Rosa's FloatVsDoubleBenchmark

Percentage Accurate: 70.4% → 99.1%

Time: 20.8s

Alternatives: 25

Speedup: 5.3×

• 46.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(3 \cdot x1\right) \cdot x1\\ t_1 := x1 \cdot x1 + 1\\ t_2 := \frac{\left(t\_0 + 2 \cdot x2\right) - x1}{t\_1}\\ x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot t\_2\right) \cdot \left(t\_2 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot t\_2 - 6\right)\right) \cdot t\_1 + t\_0 \cdot t\_2\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(t\_0 - 2 \cdot x2\right) - x1}{t\_1}\right) \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* (* 3.0 x1) x1))
        (t_1 (+ (* x1 x1) 1.0))
        (t_2 (/ (- (+ t_0 (* 2.0 x2)) x1) t_1)))
   (+
    x1
    (+
     (+
      (+
       (+
        (*
         (+
          (* (* (* 2.0 x1) t_2) (- t_2 3.0))
          (* (* x1 x1) (- (* 4.0 t_2) 6.0)))
         t_1)
        (* t_0 t_2))
       (* (* x1 x1) x1))
      x1)
     (* 3.0 (/ (- (- t_0 (* 2.0 x2)) x1) t_1))))))

C

double code(double x1, double x2) {
	double t_0 = (3.0 * x1) * x1;
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = ((t_0 + (2.0 * x2)) - x1) / t_1;
	return x1 + (((((((((2.0 * x1) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((4.0 * t_2) - 6.0))) * t_1) + (t_0 * t_2)) + ((x1 * x1) * x1)) + x1) + (3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)));
}

Fortran

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
    t_0 = (3.0d0 * x1) * x1
    t_1 = (x1 * x1) + 1.0d0
    t_2 = ((t_0 + (2.0d0 * x2)) - x1) / t_1
    code = x1 + (((((((((2.0d0 * x1) * t_2) * (t_2 - 3.0d0)) + ((x1 * x1) * ((4.0d0 * t_2) - 6.0d0))) * t_1) + (t_0 * t_2)) + ((x1 * x1) * x1)) + x1) + (3.0d0 * (((t_0 - (2.0d0 * x2)) - x1) / t_1)))
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (3.0 * x1) * x1;
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = ((t_0 + (2.0 * x2)) - x1) / t_1;
	return x1 + (((((((((2.0 * x1) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((4.0 * t_2) - 6.0))) * t_1) + (t_0 * t_2)) + ((x1 * x1) * x1)) + x1) + (3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)));
}

Python

def code(x1, x2):
	t_0 = (3.0 * x1) * x1
	t_1 = (x1 * x1) + 1.0
	t_2 = ((t_0 + (2.0 * x2)) - x1) / t_1
	return x1 + (((((((((2.0 * x1) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((4.0 * t_2) - 6.0))) * t_1) + (t_0 * t_2)) + ((x1 * x1) * x1)) + x1) + (3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)))

Julia

function code(x1, x2)
	t_0 = Float64(Float64(3.0 * x1) * x1)
	t_1 = Float64(Float64(x1 * x1) + 1.0)
	t_2 = Float64(Float64(Float64(t_0 + Float64(2.0 * x2)) - x1) / t_1)
	return Float64(x1 + Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(2.0 * x1) * t_2) * Float64(t_2 - 3.0)) + Float64(Float64(x1 * x1) * Float64(Float64(4.0 * t_2) - 6.0))) * t_1) + Float64(t_0 * t_2)) + Float64(Float64(x1 * x1) * x1)) + x1) + Float64(3.0 * Float64(Float64(Float64(t_0 - Float64(2.0 * x2)) - x1) / t_1))))
end

MATLAB

function tmp = code(x1, x2)
	t_0 = (3.0 * x1) * x1;
	t_1 = (x1 * x1) + 1.0;
	t_2 = ((t_0 + (2.0 * x2)) - x1) / t_1;
	tmp = x1 + (((((((((2.0 * x1) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((4.0 * t_2) - 6.0))) * t_1) + (t_0 * t_2)) + ((x1 * x1) * x1)) + x1) + (3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)));
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(3.0 * x1), $MachinePrecision] * x1), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]}, N[(x1 + N[(N[(N[(N[(N[(N[(N[(N[(N[(2.0 * x1), $MachinePrecision] * t$95$2), $MachinePrecision] * N[(t$95$2 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(4.0 * t$95$2), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * t$95$1), $MachinePrecision] + N[(t$95$0 * t$95$2), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * x1), $MachinePrecision]), $MachinePrecision] + x1), $MachinePrecision] + N[(3.0 * N[(N[(N[(t$95$0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Initial Program: 70.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(3 \cdot x1\right) \cdot x1\\ t_1 := x1 \cdot x1 + 1\\ t_2 := \frac{\left(t\_0 + 2 \cdot x2\right) - x1}{t\_1}\\ x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot t\_2\right) \cdot \left(t\_2 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot t\_2 - 6\right)\right) \cdot t\_1 + t\_0 \cdot t\_2\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(t\_0 - 2 \cdot x2\right) - x1}{t\_1}\right) \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* (* 3.0 x1) x1))
        (t_1 (+ (* x1 x1) 1.0))
        (t_2 (/ (- (+ t_0 (* 2.0 x2)) x1) t_1)))
   (+
    x1
    (+
     (+
      (+
       (+
        (*
         (+
          (* (* (* 2.0 x1) t_2) (- t_2 3.0))
          (* (* x1 x1) (- (* 4.0 t_2) 6.0)))
         t_1)
        (* t_0 t_2))
       (* (* x1 x1) x1))
      x1)
     (* 3.0 (/ (- (- t_0 (* 2.0 x2)) x1) t_1))))))

C

double code(double x1, double x2) {
	double t_0 = (3.0 * x1) * x1;
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = ((t_0 + (2.0 * x2)) - x1) / t_1;
	return x1 + (((((((((2.0 * x1) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((4.0 * t_2) - 6.0))) * t_1) + (t_0 * t_2)) + ((x1 * x1) * x1)) + x1) + (3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)));
}

Fortran

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
    t_0 = (3.0d0 * x1) * x1
    t_1 = (x1 * x1) + 1.0d0
    t_2 = ((t_0 + (2.0d0 * x2)) - x1) / t_1
    code = x1 + (((((((((2.0d0 * x1) * t_2) * (t_2 - 3.0d0)) + ((x1 * x1) * ((4.0d0 * t_2) - 6.0d0))) * t_1) + (t_0 * t_2)) + ((x1 * x1) * x1)) + x1) + (3.0d0 * (((t_0 - (2.0d0 * x2)) - x1) / t_1)))
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (3.0 * x1) * x1;
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = ((t_0 + (2.0 * x2)) - x1) / t_1;
	return x1 + (((((((((2.0 * x1) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((4.0 * t_2) - 6.0))) * t_1) + (t_0 * t_2)) + ((x1 * x1) * x1)) + x1) + (3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)));
}

Python

def code(x1, x2):
	t_0 = (3.0 * x1) * x1
	t_1 = (x1 * x1) + 1.0
	t_2 = ((t_0 + (2.0 * x2)) - x1) / t_1
	return x1 + (((((((((2.0 * x1) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((4.0 * t_2) - 6.0))) * t_1) + (t_0 * t_2)) + ((x1 * x1) * x1)) + x1) + (3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)))

Julia

function code(x1, x2)
	t_0 = Float64(Float64(3.0 * x1) * x1)
	t_1 = Float64(Float64(x1 * x1) + 1.0)
	t_2 = Float64(Float64(Float64(t_0 + Float64(2.0 * x2)) - x1) / t_1)
	return Float64(x1 + Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(2.0 * x1) * t_2) * Float64(t_2 - 3.0)) + Float64(Float64(x1 * x1) * Float64(Float64(4.0 * t_2) - 6.0))) * t_1) + Float64(t_0 * t_2)) + Float64(Float64(x1 * x1) * x1)) + x1) + Float64(3.0 * Float64(Float64(Float64(t_0 - Float64(2.0 * x2)) - x1) / t_1))))
end

MATLAB

function tmp = code(x1, x2)
	t_0 = (3.0 * x1) * x1;
	t_1 = (x1 * x1) + 1.0;
	t_2 = ((t_0 + (2.0 * x2)) - x1) / t_1;
	tmp = x1 + (((((((((2.0 * x1) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((4.0 * t_2) - 6.0))) * t_1) + (t_0 * t_2)) + ((x1 * x1) * x1)) + x1) + (3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)));
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(3.0 * x1), $MachinePrecision] * x1), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]}, N[(x1 + N[(N[(N[(N[(N[(N[(N[(N[(N[(2.0 * x1), $MachinePrecision] * t$95$2), $MachinePrecision] * N[(t$95$2 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(4.0 * t$95$2), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * t$95$1), $MachinePrecision] + N[(t$95$0 * t$95$2), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * x1), $MachinePrecision]), $MachinePrecision] + x1), $MachinePrecision] + N[(3.0 * N[(N[(N[(t$95$0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Alternative 1: 99.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := 2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\\ t_2 := 9 + \left(t\_0 \cdot \left(x1 \cdot \left(x1 \cdot -6\right) + \frac{t\_1}{t\_0} \cdot \left(x1 \cdot \left(-6 + t\_1 \cdot \frac{2}{t\_0}\right) + \left(x1 \cdot x1\right) \cdot 4\right)\right) + x1 \cdot \left(2 + x1 \cdot \left(x1 + 9\right)\right)\right)\\ \mathbf{if}\;x1 \leq -5.5 \cdot 10^{+102}:\\ \;\;\;\;x1 \cdot \left(\left(x1 \cdot x1\right) \cdot -3\right)\\ \mathbf{elif}\;x1 \leq -0.00068:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x1 \leq 0.0077:\\ \;\;\;\;x1 \cdot \left(-1 + x1 \cdot 9\right) + x2 \cdot \left(-6 + \left(x1 \cdot \left(x1 \cdot 12 + -12\right) + 8 \cdot \left(x1 \cdot x2\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+153}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot \left(x1 \cdot 9\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ (* x1 x1) 1.0))
        (t_1 (+ (* 2.0 x2) (* x1 (+ (* x1 3.0) -1.0))))
        (t_2
         (+
          9.0
          (+
           (*
            t_0
            (+
             (* x1 (* x1 -6.0))
             (*
              (/ t_1 t_0)
              (+ (* x1 (+ -6.0 (* t_1 (/ 2.0 t_0)))) (* (* x1 x1) 4.0)))))
           (* x1 (+ 2.0 (* x1 (+ x1 9.0))))))))
   (if (<= x1 -5.5e+102)
     (* x1 (* (* x1 x1) -3.0))
     (if (<= x1 -0.00068)
       t_2
       (if (<= x1 0.0077)
         (+
          (* x1 (+ -1.0 (* x1 9.0)))
          (* x2 (+ -6.0 (+ (* x1 (+ (* x1 12.0) -12.0)) (* 8.0 (* x1 x2))))))
         (if (<= x1 5e+153) t_2 (* x1 (* x1 9.0))))))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = (2.0 * x2) + (x1 * ((x1 * 3.0) + -1.0));
	double t_2 = 9.0 + ((t_0 * ((x1 * (x1 * -6.0)) + ((t_1 / t_0) * ((x1 * (-6.0 + (t_1 * (2.0 / t_0)))) + ((x1 * x1) * 4.0))))) + (x1 * (2.0 + (x1 * (x1 + 9.0)))));
	double tmp;
	if (x1 <= -5.5e+102) {
		tmp = x1 * ((x1 * x1) * -3.0);
	} else if (x1 <= -0.00068) {
		tmp = t_2;
	} else if (x1 <= 0.0077) {
		tmp = (x1 * (-1.0 + (x1 * 9.0))) + (x2 * (-6.0 + ((x1 * ((x1 * 12.0) + -12.0)) + (8.0 * (x1 * x2)))));
	} else if (x1 <= 5e+153) {
		tmp = t_2;
	} else {
		tmp = x1 * (x1 * 9.0);
	}
	return tmp;
}

Fortran

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) :: tmp
    t_0 = (x1 * x1) + 1.0d0
    t_1 = (2.0d0 * x2) + (x1 * ((x1 * 3.0d0) + (-1.0d0)))
    t_2 = 9.0d0 + ((t_0 * ((x1 * (x1 * (-6.0d0))) + ((t_1 / t_0) * ((x1 * ((-6.0d0) + (t_1 * (2.0d0 / t_0)))) + ((x1 * x1) * 4.0d0))))) + (x1 * (2.0d0 + (x1 * (x1 + 9.0d0)))))
    if (x1 <= (-5.5d+102)) then
        tmp = x1 * ((x1 * x1) * (-3.0d0))
    else if (x1 <= (-0.00068d0)) then
        tmp = t_2
    else if (x1 <= 0.0077d0) then
        tmp = (x1 * ((-1.0d0) + (x1 * 9.0d0))) + (x2 * ((-6.0d0) + ((x1 * ((x1 * 12.0d0) + (-12.0d0))) + (8.0d0 * (x1 * x2)))))
    else if (x1 <= 5d+153) then
        tmp = t_2
    else
        tmp = x1 * (x1 * 9.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = (2.0 * x2) + (x1 * ((x1 * 3.0) + -1.0));
	double t_2 = 9.0 + ((t_0 * ((x1 * (x1 * -6.0)) + ((t_1 / t_0) * ((x1 * (-6.0 + (t_1 * (2.0 / t_0)))) + ((x1 * x1) * 4.0))))) + (x1 * (2.0 + (x1 * (x1 + 9.0)))));
	double tmp;
	if (x1 <= -5.5e+102) {
		tmp = x1 * ((x1 * x1) * -3.0);
	} else if (x1 <= -0.00068) {
		tmp = t_2;
	} else if (x1 <= 0.0077) {
		tmp = (x1 * (-1.0 + (x1 * 9.0))) + (x2 * (-6.0 + ((x1 * ((x1 * 12.0) + -12.0)) + (8.0 * (x1 * x2)))));
	} else if (x1 <= 5e+153) {
		tmp = t_2;
	} else {
		tmp = x1 * (x1 * 9.0);
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x1 * x1) + 1.0
	t_1 = (2.0 * x2) + (x1 * ((x1 * 3.0) + -1.0))
	t_2 = 9.0 + ((t_0 * ((x1 * (x1 * -6.0)) + ((t_1 / t_0) * ((x1 * (-6.0 + (t_1 * (2.0 / t_0)))) + ((x1 * x1) * 4.0))))) + (x1 * (2.0 + (x1 * (x1 + 9.0)))))
	tmp = 0
	if x1 <= -5.5e+102:
		tmp = x1 * ((x1 * x1) * -3.0)
	elif x1 <= -0.00068:
		tmp = t_2
	elif x1 <= 0.0077:
		tmp = (x1 * (-1.0 + (x1 * 9.0))) + (x2 * (-6.0 + ((x1 * ((x1 * 12.0) + -12.0)) + (8.0 * (x1 * x2)))))
	elif x1 <= 5e+153:
		tmp = t_2
	else:
		tmp = x1 * (x1 * 9.0)
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * x1) + 1.0)
	t_1 = Float64(Float64(2.0 * x2) + Float64(x1 * Float64(Float64(x1 * 3.0) + -1.0)))
	t_2 = Float64(9.0 + Float64(Float64(t_0 * Float64(Float64(x1 * Float64(x1 * -6.0)) + Float64(Float64(t_1 / t_0) * Float64(Float64(x1 * Float64(-6.0 + Float64(t_1 * Float64(2.0 / t_0)))) + Float64(Float64(x1 * x1) * 4.0))))) + Float64(x1 * Float64(2.0 + Float64(x1 * Float64(x1 + 9.0))))))
	tmp = 0.0
	if (x1 <= -5.5e+102)
		tmp = Float64(x1 * Float64(Float64(x1 * x1) * -3.0));
	elseif (x1 <= -0.00068)
		tmp = t_2;
	elseif (x1 <= 0.0077)
		tmp = Float64(Float64(x1 * Float64(-1.0 + Float64(x1 * 9.0))) + Float64(x2 * Float64(-6.0 + Float64(Float64(x1 * Float64(Float64(x1 * 12.0) + -12.0)) + Float64(8.0 * Float64(x1 * x2))))));
	elseif (x1 <= 5e+153)
		tmp = t_2;
	else
		tmp = Float64(x1 * Float64(x1 * 9.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x1 * x1) + 1.0;
	t_1 = (2.0 * x2) + (x1 * ((x1 * 3.0) + -1.0));
	t_2 = 9.0 + ((t_0 * ((x1 * (x1 * -6.0)) + ((t_1 / t_0) * ((x1 * (-6.0 + (t_1 * (2.0 / t_0)))) + ((x1 * x1) * 4.0))))) + (x1 * (2.0 + (x1 * (x1 + 9.0)))));
	tmp = 0.0;
	if (x1 <= -5.5e+102)
		tmp = x1 * ((x1 * x1) * -3.0);
	elseif (x1 <= -0.00068)
		tmp = t_2;
	elseif (x1 <= 0.0077)
		tmp = (x1 * (-1.0 + (x1 * 9.0))) + (x2 * (-6.0 + ((x1 * ((x1 * 12.0) + -12.0)) + (8.0 * (x1 * x2)))));
	elseif (x1 <= 5e+153)
		tmp = t_2;
	else
		tmp = x1 * (x1 * 9.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$1 = N[(N[(2.0 * x2), $MachinePrecision] + N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(9.0 + N[(N[(t$95$0 * N[(N[(x1 * N[(x1 * -6.0), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$1 / t$95$0), $MachinePrecision] * N[(N[(x1 * N[(-6.0 + N[(t$95$1 * N[(2.0 / t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(2.0 + N[(x1 * N[(x1 + 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -5.5e+102], N[(x1 * N[(N[(x1 * x1), $MachinePrecision] * -3.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -0.00068], t$95$2, If[LessEqual[x1, 0.0077], N[(N[(x1 * N[(-1.0 + N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x2 * N[(-6.0 + N[(N[(x1 * N[(N[(x1 * 12.0), $MachinePrecision] + -12.0), $MachinePrecision]), $MachinePrecision] + N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 5e+153], t$95$2, N[(x1 * N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -5.49999999999999981e102

   1. Initial program 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in x1 around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, -6\right)\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-6, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 4\right)\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \color{blue}{9}\right)\right)\right)\right)\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 0.0%

      \[\leadsto \frac{3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right)}{x1 \cdot x1 + 1} + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(x1 \cdot \left(x1 \cdot -6\right) + \frac{2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)}{x1 \cdot x1 + 1} \cdot \left(x1 \cdot \left(-6 + \left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right) \cdot \frac{2}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot 4\right)\right) + x1 \cdot \left(2 + x1 \cdot \left(x1 + \color{blue}{9}\right)\right)\right) \]

   8. Taylor expanded in x1 around inf

      \[\leadsto \color{blue}{{x1}^{4} \cdot \left(6 - 3 \cdot \frac{1}{x1}\right)} \]
   9. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{4}\right), \color{blue}{\left(6 - 3 \cdot \frac{1}{x1}\right)}\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{\left(2 \cdot 2\right)}\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      3. pow-sqr N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{2} \cdot {x1}^{2}\right), \left(\color{blue}{6} - 3 \cdot \frac{1}{x1}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left({x1}^{2}\right), \left({x1}^{2}\right)\right), \left(\color{blue}{6} - 3 \cdot \frac{1}{x1}\right)\right) \]

      5. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x1 \cdot x1\right), \left({x1}^{2}\right)\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left({x1}^{2}\right)\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left(x1 \cdot x1\right)\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \left(6 + \color{blue}{\left(\mathsf{neg}\left(3 \cdot \frac{1}{x1}\right)\right)}\right)\right) \]

      10. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \color{blue}{\left(\mathsf{neg}\left(3 \cdot \frac{1}{x1}\right)\right)}\right)\right) \]

      11. associate-*r/ N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \left(\mathsf{neg}\left(\frac{3 \cdot 1}{x1}\right)\right)\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \left(\mathsf{neg}\left(\frac{3}{x1}\right)\right)\right)\right) \]

      13. distribute-neg-frac N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \left(\frac{\mathsf{neg}\left(3\right)}{\color{blue}{x1}}\right)\right)\right) \]

      14. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \left(\frac{-3}{x1}\right)\right)\right) \]

      15. /-lowering-/.f64 100.0%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \mathsf{/.f64}\left(-3, \color{blue}{x1}\right)\right)\right) \]

   10. Simplified 100.0%

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

   11. Taylor expanded in x1 around 0

       \[\leadsto \color{blue}{-3 \cdot {x1}^{3}} \]
   12. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto {x1}^{3} \cdot \color{blue}{-3} \]

       2. cube-mult N/A

          \[\leadsto \left(x1 \cdot \left(x1 \cdot x1\right)\right) \cdot -3 \]

       3. unpow2 N/A

          \[\leadsto \left(x1 \cdot {x1}^{2}\right) \cdot -3 \]

       4. associate-*l* N/A

          \[\leadsto x1 \cdot \color{blue}{\left({x1}^{2} \cdot -3\right)} \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x1, \color{blue}{\left({x1}^{2} \cdot -3\right)}\right) \]

