Rosa's FloatVsDoubleBenchmark

Average Error: 0.5 → 0.3

Time: 40.3s

Precision: binary64

Cost: 8392

Math

\[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

↓

\[\begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot x1\right)\\ t_1 := x1 \cdot \left(x1 \cdot -3\right)\\ t_2 := x1 \cdot \left(x1 \cdot 3\right)\\ t_3 := x1 \cdot x1 + 1\\ t_4 := 3 \cdot \frac{\left(t_2 + x2 \cdot -2\right) - x1}{t_3}\\ t_5 := -1 - x1 \cdot x1\\ t_6 := \frac{x1 + \left(x2 \cdot -2 + t_1\right)}{t_5}\\ t_7 := t_0 - \frac{x1 + \left(x2 \cdot -2 - t_2\right)}{t_5} \cdot t_1\\ t_8 := \frac{x1 + \left(\left(x1 \cdot x1\right) \cdot -3 + x2 \cdot -2\right)}{t_5}\\ \mathbf{if}\;x1 \leq -2 \cdot 10^{-16}:\\ \;\;\;\;\left(t_3 \cdot \left(x1 \cdot \left(-2 \cdot \left(t_6 \cdot \left(3 - t_6\right)\right) - x1 \cdot \left(6 - t_6 \cdot 4\right)\right)\right) + t_7\right) + \left(\left(x1 + x1\right) + t_4\right)\\ \mathbf{elif}\;x1 \leq 3.8 \cdot 10^{-17}:\\ \;\;\;\;\left(t_3 \cdot \left(x2 \cdot \left(x1 \cdot \left(-12 - -4 \cdot \left(2 \cdot x2\right)\right)\right)\right) + t_7\right) + \left(x2 \cdot -6 - x1\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + \left(\left(t_3 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(t_8 \cdot 4 + -6\right) - \left(x1 \cdot 2\right) \cdot \left(t_8 \cdot \left(3 - t_8\right)\right)\right) + \left(t_2 \cdot \frac{\left(t_2 + 2 \cdot x2\right) - x1}{t_3} + t_0\right)\right) + t_4\right)\right)\\ \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (+
  x1
  (+
   (+
    (+
     (+
      (*
       (+
        (*
         (*
          (* 2.0 x1)
          (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0)))
         (- (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0)) 3.0))
        (*
         (* x1 x1)
         (-
          (* 4.0 (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0)))
          6.0)))
       (+ (* x1 x1) 1.0))
      (*
       (* (* 3.0 x1) x1)
       (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0))))
     (* (* x1 x1) x1))
    x1)
   (* 3.0 (/ (- (- (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0))))))

↓

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 x1)))
        (t_1 (* x1 (* x1 -3.0)))
        (t_2 (* x1 (* x1 3.0)))
        (t_3 (+ (* x1 x1) 1.0))
        (t_4 (* 3.0 (/ (- (+ t_2 (* x2 -2.0)) x1) t_3)))
        (t_5 (- -1.0 (* x1 x1)))
        (t_6 (/ (+ x1 (+ (* x2 -2.0) t_1)) t_5))
        (t_7 (- t_0 (* (/ (+ x1 (- (* x2 -2.0) t_2)) t_5) t_1)))
        (t_8 (/ (+ x1 (+ (* (* x1 x1) -3.0) (* x2 -2.0))) t_5)))
   (if (<= x1 -2e-16)
     (+
      (+
       (*
        t_3
        (* x1 (- (* -2.0 (* t_6 (- 3.0 t_6))) (* x1 (- 6.0 (* t_6 4.0))))))
       t_7)
      (+ (+ x1 x1) t_4))
     (if (<= x1 3.8e-17)
       (+
        (+ (* t_3 (* x2 (* x1 (- -12.0 (* -4.0 (* 2.0 x2)))))) t_7)
        (- (* x2 -6.0) x1))
       (+
        x1
        (+
         x1
         (+
          (+
           (*
            t_3
            (-
             (* (* x1 x1) (+ (* t_8 4.0) -6.0))
             (* (* x1 2.0) (* t_8 (- 3.0 t_8)))))
           (+ (* t_2 (/ (- (+ t_2 (* 2.0 x2)) x1) t_3)) t_0))
          t_4)))))))

C

double code(double x1, double x2) {
	return x1 + (((((((((2.0 * x1) * (((((3.0 * x1) * x1) + (2.0 * x2)) - x1) / ((x1 * x1) + 1.0))) * ((((((3.0 * x1) * x1) + (2.0 * x2)) - x1) / ((x1 * x1) + 1.0)) - 3.0)) + ((x1 * x1) * ((4.0 * (((((3.0 * x1) * x1) + (2.0 * x2)) - x1) / ((x1 * x1) + 1.0))) - 6.0))) * ((x1 * x1) + 1.0)) + (((3.0 * x1) * x1) * (((((3.0 * x1) * x1) + (2.0 * x2)) - x1) / ((x1 * x1) + 1.0)))) + ((x1 * x1) * x1)) + x1) + (3.0 * (((((3.0 * x1) * x1) - (2.0 * x2)) - x1) / ((x1 * x1) + 1.0))));
}

↓

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * x1);
	double t_1 = x1 * (x1 * -3.0);
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = (x1 * x1) + 1.0;
	double t_4 = 3.0 * (((t_2 + (x2 * -2.0)) - x1) / t_3);
	double t_5 = -1.0 - (x1 * x1);
	double t_6 = (x1 + ((x2 * -2.0) + t_1)) / t_5;
	double t_7 = t_0 - (((x1 + ((x2 * -2.0) - t_2)) / t_5) * t_1);
	double t_8 = (x1 + (((x1 * x1) * -3.0) + (x2 * -2.0))) / t_5;
	double tmp;
	if (x1 <= -2e-16) {
		tmp = ((t_3 * (x1 * ((-2.0 * (t_6 * (3.0 - t_6))) - (x1 * (6.0 - (t_6 * 4.0)))))) + t_7) + ((x1 + x1) + t_4);
	} else if (x1 <= 3.8e-17) {
		tmp = ((t_3 * (x2 * (x1 * (-12.0 - (-4.0 * (2.0 * x2)))))) + t_7) + ((x2 * -6.0) - x1);
	} else {
		tmp = x1 + (x1 + (((t_3 * (((x1 * x1) * ((t_8 * 4.0) + -6.0)) - ((x1 * 2.0) * (t_8 * (3.0 - t_8))))) + ((t_2 * (((t_2 + (2.0 * x2)) - x1) / t_3)) + t_0)) + t_4));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    code = x1 + (((((((((2.0d0 * x1) * (((((3.0d0 * x1) * x1) + (2.0d0 * x2)) - x1) / ((x1 * x1) + 1.0d0))) * ((((((3.0d0 * x1) * x1) + (2.0d0 * x2)) - x1) / ((x1 * x1) + 1.0d0)) - 3.0d0)) + ((x1 * x1) * ((4.0d0 * (((((3.0d0 * x1) * x1) + (2.0d0 * x2)) - x1) / ((x1 * x1) + 1.0d0))) - 6.0d0))) * ((x1 * x1) + 1.0d0)) + (((3.0d0 * x1) * x1) * (((((3.0d0 * x1) * x1) + (2.0d0 * x2)) - x1) / ((x1 * x1) + 1.0d0)))) + ((x1 * x1) * x1)) + x1) + (3.0d0 * (((((3.0d0 * x1) * x1) - (2.0d0 * x2)) - x1) / ((x1 * x1) + 1.0d0))))
end function

↓

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    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) :: t_8
    real(8) :: tmp
    t_0 = x1 * (x1 * x1)
    t_1 = x1 * (x1 * (-3.0d0))
    t_2 = x1 * (x1 * 3.0d0)
    t_3 = (x1 * x1) + 1.0d0
    t_4 = 3.0d0 * (((t_2 + (x2 * (-2.0d0))) - x1) / t_3)
    t_5 = (-1.0d0) - (x1 * x1)
    t_6 = (x1 + ((x2 * (-2.0d0)) + t_1)) / t_5
    t_7 = t_0 - (((x1 + ((x2 * (-2.0d0)) - t_2)) / t_5) * t_1)
    t_8 = (x1 + (((x1 * x1) * (-3.0d0)) + (x2 * (-2.0d0)))) / t_5
    if (x1 <= (-2d-16)) then
        tmp = ((t_3 * (x1 * (((-2.0d0) * (t_6 * (3.0d0 - t_6))) - (x1 * (6.0d0 - (t_6 * 4.0d0)))))) + t_7) + ((x1 + x1) + t_4)
    else if (x1 <= 3.8d-17) then
        tmp = ((t_3 * (x2 * (x1 * ((-12.0d0) - ((-4.0d0) * (2.0d0 * x2)))))) + t_7) + ((x2 * (-6.0d0)) - x1)
    else
        tmp = x1 + (x1 + (((t_3 * (((x1 * x1) * ((t_8 * 4.0d0) + (-6.0d0))) - ((x1 * 2.0d0) * (t_8 * (3.0d0 - t_8))))) + ((t_2 * (((t_2 + (2.0d0 * x2)) - x1) / t_3)) + t_0)) + t_4))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	return x1 + (((((((((2.0 * x1) * (((((3.0 * x1) * x1) + (2.0 * x2)) - x1) / ((x1 * x1) + 1.0))) * ((((((3.0 * x1) * x1) + (2.0 * x2)) - x1) / ((x1 * x1) + 1.0)) - 3.0)) + ((x1 * x1) * ((4.0 * (((((3.0 * x1) * x1) + (2.0 * x2)) - x1) / ((x1 * x1) + 1.0))) - 6.0))) * ((x1 * x1) + 1.0)) + (((3.0 * x1) * x1) * (((((3.0 * x1) * x1) + (2.0 * x2)) - x1) / ((x1 * x1) + 1.0)))) + ((x1 * x1) * x1)) + x1) + (3.0 * (((((3.0 * x1) * x1) - (2.0 * x2)) - x1) / ((x1 * x1) + 1.0))));
}

