Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2

Average Error: 29.2 → 10.8

Time: 54.1s

Precision: binary64

Cost: 15372

Math

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

↓

\[\begin{array}{l} t_1 := b + y \cdot \left(y + a\right)\\ t_2 := t_1 \cdot t_1\\ t_3 := 27464.7644705 + y \cdot \left(z + y \cdot x\right)\\ t_4 := \left(\left(x + \left(\frac{z}{y} + \frac{\frac{27464.7644705}{y}}{y}\right)\right) - \frac{a}{y} \cdot \frac{z - x \cdot a}{y}\right) - \left(x \cdot \frac{a}{y} + \frac{b}{\frac{y}{\frac{x}{y}}}\right)\\ t_5 := y \cdot t_1\\ t_6 := y \cdot \left(c + t_5\right) + i\\ t_7 := \frac{t}{t_6}\\ \mathbf{if}\;y \leq -7.669510878221144 \cdot 10^{+62}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y \leq 2.6566715646524415:\\ \;\;\;\;t_7 + \frac{y \cdot \left(230661.510616 + y \cdot t_3\right)}{t_6}\\ \mathbf{elif}\;y \leq 1.9770035460998272 \cdot 10^{+93}:\\ \;\;\;\;t_7 + \left(\frac{t_3}{t_1} + \left(230661.510616 \cdot \frac{1}{t_5} + c \cdot \left(\left(27464.7644705 \cdot \frac{-1}{t_1 \cdot t_5} + \left(\frac{1}{t_1 \cdot \left(t_1 \cdot {y}^{2}\right)} \cdot -230661.510616 - \frac{y \cdot x}{t_2}\right)\right) - \frac{z}{t_2}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

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 (+ b (* y (+ y a))))
        (t_2 (* t_1 t_1))
        (t_3 (+ 27464.7644705 (* y (+ z (* y x)))))
        (t_4
         (-
          (-
           (+ x (+ (/ z y) (/ (/ 27464.7644705 y) y)))
           (* (/ a y) (/ (- z (* x a)) y)))
          (+ (* x (/ a y)) (/ b (/ y (/ x y))))))
        (t_5 (* y t_1))
        (t_6 (+ (* y (+ c t_5)) i))
        (t_7 (/ t t_6)))
   (if (<= y -7.669510878221144e+62)
     t_4
     (if (<= y 2.6566715646524415)
       (+ t_7 (/ (* y (+ 230661.510616 (* y t_3))) t_6))
       (if (<= y 1.9770035460998272e+93)
         (+
          t_7
          (+
           (/ t_3 t_1)
           (+
            (* 230661.510616 (/ 1.0 t_5))
            (*
             c
             (-
              (+
               (* 27464.7644705 (/ -1.0 (* t_1 t_5)))
               (-
                (* (/ 1.0 (* t_1 (* t_1 (pow y 2.0)))) -230661.510616)
                (/ (* y x) t_2)))
              (/ z t_2))))))
         t_4)))))