       6. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(\left({x1}^{2}\right), \color{blue}{-3}\right)\right) \]

       7. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(\left(x1 \cdot x1\right), -3\right)\right) \]

       8. *-lowering-*.f64 100.0%

          \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), -3\right)\right) \]

   13. Simplified 100.0%

       \[\leadsto \color{blue}{x1 \cdot \left(\left(x1 \cdot x1\right) \cdot -3\right)} \]

   if -5.49999999999999981e102 < x1 < -6.8e-4 or 0.0077000000000000002 < x1 < 5.00000000000000018e153

   1. Initial program 99.4%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x1 around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, -6\right)\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-6, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 4\right)\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \color{blue}{9}\right)\right)\right)\right)\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 99.6%

      \[\leadsto \frac{3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right)}{x1 \cdot x1 + 1} + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(x1 \cdot \left(x1 \cdot -6\right) + \frac{2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)}{x1 \cdot x1 + 1} \cdot \left(x1 \cdot \left(-6 + \left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right) \cdot \frac{2}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot 4\right)\right) + x1 \cdot \left(2 + x1 \cdot \left(x1 + \color{blue}{9}\right)\right)\right) \]

   8. Taylor expanded in x1 around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{9}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, -6\right)\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-6, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 4\right)\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, 9\right)\right)\right)\right)\right)\right) \]
   9. Step-by-step derivation

   10. Simplified 99.6%

       \[\leadsto \color{blue}{9} + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(x1 \cdot \left(x1 \cdot -6\right) + \frac{2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)}{x1 \cdot x1 + 1} \cdot \left(x1 \cdot \left(-6 + \left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right) \cdot \frac{2}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot 4\right)\right) + x1 \cdot \left(2 + x1 \cdot \left(x1 + 9\right)\right)\right) \]

   if -6.8e-4 < x1 < 0.0077000000000000002

   1. Initial program 99.4%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x1 around 0

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

   7. Simplified 88.6%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(x2 \cdot 2\right) \cdot \left(x2 \cdot 4 + -6\right) + \left(x1 \cdot \left(\left(\left(\left(9 + 3 \cdot \left(x2 \cdot 2\right)\right) + x2 \cdot 10\right) - \left(x2 \cdot 4 + -6\right)\right) + -6\right) + -1\right)\right)} \]

   8. Taylor expanded in x2 around 0

      \[\leadsto \color{blue}{x1 \cdot \left(9 \cdot x1 - 1\right) + x2 \cdot \left(\left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(12 \cdot x1 - 12\right)\right) - 6\right)} \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x1 \cdot \left(9 \cdot x1 - 1\right)\right), \color{blue}{\left(x2 \cdot \left(\left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(12 \cdot x1 - 12\right)\right) - 6\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \left(9 \cdot x1 - 1\right)\right), \left(\color{blue}{x2} \cdot \left(\left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(12 \cdot x1 - 12\right)\right) - 6\right)\right)\right) \]

      3. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \left(9 \cdot x1 + \left(\mathsf{neg}\left(1\right)\right)\right)\right), \left(x2 \cdot \left(\left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(12 \cdot x1 - 12\right)\right) - 6\right)\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \left(9 \cdot x1 + -1\right)\right), \left(x2 \cdot \left(\left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(12 \cdot x1 - 12\right)\right) - 6\right)\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\left(9 \cdot x1\right), -1\right)\right), \left(x2 \cdot \left(\left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(12 \cdot x1 - 12\right)\right) - 6\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\left(x1 \cdot 9\right), -1\right)\right), \left(x2 \cdot \left(\left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(12 \cdot x1 - 12\right)\right) - 6\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 9\right), -1\right)\right), \left(x2 \cdot \left(\left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(12 \cdot x1 - 12\right)\right) - 6\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 9\right), -1\right)\right), \mathsf{*.f64}\left(x2, \color{blue}{\left(\left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(12 \cdot x1 - 12\right)\right) - 6\right)}\right)\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 9\right), -1\right)\right), \mathsf{*.f64}\left(x2, \left(\left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(12 \cdot x1 - 12\right)\right) + \color{blue}{\left(\mathsf{neg}\left(6\right)\right)}\right)\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 9\right), -1\right)\right), \mathsf{*.f64}\left(x2, \left(\left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(12 \cdot x1 - 12\right)\right) + -6\right)\right)\right) \]

      11. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 9\right), -1\right)\right), \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(12 \cdot x1 - 12\right)\right), \color{blue}{-6}\right)\right)\right) \]

   10. Simplified 99.8%

       \[\leadsto \color{blue}{x1 \cdot \left(x1 \cdot 9 + -1\right) + x2 \cdot \left(\left(x1 \cdot \left(x1 \cdot 12 + -12\right) + 8 \cdot \left(x1 \cdot x2\right)\right) + -6\right)} \]

   if 5.00000000000000018e153 < x1

   1. Initial program 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in x1 around 0

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

   7. Simplified 69.0%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(x2 \cdot 2\right) \cdot \left(x2 \cdot 4 + -6\right) + \left(x1 \cdot \left(\left(\left(\left(9 + 3 \cdot \left(x2 \cdot 2\right)\right) + x2 \cdot 10\right) - \left(x2 \cdot 4 + -6\right)\right) + -6\right) + -1\right)\right)} \]

   8. Taylor expanded in x2 around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right), \color{blue}{\left(9 \cdot x1 - 1\right)}\right)\right)\right) \]
   9. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right), \left(9 \cdot x1 + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right), \left(9 \cdot x1 + -1\right)\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right), \mathsf{+.f64}\left(\left(9 \cdot x1\right), \color{blue}{-1}\right)\right)\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right), \mathsf{+.f64}\left(\left(x1 \cdot 9\right), -1\right)\right)\right)\right) \]

      5. *-lowering-*.f64 100.0%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 9\right), -1\right)\right)\right)\right) \]

   10. Simplified 100.0%

       \[\leadsto -6 \cdot x2 + x1 \cdot \left(\left(x2 \cdot 2\right) \cdot \left(x2 \cdot 4 + -6\right) + \color{blue}{\left(x1 \cdot 9 + -1\right)}\right) \]

   11. Taylor expanded in x1 around inf

       \[\leadsto \color{blue}{9 \cdot {x1}^{2}} \]
   12. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto {x1}^{2} \cdot \color{blue}{9} \]

       2. unpow2 N/A

          \[\leadsto \left(x1 \cdot x1\right) \cdot 9 \]

       3. associate-*l* N/A

          \[\leadsto x1 \cdot \color{blue}{\left(x1 \cdot 9\right)} \]

       4. *-commutative N/A

          \[\leadsto x1 \cdot \left(9 \cdot \color{blue}{x1}\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x1, \color{blue}{\left(9 \cdot x1\right)}\right) \]

       6. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x1, \left(x1 \cdot \color{blue}{9}\right)\right) \]

       7. *-lowering-*.f64 100.0%

          \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, \color{blue}{9}\right)\right) \]

   13. Simplified 100.0%

       \[\leadsto \color{blue}{x1 \cdot \left(x1 \cdot 9\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.5 \cdot 10^{+102}:\\ \;\;\;\;x1 \cdot \left(\left(x1 \cdot x1\right) \cdot -3\right)\\ \mathbf{elif}\;x1 \leq -0.00068:\\ \;\;\;\;9 + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(x1 \cdot \left(x1 \cdot -6\right) + \frac{2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)}{x1 \cdot x1 + 1} \cdot \left(x1 \cdot \left(-6 + \left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right) \cdot \frac{2}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot 4\right)\right) + x1 \cdot \left(2 + x1 \cdot \left(x1 + 9\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 0.0077:\\ \;\;\;\;x1 \cdot \left(-1 + x1 \cdot 9\right) + x2 \cdot \left(-6 + \left(x1 \cdot \left(x1 \cdot 12 + -12\right) + 8 \cdot \left(x1 \cdot x2\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+153}:\\ \;\;\;\;9 + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(x1 \cdot \left(x1 \cdot -6\right) + \frac{2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)}{x1 \cdot x1 + 1} \cdot \left(x1 \cdot \left(-6 + \left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right) \cdot \frac{2}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot 4\right)\right) + x1 \cdot \left(2 + x1 \cdot \left(x1 + 9\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot \left(x1 \cdot 9\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 99.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot x1\right)\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := x1 \cdot x1 + 1\\ t_3 := \frac{\left(t\_1 + 2 \cdot x2\right) - x1}{t\_2}\\ t_4 := x1 \cdot \left(x1 \cdot 3 + -1\right)\\ t_5 := 2 \cdot x2 + t\_4\\ \mathbf{if}\;x1 + \left(\left(x1 + \left(\left(t\_2 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t\_3\right) \cdot \left(t\_3 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(t\_3 \cdot 4 - 6\right)\right) + t\_1 \cdot t\_3\right) + t\_0\right)\right) + 3 \cdot \frac{\left(t\_1 - 2 \cdot x2\right) - x1}{t\_2}\right) \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(3, \frac{x2 \cdot -2 + t\_4}{t\_2}, t\_2 \cdot \left(\left(x1 \cdot x1\right) \cdot -6 + \frac{x1 \cdot \left(\left(-6 + \frac{t\_5}{\frac{t\_2}{2}}\right) + x1 \cdot 4\right)}{\frac{t\_2}{t\_5}}\right) + x1 \cdot \left(2 + x1 \cdot \left(x1 + \frac{t\_5}{\frac{t\_2}{3}}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(x1 \cdot t\_0\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 x1)))
        (t_1 (* x1 (* x1 3.0)))
        (t_2 (+ (* x1 x1) 1.0))
        (t_3 (/ (- (+ t_1 (* 2.0 x2)) x1) t_2))
        (t_4 (* x1 (+ (* x1 3.0) -1.0)))
        (t_5 (+ (* 2.0 x2) t_4)))
   (if (<=
        (+
         x1
         (+
          (+
           x1
           (+
            (+
             (*
              t_2
              (+
               (* (* (* x1 2.0) t_3) (- t_3 3.0))
               (* (* x1 x1) (- (* t_3 4.0) 6.0))))
             (* t_1 t_3))
            t_0))
          (* 3.0 (/ (- (- t_1 (* 2.0 x2)) x1) t_2))))
        INFINITY)
     (fma
      3.0
      (/ (+ (* x2 -2.0) t_4) t_2)
      (+
       (*
        t_2
        (+
         (* (* x1 x1) -6.0)
         (/ (* x1 (+ (+ -6.0 (/ t_5 (/ t_2 2.0))) (* x1 4.0))) (/ t_2 t_5))))
       (* x1 (+ 2.0 (* x1 (+ x1 (/ t_5 (/ t_2 3.0))))))))
     (* 6.0 (* x1 t_0)))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * x1);
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = ((t_1 + (2.0 * x2)) - x1) / t_2;
	double t_4 = x1 * ((x1 * 3.0) + -1.0);
	double t_5 = (2.0 * x2) + t_4;
	double tmp;
	if ((x1 + ((x1 + (((t_2 * ((((x1 * 2.0) * t_3) * (t_3 - 3.0)) + ((x1 * x1) * ((t_3 * 4.0) - 6.0)))) + (t_1 * t_3)) + t_0)) + (3.0 * (((t_1 - (2.0 * x2)) - x1) / t_2)))) <= ((double) INFINITY)) {
		tmp = fma(3.0, (((x2 * -2.0) + t_4) / t_2), ((t_2 * (((x1 * x1) * -6.0) + ((x1 * ((-6.0 + (t_5 / (t_2 / 2.0))) + (x1 * 4.0))) / (t_2 / t_5)))) + (x1 * (2.0 + (x1 * (x1 + (t_5 / (t_2 / 3.0))))))));
	} else {
		tmp = 6.0 * (x1 * t_0);
	}
	return tmp;
}

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * x1))
	t_1 = Float64(x1 * Float64(x1 * 3.0))
	t_2 = Float64(Float64(x1 * x1) + 1.0)
	t_3 = Float64(Float64(Float64(t_1 + Float64(2.0 * x2)) - x1) / t_2)
	t_4 = Float64(x1 * Float64(Float64(x1 * 3.0) + -1.0))
	t_5 = Float64(Float64(2.0 * x2) + t_4)
	tmp = 0.0
	if (Float64(x1 + Float64(Float64(x1 + Float64(Float64(Float64(t_2 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_3) * Float64(t_3 - 3.0)) + Float64(Float64(x1 * x1) * Float64(Float64(t_3 * 4.0) - 6.0)))) + Float64(t_1 * t_3)) + t_0)) + Float64(3.0 * Float64(Float64(Float64(t_1 - Float64(2.0 * x2)) - x1) / t_2)))) <= Inf)
		tmp = fma(3.0, Float64(Float64(Float64(x2 * -2.0) + t_4) / t_2), Float64(Float64(t_2 * Float64(Float64(Float64(x1 * x1) * -6.0) + Float64(Float64(x1 * Float64(Float64(-6.0 + Float64(t_5 / Float64(t_2 / 2.0))) + Float64(x1 * 4.0))) / Float64(t_2 / t_5)))) + Float64(x1 * Float64(2.0 + Float64(x1 * Float64(x1 + Float64(t_5 / Float64(t_2 / 3.0))))))));
	else
		tmp = Float64(6.0 * Float64(x1 * t_0));
	end
	return tmp
end

Wolfram

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[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(t$95$1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(2.0 * x2), $MachinePrecision] + t$95$4), $MachinePrecision]}, If[LessEqual[N[(x1 + N[(N[(x1 + N[(N[(N[(t$95$2 * N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$3), $MachinePrecision] * N[(t$95$3 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$3 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$1 * t$95$3), $MachinePrecision]), $MachinePrecision] + t$95$0), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(N[(N[(t$95$1 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(3.0 * N[(N[(N[(x2 * -2.0), $MachinePrecision] + t$95$4), $MachinePrecision] / t$95$2), $MachinePrecision] + N[(N[(t$95$2 * N[(N[(N[(x1 * x1), $MachinePrecision] * -6.0), $MachinePrecision] + N[(N[(x1 * N[(N[(-6.0 + N[(t$95$5 / N[(t$95$2 / 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t$95$2 / t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(2.0 + N[(x1 * N[(x1 + N[(t$95$5 / N[(t$95$2 / 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(6.0 * N[(x1 * t$95$0), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x1 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 (+.f64 (*.f64 (*.f64 (*.f64 #s(literal 2 binary64) x1) (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64)))) (-.f64 (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64))) #s(literal 3 binary64))) (*.f64 (*.f64 x1 x1) (-.f64 (*.f64 #s(literal 4 binary64) (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64)))) #s(literal 6 binary64)))) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64))) (*.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64))))) (*.f64 (*.f64 x1 x1) x1)) x1) (*.f64 #s(literal 3 binary64) (/.f64 (-.f64 (-.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64)))))) < +inf.0

   1. Initial program 99.4%

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

   3. Simplified 99.5%

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

   6. Applied egg-rr 99.7%

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

   if +inf.0 < (+.f64 x1 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 (+.f64 (*.f64 (*.f64 (*.f64 #s(literal 2 binary64) x1) (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64)))) (-.f64 (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64))) #s(literal 3 binary64))) (*.f64 (*.f64 x1 x1) (-.f64 (*.f64 #s(literal 4 binary64) (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64)))) #s(literal 6 binary64)))) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64))) (*.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64))))) (*.f64 (*.f64 x1 x1) x1)) x1) (*.f64 #s(literal 3 binary64) (/.f64 (-.f64 (-.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64))))))

   1. Initial program 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in x1 around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, -6\right)\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-6, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 4\right)\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \color{blue}{9}\right)\right)\right)\right)\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 0.0%

      \[\leadsto \frac{3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right)}{x1 \cdot x1 + 1} + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(x1 \cdot \left(x1 \cdot -6\right) + \frac{2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)}{x1 \cdot x1 + 1} \cdot \left(x1 \cdot \left(-6 + \left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right) \cdot \frac{2}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot 4\right)\right) + x1 \cdot \left(2 + x1 \cdot \left(x1 + \color{blue}{9}\right)\right)\right) \]

   8. Taylor expanded in x1 around inf

      \[\leadsto \color{blue}{{x1}^{4} \cdot \left(6 - 3 \cdot \frac{1}{x1}\right)} \]
   9. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{4}\right), \color{blue}{\left(6 - 3 \cdot \frac{1}{x1}\right)}\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{\left(2 \cdot 2\right)}\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      3. pow-sqr N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{2} \cdot {x1}^{2}\right), \left(\color{blue}{6} - 3 \cdot \frac{1}{x1}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left({x1}^{2}\right), \left({x1}^{2}\right)\right), \left(\color{blue}{6} - 3 \cdot \frac{1}{x1}\right)\right) \]

      5. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x1 \cdot x1\right), \left({x1}^{2}\right)\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left({x1}^{2}\right)\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left(x1 \cdot x1\right)\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \left(6 + \color{blue}{\left(\mathsf{neg}\left(3 \cdot \frac{1}{x1}\right)\right)}\right)\right) \]

      10. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \color{blue}{\left(\mathsf{neg}\left(3 \cdot \frac{1}{x1}\right)\right)}\right)\right) \]

      11. associate-*r/ N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \left(\mathsf{neg}\left(\frac{3 \cdot 1}{x1}\right)\right)\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \left(\mathsf{neg}\left(\frac{3}{x1}\right)\right)\right)\right) \]

      13. distribute-neg-frac N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \left(\frac{\mathsf{neg}\left(3\right)}{\color{blue}{x1}}\right)\right)\right) \]

      14. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \left(\frac{-3}{x1}\right)\right)\right) \]

      15. /-lowering-/.f64 100.0%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \mathsf{/.f64}\left(-3, \color{blue}{x1}\right)\right)\right) \]

   10. Simplified 100.0%

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

   11. Taylor expanded in x1 around inf

       \[\leadsto \color{blue}{6 \cdot {x1}^{4}} \]
   12. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(6, \color{blue}{\left({x1}^{4}\right)}\right) \]

       2. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(6, \left({x1}^{\left(2 \cdot \color{blue}{2}\right)}\right)\right) \]

       3. pow-sqr N/A

          \[\leadsto \mathsf{*.f64}\left(6, \left({x1}^{2} \cdot \color{blue}{{x1}^{2}}\right)\right) \]

       4. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(6, \left(\left(x1 \cdot x1\right) \cdot {\color{blue}{x1}}^{2}\right)\right) \]

       5. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(6, \left(x1 \cdot \color{blue}{\left(x1 \cdot {x1}^{2}\right)}\right)\right) \]

       6. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(6, \left(x1 \cdot \left(x1 \cdot \left(x1 \cdot \color{blue}{x1}\right)\right)\right)\right) \]

       7. cube-mult N/A

          \[\leadsto \mathsf{*.f64}\left(6, \left(x1 \cdot {x1}^{\color{blue}{3}}\right)\right) \]

       8. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(x1, \color{blue}{\left({x1}^{3}\right)}\right)\right) \]

       9. cube-mult N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(x1, \left(x1 \cdot \color{blue}{\left(x1 \cdot x1\right)}\right)\right)\right) \]

       10. unpow2 N/A

           \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(x1, \left(x1 \cdot {x1}^{\color{blue}{2}}\right)\right)\right) \]

       11. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, \color{blue}{\left({x1}^{2}\right)}\right)\right)\right) \]

       12. unpow2 N/A

           \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, \left(x1 \cdot \color{blue}{x1}\right)\right)\right)\right) \]

       13. *-lowering-*.f64 100.0%

           \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, \color{blue}{x1}\right)\right)\right)\right) \]