↓

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * x1);
	double t_1 = x1 * (x1 * -3.0);
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = (x1 * x1) + 1.0;
	double t_4 = 3.0 * (((t_2 + (x2 * -2.0)) - x1) / t_3);
	double t_5 = -1.0 - (x1 * x1);
	double t_6 = (x1 + ((x2 * -2.0) + t_1)) / t_5;
	double t_7 = t_0 - (((x1 + ((x2 * -2.0) - t_2)) / t_5) * t_1);
	double t_8 = (x1 + (((x1 * x1) * -3.0) + (x2 * -2.0))) / t_5;
	double tmp;
	if (x1 <= -2e-16) {
		tmp = ((t_3 * (x1 * ((-2.0 * (t_6 * (3.0 - t_6))) - (x1 * (6.0 - (t_6 * 4.0)))))) + t_7) + ((x1 + x1) + t_4);
	} else if (x1 <= 3.8e-17) {
		tmp = ((t_3 * (x2 * (x1 * (-12.0 - (-4.0 * (2.0 * x2)))))) + t_7) + ((x2 * -6.0) - x1);
	} else {
		tmp = x1 + (x1 + (((t_3 * (((x1 * x1) * ((t_8 * 4.0) + -6.0)) - ((x1 * 2.0) * (t_8 * (3.0 - t_8))))) + ((t_2 * (((t_2 + (2.0 * x2)) - x1) / t_3)) + t_0)) + t_4));
	}
	return tmp;
}

Python

def code(x1, x2):
	return x1 + (((((((((2.0 * x1) * (((((3.0 * x1) * x1) + (2.0 * x2)) - x1) / ((x1 * x1) + 1.0))) * ((((((3.0 * x1) * x1) + (2.0 * x2)) - x1) / ((x1 * x1) + 1.0)) - 3.0)) + ((x1 * x1) * ((4.0 * (((((3.0 * x1) * x1) + (2.0 * x2)) - x1) / ((x1 * x1) + 1.0))) - 6.0))) * ((x1 * x1) + 1.0)) + (((3.0 * x1) * x1) * (((((3.0 * x1) * x1) + (2.0 * x2)) - x1) / ((x1 * x1) + 1.0)))) + ((x1 * x1) * x1)) + x1) + (3.0 * (((((3.0 * x1) * x1) - (2.0 * x2)) - x1) / ((x1 * x1) + 1.0))))

↓

def code(x1, x2):
	t_0 = x1 * (x1 * x1)
	t_1 = x1 * (x1 * -3.0)
	t_2 = x1 * (x1 * 3.0)
	t_3 = (x1 * x1) + 1.0
	t_4 = 3.0 * (((t_2 + (x2 * -2.0)) - x1) / t_3)
	t_5 = -1.0 - (x1 * x1)
	t_6 = (x1 + ((x2 * -2.0) + t_1)) / t_5
	t_7 = t_0 - (((x1 + ((x2 * -2.0) - t_2)) / t_5) * t_1)
	t_8 = (x1 + (((x1 * x1) * -3.0) + (x2 * -2.0))) / t_5
	tmp = 0
	if x1 <= -2e-16:
		tmp = ((t_3 * (x1 * ((-2.0 * (t_6 * (3.0 - t_6))) - (x1 * (6.0 - (t_6 * 4.0)))))) + t_7) + ((x1 + x1) + t_4)
	elif x1 <= 3.8e-17:
		tmp = ((t_3 * (x2 * (x1 * (-12.0 - (-4.0 * (2.0 * x2)))))) + t_7) + ((x2 * -6.0) - x1)
	else:
		tmp = x1 + (x1 + (((t_3 * (((x1 * x1) * ((t_8 * 4.0) + -6.0)) - ((x1 * 2.0) * (t_8 * (3.0 - t_8))))) + ((t_2 * (((t_2 + (2.0 * x2)) - x1) / t_3)) + t_0)) + t_4))
	return tmp

Julia

function code(x1, x2)
	return Float64(x1 + Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(2.0 * x1) * Float64(Float64(Float64(Float64(Float64(3.0 * x1) * x1) + Float64(2.0 * x2)) - x1) / Float64(Float64(x1 * x1) + 1.0))) * Float64(Float64(Float64(Float64(Float64(Float64(3.0 * x1) * x1) + Float64(2.0 * x2)) - x1) / Float64(Float64(x1 * x1) + 1.0)) - 3.0)) + Float64(Float64(x1 * x1) * Float64(Float64(4.0 * Float64(Float64(Float64(Float64(Float64(3.0 * x1) * x1) + Float64(2.0 * x2)) - x1) / Float64(Float64(x1 * x1) + 1.0))) - 6.0))) * Float64(Float64(x1 * x1) + 1.0)) + Float64(Float64(Float64(3.0 * x1) * x1) * Float64(Float64(Float64(Float64(Float64(3.0 * x1) * x1) + Float64(2.0 * x2)) - x1) / Float64(Float64(x1 * x1) + 1.0)))) + Float64(Float64(x1 * x1) * x1)) + x1) + Float64(3.0 * Float64(Float64(Float64(Float64(Float64(3.0 * x1) * x1) - Float64(2.0 * x2)) - x1) / Float64(Float64(x1 * x1) + 1.0)))))
end

↓

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * x1))
	t_1 = Float64(x1 * Float64(x1 * -3.0))
	t_2 = Float64(x1 * Float64(x1 * 3.0))
	t_3 = Float64(Float64(x1 * x1) + 1.0)
	t_4 = Float64(3.0 * Float64(Float64(Float64(t_2 + Float64(x2 * -2.0)) - x1) / t_3))
	t_5 = Float64(-1.0 - Float64(x1 * x1))
	t_6 = Float64(Float64(x1 + Float64(Float64(x2 * -2.0) + t_1)) / t_5)
	t_7 = Float64(t_0 - Float64(Float64(Float64(x1 + Float64(Float64(x2 * -2.0) - t_2)) / t_5) * t_1))
	t_8 = Float64(Float64(x1 + Float64(Float64(Float64(x1 * x1) * -3.0) + Float64(x2 * -2.0))) / t_5)
	tmp = 0.0
	if (x1 <= -2e-16)
		tmp = Float64(Float64(Float64(t_3 * Float64(x1 * Float64(Float64(-2.0 * Float64(t_6 * Float64(3.0 - t_6))) - Float64(x1 * Float64(6.0 - Float64(t_6 * 4.0)))))) + t_7) + Float64(Float64(x1 + x1) + t_4));
	elseif (x1 <= 3.8e-17)
		tmp = Float64(Float64(Float64(t_3 * Float64(x2 * Float64(x1 * Float64(-12.0 - Float64(-4.0 * Float64(2.0 * x2)))))) + t_7) + Float64(Float64(x2 * -6.0) - x1));
	else
		tmp = Float64(x1 + Float64(x1 + Float64(Float64(Float64(t_3 * Float64(Float64(Float64(x1 * x1) * Float64(Float64(t_8 * 4.0) + -6.0)) - Float64(Float64(x1 * 2.0) * Float64(t_8 * Float64(3.0 - t_8))))) + Float64(Float64(t_2 * Float64(Float64(Float64(t_2 + Float64(2.0 * x2)) - x1) / t_3)) + t_0)) + t_4)));
	end
	return tmp
end

MATLAB

function tmp = code(x1, x2)
	tmp = x1 + (((((((((2.0 * x1) * (((((3.0 * x1) * x1) + (2.0 * x2)) - x1) / ((x1 * x1) + 1.0))) * ((((((3.0 * x1) * x1) + (2.0 * x2)) - x1) / ((x1 * x1) + 1.0)) - 3.0)) + ((x1 * x1) * ((4.0 * (((((3.0 * x1) * x1) + (2.0 * x2)) - x1) / ((x1 * x1) + 1.0))) - 6.0))) * ((x1 * x1) + 1.0)) + (((3.0 * x1) * x1) * (((((3.0 * x1) * x1) + (2.0 * x2)) - x1) / ((x1 * x1) + 1.0)))) + ((x1 * x1) * x1)) + x1) + (3.0 * (((((3.0 * x1) * x1) - (2.0 * x2)) - x1) / ((x1 * x1) + 1.0))));
end

