Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, I

Average Error: 3.9 → 29.4

Time: 22.3s

Precision: binary64

Cost: 8820

Math

\[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

↓

\[\begin{array}{l} t_1 := \frac{x}{y \cdot e^{-1.6666666666666667 \cdot \left(b - c\right)}}\\ t_2 := \frac{x}{x + y \cdot e^{c \cdot \frac{-1.3333333333333333}{t}}}\\ t_3 := \frac{x}{x + \left(y + \left(b \cdot \left(y \cdot a\right)\right) \cdot -2\right)}\\ \mathbf{if}\;c \leq -1.3789026442831328 \cdot 10^{-8}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -4.0666517143844075 \cdot 10^{-77}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq -4.747189572510168 \cdot 10^{-303}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 2.3163471495837582 \cdot 10^{-297}:\\ \;\;\;\;\frac{x}{x \cdot x - y \cdot y} \cdot \left(x - y\right)\\ \mathbf{elif}\;c \leq 2.750494052163473 \cdot 10^{-283}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 1.4954040967811104 \cdot 10^{-226}:\\ \;\;\;\;\frac{x}{x + \left(y + 2 \cdot \left(\frac{0.6944444444444444 + \frac{-0.4444444444444444}{t \cdot t}}{-0.8333333333333334 - \frac{0.6666666666666666}{t}} \cdot \left(y \cdot b\right)\right)\right)}\\ \mathbf{elif}\;c \leq 7.809697862958332 \cdot 10^{-188}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq 9.360673320253991 \cdot 10^{-177}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 1.3704276327964007 \cdot 10^{-155}:\\ \;\;\;\;-0.5 \cdot \frac{\frac{x}{y}}{b \cdot a}\\ \mathbf{elif}\;c \leq 8.914894226126018 \cdot 10^{-128}:\\ \;\;\;\;\frac{x}{\left(y \cdot b\right) \cdot -1.6666666666666667 + \left(x + y\right)}\\ \mathbf{elif}\;c \leq 816724496.5545095:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 1.4201743830549502 \cdot 10^{+59}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 2.812119454569072 \cdot 10^{+142}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (/
  x
  (+
   x
   (*
    y
    (exp
     (*
      2.0
      (-
       (/ (* z (sqrt (+ t a))) t)
       (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))))))))

↓

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ x (* y (exp (* -1.6666666666666667 (- b c))))))
        (t_2 (/ x (+ x (* y (exp (* c (/ -1.3333333333333333 t)))))))
        (t_3 (/ x (+ x (+ y (* (* b (* y a)) -2.0))))))
   (if (<= c -1.3789026442831328e-8)
     1.0
     (if (<= c -4.0666517143844075e-77)
       t_3
       (if (<= c -4.747189572510168e-303)
         1.0
         (if (<= c 2.3163471495837582e-297)
           (* (/ x (- (* x x) (* y y))) (- x y))
           (if (<= c 2.750494052163473e-283)
             1.0
             (if (<= c 1.4954040967811104e-226)
               (/
                x
                (+
                 x
                 (+
                  y
                  (*
                   2.0
                   (*
                    (/
                     (+ 0.6944444444444444 (/ -0.4444444444444444 (* t t)))
                     (- -0.8333333333333334 (/ 0.6666666666666666 t)))
                    (* y b))))))
               (if (<= c 7.809697862958332e-188)
                 t_3
                 (if (<= c 9.360673320253991e-177)
                   1.0
                   (if (<= c 1.3704276327964007e-155)
                     (* -0.5 (/ (/ x y) (* b a)))
                     (if (<= c 8.914894226126018e-128)
                       (/ x (+ (* (* y b) -1.6666666666666667) (+ x y)))
                       (if (<= c 816724496.5545095)
                         t_2
                         (if (<= c 1.4201743830549502e+59)
                           t_1
                           (if (<= c 2.812119454569072e+142)
                             t_2
                             t_1)))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return x / (x + (y * exp((2.0 * (((z * sqrt((t + a))) / t) - ((b - c) * ((a + (5.0 / 6.0)) - (2.0 / (t * 3.0)))))))));
}

↓

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = x / (y * exp((-1.6666666666666667 * (b - c))));
	double t_2 = x / (x + (y * exp((c * (-1.3333333333333333 / t)))));
	double t_3 = x / (x + (y + ((b * (y * a)) * -2.0)));
	double tmp;
	if (c <= -1.3789026442831328e-8) {
		tmp = 1.0;
	} else if (c <= -4.0666517143844075e-77) {
		tmp = t_3;
	} else if (c <= -4.747189572510168e-303) {
		tmp = 1.0;
	} else if (c <= 2.3163471495837582e-297) {
		tmp = (x / ((x * x) - (y * y))) * (x - y);
	} else if (c <= 2.750494052163473e-283) {
		tmp = 1.0;
	} else if (c <= 1.4954040967811104e-226) {
		tmp = x / (x + (y + (2.0 * (((0.6944444444444444 + (-0.4444444444444444 / (t * t))) / (-0.8333333333333334 - (0.6666666666666666 / t))) * (y * b)))));
	} else if (c <= 7.809697862958332e-188) {
		tmp = t_3;
	} else if (c <= 9.360673320253991e-177) {
		tmp = 1.0;
	} else if (c <= 1.3704276327964007e-155) {
		tmp = -0.5 * ((x / y) / (b * a));
	} else if (c <= 8.914894226126018e-128) {
		tmp = x / (((y * b) * -1.6666666666666667) + (x + y));
	} else if (c <= 816724496.5545095) {
		tmp = t_2;
	} else if (c <= 1.4201743830549502e+59) {
		tmp = t_1;
	} else if (c <= 2.812119454569072e+142) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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
    code = x / (x + (y * exp((2.0d0 * (((z * sqrt((t + a))) / t) - ((b - c) * ((a + (5.0d0 / 6.0d0)) - (2.0d0 / (t * 3.0d0)))))))))
end function