   13. Simplified 100.0%

       \[\leadsto \color{blue}{6 \cdot \left(x1 \cdot \left(x1 \cdot \left(x1 \cdot x1\right)\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 + \left(\left(x1 + \left(\left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right)\right) + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(3, \frac{x2 \cdot -2 + x1 \cdot \left(x1 \cdot 3 + -1\right)}{x1 \cdot x1 + 1}, \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot -6 + \frac{x1 \cdot \left(\left(-6 + \frac{2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)}{\frac{x1 \cdot x1 + 1}{2}}\right) + x1 \cdot 4\right)}{\frac{x1 \cdot x1 + 1}{2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)}}\right) + x1 \cdot \left(2 + x1 \cdot \left(x1 + \frac{2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)}{\frac{x1 \cdot x1 + 1}{3}}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(x1 \cdot \left(x1 \cdot \left(x1 \cdot x1\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 99.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot x1\right)\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := x1 \cdot x1 + 1\\ t_3 := \frac{\left(t\_1 + 2 \cdot x2\right) - x1}{t\_2}\\ t_4 := x1 \cdot \left(x1 \cdot 3 + -1\right)\\ t_5 := 2 \cdot x2 + t\_4\\ \mathbf{if}\;x1 + \left(\left(x1 + \left(\left(t\_2 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t\_3\right) \cdot \left(t\_3 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(t\_3 \cdot 4 - 6\right)\right) + t\_1 \cdot t\_3\right) + t\_0\right)\right) + 3 \cdot \frac{\left(t\_1 - 2 \cdot x2\right) - x1}{t\_2}\right) \leq \infty:\\ \;\;\;\;\frac{3 \cdot \left(x2 \cdot -2 + t\_4\right)}{t\_2} + \left(t\_2 \cdot \left(x1 \cdot \left(x1 \cdot -6\right) + \frac{t\_5}{t\_2} \cdot \left(x1 \cdot \left(-6 + t\_5 \cdot \frac{2}{t\_2}\right) + \left(x1 \cdot x1\right) \cdot 4\right)\right) + x1 \cdot \left(2 + x1 \cdot \left(x1 + t\_5 \cdot \frac{3}{t\_2}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(x1 \cdot t\_0\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 x1)))
        (t_1 (* x1 (* x1 3.0)))
        (t_2 (+ (* x1 x1) 1.0))
        (t_3 (/ (- (+ t_1 (* 2.0 x2)) x1) t_2))
        (t_4 (* x1 (+ (* x1 3.0) -1.0)))
        (t_5 (+ (* 2.0 x2) t_4)))
   (if (<=
        (+
         x1
         (+
          (+
           x1
           (+
            (+
             (*
              t_2
              (+
               (* (* (* x1 2.0) t_3) (- t_3 3.0))
               (* (* x1 x1) (- (* t_3 4.0) 6.0))))
             (* t_1 t_3))
            t_0))
          (* 3.0 (/ (- (- t_1 (* 2.0 x2)) x1) t_2))))
        INFINITY)
     (+
      (/ (* 3.0 (+ (* x2 -2.0) t_4)) t_2)
      (+
       (*
        t_2
        (+
         (* x1 (* x1 -6.0))
         (*
          (/ t_5 t_2)
          (+ (* x1 (+ -6.0 (* t_5 (/ 2.0 t_2)))) (* (* x1 x1) 4.0)))))
       (* x1 (+ 2.0 (* x1 (+ x1 (* t_5 (/ 3.0 t_2))))))))
     (* 6.0 (* x1 t_0)))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * x1);
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = ((t_1 + (2.0 * x2)) - x1) / t_2;
	double t_4 = x1 * ((x1 * 3.0) + -1.0);
	double t_5 = (2.0 * x2) + t_4;
	double tmp;
	if ((x1 + ((x1 + (((t_2 * ((((x1 * 2.0) * t_3) * (t_3 - 3.0)) + ((x1 * x1) * ((t_3 * 4.0) - 6.0)))) + (t_1 * t_3)) + t_0)) + (3.0 * (((t_1 - (2.0 * x2)) - x1) / t_2)))) <= ((double) INFINITY)) {
		tmp = ((3.0 * ((x2 * -2.0) + t_4)) / t_2) + ((t_2 * ((x1 * (x1 * -6.0)) + ((t_5 / t_2) * ((x1 * (-6.0 + (t_5 * (2.0 / t_2)))) + ((x1 * x1) * 4.0))))) + (x1 * (2.0 + (x1 * (x1 + (t_5 * (3.0 / t_2)))))));
	} else {
		tmp = 6.0 * (x1 * t_0);
	}
	return tmp;
}

Java

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) + 1.0;
	double t_3 = ((t_1 + (2.0 * x2)) - x1) / t_2;
	double t_4 = x1 * ((x1 * 3.0) + -1.0);
	double t_5 = (2.0 * x2) + t_4;
	double tmp;
	if ((x1 + ((x1 + (((t_2 * ((((x1 * 2.0) * t_3) * (t_3 - 3.0)) + ((x1 * x1) * ((t_3 * 4.0) - 6.0)))) + (t_1 * t_3)) + t_0)) + (3.0 * (((t_1 - (2.0 * x2)) - x1) / t_2)))) <= Double.POSITIVE_INFINITY) {
		tmp = ((3.0 * ((x2 * -2.0) + t_4)) / t_2) + ((t_2 * ((x1 * (x1 * -6.0)) + ((t_5 / t_2) * ((x1 * (-6.0 + (t_5 * (2.0 / t_2)))) + ((x1 * x1) * 4.0))))) + (x1 * (2.0 + (x1 * (x1 + (t_5 * (3.0 / t_2)))))));
	} else {
		tmp = 6.0 * (x1 * t_0);
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * x1)
	t_1 = x1 * (x1 * 3.0)
	t_2 = (x1 * x1) + 1.0
	t_3 = ((t_1 + (2.0 * x2)) - x1) / t_2
	t_4 = x1 * ((x1 * 3.0) + -1.0)
	t_5 = (2.0 * x2) + t_4
	tmp = 0
	if (x1 + ((x1 + (((t_2 * ((((x1 * 2.0) * t_3) * (t_3 - 3.0)) + ((x1 * x1) * ((t_3 * 4.0) - 6.0)))) + (t_1 * t_3)) + t_0)) + (3.0 * (((t_1 - (2.0 * x2)) - x1) / t_2)))) <= math.inf:
		tmp = ((3.0 * ((x2 * -2.0) + t_4)) / t_2) + ((t_2 * ((x1 * (x1 * -6.0)) + ((t_5 / t_2) * ((x1 * (-6.0 + (t_5 * (2.0 / t_2)))) + ((x1 * x1) * 4.0))))) + (x1 * (2.0 + (x1 * (x1 + (t_5 * (3.0 / t_2)))))))
	else:
		tmp = 6.0 * (x1 * t_0)
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * x1))
	t_1 = Float64(x1 * Float64(x1 * 3.0))
	t_2 = Float64(Float64(x1 * x1) + 1.0)
	t_3 = Float64(Float64(Float64(t_1 + Float64(2.0 * x2)) - x1) / t_2)
	t_4 = Float64(x1 * Float64(Float64(x1 * 3.0) + -1.0))
	t_5 = Float64(Float64(2.0 * x2) + t_4)
	tmp = 0.0
	if (Float64(x1 + Float64(Float64(x1 + Float64(Float64(Float64(t_2 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_3) * Float64(t_3 - 3.0)) + Float64(Float64(x1 * x1) * Float64(Float64(t_3 * 4.0) - 6.0)))) + Float64(t_1 * t_3)) + t_0)) + Float64(3.0 * Float64(Float64(Float64(t_1 - Float64(2.0 * x2)) - x1) / t_2)))) <= Inf)
		tmp = Float64(Float64(Float64(3.0 * Float64(Float64(x2 * -2.0) + t_4)) / t_2) + Float64(Float64(t_2 * Float64(Float64(x1 * Float64(x1 * -6.0)) + Float64(Float64(t_5 / t_2) * Float64(Float64(x1 * Float64(-6.0 + Float64(t_5 * Float64(2.0 / t_2)))) + Float64(Float64(x1 * x1) * 4.0))))) + Float64(x1 * Float64(2.0 + Float64(x1 * Float64(x1 + Float64(t_5 * Float64(3.0 / t_2))))))));
	else
		tmp = Float64(6.0 * Float64(x1 * t_0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * x1);
	t_1 = x1 * (x1 * 3.0);
	t_2 = (x1 * x1) + 1.0;
	t_3 = ((t_1 + (2.0 * x2)) - x1) / t_2;
	t_4 = x1 * ((x1 * 3.0) + -1.0);
	t_5 = (2.0 * x2) + t_4;
	tmp = 0.0;
	if ((x1 + ((x1 + (((t_2 * ((((x1 * 2.0) * t_3) * (t_3 - 3.0)) + ((x1 * x1) * ((t_3 * 4.0) - 6.0)))) + (t_1 * t_3)) + t_0)) + (3.0 * (((t_1 - (2.0 * x2)) - x1) / t_2)))) <= Inf)
		tmp = ((3.0 * ((x2 * -2.0) + t_4)) / t_2) + ((t_2 * ((x1 * (x1 * -6.0)) + ((t_5 / t_2) * ((x1 * (-6.0 + (t_5 * (2.0 / t_2)))) + ((x1 * x1) * 4.0))))) + (x1 * (2.0 + (x1 * (x1 + (t_5 * (3.0 / t_2)))))));
	else
		tmp = 6.0 * (x1 * t_0);
	end
	tmp_2 = tmp;
end

Wolfram

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[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(t$95$1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(2.0 * x2), $MachinePrecision] + t$95$4), $MachinePrecision]}, If[LessEqual[N[(x1 + N[(N[(x1 + N[(N[(N[(t$95$2 * N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$3), $MachinePrecision] * N[(t$95$3 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$3 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$1 * t$95$3), $MachinePrecision]), $MachinePrecision] + t$95$0), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(N[(N[(t$95$1 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[(N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] + t$95$4), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision] + N[(N[(t$95$2 * N[(N[(x1 * N[(x1 * -6.0), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$5 / t$95$2), $MachinePrecision] * N[(N[(x1 * N[(-6.0 + N[(t$95$5 * N[(2.0 / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(2.0 + N[(x1 * N[(x1 + N[(t$95$5 * N[(3.0 / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(6.0 * N[(x1 * t$95$0), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x1 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 (+.f64 (*.f64 (*.f64 (*.f64 #s(literal 2 binary64) x1) (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64)))) (-.f64 (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64))) #s(literal 3 binary64))) (*.f64 (*.f64 x1 x1) (-.f64 (*.f64 #s(literal 4 binary64) (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64)))) #s(literal 6 binary64)))) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64))) (*.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64))))) (*.f64 (*.f64 x1 x1) x1)) x1) (*.f64 #s(literal 3 binary64) (/.f64 (-.f64 (-.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64)))))) < +inf.0

   1. Initial program 99.4%

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

   3. Simplified 99.5%

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

   if +inf.0 < (+.f64 x1 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 (+.f64 (*.f64 (*.f64 (*.f64 #s(literal 2 binary64) x1) (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64)))) (-.f64 (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64))) #s(literal 3 binary64))) (*.f64 (*.f64 x1 x1) (-.f64 (*.f64 #s(literal 4 binary64) (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64)))) #s(literal 6 binary64)))) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64))) (*.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64))))) (*.f64 (*.f64 x1 x1) x1)) x1) (*.f64 #s(literal 3 binary64) (/.f64 (-.f64 (-.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64))))))

   1. Initial program 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in x1 around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, -6\right)\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-6, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 4\right)\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \color{blue}{9}\right)\right)\right)\right)\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 0.0%

      \[\leadsto \frac{3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right)}{x1 \cdot x1 + 1} + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(x1 \cdot \left(x1 \cdot -6\right) + \frac{2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)}{x1 \cdot x1 + 1} \cdot \left(x1 \cdot \left(-6 + \left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right) \cdot \frac{2}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot 4\right)\right) + x1 \cdot \left(2 + x1 \cdot \left(x1 + \color{blue}{9}\right)\right)\right) \]

   8. Taylor expanded in x1 around inf

      \[\leadsto \color{blue}{{x1}^{4} \cdot \left(6 - 3 \cdot \frac{1}{x1}\right)} \]
   9. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{4}\right), \color{blue}{\left(6 - 3 \cdot \frac{1}{x1}\right)}\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{\left(2 \cdot 2\right)}\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      3. pow-sqr N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{2} \cdot {x1}^{2}\right), \left(\color{blue}{6} - 3 \cdot \frac{1}{x1}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left({x1}^{2}\right), \left({x1}^{2}\right)\right), \left(\color{blue}{6} - 3 \cdot \frac{1}{x1}\right)\right) \]

      5. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x1 \cdot x1\right), \left({x1}^{2}\right)\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left({x1}^{2}\right)\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left(x1 \cdot x1\right)\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \left(6 + \color{blue}{\left(\mathsf{neg}\left(3 \cdot \frac{1}{x1}\right)\right)}\right)\right) \]

      10. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \color{blue}{\left(\mathsf{neg}\left(3 \cdot \frac{1}{x1}\right)\right)}\right)\right) \]

      11. associate-*r/ N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \left(\mathsf{neg}\left(\frac{3 \cdot 1}{x1}\right)\right)\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \left(\mathsf{neg}\left(\frac{3}{x1}\right)\right)\right)\right) \]

      13. distribute-neg-frac N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \left(\frac{\mathsf{neg}\left(3\right)}{\color{blue}{x1}}\right)\right)\right) \]

      14. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \left(\frac{-3}{x1}\right)\right)\right) \]

      15. /-lowering-/.f64 100.0%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \mathsf{/.f64}\left(-3, \color{blue}{x1}\right)\right)\right) \]

   10. Simplified 100.0%

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

   11. Taylor expanded in x1 around inf

       \[\leadsto \color{blue}{6 \cdot {x1}^{4}} \]
   12. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(6, \color{blue}{\left({x1}^{4}\right)}\right) \]

       2. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(6, \left({x1}^{\left(2 \cdot \color{blue}{2}\right)}\right)\right) \]

       3. pow-sqr N/A

          \[\leadsto \mathsf{*.f64}\left(6, \left({x1}^{2} \cdot \color{blue}{{x1}^{2}}\right)\right) \]

       4. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(6, \left(\left(x1 \cdot x1\right) \cdot {\color{blue}{x1}}^{2}\right)\right) \]

       5. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(6, \left(x1 \cdot \color{blue}{\left(x1 \cdot {x1}^{2}\right)}\right)\right) \]

       6. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(6, \left(x1 \cdot \left(x1 \cdot \left(x1 \cdot \color{blue}{x1}\right)\right)\right)\right) \]

       7. cube-mult N/A

          \[\leadsto \mathsf{*.f64}\left(6, \left(x1 \cdot {x1}^{\color{blue}{3}}\right)\right) \]

       8. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(x1, \color{blue}{\left({x1}^{3}\right)}\right)\right) \]

       9. cube-mult N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(x1, \left(x1 \cdot \color{blue}{\left(x1 \cdot x1\right)}\right)\right)\right) \]

       10. unpow2 N/A

           \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(x1, \left(x1 \cdot {x1}^{\color{blue}{2}}\right)\right)\right) \]

       11. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, \color{blue}{\left({x1}^{2}\right)}\right)\right)\right) \]

       12. unpow2 N/A

           \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, \left(x1 \cdot \color{blue}{x1}\right)\right)\right)\right) \]

       13. *-lowering-*.f64 100.0%

           \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, \color{blue}{x1}\right)\right)\right)\right) \]

   13. Simplified 100.0%

       \[\leadsto \color{blue}{6 \cdot \left(x1 \cdot \left(x1 \cdot \left(x1 \cdot x1\right)\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 + \left(\left(x1 + \left(\left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right)\right) + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \leq \infty:\\ \;\;\;\;\frac{3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right)}{x1 \cdot x1 + 1} + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(x1 \cdot \left(x1 \cdot -6\right) + \frac{2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)}{x1 \cdot x1 + 1} \cdot \left(x1 \cdot \left(-6 + \left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right) \cdot \frac{2}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot 4\right)\right) + x1 \cdot \left(2 + x1 \cdot \left(x1 + \left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right) \cdot \frac{3}{x1 \cdot x1 + 1}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(x1 \cdot \left(x1 \cdot \left(x1 \cdot x1\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 99.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := x1 \cdot 3 + -1\\ t_2 := 2 \cdot x2 + x1 \cdot t\_1\\ \mathbf{if}\;x1 \leq -5.5 \cdot 10^{+102}:\\ \;\;\;\;x1 \cdot \left(\left(x1 \cdot x1\right) \cdot -3\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+153}:\\ \;\;\;\;\left(t\_0 \cdot \left(\left(x1 \cdot x1\right) \cdot -6 + \frac{x1 \cdot \left(\left(-6 + \frac{t\_2}{\frac{t\_0}{2}}\right) + x1 \cdot 4\right)}{\frac{t\_0}{t\_2}}\right) + x1 \cdot \left(2 + x1 \cdot \left(x1 + \frac{t\_2}{\frac{t\_0}{3}}\right)\right)\right) + \frac{\left(x1 \cdot 3\right) \cdot t\_1 + x2 \cdot -6}{t\_0}\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot \left(x1 \cdot 9\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ (* x1 x1) 1.0))
        (t_1 (+ (* x1 3.0) -1.0))
        (t_2 (+ (* 2.0 x2) (* x1 t_1))))
   (if (<= x1 -5.5e+102)
     (* x1 (* (* x1 x1) -3.0))
     (if (<= x1 5e+153)
       (+
        (+
         (*
          t_0
          (+
           (* (* x1 x1) -6.0)
           (/ (* x1 (+ (+ -6.0 (/ t_2 (/ t_0 2.0))) (* x1 4.0))) (/ t_0 t_2))))
         (* x1 (+ 2.0 (* x1 (+ x1 (/ t_2 (/ t_0 3.0)))))))
        (/ (+ (* (* x1 3.0) t_1) (* x2 -6.0)) t_0))
       (* x1 (* x1 9.0))))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = (x1 * 3.0) + -1.0;
	double t_2 = (2.0 * x2) + (x1 * t_1);
	double tmp;
	if (x1 <= -5.5e+102) {
		tmp = x1 * ((x1 * x1) * -3.0);
	} else if (x1 <= 5e+153) {
		tmp = ((t_0 * (((x1 * x1) * -6.0) + ((x1 * ((-6.0 + (t_2 / (t_0 / 2.0))) + (x1 * 4.0))) / (t_0 / t_2)))) + (x1 * (2.0 + (x1 * (x1 + (t_2 / (t_0 / 3.0))))))) + ((((x1 * 3.0) * t_1) + (x2 * -6.0)) / t_0);
	} else {
		tmp = x1 * (x1 * 9.0);
	}
	return tmp;
}

Fortran

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) :: tmp
    t_0 = (x1 * x1) + 1.0d0
    t_1 = (x1 * 3.0d0) + (-1.0d0)
    t_2 = (2.0d0 * x2) + (x1 * t_1)
    if (x1 <= (-5.5d+102)) then
        tmp = x1 * ((x1 * x1) * (-3.0d0))
    else if (x1 <= 5d+153) then
        tmp = ((t_0 * (((x1 * x1) * (-6.0d0)) + ((x1 * (((-6.0d0) + (t_2 / (t_0 / 2.0d0))) + (x1 * 4.0d0))) / (t_0 / t_2)))) + (x1 * (2.0d0 + (x1 * (x1 + (t_2 / (t_0 / 3.0d0))))))) + ((((x1 * 3.0d0) * t_1) + (x2 * (-6.0d0))) / t_0)
    else
        tmp = x1 * (x1 * 9.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = (x1 * 3.0) + -1.0;
	double t_2 = (2.0 * x2) + (x1 * t_1);
	double tmp;
	if (x1 <= -5.5e+102) {
		tmp = x1 * ((x1 * x1) * -3.0);
	} else if (x1 <= 5e+153) {
		tmp = ((t_0 * (((x1 * x1) * -6.0) + ((x1 * ((-6.0 + (t_2 / (t_0 / 2.0))) + (x1 * 4.0))) / (t_0 / t_2)))) + (x1 * (2.0 + (x1 * (x1 + (t_2 / (t_0 / 3.0))))))) + ((((x1 * 3.0) * t_1) + (x2 * -6.0)) / t_0);
	} else {
		tmp = x1 * (x1 * 9.0);
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x1 * x1) + 1.0
	t_1 = (x1 * 3.0) + -1.0
	t_2 = (2.0 * x2) + (x1 * t_1)
	tmp = 0
	if x1 <= -5.5e+102:
		tmp = x1 * ((x1 * x1) * -3.0)
	elif x1 <= 5e+153:
		tmp = ((t_0 * (((x1 * x1) * -6.0) + ((x1 * ((-6.0 + (t_2 / (t_0 / 2.0))) + (x1 * 4.0))) / (t_0 / t_2)))) + (x1 * (2.0 + (x1 * (x1 + (t_2 / (t_0 / 3.0))))))) + ((((x1 * 3.0) * t_1) + (x2 * -6.0)) / t_0)
	else:
		tmp = x1 * (x1 * 9.0)
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * x1) + 1.0)
	t_1 = Float64(Float64(x1 * 3.0) + -1.0)
	t_2 = Float64(Float64(2.0 * x2) + Float64(x1 * t_1))
	tmp = 0.0
	if (x1 <= -5.5e+102)
		tmp = Float64(x1 * Float64(Float64(x1 * x1) * -3.0));
	elseif (x1 <= 5e+153)
		tmp = Float64(Float64(Float64(t_0 * Float64(Float64(Float64(x1 * x1) * -6.0) + Float64(Float64(x1 * Float64(Float64(-6.0 + Float64(t_2 / Float64(t_0 / 2.0))) + Float64(x1 * 4.0))) / Float64(t_0 / t_2)))) + Float64(x1 * Float64(2.0 + Float64(x1 * Float64(x1 + Float64(t_2 / Float64(t_0 / 3.0))))))) + Float64(Float64(Float64(Float64(x1 * 3.0) * t_1) + Float64(x2 * -6.0)) / t_0));
	else
		tmp = Float64(x1 * Float64(x1 * 9.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x1 * x1) + 1.0;
	t_1 = (x1 * 3.0) + -1.0;
	t_2 = (2.0 * x2) + (x1 * t_1);
	tmp = 0.0;
	if (x1 <= -5.5e+102)
		tmp = x1 * ((x1 * x1) * -3.0);
	elseif (x1 <= 5e+153)
		tmp = ((t_0 * (((x1 * x1) * -6.0) + ((x1 * ((-6.0 + (t_2 / (t_0 / 2.0))) + (x1 * 4.0))) / (t_0 / t_2)))) + (x1 * (2.0 + (x1 * (x1 + (t_2 / (t_0 / 3.0))))))) + ((((x1 * 3.0) * t_1) + (x2 * -6.0)) / t_0);
	else
		tmp = x1 * (x1 * 9.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x1 * 3.0), $MachinePrecision] + -1.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(2.0 * x2), $MachinePrecision] + N[(x1 * t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -5.5e+102], N[(x1 * N[(N[(x1 * x1), $MachinePrecision] * -3.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 5e+153], N[(N[(N[(t$95$0 * N[(N[(N[(x1 * x1), $MachinePrecision] * -6.0), $MachinePrecision] + N[(N[(x1 * N[(N[(-6.0 + N[(t$95$2 / N[(t$95$0 / 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t$95$0 / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(2.0 + N[(x1 * N[(x1 + N[(t$95$2 / N[(t$95$0 / 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(N[(x1 * 3.0), $MachinePrecision] * t$95$1), $MachinePrecision] + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision], N[(x1 * N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -5.49999999999999981e102