↓

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * x1);
	t_1 = x1 * (x1 * -3.0);
	t_2 = x1 * (x1 * 3.0);
	t_3 = (x1 * x1) + 1.0;
	t_4 = 3.0 * (((t_2 + (x2 * -2.0)) - x1) / t_3);
	t_5 = -1.0 - (x1 * x1);
	t_6 = (x1 + ((x2 * -2.0) + t_1)) / t_5;
	t_7 = t_0 - (((x1 + ((x2 * -2.0) - t_2)) / t_5) * t_1);
	t_8 = (x1 + (((x1 * x1) * -3.0) + (x2 * -2.0))) / t_5;
	tmp = 0.0;
	if (x1 <= -2e-16)
		tmp = ((t_3 * (x1 * ((-2.0 * (t_6 * (3.0 - t_6))) - (x1 * (6.0 - (t_6 * 4.0)))))) + t_7) + ((x1 + x1) + t_4);
	elseif (x1 <= 3.8e-17)
		tmp = ((t_3 * (x2 * (x1 * (-12.0 - (-4.0 * (2.0 * x2)))))) + t_7) + ((x2 * -6.0) - x1);
	else
		tmp = x1 + (x1 + (((t_3 * (((x1 * x1) * ((t_8 * 4.0) + -6.0)) - ((x1 * 2.0) * (t_8 * (3.0 - t_8))))) + ((t_2 * (((t_2 + (2.0 * x2)) - x1) / t_3)) + t_0)) + t_4));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := N[(x1 + N[(N[(N[(N[(N[(N[(N[(N[(N[(2.0 * x1), $MachinePrecision] * N[(N[(N[(N[(N[(3.0 * x1), $MachinePrecision] * x1), $MachinePrecision] + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(N[(N[(N[(N[(3.0 * x1), $MachinePrecision] * x1), $MachinePrecision] + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(4.0 * N[(N[(N[(N[(N[(3.0 * x1), $MachinePrecision] * x1), $MachinePrecision] + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(3.0 * x1), $MachinePrecision] * x1), $MachinePrecision] * N[(N[(N[(N[(N[(3.0 * x1), $MachinePrecision] * x1), $MachinePrecision] + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * x1), $MachinePrecision]), $MachinePrecision] + x1), $MachinePrecision] + N[(3.0 * N[(N[(N[(N[(N[(3.0 * x1), $MachinePrecision] * x1), $MachinePrecision] - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

↓

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * -3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$4 = N[(3.0 * N[(N[(N[(t$95$2 + N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(x1 + N[(N[(x2 * -2.0), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision] / t$95$5), $MachinePrecision]}, Block[{t$95$7 = N[(t$95$0 - N[(N[(N[(x1 + N[(N[(x2 * -2.0), $MachinePrecision] - t$95$2), $MachinePrecision]), $MachinePrecision] / t$95$5), $MachinePrecision] * t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$8 = N[(N[(x1 + N[(N[(N[(x1 * x1), $MachinePrecision] * -3.0), $MachinePrecision] + N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$5), $MachinePrecision]}, If[LessEqual[x1, -2e-16], N[(N[(N[(t$95$3 * N[(x1 * N[(N[(-2.0 * N[(t$95$6 * N[(3.0 - t$95$6), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x1 * N[(6.0 - N[(t$95$6 * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$7), $MachinePrecision] + N[(N[(x1 + x1), $MachinePrecision] + t$95$4), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 3.8e-17], N[(N[(N[(t$95$3 * N[(x2 * N[(x1 * N[(-12.0 - N[(-4.0 * N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$7), $MachinePrecision] + N[(N[(x2 * -6.0), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(x1 + N[(N[(N[(t$95$3 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$8 * 4.0), $MachinePrecision] + -6.0), $MachinePrecision]), $MachinePrecision] - N[(N[(x1 * 2.0), $MachinePrecision] * N[(t$95$8 * N[(3.0 - t$95$8), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$2 * N[(N[(N[(t$95$2 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$3), $MachinePrecision]), $MachinePrecision] + t$95$0), $MachinePrecision]), $MachinePrecision] + t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -2e-16

   1. Initial program 0.8

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Simplified 0.8

      \[\leadsto \color{blue}{\left(\left(x1 \cdot x1 + 1\right) \cdot \left(\frac{x1 + \left(x2 \cdot -2 - x1 \cdot \left(x1 \cdot 3\right)\right)}{-1 - x1 \cdot x1} \cdot \left(\left(x1 \cdot 2\right) \cdot \left(\frac{x1 + \left(x2 \cdot -2 - x1 \cdot \left(x1 \cdot 3\right)\right)}{-1 - x1 \cdot x1} + -3\right)\right) + \left(x1 \cdot x1\right) \cdot \left(\frac{x1 + \left(x2 \cdot -2 - x1 \cdot \left(x1 \cdot 3\right)\right)}{-1 - x1 \cdot x1} \cdot 4 + -6\right)\right) + \left(x1 \cdot \left(x1 \cdot x1\right) - \frac{x1 + \left(x2 \cdot -2 - x1 \cdot \left(x1 \cdot 3\right)\right)}{-1 - x1 \cdot x1} \cdot \left(x1 \cdot \left(x1 \cdot -3\right)\right)\right)\right) + \left(\left(x1 + x1\right) + 3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot -2\right) - x1}{x1 \cdot x1 + 1}\right)} \]
      Proof

      [Start] 0.8

      \[ x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      rational_best-simplify-116 [=>] 0.8

      \[ \color{blue}{3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right)\right)} \]

   3. Applied egg-rr 0.7

      \[\leadsto \left(\left(x1 \cdot x1 + 1\right) \cdot \left(\frac{x1 + \left(x2 \cdot -2 - x1 \cdot \left(x1 \cdot 3\right)\right)}{-1 - x1 \cdot x1} \cdot \left(\left(x1 \cdot 2\right) \cdot \left(\frac{x1 + \left(x2 \cdot -2 - x1 \cdot \left(x1 \cdot 3\right)\right)}{-1 - x1 \cdot x1} + -3\right)\right) + \color{blue}{\left(\left(x1 \cdot x1\right) \cdot \left(\frac{x1 + \left(x2 \cdot -2 + x1 \cdot \left(x1 \cdot -3\right)\right)}{-1 - x1 \cdot x1} \cdot 4\right) - \left(x1 \cdot x1\right) \cdot 6\right)}\right) + \left(x1 \cdot \left(x1 \cdot x1\right) - \frac{x1 + \left(x2 \cdot -2 - x1 \cdot \left(x1 \cdot 3\right)\right)}{-1 - x1 \cdot x1} \cdot \left(x1 \cdot \left(x1 \cdot -3\right)\right)\right)\right) + \left(\left(x1 + x1\right) + 3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot -2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   4. Applied egg-rr 0.7

      \[\leadsto \left(\left(x1 \cdot x1 + 1\right) \cdot \color{blue}{\left(\left(3 - \frac{\left(x1 + x2 \cdot -2\right) - \left(x1 \cdot x1\right) \cdot 3}{-1 - x1 \cdot x1}\right) \cdot \left(\frac{\left(x1 + x2 \cdot -2\right) - \left(x1 \cdot x1\right) \cdot 3}{-1 - x1 \cdot x1} \cdot \left(x1 \cdot -2\right)\right) - \left(x1 \cdot x1\right) \cdot \left(6 + \frac{\left(x1 + x2 \cdot -2\right) - \left(x1 \cdot x1\right) \cdot 3}{-1 - x1 \cdot x1} \cdot -4\right)\right)} + \left(x1 \cdot \left(x1 \cdot x1\right) - \frac{x1 + \left(x2 \cdot -2 - x1 \cdot \left(x1 \cdot 3\right)\right)}{-1 - x1 \cdot x1} \cdot \left(x1 \cdot \left(x1 \cdot -3\right)\right)\right)\right) + \left(\left(x1 + x1\right) + 3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot -2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   5. Simplified 0.7

      \[\leadsto \left(\left(x1 \cdot x1 + 1\right) \cdot \color{blue}{\left(\frac{\left(x1 + x2 \cdot -2\right) - 3 \cdot \left(x1 \cdot x1\right)}{-1 - x1 \cdot x1} \cdot \left(\left(3 - \frac{\left(x1 + x2 \cdot -2\right) - 3 \cdot \left(x1 \cdot x1\right)}{-1 - x1 \cdot x1}\right) \cdot \left(x1 \cdot -2\right)\right) - \left(x1 \cdot x1\right) \cdot \left(6 + -4 \cdot \frac{\left(x1 + x2 \cdot -2\right) - 3 \cdot \left(x1 \cdot x1\right)}{-1 - x1 \cdot x1}\right)\right)} + \left(x1 \cdot \left(x1 \cdot x1\right) - \frac{x1 + \left(x2 \cdot -2 - x1 \cdot \left(x1 \cdot 3\right)\right)}{-1 - x1 \cdot x1} \cdot \left(x1 \cdot \left(x1 \cdot -3\right)\right)\right)\right) + \left(\left(x1 + x1\right) + 3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot -2\right) - x1}{x1 \cdot x1 + 1}\right) \]
      Proof