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 = b + (y * (y + a));
	double t_2 = t_1 * t_1;
	double t_3 = 27464.7644705 + (y * (z + (y * x)));
	double t_4 = ((x + ((z / y) + ((27464.7644705 / y) / y))) - ((a / y) * ((z - (x * a)) / y))) - ((x * (a / y)) + (b / (y / (x / y))));
	double t_5 = y * t_1;
	double t_6 = (y * (c + t_5)) + i;
	double t_7 = t / t_6;
	double tmp;
	if (y <= -7.669510878221144e+62) {
		tmp = t_4;
	} else if (y <= 2.6566715646524415) {
		tmp = t_7 + ((y * (230661.510616 + (y * t_3))) / t_6);
	} else if (y <= 1.9770035460998272e+93) {
		tmp = t_7 + ((t_3 / t_1) + ((230661.510616 * (1.0 / t_5)) + (c * (((27464.7644705 * (-1.0 / (t_1 * t_5))) + (((1.0 / (t_1 * (t_1 * pow(y, 2.0)))) * -230661.510616) - ((y * x) / t_2))) - (z / t_2)))));
	} else {
		tmp = t_4;
	}
	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 = b + (y * (y + a))
    t_2 = t_1 * t_1
    t_3 = 27464.7644705d0 + (y * (z + (y * x)))
    t_4 = ((x + ((z / y) + ((27464.7644705d0 / y) / y))) - ((a / y) * ((z - (x * a)) / y))) - ((x * (a / y)) + (b / (y / (x / y))))
    t_5 = y * t_1
    t_6 = (y * (c + t_5)) + i
    t_7 = t / t_6
    if (y <= (-7.669510878221144d+62)) then
        tmp = t_4
    else if (y <= 2.6566715646524415d0) then
        tmp = t_7 + ((y * (230661.510616d0 + (y * t_3))) / t_6)
    else if (y <= 1.9770035460998272d+93) then
        tmp = t_7 + ((t_3 / t_1) + ((230661.510616d0 * (1.0d0 / t_5)) + (c * (((27464.7644705d0 * ((-1.0d0) / (t_1 * t_5))) + (((1.0d0 / (t_1 * (t_1 * (y ** 2.0d0)))) * (-230661.510616d0)) - ((y * x) / t_2))) - (z / t_2)))))
    else
        tmp = t_4
    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 = b + (y * (y + a));
	double t_2 = t_1 * t_1;
	double t_3 = 27464.7644705 + (y * (z + (y * x)));
	double t_4 = ((x + ((z / y) + ((27464.7644705 / y) / y))) - ((a / y) * ((z - (x * a)) / y))) - ((x * (a / y)) + (b / (y / (x / y))));
	double t_5 = y * t_1;
	double t_6 = (y * (c + t_5)) + i;
	double t_7 = t / t_6;
	double tmp;
	if (y <= -7.669510878221144e+62) {
		tmp = t_4;
	} else if (y <= 2.6566715646524415) {
		tmp = t_7 + ((y * (230661.510616 + (y * t_3))) / t_6);
	} else if (y <= 1.9770035460998272e+93) {
		tmp = t_7 + ((t_3 / t_1) + ((230661.510616 * (1.0 / t_5)) + (c * (((27464.7644705 * (-1.0 / (t_1 * t_5))) + (((1.0 / (t_1 * (t_1 * Math.pow(y, 2.0)))) * -230661.510616) - ((y * x) / t_2))) - (z / t_2)))));
	} else {
		tmp = t_4;
	}
	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 = b + (y * (y + a))
	t_2 = t_1 * t_1
	t_3 = 27464.7644705 + (y * (z + (y * x)))
	t_4 = ((x + ((z / y) + ((27464.7644705 / y) / y))) - ((a / y) * ((z - (x * a)) / y))) - ((x * (a / y)) + (b / (y / (x / y))))
	t_5 = y * t_1
	t_6 = (y * (c + t_5)) + i
	t_7 = t / t_6
	tmp = 0
	if y <= -7.669510878221144e+62:
		tmp = t_4
	elif y <= 2.6566715646524415:
		tmp = t_7 + ((y * (230661.510616 + (y * t_3))) / t_6)
	elif y <= 1.9770035460998272e+93:
		tmp = t_7 + ((t_3 / t_1) + ((230661.510616 * (1.0 / t_5)) + (c * (((27464.7644705 * (-1.0 / (t_1 * t_5))) + (((1.0 / (t_1 * (t_1 * math.pow(y, 2.0)))) * -230661.510616) - ((y * x) / t_2))) - (z / t_2)))))
	else:
		tmp = t_4
	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(b + Float64(y * Float64(y + a)))
	t_2 = Float64(t_1 * t_1)
	t_3 = Float64(27464.7644705 + Float64(y * Float64(z + Float64(y * x))))