   1. Initial program 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in x1 around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, -6\right)\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-6, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 4\right)\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \color{blue}{9}\right)\right)\right)\right)\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 0.0%

      \[\leadsto \frac{3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right)}{x1 \cdot x1 + 1} + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(x1 \cdot \left(x1 \cdot -6\right) + \frac{2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)}{x1 \cdot x1 + 1} \cdot \left(x1 \cdot \left(-6 + \left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right) \cdot \frac{2}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot 4\right)\right) + x1 \cdot \left(2 + x1 \cdot \left(x1 + \color{blue}{9}\right)\right)\right) \]

   8. Taylor expanded in x1 around inf

      \[\leadsto \color{blue}{{x1}^{4} \cdot \left(6 - 3 \cdot \frac{1}{x1}\right)} \]
   9. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{4}\right), \color{blue}{\left(6 - 3 \cdot \frac{1}{x1}\right)}\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{\left(2 \cdot 2\right)}\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      3. pow-sqr N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{2} \cdot {x1}^{2}\right), \left(\color{blue}{6} - 3 \cdot \frac{1}{x1}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left({x1}^{2}\right), \left({x1}^{2}\right)\right), \left(\color{blue}{6} - 3 \cdot \frac{1}{x1}\right)\right) \]

      5. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x1 \cdot x1\right), \left({x1}^{2}\right)\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left({x1}^{2}\right)\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left(x1 \cdot x1\right)\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \left(6 + \color{blue}{\left(\mathsf{neg}\left(3 \cdot \frac{1}{x1}\right)\right)}\right)\right) \]

      10. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \color{blue}{\left(\mathsf{neg}\left(3 \cdot \frac{1}{x1}\right)\right)}\right)\right) \]

      11. associate-*r/ N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \left(\mathsf{neg}\left(\frac{3 \cdot 1}{x1}\right)\right)\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \left(\mathsf{neg}\left(\frac{3}{x1}\right)\right)\right)\right) \]

      13. distribute-neg-frac N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \left(\frac{\mathsf{neg}\left(3\right)}{\color{blue}{x1}}\right)\right)\right) \]

      14. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \left(\frac{-3}{x1}\right)\right)\right) \]

      15. /-lowering-/.f64 100.0%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \mathsf{/.f64}\left(-3, \color{blue}{x1}\right)\right)\right) \]

   10. Simplified 100.0%

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

   11. Taylor expanded in x1 around 0

       \[\leadsto \color{blue}{-3 \cdot {x1}^{3}} \]
   12. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto {x1}^{3} \cdot \color{blue}{-3} \]

       2. cube-mult N/A

          \[\leadsto \left(x1 \cdot \left(x1 \cdot x1\right)\right) \cdot -3 \]

       3. unpow2 N/A

          \[\leadsto \left(x1 \cdot {x1}^{2}\right) \cdot -3 \]

       4. associate-*l* N/A

          \[\leadsto x1 \cdot \color{blue}{\left({x1}^{2} \cdot -3\right)} \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x1, \color{blue}{\left({x1}^{2} \cdot -3\right)}\right) \]

       6. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(\left({x1}^{2}\right), \color{blue}{-3}\right)\right) \]

       7. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(\left(x1 \cdot x1\right), -3\right)\right) \]

       8. *-lowering-*.f64 100.0%

          \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), -3\right)\right) \]

   13. Simplified 100.0%

       \[\leadsto \color{blue}{x1 \cdot \left(\left(x1 \cdot x1\right) \cdot -3\right)} \]

   if -5.49999999999999981e102 < x1 < 5.00000000000000018e153

   1. Initial program 99.4%

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

   3. Simplified 99.5%

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

   6. Applied egg-rr 99.5%

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

   if 5.00000000000000018e153 < x1

   1. Initial program 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in x1 around 0

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

   7. Simplified 69.0%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(x2 \cdot 2\right) \cdot \left(x2 \cdot 4 + -6\right) + \left(x1 \cdot \left(\left(\left(\left(9 + 3 \cdot \left(x2 \cdot 2\right)\right) + x2 \cdot 10\right) - \left(x2 \cdot 4 + -6\right)\right) + -6\right) + -1\right)\right)} \]

   8. Taylor expanded in x2 around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right), \color{blue}{\left(9 \cdot x1 - 1\right)}\right)\right)\right) \]
   9. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right), \left(9 \cdot x1 + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right), \left(9 \cdot x1 + -1\right)\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right), \mathsf{+.f64}\left(\left(9 \cdot x1\right), \color{blue}{-1}\right)\right)\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right), \mathsf{+.f64}\left(\left(x1 \cdot 9\right), -1\right)\right)\right)\right) \]

      5. *-lowering-*.f64 100.0%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 9\right), -1\right)\right)\right)\right) \]

   10. Simplified 100.0%

       \[\leadsto -6 \cdot x2 + x1 \cdot \left(\left(x2 \cdot 2\right) \cdot \left(x2 \cdot 4 + -6\right) + \color{blue}{\left(x1 \cdot 9 + -1\right)}\right) \]

   11. Taylor expanded in x1 around inf

       \[\leadsto \color{blue}{9 \cdot {x1}^{2}} \]
   12. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto {x1}^{2} \cdot \color{blue}{9} \]

       2. unpow2 N/A

          \[\leadsto \left(x1 \cdot x1\right) \cdot 9 \]

       3. associate-*l* N/A

          \[\leadsto x1 \cdot \color{blue}{\left(x1 \cdot 9\right)} \]

       4. *-commutative N/A

          \[\leadsto x1 \cdot \left(9 \cdot \color{blue}{x1}\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x1, \color{blue}{\left(9 \cdot x1\right)}\right) \]

       6. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x1, \left(x1 \cdot \color{blue}{9}\right)\right) \]

       7. *-lowering-*.f64 100.0%

          \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, \color{blue}{9}\right)\right) \]

   13. Simplified 100.0%

       \[\leadsto \color{blue}{x1 \cdot \left(x1 \cdot 9\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 99.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.5 \cdot 10^{+102}:\\ \;\;\;\;x1 \cdot \left(\left(x1 \cdot x1\right) \cdot -3\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+153}:\\ \;\;\;\;\left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot -6 + \frac{x1 \cdot \left(\left(-6 + \frac{2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)}{\frac{x1 \cdot x1 + 1}{2}}\right) + x1 \cdot 4\right)}{\frac{x1 \cdot x1 + 1}{2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)}}\right) + x1 \cdot \left(2 + x1 \cdot \left(x1 + \frac{2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)}{\frac{x1 \cdot x1 + 1}{3}}\right)\right)\right) + \frac{\left(x1 \cdot 3\right) \cdot \left(x1 \cdot 3 + -1\right) + x2 \cdot -6}{x1 \cdot x1 + 1}\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot \left(x1 \cdot 9\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 98.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3 + -1\right)\\ t_1 := 2 \cdot x2 + t\_0\\ t_2 := x1 \cdot x1 + 1\\ \mathbf{if}\;x1 \leq -5.5 \cdot 10^{+102}:\\ \;\;\;\;x1 \cdot \left(\left(x1 \cdot x1\right) \cdot -3\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+153}:\\ \;\;\;\;\frac{3 \cdot \left(x2 \cdot -2 + t\_0\right)}{t\_2} + \left(t\_2 \cdot \left(x1 \cdot \left(x1 \cdot -6\right) + \frac{t\_1}{t\_2} \cdot \left(x1 \cdot \left(-6 + t\_1 \cdot \frac{2}{t\_2}\right) + \left(x1 \cdot x1\right) \cdot 4\right)\right) + x1 \cdot \left(2 + x1 \cdot \left(x1 + 9\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot \left(x1 \cdot 9\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (+ (* x1 3.0) -1.0)))
        (t_1 (+ (* 2.0 x2) t_0))
        (t_2 (+ (* x1 x1) 1.0)))
   (if (<= x1 -5.5e+102)
     (* x1 (* (* x1 x1) -3.0))
     (if (<= x1 5e+153)
       (+
        (/ (* 3.0 (+ (* x2 -2.0) t_0)) t_2)
        (+
         (*
          t_2
          (+
           (* x1 (* x1 -6.0))
           (*
            (/ t_1 t_2)
            (+ (* x1 (+ -6.0 (* t_1 (/ 2.0 t_2)))) (* (* x1 x1) 4.0)))))
         (* x1 (+ 2.0 (* x1 (+ x1 9.0))))))
       (* x1 (* x1 9.0))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * ((x1 * 3.0) + -1.0);
	double t_1 = (2.0 * x2) + t_0;
	double t_2 = (x1 * x1) + 1.0;
	double tmp;
	if (x1 <= -5.5e+102) {
		tmp = x1 * ((x1 * x1) * -3.0);
	} else if (x1 <= 5e+153) {
		tmp = ((3.0 * ((x2 * -2.0) + t_0)) / t_2) + ((t_2 * ((x1 * (x1 * -6.0)) + ((t_1 / t_2) * ((x1 * (-6.0 + (t_1 * (2.0 / t_2)))) + ((x1 * x1) * 4.0))))) + (x1 * (2.0 + (x1 * (x1 + 9.0)))));
	} else {
		tmp = x1 * (x1 * 9.0);
	}
	return tmp;
}

Fortran

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) :: tmp
    t_0 = x1 * ((x1 * 3.0d0) + (-1.0d0))
    t_1 = (2.0d0 * x2) + t_0
    t_2 = (x1 * x1) + 1.0d0
    if (x1 <= (-5.5d+102)) then
        tmp = x1 * ((x1 * x1) * (-3.0d0))
    else if (x1 <= 5d+153) then
        tmp = ((3.0d0 * ((x2 * (-2.0d0)) + t_0)) / t_2) + ((t_2 * ((x1 * (x1 * (-6.0d0))) + ((t_1 / t_2) * ((x1 * ((-6.0d0) + (t_1 * (2.0d0 / t_2)))) + ((x1 * x1) * 4.0d0))))) + (x1 * (2.0d0 + (x1 * (x1 + 9.0d0)))))
    else
        tmp = x1 * (x1 * 9.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * ((x1 * 3.0) + -1.0);
	double t_1 = (2.0 * x2) + t_0;
	double t_2 = (x1 * x1) + 1.0;
	double tmp;
	if (x1 <= -5.5e+102) {
		tmp = x1 * ((x1 * x1) * -3.0);
	} else if (x1 <= 5e+153) {
		tmp = ((3.0 * ((x2 * -2.0) + t_0)) / t_2) + ((t_2 * ((x1 * (x1 * -6.0)) + ((t_1 / t_2) * ((x1 * (-6.0 + (t_1 * (2.0 / t_2)))) + ((x1 * x1) * 4.0))))) + (x1 * (2.0 + (x1 * (x1 + 9.0)))));
	} else {
		tmp = x1 * (x1 * 9.0);
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * ((x1 * 3.0) + -1.0)
	t_1 = (2.0 * x2) + t_0
	t_2 = (x1 * x1) + 1.0
	tmp = 0
	if x1 <= -5.5e+102:
		tmp = x1 * ((x1 * x1) * -3.0)
	elif x1 <= 5e+153:
		tmp = ((3.0 * ((x2 * -2.0) + t_0)) / t_2) + ((t_2 * ((x1 * (x1 * -6.0)) + ((t_1 / t_2) * ((x1 * (-6.0 + (t_1 * (2.0 / t_2)))) + ((x1 * x1) * 4.0))))) + (x1 * (2.0 + (x1 * (x1 + 9.0)))))
	else:
		tmp = x1 * (x1 * 9.0)
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(Float64(x1 * 3.0) + -1.0))
	t_1 = Float64(Float64(2.0 * x2) + t_0)
	t_2 = Float64(Float64(x1 * x1) + 1.0)
	tmp = 0.0
	if (x1 <= -5.5e+102)
		tmp = Float64(x1 * Float64(Float64(x1 * x1) * -3.0));
	elseif (x1 <= 5e+153)
		tmp = Float64(Float64(Float64(3.0 * Float64(Float64(x2 * -2.0) + t_0)) / t_2) + Float64(Float64(t_2 * Float64(Float64(x1 * Float64(x1 * -6.0)) + Float64(Float64(t_1 / t_2) * Float64(Float64(x1 * Float64(-6.0 + Float64(t_1 * Float64(2.0 / t_2)))) + Float64(Float64(x1 * x1) * 4.0))))) + Float64(x1 * Float64(2.0 + Float64(x1 * Float64(x1 + 9.0))))));
	else
		tmp = Float64(x1 * Float64(x1 * 9.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * ((x1 * 3.0) + -1.0);
	t_1 = (2.0 * x2) + t_0;
	t_2 = (x1 * x1) + 1.0;
	tmp = 0.0;
	if (x1 <= -5.5e+102)
		tmp = x1 * ((x1 * x1) * -3.0);
	elseif (x1 <= 5e+153)
		tmp = ((3.0 * ((x2 * -2.0) + t_0)) / t_2) + ((t_2 * ((x1 * (x1 * -6.0)) + ((t_1 / t_2) * ((x1 * (-6.0 + (t_1 * (2.0 / t_2)))) + ((x1 * x1) * 4.0))))) + (x1 * (2.0 + (x1 * (x1 + 9.0)))));
	else
		tmp = x1 * (x1 * 9.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(2.0 * x2), $MachinePrecision] + t$95$0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, If[LessEqual[x1, -5.5e+102], N[(x1 * N[(N[(x1 * x1), $MachinePrecision] * -3.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 5e+153], N[(N[(N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] + t$95$0), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision] + N[(N[(t$95$2 * N[(N[(x1 * N[(x1 * -6.0), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$1 / t$95$2), $MachinePrecision] * N[(N[(x1 * N[(-6.0 + N[(t$95$1 * N[(2.0 / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(2.0 + N[(x1 * N[(x1 + 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 * N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -5.49999999999999981e102

   1. Initial program 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in x1 around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, -6\right)\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-6, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 4\right)\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \color{blue}{9}\right)\right)\right)\right)\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 0.0%

      \[\leadsto \frac{3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right)}{x1 \cdot x1 + 1} + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(x1 \cdot \left(x1 \cdot -6\right) + \frac{2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)}{x1 \cdot x1 + 1} \cdot \left(x1 \cdot \left(-6 + \left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right) \cdot \frac{2}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot 4\right)\right) + x1 \cdot \left(2 + x1 \cdot \left(x1 + \color{blue}{9}\right)\right)\right) \]

   8. Taylor expanded in x1 around inf

      \[\leadsto \color{blue}{{x1}^{4} \cdot \left(6 - 3 \cdot \frac{1}{x1}\right)} \]
   9. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{4}\right), \color{blue}{\left(6 - 3 \cdot \frac{1}{x1}\right)}\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{\left(2 \cdot 2\right)}\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      3. pow-sqr N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{2} \cdot {x1}^{2}\right), \left(\color{blue}{6} - 3 \cdot \frac{1}{x1}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left({x1}^{2}\right), \left({x1}^{2}\right)\right), \left(\color{blue}{6} - 3 \cdot \frac{1}{x1}\right)\right) \]

      5. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x1 \cdot x1\right), \left({x1}^{2}\right)\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left({x1}^{2}\right)\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left(x1 \cdot x1\right)\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \left(6 + \color{blue}{\left(\mathsf{neg}\left(3 \cdot \frac{1}{x1}\right)\right)}\right)\right) \]

      10. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \color{blue}{\left(\mathsf{neg}\left(3 \cdot \frac{1}{x1}\right)\right)}\right)\right) \]

      11. associate-*r/ N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \left(\mathsf{neg}\left(\frac{3 \cdot 1}{x1}\right)\right)\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \left(\mathsf{neg}\left(\frac{3}{x1}\right)\right)\right)\right) \]

      13. distribute-neg-frac N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \left(\frac{\mathsf{neg}\left(3\right)}{\color{blue}{x1}}\right)\right)\right) \]

      14. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \left(\frac{-3}{x1}\right)\right)\right) \]

      15. /-lowering-/.f64 100.0%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \mathsf{/.f64}\left(-3, \color{blue}{x1}\right)\right)\right) \]

   10. Simplified 100.0%

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

   11. Taylor expanded in x1 around 0

       \[\leadsto \color{blue}{-3 \cdot {x1}^{3}} \]
   12. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto {x1}^{3} \cdot \color{blue}{-3} \]

       2. cube-mult N/A

          \[\leadsto \left(x1 \cdot \left(x1 \cdot x1\right)\right) \cdot -3 \]

       3. unpow2 N/A

          \[\leadsto \left(x1 \cdot {x1}^{2}\right) \cdot -3 \]

       4. associate-*l* N/A

          \[\leadsto x1 \cdot \color{blue}{\left({x1}^{2} \cdot -3\right)} \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x1, \color{blue}{\left({x1}^{2} \cdot -3\right)}\right) \]

       6. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(\left({x1}^{2}\right), \color{blue}{-3}\right)\right) \]

       7. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(\left(x1 \cdot x1\right), -3\right)\right) \]

       8. *-lowering-*.f64 100.0%

          \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), -3\right)\right) \]

   13. Simplified 100.0%

       \[\leadsto \color{blue}{x1 \cdot \left(\left(x1 \cdot x1\right) \cdot -3\right)} \]

   if -5.49999999999999981e102 < x1 < 5.00000000000000018e153

   1. Initial program 99.4%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x1 around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, -6\right)\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-6, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 4\right)\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \color{blue}{9}\right)\right)\right)\right)\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 99.2%

      \[\leadsto \frac{3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right)}{x1 \cdot x1 + 1} + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(x1 \cdot \left(x1 \cdot -6\right) + \frac{2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)}{x1 \cdot x1 + 1} \cdot \left(x1 \cdot \left(-6 + \left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right) \cdot \frac{2}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot 4\right)\right) + x1 \cdot \left(2 + x1 \cdot \left(x1 + \color{blue}{9}\right)\right)\right) \]

   if 5.00000000000000018e153 < x1

   1. Initial program 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in x1 around 0

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

   7. Simplified 69.0%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(x2 \cdot 2\right) \cdot \left(x2 \cdot 4 + -6\right) + \left(x1 \cdot \left(\left(\left(\left(9 + 3 \cdot \left(x2 \cdot 2\right)\right) + x2 \cdot 10\right) - \left(x2 \cdot 4 + -6\right)\right) + -6\right) + -1\right)\right)} \]

   8. Taylor expanded in x2 around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right), \color{blue}{\left(9 \cdot x1 - 1\right)}\right)\right)\right) \]
   9. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right), \left(9 \cdot x1 + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right), \left(9 \cdot x1 + -1\right)\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right), \mathsf{+.f64}\left(\left(9 \cdot x1\right), \color{blue}{-1}\right)\right)\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right), \mathsf{+.f64}\left(\left(x1 \cdot 9\right), -1\right)\right)\right)\right) \]

      5. *-lowering-*.f64 100.0%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 9\right), -1\right)\right)\right)\right) \]

   10. Simplified 100.0%

       \[\leadsto -6 \cdot x2 + x1 \cdot \left(\left(x2 \cdot 2\right) \cdot \left(x2 \cdot 4 + -6\right) + \color{blue}{\left(x1 \cdot 9 + -1\right)}\right) \]

   11. Taylor expanded in x1 around inf

       \[\leadsto \color{blue}{9 \cdot {x1}^{2}} \]
   12. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto {x1}^{2} \cdot \color{blue}{9} \]

       2. unpow2 N/A

          \[\leadsto \left(x1 \cdot x1\right) \cdot 9 \]

       3. associate-*l* N/A

          \[\leadsto x1 \cdot \color{blue}{\left(x1 \cdot 9\right)} \]

       4. *-commutative N/A

          \[\leadsto x1 \cdot \left(9 \cdot \color{blue}{x1}\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x1, \color{blue}{\left(9 \cdot x1\right)}\right) \]

       6. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x1, \left(x1 \cdot \color{blue}{9}\right)\right) \]

       7. *-lowering-*.f64 100.0%

          \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, \color{blue}{9}\right)\right) \]

