Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2

Average Error: 29.4 → 10.1

Time: 59.0s

Precision: binary64

Cost: 3400

Math

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

↓

\[\begin{array}{l} t_1 := y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right) + i\\ t_2 := x + \left(\frac{z}{y} + \frac{27464.7644705}{y \cdot y}\right)\\ \mathbf{if}\;y \leq -2.9144796754912003 \cdot 10^{+40}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 2.955388695141755 \cdot 10^{+36}:\\ \;\;\;\;\frac{t}{t_1} + \frac{y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{t_1}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

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 (+ c (* y (+ (* y (+ y a)) b)))) i))
        (t_2 (+ x (+ (/ z y) (/ 27464.7644705 (* y y))))))
   (if (<= y -2.9144796754912003e+40)
     t_2
     (if (<= y 2.955388695141755e+36)
       (+
        (/ t t_1)
        (/
         (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ z (* y x)))))))
         t_1))
       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 * (c + (y * ((y * (y + a)) + b)))) + i;
	double t_2 = x + ((z / y) + (27464.7644705 / (y * y)));
	double tmp;
	if (y <= -2.9144796754912003e+40) {
		tmp = t_2;
	} else if (y <= 2.955388695141755e+36) {
		tmp = (t / t_1) + ((y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x))))))) / t_1);
	} else {
		tmp = t_2;
	}
	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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (y * (c + (y * ((y * (y + a)) + b)))) + i
    t_2 = x + ((z / y) + (27464.7644705d0 / (y * y)))
    if (y <= (-2.9144796754912003d+40)) then
        tmp = t_2
    else if (y <= 2.955388695141755d+36) then
        tmp = (t / t_1) + ((y * (230661.510616d0 + (y * (27464.7644705d0 + (y * (z + (y * x))))))) / t_1)
    else
        tmp = t_2
    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 t_1 = (y * (c + (y * ((y * (y + a)) + b)))) + i;
	double t_2 = x + ((z / y) + (27464.7644705 / (y * y)));
	double tmp;
	if (y <= -2.9144796754912003e+40) {
		tmp = t_2;
	} else if (y <= 2.955388695141755e+36) {
		tmp = (t / t_1) + ((y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x))))))) / t_1);
	} else {
		tmp = t_2;
	}
	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):
	t_1 = (y * (c + (y * ((y * (y + a)) + b)))) + i
	t_2 = x + ((z / y) + (27464.7644705 / (y * y)))
	tmp = 0
	if y <= -2.9144796754912003e+40:
		tmp = t_2
	elif y <= 2.955388695141755e+36:
		tmp = (t / t_1) + ((y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x))))))) / t_1)
	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(Float64(y * Float64(c + Float64(y * Float64(Float64(y * Float64(y + a)) + b)))) + i)
	t_2 = Float64(x + Float64(Float64(z / y) + Float64(27464.7644705 / Float64(y * y))))
	tmp = 0.0
	if (y <= -2.9144796754912003e+40)
		tmp = t_2;
	elseif (y <= 2.955388695141755e+36)
		tmp = Float64(Float64(t / t_1) + Float64(Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(z + Float64(y * x))))))) / t_1));
	else
		tmp = t_2;
	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)
	t_1 = (y * (c + (y * ((y * (y + a)) + b)))) + i;
	t_2 = x + ((z / y) + (27464.7644705 / (y * y)));
	tmp = 0.0;
	if (y <= -2.9144796754912003e+40)
		tmp = t_2;
	elseif (y <= 2.955388695141755e+36)
		tmp = (t / t_1) + ((y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x))))))) / t_1);
	else
		tmp = t_2;
	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_] := Block[{t$95$1 = N[(N[(y * N[(c + N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(z / y), $MachinePrecision] + N[(27464.7644705 / N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.9144796754912003e+40], t$95$2, If[LessEqual[y, 2.955388695141755e+36], N[(N[(t / t$95$1), $MachinePrecision] + 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$95$1), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.91447967549120032e40 or 2.9553886951417548e36 < y

   1. Initial program 61.6

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

   2. Taylor expanded in y around inf 62.3

      \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\color{blue}{{y}^{3}} + c\right) \cdot y + i} \]