	t_4 = Float64(Float64(Float64(x + Float64(Float64(z / y) + Float64(Float64(27464.7644705 / y) / y))) - Float64(Float64(a / y) * Float64(Float64(z - Float64(x * a)) / y))) - Float64(Float64(x * Float64(a / y)) + Float64(b / Float64(y / Float64(x / y)))))
	t_5 = Float64(y * t_1)
	t_6 = Float64(Float64(y * Float64(c + t_5)) + i)
	t_7 = Float64(t / t_6)
	tmp = 0.0
	if (y <= -7.669510878221144e+62)
		tmp = t_4;
	elseif (y <= 2.6566715646524415)
		tmp = Float64(t_7 + Float64(Float64(y * Float64(230661.510616 + Float64(y * t_3))) / t_6));
	elseif (y <= 1.9770035460998272e+93)
		tmp = Float64(t_7 + Float64(Float64(t_3 / t_1) + Float64(Float64(230661.510616 * Float64(1.0 / t_5)) + Float64(c * Float64(Float64(Float64(27464.7644705 * Float64(-1.0 / Float64(t_1 * t_5))) + Float64(Float64(Float64(1.0 / Float64(t_1 * Float64(t_1 * (y ^ 2.0)))) * -230661.510616) - Float64(Float64(y * x) / t_2))) - Float64(z / t_2))))));
	else
		tmp = t_4;
	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 = b + (y * (y + a));
	t_2 = t_1 * t_1;
	t_3 = 27464.7644705 + (y * (z + (y * x)));
	t_4 = ((x + ((z / y) + ((27464.7644705 / y) / y))) - ((a / y) * ((z - (x * a)) / y))) - ((x * (a / y)) + (b / (y / (x / y))));
	t_5 = y * t_1;
	t_6 = (y * (c + t_5)) + i;
	t_7 = t / t_6;
	tmp = 0.0;
	if (y <= -7.669510878221144e+62)
		tmp = t_4;
	elseif (y <= 2.6566715646524415)
		tmp = t_7 + ((y * (230661.510616 + (y * t_3))) / t_6);
	elseif (y <= 1.9770035460998272e+93)
		tmp = t_7 + ((t_3 / t_1) + ((230661.510616 * (1.0 / t_5)) + (c * (((27464.7644705 * (-1.0 / (t_1 * t_5))) + (((1.0 / (t_1 * (t_1 * (y ^ 2.0)))) * -230661.510616) - ((y * x) / t_2))) - (z / t_2)))));
	else
		tmp = t_4;
	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[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 * t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(27464.7644705 + N[(y * N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(x + N[(N[(z / y), $MachinePrecision] + N[(N[(27464.7644705 / y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(a / y), $MachinePrecision] * N[(N[(z - N[(x * a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x * N[(a / y), $MachinePrecision]), $MachinePrecision] + N[(b / N[(y / N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(y * t$95$1), $MachinePrecision]}, Block[{t$95$6 = N[(N[(y * N[(c + t$95$5), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]}, Block[{t$95$7 = N[(t / t$95$6), $MachinePrecision]}, If[LessEqual[y, -7.669510878221144e+62], t$95$4, If[LessEqual[y, 2.6566715646524415], N[(t$95$7 + N[(N[(y * N[(230661.510616 + N[(y * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$6), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.9770035460998272e+93], N[(t$95$7 + N[(N[(t$95$3 / t$95$1), $MachinePrecision] + N[(N[(230661.510616 * N[(1.0 / t$95$5), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(N[(27464.7644705 * N[(-1.0 / N[(t$95$1 * t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(1.0 / N[(t$95$1 * N[(t$95$1 * N[Power[y, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * -230661.510616), $MachinePrecision] - N[(N[(y * x), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$4]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.6695108782211436e62 or 1.97700354609982721e93 < y

