Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2

Average Error: 28.4 → 11.1

Time: 1.1min

Precision: binary64

Cost: 17164

Math

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

↓

\[\begin{array}{l} t_1 := c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\\ t_2 := t_1 \cdot t_1\\ t_3 := y \cdot \left(z + y \cdot x\right)\\ t_4 := 230661.510616 + y \cdot \left(27464.7644705 + t_3\right)\\ t_5 := \frac{z - x \cdot a}{y}\\ t_6 := t_5 + \left(\left(\frac{27464.7644705}{y \cdot y} - \frac{x}{y} \cdot \frac{b}{y}\right) + \left(x - \frac{a}{y} \cdot t_5\right)\right)\\ t_7 := y \cdot t_1\\ \mathbf{if}\;y \leq -1.4208957114816286 \cdot 10^{+60}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;y \leq 11875.750788032889:\\ \;\;\;\;\frac{y \cdot t_4 + t}{i + t_7}\\ \mathbf{elif}\;y \leq 2.0917814408989145 \cdot 10^{+31}:\\ \;\;\;\;\frac{t}{t_7} + \left(\frac{t_4}{t_1} - i \cdot \left(\frac{t}{{y}^{2} \cdot t_2} + \left(230661.510616 \cdot \frac{1}{y \cdot t_2} + \left(27464.7644705 \cdot \frac{1}{t_2} + \frac{t_3}{t_2}\right)\right)\right)\right)\\ \mathbf{elif}\;y \leq 7.220778728047763 \cdot 10^{+244}:\\ \;\;\;\;t_6\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