      [Start] 0.7	\[ \left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(3 - \frac{\left(x1 + x2 \cdot -2\right) - \left(x1 \cdot x1\right) \cdot 3}{-1 - x1 \cdot x1}\right) \cdot \left(\frac{\left(x1 + x2 \cdot -2\right) - \left(x1 \cdot x1\right) \cdot 3}{-1 - x1 \cdot x1} \cdot \left(x1 \cdot -2\right)\right) - \left(x1 \cdot x1\right) \cdot \left(6 + \frac{\left(x1 + x2 \cdot -2\right) - \left(x1 \cdot x1\right) \cdot 3}{-1 - x1 \cdot x1} \cdot -4\right)\right) + \left(x1 \cdot \left(x1 \cdot x1\right) - \frac{x1 + \left(x2 \cdot -2 - x1 \cdot \left(x1 \cdot 3\right)\right)}{-1 - x1 \cdot x1} \cdot \left(x1 \cdot \left(x1 \cdot -3\right)\right)\right)\right) + \left(\left(x1 + x1\right) + 3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot -2\right) - x1}{x1 \cdot x1 + 1}\right) \]
      rational_best-simplify-113 [=>] 0.7	\[ \left(\left(x1 \cdot x1 + 1\right) \cdot \left(\color{blue}{\frac{\left(x1 + x2 \cdot -2\right) - \left(x1 \cdot x1\right) \cdot 3}{-1 - x1 \cdot x1} \cdot \left(\left(3 - \frac{\left(x1 + x2 \cdot -2\right) - \left(x1 \cdot x1\right) \cdot 3}{-1 - x1 \cdot x1}\right) \cdot \left(x1 \cdot -2\right)\right)} - \left(x1 \cdot x1\right) \cdot \left(6 + \frac{\left(x1 + x2 \cdot -2\right) - \left(x1 \cdot x1\right) \cdot 3}{-1 - x1 \cdot x1} \cdot -4\right)\right) + \left(x1 \cdot \left(x1 \cdot x1\right) - \frac{x1 + \left(x2 \cdot -2 - x1 \cdot \left(x1 \cdot 3\right)\right)}{-1 - x1 \cdot x1} \cdot \left(x1 \cdot \left(x1 \cdot -3\right)\right)\right)\right) + \left(\left(x1 + x1\right) + 3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot -2\right) - x1}{x1 \cdot x1 + 1}\right) \]
      rational_best-simplify-3 [=>] 0.7	\[ \left(\left(x1 \cdot x1 + 1\right) \cdot \left(\frac{\left(x1 + x2 \cdot -2\right) - \color{blue}{3 \cdot \left(x1 \cdot x1\right)}}{-1 - x1 \cdot x1} \cdot \left(\left(3 - \frac{\left(x1 + x2 \cdot -2\right) - \left(x1 \cdot x1\right) \cdot 3}{-1 - x1 \cdot x1}\right) \cdot \left(x1 \cdot -2\right)\right) - \left(x1 \cdot x1\right) \cdot \left(6 + \frac{\left(x1 + x2 \cdot -2\right) - \left(x1 \cdot x1\right) \cdot 3}{-1 - x1 \cdot x1} \cdot -4\right)\right) + \left(x1 \cdot \left(x1 \cdot x1\right) - \frac{x1 + \left(x2 \cdot -2 - x1 \cdot \left(x1 \cdot 3\right)\right)}{-1 - x1 \cdot x1} \cdot \left(x1 \cdot \left(x1 \cdot -3\right)\right)\right)\right) + \left(\left(x1 + x1\right) + 3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot -2\right) - x1}{x1 \cdot x1 + 1}\right) \]
      rational_best-simplify-3 [=>] 0.7	\[ \left(\left(x1 \cdot x1 + 1\right) \cdot \left(\frac{\left(x1 + x2 \cdot -2\right) - 3 \cdot \left(x1 \cdot x1\right)}{-1 - x1 \cdot x1} \cdot \left(\left(3 - \frac{\left(x1 + x2 \cdot -2\right) - \color{blue}{3 \cdot \left(x1 \cdot x1\right)}}{-1 - x1 \cdot x1}\right) \cdot \left(x1 \cdot -2\right)\right) - \left(x1 \cdot x1\right) \cdot \left(6 + \frac{\left(x1 + x2 \cdot -2\right) - \left(x1 \cdot x1\right) \cdot 3}{-1 - x1 \cdot x1} \cdot -4\right)\right) + \left(x1 \cdot \left(x1 \cdot x1\right) - \frac{x1 + \left(x2 \cdot -2 - x1 \cdot \left(x1 \cdot 3\right)\right)}{-1 - x1 \cdot x1} \cdot \left(x1 \cdot \left(x1 \cdot -3\right)\right)\right)\right) + \left(\left(x1 + x1\right) + 3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot -2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   6. Applied egg-rr 0.9

      \[\leadsto \left(\left(x1 \cdot x1 + 1\right) \cdot \color{blue}{\left(x1 \cdot \left(-2 \cdot \left(\frac{x1 + \left(x2 \cdot -2 + x1 \cdot \left(x1 \cdot -3\right)\right)}{-1 - x1 \cdot x1} \cdot \left(3 - \frac{x1 + \left(x2 \cdot -2 + x1 \cdot \left(x1 \cdot -3\right)\right)}{-1 - x1 \cdot x1}\right)\right) - x1 \cdot \left(6 - \frac{x1 + \left(x2 \cdot -2 + x1 \cdot \left(x1 \cdot -3\right)\right)}{-1 - x1 \cdot x1} \cdot 4\right)\right)\right)} + \left(x1 \cdot \left(x1 \cdot x1\right) - \frac{x1 + \left(x2 \cdot -2 - x1 \cdot \left(x1 \cdot 3\right)\right)}{-1 - x1 \cdot x1} \cdot \left(x1 \cdot \left(x1 \cdot -3\right)\right)\right)\right) + \left(\left(x1 + x1\right) + 3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot -2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   if -2e-16 < x1 < 3.8000000000000001e-17

   1. Initial program 0.4

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Simplified 0.4

      \[\leadsto \color{blue}{\left(\left(x1 \cdot x1 + 1\right) \cdot \left(\frac{x1 + \left(x2 \cdot -2 - x1 \cdot \left(x1 \cdot 3\right)\right)}{-1 - x1 \cdot x1} \cdot \left(\left(x1 \cdot 2\right) \cdot \left(\frac{x1 + \left(x2 \cdot -2 - x1 \cdot \left(x1 \cdot 3\right)\right)}{-1 - x1 \cdot x1} + -3\right)\right) + \left(x1 \cdot x1\right) \cdot \left(\frac{x1 + \left(x2 \cdot -2 - x1 \cdot \left(x1 \cdot 3\right)\right)}{-1 - x1 \cdot x1} \cdot 4 + -6\right)\right) + \left(x1 \cdot \left(x1 \cdot x1\right) - \frac{x1 + \left(x2 \cdot -2 - x1 \cdot \left(x1 \cdot 3\right)\right)}{-1 - x1 \cdot x1} \cdot \left(x1 \cdot \left(x1 \cdot -3\right)\right)\right)\right) + \left(\left(x1 + x1\right) + 3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot -2\right) - x1}{x1 \cdot x1 + 1}\right)} \]
      Proof

      [Start] 0.4

      \[ x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      rational_best-simplify-116 [=>] 0.4

      \[ \color{blue}{3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right)\right)} \]

   3. Taylor expanded in x1 around 0 0.4

      \[\leadsto \left(\left(x1 \cdot x1 + 1\right) \cdot \color{blue}{\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right)} + \left(x1 \cdot \left(x1 \cdot x1\right) - \frac{x1 + \left(x2 \cdot -2 - x1 \cdot \left(x1 \cdot 3\right)\right)}{-1 - x1 \cdot x1} \cdot \left(x1 \cdot \left(x1 \cdot -3\right)\right)\right)\right) + \left(\left(x1 + x1\right) + 3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot -2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   4. Simplified 0.4

      \[\leadsto \left(\left(x1 \cdot x1 + 1\right) \cdot \color{blue}{\left(x2 \cdot \left(x1 \cdot \left(-12 - -4 \cdot \left(2 \cdot x2\right)\right)\right)\right)} + \left(x1 \cdot \left(x1 \cdot x1\right) - \frac{x1 + \left(x2 \cdot -2 - x1 \cdot \left(x1 \cdot 3\right)\right)}{-1 - x1 \cdot x1} \cdot \left(x1 \cdot \left(x1 \cdot -3\right)\right)\right)\right) + \left(\left(x1 + x1\right) + 3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot -2\right) - x1}{x1 \cdot x1 + 1}\right) \]
      Proof