   13. Simplified 100.0%

       \[\leadsto \color{blue}{x1 \cdot \left(x1 \cdot 9\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 6: 95.9% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -2.02 \cdot 10^{+14}:\\ \;\;\;\;\left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right)\right) \cdot \left(6 - \frac{\frac{x2 \cdot -8}{x1}}{x1}\right)\\ \mathbf{elif}\;x1 \leq 150000:\\ \;\;\;\;x1 \cdot \left(-1 + x1 \cdot 9\right) + x2 \cdot \left(-6 + \left(x1 \cdot \left(x1 \cdot 12 + -12\right) + 8 \cdot \left(x1 \cdot x2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x1 \cdot x1\right) \cdot \left(x1 \cdot \left(-3 + x1 \cdot 6\right) + \left(-3 + x2 \cdot 8\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -2.02e+14)
   (* (* (* x1 x1) (* x1 x1)) (- 6.0 (/ (/ (* x2 -8.0) x1) x1)))
   (if (<= x1 150000.0)
     (+
      (* x1 (+ -1.0 (* x1 9.0)))
      (* x2 (+ -6.0 (+ (* x1 (+ (* x1 12.0) -12.0)) (* 8.0 (* x1 x2))))))
     (* (* x1 x1) (+ (* x1 (+ -3.0 (* x1 6.0))) (+ -3.0 (* x2 8.0)))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -2.02e+14) {
		tmp = ((x1 * x1) * (x1 * x1)) * (6.0 - (((x2 * -8.0) / x1) / x1));
	} else if (x1 <= 150000.0) {
		tmp = (x1 * (-1.0 + (x1 * 9.0))) + (x2 * (-6.0 + ((x1 * ((x1 * 12.0) + -12.0)) + (8.0 * (x1 * x2)))));
	} else {
		tmp = (x1 * x1) * ((x1 * (-3.0 + (x1 * 6.0))) + (-3.0 + (x2 * 8.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x1 <= (-2.02d+14)) then
        tmp = ((x1 * x1) * (x1 * x1)) * (6.0d0 - (((x2 * (-8.0d0)) / x1) / x1))
    else if (x1 <= 150000.0d0) then
        tmp = (x1 * ((-1.0d0) + (x1 * 9.0d0))) + (x2 * ((-6.0d0) + ((x1 * ((x1 * 12.0d0) + (-12.0d0))) + (8.0d0 * (x1 * x2)))))
    else
        tmp = (x1 * x1) * ((x1 * ((-3.0d0) + (x1 * 6.0d0))) + ((-3.0d0) + (x2 * 8.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= -2.02e+14) {
		tmp = ((x1 * x1) * (x1 * x1)) * (6.0 - (((x2 * -8.0) / x1) / x1));
	} else if (x1 <= 150000.0) {
		tmp = (x1 * (-1.0 + (x1 * 9.0))) + (x2 * (-6.0 + ((x1 * ((x1 * 12.0) + -12.0)) + (8.0 * (x1 * x2)))));
	} else {
		tmp = (x1 * x1) * ((x1 * (-3.0 + (x1 * 6.0))) + (-3.0 + (x2 * 8.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -2.02e+14:
		tmp = ((x1 * x1) * (x1 * x1)) * (6.0 - (((x2 * -8.0) / x1) / x1))
	elif x1 <= 150000.0:
		tmp = (x1 * (-1.0 + (x1 * 9.0))) + (x2 * (-6.0 + ((x1 * ((x1 * 12.0) + -12.0)) + (8.0 * (x1 * x2)))))
	else:
		tmp = (x1 * x1) * ((x1 * (-3.0 + (x1 * 6.0))) + (-3.0 + (x2 * 8.0)))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -2.02e+14)
		tmp = Float64(Float64(Float64(x1 * x1) * Float64(x1 * x1)) * Float64(6.0 - Float64(Float64(Float64(x2 * -8.0) / x1) / x1)));
	elseif (x1 <= 150000.0)
		tmp = Float64(Float64(x1 * Float64(-1.0 + Float64(x1 * 9.0))) + Float64(x2 * Float64(-6.0 + Float64(Float64(x1 * Float64(Float64(x1 * 12.0) + -12.0)) + Float64(8.0 * Float64(x1 * x2))))));
	else
		tmp = Float64(Float64(x1 * x1) * Float64(Float64(x1 * Float64(-3.0 + Float64(x1 * 6.0))) + Float64(-3.0 + Float64(x2 * 8.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -2.02e+14)
		tmp = ((x1 * x1) * (x1 * x1)) * (6.0 - (((x2 * -8.0) / x1) / x1));
	elseif (x1 <= 150000.0)
		tmp = (x1 * (-1.0 + (x1 * 9.0))) + (x2 * (-6.0 + ((x1 * ((x1 * 12.0) + -12.0)) + (8.0 * (x1 * x2)))));
	else
		tmp = (x1 * x1) * ((x1 * (-3.0 + (x1 * 6.0))) + (-3.0 + (x2 * 8.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -2.02e+14], N[(N[(N[(x1 * x1), $MachinePrecision] * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] * N[(6.0 - N[(N[(N[(x2 * -8.0), $MachinePrecision] / x1), $MachinePrecision] / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 150000.0], N[(N[(x1 * N[(-1.0 + N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x2 * N[(-6.0 + N[(N[(x1 * N[(N[(x1 * 12.0), $MachinePrecision] + -12.0), $MachinePrecision]), $MachinePrecision] + N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x1 * x1), $MachinePrecision] * N[(N[(x1 * N[(-3.0 + N[(x1 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-3.0 + N[(x2 * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -2.02e14

   1. Initial program 27.1%

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

   3. Simplified 27.1%

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

   5. Taylor expanded in x1 around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, -6\right)\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-6, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 4\right)\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \color{blue}{9}\right)\right)\right)\right)\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 27.1%

      \[\leadsto \frac{3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right)}{x1 \cdot x1 + 1} + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(x1 \cdot \left(x1 \cdot -6\right) + \frac{2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)}{x1 \cdot x1 + 1} \cdot \left(x1 \cdot \left(-6 + \left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right) \cdot \frac{2}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot 4\right)\right) + x1 \cdot \left(2 + x1 \cdot \left(x1 + \color{blue}{9}\right)\right)\right) \]

   8. Taylor expanded in x1 around -inf

      \[\leadsto \color{blue}{{x1}^{4} \cdot \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)} \]
   9. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{4}\right), \color{blue}{\left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)}\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{\left(2 \cdot 2\right)}\right), \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)\right) \]

      3. pow-sqr N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{2} \cdot {x1}^{2}\right), \left(\color{blue}{6} + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left({x1}^{2}\right), \left({x1}^{2}\right)\right), \left(\color{blue}{6} + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)\right) \]

      5. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x1 \cdot x1\right), \left({x1}^{2}\right)\right), \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left({x1}^{2}\right)\right), \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left(x1 \cdot x1\right)\right), \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)\right) \]

      9. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \left(6 + \left(\mathsf{neg}\left(\frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)\right)\right)\right) \]

      10. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \left(6 - \color{blue}{\frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}}\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \color{blue}{\left(\frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)}\right)\right) \]

      12. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \mathsf{/.f64}\left(\left(3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}\right), \color{blue}{x1}\right)\right)\right) \]

   10. Simplified 94.9%

       \[\leadsto \color{blue}{\left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right)\right) \cdot \left(6 - \frac{3 - \frac{x2 \cdot 8 + -3}{x1}}{x1}\right)} \]

   11. Taylor expanded in x2 around inf

       \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \color{blue}{\left(-8 \cdot \frac{x2}{{x1}^{2}}\right)}\right)\right) \]
   12. Step-by-step derivation

       1. associate-*r/ N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \left(\frac{-8 \cdot x2}{\color{blue}{{x1}^{2}}}\right)\right)\right) \]

       2. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \left(\frac{\left(\mathsf{neg}\left(8\right)\right) \cdot x2}{{x1}^{2}}\right)\right)\right) \]

       3. distribute-lft-neg-in N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \left(\frac{\mathsf{neg}\left(8 \cdot x2\right)}{{\color{blue}{x1}}^{2}}\right)\right)\right) \]

       4. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \left(\frac{\mathsf{neg}\left(8 \cdot x2\right)}{x1 \cdot \color{blue}{x1}}\right)\right)\right) \]

       5. associate-/r* N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \left(\frac{\frac{\mathsf{neg}\left(8 \cdot x2\right)}{x1}}{\color{blue}{x1}}\right)\right)\right) \]

       6. distribute-neg-frac N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \left(\frac{\mathsf{neg}\left(\frac{8 \cdot x2}{x1}\right)}{x1}\right)\right)\right) \]

       7. associate-*r/ N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \left(\frac{\mathsf{neg}\left(8 \cdot \frac{x2}{x1}\right)}{x1}\right)\right)\right) \]

       8. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \mathsf{/.f64}\left(\left(\mathsf{neg}\left(8 \cdot \frac{x2}{x1}\right)\right), \color{blue}{x1}\right)\right)\right) \]

       9. associate-*r/ N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \mathsf{/.f64}\left(\left(\mathsf{neg}\left(\frac{8 \cdot x2}{x1}\right)\right), x1\right)\right)\right) \]

       10. distribute-neg-frac N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \mathsf{/.f64}\left(\left(\frac{\mathsf{neg}\left(8 \cdot x2\right)}{x1}\right), x1\right)\right)\right) \]

       11. /-lowering-/.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(\mathsf{neg}\left(8 \cdot x2\right)\right), x1\right), x1\right)\right)\right) \]

       12. *-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(\mathsf{neg}\left(x2 \cdot 8\right)\right), x1\right), x1\right)\right)\right) \]

       13. distribute-rgt-neg-in N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(x2 \cdot \left(\mathsf{neg}\left(8\right)\right)\right), x1\right), x1\right)\right)\right) \]

       14. metadata-eval N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(x2 \cdot -8\right), x1\right), x1\right)\right)\right) \]

       15. *-lowering-*.f64 94.9%

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x2, -8\right), x1\right), x1\right)\right)\right) \]

   13. Simplified 94.9%

       \[\leadsto \left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right)\right) \cdot \left(6 - \color{blue}{\frac{\frac{x2 \cdot -8}{x1}}{x1}}\right) \]

   if -2.02e14 < x1 < 1.5e5

   1. Initial program 99.4%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x1 around 0

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

   7. Simplified 87.5%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(x2 \cdot 2\right) \cdot \left(x2 \cdot 4 + -6\right) + \left(x1 \cdot \left(\left(\left(\left(9 + 3 \cdot \left(x2 \cdot 2\right)\right) + x2 \cdot 10\right) - \left(x2 \cdot 4 + -6\right)\right) + -6\right) + -1\right)\right)} \]

   8. Taylor expanded in x2 around 0

      \[\leadsto \color{blue}{x1 \cdot \left(9 \cdot x1 - 1\right) + x2 \cdot \left(\left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(12 \cdot x1 - 12\right)\right) - 6\right)} \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x1 \cdot \left(9 \cdot x1 - 1\right)\right), \color{blue}{\left(x2 \cdot \left(\left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(12 \cdot x1 - 12\right)\right) - 6\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \left(9 \cdot x1 - 1\right)\right), \left(\color{blue}{x2} \cdot \left(\left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(12 \cdot x1 - 12\right)\right) - 6\right)\right)\right) \]

      3. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \left(9 \cdot x1 + \left(\mathsf{neg}\left(1\right)\right)\right)\right), \left(x2 \cdot \left(\left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(12 \cdot x1 - 12\right)\right) - 6\right)\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \left(9 \cdot x1 + -1\right)\right), \left(x2 \cdot \left(\left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(12 \cdot x1 - 12\right)\right) - 6\right)\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\left(9 \cdot x1\right), -1\right)\right), \left(x2 \cdot \left(\left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(12 \cdot x1 - 12\right)\right) - 6\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\left(x1 \cdot 9\right), -1\right)\right), \left(x2 \cdot \left(\left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(12 \cdot x1 - 12\right)\right) - 6\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 9\right), -1\right)\right), \left(x2 \cdot \left(\left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(12 \cdot x1 - 12\right)\right) - 6\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 9\right), -1\right)\right), \mathsf{*.f64}\left(x2, \color{blue}{\left(\left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(12 \cdot x1 - 12\right)\right) - 6\right)}\right)\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 9\right), -1\right)\right), \mathsf{*.f64}\left(x2, \left(\left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(12 \cdot x1 - 12\right)\right) + \color{blue}{\left(\mathsf{neg}\left(6\right)\right)}\right)\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 9\right), -1\right)\right), \mathsf{*.f64}\left(x2, \left(\left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(12 \cdot x1 - 12\right)\right) + -6\right)\right)\right) \]

      11. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 9\right), -1\right)\right), \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(12 \cdot x1 - 12\right)\right), \color{blue}{-6}\right)\right)\right) \]

   10. Simplified 98.4%

       \[\leadsto \color{blue}{x1 \cdot \left(x1 \cdot 9 + -1\right) + x2 \cdot \left(\left(x1 \cdot \left(x1 \cdot 12 + -12\right) + 8 \cdot \left(x1 \cdot x2\right)\right) + -6\right)} \]

   if 1.5e5 < x1

   1. Initial program 48.9%

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

   3. Simplified 49.0%

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

   5. Taylor expanded in x1 around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, -6\right)\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-6, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 4\right)\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \color{blue}{9}\right)\right)\right)\right)\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 49.0%

      \[\leadsto \frac{3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right)}{x1 \cdot x1 + 1} + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(x1 \cdot \left(x1 \cdot -6\right) + \frac{2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)}{x1 \cdot x1 + 1} \cdot \left(x1 \cdot \left(-6 + \left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right) \cdot \frac{2}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot 4\right)\right) + x1 \cdot \left(2 + x1 \cdot \left(x1 + \color{blue}{9}\right)\right)\right) \]

   8. Taylor expanded in x1 around -inf

      \[\leadsto \color{blue}{{x1}^{4} \cdot \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)} \]
   9. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{4}\right), \color{blue}{\left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)}\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{\left(2 \cdot 2\right)}\right), \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)\right) \]

      3. pow-sqr N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{2} \cdot {x1}^{2}\right), \left(\color{blue}{6} + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left({x1}^{2}\right), \left({x1}^{2}\right)\right), \left(\color{blue}{6} + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)\right) \]

      5. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x1 \cdot x1\right), \left({x1}^{2}\right)\right), \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left({x1}^{2}\right)\right), \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left(x1 \cdot x1\right)\right), \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)\right) \]

      9. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \left(6 + \left(\mathsf{neg}\left(\frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)\right)\right)\right) \]

      10. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \left(6 - \color{blue}{\frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}}\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \color{blue}{\left(\frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)}\right)\right) \]

      12. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \mathsf{/.f64}\left(\left(3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}\right), \color{blue}{x1}\right)\right)\right) \]

   10. Simplified 90.8%

       \[\leadsto \color{blue}{\left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right)\right) \cdot \left(6 - \frac{3 - \frac{x2 \cdot 8 + -3}{x1}}{x1}\right)} \]

   11. Taylor expanded in x1 around 0

       \[\leadsto \color{blue}{{x1}^{2} \cdot \left(\left(8 \cdot x2 + x1 \cdot \left(6 \cdot x1 - 3\right)\right) - 3\right)} \]
   12. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\left({x1}^{2}\right), \color{blue}{\left(\left(8 \cdot x2 + x1 \cdot \left(6 \cdot x1 - 3\right)\right) - 3\right)}\right) \]

       2. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(\left(x1 \cdot x1\right), \left(\color{blue}{\left(8 \cdot x2 + x1 \cdot \left(6 \cdot x1 - 3\right)\right)} - 3\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left(\color{blue}{\left(8 \cdot x2 + x1 \cdot \left(6 \cdot x1 - 3\right)\right)} - 3\right)\right) \]

       4. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left(\left(x1 \cdot \left(6 \cdot x1 - 3\right) + 8 \cdot x2\right) - 3\right)\right) \]

       5. associate--l+ N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left(x1 \cdot \left(6 \cdot x1 - 3\right) + \color{blue}{\left(8 \cdot x2 - 3\right)}\right)\right) \]

       6. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\left(x1 \cdot \left(6 \cdot x1 - 3\right)\right), \color{blue}{\left(8 \cdot x2 - 3\right)}\right)\right) \]

       7. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \left(6 \cdot x1 - 3\right)\right), \left(\color{blue}{8 \cdot x2} - 3\right)\right)\right) \]

       8. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \left(6 \cdot x1 + \left(\mathsf{neg}\left(3\right)\right)\right)\right), \left(8 \cdot \color{blue}{x2} - 3\right)\right)\right) \]

       9. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \left(6 \cdot x1 + -3\right)\right), \left(8 \cdot x2 - 3\right)\right)\right) \]

       10. +-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \left(-3 + 6 \cdot x1\right)\right), \left(8 \cdot \color{blue}{x2} - 3\right)\right)\right) \]

       11. +-lowering-+.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-3, \left(6 \cdot x1\right)\right)\right), \left(8 \cdot \color{blue}{x2} - 3\right)\right)\right) \]

       12. *-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-3, \left(x1 \cdot 6\right)\right)\right), \left(8 \cdot x2 - 3\right)\right)\right) \]

       13. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-3, \mathsf{*.f64}\left(x1, 6\right)\right)\right), \left(8 \cdot x2 - 3\right)\right)\right) \]

       14. sub-neg N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-3, \mathsf{*.f64}\left(x1, 6\right)\right)\right), \left(8 \cdot x2 + \color{blue}{\left(\mathsf{neg}\left(3\right)\right)}\right)\right)\right) \]

       15. metadata-eval N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-3, \mathsf{*.f64}\left(x1, 6\right)\right)\right), \left(8 \cdot x2 + -3\right)\right)\right) \]

       16. +-lowering-+.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-3, \mathsf{*.f64}\left(x1, 6\right)\right)\right), \mathsf{+.f64}\left(\left(8 \cdot x2\right), \color{blue}{-3}\right)\right)\right) \]

       17. *-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-3, \mathsf{*.f64}\left(x1, 6\right)\right)\right), \mathsf{+.f64}\left(\left(x2 \cdot 8\right), -3\right)\right)\right) \]

       18. *-lowering-*.f64 91.0%

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-3, \mathsf{*.f64}\left(x1, 6\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 8\right), -3\right)\right)\right) \]

   13. Simplified 91.0%

       \[\leadsto \color{blue}{\left(x1 \cdot x1\right) \cdot \left(x1 \cdot \left(-3 + x1 \cdot 6\right) + \left(x2 \cdot 8 + -3\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 95.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -2.02 \cdot 10^{+14}:\\ \;\;\;\;\left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right)\right) \cdot \left(6 - \frac{\frac{x2 \cdot -8}{x1}}{x1}\right)\\ \mathbf{elif}\;x1 \leq 150000:\\ \;\;\;\;x1 \cdot \left(-1 + x1 \cdot 9\right) + x2 \cdot \left(-6 + \left(x1 \cdot \left(x1 \cdot 12 + -12\right) + 8 \cdot \left(x1 \cdot x2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x1 \cdot x1\right) \cdot \left(x1 \cdot \left(-3 + x1 \cdot 6\right) + \left(-3 + x2 \cdot 8\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 83.7% accurate, 4.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -2 \cdot 10^{+14}:\\ \;\;\;\;\left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right)\right) \cdot \left(6 - \frac{\frac{x2 \cdot -8}{x1}}{x1}\right)\\ \mathbf{elif}\;x1 \leq 2.2 \cdot 10^{-279}:\\ \;\;\;\;x2 \cdot -6 + x2 \cdot \left(x1 \cdot \left(x2 \cdot 8\right)\right)\\ \mathbf{elif}\;x1 \leq 0.07:\\ \;\;\;\;x1 \cdot \left(-1 + x1 \cdot 9\right) + x2 \cdot -6\\ \mathbf{else}:\\ \;\;\;\;\left(x1 \cdot x1\right) \cdot \left(x1 \cdot \left(-3 + x1 \cdot 6\right) + \left(-3 + x2 \cdot 8\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -2e+14)
   (* (* (* x1 x1) (* x1 x1)) (- 6.0 (/ (/ (* x2 -8.0) x1) x1)))
   (if (<= x1 2.2e-279)
     (+ (* x2 -6.0) (* x2 (* x1 (* x2 8.0))))
     (if (<= x1 0.07)
       (+ (* x1 (+ -1.0 (* x1 9.0))) (* x2 -6.0))
       (* (* x1 x1) (+ (* x1 (+ -3.0 (* x1 6.0))) (+ -3.0 (* x2 8.0))))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -2e+14) {
		tmp = ((x1 * x1) * (x1 * x1)) * (6.0 - (((x2 * -8.0) / x1) / x1));
	} else if (x1 <= 2.2e-279) {
		tmp = (x2 * -6.0) + (x2 * (x1 * (x2 * 8.0)));
	} else if (x1 <= 0.07) {
		tmp = (x1 * (-1.0 + (x1 * 9.0))) + (x2 * -6.0);
	} else {
		tmp = (x1 * x1) * ((x1 * (-3.0 + (x1 * 6.0))) + (-3.0 + (x2 * 8.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x1 <= (-2d+14)) then
        tmp = ((x1 * x1) * (x1 * x1)) * (6.0d0 - (((x2 * (-8.0d0)) / x1) / x1))
    else if (x1 <= 2.2d-279) then
        tmp = (x2 * (-6.0d0)) + (x2 * (x1 * (x2 * 8.0d0)))
    else if (x1 <= 0.07d0) then
        tmp = (x1 * ((-1.0d0) + (x1 * 9.0d0))) + (x2 * (-6.0d0))
    else
        tmp = (x1 * x1) * ((x1 * ((-3.0d0) + (x1 * 6.0d0))) + ((-3.0d0) + (x2 * 8.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= -2e+14) {
		tmp = ((x1 * x1) * (x1 * x1)) * (6.0 - (((x2 * -8.0) / x1) / x1));
	} else if (x1 <= 2.2e-279) {
		tmp = (x2 * -6.0) + (x2 * (x1 * (x2 * 8.0)));
	} else if (x1 <= 0.07) {
		tmp = (x1 * (-1.0 + (x1 * 9.0))) + (x2 * -6.0);
	} else {
		tmp = (x1 * x1) * ((x1 * (-3.0 + (x1 * 6.0))) + (-3.0 + (x2 * 8.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -2e+14:
		tmp = ((x1 * x1) * (x1 * x1)) * (6.0 - (((x2 * -8.0) / x1) / x1))
	elif x1 <= 2.2e-279:
		tmp = (x2 * -6.0) + (x2 * (x1 * (x2 * 8.0)))
	elif x1 <= 0.07:
		tmp = (x1 * (-1.0 + (x1 * 9.0))) + (x2 * -6.0)
	else:
		tmp = (x1 * x1) * ((x1 * (-3.0 + (x1 * 6.0))) + (-3.0 + (x2 * 8.0)))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -2e+14)
		tmp = Float64(Float64(Float64(x1 * x1) * Float64(x1 * x1)) * Float64(6.0 - Float64(Float64(Float64(x2 * -8.0) / x1) / x1)));
	elseif (x1 <= 2.2e-279)
		tmp = Float64(Float64(x2 * -6.0) + Float64(x2 * Float64(x1 * Float64(x2 * 8.0))));
	elseif (x1 <= 0.07)
		tmp = Float64(Float64(x1 * Float64(-1.0 + Float64(x1 * 9.0))) + Float64(x2 * -6.0));
	else
		tmp = Float64(Float64(x1 * x1) * Float64(Float64(x1 * Float64(-3.0 + Float64(x1 * 6.0))) + Float64(-3.0 + Float64(x2 * 8.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -2e+14)
		tmp = ((x1 * x1) * (x1 * x1)) * (6.0 - (((x2 * -8.0) / x1) / x1));
	elseif (x1 <= 2.2e-279)
		tmp = (x2 * -6.0) + (x2 * (x1 * (x2 * 8.0)));
	elseif (x1 <= 0.07)
		tmp = (x1 * (-1.0 + (x1 * 9.0))) + (x2 * -6.0);
	else
		tmp = (x1 * x1) * ((x1 * (-3.0 + (x1 * 6.0))) + (-3.0 + (x2 * 8.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -2e+14], N[(N[(N[(x1 * x1), $MachinePrecision] * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] * N[(6.0 - N[(N[(N[(x2 * -8.0), $MachinePrecision] / x1), $MachinePrecision] / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 2.2e-279], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x2 * N[(x1 * N[(x2 * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 0.07], N[(N[(x1 * N[(-1.0 + N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision], N[(N[(x1 * x1), $MachinePrecision] * N[(N[(x1 * N[(-3.0 + N[(x1 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-3.0 + N[(x2 * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -2e14