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 (+ c (* y (+ b (* y (+ y a))))))
        (t_2 (* t_1 t_1))
        (t_3 (* y (+ z (* y x))))
        (t_4 (+ 230661.510616 (* y (+ 27464.7644705 t_3))))
        (t_5 (/ (- z (* x a)) y))
        (t_6
         (+
          t_5
          (+
           (- (/ 27464.7644705 (* y y)) (* (/ x y) (/ b y)))
           (- x (* (/ a y) t_5)))))
        (t_7 (* y t_1)))
   (if (<= y -1.4208957114816286e+60)
     t_6
     (if (<= y 11875.750788032889)
       (/ (+ (* y t_4) t) (+ i t_7))
       (if (<= y 2.0917814408989145e+31)
         (+
          (/ t t_7)
          (-
           (/ t_4 t_1)
           (*
            i
            (+
             (/ t (* (pow y 2.0) t_2))
             (+
              (* 230661.510616 (/ 1.0 (* y t_2)))
              (+ (* 27464.7644705 (/ 1.0 t_2)) (/ t_3 t_2)))))))
         (if (<= y 7.220778728047763e+244) t_6 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 t_1 = c + (y * (b + (y * (y + a))));
	double t_2 = t_1 * t_1;
	double t_3 = y * (z + (y * x));
	double t_4 = 230661.510616 + (y * (27464.7644705 + t_3));
	double t_5 = (z - (x * a)) / y;
	double t_6 = t_5 + (((27464.7644705 / (y * y)) - ((x / y) * (b / y))) + (x - ((a / y) * t_5)));
	double t_7 = y * t_1;
	double tmp;
	if (y <= -1.4208957114816286e+60) {
		tmp = t_6;
	} else if (y <= 11875.750788032889) {
		tmp = ((y * t_4) + t) / (i + t_7);
	} else if (y <= 2.0917814408989145e+31) {
		tmp = (t / t_7) + ((t_4 / t_1) - (i * ((t / (pow(y, 2.0) * t_2)) + ((230661.510616 * (1.0 / (y * t_2))) + ((27464.7644705 * (1.0 / t_2)) + (t_3 / t_2))))));
	} else if (y <= 7.220778728047763e+244) {
		tmp = t_6;
	} else {
		tmp = 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) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: tmp
    t_1 = c + (y * (b + (y * (y + a))))
    t_2 = t_1 * t_1
    t_3 = y * (z + (y * x))
    t_4 = 230661.510616d0 + (y * (27464.7644705d0 + t_3))
    t_5 = (z - (x * a)) / y
    t_6 = t_5 + (((27464.7644705d0 / (y * y)) - ((x / y) * (b / y))) + (x - ((a / y) * t_5)))
    t_7 = y * t_1
    if (y <= (-1.4208957114816286d+60)) then
        tmp = t_6
    else if (y <= 11875.750788032889d0) then
        tmp = ((y * t_4) + t) / (i + t_7)
    else if (y <= 2.0917814408989145d+31) then
        tmp = (t / t_7) + ((t_4 / t_1) - (i * ((t / ((y ** 2.0d0) * t_2)) + ((230661.510616d0 * (1.0d0 / (y * t_2))) + ((27464.7644705d0 * (1.0d0 / t_2)) + (t_3 / t_2))))))
    else if (y <= 7.220778728047763d+244) then
        tmp = t_6
    else
        tmp = 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 t_1 = c + (y * (b + (y * (y + a))));
	double t_2 = t_1 * t_1;
	double t_3 = y * (z + (y * x));
	double t_4 = 230661.510616 + (y * (27464.7644705 + t_3));
	double t_5 = (z - (x * a)) / y;
	double t_6 = t_5 + (((27464.7644705 / (y * y)) - ((x / y) * (b / y))) + (x - ((a / y) * t_5)));
	double t_7 = y * t_1;
	double tmp;
	if (y <= -1.4208957114816286e+60) {
		tmp = t_6;
	} else if (y <= 11875.750788032889) {
		tmp = ((y * t_4) + t) / (i + t_7);
	} else if (y <= 2.0917814408989145e+31) {
		tmp = (t / t_7) + ((t_4 / t_1) - (i * ((t / (Math.pow(y, 2.0) * t_2)) + ((230661.510616 * (1.0 / (y * t_2))) + ((27464.7644705 * (1.0 / t_2)) + (t_3 / t_2))))));
	} else if (y <= 7.220778728047763e+244) {
		tmp = t_6;
	} else {
		tmp = 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):
	t_1 = c + (y * (b + (y * (y + a))))
	t_2 = t_1 * t_1
	t_3 = y * (z + (y * x))
	t_4 = 230661.510616 + (y * (27464.7644705 + t_3))
	t_5 = (z - (x * a)) / y
	t_6 = t_5 + (((27464.7644705 / (y * y)) - ((x / y) * (b / y))) + (x - ((a / y) * t_5)))
	t_7 = y * t_1
	tmp = 0
	if y <= -1.4208957114816286e+60:
		tmp = t_6
	elif y <= 11875.750788032889:
		tmp = ((y * t_4) + t) / (i + t_7)
	elif y <= 2.0917814408989145e+31:
		tmp = (t / t_7) + ((t_4 / t_1) - (i * ((t / (math.pow(y, 2.0) * t_2)) + ((230661.510616 * (1.0 / (y * t_2))) + ((27464.7644705 * (1.0 / t_2)) + (t_3 / t_2))))))
	elif y <= 7.220778728047763e+244:
		tmp = t_6
	else:
		tmp = 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)
	t_1 = Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a)))))
	t_2 = Float64(t_1 * t_1)
	t_3 = Float64(y * Float64(z + Float64(y * x)))
	t_4 = Float64(230661.510616 + Float64(y * Float64(27464.7644705 + t_3)))
	t_5 = Float64(Float64(z - Float64(x * a)) / y)
	t_6 = Float64(t_5 + Float64(Float64(Float64(27464.7644705 / Float64(y * y)) - Float64(Float64(x / y) * Float64(b / y))) + Float64(x - Float64(Float64(a / y) * t_5))))
	t_7 = Float64(y * t_1)
	tmp = 0.0
	if (y <= -1.4208957114816286e+60)
		tmp = t_6;
	elseif (y <= 11875.750788032889)
		tmp = Float64(Float64(Float64(y * t_4) + t) / Float64(i + t_7));
	elseif (y <= 2.0917814408989145e+31)
		tmp = Float64(Float64(t / t_7) + Float64(Float64(t_4 / t_1) - Float64(i * Float64(Float64(t / Float64((y ^ 2.0) * t_2)) + Float64(Float64(230661.510616 * Float64(1.0 / Float64(y * t_2))) + Float64(Float64(27464.7644705 * Float64(1.0 / t_2)) + Float64(t_3 / t_2)))))));
	elseif (y <= 7.220778728047763e+244)
		tmp = t_6;
	else
		tmp = 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)
	t_1 = c + (y * (b + (y * (y + a))));
	t_2 = t_1 * t_1;
	t_3 = y * (z + (y * x));
	t_4 = 230661.510616 + (y * (27464.7644705 + t_3));
	t_5 = (z - (x * a)) / y;
	t_6 = t_5 + (((27464.7644705 / (y * y)) - ((x / y) * (b / y))) + (x - ((a / y) * t_5)));
	t_7 = y * t_1;
	tmp = 0.0;
	if (y <= -1.4208957114816286e+60)
		tmp = t_6;
	elseif (y <= 11875.750788032889)
		tmp = ((y * t_4) + t) / (i + t_7);
	elseif (y <= 2.0917814408989145e+31)
		tmp = (t / t_7) + ((t_4 / t_1) - (i * ((t / ((y ^ 2.0) * t_2)) + ((230661.510616 * (1.0 / (y * t_2))) + ((27464.7644705 * (1.0 / t_2)) + (t_3 / t_2))))));
	elseif (y <= 7.220778728047763e+244)
		tmp = t_6;
	else
		tmp = 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_] := Block[{t$95$1 = N[(c + N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 * t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(y * N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(230661.510616 + N[(y * N[(27464.7644705 + t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(z - N[(x * a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, Block[{t$95$6 = N[(t$95$5 + N[(N[(N[(27464.7644705 / N[(y * y), $MachinePrecision]), $MachinePrecision] - N[(N[(x / y), $MachinePrecision] * N[(b / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x - N[(N[(a / y), $MachinePrecision] * t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(y * t$95$1), $MachinePrecision]}, If[LessEqual[y, -1.4208957114816286e+60], t$95$6, If[LessEqual[y, 11875.750788032889], N[(N[(N[(y * t$95$4), $MachinePrecision] + t), $MachinePrecision] / N[(i + t$95$7), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.0917814408989145e+31], N[(N[(t / t$95$7), $MachinePrecision] + N[(N[(t$95$4 / t$95$1), $MachinePrecision] - N[(i * N[(N[(t / N[(N[Power[y, 2.0], $MachinePrecision] * t$95$2), $MachinePrecision]), $MachinePrecision] + N[(N[(230661.510616 * N[(1.0 / N[(y * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(27464.7644705 * N[(1.0 / t$95$2), $MachinePrecision]), $MachinePrecision] + N[(t$95$3 / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.220778728047763e+244], t$95$6, x]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.4208957114816286e60 or 2.0917814408989145e31 < y < 7.220778728047763e244