      [Start] 0.4	\[ \left(\left(x1 \cdot x1 + 1\right) \cdot \left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right) + \left(x1 \cdot \left(x1 \cdot x1\right) - \frac{x1 + \left(x2 \cdot -2 - x1 \cdot \left(x1 \cdot 3\right)\right)}{-1 - x1 \cdot x1} \cdot \left(x1 \cdot \left(x1 \cdot -3\right)\right)\right)\right) + \left(\left(x1 + x1\right) + 3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot -2\right) - x1}{x1 \cdot x1 + 1}\right) \]
      rational_best-simplify-113 [=>] 0.4	\[ \left(\left(x1 \cdot x1 + 1\right) \cdot \color{blue}{\left(x2 \cdot \left(4 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right)} + \left(x1 \cdot \left(x1 \cdot x1\right) - \frac{x1 + \left(x2 \cdot -2 - x1 \cdot \left(x1 \cdot 3\right)\right)}{-1 - x1 \cdot x1} \cdot \left(x1 \cdot \left(x1 \cdot -3\right)\right)\right)\right) + \left(\left(x1 + x1\right) + 3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot -2\right) - x1}{x1 \cdot x1 + 1}\right) \]
      rational_best-simplify-113 [=>] 0.4	\[ \left(\left(x1 \cdot x1 + 1\right) \cdot \left(x2 \cdot \color{blue}{\left(x1 \cdot \left(4 \cdot \left(2 \cdot x2 - 3\right)\right)\right)}\right) + \left(x1 \cdot \left(x1 \cdot x1\right) - \frac{x1 + \left(x2 \cdot -2 - x1 \cdot \left(x1 \cdot 3\right)\right)}{-1 - x1 \cdot x1} \cdot \left(x1 \cdot \left(x1 \cdot -3\right)\right)\right)\right) + \left(\left(x1 + x1\right) + 3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot -2\right) - x1}{x1 \cdot x1 + 1}\right) \]
      rational_best-simplify-65 [=>] 0.4	\[ \left(\left(x1 \cdot x1 + 1\right) \cdot \left(x2 \cdot \left(x1 \cdot \left(4 \cdot \color{blue}{\left(-\left(3 - 2 \cdot x2\right)\right)}\right)\right)\right) + \left(x1 \cdot \left(x1 \cdot x1\right) - \frac{x1 + \left(x2 \cdot -2 - x1 \cdot \left(x1 \cdot 3\right)\right)}{-1 - x1 \cdot x1} \cdot \left(x1 \cdot \left(x1 \cdot -3\right)\right)\right)\right) + \left(\left(x1 + x1\right) + 3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot -2\right) - x1}{x1 \cdot x1 + 1}\right) \]
      rational_best-simplify-3 [=>] 0.4	\[ \left(\left(x1 \cdot x1 + 1\right) \cdot \left(x2 \cdot \left(x1 \cdot \left(4 \cdot \left(-\left(3 - \color{blue}{x2 \cdot 2}\right)\right)\right)\right)\right) + \left(x1 \cdot \left(x1 \cdot x1\right) - \frac{x1 + \left(x2 \cdot -2 - x1 \cdot \left(x1 \cdot 3\right)\right)}{-1 - x1 \cdot x1} \cdot \left(x1 \cdot \left(x1 \cdot -3\right)\right)\right)\right) + \left(\left(x1 + x1\right) + 3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot -2\right) - x1}{x1 \cdot x1 + 1}\right) \]
      metadata-eval [<=] 0.4	\[ \left(\left(x1 \cdot x1 + 1\right) \cdot \left(x2 \cdot \left(x1 \cdot \left(4 \cdot \left(-\left(3 - x2 \cdot \color{blue}{\left(--2\right)}\right)\right)\right)\right)\right) + \left(x1 \cdot \left(x1 \cdot x1\right) - \frac{x1 + \left(x2 \cdot -2 - x1 \cdot \left(x1 \cdot 3\right)\right)}{-1 - x1 \cdot x1} \cdot \left(x1 \cdot \left(x1 \cdot -3\right)\right)\right)\right) + \left(\left(x1 + x1\right) + 3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot -2\right) - x1}{x1 \cdot x1 + 1}\right) \]
      rational_best-simplify-52 [<=] 0.4	\[ \left(\left(x1 \cdot x1 + 1\right) \cdot \left(x2 \cdot \left(x1 \cdot \left(4 \cdot \left(-\left(3 - \color{blue}{\left(--2 \cdot x2\right)}\right)\right)\right)\right)\right) + \left(x1 \cdot \left(x1 \cdot x1\right) - \frac{x1 + \left(x2 \cdot -2 - x1 \cdot \left(x1 \cdot 3\right)\right)}{-1 - x1 \cdot x1} \cdot \left(x1 \cdot \left(x1 \cdot -3\right)\right)\right)\right) + \left(\left(x1 + x1\right) + 3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot -2\right) - x1}{x1 \cdot x1 + 1}\right) \]
      rational_best-simplify-62 [<=] 0.4	\[ \left(\left(x1 \cdot x1 + 1\right) \cdot \left(x2 \cdot \left(x1 \cdot \left(4 \cdot \left(-\color{blue}{\left(-2 \cdot x2 + 3\right)}\right)\right)\right)\right) + \left(x1 \cdot \left(x1 \cdot x1\right) - \frac{x1 + \left(x2 \cdot -2 - x1 \cdot \left(x1 \cdot 3\right)\right)}{-1 - x1 \cdot x1} \cdot \left(x1 \cdot \left(x1 \cdot -3\right)\right)\right)\right) + \left(\left(x1 + x1\right) + 3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot -2\right) - x1}{x1 \cdot x1 + 1}\right) \]
      rational_best-simplify-52 [<=] 0.4	\[ \left(\left(x1 \cdot x1 + 1\right) \cdot \left(x2 \cdot \left(x1 \cdot \color{blue}{\left(-\left(-2 \cdot x2 + 3\right) \cdot 4\right)}\right)\right) + \left(x1 \cdot \left(x1 \cdot x1\right) - \frac{x1 + \left(x2 \cdot -2 - x1 \cdot \left(x1 \cdot 3\right)\right)}{-1 - x1 \cdot x1} \cdot \left(x1 \cdot \left(x1 \cdot -3\right)\right)\right)\right) + \left(\left(x1 + x1\right) + 3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot -2\right) - x1}{x1 \cdot x1 + 1}\right) \]
      rational_best-simplify-3 [<=] 0.4	\[ \left(\left(x1 \cdot x1 + 1\right) \cdot \left(x2 \cdot \left(x1 \cdot \left(-\color{blue}{4 \cdot \left(-2 \cdot x2 + 3\right)}\right)\right)\right) + \left(x1 \cdot \left(x1 \cdot x1\right) - \frac{x1 + \left(x2 \cdot -2 - x1 \cdot \left(x1 \cdot 3\right)\right)}{-1 - x1 \cdot x1} \cdot \left(x1 \cdot \left(x1 \cdot -3\right)\right)\right)\right) + \left(\left(x1 + x1\right) + 3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot -2\right) - x1}{x1 \cdot x1 + 1}\right) \]
      rational_best-simplify-52 [=>] 0.4	\[ \left(\left(x1 \cdot x1 + 1\right) \cdot \left(x2 \cdot \left(x1 \cdot \color{blue}{\left(\left(-2 \cdot x2 + 3\right) \cdot \left(-4\right)\right)}\right)\right) + \left(x1 \cdot \left(x1 \cdot x1\right) - \frac{x1 + \left(x2 \cdot -2 - x1 \cdot \left(x1 \cdot 3\right)\right)}{-1 - x1 \cdot x1} \cdot \left(x1 \cdot \left(x1 \cdot -3\right)\right)\right)\right) + \left(\left(x1 + x1\right) + 3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot -2\right) - x1}{x1 \cdot x1 + 1}\right) \]
      metadata-eval [=>] 0.4	\[ \left(\left(x1 \cdot x1 + 1\right) \cdot \left(x2 \cdot \left(x1 \cdot \left(\left(-2 \cdot x2 + 3\right) \cdot \color{blue}{-4}\right)\right)\right) + \left(x1 \cdot \left(x1 \cdot x1\right) - \frac{x1 + \left(x2 \cdot -2 - x1 \cdot \left(x1 \cdot 3\right)\right)}{-1 - x1 \cdot x1} \cdot \left(x1 \cdot \left(x1 \cdot -3\right)\right)\right)\right) + \left(\left(x1 + x1\right) + 3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot -2\right) - x1}{x1 \cdot x1 + 1}\right) \]
      rational_best-simplify-3 [<=] 0.4	\[ \left(\left(x1 \cdot x1 + 1\right) \cdot \left(x2 \cdot \left(x1 \cdot \color{blue}{\left(-4 \cdot \left(-2 \cdot x2 + 3\right)\right)}\right)\right) + \left(x1 \cdot \left(x1 \cdot x1\right) - \frac{x1 + \left(x2 \cdot -2 - x1 \cdot \left(x1 \cdot 3\right)\right)}{-1 - x1 \cdot x1} \cdot \left(x1 \cdot \left(x1 \cdot -3\right)\right)\right)\right) + \left(\left(x1 + x1\right) + 3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot -2\right) - x1}{x1 \cdot x1 + 1}\right) \]
      rational_best-simplify-62 [=>] 0.4	\[ \left(\left(x1 \cdot x1 + 1\right) \cdot \left(x2 \cdot \left(x1 \cdot \left(-4 \cdot \color{blue}{\left(3 - \left(--2 \cdot x2\right)\right)}\right)\right)\right) + \left(x1 \cdot \left(x1 \cdot x1\right) - \frac{x1 + \left(x2 \cdot -2 - x1 \cdot \left(x1 \cdot 3\right)\right)}{-1 - x1 \cdot x1} \cdot \left(x1 \cdot \left(x1 \cdot -3\right)\right)\right)\right) + \left(\left(x1 + x1\right) + 3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot -2\right) - x1}{x1 \cdot x1 + 1}\right) \]
      rational_best-simplify-52 [=>] 0.4	\[ \left(\left(x1 \cdot x1 + 1\right) \cdot \left(x2 \cdot \left(x1 \cdot \left(-4 \cdot \left(3 - \color{blue}{x2 \cdot \left(--2\right)}\right)\right)\right)\right) + \left(x1 \cdot \left(x1 \cdot x1\right) - \frac{x1 + \left(x2 \cdot -2 - x1 \cdot \left(x1 \cdot 3\right)\right)}{-1 - x1 \cdot x1} \cdot \left(x1 \cdot \left(x1 \cdot -3\right)\right)\right)\right) + \left(\left(x1 + x1\right) + 3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot -2\right) - x1}{x1 \cdot x1 + 1}\right) \]
      metadata-eval [=>] 0.4	\[ \left(\left(x1 \cdot x1 + 1\right) \cdot \left(x2 \cdot \left(x1 \cdot \left(-4 \cdot \left(3 - x2 \cdot \color{blue}{2}\right)\right)\right)\right) + \left(x1 \cdot \left(x1 \cdot x1\right) - \frac{x1 + \left(x2 \cdot -2 - x1 \cdot \left(x1 \cdot 3\right)\right)}{-1 - x1 \cdot x1} \cdot \left(x1 \cdot \left(x1 \cdot -3\right)\right)\right)\right) + \left(\left(x1 + x1\right) + 3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot -2\right) - x1}{x1 \cdot x1 + 1}\right) \]
      rational_best-simplify-3 [<=] 0.4	\[ \left(\left(x1 \cdot x1 + 1\right) \cdot \left(x2 \cdot \left(x1 \cdot \left(-4 \cdot \left(3 - \color{blue}{2 \cdot x2}\right)\right)\right)\right) + \left(x1 \cdot \left(x1 \cdot x1\right) - \frac{x1 + \left(x2 \cdot -2 - x1 \cdot \left(x1 \cdot 3\right)\right)}{-1 - x1 \cdot x1} \cdot \left(x1 \cdot \left(x1 \cdot -3\right)\right)\right)\right) + \left(\left(x1 + x1\right) + 3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot -2\right) - x1}{x1 \cdot x1 + 1}\right) \]
      rational_best-simplify-111 [=>] 0.4	\[ \left(\left(x1 \cdot x1 + 1\right) \cdot \left(x2 \cdot \left(x1 \cdot \color{blue}{\left(-4 \cdot 3 - -4 \cdot \left(2 \cdot x2\right)\right)}\right)\right) + \left(x1 \cdot \left(x1 \cdot x1\right) - \frac{x1 + \left(x2 \cdot -2 - x1 \cdot \left(x1 \cdot 3\right)\right)}{-1 - x1 \cdot x1} \cdot \left(x1 \cdot \left(x1 \cdot -3\right)\right)\right)\right) + \left(\left(x1 + x1\right) + 3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot -2\right) - x1}{x1 \cdot x1 + 1}\right) \]
      metadata-eval [=>] 0.4	\[ \left(\left(x1 \cdot x1 + 1\right) \cdot \left(x2 \cdot \left(x1 \cdot \left(\color{blue}{-12} - -4 \cdot \left(2 \cdot x2\right)\right)\right)\right) + \left(x1 \cdot \left(x1 \cdot x1\right) - \frac{x1 + \left(x2 \cdot -2 - x1 \cdot \left(x1 \cdot 3\right)\right)}{-1 - x1 \cdot x1} \cdot \left(x1 \cdot \left(x1 \cdot -3\right)\right)\right)\right) + \left(\left(x1 + x1\right) + 3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot -2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   5. Taylor expanded in x1 around 0 0.1

