000000000000024e40 < y

   1. Initial program 61.5

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

   2. Taylor expanded in t around 0 61.9

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

   3. Simplified 60.7

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

      [Start] 61.9	\[ \frac{\left(230661.510616 + y \cdot \left(27464.7644705 + \left(y \cdot x + z\right) \cdot y\right)\right) \cdot y}{y \cdot \left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) + i} \]
      *-commutative [<=] 61.9	\[ \frac{\color{blue}{y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + \left(y \cdot x + z\right) \cdot y\right)\right)}}{y \cdot \left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) + i} \]
      associate-/l* [=>] 60.7	\[ \color{blue}{\frac{y}{\frac{y \cdot \left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) + i}{230661.510616 + y \cdot \left(27464.7644705 + \left(y \cdot x + z\right) \cdot y\right)}}} \]
      fma-def [=>] 60.7	\[ \frac{y}{\frac{\color{blue}{\mathsf{fma}\left(y, c + y \cdot \left(\left(y + a\right) \cdot y + b\right), i\right)}}{230661.510616 + y \cdot \left(27464.7644705 + \left(y \cdot x + z\right) \cdot y\right)}} \]
      +-commutative [=>] 60.7	\[ \frac{y}{\frac{\mathsf{fma}\left(y, \color{blue}{y \cdot \left(\left(y + a\right) \cdot y + b\right) + c}, i\right)}{230661.510616 + y \cdot \left(27464.7644705 + \left(y \cdot x + z\right) \cdot y\right)}} \]
      *-commutative [=>] 60.7	\[ \frac{y}{\frac{\mathsf{fma}\left(y, \color{blue}{\left(\left(y + a\right) \cdot y + b\right) \cdot y} + c, i\right)}{230661.510616 + y \cdot \left(27464.7644705 + \left(y \cdot x + z\right) \cdot y\right)}} \]
      fma-udef [<=] 60.7	\[ \frac{y}{\frac{\mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(\left(y + a\right) \cdot y + b, y, c\right)}, i\right)}{230661.510616 + y \cdot \left(27464.7644705 + \left(y \cdot x + z\right) \cdot y\right)}} \]
      fma-def [=>] 60.7	\[ \frac{y}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(y + a, y, b\right)}, y, c\right), i\right)}{230661.510616 + y \cdot \left(27464.7644705 + \left(y \cdot x + z\right) \cdot y\right)}} \]
      +-commutative [=>] 60.7	\[ \frac{y}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(\mathsf{fma}\left(y + a, y, b\right), y, c\right), i\right)}{\color{blue}{y \cdot \left(27464.7644705 + \left(y \cdot x + z\right) \cdot y\right) + 230661.510616}}} \]

   4. Taylor expanded in y around inf 21.3

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

   5. Simplified 18.8

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

      [Start] 21.3	\[ \left(\frac{z}{y} + x\right) - \frac{a \cdot x}{y} \]
      associate--l+ [=>] 21.3	\[ \color{blue}{\frac{z}{y} + \left(x - \frac{a \cdot x}{y}\right)} \]
      associate-/l* [=>] 18.8	\[ \frac{z}{y} + \left(x - \color{blue}{\frac{a}{\frac{y}{x}}}\right) \]

3. Recombined 3 regimes into one program.

4. Final simplification 12.1

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+61}:\\ \;\;\;\;\frac{y}{\frac{y}{x} + \left(\frac{a}{x} - \frac{z}{x \cdot x}\right)}\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+40}:\\ \;\;\;\;\frac{y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right) + t}{i + y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	14.2
Cost	2512

\[\begin{array}{l} t_1 := i + y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right)\\ t_2 := \frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + x \cdot \left(y \cdot y\right)\right)\right)}{t_1}\\ \mathbf{if}\;y \leq -7 \cdot 10^{+60}:\\ \;\;\;\;\frac{y}{\frac{y}{x} + \left(\frac{a}{x} - \frac{z}{x \cdot x}\right)}\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-20}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 10^{-34}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(y \cdot z\right)\right)}{t_1}\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{+40}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]

Alternative 2
Error	14.2
Cost	2512

\[\begin{array}{l} t_1 := i + y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right)\\ \mathbf{if}\;y \leq -7.2 \cdot 10^{+60}:\\ \;\;\;\;\frac{y}{\frac{y}{x} + \left(\frac{a}{x} - \frac{z}{x \cdot x}\right)}\\ \mathbf{elif}\;y \leq -1 \cdot 10^{-21}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + x \cdot \left(y \cdot y\right)\right)\right)}{t_1}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-37}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(y \cdot z\right)\right)}{t_1}\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+42}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(y \cdot x\right)\right)\right)}{t_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]