   1. Initial program 61.0

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

   2. Applied egg-rr 61.0

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

   3. Taylor expanded in t around 0 61.4

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

   4. Taylor expanded in y around -inf 29.6

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

   5. Simplified 22.2

      \[\leadsto \color{blue}{\left(\left(\frac{27464.7644705}{y \cdot y} - \frac{x}{y} \cdot \frac{b}{y}\right) + \left(x - \frac{a}{y} \cdot \frac{z - x \cdot a}{y}\right)\right) + \frac{z - x \cdot a}{y}} \]
      Proof
      (+.f64 (+.f64 (-.f64 (/.f64 54929528941/2000000 (*.f64 y y)) (*.f64 (/.f64 x y) (/.f64 b y))) (-.f64 x (*.f64 (/.f64 a y) (/.f64 (-.f64 z (*.f64 x a)) y)))) (/.f64 (-.f64 z (*.f64 x a)) y)): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (-.f64 (/.f64 (Rewrite<= metadata-eval (*.f64 54929528941/2000000 1)) (*.f64 y y)) (*.f64 (/.f64 x y) (/.f64 b y))) (-.f64 x (*.f64 (/.f64 a y) (/.f64 (-.f64 z (*.f64 x a)) y)))) (/.f64 (-.f64 z (*.f64 x a)) y)): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (-.f64 (/.f64 (*.f64 54929528941/2000000 1) (Rewrite<= unpow2_binary64 (pow.f64 y 2))) (*.f64 (/.f64 x y) (/.f64 b y))) (-.f64 x (*.f64 (/.f64 a y) (/.f64 (-.f64 z (*.f64 x a)) y)))) (/.f64 (-.f64 z (*.f64 x a)) y)): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (-.f64 (Rewrite<= associate-*r/_binary64 (*.f64 54929528941/2000000 (/.f64 1 (pow.f64 y 2)))) (*.f64 (/.f64 x y) (/.f64 b y))) (-.f64 x (*.f64 (/.f64 a y) (/.f64 (-.f64 z (*.f64 x a)) y)))) (/.f64 (-.f64 z (*.f64 x a)) y)): 1 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (-.f64 (*.f64 54929528941/2000000 (/.f64 1 (pow.f64 y 2))) (Rewrite<= times-frac_binary64 (/.f64 (*.f64 x b) (*.f64 y y)))) (-.f64 x (*.f64 (/.f64 a y) (/.f64 (-.f64 z (*.f64 x a)) y)))) (/.f64 (-.f64 z (*.f64 x a)) y)): 11 points increase in error, 2 points decrease in error
      (+.f64 (+.f64 (-.f64 (*.f64 54929528941/2000000 (/.f64 1 (pow.f64 y 2))) (/.f64 (Rewrite<= *-commutative_binary64 (*.f64 b x)) (*.f64 y y))) (-.f64 x (*.f64 (/.f64 a y) (/.f64 (-.f64 z (*.f64 x a)) y)))) (/.f64 (-.f64 z (*.f64 x a)) y)): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (-.f64 (*.f64 54929528941/2000000 (/.f64 1 (pow.f64 y 2))) (/.f64 (*.f64 b x) (Rewrite<= unpow2_binary64 (pow.f64 y 2)))) (-.f64 x (*.f64 (/.f64 a y) (/.f64 (-.f64 z (*.f64 x a)) y)))) (/.f64 (-.f64 z (*.f64 x a)) y)): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (Rewrite<= unsub-neg_binary64 (+.f64 (*.f64 54929528941/2000000 (/.f64 1 (pow.f64 y 2))) (neg.f64 (/.f64 (*.f64 b x) (pow.f64 y 2))))) (-.f64 x (*.f64 (/.f64 a y) (/.f64 (-.f64 z (*.f64 x a)) y)))) (/.f64 (-.f64 z (*.f64 x a)) y)): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (+.f64 (*.f64 54929528941/2000000 (/.f64 1 (pow.f64 y 2))) (Rewrite<= mul-1-neg_binary64 (*.f64 -1 (/.f64 (*.f64 b x) (pow.f64 y 2))))) (-.f64 x (*.f64 (/.f64 a y) (/.f64 (-.f64 z (*.f64 x a)) y)))) (/.f64 (-.f64 z (*.f64 x a)) y)): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (+.f64 (*.f64 54929528941/2000000 (/.f64 1 (pow.f64 y 2))) (*.f64 -1 (/.f64 (*.f64 b x) (pow.f64 y 2)))) (-.f64 x (*.f64 (/.f64 a y) (/.f64 (-.f64 z (Rewrite<= *-commutative_binary64 (*.f64 a x))) y)))) (/.f64 (-.f64 z (*.f64 x a)) y)): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (+.f64 (*.f64 54929528941/2000000 (/.f64 1 (pow.f64 y 2))) (*.f64 -1 (/.f64 (*.f64 b x) (pow.f64 y 2)))) (-.f64 x (Rewrite<= times-frac_binary64 (/.f64 (*.f64 a (-.f64 z (*.f64 a x))) (*.f64 y y))))) (/.f64 (-.f64 z (*.f64 x a)) y)): 19 points increase in error, 2 points decrease in error