   1. Initial program 27.1%

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

   3. Simplified 27.1%

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

   5. Taylor expanded in x1 around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, -6\right)\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-6, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 4\right)\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \color{blue}{9}\right)\right)\right)\right)\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 27.1%

      \[\leadsto \frac{3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right)}{x1 \cdot x1 + 1} + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(x1 \cdot \left(x1 \cdot -6\right) + \frac{2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)}{x1 \cdot x1 + 1} \cdot \left(x1 \cdot \left(-6 + \left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right) \cdot \frac{2}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot 4\right)\right) + x1 \cdot \left(2 + x1 \cdot \left(x1 + \color{blue}{9}\right)\right)\right) \]

   8. Taylor expanded in x1 around -inf

      \[\leadsto \color{blue}{{x1}^{4} \cdot \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)} \]
   9. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{4}\right), \color{blue}{\left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)}\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{\left(2 \cdot 2\right)}\right), \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)\right) \]

      3. pow-sqr N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{2} \cdot {x1}^{2}\right), \left(\color{blue}{6} + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left({x1}^{2}\right), \left({x1}^{2}\right)\right), \left(\color{blue}{6} + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)\right) \]

      5. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x1 \cdot x1\right), \left({x1}^{2}\right)\right), \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left({x1}^{2}\right)\right), \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left(x1 \cdot x1\right)\right), \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)\right) \]

      9. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \left(6 + \left(\mathsf{neg}\left(\frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)\right)\right)\right) \]

      10. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \left(6 - \color{blue}{\frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}}\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \color{blue}{\left(\frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)}\right)\right) \]

      12. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \mathsf{/.f64}\left(\left(3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}\right), \color{blue}{x1}\right)\right)\right) \]

   10. Simplified 94.9%

       \[\leadsto \color{blue}{\left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right)\right) \cdot \left(6 - \frac{3 - \frac{x2 \cdot 8 + -3}{x1}}{x1}\right)} \]

   11. Taylor expanded in x2 around inf

       \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \color{blue}{\left(-8 \cdot \frac{x2}{{x1}^{2}}\right)}\right)\right) \]
   12. Step-by-step derivation

       1. associate-*r/ N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \left(\frac{-8 \cdot x2}{\color{blue}{{x1}^{2}}}\right)\right)\right) \]

       2. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \left(\frac{\left(\mathsf{neg}\left(8\right)\right) \cdot x2}{{x1}^{2}}\right)\right)\right) \]

       3. distribute-lft-neg-in N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \left(\frac{\mathsf{neg}\left(8 \cdot x2\right)}{{\color{blue}{x1}}^{2}}\right)\right)\right) \]

       4. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \left(\frac{\mathsf{neg}\left(8 \cdot x2\right)}{x1 \cdot \color{blue}{x1}}\right)\right)\right) \]

       5. associate-/r* N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \left(\frac{\frac{\mathsf{neg}\left(8 \cdot x2\right)}{x1}}{\color{blue}{x1}}\right)\right)\right) \]

       6. distribute-neg-frac N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \left(\frac{\mathsf{neg}\left(\frac{8 \cdot x2}{x1}\right)}{x1}\right)\right)\right) \]

       7. associate-*r/ N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \left(\frac{\mathsf{neg}\left(8 \cdot \frac{x2}{x1}\right)}{x1}\right)\right)\right) \]

       8. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \mathsf{/.f64}\left(\left(\mathsf{neg}\left(8 \cdot \frac{x2}{x1}\right)\right), \color{blue}{x1}\right)\right)\right) \]

       9. associate-*r/ N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \mathsf{/.f64}\left(\left(\mathsf{neg}\left(\frac{8 \cdot x2}{x1}\right)\right), x1\right)\right)\right) \]

       10. distribute-neg-frac N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \mathsf{/.f64}\left(\left(\frac{\mathsf{neg}\left(8 \cdot x2\right)}{x1}\right), x1\right)\right)\right) \]

       11. /-lowering-/.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(\mathsf{neg}\left(8 \cdot x2\right)\right), x1\right), x1\right)\right)\right) \]

       12. *-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(\mathsf{neg}\left(x2 \cdot 8\right)\right), x1\right), x1\right)\right)\right) \]

       13. distribute-rgt-neg-in N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(x2 \cdot \left(\mathsf{neg}\left(8\right)\right)\right), x1\right), x1\right)\right)\right) \]

       14. metadata-eval N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(x2 \cdot -8\right), x1\right), x1\right)\right)\right) \]

       15. *-lowering-*.f64 94.9%

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x2, -8\right), x1\right), x1\right)\right)\right) \]

   13. Simplified 94.9%

       \[\leadsto \left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right)\right) \cdot \left(6 - \color{blue}{\frac{\frac{x2 \cdot -8}{x1}}{x1}}\right) \]

   if -2e14 < x1 < 2.2e-279

   1. Initial program 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x1 around 0

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

   7. Simplified 83.4%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(x2 \cdot 2\right) \cdot \left(x2 \cdot 4 + -6\right) + \left(x1 \cdot \left(\left(\left(\left(9 + 3 \cdot \left(x2 \cdot 2\right)\right) + x2 \cdot 10\right) - \left(x2 \cdot 4 + -6\right)\right) + -6\right) + -1\right)\right)} \]

   8. Taylor expanded in x2 around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right), \color{blue}{\left(9 \cdot x1 - 1\right)}\right)\right)\right) \]
   9. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right), \left(9 \cdot x1 + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right), \left(9 \cdot x1 + -1\right)\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right), \mathsf{+.f64}\left(\left(9 \cdot x1\right), \color{blue}{-1}\right)\right)\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right), \mathsf{+.f64}\left(\left(x1 \cdot 9\right), -1\right)\right)\right)\right) \]

      5. *-lowering-*.f64 83.4%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 9\right), -1\right)\right)\right)\right) \]

   10. Simplified 83.4%

       \[\leadsto -6 \cdot x2 + x1 \cdot \left(\left(x2 \cdot 2\right) \cdot \left(x2 \cdot 4 + -6\right) + \color{blue}{\left(x1 \cdot 9 + -1\right)}\right) \]

   11. Taylor expanded in x2 around inf

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \color{blue}{\left(8 \cdot \left(x1 \cdot {x2}^{2}\right)\right)}\right) \]
   12. Step-by-step derivation

       1. unpow2 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \left(8 \cdot \left(x1 \cdot \left(x2 \cdot \color{blue}{x2}\right)\right)\right)\right) \]

       2. associate-*r* N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \left(8 \cdot \left(\left(x1 \cdot x2\right) \cdot \color{blue}{x2}\right)\right)\right) \]

       3. associate-*l* N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \left(\left(8 \cdot \left(x1 \cdot x2\right)\right) \cdot \color{blue}{x2}\right)\right) \]

       4. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \left(x2 \cdot \color{blue}{\left(8 \cdot \left(x1 \cdot x2\right)\right)}\right)\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x2, \color{blue}{\left(8 \cdot \left(x1 \cdot x2\right)\right)}\right)\right) \]

       6. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x2, \left(\left(x1 \cdot x2\right) \cdot \color{blue}{8}\right)\right)\right) \]

       7. associate-*l* N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x2, \left(x1 \cdot \color{blue}{\left(x2 \cdot 8\right)}\right)\right)\right) \]

       8. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x2, \left(x1 \cdot \left(8 \cdot \color{blue}{x2}\right)\right)\right)\right) \]

       9. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x2, \mathsf{*.f64}\left(x1, \color{blue}{\left(8 \cdot x2\right)}\right)\right)\right) \]

       10. *-commutative N/A

           \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x2, \mathsf{*.f64}\left(x1, \left(x2 \cdot \color{blue}{8}\right)\right)\right)\right) \]

       11. *-lowering-*.f64 81.4%

           \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x2, \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x2, \color{blue}{8}\right)\right)\right)\right) \]

   13. Simplified 81.4%

       \[\leadsto -6 \cdot x2 + \color{blue}{x2 \cdot \left(x1 \cdot \left(x2 \cdot 8\right)\right)} \]

   if 2.2e-279 < x1 < 0.070000000000000007

   1. Initial program 99.3%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in x1 around 0

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

   7. Simplified 95.7%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(x2 \cdot 2\right) \cdot \left(x2 \cdot 4 + -6\right) + \left(x1 \cdot \left(\left(\left(\left(9 + 3 \cdot \left(x2 \cdot 2\right)\right) + x2 \cdot 10\right) - \left(x2 \cdot 4 + -6\right)\right) + -6\right) + -1\right)\right)} \]

   8. Taylor expanded in x2 around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \color{blue}{\left(x1 \cdot \left(9 \cdot x1 - 1\right)\right)}\right) \]
   9. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \color{blue}{\left(9 \cdot x1 - 1\right)}\right)\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \left(9 \cdot x1 + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right) \]

      3. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \left(9 \cdot x1 + -1\right)\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\left(9 \cdot x1\right), \color{blue}{-1}\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\left(x1 \cdot 9\right), -1\right)\right)\right) \]

      6. *-lowering-*.f64 82.8%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 9\right), -1\right)\right)\right) \]

   10. Simplified 82.8%

       \[\leadsto -6 \cdot x2 + \color{blue}{x1 \cdot \left(x1 \cdot 9 + -1\right)} \]

   if 0.070000000000000007 < x1

   1. Initial program 50.6%

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

   3. Simplified 50.7%

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

   5. Taylor expanded in x1 around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, -6\right)\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-6, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 4\right)\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \color{blue}{9}\right)\right)\right)\right)\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 50.7%

      \[\leadsto \frac{3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right)}{x1 \cdot x1 + 1} + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(x1 \cdot \left(x1 \cdot -6\right) + \frac{2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)}{x1 \cdot x1 + 1} \cdot \left(x1 \cdot \left(-6 + \left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right) \cdot \frac{2}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot 4\right)\right) + x1 \cdot \left(2 + x1 \cdot \left(x1 + \color{blue}{9}\right)\right)\right) \]

   8. Taylor expanded in x1 around -inf

      \[\leadsto \color{blue}{{x1}^{4} \cdot \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)} \]
   9. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{4}\right), \color{blue}{\left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)}\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{\left(2 \cdot 2\right)}\right), \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)\right) \]

      3. pow-sqr N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{2} \cdot {x1}^{2}\right), \left(\color{blue}{6} + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left({x1}^{2}\right), \left({x1}^{2}\right)\right), \left(\color{blue}{6} + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)\right) \]

      5. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x1 \cdot x1\right), \left({x1}^{2}\right)\right), \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left({x1}^{2}\right)\right), \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left(x1 \cdot x1\right)\right), \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)\right) \]

      9. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \left(6 + \left(\mathsf{neg}\left(\frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)\right)\right)\right) \]

      10. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \left(6 - \color{blue}{\frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}}\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \color{blue}{\left(\frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)}\right)\right) \]

      12. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \mathsf{/.f64}\left(\left(3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}\right), \color{blue}{x1}\right)\right)\right) \]

   10. Simplified 88.0%

       \[\leadsto \color{blue}{\left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right)\right) \cdot \left(6 - \frac{3 - \frac{x2 \cdot 8 + -3}{x1}}{x1}\right)} \]

   11. Taylor expanded in x1 around 0

       \[\leadsto \color{blue}{{x1}^{2} \cdot \left(\left(8 \cdot x2 + x1 \cdot \left(6 \cdot x1 - 3\right)\right) - 3\right)} \]
   12. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\left({x1}^{2}\right), \color{blue}{\left(\left(8 \cdot x2 + x1 \cdot \left(6 \cdot x1 - 3\right)\right) - 3\right)}\right) \]

       2. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(\left(x1 \cdot x1\right), \left(\color{blue}{\left(8 \cdot x2 + x1 \cdot \left(6 \cdot x1 - 3\right)\right)} - 3\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left(\color{blue}{\left(8 \cdot x2 + x1 \cdot \left(6 \cdot x1 - 3\right)\right)} - 3\right)\right) \]

       4. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left(\left(x1 \cdot \left(6 \cdot x1 - 3\right) + 8 \cdot x2\right) - 3\right)\right) \]

       5. associate--l+ N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left(x1 \cdot \left(6 \cdot x1 - 3\right) + \color{blue}{\left(8 \cdot x2 - 3\right)}\right)\right) \]

       6. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\left(x1 \cdot \left(6 \cdot x1 - 3\right)\right), \color{blue}{\left(8 \cdot x2 - 3\right)}\right)\right) \]

       7. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \left(6 \cdot x1 - 3\right)\right), \left(\color{blue}{8 \cdot x2} - 3\right)\right)\right) \]

       8. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \left(6 \cdot x1 + \left(\mathsf{neg}\left(3\right)\right)\right)\right), \left(8 \cdot \color{blue}{x2} - 3\right)\right)\right) \]

       9. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \left(6 \cdot x1 + -3\right)\right), \left(8 \cdot x2 - 3\right)\right)\right) \]

       10. +-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \left(-3 + 6 \cdot x1\right)\right), \left(8 \cdot \color{blue}{x2} - 3\right)\right)\right) \]

       11. +-lowering-+.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-3, \left(6 \cdot x1\right)\right)\right), \left(8 \cdot \color{blue}{x2} - 3\right)\right)\right) \]

       12. *-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-3, \left(x1 \cdot 6\right)\right)\right), \left(8 \cdot x2 - 3\right)\right)\right) \]

       13. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-3, \mathsf{*.f64}\left(x1, 6\right)\right)\right), \left(8 \cdot x2 - 3\right)\right)\right) \]

       14. sub-neg N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-3, \mathsf{*.f64}\left(x1, 6\right)\right)\right), \left(8 \cdot x2 + \color{blue}{\left(\mathsf{neg}\left(3\right)\right)}\right)\right)\right) \]

       15. metadata-eval N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-3, \mathsf{*.f64}\left(x1, 6\right)\right)\right), \left(8 \cdot x2 + -3\right)\right)\right) \]

       16. +-lowering-+.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-3, \mathsf{*.f64}\left(x1, 6\right)\right)\right), \mathsf{+.f64}\left(\left(8 \cdot x2\right), \color{blue}{-3}\right)\right)\right) \]

       17. *-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-3, \mathsf{*.f64}\left(x1, 6\right)\right)\right), \mathsf{+.f64}\left(\left(x2 \cdot 8\right), -3\right)\right)\right) \]

       18. *-lowering-*.f64 88.2%

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-3, \mathsf{*.f64}\left(x1, 6\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 8\right), -3\right)\right)\right) \]

   13. Simplified 88.2%

       \[\leadsto \color{blue}{\left(x1 \cdot x1\right) \cdot \left(x1 \cdot \left(-3 + x1 \cdot 6\right) + \left(x2 \cdot 8 + -3\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -2 \cdot 10^{+14}:\\ \;\;\;\;\left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right)\right) \cdot \left(6 - \frac{\frac{x2 \cdot -8}{x1}}{x1}\right)\\ \mathbf{elif}\;x1 \leq 2.2 \cdot 10^{-279}:\\ \;\;\;\;x2 \cdot -6 + x2 \cdot \left(x1 \cdot \left(x2 \cdot 8\right)\right)\\ \mathbf{elif}\;x1 \leq 0.07:\\ \;\;\;\;x1 \cdot \left(-1 + x1 \cdot 9\right) + x2 \cdot -6\\ \mathbf{else}:\\ \;\;\;\;\left(x1 \cdot x1\right) \cdot \left(x1 \cdot \left(-3 + x1 \cdot 6\right) + \left(-3 + x2 \cdot 8\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 83.7% accurate, 4.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -3 + x2 \cdot 8\\ \mathbf{if}\;x1 \leq -2 \cdot 10^{+14}:\\ \;\;\;\;\left(x1 \cdot x1\right) \cdot \left(t\_0 + x1 \cdot \left(x1 \cdot 6\right)\right)\\ \mathbf{elif}\;x1 \leq 8 \cdot 10^{-279}:\\ \;\;\;\;x2 \cdot -6 + x2 \cdot \left(x1 \cdot \left(x2 \cdot 8\right)\right)\\ \mathbf{elif}\;x1 \leq 0.07:\\ \;\;\;\;x1 \cdot \left(-1 + x1 \cdot 9\right) + x2 \cdot -6\\ \mathbf{else}:\\ \;\;\;\;\left(x1 \cdot x1\right) \cdot \left(x1 \cdot \left(-3 + x1 \cdot 6\right) + t\_0\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ -3.0 (* x2 8.0))))
   (if (<= x1 -2e+14)
     (* (* x1 x1) (+ t_0 (* x1 (* x1 6.0))))
     (if (<= x1 8e-279)
       (+ (* x2 -6.0) (* x2 (* x1 (* x2 8.0))))
       (if (<= x1 0.07)
         (+ (* x1 (+ -1.0 (* x1 9.0))) (* x2 -6.0))
         (* (* x1 x1) (+ (* x1 (+ -3.0 (* x1 6.0))) t_0)))))))