↓

real(8) function code(x, y, z, t, a, b, c)
    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) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x / (y * exp(((-1.6666666666666667d0) * (b - c))))
    t_2 = x / (x + (y * exp((c * ((-1.3333333333333333d0) / t)))))
    t_3 = x / (x + (y + ((b * (y * a)) * (-2.0d0))))
    if (c <= (-1.3789026442831328d-8)) then
        tmp = 1.0d0
    else if (c <= (-4.0666517143844075d-77)) then
        tmp = t_3
    else if (c <= (-4.747189572510168d-303)) then
        tmp = 1.0d0
    else if (c <= 2.3163471495837582d-297) then
        tmp = (x / ((x * x) - (y * y))) * (x - y)
    else if (c <= 2.750494052163473d-283) then
        tmp = 1.0d0
    else if (c <= 1.4954040967811104d-226) then
        tmp = x / (x + (y + (2.0d0 * (((0.6944444444444444d0 + ((-0.4444444444444444d0) / (t * t))) / ((-0.8333333333333334d0) - (0.6666666666666666d0 / t))) * (y * b)))))
    else if (c <= 7.809697862958332d-188) then
        tmp = t_3
    else if (c <= 9.360673320253991d-177) then
        tmp = 1.0d0
    else if (c <= 1.3704276327964007d-155) then
        tmp = (-0.5d0) * ((x / y) / (b * a))
    else if (c <= 8.914894226126018d-128) then
        tmp = x / (((y * b) * (-1.6666666666666667d0)) + (x + y))
    else if (c <= 816724496.5545095d0) then
        tmp = t_2
    else if (c <= 1.4201743830549502d+59) then
        tmp = t_1
    else if (c <= 2.812119454569072d+142) then
        tmp = t_2
    else
        tmp = t_1
    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) {
	return x / (x + (y * Math.exp((2.0 * (((z * Math.sqrt((t + a))) / t) - ((b - c) * ((a + (5.0 / 6.0)) - (2.0 / (t * 3.0)))))))));
}

↓

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = x / (y * Math.exp((-1.6666666666666667 * (b - c))));
	double t_2 = x / (x + (y * Math.exp((c * (-1.3333333333333333 / t)))));
	double t_3 = x / (x + (y + ((b * (y * a)) * -2.0)));
	double tmp;
	if (c <= -1.3789026442831328e-8) {
		tmp = 1.0;
	} else if (c <= -4.0666517143844075e-77) {
		tmp = t_3;
	} else if (c <= -4.747189572510168e-303) {
		tmp = 1.0;
	} else if (c <= 2.3163471495837582e-297) {
		tmp = (x / ((x * x) - (y * y))) * (x - y);
	} else if (c <= 2.750494052163473e-283) {
		tmp = 1.0;
	} else if (c <= 1.4954040967811104e-226) {
		tmp = x / (x + (y + (2.0 * (((0.6944444444444444 + (-0.4444444444444444 / (t * t))) / (-0.8333333333333334 - (0.6666666666666666 / t))) * (y * b)))));
	} else if (c <= 7.809697862958332e-188) {
		tmp = t_3;
	} else if (c <= 9.360673320253991e-177) {
		tmp = 1.0;
	} else if (c <= 1.3704276327964007e-155) {
		tmp = -0.5 * ((x / y) / (b * a));
	} else if (c <= 8.914894226126018e-128) {
		tmp = x / (((y * b) * -1.6666666666666667) + (x + y));
	} else if (c <= 816724496.5545095) {
		tmp = t_2;
	} else if (c <= 1.4201743830549502e+59) {
		tmp = t_1;
	} else if (c <= 2.812119454569072e+142) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	return x / (x + (y * math.exp((2.0 * (((z * math.sqrt((t + a))) / t) - ((b - c) * ((a + (5.0 / 6.0)) - (2.0 / (t * 3.0)))))))))