   1. Initial program 63.3

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

   2. Simplified 63.3

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right), 230661.510616\right), t\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}} \]
      Proof
      (/.f64 (fma.f64 y (fma.f64 y (fma.f64 y (fma.f64 x y z) 54929528941/2000000) 28832688827/125000) t) (fma.f64 y (fma.f64 y (fma.f64 y (+.f64 y a) b) c) i)): 0 points increase in error, 0 points decrease in error
      (/.f64 (fma.f64 y (fma.f64 y (fma.f64 y (Rewrite<= fma-def_binary64 (+.f64 (*.f64 x y) z)) 54929528941/2000000) 28832688827/125000) t) (fma.f64 y (fma.f64 y (fma.f64 y (+.f64 y a) b) c) i)): 0 points increase in error, 0 points decrease in error
      (/.f64 (fma.f64 y (fma.f64 y (Rewrite<= fma-def_binary64 (+.f64 (*.f64 y (+.f64 (*.f64 x y) z)) 54929528941/2000000)) 28832688827/125000) t) (fma.f64 y (fma.f64 y (fma.f64 y (+.f64 y a) b) c) i)): 0 points increase in error, 0 points decrease in error
      (/.f64 (fma.f64 y (fma.f64 y (+.f64 (Rewrite<= *-commutative_binary64 (*.f64 (+.f64 (*.f64 x y) z) y)) 54929528941/2000000) 28832688827/125000) t) (fma.f64 y (fma.f64 y (fma.f64 y (+.f64 y a) b) c) i)): 0 points increase in error, 0 points decrease in error
      (/.f64 (fma.f64 y (Rewrite<= fma-def_binary64 (+.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) 54929528941/2000000)) 28832688827/125000)) t) (fma.f64 y (fma.f64 y (fma.f64 y (+.f64 y a) b) c) i)): 0 points increase in error, 0 points decrease in error
      (/.f64 (fma.f64 y (+.f64 (Rewrite<= *-commutative_binary64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) 54929528941/2000000) y)) 28832688827/125000) t) (fma.f64 y (fma.f64 y (fma.f64 y (+.f64 y a) b) c) i)): 0 points increase in error, 0 points decrease in error
      (/.f64 (Rewrite<= fma-def_binary64 (+.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) 54929528941/2000000) y) 28832688827/125000)) t)) (fma.f64 y (fma.f64 y (fma.f64 y (+.f64 y a) b) c) i)): 0 points increase in error, 0 points decrease in error
      (/.f64 (+.f64 (Rewrite<= *-commutative_binary64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) 54929528941/2000000) y) 28832688827/125000) y)) t) (fma.f64 y (fma.f64 y (fma.f64 y (+.f64 y a) b) c) i)): 0 points increase in error, 0 points decrease in error
      (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) 54929528941/2000000) y) 28832688827/125000) y) t) (fma.f64 y (fma.f64 y (Rewrite<= fma-def_binary64 (+.f64 (*.f64 y (+.f64 y a)) b)) c) i)): 1 points increase in error, 0 points decrease in error
      (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) 54929528941/2000000) y) 28832688827/125000) y) t) (fma.f64 y (fma.f64 y (+.f64 (Rewrite<= *-commutative_binary64 (*.f64 (+.f64 y a) y)) b) c) i)): 0 points increase in error, 0 points decrease in error
      (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) 54929528941/2000000) y) 28832688827/125000) y) t) (fma.f64 y (Rewrite<= fma-def_binary64 (+.f64 (*.f64 y (+.f64 (*.f64 (+.f64 y a) y) b)) c)) i)): 0 points increase in error, 0 points decrease in error
      (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) 54929528941/2000000) y) 28832688827/125000) y) t) (fma.f64 y (+.f64 (Rewrite<= *-commutative_binary64 (*.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y)) c) i)): 0 points increase in error, 0 points decrease in error
      (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) 54929528941/2000000) y) 28832688827/125000) y) t) (Rewrite<= fma-def_binary64 (+.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c)) i))): 0 points increase in error, 0 points decrease in error
      (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) 54929528941/2000000) y) 28832688827/125000) y) t) (+.f64 (Rewrite<= *-commutative_binary64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c) y)) i)): 0 points increase in error, 0 points decrease in error