Alternative 3
Error	14.5
Cost	2124

\[\begin{array}{l} t_1 := y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\\ \mathbf{if}\;y \leq -7.4 \cdot 10^{+50}:\\ \;\;\;\;\frac{y}{\frac{y}{x} + \left(\frac{a}{x} - \frac{z}{x \cdot x}\right)}\\ \mathbf{elif}\;y \leq -4.4 \cdot 10^{-20}:\\ \;\;\;\;\frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)}{t_1}\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{+21}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(y \cdot z\right)\right)}{i + y \cdot t_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]

Alternative 4
Error	16.8
Cost	1996

\[\begin{array}{l} t_1 := y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\\ \mathbf{if}\;y \leq -1.3 \cdot 10^{+50}:\\ \;\;\;\;\frac{y}{\frac{y}{x} + \left(\frac{a}{x} - \frac{z}{x \cdot x}\right)}\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{-40}:\\ \;\;\;\;\frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)}{t_1}\\ \mathbf{elif}\;y \leq 21000000:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{i + y \cdot t_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]

Alternative 5
Error	16.9
Cost	1864

\[\begin{array}{l} t_1 := y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\\ \mathbf{if}\;y \leq -2.7 \cdot 10^{+50}:\\ \;\;\;\;\frac{y}{\frac{y}{x} + \left(\frac{a}{x} - \frac{z}{x \cdot x}\right)}\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{-40}:\\ \;\;\;\;\frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)}{t_1}\\ \mathbf{elif}\;y \leq 21000000:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot t_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]

Alternative 6
Error	17.7
Cost	1608

\[\begin{array}{l} \mathbf{if}\;y \leq -9.4 \cdot 10^{-20}:\\ \;\;\;\;\frac{y}{\frac{y}{x} + \left(\frac{a}{x} - \frac{z}{x \cdot x}\right)}\\ \mathbf{elif}\;y \leq 16500000:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]

Alternative 7
Error	19.9
Cost	1484

\[\begin{array}{l} t_1 := t + y \cdot \left(230661.510616 + y \cdot \left(y \cdot z\right)\right)\\ \mathbf{if}\;y \leq -9.4 \cdot 10^{-20}:\\ \;\;\;\;\frac{y}{\frac{y}{x} + \left(\frac{a}{x} - \frac{z}{x \cdot x}\right)}\\ \mathbf{elif}\;y \leq -1.78 \cdot 10^{-109}:\\ \;\;\;\;\frac{t_1}{i + b \cdot \left(y \cdot y\right)}\\ \mathbf{elif}\;y \leq 270000000:\\ \;\;\;\;\frac{t_1}{i + y \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]

Alternative 8
Error	22.4
Cost	1352

\[\begin{array}{l} \mathbf{if}\;y \leq -9.4 \cdot 10^{-20}:\\ \;\;\;\;\frac{y}{\frac{y}{x} + \left(\frac{a}{x} - \frac{z}{x \cdot x}\right)}\\ \mathbf{elif}\;y \leq 21000000:\\ \;\;\;\;\frac{t}{i + y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]

Alternative 9
Error	19.4
Cost	1352

\[\begin{array}{l} \mathbf{if}\;y \leq -9.4 \cdot 10^{-20}:\\ \;\;\;\;\frac{y}{\frac{y}{x} + \left(\frac{a}{x} - \frac{z}{x \cdot x}\right)}\\ \mathbf{elif}\;y \leq 260000000:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(y \cdot z\right)\right)}{i + y \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]

Alternative 10
Error	27.2
Cost	1232

\[\begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+15}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{x}{\frac{y}{a}}\right)\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-83}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-40}:\\ \;\;\;\;\frac{y}{\frac{i}{230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)}}\\ \mathbf{elif}\;y \leq 25000:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]

Alternative 11
Error	29.1
Cost	1232

\[\begin{array}{l} \mathbf{if}\;y \leq -2.25 \cdot 10^{-35}:\\ \;\;\;\;\frac{y}{\frac{y}{x} + \left(\frac{a}{x} - \frac{z}{x \cdot x}\right)}\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-82}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-37}:\\ \;\;\;\;\frac{y}{\frac{i}{230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)}}\\ \mathbf{elif}\;y \leq 17000:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]

Alternative 12
Error	27.1
Cost	969

\[\begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+18} \lor \neg \left(y \leq 24000\right):\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{x}{\frac{y}{a}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i}\\ \end{array} \]

Alternative 13
Error	27.1
Cost	968

\[\begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+16}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{x}{\frac{y}{a}}\right)\\ \mathbf{elif}\;y \leq 25500:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]

Alternative 14
Error	46.3
Cost	456

\[\begin{array}{l} \mathbf{if}\;y \leq -1.22 \cdot 10^{-95}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-80}:\\ \;\;\;\;\frac{230661.510616}{c}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 15
Error	31.7
Cost	456

\[\begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+21}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 580:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 16
Error	47.3
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023055 
(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)))