↓

def code(x, y, z, t, a, b, c):
	t_1 = x / (y * math.exp((-1.6666666666666667 * (b - c))))
	t_2 = x / (x + (y * math.exp((c * (-1.3333333333333333 / t)))))
	t_3 = x / (x + (y + ((b * (y * a)) * -2.0)))
	tmp = 0
	if c <= -1.3789026442831328e-8:
		tmp = 1.0
	elif c <= -4.0666517143844075e-77:
		tmp = t_3
	elif c <= -4.747189572510168e-303:
		tmp = 1.0
	elif c <= 2.3163471495837582e-297:
		tmp = (x / ((x * x) - (y * y))) * (x - y)
	elif c <= 2.750494052163473e-283:
		tmp = 1.0
	elif c <= 1.4954040967811104e-226:
		tmp = x / (x + (y + (2.0 * (((0.6944444444444444 + (-0.4444444444444444 / (t * t))) / (-0.8333333333333334 - (0.6666666666666666 / t))) * (y * b)))))
	elif c <= 7.809697862958332e-188:
		tmp = t_3
	elif c <= 9.360673320253991e-177:
		tmp = 1.0
	elif c <= 1.3704276327964007e-155:
		tmp = -0.5 * ((x / y) / (b * a))
	elif c <= 8.914894226126018e-128:
		tmp = x / (((y * b) * -1.6666666666666667) + (x + y))
	elif c <= 816724496.5545095:
		tmp = t_2
	elif c <= 1.4201743830549502e+59:
		tmp = t_1
	elif c <= 2.812119454569072e+142:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	return Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(Float64(z * sqrt(Float64(t + a))) / t) - Float64(Float64(b - c) * Float64(Float64(a + Float64(5.0 / 6.0)) - Float64(2.0 / Float64(t * 3.0))))))))))
end

↓

function code(x, y, z, t, a, b, c)
	t_1 = Float64(x / Float64(y * exp(Float64(-1.6666666666666667 * Float64(b - c)))))
	t_2 = Float64(x / Float64(x + Float64(y * exp(Float64(c * Float64(-1.3333333333333333 / t))))))
	t_3 = Float64(x / Float64(x + Float64(y + Float64(Float64(b * Float64(y * a)) * -2.0))))
	tmp = 0.0
	if (c <= -1.3789026442831328e-8)
		tmp = 1.0;
	elseif (c <= -4.0666517143844075e-77)
		tmp = t_3;
	elseif (c <= -4.747189572510168e-303)
		tmp = 1.0;
	elseif (c <= 2.3163471495837582e-297)
		tmp = Float64(Float64(x / Float64(Float64(x * x) - Float64(y * y))) * Float64(x - y));
	elseif (c <= 2.750494052163473e-283)
		tmp = 1.0;
	elseif (c <= 1.4954040967811104e-226)
		tmp = Float64(x / Float64(x + Float64(y + Float64(2.0 * Float64(Float64(Float64(0.6944444444444444 + Float64(-0.4444444444444444 / Float64(t * t))) / Float64(-0.8333333333333334 - Float64(0.6666666666666666 / t))) * Float64(y * b))))));
	elseif (c <= 7.809697862958332e-188)
		tmp = t_3;
	elseif (c <= 9.360673320253991e-177)
		tmp = 1.0;
	elseif (c <= 1.3704276327964007e-155)
		tmp = Float64(-0.5 * Float64(Float64(x / y) / Float64(b * a)));
	elseif (c <= 8.914894226126018e-128)
		tmp = Float64(x / Float64(Float64(Float64(y * b) * -1.6666666666666667) + Float64(x + y)));
	elseif (c <= 816724496.5545095)
		tmp = t_2;
	elseif (c <= 1.4201743830549502e+59)
		tmp = t_1;
	elseif (c <= 2.812119454569072e+142)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp = code(x, y, z, t, a, b, c)
	tmp = x / (x + (y * exp((2.0 * (((z * sqrt((t + a))) / t) - ((b - c) * ((a + (5.0 / 6.0)) - (2.0 / (t * 3.0)))))))));
end