C

double code(double x1, double x2) {
	double t_0 = -3.0 + (x2 * 8.0);
	double tmp;
	if (x1 <= -2e+14) {
		tmp = (x1 * x1) * (t_0 + (x1 * (x1 * 6.0)));
	} else if (x1 <= 8e-279) {
		tmp = (x2 * -6.0) + (x2 * (x1 * (x2 * 8.0)));
	} else if (x1 <= 0.07) {
		tmp = (x1 * (-1.0 + (x1 * 9.0))) + (x2 * -6.0);
	} else {
		tmp = (x1 * x1) * ((x1 * (-3.0 + (x1 * 6.0))) + t_0);
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (-3.0d0) + (x2 * 8.0d0)
    if (x1 <= (-2d+14)) then
        tmp = (x1 * x1) * (t_0 + (x1 * (x1 * 6.0d0)))
    else if (x1 <= 8d-279) then
        tmp = (x2 * (-6.0d0)) + (x2 * (x1 * (x2 * 8.0d0)))
    else if (x1 <= 0.07d0) then
        tmp = (x1 * ((-1.0d0) + (x1 * 9.0d0))) + (x2 * (-6.0d0))
    else
        tmp = (x1 * x1) * ((x1 * ((-3.0d0) + (x1 * 6.0d0))) + t_0)
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = -3.0 + (x2 * 8.0);
	double tmp;
	if (x1 <= -2e+14) {
		tmp = (x1 * x1) * (t_0 + (x1 * (x1 * 6.0)));
	} else if (x1 <= 8e-279) {
		tmp = (x2 * -6.0) + (x2 * (x1 * (x2 * 8.0)));
	} else if (x1 <= 0.07) {
		tmp = (x1 * (-1.0 + (x1 * 9.0))) + (x2 * -6.0);
	} else {
		tmp = (x1 * x1) * ((x1 * (-3.0 + (x1 * 6.0))) + t_0);
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = -3.0 + (x2 * 8.0)
	tmp = 0
	if x1 <= -2e+14:
		tmp = (x1 * x1) * (t_0 + (x1 * (x1 * 6.0)))
	elif x1 <= 8e-279:
		tmp = (x2 * -6.0) + (x2 * (x1 * (x2 * 8.0)))
	elif x1 <= 0.07:
		tmp = (x1 * (-1.0 + (x1 * 9.0))) + (x2 * -6.0)
	else:
		tmp = (x1 * x1) * ((x1 * (-3.0 + (x1 * 6.0))) + t_0)
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(-3.0 + Float64(x2 * 8.0))
	tmp = 0.0
	if (x1 <= -2e+14)
		tmp = Float64(Float64(x1 * x1) * Float64(t_0 + Float64(x1 * Float64(x1 * 6.0))));
	elseif (x1 <= 8e-279)
		tmp = Float64(Float64(x2 * -6.0) + Float64(x2 * Float64(x1 * Float64(x2 * 8.0))));
	elseif (x1 <= 0.07)
		tmp = Float64(Float64(x1 * Float64(-1.0 + Float64(x1 * 9.0))) + Float64(x2 * -6.0));
	else
		tmp = Float64(Float64(x1 * x1) * Float64(Float64(x1 * Float64(-3.0 + Float64(x1 * 6.0))) + t_0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = -3.0 + (x2 * 8.0);
	tmp = 0.0;
	if (x1 <= -2e+14)
		tmp = (x1 * x1) * (t_0 + (x1 * (x1 * 6.0)));
	elseif (x1 <= 8e-279)
		tmp = (x2 * -6.0) + (x2 * (x1 * (x2 * 8.0)));
	elseif (x1 <= 0.07)
		tmp = (x1 * (-1.0 + (x1 * 9.0))) + (x2 * -6.0);
	else
		tmp = (x1 * x1) * ((x1 * (-3.0 + (x1 * 6.0))) + t_0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(-3.0 + N[(x2 * 8.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -2e+14], N[(N[(x1 * x1), $MachinePrecision] * N[(t$95$0 + N[(x1 * N[(x1 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 8e-279], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x2 * N[(x1 * N[(x2 * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 0.07], N[(N[(x1 * N[(-1.0 + N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision], N[(N[(x1 * x1), $MachinePrecision] * N[(N[(x1 * N[(-3.0 + N[(x1 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -2e14

   1. Initial program 27.1%

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

   3. Simplified 27.1%

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

   5. Taylor expanded in x1 around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, -6\right)\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-6, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 4\right)\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \color{blue}{9}\right)\right)\right)\right)\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 27.1%

      \[\leadsto \frac{3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right)}{x1 \cdot x1 + 1} + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(x1 \cdot \left(x1 \cdot -6\right) + \frac{2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)}{x1 \cdot x1 + 1} \cdot \left(x1 \cdot \left(-6 + \left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right) \cdot \frac{2}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot 4\right)\right) + x1 \cdot \left(2 + x1 \cdot \left(x1 + \color{blue}{9}\right)\right)\right) \]

   8. Taylor expanded in x1 around -inf

      \[\leadsto \color{blue}{{x1}^{4} \cdot \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)} \]
   9. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{4}\right), \color{blue}{\left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)}\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{\left(2 \cdot 2\right)}\right), \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)\right) \]

      3. pow-sqr N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{2} \cdot {x1}^{2}\right), \left(\color{blue}{6} + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left({x1}^{2}\right), \left({x1}^{2}\right)\right), \left(\color{blue}{6} + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)\right) \]

      5. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x1 \cdot x1\right), \left({x1}^{2}\right)\right), \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left({x1}^{2}\right)\right), \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left(x1 \cdot x1\right)\right), \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)\right) \]

      9. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \left(6 + \left(\mathsf{neg}\left(\frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)\right)\right)\right) \]

      10. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \left(6 - \color{blue}{\frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}}\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \color{blue}{\left(\frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)}\right)\right) \]

      12. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \mathsf{/.f64}\left(\left(3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}\right), \color{blue}{x1}\right)\right)\right) \]

   10. Simplified 94.9%

       \[\leadsto \color{blue}{\left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right)\right) \cdot \left(6 - \frac{3 - \frac{x2 \cdot 8 + -3}{x1}}{x1}\right)} \]

   11. Taylor expanded in x1 around 0

       \[\leadsto \color{blue}{{x1}^{2} \cdot \left(\left(8 \cdot x2 + x1 \cdot \left(6 \cdot x1 - 3\right)\right) - 3\right)} \]
   12. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\left({x1}^{2}\right), \color{blue}{\left(\left(8 \cdot x2 + x1 \cdot \left(6 \cdot x1 - 3\right)\right) - 3\right)}\right) \]

       2. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(\left(x1 \cdot x1\right), \left(\color{blue}{\left(8 \cdot x2 + x1 \cdot \left(6 \cdot x1 - 3\right)\right)} - 3\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left(\color{blue}{\left(8 \cdot x2 + x1 \cdot \left(6 \cdot x1 - 3\right)\right)} - 3\right)\right) \]

       4. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left(\left(x1 \cdot \left(6 \cdot x1 - 3\right) + 8 \cdot x2\right) - 3\right)\right) \]

       5. associate--l+ N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left(x1 \cdot \left(6 \cdot x1 - 3\right) + \color{blue}{\left(8 \cdot x2 - 3\right)}\right)\right) \]

       6. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\left(x1 \cdot \left(6 \cdot x1 - 3\right)\right), \color{blue}{\left(8 \cdot x2 - 3\right)}\right)\right) \]

       7. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \left(6 \cdot x1 - 3\right)\right), \left(\color{blue}{8 \cdot x2} - 3\right)\right)\right) \]

       8. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \left(6 \cdot x1 + \left(\mathsf{neg}\left(3\right)\right)\right)\right), \left(8 \cdot \color{blue}{x2} - 3\right)\right)\right) \]

       9. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \left(6 \cdot x1 + -3\right)\right), \left(8 \cdot x2 - 3\right)\right)\right) \]

       10. +-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \left(-3 + 6 \cdot x1\right)\right), \left(8 \cdot \color{blue}{x2} - 3\right)\right)\right) \]

       11. +-lowering-+.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-3, \left(6 \cdot x1\right)\right)\right), \left(8 \cdot \color{blue}{x2} - 3\right)\right)\right) \]

       12. *-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-3, \left(x1 \cdot 6\right)\right)\right), \left(8 \cdot x2 - 3\right)\right)\right) \]

       13. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-3, \mathsf{*.f64}\left(x1, 6\right)\right)\right), \left(8 \cdot x2 - 3\right)\right)\right) \]

       14. sub-neg N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-3, \mathsf{*.f64}\left(x1, 6\right)\right)\right), \left(8 \cdot x2 + \color{blue}{\left(\mathsf{neg}\left(3\right)\right)}\right)\right)\right) \]

       15. metadata-eval N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-3, \mathsf{*.f64}\left(x1, 6\right)\right)\right), \left(8 \cdot x2 + -3\right)\right)\right) \]

       16. +-lowering-+.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-3, \mathsf{*.f64}\left(x1, 6\right)\right)\right), \mathsf{+.f64}\left(\left(8 \cdot x2\right), \color{blue}{-3}\right)\right)\right) \]

       17. *-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-3, \mathsf{*.f64}\left(x1, 6\right)\right)\right), \mathsf{+.f64}\left(\left(x2 \cdot 8\right), -3\right)\right)\right) \]

       18. *-lowering-*.f64 94.9%

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-3, \mathsf{*.f64}\left(x1, 6\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 8\right), -3\right)\right)\right) \]

   13. Simplified 94.9%

       \[\leadsto \color{blue}{\left(x1 \cdot x1\right) \cdot \left(x1 \cdot \left(-3 + x1 \cdot 6\right) + \left(x2 \cdot 8 + -3\right)\right)} \]

   14. Taylor expanded in x1 around inf

       \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\color{blue}{\left(6 \cdot {x1}^{2}\right)}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 8\right), -3\right)\right)\right) \]
   15. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\left({x1}^{2} \cdot 6\right), \mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(x2, 8\right)}, -3\right)\right)\right) \]

       2. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\left(\left(x1 \cdot x1\right) \cdot 6\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\color{blue}{x2}, 8\right), -3\right)\right)\right) \]

       3. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\left(x1 \cdot \left(x1 \cdot 6\right)\right), \mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(x2, 8\right)}, -3\right)\right)\right) \]

       4. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\left(x1 \cdot \left(6 \cdot x1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, \color{blue}{8}\right), -3\right)\right)\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \left(6 \cdot x1\right)\right), \mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(x2, 8\right)}, -3\right)\right)\right) \]

       6. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \left(x1 \cdot 6\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, \color{blue}{8}\right), -3\right)\right)\right) \]

       7. *-lowering-*.f64 94.9%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, 6\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, \color{blue}{8}\right), -3\right)\right)\right) \]

   16. Simplified 94.9%

       \[\leadsto \left(x1 \cdot x1\right) \cdot \left(\color{blue}{x1 \cdot \left(x1 \cdot 6\right)} + \left(x2 \cdot 8 + -3\right)\right) \]

   if -2e14 < x1 < 8.00000000000000044e-279

   1. Initial program 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x1 around 0

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

   7. Simplified 83.4%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(x2 \cdot 2\right) \cdot \left(x2 \cdot 4 + -6\right) + \left(x1 \cdot \left(\left(\left(\left(9 + 3 \cdot \left(x2 \cdot 2\right)\right) + x2 \cdot 10\right) - \left(x2 \cdot 4 + -6\right)\right) + -6\right) + -1\right)\right)} \]

   8. Taylor expanded in x2 around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right), \color{blue}{\left(9 \cdot x1 - 1\right)}\right)\right)\right) \]
   9. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right), \left(9 \cdot x1 + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right), \left(9 \cdot x1 + -1\right)\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right), \mathsf{+.f64}\left(\left(9 \cdot x1\right), \color{blue}{-1}\right)\right)\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right), \mathsf{+.f64}\left(\left(x1 \cdot 9\right), -1\right)\right)\right)\right) \]

      5. *-lowering-*.f64 83.4%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 9\right), -1\right)\right)\right)\right) \]

   10. Simplified 83.4%

       \[\leadsto -6 \cdot x2 + x1 \cdot \left(\left(x2 \cdot 2\right) \cdot \left(x2 \cdot 4 + -6\right) + \color{blue}{\left(x1 \cdot 9 + -1\right)}\right) \]

   11. Taylor expanded in x2 around inf

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \color{blue}{\left(8 \cdot \left(x1 \cdot {x2}^{2}\right)\right)}\right) \]
   12. Step-by-step derivation

       1. unpow2 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \left(8 \cdot \left(x1 \cdot \left(x2 \cdot \color{blue}{x2}\right)\right)\right)\right) \]

       2. associate-*r* N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \left(8 \cdot \left(\left(x1 \cdot x2\right) \cdot \color{blue}{x2}\right)\right)\right) \]

       3. associate-*l* N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \left(\left(8 \cdot \left(x1 \cdot x2\right)\right) \cdot \color{blue}{x2}\right)\right) \]

       4. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \left(x2 \cdot \color{blue}{\left(8 \cdot \left(x1 \cdot x2\right)\right)}\right)\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x2, \color{blue}{\left(8 \cdot \left(x1 \cdot x2\right)\right)}\right)\right) \]

       6. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x2, \left(\left(x1 \cdot x2\right) \cdot \color{blue}{8}\right)\right)\right) \]

       7. associate-*l* N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x2, \left(x1 \cdot \color{blue}{\left(x2 \cdot 8\right)}\right)\right)\right) \]

       8. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x2, \left(x1 \cdot \left(8 \cdot \color{blue}{x2}\right)\right)\right)\right) \]

       9. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x2, \mathsf{*.f64}\left(x1, \color{blue}{\left(8 \cdot x2\right)}\right)\right)\right) \]

       10. *-commutative N/A

           \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x2, \mathsf{*.f64}\left(x1, \left(x2 \cdot \color{blue}{8}\right)\right)\right)\right) \]

       11. *-lowering-*.f64 81.4%

           \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x2, \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x2, \color{blue}{8}\right)\right)\right)\right) \]

   13. Simplified 81.4%

       \[\leadsto -6 \cdot x2 + \color{blue}{x2 \cdot \left(x1 \cdot \left(x2 \cdot 8\right)\right)} \]

   if 8.00000000000000044e-279 < x1 < 0.070000000000000007

   1. Initial program 99.3%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in x1 around 0

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

   7. Simplified 95.7%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(x2 \cdot 2\right) \cdot \left(x2 \cdot 4 + -6\right) + \left(x1 \cdot \left(\left(\left(\left(9 + 3 \cdot \left(x2 \cdot 2\right)\right) + x2 \cdot 10\right) - \left(x2 \cdot 4 + -6\right)\right) + -6\right) + -1\right)\right)} \]

   8. Taylor expanded in x2 around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \color{blue}{\left(x1 \cdot \left(9 \cdot x1 - 1\right)\right)}\right) \]
   9. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \color{blue}{\left(9 \cdot x1 - 1\right)}\right)\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \left(9 \cdot x1 + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right) \]

      3. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \left(9 \cdot x1 + -1\right)\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\left(9 \cdot x1\right), \color{blue}{-1}\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\left(x1 \cdot 9\right), -1\right)\right)\right) \]

      6. *-lowering-*.f64 82.8%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 9\right), -1\right)\right)\right) \]

   10. Simplified 82.8%

       \[\leadsto -6 \cdot x2 + \color{blue}{x1 \cdot \left(x1 \cdot 9 + -1\right)} \]

   if 0.070000000000000007 < x1

   1. Initial program 50.6%

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

   3. Simplified 50.7%

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

   5. Taylor expanded in x1 around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, -6\right)\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-6, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 4\right)\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \color{blue}{9}\right)\right)\right)\right)\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 50.7%

      \[\leadsto \frac{3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right)}{x1 \cdot x1 + 1} + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(x1 \cdot \left(x1 \cdot -6\right) + \frac{2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)}{x1 \cdot x1 + 1} \cdot \left(x1 \cdot \left(-6 + \left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right) \cdot \frac{2}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot 4\right)\right) + x1 \cdot \left(2 + x1 \cdot \left(x1 + \color{blue}{9}\right)\right)\right) \]

   8. Taylor expanded in x1 around -inf

      \[\leadsto \color{blue}{{x1}^{4} \cdot \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)} \]
   9. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{4}\right), \color{blue}{\left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)}\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{\left(2 \cdot 2\right)}\right), \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)\right) \]

      3. pow-sqr N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{2} \cdot {x1}^{2}\right), \left(\color{blue}{6} + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left({x1}^{2}\right), \left({x1}^{2}\right)\right), \left(\color{blue}{6} + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)\right) \]

      5. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x1 \cdot x1\right), \left({x1}^{2}\right)\right), \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left({x1}^{2}\right)\right), \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left(x1 \cdot x1\right)\right), \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)\right) \]

      9. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \left(6 + \left(\mathsf{neg}\left(\frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)\right)\right)\right) \]

      10. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \left(6 - \color{blue}{\frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}}\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \color{blue}{\left(\frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)}\right)\right) \]

      12. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \mathsf{/.f64}\left(\left(3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}\right), \color{blue}{x1}\right)\right)\right) \]

   10. Simplified 88.0%

       \[\leadsto \color{blue}{\left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right)\right) \cdot \left(6 - \frac{3 - \frac{x2 \cdot 8 + -3}{x1}}{x1}\right)} \]

   11. Taylor expanded in x1 around 0

       \[\leadsto \color{blue}{{x1}^{2} \cdot \left(\left(8 \cdot x2 + x1 \cdot \left(6 \cdot x1 - 3\right)\right) - 3\right)} \]
   12. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\left({x1}^{2}\right), \color{blue}{\left(\left(8 \cdot x2 + x1 \cdot \left(6 \cdot x1 - 3\right)\right) - 3\right)}\right) \]

       2. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(\left(x1 \cdot x1\right), \left(\color{blue}{\left(8 \cdot x2 + x1 \cdot \left(6 \cdot x1 - 3\right)\right)} - 3\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left(\color{blue}{\left(8 \cdot x2 + x1 \cdot \left(6 \cdot x1 - 3\right)\right)} - 3\right)\right) \]

       4. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left(\left(x1 \cdot \left(6 \cdot x1 - 3\right) + 8 \cdot x2\right) - 3\right)\right) \]

       5. associate--l+ N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left(x1 \cdot \left(6 \cdot x1 - 3\right) + \color{blue}{\left(8 \cdot x2 - 3\right)}\right)\right) \]

       6. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\left(x1 \cdot \left(6 \cdot x1 - 3\right)\right), \color{blue}{\left(8 \cdot x2 - 3\right)}\right)\right) \]

       7. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \left(6 \cdot x1 - 3\right)\right), \left(\color{blue}{8 \cdot x2} - 3\right)\right)\right) \]

       8. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \left(6 \cdot x1 + \left(\mathsf{neg}\left(3\right)\right)\right)\right), \left(8 \cdot \color{blue}{x2} - 3\right)\right)\right) \]

       9. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \left(6 \cdot x1 + -3\right)\right), \left(8 \cdot x2 - 3\right)\right)\right) \]

       10. +-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \left(-3 + 6 \cdot x1\right)\right), \left(8 \cdot \color{blue}{x2} - 3\right)\right)\right) \]

       11. +-lowering-+.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-3, \left(6 \cdot x1\right)\right)\right), \left(8 \cdot \color{blue}{x2} - 3\right)\right)\right) \]

       12. *-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-3, \left(x1 \cdot 6\right)\right)\right), \left(8 \cdot x2 - 3\right)\right)\right) \]

       13. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-3, \mathsf{*.f64}\left(x1, 6\right)\right)\right), \left(8 \cdot x2 - 3\right)\right)\right) \]

       14. sub-neg N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-3, \mathsf{*.f64}\left(x1, 6\right)\right)\right), \left(8 \cdot x2 + \color{blue}{\left(\mathsf{neg}\left(3\right)\right)}\right)\right)\right) \]

       15. metadata-eval N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-3, \mathsf{*.f64}\left(x1, 6\right)\right)\right), \left(8 \cdot x2 + -3\right)\right)\right) \]

       16. +-lowering-+.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-3, \mathsf{*.f64}\left(x1, 6\right)\right)\right), \mathsf{+.f64}\left(\left(8 \cdot x2\right), \color{blue}{-3}\right)\right)\right) \]

       17. *-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-3, \mathsf{*.f64}\left(x1, 6\right)\right)\right), \mathsf{+.f64}\left(\left(x2 \cdot 8\right), -3\right)\right)\right) \]

       18. *-lowering-*.f64 88.2%

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-3, \mathsf{*.f64}\left(x1, 6\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 8\right), -3\right)\right)\right) \]