   3. Taylor expanded in y around inf 27.1

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

   4. Simplified 17.8

      \[\leadsto \color{blue}{\left(\left(x + \left(\frac{z}{y} + \frac{\frac{27464.7644705}{y}}{y}\right)\right) - \frac{a}{y} \cdot \frac{z - a \cdot x}{y}\right) - \left(\frac{a}{y} \cdot x + \frac{b}{\frac{y}{\frac{x}{y}}}\right)} \]
      Proof
      (-.f64 (-.f64 (+.f64 x (+.f64 (/.f64 z y) (/.f64 (/.f64 54929528941/2000000 y) y))) (*.f64 (/.f64 a y) (/.f64 (-.f64 z (*.f64 a x)) y))) (+.f64 (*.f64 (/.f64 a y) x) (/.f64 b (/.f64 y (/.f64 x y))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (-.f64 (+.f64 x (+.f64 (/.f64 z y) (Rewrite<= associate-/r*_binary64 (/.f64 54929528941/2000000 (*.f64 y y))))) (*.f64 (/.f64 a y) (/.f64 (-.f64 z (*.f64 a x)) y))) (+.f64 (*.f64 (/.f64 a y) x) (/.f64 b (/.f64 y (/.f64 x y))))): 1 points increase in error, 0 points decrease in error
      (-.f64 (-.f64 (+.f64 x (+.f64 (/.f64 z y) (/.f64 (Rewrite<= metadata-eval (*.f64 54929528941/2000000 1)) (*.f64 y y)))) (*.f64 (/.f64 a y) (/.f64 (-.f64 z (*.f64 a x)) y))) (+.f64 (*.f64 (/.f64 a y) x) (/.f64 b (/.f64 y (/.f64 x y))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (-.f64 (+.f64 x (+.f64 (/.f64 z y) (/.f64 (*.f64 54929528941/2000000 1) (Rewrite<= unpow2_binary64 (pow.f64 y 2))))) (*.f64 (/.f64 a y) (/.f64 (-.f64 z (*.f64 a x)) y))) (+.f64 (*.f64 (/.f64 a y) x) (/.f64 b (/.f64 y (/.f64 x y))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (-.f64 (+.f64 x (+.f64 (/.f64 z y) (Rewrite<= associate-*r/_binary64 (*.f64 54929528941/2000000 (/.f64 1 (pow.f64 y 2)))))) (*.f64 (/.f64 a y) (/.f64 (-.f64 z (*.f64 a x)) y))) (+.f64 (*.f64 (/.f64 a y) x) (/.f64 b (/.f64 y (/.f64 x y))))): 1 points increase in error, 4 points decrease in error
      (-.f64 (-.f64 (Rewrite<= +-commutative_binary64 (+.f64 (+.f64 (/.f64 z y) (*.f64 54929528941/2000000 (/.f64 1 (pow.f64 y 2)))) x)) (*.f64 (/.f64 a y) (/.f64 (-.f64 z (*.f64 a x)) y))) (+.f64 (*.f64 (/.f64 a y) x) (/.f64 b (/.f64 y (/.f64 x y))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (-.f64 (Rewrite<= associate-+r+_binary64 (+.f64 (/.f64 z y) (+.f64 (*.f64 54929528941/2000000 (/.f64 1 (pow.f64 y 2))) x))) (*.f64 (/.f64 a y) (/.f64 (-.f64 z (*.f64 a x)) y))) (+.f64 (*.f64 (/.f64 a y) x) (/.f64 b (/.f64 y (/.f64 x y))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (-.f64 (+.f64 (/.f64 z y) (+.f64 (*.f64 54929528941/2000000 (/.f64 1 (pow.f64 y 2))) x)) (Rewrite<= times-frac_binary64 (/.f64 (*.f64 a (-.f64 z (*.f64 a x))) (*.f64 y y)))) (+.f64 (*.f64 (/.f64 a y) x) (/.f64 b (/.f64 y (/.f64 x y))))): 25 points increase in error, 5 points decrease in error
      (-.f64 (-.f64 (+.f64 (/.f64 z y) (+.f64 (*.f64 54929528941/2000000 (/.f64 1 (pow.f64 y 2))) x)) (/.f64 (Rewrite=> *-commutative_binary64 (*.f64 (-.f64 z (*.f64 a x)) a)) (*.f64 y y))) (+.f64 (*.f64 (/.f64 a y) x) (/.f64 b (/.f64 y (/.f64 x y))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (-.f64 (+.f64 (/.f64 z y) (+.f64 (*.f64 54929528941/2000000 (/.f64 1 (pow.f64 y 2))) x)) (/.f64 (*.f64 (-.f64 z (*.f64 a x)) a) (Rewrite<= unpow2_binary64 (pow.f64 y 2)))) (+.f64 (*.f64 (/.f64 a y) x) (/.f64 b (/.f64 y (/.f64 x y))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (-.f64 (+.f64 (/.f64 z y) (+.f64 (*.f64 54929528941/2000000 (/.f64 1 (pow.f64 y 2))) x)) (/.f64 (*.f64 (-.f64 z (*.f64 a x)) a) (pow.f64 y 2))) (+.f64 (Rewrite<= associate-/r/_binary64 (/.f64 a (/.f64 y x))) (/.f64 b (/.f64 y (/.f64 x y))))): 0 points increase in error, 1 points decrease in error
      (-.f64 (-.f64 (+.f64 (/.f64 z y) (+.f64 (*.f64 54929528941/2000000 (/.f64 1 (pow.f64 y 2))) x)) (/.f64 (*.f64 (-.f64 z (*.f64 a x)) a) (pow.f64 y 2))) (+.f64 (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 a x) y)) (/.f64 b (/.f64 y (/.f64 x y))))): 1 points increase in error, 0 points decrease in error
      (-.f64 (-.f64 (+.f64 (/.f64 z y) (+.f64 (*.f64 54929528941/2000000 (/.f64 1 (pow.f64 y 2))) x)) (/.f64 (*.f64 (-.f64 z (*.f64 a x)) a) (pow.f64 y 2))) (+.f64 (/.f64 (*.f64 a x) y) (/.f64 b (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 y y) x))))): 0 points increase in error, 1 points decrease in error
      (-.f64 (-.f64 (+.f64 (/.f64 z y) (+.f64 (*.f64 54929528941/2000000 (/.f64 1 (pow.f64 y 2))) x)) (/.f64 (*.f64 (-.f64 z (*.f64 a x)) a) (pow.f64 y 2))) (+.f64 (/.f64 (*.f64 a x) y) (/.f64 b (/.f64 (Rewrite<= unpow2_binary64 (pow.f64 y 2)) x)))): 0 points increase in error, 0 points decrease in error
      (-.f64 (-.f64 (+.f64 (/.f64 z y) (+.f64 (*.f64 54929528941/2000000 (/.f64 1 (pow.f64 y 2))) x)) (/.f64 (*.f64 (-.f64 z (*.f64 a x)) a) (pow.f64 y 2))) (+.f64 (/.f64 (*.f64 a x) y) (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 b x) (pow.f64 y 2))))): 12 points increase in error, 4 points decrease in error
      (Rewrite<= associate--r+_binary64 (-.f64 (+.f64 (/.f64 z y) (+.f64 (*.f64 54929528941/2000000 (/.f64 1 (pow.f64 y 2))) x)) (+.f64 (/.f64 (*.f64 (-.f64 z (*.f64 a x)) a) (pow.f64 y 2)) (+.f64 (/.f64 (*.f64 a x) y) (/.f64 (*.f64 b x) (pow.f64 y 2)))))): 0 points increase in error, 0 points decrease in error