↓

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = x / (y * exp((-1.6666666666666667 * (b - c))));
	t_2 = x / (x + (y * exp((c * (-1.3333333333333333 / t)))));
	t_3 = x / (x + (y + ((b * (y * a)) * -2.0)));
	tmp = 0.0;
	if (c <= -1.3789026442831328e-8)
		tmp = 1.0;
	elseif (c <= -4.0666517143844075e-77)
		tmp = t_3;
	elseif (c <= -4.747189572510168e-303)
		tmp = 1.0;
	elseif (c <= 2.3163471495837582e-297)
		tmp = (x / ((x * x) - (y * y))) * (x - y);
	elseif (c <= 2.750494052163473e-283)
		tmp = 1.0;
	elseif (c <= 1.4954040967811104e-226)
		tmp = x / (x + (y + (2.0 * (((0.6944444444444444 + (-0.4444444444444444 / (t * t))) / (-0.8333333333333334 - (0.6666666666666666 / t))) * (y * b)))));
	elseif (c <= 7.809697862958332e-188)
		tmp = t_3;
	elseif (c <= 9.360673320253991e-177)
		tmp = 1.0;
	elseif (c <= 1.3704276327964007e-155)
		tmp = -0.5 * ((x / y) / (b * a));
	elseif (c <= 8.914894226126018e-128)
		tmp = x / (((y * b) * -1.6666666666666667) + (x + y));
	elseif (c <= 816724496.5545095)
		tmp = t_2;
	elseif (c <= 1.4201743830549502e+59)
		tmp = t_1;
	elseif (c <= 2.812119454569072e+142)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(N[(z * N[Sqrt[N[(t + a), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision] - N[(N[(b - c), $MachinePrecision] * N[(N[(a + N[(5.0 / 6.0), $MachinePrecision]), $MachinePrecision] - N[(2.0 / N[(t * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(x / N[(y * N[Exp[N[(-1.6666666666666667 * N[(b - c), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(x + N[(y * N[Exp[N[(c * N[(-1.3333333333333333 / t), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x / N[(x + N[(y + N[(N[(b * N[(y * a), $MachinePrecision]), $MachinePrecision] * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.3789026442831328e-8], 1.0, If[LessEqual[c, -4.0666517143844075e-77], t$95$3, If[LessEqual[c, -4.747189572510168e-303], 1.0, If[LessEqual[c, 2.3163471495837582e-297], N[(N[(x / N[(N[(x * x), $MachinePrecision] - N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.750494052163473e-283], 1.0, If[LessEqual[c, 1.4954040967811104e-226], N[(x / N[(x + N[(y + N[(2.0 * N[(N[(N[(0.6944444444444444 + N[(-0.4444444444444444 / N[(t * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(-0.8333333333333334 - N[(0.6666666666666666 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 7.809697862958332e-188], t$95$3, If[LessEqual[c, 9.360673320253991e-177], 1.0, If[LessEqual[c, 1.3704276327964007e-155], N[(-0.5 * N[(N[(x / y), $MachinePrecision] / N[(b * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 8.914894226126018e-128], N[(x / N[(N[(N[(y * b), $MachinePrecision] * -1.6666666666666667), $MachinePrecision] + N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 816724496.5545095], t$95$2, If[LessEqual[c, 1.4201743830549502e+59], t$95$1, If[LessEqual[c, 2.812119454569072e+142], t$95$2, t$95$1]]]]]]]]]]]]]]]]

Target

Original	3.9
Target	3.0
Herbie	29.4

\[\begin{array}{l} \mathbf{if}\;t < -2.118326644891581 \cdot 10^{-50}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(a \cdot c + 0.8333333333333334 \cdot c\right) - a \cdot b\right)}}\\ \mathbf{elif}\;t < 5.196588770651547 \cdot 10^{-123}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{\left(z \cdot \sqrt{t + a}\right) \cdot \left(\left(3 \cdot t\right) \cdot \left(a - \frac{5}{6}\right)\right) - \left(\left(\frac{5}{6} + a\right) \cdot \left(3 \cdot t\right) - 2\right) \cdot \left(\left(a - \frac{5}{6}\right) \cdot \left(\left(b - c\right) \cdot t\right)\right)}{\left(\left(t \cdot t\right) \cdot 3\right) \cdot \left(a - \frac{5}{6}\right)}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\\ \end{array} \]

Derivation

1. Split input into 8 regimes

2. if c < -1.37890264428313281e-8 or -4.0666517143844075e-77 < c < -4.74718957251016815e-303 or 2.31634714958375821e-297 < c < 2.750494052163473e-283 or 7.8096978629583324e-188 < c < 9.36067332025399111e-177

   1. Initial program 3.9

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in a around inf 21.9

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

   3. Taylor expanded in x around inf 26.2

      \[\leadsto \color{blue}{1} \]

   if -1.37890264428313281e-8 < c < -4.0666517143844075e-77 or 1.49540409678111035e-226 < c < 7.8096978629583324e-188

   1. Initial program 2.2

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in b around inf 15.1

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(\left(0.6666666666666666 \cdot \frac{1}{t} - \left(0.8333333333333334 + a\right)\right) \cdot b\right)}}} \]

   3. Simplified 15.1

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(b \cdot \left(\frac{0.6666666666666666}{t} + \left(-0.8333333333333334 - a\right)\right)\right)}}} \]

   4. Taylor expanded in b around 0 36.7

      \[\leadsto \frac{x}{x + \color{blue}{\left(y + 2 \cdot \left(\left(0.6666666666666666 \cdot \frac{1}{t} - \left(0.8333333333333334 + a\right)\right) \cdot \left(y \cdot b\right)\right)\right)}} \]

   5. Taylor expanded in a around inf 36.4

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

   6. Simplified 36.4

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

   if -4.74718957251016815e-303 < c < 2.31634714958375821e-297

   1. Initial program 4.2

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in z around inf 22.8

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

   3. Taylor expanded in z around 0 36.7

      \[\leadsto \color{blue}{\frac{x}{y + x}} \]

   4. Simplified 36.7

      \[\leadsto \color{blue}{\frac{x}{x + y}} \]

   5. Applied egg-rr 34.2

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

   if 2.750494052163473e-283 < c < 1.49540409678111035e-226

   1. Initial program 1.9

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in b around inf 12.4

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(\left(0.6666666666666666 \cdot \frac{1}{t} - \left(0.8333333333333334 + a\right)\right) \cdot b\right)}}} \]