      \[\leadsto \left(\left(x1 \cdot x1 + 1\right) \cdot \left(x2 \cdot \left(x1 \cdot \left(-12 - -4 \cdot \left(2 \cdot x2\right)\right)\right)\right) + \left(x1 \cdot \left(x1 \cdot x1\right) - \frac{x1 + \left(x2 \cdot -2 - x1 \cdot \left(x1 \cdot 3\right)\right)}{-1 - x1 \cdot x1} \cdot \left(x1 \cdot \left(x1 \cdot -3\right)\right)\right)\right) + \color{blue}{\left(-1 \cdot x1 + -6 \cdot x2\right)} \]

   6. Simplified 0.1

      \[\leadsto \left(\left(x1 \cdot x1 + 1\right) \cdot \left(x2 \cdot \left(x1 \cdot \left(-12 - -4 \cdot \left(2 \cdot x2\right)\right)\right)\right) + \left(x1 \cdot \left(x1 \cdot x1\right) - \frac{x1 + \left(x2 \cdot -2 - x1 \cdot \left(x1 \cdot 3\right)\right)}{-1 - x1 \cdot x1} \cdot \left(x1 \cdot \left(x1 \cdot -3\right)\right)\right)\right) + \color{blue}{\left(x2 \cdot -6 - x1\right)} \]
      Proof

      [Start] 0.1	\[ \left(\left(x1 \cdot x1 + 1\right) \cdot \left(x2 \cdot \left(x1 \cdot \left(-12 - -4 \cdot \left(2 \cdot x2\right)\right)\right)\right) + \left(x1 \cdot \left(x1 \cdot x1\right) - \frac{x1 + \left(x2 \cdot -2 - x1 \cdot \left(x1 \cdot 3\right)\right)}{-1 - x1 \cdot x1} \cdot \left(x1 \cdot \left(x1 \cdot -3\right)\right)\right)\right) + \left(-1 \cdot x1 + -6 \cdot x2\right) \]
      rational_best-simplify-62 [=>] 0.1	\[ \left(\left(x1 \cdot x1 + 1\right) \cdot \left(x2 \cdot \left(x1 \cdot \left(-12 - -4 \cdot \left(2 \cdot x2\right)\right)\right)\right) + \left(x1 \cdot \left(x1 \cdot x1\right) - \frac{x1 + \left(x2 \cdot -2 - x1 \cdot \left(x1 \cdot 3\right)\right)}{-1 - x1 \cdot x1} \cdot \left(x1 \cdot \left(x1 \cdot -3\right)\right)\right)\right) + \color{blue}{\left(-6 \cdot x2 - \left(--1 \cdot x1\right)\right)} \]
      rational_best-simplify-3 [=>] 0.1	\[ \left(\left(x1 \cdot x1 + 1\right) \cdot \left(x2 \cdot \left(x1 \cdot \left(-12 - -4 \cdot \left(2 \cdot x2\right)\right)\right)\right) + \left(x1 \cdot \left(x1 \cdot x1\right) - \frac{x1 + \left(x2 \cdot -2 - x1 \cdot \left(x1 \cdot 3\right)\right)}{-1 - x1 \cdot x1} \cdot \left(x1 \cdot \left(x1 \cdot -3\right)\right)\right)\right) + \left(\color{blue}{x2 \cdot -6} - \left(--1 \cdot x1\right)\right) \]
      rational_best-simplify-3 [=>] 0.1	\[ \left(\left(x1 \cdot x1 + 1\right) \cdot \left(x2 \cdot \left(x1 \cdot \left(-12 - -4 \cdot \left(2 \cdot x2\right)\right)\right)\right) + \left(x1 \cdot \left(x1 \cdot x1\right) - \frac{x1 + \left(x2 \cdot -2 - x1 \cdot \left(x1 \cdot 3\right)\right)}{-1 - x1 \cdot x1} \cdot \left(x1 \cdot \left(x1 \cdot -3\right)\right)\right)\right) + \left(x2 \cdot -6 - \left(-\color{blue}{x1 \cdot -1}\right)\right) \]
      rational_best-simplify-18 [<=] 0.1	\[ \left(\left(x1 \cdot x1 + 1\right) \cdot \left(x2 \cdot \left(x1 \cdot \left(-12 - -4 \cdot \left(2 \cdot x2\right)\right)\right)\right) + \left(x1 \cdot \left(x1 \cdot x1\right) - \frac{x1 + \left(x2 \cdot -2 - x1 \cdot \left(x1 \cdot 3\right)\right)}{-1 - x1 \cdot x1} \cdot \left(x1 \cdot \left(x1 \cdot -3\right)\right)\right)\right) + \left(x2 \cdot -6 - \left(-\color{blue}{\left(-x1\right)}\right)\right) \]
      rational_best-simplify-51 [=>] 0.1	\[ \left(\left(x1 \cdot x1 + 1\right) \cdot \left(x2 \cdot \left(x1 \cdot \left(-12 - -4 \cdot \left(2 \cdot x2\right)\right)\right)\right) + \left(x1 \cdot \left(x1 \cdot x1\right) - \frac{x1 + \left(x2 \cdot -2 - x1 \cdot \left(x1 \cdot 3\right)\right)}{-1 - x1 \cdot x1} \cdot \left(x1 \cdot \left(x1 \cdot -3\right)\right)\right)\right) + \left(x2 \cdot -6 - \color{blue}{x1}\right) \]

   if 3.8000000000000001e-17 < x1

   1. Initial program 0.8

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Simplified 0.9

      \[\leadsto \color{blue}{x1 + \left(x1 + \left(\left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(\left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + -3\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + x1 \cdot \left(\left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 + -6\right) \cdot x1\right)\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot -2\right) - x1}{x1 \cdot x1 + 1}\right)\right)} \]
      Proof

      [Start] 0.8

      \[ x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      rational_best-simplify-1 [=>] 0.8

      \[ x1 + \color{blue}{\left(3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right)\right)} \]

   3. Applied egg-rr 0.8

      \[\leadsto x1 + \left(x1 + \left(\left(\left(x1 \cdot x1 + 1\right) \cdot \color{blue}{\left(\left(x1 \cdot x1\right) \cdot \left(\frac{x1 + \left(\left(x1 \cdot x1\right) \cdot -3 + x2 \cdot -2\right)}{-1 - x1 \cdot x1} \cdot 4 + -6\right) - \left(x1 \cdot 2\right) \cdot \left(\frac{x1 + \left(\left(x1 \cdot x1\right) \cdot -3 + x2 \cdot -2\right)}{-1 - x1 \cdot x1} \cdot \left(3 - \frac{x1 + \left(\left(x1 \cdot x1\right) \cdot -3 + x2 \cdot -2\right)}{-1 - x1 \cdot x1}\right)\right)\right)} + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot -2\right) - x1}{x1 \cdot x1 + 1}\right)\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 0.3