      (+.f64 (+.f64 (+.f64 (*.f64 54929528941/2000000 (/.f64 1 (pow.f64 y 2))) (*.f64 -1 (/.f64 (*.f64 b x) (pow.f64 y 2)))) (-.f64 x (/.f64 (Rewrite=> *-commutative_binary64 (*.f64 (-.f64 z (*.f64 a x)) a)) (*.f64 y y)))) (/.f64 (-.f64 z (*.f64 x a)) y)): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (+.f64 (*.f64 54929528941/2000000 (/.f64 1 (pow.f64 y 2))) (*.f64 -1 (/.f64 (*.f64 b x) (pow.f64 y 2)))) (-.f64 x (/.f64 (*.f64 (-.f64 z (*.f64 a x)) a) (Rewrite<= unpow2_binary64 (pow.f64 y 2))))) (/.f64 (-.f64 z (*.f64 x a)) y)): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (+.f64 (*.f64 54929528941/2000000 (/.f64 1 (pow.f64 y 2))) (*.f64 -1 (/.f64 (*.f64 b x) (pow.f64 y 2)))) (Rewrite<= unsub-neg_binary64 (+.f64 x (neg.f64 (/.f64 (*.f64 (-.f64 z (*.f64 a x)) a) (pow.f64 y 2)))))) (/.f64 (-.f64 z (*.f64 x a)) y)): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (+.f64 (*.f64 54929528941/2000000 (/.f64 1 (pow.f64 y 2))) (*.f64 -1 (/.f64 (*.f64 b x) (pow.f64 y 2)))) (+.f64 x (Rewrite<= mul-1-neg_binary64 (*.f64 -1 (/.f64 (*.f64 (-.f64 z (*.f64 a x)) a) (pow.f64 y 2)))))) (/.f64 (-.f64 z (*.f64 x a)) y)): 0 points increase in error, 0 points decrease in error
      (+.f64 (Rewrite<= associate-+l+_binary64 (+.f64 (+.f64 (+.f64 (*.f64 54929528941/2000000 (/.f64 1 (pow.f64 y 2))) (*.f64 -1 (/.f64 (*.f64 b x) (pow.f64 y 2)))) x) (*.f64 -1 (/.f64 (*.f64 (-.f64 z (*.f64 a x)) a) (pow.f64 y 2))))) (/.f64 (-.f64 z (*.f64 x a)) y)): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (Rewrite<= associate-+r+_binary64 (+.f64 (*.f64 54929528941/2000000 (/.f64 1 (pow.f64 y 2))) (+.f64 (*.f64 -1 (/.f64 (*.f64 b x) (pow.f64 y 2))) x))) (*.f64 -1 (/.f64 (*.f64 (-.f64 z (*.f64 a x)) a) (pow.f64 y 2)))) (/.f64 (-.f64 z (*.f64 x a)) y)): 0 points increase in error, 0 points decrease in error
      (+.f64 (Rewrite<= +-commutative_binary64 (+.f64 (*.f64 -1 (/.f64 (*.f64 (-.f64 z (*.f64 a x)) a) (pow.f64 y 2))) (+.f64 (*.f64 54929528941/2000000 (/.f64 1 (pow.f64 y 2))) (+.f64 (*.f64 -1 (/.f64 (*.f64 b x) (pow.f64 y 2))) x)))) (/.f64 (-.f64 z (*.f64 x a)) y)): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (*.f64 -1 (/.f64 (*.f64 (-.f64 z (*.f64 a x)) a) (pow.f64 y 2))) (+.f64 (*.f64 54929528941/2000000 (/.f64 1 (pow.f64 y 2))) (+.f64 (*.f64 -1 (/.f64 (*.f64 b x) (pow.f64 y 2))) x))) (/.f64 (-.f64 z (Rewrite<= *-commutative_binary64 (*.f64 a x))) y)): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (*.f64 -1 (/.f64 (*.f64 (-.f64 z (*.f64 a x)) a) (pow.f64 y 2))) (+.f64 (*.f64 54929528941/2000000 (/.f64 1 (pow.f64 y 2))) (+.f64 (*.f64 -1 (/.f64 (*.f64 b x) (pow.f64 y 2))) x))) (Rewrite=> div-sub_binary64 (-.f64 (/.f64 z y) (/.f64 (*.f64 a x) y)))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= associate--l+_binary64 (-.f64 (+.f64 (+.f64 (*.f64 -1 (/.f64 (*.f64 (-.f64 z (*.f64 a x)) a) (pow.f64 y 2))) (+.f64 (*.f64 54929528941/2000000 (/.f64 1 (pow.f64 y 2))) (+.f64 (*.f64 -1 (/.f64 (*.f64 b x) (pow.f64 y 2))) x))) (/.f64 z y)) (/.f64 (*.f64 a x) y))): 0 points increase in error, 0 points decrease in error
      (-.f64 (Rewrite<= +-commutative_binary64 (+.f64 (/.f64 z y) (+.f64 (*.f64 -1 (/.f64 (*.f64 (-.f64 z (*.f64 a x)) a) (pow.f64 y 2))) (+.f64 (*.f64 54929528941/2000000 (/.f64 1 (pow.f64 y 2))) (+.f64 (*.f64 -1 (/.f64 (*.f64 b x) (pow.f64 y 2))) x))))) (/.f64 (*.f64 a x) y)): 0 points increase in error, 0 points decrease in error