   3. Simplified 12.4

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(b \cdot \left(\frac{0.6666666666666666}{t} + \left(-0.8333333333333334 - a\right)\right)\right)}}} \]

   4. Taylor expanded in b around 0 32.8

      \[\leadsto \frac{x}{x + \color{blue}{\left(y + 2 \cdot \left(\left(0.6666666666666666 \cdot \frac{1}{t} - \left(0.8333333333333334 + a\right)\right) \cdot \left(y \cdot b\right)\right)\right)}} \]

   5. Taylor expanded in a around 0 32.2

      \[\leadsto \frac{x}{x + \left(y + 2 \cdot \left(\color{blue}{\left(0.6666666666666666 \cdot \frac{1}{t} - 0.8333333333333334\right)} \cdot \left(y \cdot b\right)\right)\right)} \]

   6. Simplified 32.2

      \[\leadsto \frac{x}{x + \left(y + 2 \cdot \left(\color{blue}{\left(\frac{0.6666666666666666}{t} + -0.8333333333333334\right)} \cdot \left(y \cdot b\right)\right)\right)} \]

   7. Applied egg-rr 31.8

      \[\leadsto \frac{x}{x + \left(y + 2 \cdot \left(\color{blue}{\frac{0.6944444444444444 - \frac{0.4444444444444444}{t \cdot t}}{-0.8333333333333334 - \frac{0.6666666666666666}{t}}} \cdot \left(y \cdot b\right)\right)\right)} \]

   if 9.36067332025399111e-177 < c < 1.37042763279640069e-155

   1. Initial program 1.4

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in b around inf 12.1

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(\left(0.6666666666666666 \cdot \frac{1}{t} - \left(0.8333333333333334 + a\right)\right) \cdot b\right)}}} \]

   3. Simplified 12.1

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(b \cdot \left(\frac{0.6666666666666666}{t} + \left(-0.8333333333333334 - a\right)\right)\right)}}} \]

   4. Taylor expanded in b around 0 37.3

      \[\leadsto \frac{x}{x + \color{blue}{\left(y + 2 \cdot \left(\left(0.6666666666666666 \cdot \frac{1}{t} - \left(0.8333333333333334 + a\right)\right) \cdot \left(y \cdot b\right)\right)\right)}} \]

   5. Taylor expanded in a around inf 54.6

      \[\leadsto \color{blue}{-0.5 \cdot \frac{x}{y \cdot \left(a \cdot b\right)}} \]

   6. Simplified 55.3

      \[\leadsto \color{blue}{-0.5 \cdot \frac{\frac{x}{y}}{a \cdot b}} \]

   if 1.37042763279640069e-155 < c < 8.9148942261260178e-128

   1. Initial program 2.6

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in b around inf 12.0

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(\left(0.6666666666666666 \cdot \frac{1}{t} - \left(0.8333333333333334 + a\right)\right) \cdot b\right)}}} \]

   3. Simplified 12.0

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(b \cdot \left(\frac{0.6666666666666666}{t} + \left(-0.8333333333333334 - a\right)\right)\right)}}} \]

   4. Taylor expanded in b around 0 32.8

      \[\leadsto \frac{x}{x + \color{blue}{\left(y + 2 \cdot \left(\left(0.6666666666666666 \cdot \frac{1}{t} - \left(0.8333333333333334 + a\right)\right) \cdot \left(y \cdot b\right)\right)\right)}} \]

   5. Taylor expanded in a around 0 32.2

      \[\leadsto \frac{x}{x + \left(y + 2 \cdot \left(\color{blue}{\left(0.6666666666666666 \cdot \frac{1}{t} - 0.8333333333333334\right)} \cdot \left(y \cdot b\right)\right)\right)} \]

   6. Simplified 32.2

      \[\leadsto \frac{x}{x + \left(y + 2 \cdot \left(\color{blue}{\left(\frac{0.6666666666666666}{t} + -0.8333333333333334\right)} \cdot \left(y \cdot b\right)\right)\right)} \]

   7. Taylor expanded in t around inf 34.8

      \[\leadsto \color{blue}{\frac{x}{-1.6666666666666667 \cdot \left(y \cdot b\right) + \left(y + x\right)}} \]

   if 8.9148942261260178e-128 < c < 816724496.554509521 or 1.4201743830549502e59 < c < 2.8121194545690723e142

   1. Initial program 4.0

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in c around inf 23.0

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(c \cdot \left(\left(0.8333333333333334 + a\right) - 0.6666666666666666 \cdot \frac{1}{t}\right)\right)}}} \]

   3. Simplified 23.0

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(c \cdot \left(\frac{-0.6666666666666666}{t} - \left(-0.8333333333333334 - a\right)\right)\right)}}} \]

   4. Taylor expanded in t around 0 33.5

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \color{blue}{\frac{-0.6666666666666666}{t}}\right)}} \]

   5. Taylor expanded in c around 0 33.5

      \[\leadsto \frac{x}{x + y \cdot e^{\color{blue}{-1.3333333333333333 \cdot \frac{c}{t}}}} \]