   if -7.6695108782211436e62 < y < 2.656671564652441

   1. Initial program 3.2

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

   2. Taylor expanded in t around inf 3.2

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

   if 2.656671564652441 < y < 1.97700354609982721e93

   1. Initial program 39.6

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

   2. Taylor expanded in t around inf 39.6

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

   3. Taylor expanded in i around 0 34.8

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

   4. Taylor expanded in c around 0 30.3

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

4. Final simplification 10.8

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.669510878221144 \cdot 10^{+62}:\\ \;\;\;\;\left(\left(x + \left(\frac{z}{y} + \frac{\frac{27464.7644705}{y}}{y}\right)\right) - \frac{a}{y} \cdot \frac{z - x \cdot a}{y}\right) - \left(x \cdot \frac{a}{y} + \frac{b}{\frac{y}{\frac{x}{y}}}\right)\\ \mathbf{elif}\;y \leq 2.6566715646524415:\\ \;\;\;\;\frac{t}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) + i} + \frac{y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) + i}\\ \mathbf{elif}\;y \leq 1.9770035460998272 \cdot 10^{+93}:\\ \;\;\;\;\frac{t}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) + i} + \left(\frac{27464.7644705 + y \cdot \left(z + y \cdot x\right)}{b + y \cdot \left(y + a\right)} + \left(230661.510616 \cdot \frac{1}{y \cdot \left(b + y \cdot \left(y + a\right)\right)} + c \cdot \left(\left(27464.7644705 \cdot \frac{-1}{\left(b + y \cdot \left(y + a\right)\right) \cdot \left(y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)} + \left(\frac{1}{\left(b + y \cdot \left(y + a\right)\right) \cdot \left(\left(b + y \cdot \left(y + a\right)\right) \cdot {y}^{2}\right)} \cdot -230661.510616 - \frac{y \cdot x}{\left(b + y \cdot \left(y + a\right)\right) \cdot \left(b + y \cdot \left(y + a\right)\right)}\right)\right) - \frac{z}{\left(b + y \cdot \left(y + a\right)\right) \cdot \left(b + y \cdot \left(y + a\right)\right)}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x + \left(\frac{z}{y} + \frac{\frac{27464.7644705}{y}}{y}\right)\right) - \frac{a}{y} \cdot \frac{z - x \cdot a}{y}\right) - \left(x \cdot \frac{a}{y} + \frac{b}{\frac{y}{\frac{x}{y}}}\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	11.1
Cost	3400