   if -1.4208957114816286e60 < y < 11875.750788032889

   1. Initial program 2.9

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

   if 11875.750788032889 < y < 2.0917814408989145e31

   1. Initial program 18.6

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

   2. Applied egg-rr 18.6

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

   3. Taylor expanded in i around 0 22.6

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

   if 7.220778728047763e244 < y

   1. Initial program 64.0

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

   2. Taylor expanded in y around inf 12.1

      \[\leadsto \color{blue}{x} \]
3. Recombined 4 regimes into one program.

4. Final simplification 11.1

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4208957114816286 \cdot 10^{+60}:\\ \;\;\;\;\frac{z - x \cdot a}{y} + \left(\left(\frac{27464.7644705}{y \cdot y} - \frac{x}{y} \cdot \frac{b}{y}\right) + \left(x - \frac{a}{y} \cdot \frac{z - x \cdot a}{y}\right)\right)\\ \mathbf{elif}\;y \leq 11875.750788032889:\\ \;\;\;\;\frac{y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right) + t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{elif}\;y \leq 2.0917814408989145 \cdot 10^{+31}:\\ \;\;\;\;\frac{t}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)} + \left(\frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)}{c + y \cdot \left(b + y \cdot \left(y + a\right)\right)} - i \cdot \left(\frac{t}{{y}^{2} \cdot \left(\left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)\right)} + \left(230661.510616 \cdot \frac{1}{y \cdot \left(\left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)\right)} + \left(27464.7644705 \cdot \frac{1}{\left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)} + \frac{y \cdot \left(z + y \cdot x\right)}{\left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\right)\right)\right)\right)\\ \mathbf{elif}\;y \leq 7.220778728047763 \cdot 10^{+244}:\\ \;\;\;\;\frac{z - x \cdot a}{y} + \left(\left(\frac{27464.7644705}{y \cdot y} - \frac{x}{y} \cdot \frac{b}{y}\right) + \left(x - \frac{a}{y} \cdot \frac{z - x \cdot a}{y}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternatives

Alternative 1
Error	11.0
Cost	2636

\[\begin{array}{l} t_1 := \frac{z - x \cdot a}{y}\\ t_2 := t_1 + \left(\left(\frac{27464.7644705}{y \cdot y} - \frac{x}{y} \cdot \frac{b}{y}\right) + \left(x - \frac{a}{y} \cdot t_1\right)\right)\\ \mathbf{if}\;y \leq -1.4208957114816286 \cdot 10^{+60}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 2.0917814408989145 \cdot 10^{+31}:\\ \;\;\;\;\frac{y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right) + t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{elif}\;y \leq 7.220778728047763 \cdot 10^{+244}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 2
Error	11.3
Cost	2376

\[\begin{array}{l} t_1 := x + \frac{z - x \cdot a}{y}\\ \mathbf{if}\;y \leq -1.4208957114816286 \cdot 10^{+60}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.0917814408989145 \cdot 10^{+31}:\\ \;\;\;\;\frac{y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right) + t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{elif}\;y \leq 7.220778728047763 \cdot 10^{+244}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3
Error	13.7
Cost	2248