   3. Taylor expanded in y around inf 18.8

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

   4. Simplified 18.8

      \[\leadsto \color{blue}{x + \left(\frac{z}{y} + \frac{27464.7644705}{y \cdot y}\right)} \]
      Proof
      (+.f64 x (+.f64 (/.f64 z y) (/.f64 54929528941/2000000 (*.f64 y y)))): 0 points increase in error, 0 points decrease in error
      (+.f64 x (+.f64 (/.f64 z y) (/.f64 (Rewrite<= metadata-eval (*.f64 54929528941/2000000 1)) (*.f64 y y)))): 0 points increase in error, 0 points decrease in error
      (+.f64 x (+.f64 (/.f64 z y) (/.f64 (*.f64 54929528941/2000000 1) (Rewrite<= unpow2_binary64 (pow.f64 y 2))))): 0 points increase in error, 0 points decrease in error
      (+.f64 x (+.f64 (/.f64 z y) (Rewrite<= associate-*r/_binary64 (*.f64 54929528941/2000000 (/.f64 1 (pow.f64 y 2)))))): 8 points increase in error, 2 points decrease in error
      (Rewrite<= +-commutative_binary64 (+.f64 (+.f64 (/.f64 z y) (*.f64 54929528941/2000000 (/.f64 1 (pow.f64 y 2)))) x)): 0 points increase in error, 0 points decrease in error
      (Rewrite<= associate-+r+_binary64 (+.f64 (/.f64 z y) (+.f64 (*.f64 54929528941/2000000 (/.f64 1 (pow.f64 y 2))) x))): 0 points increase in error, 0 points decrease in error

   if -2.91447967549120032e40 < y < 2.9553886951417548e36

   1. Initial program 2.8

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

   2. Taylor expanded in t around inf 2.8

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

4. Final simplification 10.1

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.9144796754912003 \cdot 10^{+40}:\\ \;\;\;\;x + \left(\frac{z}{y} + \frac{27464.7644705}{y \cdot y}\right)\\ \mathbf{elif}\;y \leq 2.955388695141755 \cdot 10^{+36}:\\ \;\;\;\;\frac{t}{y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right) + i} + \frac{y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right) + i}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} + \frac{27464.7644705}{y \cdot y}\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	12.2
Cost	2512

\[\begin{array}{l} t_1 := x + \left(\frac{z}{y} + \frac{27464.7644705}{y \cdot y}\right)\\ t_2 := t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)\\ \mathbf{if}\;y \leq -2.9144796754912003 \cdot 10^{+40}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.402156146393542 \cdot 10^{-63}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + z \cdot \left(y \cdot y\right)\right)}{y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right) + i}\\ \mathbf{elif}\;y \leq 122332810531745940:\\ \;\;\;\;\frac{t_2}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{elif}\;y \leq 2.955388695141755 \cdot 10^{+36}:\\ \;\;\;\;\frac{t_2}{i + y \cdot \left(c + \left(y \cdot y\right) \cdot \left(y + a\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Error	12.2
Cost	2512

\[\begin{array}{l} t_1 := x + \left(\frac{z}{y} + \frac{27464.7644705}{y \cdot y}\right)\\ t_2 := t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)\\ t_3 := y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)\\ \mathbf{if}\;y \leq -2.9144796754912003 \cdot 10^{+40}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.402156146393542 \cdot 10^{-63}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + z \cdot \left(y \cdot y\right)\right)}{t_3 + i}\\ \mathbf{elif}\;y \leq 122332810531745940:\\ \;\;\;\;\frac{t_2}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{elif}\;y \leq 2.955388695141755 \cdot 10^{+36}:\\ \;\;\;\;\frac{t_2}{t_3}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 3
Error	10.1
Cost	2376

\[\begin{array}{l} t_1 := x + \left(\frac{z}{y} + \frac{27464.7644705}{y \cdot y}\right)\\ \mathbf{if}\;y \leq -2.9144796754912003 \cdot 10^{+40}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.955388695141755 \cdot 10^{+36}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right) + i}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Error	12.4
Cost	2124

\[\begin{array}{l} t_1 := x + \left(\frac{z}{y} + \frac{27464.7644705}{y \cdot y}\right)\\ \mathbf{if}\;y \leq -2.9144796754912003 \cdot 10^{+40}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.402156146393542 \cdot 10^{-63}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + z \cdot \left(y \cdot y\right)\right)}{y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right) + i}\\ \mathbf{elif}\;y \leq 122332810531745940:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{elif}\;y \leq 1.0979683359360692 \cdot 10^{+78}:\\ \;\;\;\;\left(\frac{z}{a} + \frac{\frac{27464.7644705}{y}}{a}\right) + x \cdot \left(\frac{y}{a} - \frac{c}{y \cdot \left(a \cdot a\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 5
Error	12.7
Cost	1992