\[\begin{array}{l} t_1 := 230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\\ t_2 := c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\\ t_3 := y \cdot t_2 + i\\ t_4 := \frac{t}{t_3}\\ t_5 := \left(\left(x + \left(\frac{z}{y} + \frac{\frac{27464.7644705}{y}}{y}\right)\right) - \frac{a}{y} \cdot \frac{z - x \cdot a}{y}\right) - \left(x \cdot \frac{a}{y} + \frac{b}{\frac{y}{\frac{x}{y}}}\right)\\ \mathbf{if}\;y \leq -7.669510878221144 \cdot 10^{+62}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;y \leq 1.3951159895116993 \cdot 10^{-12}:\\ \;\;\;\;t_4 + \frac{y \cdot t_1}{t_3}\\ \mathbf{elif}\;y \leq 8.1085984108008 \cdot 10^{+64}:\\ \;\;\;\;t_4 + \frac{t_1}{t_2}\\ \mathbf{else}:\\ \;\;\;\;t_5\\ \end{array} \]

Alternative 2
Error	11.1
Cost	3148

\[\begin{array}{l} t_1 := c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\\ t_2 := y \cdot t_1 + i\\ t_3 := 230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\\ t_4 := \left(\left(x + \left(\frac{z}{y} + \frac{\frac{27464.7644705}{y}}{y}\right)\right) - \frac{a}{y} \cdot \frac{z - x \cdot a}{y}\right) - \left(x \cdot \frac{a}{y} + \frac{b}{\frac{y}{\frac{x}{y}}}\right)\\ \mathbf{if}\;y \leq -7.669510878221144 \cdot 10^{+62}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y \leq 1.3951159895116993 \cdot 10^{-12}:\\ \;\;\;\;\frac{t + y \cdot t_3}{t_2}\\ \mathbf{elif}\;y \leq 8.1085984108008 \cdot 10^{+64}:\\ \;\;\;\;\frac{t}{t_2} + \frac{t_3}{t_1}\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 3
Error	13.9
Cost	2640

\[\begin{array}{l} t_1 := c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\\ t_2 := y \cdot t_1 + i\\ t_3 := x + \frac{z - x \cdot a}{y}\\ \mathbf{if}\;y \leq -7.669510878221144 \cdot 10^{+62}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -7.830866481931518 \cdot 10^{-16}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(y \cdot x\right)\right)\right)}{t_2}\\ \mathbf{elif}\;y \leq 4.380022122961461 \cdot 10^{-12}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(y \cdot z\right)\right)}{t_2}\\ \mathbf{elif}\;y \leq 8.1085984108008 \cdot 10^{+64}:\\ \;\;\;\;\frac{t}{b \cdot \left(y \cdot y\right)} - \frac{-230661.510616 - y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)}{t_1}\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 4
Error	11.0
Cost	2632

\[\begin{array}{l} t_1 := \left(\left(x + \left(\frac{z}{y} + \frac{\frac{27464.7644705}{y}}{y}\right)\right) - \frac{a}{y} \cdot \frac{z - x \cdot a}{y}\right) - \left(x \cdot \frac{a}{y} + \frac{b}{\frac{y}{\frac{x}{y}}}\right)\\ \mathbf{if}\;y \leq -7.669510878221144 \cdot 10^{+62}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.612097574612221 \cdot 10^{+58}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) + i}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 5
Error	13.6
Cost	2512