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -2 \cdot 10^{-16}:\\ \;\;\;\;\left(\left(x1 \cdot x1 + 1\right) \cdot \left(x1 \cdot \left(-2 \cdot \left(\frac{x1 + \left(x2 \cdot -2 + x1 \cdot \left(x1 \cdot -3\right)\right)}{-1 - x1 \cdot x1} \cdot \left(3 - \frac{x1 + \left(x2 \cdot -2 + x1 \cdot \left(x1 \cdot -3\right)\right)}{-1 - x1 \cdot x1}\right)\right) - x1 \cdot \left(6 - \frac{x1 + \left(x2 \cdot -2 + x1 \cdot \left(x1 \cdot -3\right)\right)}{-1 - x1 \cdot x1} \cdot 4\right)\right)\right) + \left(x1 \cdot \left(x1 \cdot x1\right) - \frac{x1 + \left(x2 \cdot -2 - x1 \cdot \left(x1 \cdot 3\right)\right)}{-1 - x1 \cdot x1} \cdot \left(x1 \cdot \left(x1 \cdot -3\right)\right)\right)\right) + \left(\left(x1 + x1\right) + 3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot -2\right) - x1}{x1 \cdot x1 + 1}\right)\\ \mathbf{elif}\;x1 \leq 3.8 \cdot 10^{-17}:\\ \;\;\;\;\left(\left(x1 \cdot x1 + 1\right) \cdot \left(x2 \cdot \left(x1 \cdot \left(-12 - -4 \cdot \left(2 \cdot x2\right)\right)\right)\right) + \left(x1 \cdot \left(x1 \cdot x1\right) - \frac{x1 + \left(x2 \cdot -2 - x1 \cdot \left(x1 \cdot 3\right)\right)}{-1 - x1 \cdot x1} \cdot \left(x1 \cdot \left(x1 \cdot -3\right)\right)\right)\right) + \left(x2 \cdot -6 - x1\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + \left(\left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(\frac{x1 + \left(\left(x1 \cdot x1\right) \cdot -3 + x2 \cdot -2\right)}{-1 - x1 \cdot x1} \cdot 4 + -6\right) - \left(x1 \cdot 2\right) \cdot \left(\frac{x1 + \left(\left(x1 \cdot x1\right) \cdot -3 + x2 \cdot -2\right)}{-1 - x1 \cdot x1} \cdot \left(3 - \frac{x1 + \left(\left(x1 \cdot x1\right) \cdot -3 + x2 \cdot -2\right)}{-1 - x1 \cdot x1}\right)\right)\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot -2\right) - x1}{x1 \cdot x1 + 1}\right)\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	0.4
Cost	8384

\[\begin{array}{l} t_0 := -1 - x1 \cdot x1\\ t_1 := x1 \cdot x1 + 1\\ t_2 := x1 \cdot \left(x1 \cdot 3\right)\\ t_3 := \frac{x1 + \left(x2 \cdot -2 - t_2\right)}{t_0}\\ t_4 := x1 \cdot \left(x1 \cdot -3\right)\\ \left(t_1 \cdot \left(t_3 \cdot \left(\left(x1 \cdot 2\right) \cdot \left(t_3 + -3\right)\right) + \left(\left(x1 \cdot x1\right) \cdot \left(\frac{x1 + \left(x2 \cdot -2 + t_4\right)}{t_0} \cdot 4\right) - \left(x1 \cdot x1\right) \cdot 6\right)\right) + \left(x1 \cdot \left(x1 \cdot x1\right) - t_3 \cdot t_4\right)\right) + \left(\left(x1 + x1\right) + 3 \cdot \frac{\left(t_2 + x2 \cdot -2\right) - x1}{t_1}\right) \end{array} \]

Alternative 2
Error	0.3
Cost	8264

\[\begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot x1\right)\\ t_1 := x1 \cdot x1 + 1\\ t_2 := x1 \cdot \left(x1 \cdot 3\right)\\ t_3 := \frac{t_2 - \left(x1 + -2 \cdot x2\right)}{t_1}\\ t_4 := x1 + \left(x1 + \left(\left(t_1 \cdot \left(x1 \cdot \left(x1 \cdot \left(-6 + t_3 \cdot 4\right) - t_3 \cdot \left(-2 \cdot t_3 - -6\right)\right)\right) + \left(t_2 \cdot \frac{\left(t_2 + 2 \cdot x2\right) - x1}{t_1} + t_0\right)\right) + 3 \cdot \frac{\left(t_2 + x2 \cdot -2\right) - x1}{t_1}\right)\right)\\ \mathbf{if}\;x1 \leq -1.02 \cdot 10^{-14}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x1 \leq 4 \cdot 10^{-17}:\\ \;\;\;\;\left(t_1 \cdot \left(x2 \cdot \left(x1 \cdot \left(-12 - -4 \cdot \left(2 \cdot x2\right)\right)\right)\right) + \left(t_0 - \frac{x1 + \left(x2 \cdot -2 - t_2\right)}{-1 - x1 \cdot x1} \cdot \left(x1 \cdot \left(x1 \cdot -3\right)\right)\right)\right) + \left(x2 \cdot -6 - x1\right)\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 3
Error	0.3
Cost	8264

\[\begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := x1 \cdot \left(x1 \cdot -3\right)\\ t_2 := x1 \cdot x1 + 1\\ t_3 := -1 - x1 \cdot x1\\ t_4 := \frac{x1 + \left(x2 \cdot -2 + t_1\right)}{t_3}\\ t_5 := x1 \cdot \left(x1 \cdot x1\right) - \frac{x1 + \left(x2 \cdot -2 - t_0\right)}{t_3} \cdot t_1\\ t_6 := \left(t_2 \cdot \left(x1 \cdot \left(-2 \cdot \left(t_4 \cdot \left(3 - t_4\right)\right) - x1 \cdot \left(6 - t_4 \cdot 4\right)\right)\right) + t_5\right) + \left(\left(x1 + x1\right) + 3 \cdot \frac{\left(t_0 + x2 \cdot -2\right) - x1}{t_2}\right)\\ \mathbf{if}\;x1 \leq -1 \cdot 10^{-17}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;x1 \leq 2.4 \cdot 10^{-17}:\\ \;\;\;\;\left(t_2 \cdot \left(x2 \cdot \left(x1 \cdot \left(-12 - -4 \cdot \left(2 \cdot x2\right)\right)\right)\right) + t_5\right) + \left(x2 \cdot -6 - x1\right)\\ \mathbf{else}:\\ \;\;\;\;t_6\\ \end{array} \]

Alternative 4
Error	0.5
Cost	8128

\[\begin{array}{l} t_0 := \left(3 \cdot x1\right) \cdot x1\\ t_1 := x1 \cdot x1 + 1\\ t_2 := \frac{\left(t_0 + 2 \cdot x2\right) - x1}{t_1}\\ x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot t_2\right) \cdot \left(t_2 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot t_2 - 6\right)\right) \cdot t_1 + t_0 \cdot t_2\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(t_0 - 2 \cdot x2\right) - x1}{t_1}\right) \end{array} \]

Alternative 5
Error	0.4
Cost	8128

\[\begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := x1 \cdot x1 + 1\\ t_2 := \frac{x1 + \left(x2 \cdot -2 - t_0\right)}{-1 - x1 \cdot x1}\\ \left(t_1 \cdot \left(t_2 \cdot \left(\left(x1 \cdot 2\right) \cdot \left(t_2 + -3\right)\right) + \left(x1 \cdot x1\right) \cdot \left(t_2 \cdot 4 + -6\right)\right) + \left(x1 \cdot \left(x1 \cdot x1\right) - t_2 \cdot \left(x1 \cdot \left(x1 \cdot -3\right)\right)\right)\right) + \left(\left(x1 + x1\right) + 3 \cdot \frac{\left(t_0 + x2 \cdot -2\right) - x1}{t_1}\right) \end{array} \]

Alternative 6
Error	3.7
Cost	7364

\[\begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := x1 \cdot x1 + 1\\ t_2 := \left(3 \cdot x1\right) \cdot x1\\ t_3 := \frac{\left(t_2 + 2 \cdot x2\right) - x1}{t_1}\\ t_4 := \frac{\left(t_0 + 2 \cdot x2\right) - x1}{t_1}\\ \mathbf{if}\;x1 \leq -1.75:\\ \;\;\;\;x1 + \left(x1 + \left(\left(t_1 \cdot \left(\left(-6 + 2 \cdot \frac{1 + \left(x2 \cdot 6 + -9\right)}{x1}\right) + x1 \cdot \left(\left(t_4 \cdot 4 + -6\right) \cdot x1\right)\right) + \left(t_0 \cdot t_4 + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 3 \cdot \frac{\left(t_0 + x2 \cdot -2\right) - x1}{t_1}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot t_3\right) \cdot \left(2 \cdot x2 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot t_3 - 6\right)\right) \cdot t_1 + t_2 \cdot t_3\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(t_2 - 2 \cdot x2\right) - x1}{t_1}\right)\\ \end{array} \]

Alternative 7
Error	3.7
Cost	7364

\[\begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := \frac{x1 + \left(x2 \cdot -2 - t_0\right)}{-1 - x1 \cdot x1}\\ t_2 := x1 \cdot \left(x1 \cdot x1\right)\\ t_3 := x1 \cdot x1 + 1\\ t_4 := 3 \cdot \frac{\left(t_0 + x2 \cdot -2\right) - x1}{t_3}\\ t_5 := \frac{\left(t_0 + 2 \cdot x2\right) - x1}{t_3}\\ \mathbf{if}\;x1 \leq -5.6:\\ \;\;\;\;x1 + \left(x1 + \left(\left(t_3 \cdot \left(\left(-6 + 2 \cdot \frac{1 + \left(x2 \cdot 6 + -9\right)}{x1}\right) + x1 \cdot \left(\left(t_5 \cdot 4 + -6\right) \cdot x1\right)\right) + \left(t_0 \cdot t_5 + t_2\right)\right) + t_4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t_3 \cdot \left(t_1 \cdot \left(\left(x1 \cdot 2\right) \cdot \left(2 \cdot x2 - 3\right)\right) + \left(x1 \cdot x1\right) \cdot \left(t_1 \cdot 4 + -6\right)\right) + \left(t_2 - t_1 \cdot \left(x1 \cdot \left(x1 \cdot -3\right)\right)\right)\right) + \left(\left(x1 + x1\right) + t_4\right)\\ \end{array} \]