\[\begin{array}{l} t_1 := x + \left(\frac{z}{y} + \frac{27464.7644705}{y \cdot y}\right)\\ \mathbf{if}\;y \leq -1.120241772682108 \cdot 10^{+37}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 122332810531745940:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Error	15.1
Cost	1864

\[\begin{array}{l} \mathbf{if}\;y \leq -1.5904702048145574 \cdot 10^{+73}:\\ \;\;\;\;x + \frac{z}{y}\\ \mathbf{elif}\;y \leq 122332810531745940:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right) + i}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} + \frac{27464.7644705}{y \cdot y}\right)\\ \end{array} \]

Alternative 7
Error	15.1
Cost	1608

\[\begin{array}{l} t_1 := x + \left(\frac{z}{y} + \frac{27464.7644705}{y \cdot y}\right)\\ \mathbf{if}\;y \leq -2.9144796754912003 \cdot 10^{+40}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 122332810531745940:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right) + i}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 8
Error	17.5
Cost	1480

\[\begin{array}{l} t_1 := x + \left(\frac{z}{y} + \frac{27464.7644705}{y \cdot y}\right)\\ \mathbf{if}\;y \leq -2.9144796754912003 \cdot 10^{+40}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 122332810531745940:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + \left(y \cdot y\right) \cdot \left(y + a\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 9
Error	17.6
Cost	1356

\[\begin{array}{l} t_1 := x + \left(\frac{z}{y} + \frac{27464.7644705}{y \cdot y}\right)\\ \mathbf{if}\;y \leq -2.9144796754912003 \cdot 10^{+40}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 5.753864102925535 \cdot 10^{-30}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + \left(y \cdot y\right) \cdot a\right)}\\ \mathbf{elif}\;y \leq 122332810531745940:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot \left(y \cdot y + b\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 10
Error	20.7
Cost	1224

\[\begin{array}{l} t_1 := x + \left(\frac{z}{y} + \frac{27464.7644705}{y \cdot y}\right)\\ \mathbf{if}\;y \leq -2.9144796754912003 \cdot 10^{+40}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 122332810531745940:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot \left(y \cdot y + b\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 11
Error	21.7
Cost	1096

\[\begin{array}{l} t_1 := x + \left(\frac{z}{y} + \frac{27464.7644705}{y \cdot y}\right)\\ \mathbf{if}\;y \leq -2.9144796754912003 \cdot 10^{+40}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 122332810531745940:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot \left(y \cdot a\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 12
Error	22.5
Cost	968

\[\begin{array}{l} t_1 := x + \left(\frac{z}{y} + \frac{27464.7644705}{y \cdot y}\right)\\ \mathbf{if}\;y \leq -1.3035764768050996 \cdot 10^{+39}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 122332810531745940:\\ \;\;\;\;\frac{t}{i + y \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 13
Error	23.2
Cost	712

\[\begin{array}{l} t_1 := x + \frac{z}{y}\\ \mathbf{if}\;y \leq -1.5904702048145574 \cdot 10^{+73}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 122332810531745940:\\ \;\;\;\;\frac{t}{i + y \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 14
Error	27.8
Cost	584

\[\begin{array}{l} t_1 := x + \frac{z}{y}\\ \mathbf{if}\;y \leq -83.66048530862433:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 122332810531745940:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 15
Error	46.7
Cost	456

\[\begin{array}{l} \mathbf{if}\;x \leq -4.666692476162828 \cdot 10^{-190}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 3.194074026215455 \cdot 10^{-69}:\\ \;\;\;\;\frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 16
Error	46.5
Cost	456

\[\begin{array}{l} \mathbf{if}\;y \leq -1.5904702048145574 \cdot 10^{+73}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6.518600554451059 \cdot 10^{+65}:\\ \;\;\;\;\frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 17
Error	32.3
Cost	456

\[\begin{array}{l} \mathbf{if}\;y \leq -83.66048530862433:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.5670875339839613 \cdot 10^{+25}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 18
Error	46.9
Cost	64

\[x \]

Reproduce

herbie shell --seed 2022316 
(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)))