   6. Simplified 33.5

      \[\leadsto \frac{x}{x + y \cdot e^{\color{blue}{c \cdot \frac{-1.3333333333333333}{t}}}} \]

   if 816724496.554509521 < c < 1.4201743830549502e59 or 2.8121194545690723e142 < c

   1. Initial program 5.7

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in t around inf 17.3

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(-1 \cdot \left(\left(b - c\right) \cdot \left(0.8333333333333334 + a\right)\right)\right)}}} \]

   3. Simplified 17.3

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(\left(b - c\right) \cdot \left(-0.8333333333333334 - a\right)\right)}}} \]

   4. Taylor expanded in a around 0 20.9

      \[\leadsto \frac{x}{x + \color{blue}{e^{-1.6666666666666667 \cdot \left(b - c\right)} \cdot y}} \]

   5. Taylor expanded in x around 0 25.9

      \[\leadsto \color{blue}{\frac{x}{e^{-1.6666666666666667 \cdot \left(b - c\right)} \cdot y}} \]
3. Recombined 8 regimes into one program.

4. Final simplification 29.4

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.3789026442831328 \cdot 10^{-8}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -4.0666517143844075 \cdot 10^{-77}:\\ \;\;\;\;\frac{x}{x + \left(y + \left(b \cdot \left(y \cdot a\right)\right) \cdot -2\right)}\\ \mathbf{elif}\;c \leq -4.747189572510168 \cdot 10^{-303}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 2.3163471495837582 \cdot 10^{-297}:\\ \;\;\;\;\frac{x}{x \cdot x - y \cdot y} \cdot \left(x - y\right)\\ \mathbf{elif}\;c \leq 2.750494052163473 \cdot 10^{-283}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 1.4954040967811104 \cdot 10^{-226}:\\ \;\;\;\;\frac{x}{x + \left(y + 2 \cdot \left(\frac{0.6944444444444444 + \frac{-0.4444444444444444}{t \cdot t}}{-0.8333333333333334 - \frac{0.6666666666666666}{t}} \cdot \left(y \cdot b\right)\right)\right)}\\ \mathbf{elif}\;c \leq 7.809697862958332 \cdot 10^{-188}:\\ \;\;\;\;\frac{x}{x + \left(y + \left(b \cdot \left(y \cdot a\right)\right) \cdot -2\right)}\\ \mathbf{elif}\;c \leq 9.360673320253991 \cdot 10^{-177}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 1.3704276327964007 \cdot 10^{-155}:\\ \;\;\;\;-0.5 \cdot \frac{\frac{x}{y}}{b \cdot a}\\ \mathbf{elif}\;c \leq 8.914894226126018 \cdot 10^{-128}:\\ \;\;\;\;\frac{x}{\left(y \cdot b\right) \cdot -1.6666666666666667 + \left(x + y\right)}\\ \mathbf{elif}\;c \leq 816724496.5545095:\\ \;\;\;\;\frac{x}{x + y \cdot e^{c \cdot \frac{-1.3333333333333333}{t}}}\\ \mathbf{elif}\;c \leq 1.4201743830549502 \cdot 10^{+59}:\\ \;\;\;\;\frac{x}{y \cdot e^{-1.6666666666666667 \cdot \left(b - c\right)}}\\ \mathbf{elif}\;c \leq 2.812119454569072 \cdot 10^{+142}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{c \cdot \frac{-1.3333333333333333}{t}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot e^{-1.6666666666666667 \cdot \left(b - c\right)}}\\ \end{array} \]

Alternatives

Alternative 1
Error	31.5
Cost	8956

\[\begin{array}{l} t_1 := \frac{x}{y \cdot e^{2 \cdot \left(c \cdot a\right)}}\\ t_2 := \frac{x}{x + \left(y + \left(b \cdot \left(y \cdot a\right)\right) \cdot -2\right)}\\ t_3 := \frac{x}{\left(y \cdot b\right) \cdot -1.6666666666666667 + \left(x + y\right)}\\ \mathbf{if}\;c \leq -1.3789026442831328 \cdot 10^{-8}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -4.0666517143844075 \cdot 10^{-77}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -4.747189572510168 \cdot 10^{-303}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 2.3163471495837582 \cdot 10^{-297}:\\ \;\;\;\;\frac{x}{x \cdot x - y \cdot y} \cdot \left(x - y\right)\\ \mathbf{elif}\;c \leq 2.750494052163473 \cdot 10^{-283}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 1.4954040967811104 \cdot 10^{-226}:\\ \;\;\;\;\frac{x}{x + \left(y + 2 \cdot \left(\frac{0.6944444444444444 + \frac{-0.4444444444444444}{t \cdot t}}{-0.8333333333333334 - \frac{0.6666666666666666}{t}} \cdot \left(y \cdot b\right)\right)\right)}\\ \mathbf{elif}\;c \leq 7.809697862958332 \cdot 10^{-188}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 9.360673320253991 \cdot 10^{-177}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 1.3704276327964007 \cdot 10^{-155}:\\ \;\;\;\;-0.5 \cdot \frac{\frac{x}{y}}{b \cdot a}\\ \mathbf{elif}\;c \leq 8.914894226126018 \cdot 10^{-128}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq 816724496.5545095:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 1.4201743830549502 \cdot 10^{+59}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 5.699795176099973 \cdot 10^{+102}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 1.1667444518721299 \cdot 10^{+111}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 2.812119454569072 \cdot 10^{+142}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Error	29.9
Cost	8692