\[\begin{array}{l} t_1 := y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) + i\\ t_2 := \frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(y \cdot x\right)\right)\right)}{t_1}\\ t_3 := x + \frac{z - x \cdot a}{y}\\ \mathbf{if}\;y \leq -7.669510878221144 \cdot 10^{+62}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -7.830866481931518 \cdot 10^{-16}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 4.4088958217547665 \cdot 10^{-16}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(y \cdot z\right)\right)}{t_1}\\ \mathbf{elif}\;y \leq 3.612097574612221 \cdot 10^{+58}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 6
Error	11.3
Cost	2376

\[\begin{array}{l} t_1 := x + \frac{z - x \cdot a}{y}\\ \mathbf{if}\;y \leq -7.669510878221144 \cdot 10^{+62}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.612097574612221 \cdot 10^{+58}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) + i}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 7
Error	14.1
Cost	1992

\[\begin{array}{l} t_1 := x + \frac{z - x \cdot a}{y}\\ \mathbf{if}\;y \leq -5.453422985695381 \cdot 10^{+37}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 8.005544276151222 \cdot 10^{+48}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(y \cdot z\right)\right)}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) + i}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 8
Error	16.6
Cost	1864

\[\begin{array}{l} t_1 := x + \frac{z - x \cdot a}{y}\\ \mathbf{if}\;y \leq -5.453422985695381 \cdot 10^{+37}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 8.1085984108008 \cdot 10^{+64}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) + i}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 9
Error	19.8
Cost	1616

\[\begin{array}{l} t_1 := \frac{t + y \cdot \left(230661.510616 + y \cdot \left(y \cdot z\right)\right)}{i + y \cdot c}\\ t_2 := x + \frac{z - x \cdot a}{y}\\ \mathbf{if}\;y \leq -5.453422985695381 \cdot 10^{+37}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 10^{-270}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.7127468409826577 \cdot 10^{-68}:\\ \;\;\;\;\frac{t}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) + i}\\ \mathbf{elif}\;y \leq 5.4139928888472286 \cdot 10^{+42}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 10
Error	17.0
Cost	1608

\[\begin{array}{l} t_1 := x + \frac{z - x \cdot a}{y}\\ \mathbf{if}\;y \leq -5.453422985695381 \cdot 10^{+37}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 8.005544276151222 \cdot 10^{+48}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) + i}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 11
Error	25.8
Cost	1352

\[\begin{array}{l} t_1 := x + \frac{z - x \cdot a}{y}\\ \mathbf{if}\;y \leq -1.6983072927285387 \cdot 10^{+25}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.60480032480423 \cdot 10^{+24}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(y \cdot x\right)\right)\right)}{i}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 12
Error	18.6
Cost	1352

\[\begin{array}{l} t_1 := x + \frac{z - x \cdot a}{y}\\ \mathbf{if}\;y \leq -5.453422985695381 \cdot 10^{+37}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 5.4139928888472286 \cdot 10^{+42}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(y \cdot z\right)\right)}{i + y \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 13
Error	25.6
Cost	1096

\[\begin{array}{l} t_1 := x + \frac{z - x \cdot a}{y}\\ \mathbf{if}\;y \leq -16811409.182096895:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.9630087874493635 \cdot 10^{+37}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + z \cdot \left(y \cdot y\right)\right)}{i}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 14
Error	26.4
Cost	968

\[\begin{array}{l} t_1 := x + \frac{z - x \cdot a}{y}\\ \mathbf{if}\;y \leq -40121349851700.14:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 5.038409651994074 \cdot 10^{+47}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{i}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 15
Error	26.5
Cost	840

\[\begin{array}{l} t_1 := x + \frac{z - x \cdot a}{y}\\ \mathbf{if}\;y \leq -565858753113912700:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 5.038409651994074 \cdot 10^{+47}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 16
Error	29.8
Cost	712

\[\begin{array}{l} \mathbf{if}\;y \leq -565858753113912700:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4.2584048593716736 \cdot 10^{+38}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 17
Error	46.4
Cost	456

\[\begin{array}{l} \mathbf{if}\;x \leq -4.156824646028263 \cdot 10^{-215}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.783753960047211 \cdot 10^{-96}:\\ \;\;\;\;\frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 18
Error	32.8
Cost	456

\[\begin{array}{l} \mathbf{if}\;y \leq -565858753113912700:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.1114183415011 \cdot 10^{-84}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 19
Error	47.2
Cost	64

\[x \]

Reproduce

herbie shell --seed 2022294 
(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)))