\[\begin{array}{l} t_1 := c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\\ t_2 := i + y \cdot t_1\\ t_3 := 230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\\ t_4 := x + \frac{z - x \cdot a}{y}\\ \mathbf{if}\;y \leq -1.4208957114816286 \cdot 10^{+60}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y \leq -3.529532382851967 \cdot 10^{-27}:\\ \;\;\;\;\frac{y \cdot t_3}{t_2}\\ \mathbf{elif}\;y \leq 2.7794551744333386 \cdot 10^{-13}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(y \cdot z\right)\right)}{t_2}\\ \mathbf{elif}\;y \leq 2.0917814408989145 \cdot 10^{+31}:\\ \;\;\;\;\frac{t_3}{t_1}\\ \mathbf{elif}\;y \leq 7.220778728047763 \cdot 10^{+244}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4
Error	15.7
Cost	2128

\[\begin{array}{l} t_1 := x + \frac{z - x \cdot a}{y}\\ t_2 := c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\\ t_3 := \frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)}{t_2}\\ \mathbf{if}\;y \leq -1.4208957114816286 \cdot 10^{+60}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -8.537250610354983 \cdot 10^{-44}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 2.7794551744333386 \cdot 10^{-13}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot t_2}\\ \mathbf{elif}\;y \leq 2.0917814408989145 \cdot 10^{+31}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 7.220778728047763 \cdot 10^{+244}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 5
Error	16.2
Cost	1996

\[\begin{array}{l} t_1 := c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\\ t_2 := x + \frac{z - x \cdot a}{y}\\ \mathbf{if}\;y \leq -1.4208957114816286 \cdot 10^{+60}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 2.7794551744333386 \cdot 10^{-13}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{i + y \cdot t_1}\\ \mathbf{elif}\;y \leq 2.0917814408989145 \cdot 10^{+31}:\\ \;\;\;\;\frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)}{t_1}\\ \mathbf{elif}\;y \leq 7.220778728047763 \cdot 10^{+244}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6
Error	14.1
Cost	1996

\[\begin{array}{l} t_1 := c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\\ t_2 := x + \frac{z - x \cdot a}{y}\\ \mathbf{if}\;y \leq -1.4208957114816286 \cdot 10^{+60}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 2.7794551744333386 \cdot 10^{-13}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(y \cdot z\right)\right)}{i + y \cdot t_1}\\ \mathbf{elif}\;y \leq 2.0917814408989145 \cdot 10^{+31}:\\ \;\;\;\;\frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)}{t_1}\\ \mathbf{elif}\;y \leq 7.220778728047763 \cdot 10^{+244}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 7
Error	17.0
Cost	1608

\[\begin{array}{l} t_1 := x + \frac{z - x \cdot a}{y}\\ \mathbf{if}\;y \leq -1.4208957114816286 \cdot 10^{+60}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.494619323805091 \cdot 10^{+25}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{elif}\;y \leq 7.220778728047763 \cdot 10^{+244}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 8
Error	27.1
Cost	1368

\[\begin{array}{l} t_1 := t + y \cdot 230661.510616\\ t_2 := \frac{t_1}{i}\\ t_3 := x + \frac{z - x \cdot a}{y}\\ \mathbf{if}\;y \leq -5.857966351630198 \cdot 10^{-8}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 9.508931387757446 \cdot 10^{-89}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 8.251152140388205 \cdot 10^{-30}:\\ \;\;\;\;\frac{t_1}{y \cdot c}\\ \mathbf{elif}\;y \leq 2.7794551744333386 \cdot 10^{-13}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.1656838774858534 \cdot 10^{+57}:\\ \;\;\;\;\left(y \cdot y\right) \cdot \frac{x}{b}\\ \mathbf{elif}\;y \leq 7.220778728047763 \cdot 10^{+244}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9
Error	18.8
Cost	1352

\[\begin{array}{l} t_1 := x + \frac{z - x \cdot a}{y}\\ \mathbf{if}\;y \leq -9.370870955676522 \cdot 10^{+37}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.494619323805091 \cdot 10^{+25}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(y \cdot z\right)\right)}{i + y \cdot c}\\ \mathbf{elif}\;y \leq 7.220778728047763 \cdot 10^{+244}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 10
Error	30.3
Cost	1236