\[\begin{array}{l} t_1 := \frac{x}{y \cdot e^{-1.6666666666666667 \cdot \left(b - c\right)}}\\ t_2 := \frac{x}{x + \left(y + \left(b \cdot \left(y \cdot a\right)\right) \cdot -2\right)}\\ \mathbf{if}\;c \leq -1.3789026442831328 \cdot 10^{-8}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -4.0666517143844075 \cdot 10^{-77}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -4.747189572510168 \cdot 10^{-303}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 2.3163471495837582 \cdot 10^{-297}:\\ \;\;\;\;\frac{x}{x \cdot x - y \cdot y} \cdot \left(x - y\right)\\ \mathbf{elif}\;c \leq 2.750494052163473 \cdot 10^{-283}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 1.4954040967811104 \cdot 10^{-226}:\\ \;\;\;\;\frac{x}{x + \left(y + 2 \cdot \left(\frac{0.6944444444444444 + \frac{-0.4444444444444444}{t \cdot t}}{-0.8333333333333334 - \frac{0.6666666666666666}{t}} \cdot \left(y \cdot b\right)\right)\right)}\\ \mathbf{elif}\;c \leq 7.809697862958332 \cdot 10^{-188}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 9.360673320253991 \cdot 10^{-177}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 1.3704276327964007 \cdot 10^{-155}:\\ \;\;\;\;-0.5 \cdot \frac{\frac{x}{y}}{b \cdot a}\\ \mathbf{elif}\;c \leq 8.914894226126018 \cdot 10^{-128}:\\ \;\;\;\;\frac{x}{\left(y \cdot b\right) \cdot -1.6666666666666667 + \left(x + y\right)}\\ \mathbf{elif}\;c \leq 816724496.5545095:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 1.4201743830549502 \cdot 10^{+59}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 2.812119454569072 \cdot 10^{+142}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 3
Error	32.4
Cost	2548

\[\begin{array}{l} t_1 := \frac{x}{x + \left(y + \left(b \cdot \left(y \cdot a\right)\right) \cdot -2\right)}\\ t_2 := \frac{x}{\left(y \cdot b\right) \cdot -1.6666666666666667 + \left(x + y\right)}\\ \mathbf{if}\;c \leq -1.3789026442831328 \cdot 10^{-8}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -4.0666517143844075 \cdot 10^{-77}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -4.747189572510168 \cdot 10^{-303}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 2.3163471495837582 \cdot 10^{-297}:\\ \;\;\;\;\frac{x}{x \cdot x - y \cdot y} \cdot \left(x - y\right)\\ \mathbf{elif}\;c \leq 2.750494052163473 \cdot 10^{-283}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 1.4954040967811104 \cdot 10^{-226}:\\ \;\;\;\;\frac{x}{x + \left(y + 2 \cdot \left(\frac{0.6944444444444444 + \frac{-0.4444444444444444}{t \cdot t}}{-0.8333333333333334 - \frac{0.6666666666666666}{t}} \cdot \left(y \cdot b\right)\right)\right)}\\ \mathbf{elif}\;c \leq 7.809697862958332 \cdot 10^{-188}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 9.360673320253991 \cdot 10^{-177}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 1.3704276327964007 \cdot 10^{-155}:\\ \;\;\;\;-0.5 \cdot \frac{\frac{x}{y}}{b \cdot a}\\ \mathbf{elif}\;c \leq 8.914894226126018 \cdot 10^{-128}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 2.324498920503022 \cdot 10^{-20}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 4.9417486255329515 \cdot 10^{+176}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 2.050106759502565 \cdot 10^{+239}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y + 2 \cdot \left(a \cdot \left(y \cdot \left(c - b\right)\right)\right)}\\ \end{array} \]

Alternative 4
Error	33.1
Cost	2152

\[\begin{array}{l} t_1 := \frac{x}{y + 2 \cdot \left(a \cdot \left(y \cdot \left(c - b\right)\right)\right)}\\ \mathbf{if}\;x \leq -2.082525563661615 \cdot 10^{-55}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -5.66967484024032 \cdot 10^{-137}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -9.664701196836904 \cdot 10^{-155}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -4.0955131159809486 \cdot 10^{-240}:\\ \;\;\;\;\left(1 + \frac{x}{y}\right) + -1\\ \mathbf{elif}\;x \leq -2.396151615515064 \cdot 10^{-299}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.3100871746318377 \cdot 10^{-247}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 3.918476266315212 \cdot 10^{-233}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.371860736538561 \cdot 10^{-171}:\\ \;\;\;\;\frac{x}{\left(y \cdot b\right) \cdot -1.6666666666666667 + \left(x + y\right)}\\ \mathbf{elif}\;x \leq 9.819671932685324 \cdot 10^{-116}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.4981515348114123 \cdot 10^{-64}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 5
Error	32.9
Cost	2152