Alternative 8
Error	2.8
Cost	6600

\[\begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := x1 \cdot \left(x1 \cdot x1\right)\\ t_2 := x1 \cdot x1 + 1\\ t_3 := 3 \cdot \frac{\left(t_0 + x2 \cdot -2\right) - x1}{t_2}\\ t_4 := \frac{\left(t_0 + 2 \cdot x2\right) - x1}{t_2}\\ t_5 := x1 + \left(x1 + \left(\left(t_2 \cdot \left(\left(-6 + 2 \cdot \frac{1 + \left(x2 \cdot 6 + -9\right)}{x1}\right) + x1 \cdot \left(\left(t_4 \cdot 4 + -6\right) \cdot x1\right)\right) + \left(t_0 \cdot t_4 + t_1\right)\right) + t_3\right)\right)\\ \mathbf{if}\;x1 \leq -1.8:\\ \;\;\;\;t_5\\ \mathbf{elif}\;x1 \leq 0.44:\\ \;\;\;\;\left(t_2 \cdot \left(x2 \cdot \left(x1 \cdot \left(-12 - -4 \cdot \left(2 \cdot x2\right)\right)\right)\right) + \left(t_1 - \frac{x1 + \left(x2 \cdot -2 - t_0\right)}{-1 - x1 \cdot x1} \cdot \left(x1 \cdot \left(x1 \cdot -3\right)\right)\right)\right) + \left(\left(x1 + x1\right) + t_3\right)\\ \mathbf{else}:\\ \;\;\;\;t_5\\ \end{array} \]

Alternative 9
Error	2.8
Cost	5832

\[\begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot x1\right)\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := x1 \cdot x1 + 1\\ t_3 := 3 \cdot \frac{\left(t_1 + x2 \cdot -2\right) - x1}{t_2}\\ t_4 := \frac{\left(t_1 + 2 \cdot x2\right) - x1}{t_2}\\ t_5 := x1 + \left(x1 + \left(\left(t_2 \cdot \left(-6 + x1 \cdot \left(\left(t_4 \cdot 4 + -6\right) \cdot x1\right)\right) + \left(t_1 \cdot t_4 + t_0\right)\right) + t_3\right)\right)\\ \mathbf{if}\;x1 \leq -1.95:\\ \;\;\;\;t_5\\ \mathbf{elif}\;x1 \leq 0.29:\\ \;\;\;\;\left(t_2 \cdot \left(x2 \cdot \left(x1 \cdot \left(-12 - -4 \cdot \left(2 \cdot x2\right)\right)\right)\right) + \left(t_0 - \frac{x1 + \left(x2 \cdot -2 - t_1\right)}{-1 - x1 \cdot x1} \cdot \left(x1 \cdot \left(x1 \cdot -3\right)\right)\right)\right) + \left(\left(x1 + x1\right) + t_3\right)\\ \mathbf{else}:\\ \;\;\;\;t_5\\ \end{array} \]

Alternative 10
Error	4.9
Cost	4808

\[\begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := x1 \cdot x1 + 1\\ t_2 := 1 + x1 \cdot x1\\ t_3 := 3 \cdot \left(x1 \cdot x1\right)\\ t_4 := x1 + \left(x1 - \left(x1 \cdot \left(t_2 \cdot \left(x2 \cdot \left(12 + x2 \cdot -8\right) - x1 \cdot \left(-6 + \frac{\left(x2 \cdot 2 + t_3\right) - x1}{t_2} \cdot 4\right)\right)\right) + \left(x1 \cdot \left(x1 \cdot \left(-x1\right)\right) + -3 \cdot \frac{\left(x2 \cdot -2 + t_3\right) - x1}{t_2}\right)\right)\right)\\ \mathbf{if}\;x1 \leq -0.00085:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x1 \leq 0.042:\\ \;\;\;\;\left(t_1 \cdot \left(x2 \cdot \left(x1 \cdot \left(-12 - -4 \cdot \left(2 \cdot x2\right)\right)\right)\right) + \left(x1 \cdot \left(x1 \cdot x1\right) - \frac{x1 + \left(x2 \cdot -2 - t_0\right)}{-1 - x1 \cdot x1} \cdot \left(x1 \cdot \left(x1 \cdot -3\right)\right)\right)\right) + \left(\left(x1 + x1\right) + 3 \cdot \frac{\left(t_0 + x2 \cdot -2\right) - x1}{t_1}\right)\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 11
Error	5.0
Cost	4744

\[\begin{array}{l} t_0 := 1 + x1 \cdot x1\\ t_1 := 3 \cdot \left(x1 \cdot x1\right)\\ t_2 := -3 \cdot \frac{\left(x2 \cdot -2 + t_1\right) - x1}{t_0}\\ t_3 := \frac{\left(x2 \cdot 2 + t_1\right) - x1}{t_0}\\ t_4 := x1 + \left(x1 - \left(x1 \cdot \left(t_0 \cdot \left(x2 \cdot \left(12 + x2 \cdot -8\right) - x1 \cdot \left(-6 + t_3 \cdot 4\right)\right)\right) + \left(x1 \cdot \left(x1 \cdot \left(-x1\right)\right) + t_2\right)\right)\right)\\ \mathbf{if}\;x1 \leq -1.75:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x1 \leq 0.7:\\ \;\;\;\;x1 + \left(x1 - \left(\left(12 + -8 \cdot x2\right) \cdot \left(x2 \cdot x1\right) + \left(x1 \cdot \left(x1 \cdot \left(-3 \cdot t_3 - x1\right)\right) + t_2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 12
Error	12.2
Cost	3776

\[\begin{array}{l} t_0 := 3 \cdot \left(x1 \cdot x1\right)\\ t_1 := 1 + x1 \cdot x1\\ x1 + \left(x1 - \left(\left(12 + -8 \cdot x2\right) \cdot \left(x2 \cdot x1\right) + \left(x1 \cdot \left(x1 \cdot \left(-3 \cdot \frac{\left(x2 \cdot 2 + t_0\right) - x1}{t_1} - x1\right)\right) + -3 \cdot \frac{\left(x2 \cdot -2 + t_0\right) - x1}{t_1}\right)\right)\right) \end{array} \]

Alternative 13
Error	12.4
Cost	3528

\[\begin{array}{l} t_0 := \left(\left(x1 \cdot x1 + 1\right) \cdot \left(x2 \cdot \left(x1 \cdot \left(-12 - -4 \cdot \left(2 \cdot x2\right)\right)\right)\right) + \left(x1 \cdot \left(x1 \cdot x1\right) - \frac{x1 + \left(x2 \cdot -2 - x1 \cdot \left(x1 \cdot 3\right)\right)}{-1 - x1 \cdot x1} \cdot \left(x1 \cdot \left(x1 \cdot -3\right)\right)\right)\right) + x2 \cdot -6\\ \mathbf{if}\;x2 \leq -5 \cdot 10^{+153}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x2 \leq 1.75 \cdot 10^{+99}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x2 \cdot \left(-12 + x2 \cdot 8\right) + -2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 14
Error	12.4
Cost	3392

\[\left(\left(x1 \cdot x1 + 1\right) \cdot \left(x2 \cdot \left(x1 \cdot \left(-12 - -4 \cdot \left(2 \cdot x2\right)\right)\right)\right) + \left(x1 \cdot \left(x1 \cdot x1\right) - \frac{x1 + \left(x2 \cdot -2 - x1 \cdot \left(x1 \cdot 3\right)\right)}{-1 - x1 \cdot x1} \cdot \left(x1 \cdot \left(x1 \cdot -3\right)\right)\right)\right) + \left(x2 \cdot -6 - x1\right) \]

Alternative 15
Error	16.2
Cost	1352

\[\begin{array}{l} t_0 := x1 + x2 \cdot -6\\ \mathbf{if}\;x2 \leq -2.15 \cdot 10^{+153}:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;x1 \ne 0:\\ \;\;\;\;\frac{x1 \cdot t_0}{x1}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array}\\ \mathbf{elif}\;x2 \leq 4.7 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x2 \cdot \left(-12 + x2 \cdot 8\right) + -2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot x2\\ \end{array} \]

Alternative 16
Error	34.1
Cost	192

\[-6 \cdot x2 \]

Alternative 17
Error	61.8
Cost	64

\[x1 \]

Reproduce

herbie shell --seed 2023104 
(FPCore (x1 x2)
  :name "Rosa's FloatVsDoubleBenchmark"
  :precision binary64
  (+ x1 (+ (+ (+ (+ (* (+ (* (* (* 2.0 x1) (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0))) (- (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0)) 3.0)) (* (* x1 x1) (- (* 4.0 (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0))) 6.0))) (+ (* x1 x1) 1.0)) (* (* (* 3.0 x1) x1) (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0)))) (* (* x1 x1) x1)) x1) (* 3.0 (/ (- (- (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0))))))