\[\begin{array}{l} t_1 := t + y \cdot 230661.510616\\ t_2 := \frac{t_1}{i}\\ \mathbf{if}\;y \leq -9.370870955676522 \cdot 10^{+37}:\\ \;\;\;\;x - \frac{x}{\frac{y}{a}}\\ \mathbf{elif}\;y \leq 9.508931387757446 \cdot 10^{-89}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 8.251152140388205 \cdot 10^{-30}:\\ \;\;\;\;\frac{t_1}{y \cdot c}\\ \mathbf{elif}\;y \leq 2.7794551744333386 \cdot 10^{-13}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.1656838774858534 \cdot 10^{+57}:\\ \;\;\;\;\left(y \cdot y\right) \cdot \frac{x}{b}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x}{y} \cdot \frac{b}{y}\\ \end{array} \]

Alternative 11
Error	20.6
Cost	1104

\[\begin{array}{l} t_1 := x + \frac{z - x \cdot a}{y}\\ \mathbf{if}\;y \leq -9.370870955676522 \cdot 10^{+37}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.7794551744333386 \cdot 10^{-13}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot c}\\ \mathbf{elif}\;y \leq 1.1656838774858534 \cdot 10^{+57}:\\ \;\;\;\;\left(y \cdot y\right) \cdot \frac{x}{b}\\ \mathbf{elif}\;y \leq 7.220778728047763 \cdot 10^{+244}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 12
Error	30.0
Cost	972

\[\begin{array}{l} \mathbf{if}\;y \leq -9.370870955676522 \cdot 10^{+37}:\\ \;\;\;\;x - \frac{x}{\frac{y}{a}}\\ \mathbf{elif}\;y \leq 2.7794551744333386 \cdot 10^{-13}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{elif}\;y \leq 1.1656838774858534 \cdot 10^{+57}:\\ \;\;\;\;\left(y \cdot y\right) \cdot \frac{x}{b}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x}{y} \cdot \frac{b}{y}\\ \end{array} \]

Alternative 13
Error	22.5
Cost	972

\[\begin{array}{l} t_1 := x + \frac{z - x \cdot a}{y}\\ \mathbf{if}\;y \leq -7.692862823078188 \cdot 10^{+59}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 487693779857627260:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{elif}\;y \leq 7.220778728047763 \cdot 10^{+244}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 14
Error	32.1
Cost	844

\[\begin{array}{l} \mathbf{if}\;y \leq -9.370870955676522 \cdot 10^{+37}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.7794551744333386 \cdot 10^{-13}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{elif}\;y \leq 1.1656838774858534 \cdot 10^{+57}:\\ \;\;\;\;\left(y \cdot y\right) \cdot \frac{x}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 15
Error	32.2
Cost	844

\[\begin{array}{l} \mathbf{if}\;y \leq -1.3869087554417991 \cdot 10^{+65}:\\ \;\;\;\;x - \frac{x}{\frac{y}{a}}\\ \mathbf{elif}\;y \leq 2.7794551744333386 \cdot 10^{-13}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{elif}\;y \leq 1.1656838774858534 \cdot 10^{+57}:\\ \;\;\;\;\left(y \cdot y\right) \cdot \frac{x}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 16
Error	30.0
Cost	844

\[\begin{array}{l} \mathbf{if}\;y \leq -9.370870955676522 \cdot 10^{+37}:\\ \;\;\;\;x - \frac{x}{\frac{y}{a}}\\ \mathbf{elif}\;y \leq 2.7794551744333386 \cdot 10^{-13}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{elif}\;y \leq 1.1656838774858534 \cdot 10^{+57}:\\ \;\;\;\;\left(y \cdot y\right) \cdot \frac{x}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 17
Error	46.7
Cost	456

\[\begin{array}{l} \mathbf{if}\;x \leq -7.903076349706459 \cdot 10^{-257}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 5.452098076990655 \cdot 10^{-212}:\\ \;\;\;\;\frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 18
Error	32.1
Cost	456

\[\begin{array}{l} \mathbf{if}\;y \leq -9.370870955676522 \cdot 10^{+37}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 16009.817690160797:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 19
Error	47.3
Cost	64

\[x \]

Reproduce

herbie shell --seed 2022317 
(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)))