\[\begin{array}{l} t_1 := \frac{x}{y + 2 \cdot \left(a \cdot \left(y \cdot \left(c - b\right)\right)\right)}\\ \mathbf{if}\;x \leq -2.082525563661615 \cdot 10^{-55}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -5.66967484024032 \cdot 10^{-137}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -9.664701196836904 \cdot 10^{-155}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -4.0955131159809486 \cdot 10^{-240}:\\ \;\;\;\;\left(1 + \frac{x}{y}\right) + -1\\ \mathbf{elif}\;x \leq -2.396151615515064 \cdot 10^{-299}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.3100871746318377 \cdot 10^{-247}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 3.918476266315212 \cdot 10^{-233}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.371860736538561 \cdot 10^{-171}:\\ \;\;\;\;\frac{x}{\left(y \cdot b\right) \cdot -1.6666666666666667 + \left(x + y\right)}\\ \mathbf{elif}\;x \leq 8.962353119344293 \cdot 10^{-107}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.326135055713571 \cdot 10^{-56}:\\ \;\;\;\;\frac{x}{x \cdot x - y \cdot y} \cdot \left(x - y\right)\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 6
Error	32.2
Cost	2020

\[\begin{array}{l} t_1 := \frac{x}{x + \left(y + \left(b \cdot \left(y \cdot a\right)\right) \cdot -2\right)}\\ \mathbf{if}\;c \leq -1.3789026442831328 \cdot 10^{-8}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -4.0666517143844075 \cdot 10^{-77}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -4.747189572510168 \cdot 10^{-303}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 2.3163471495837582 \cdot 10^{-297}:\\ \;\;\;\;\frac{x}{x \cdot x - y \cdot y} \cdot \left(x - y\right)\\ \mathbf{elif}\;c \leq 1.501868760859669 \cdot 10^{-283}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 8.914894226126018 \cdot 10^{-128}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 2.324498920503022 \cdot 10^{-20}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 4.9417486255329515 \cdot 10^{+176}:\\ \;\;\;\;\frac{x}{\left(y \cdot b\right) \cdot -1.6666666666666667 + \left(x + y\right)}\\ \mathbf{elif}\;c \leq 2.050106759502565 \cdot 10^{+239}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y + 2 \cdot \left(a \cdot \left(y \cdot \left(c - b\right)\right)\right)}\\ \end{array} \]

Alternative 7
Error	31.6
Cost	1372

\[\begin{array}{l} t_1 := \left(1 + \frac{x}{y}\right) + -1\\ \mathbf{if}\;c \leq -4.747189572510168 \cdot 10^{-303}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 2.3163471495837582 \cdot 10^{-297}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 816724496.5545095:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 1.4201743830549502 \cdot 10^{+59}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 1.1667444518721299 \cdot 10^{+111}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 6.977631340822468 \cdot 10^{+180}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 1.0635469828111217 \cdot 10^{+245}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 8
Error	32.1
Cost	1232

\[\begin{array}{l} t_1 := \left(1 + \frac{x}{y}\right) + -1\\ \mathbf{if}\;c \leq -4.747189572510168 \cdot 10^{-303}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 2.3163471495837582 \cdot 10^{-297}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 2.324498920503022 \cdot 10^{-20}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 2.557962286492523 \cdot 10^{+228}:\\ \;\;\;\;\frac{x}{\left(y \cdot b\right) \cdot -1.6666666666666667 + \left(x + y\right)}\\ \mathbf{elif}\;c \leq 1.0635469828111217 \cdot 10^{+245}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 9
Error	30.7
Cost	584

\[\begin{array}{l} \mathbf{if}\;b \leq -8.543796380183112 \cdot 10^{+195}:\\ \;\;\;\;1\\ \mathbf{elif}\;b \leq -3.1 \cdot 10^{+152}:\\ \;\;\;\;\frac{x}{x + y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 10
Error	31.0
Cost	456

\[\begin{array}{l} \mathbf{if}\;b \leq -8.543796380183112 \cdot 10^{+195}:\\ \;\;\;\;1\\ \mathbf{elif}\;b \leq -3.1 \cdot 10^{+152}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 11
Error	30.4
Cost	64

\[1 \]

Reproduce

herbie shell --seed 2022228 
(FPCore (x y z t a b c)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, I"
  :precision binary64

  :herbie-target
  (if (< t -2.118326644891581e-50) (/ x (+ x (* y (exp (* 2.0 (- (+ (* a c) (* 0.8333333333333334 c)) (* a b))))))) (if (< t 5.196588770651547e-123) (/ x (+ x (* y (exp (* 2.0 (/ (- (* (* z (sqrt (+ t a))) (* (* 3.0 t) (- a (/ 5.0 6.0)))) (* (- (* (+ (/ 5.0 6.0) a) (* 3.0 t)) 2.0) (* (- a (/ 5.0 6.0)) (* (- b c) t)))) (* (* (* t t) 3.0) (- a (/ 5.0 6.0))))))))) (/ x (+ x (* y (exp (* 2.0 (- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))))))))))

  (/ x (+ x (* y (exp (* 2.0 (- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))))))))