   13. Simplified 88.2%

       \[\leadsto \color{blue}{\left(x1 \cdot x1\right) \cdot \left(x1 \cdot \left(-3 + x1 \cdot 6\right) + \left(x2 \cdot 8 + -3\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -2 \cdot 10^{+14}:\\ \;\;\;\;\left(x1 \cdot x1\right) \cdot \left(\left(-3 + x2 \cdot 8\right) + x1 \cdot \left(x1 \cdot 6\right)\right)\\ \mathbf{elif}\;x1 \leq 8 \cdot 10^{-279}:\\ \;\;\;\;x2 \cdot -6 + x2 \cdot \left(x1 \cdot \left(x2 \cdot 8\right)\right)\\ \mathbf{elif}\;x1 \leq 0.07:\\ \;\;\;\;x1 \cdot \left(-1 + x1 \cdot 9\right) + x2 \cdot -6\\ \mathbf{else}:\\ \;\;\;\;\left(x1 \cdot x1\right) \cdot \left(x1 \cdot \left(-3 + x1 \cdot 6\right) + \left(-3 + x2 \cdot 8\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 83.5% accurate, 4.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(x1 \cdot x1\right) \cdot \left(\left(-3 + x2 \cdot 8\right) + x1 \cdot \left(x1 \cdot 6\right)\right)\\ \mathbf{if}\;x1 \leq -2 \cdot 10^{+14}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x1 \leq 4.2 \cdot 10^{-279}:\\ \;\;\;\;x2 \cdot -6 + x2 \cdot \left(x1 \cdot \left(x2 \cdot 8\right)\right)\\ \mathbf{elif}\;x1 \leq 0.044:\\ \;\;\;\;x1 \cdot \left(-1 + x1 \cdot 9\right) + x2 \cdot -6\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* (* x1 x1) (+ (+ -3.0 (* x2 8.0)) (* x1 (* x1 6.0))))))
   (if (<= x1 -2e+14)
     t_0
     (if (<= x1 4.2e-279)
       (+ (* x2 -6.0) (* x2 (* x1 (* x2 8.0))))
       (if (<= x1 0.044) (+ (* x1 (+ -1.0 (* x1 9.0))) (* x2 -6.0)) t_0)))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * x1) * ((-3.0 + (x2 * 8.0)) + (x1 * (x1 * 6.0)));
	double tmp;
	if (x1 <= -2e+14) {
		tmp = t_0;
	} else if (x1 <= 4.2e-279) {
		tmp = (x2 * -6.0) + (x2 * (x1 * (x2 * 8.0)));
	} else if (x1 <= 0.044) {
		tmp = (x1 * (-1.0 + (x1 * 9.0))) + (x2 * -6.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (x1 * x1) * (((-3.0d0) + (x2 * 8.0d0)) + (x1 * (x1 * 6.0d0)))
    if (x1 <= (-2d+14)) then
        tmp = t_0
    else if (x1 <= 4.2d-279) then
        tmp = (x2 * (-6.0d0)) + (x2 * (x1 * (x2 * 8.0d0)))
    else if (x1 <= 0.044d0) then
        tmp = (x1 * ((-1.0d0) + (x1 * 9.0d0))) + (x2 * (-6.0d0))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (x1 * x1) * ((-3.0 + (x2 * 8.0)) + (x1 * (x1 * 6.0)));
	double tmp;
	if (x1 <= -2e+14) {
		tmp = t_0;
	} else if (x1 <= 4.2e-279) {
		tmp = (x2 * -6.0) + (x2 * (x1 * (x2 * 8.0)));
	} else if (x1 <= 0.044) {
		tmp = (x1 * (-1.0 + (x1 * 9.0))) + (x2 * -6.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x1 * x1) * ((-3.0 + (x2 * 8.0)) + (x1 * (x1 * 6.0)))
	tmp = 0
	if x1 <= -2e+14:
		tmp = t_0
	elif x1 <= 4.2e-279:
		tmp = (x2 * -6.0) + (x2 * (x1 * (x2 * 8.0)))
	elif x1 <= 0.044:
		tmp = (x1 * (-1.0 + (x1 * 9.0))) + (x2 * -6.0)
	else:
		tmp = t_0
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * x1) * Float64(Float64(-3.0 + Float64(x2 * 8.0)) + Float64(x1 * Float64(x1 * 6.0))))
	tmp = 0.0
	if (x1 <= -2e+14)
		tmp = t_0;
	elseif (x1 <= 4.2e-279)
		tmp = Float64(Float64(x2 * -6.0) + Float64(x2 * Float64(x1 * Float64(x2 * 8.0))));
	elseif (x1 <= 0.044)
		tmp = Float64(Float64(x1 * Float64(-1.0 + Float64(x1 * 9.0))) + Float64(x2 * -6.0));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x1 * x1) * ((-3.0 + (x2 * 8.0)) + (x1 * (x1 * 6.0)));
	tmp = 0.0;
	if (x1 <= -2e+14)
		tmp = t_0;
	elseif (x1 <= 4.2e-279)
		tmp = (x2 * -6.0) + (x2 * (x1 * (x2 * 8.0)));
	elseif (x1 <= 0.044)
		tmp = (x1 * (-1.0 + (x1 * 9.0))) + (x2 * -6.0);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x1 * x1), $MachinePrecision] * N[(N[(-3.0 + N[(x2 * 8.0), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(x1 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -2e+14], t$95$0, If[LessEqual[x1, 4.2e-279], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x2 * N[(x1 * N[(x2 * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 0.044], N[(N[(x1 * N[(-1.0 + N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -2e14 or 0.043999999999999997 < x1

   1. Initial program 37.3%

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

   3. Simplified 37.4%

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

   5. Taylor expanded in x1 around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, -6\right)\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-6, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 4\right)\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \color{blue}{9}\right)\right)\right)\right)\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 37.4%

      \[\leadsto \frac{3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right)}{x1 \cdot x1 + 1} + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(x1 \cdot \left(x1 \cdot -6\right) + \frac{2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)}{x1 \cdot x1 + 1} \cdot \left(x1 \cdot \left(-6 + \left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right) \cdot \frac{2}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot 4\right)\right) + x1 \cdot \left(2 + x1 \cdot \left(x1 + \color{blue}{9}\right)\right)\right) \]

   8. Taylor expanded in x1 around -inf

      \[\leadsto \color{blue}{{x1}^{4} \cdot \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)} \]
   9. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{4}\right), \color{blue}{\left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)}\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{\left(2 \cdot 2\right)}\right), \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)\right) \]

      3. pow-sqr N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{2} \cdot {x1}^{2}\right), \left(\color{blue}{6} + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left({x1}^{2}\right), \left({x1}^{2}\right)\right), \left(\color{blue}{6} + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)\right) \]

      5. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x1 \cdot x1\right), \left({x1}^{2}\right)\right), \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left({x1}^{2}\right)\right), \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left(x1 \cdot x1\right)\right), \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)\right) \]

      9. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \left(6 + \left(\mathsf{neg}\left(\frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)\right)\right)\right) \]

      10. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \left(6 - \color{blue}{\frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}}\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \color{blue}{\left(\frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)}\right)\right) \]

      12. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \mathsf{/.f64}\left(\left(3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}\right), \color{blue}{x1}\right)\right)\right) \]

   10. Simplified 91.9%

       \[\leadsto \color{blue}{\left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right)\right) \cdot \left(6 - \frac{3 - \frac{x2 \cdot 8 + -3}{x1}}{x1}\right)} \]

   11. Taylor expanded in x1 around 0

       \[\leadsto \color{blue}{{x1}^{2} \cdot \left(\left(8 \cdot x2 + x1 \cdot \left(6 \cdot x1 - 3\right)\right) - 3\right)} \]
   12. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\left({x1}^{2}\right), \color{blue}{\left(\left(8 \cdot x2 + x1 \cdot \left(6 \cdot x1 - 3\right)\right) - 3\right)}\right) \]

       2. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(\left(x1 \cdot x1\right), \left(\color{blue}{\left(8 \cdot x2 + x1 \cdot \left(6 \cdot x1 - 3\right)\right)} - 3\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left(\color{blue}{\left(8 \cdot x2 + x1 \cdot \left(6 \cdot x1 - 3\right)\right)} - 3\right)\right) \]

       4. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left(\left(x1 \cdot \left(6 \cdot x1 - 3\right) + 8 \cdot x2\right) - 3\right)\right) \]

       5. associate--l+ N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left(x1 \cdot \left(6 \cdot x1 - 3\right) + \color{blue}{\left(8 \cdot x2 - 3\right)}\right)\right) \]

       6. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\left(x1 \cdot \left(6 \cdot x1 - 3\right)\right), \color{blue}{\left(8 \cdot x2 - 3\right)}\right)\right) \]

       7. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \left(6 \cdot x1 - 3\right)\right), \left(\color{blue}{8 \cdot x2} - 3\right)\right)\right) \]

       8. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \left(6 \cdot x1 + \left(\mathsf{neg}\left(3\right)\right)\right)\right), \left(8 \cdot \color{blue}{x2} - 3\right)\right)\right) \]

       9. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \left(6 \cdot x1 + -3\right)\right), \left(8 \cdot x2 - 3\right)\right)\right) \]

       10. +-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \left(-3 + 6 \cdot x1\right)\right), \left(8 \cdot \color{blue}{x2} - 3\right)\right)\right) \]

       11. +-lowering-+.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-3, \left(6 \cdot x1\right)\right)\right), \left(8 \cdot \color{blue}{x2} - 3\right)\right)\right) \]

       12. *-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-3, \left(x1 \cdot 6\right)\right)\right), \left(8 \cdot x2 - 3\right)\right)\right) \]

       13. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-3, \mathsf{*.f64}\left(x1, 6\right)\right)\right), \left(8 \cdot x2 - 3\right)\right)\right) \]

       14. sub-neg N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-3, \mathsf{*.f64}\left(x1, 6\right)\right)\right), \left(8 \cdot x2 + \color{blue}{\left(\mathsf{neg}\left(3\right)\right)}\right)\right)\right) \]

       15. metadata-eval N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-3, \mathsf{*.f64}\left(x1, 6\right)\right)\right), \left(8 \cdot x2 + -3\right)\right)\right) \]

       16. +-lowering-+.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-3, \mathsf{*.f64}\left(x1, 6\right)\right)\right), \mathsf{+.f64}\left(\left(8 \cdot x2\right), \color{blue}{-3}\right)\right)\right) \]

       17. *-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-3, \mathsf{*.f64}\left(x1, 6\right)\right)\right), \mathsf{+.f64}\left(\left(x2 \cdot 8\right), -3\right)\right)\right) \]

       18. *-lowering-*.f64 92.0%

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-3, \mathsf{*.f64}\left(x1, 6\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 8\right), -3\right)\right)\right) \]

   13. Simplified 92.0%

       \[\leadsto \color{blue}{\left(x1 \cdot x1\right) \cdot \left(x1 \cdot \left(-3 + x1 \cdot 6\right) + \left(x2 \cdot 8 + -3\right)\right)} \]

   14. Taylor expanded in x1 around inf

       \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\color{blue}{\left(6 \cdot {x1}^{2}\right)}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 8\right), -3\right)\right)\right) \]
   15. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\left({x1}^{2} \cdot 6\right), \mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(x2, 8\right)}, -3\right)\right)\right) \]

       2. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\left(\left(x1 \cdot x1\right) \cdot 6\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\color{blue}{x2}, 8\right), -3\right)\right)\right) \]

       3. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\left(x1 \cdot \left(x1 \cdot 6\right)\right), \mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(x2, 8\right)}, -3\right)\right)\right) \]

       4. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\left(x1 \cdot \left(6 \cdot x1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, \color{blue}{8}\right), -3\right)\right)\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \left(6 \cdot x1\right)\right), \mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(x2, 8\right)}, -3\right)\right)\right) \]

       6. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \left(x1 \cdot 6\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, \color{blue}{8}\right), -3\right)\right)\right) \]

       7. *-lowering-*.f64 91.9%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, 6\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, \color{blue}{8}\right), -3\right)\right)\right) \]

   16. Simplified 91.9%

       \[\leadsto \left(x1 \cdot x1\right) \cdot \left(\color{blue}{x1 \cdot \left(x1 \cdot 6\right)} + \left(x2 \cdot 8 + -3\right)\right) \]

   if -2e14 < x1 < 4.20000000000000011e-279

   1. Initial program 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x1 around 0

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

   7. Simplified 83.4%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(x2 \cdot 2\right) \cdot \left(x2 \cdot 4 + -6\right) + \left(x1 \cdot \left(\left(\left(\left(9 + 3 \cdot \left(x2 \cdot 2\right)\right) + x2 \cdot 10\right) - \left(x2 \cdot 4 + -6\right)\right) + -6\right) + -1\right)\right)} \]

   8. Taylor expanded in x2 around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right), \color{blue}{\left(9 \cdot x1 - 1\right)}\right)\right)\right) \]
   9. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right), \left(9 \cdot x1 + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right), \left(9 \cdot x1 + -1\right)\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right), \mathsf{+.f64}\left(\left(9 \cdot x1\right), \color{blue}{-1}\right)\right)\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right), \mathsf{+.f64}\left(\left(x1 \cdot 9\right), -1\right)\right)\right)\right) \]

      5. *-lowering-*.f64 83.4%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 9\right), -1\right)\right)\right)\right) \]

   10. Simplified 83.4%

       \[\leadsto -6 \cdot x2 + x1 \cdot \left(\left(x2 \cdot 2\right) \cdot \left(x2 \cdot 4 + -6\right) + \color{blue}{\left(x1 \cdot 9 + -1\right)}\right) \]

   11. Taylor expanded in x2 around inf

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \color{blue}{\left(8 \cdot \left(x1 \cdot {x2}^{2}\right)\right)}\right) \]
   12. Step-by-step derivation

       1. unpow2 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \left(8 \cdot \left(x1 \cdot \left(x2 \cdot \color{blue}{x2}\right)\right)\right)\right) \]

       2. associate-*r* N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \left(8 \cdot \left(\left(x1 \cdot x2\right) \cdot \color{blue}{x2}\right)\right)\right) \]

       3. associate-*l* N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \left(\left(8 \cdot \left(x1 \cdot x2\right)\right) \cdot \color{blue}{x2}\right)\right) \]

       4. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \left(x2 \cdot \color{blue}{\left(8 \cdot \left(x1 \cdot x2\right)\right)}\right)\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x2, \color{blue}{\left(8 \cdot \left(x1 \cdot x2\right)\right)}\right)\right) \]

       6. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x2, \left(\left(x1 \cdot x2\right) \cdot \color{blue}{8}\right)\right)\right) \]

       7. associate-*l* N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x2, \left(x1 \cdot \color{blue}{\left(x2 \cdot 8\right)}\right)\right)\right) \]

       8. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x2, \left(x1 \cdot \left(8 \cdot \color{blue}{x2}\right)\right)\right)\right) \]

       9. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x2, \mathsf{*.f64}\left(x1, \color{blue}{\left(8 \cdot x2\right)}\right)\right)\right) \]

       10. *-commutative N/A

           \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x2, \mathsf{*.f64}\left(x1, \left(x2 \cdot \color{blue}{8}\right)\right)\right)\right) \]

       11. *-lowering-*.f64 81.4%

           \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x2, \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x2, \color{blue}{8}\right)\right)\right)\right) \]

   13. Simplified 81.4%

       \[\leadsto -6 \cdot x2 + \color{blue}{x2 \cdot \left(x1 \cdot \left(x2 \cdot 8\right)\right)} \]

   if 4.20000000000000011e-279 < x1 < 0.043999999999999997

   1. Initial program 99.3%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in x1 around 0

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

   7. Simplified 95.7%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(x2 \cdot 2\right) \cdot \left(x2 \cdot 4 + -6\right) + \left(x1 \cdot \left(\left(\left(\left(9 + 3 \cdot \left(x2 \cdot 2\right)\right) + x2 \cdot 10\right) - \left(x2 \cdot 4 + -6\right)\right) + -6\right) + -1\right)\right)} \]

   8. Taylor expanded in x2 around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \color{blue}{\left(x1 \cdot \left(9 \cdot x1 - 1\right)\right)}\right) \]
   9. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \color{blue}{\left(9 \cdot x1 - 1\right)}\right)\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \left(9 \cdot x1 + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right) \]

      3. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \left(9 \cdot x1 + -1\right)\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\left(9 \cdot x1\right), \color{blue}{-1}\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\left(x1 \cdot 9\right), -1\right)\right)\right) \]

      6. *-lowering-*.f64 82.8%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 9\right), -1\right)\right)\right) \]

   10. Simplified 82.8%

       \[\leadsto -6 \cdot x2 + \color{blue}{x1 \cdot \left(x1 \cdot 9 + -1\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 87.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -2 \cdot 10^{+14}:\\ \;\;\;\;\left(x1 \cdot x1\right) \cdot \left(\left(-3 + x2 \cdot 8\right) + x1 \cdot \left(x1 \cdot 6\right)\right)\\ \mathbf{elif}\;x1 \leq 4.2 \cdot 10^{-279}:\\ \;\;\;\;x2 \cdot -6 + x2 \cdot \left(x1 \cdot \left(x2 \cdot 8\right)\right)\\ \mathbf{elif}\;x1 \leq 0.044:\\ \;\;\;\;x1 \cdot \left(-1 + x1 \cdot 9\right) + x2 \cdot -6\\ \mathbf{else}:\\ \;\;\;\;\left(x1 \cdot x1\right) \cdot \left(\left(-3 + x2 \cdot 8\right) + x1 \cdot \left(x1 \cdot 6\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 96.0% accurate, 4.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -2 \cdot 10^{+14}:\\ \;\;\;\;\left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right)\right) \cdot \left(6 - \frac{\frac{x2 \cdot -8}{x1}}{x1}\right)\\ \mathbf{elif}\;x1 \leq 15000:\\ \;\;\;\;x1 \cdot \left(-1 + x1 \cdot 9\right) + x2 \cdot \left(-6 + x1 \cdot \left(-12 + x2 \cdot 8\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x1 \cdot x1\right) \cdot \left(x1 \cdot \left(-3 + x1 \cdot 6\right) + \left(-3 + x2 \cdot 8\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -2e+14)
   (* (* (* x1 x1) (* x1 x1)) (- 6.0 (/ (/ (* x2 -8.0) x1) x1)))
   (if (<= x1 15000.0)
     (+ (* x1 (+ -1.0 (* x1 9.0))) (* x2 (+ -6.0 (* x1 (+ -12.0 (* x2 8.0))))))
     (* (* x1 x1) (+ (* x1 (+ -3.0 (* x1 6.0))) (+ -3.0 (* x2 8.0)))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -2e+14) {
		tmp = ((x1 * x1) * (x1 * x1)) * (6.0 - (((x2 * -8.0) / x1) / x1));
	} else if (x1 <= 15000.0) {
		tmp = (x1 * (-1.0 + (x1 * 9.0))) + (x2 * (-6.0 + (x1 * (-12.0 + (x2 * 8.0)))));
	} else {
		tmp = (x1 * x1) * ((x1 * (-3.0 + (x1 * 6.0))) + (-3.0 + (x2 * 8.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x1 <= (-2d+14)) then
        tmp = ((x1 * x1) * (x1 * x1)) * (6.0d0 - (((x2 * (-8.0d0)) / x1) / x1))
    else if (x1 <= 15000.0d0) then
        tmp = (x1 * ((-1.0d0) + (x1 * 9.0d0))) + (x2 * ((-6.0d0) + (x1 * ((-12.0d0) + (x2 * 8.0d0)))))
    else
        tmp = (x1 * x1) * ((x1 * ((-3.0d0) + (x1 * 6.0d0))) + ((-3.0d0) + (x2 * 8.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= -2e+14) {
		tmp = ((x1 * x1) * (x1 * x1)) * (6.0 - (((x2 * -8.0) / x1) / x1));
	} else if (x1 <= 15000.0) {
		tmp = (x1 * (-1.0 + (x1 * 9.0))) + (x2 * (-6.0 + (x1 * (-12.0 + (x2 * 8.0)))));
	} else {
		tmp = (x1 * x1) * ((x1 * (-3.0 + (x1 * 6.0))) + (-3.0 + (x2 * 8.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -2e+14:
		tmp = ((x1 * x1) * (x1 * x1)) * (6.0 - (((x2 * -8.0) / x1) / x1))
	elif x1 <= 15000.0:
		tmp = (x1 * (-1.0 + (x1 * 9.0))) + (x2 * (-6.0 + (x1 * (-12.0 + (x2 * 8.0)))))
	else:
		tmp = (x1 * x1) * ((x1 * (-3.0 + (x1 * 6.0))) + (-3.0 + (x2 * 8.0)))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -2e+14)
		tmp = Float64(Float64(Float64(x1 * x1) * Float64(x1 * x1)) * Float64(6.0 - Float64(Float64(Float64(x2 * -8.0) / x1) / x1)));
	elseif (x1 <= 15000.0)
		tmp = Float64(Float64(x1 * Float64(-1.0 + Float64(x1 * 9.0))) + Float64(x2 * Float64(-6.0 + Float64(x1 * Float64(-12.0 + Float64(x2 * 8.0))))));
	else
		tmp = Float64(Float64(x1 * x1) * Float64(Float64(x1 * Float64(-3.0 + Float64(x1 * 6.0))) + Float64(-3.0 + Float64(x2 * 8.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -2e+14)
		tmp = ((x1 * x1) * (x1 * x1)) * (6.0 - (((x2 * -8.0) / x1) / x1));
	elseif (x1 <= 15000.0)
		tmp = (x1 * (-1.0 + (x1 * 9.0))) + (x2 * (-6.0 + (x1 * (-12.0 + (x2 * 8.0)))));
	else
		tmp = (x1 * x1) * ((x1 * (-3.0 + (x1 * 6.0))) + (-3.0 + (x2 * 8.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -2e+14], N[(N[(N[(x1 * x1), $MachinePrecision] * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] * N[(6.0 - N[(N[(N[(x2 * -8.0), $MachinePrecision] / x1), $MachinePrecision] / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 15000.0], N[(N[(x1 * N[(-1.0 + N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x2 * N[(-6.0 + N[(x1 * N[(-12.0 + N[(x2 * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x1 * x1), $MachinePrecision] * N[(N[(x1 * N[(-3.0 + N[(x1 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-3.0 + N[(x2 * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -2e14

   1. Initial program 27.1%

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

   3. Simplified 27.1%

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

   5. Taylor expanded in x1 around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, -6\right)\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-6, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 4\right)\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \color{blue}{9}\right)\right)\right)\right)\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 27.1%

      \[\leadsto \frac{3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right)}{x1 \cdot x1 + 1} + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(x1 \cdot \left(x1 \cdot -6\right) + \frac{2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)}{x1 \cdot x1 + 1} \cdot \left(x1 \cdot \left(-6 + \left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right) \cdot \frac{2}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot 4\right)\right) + x1 \cdot \left(2 + x1 \cdot \left(x1 + \color{blue}{9}\right)\right)\right) \]

   8. Taylor expanded in x1 around -inf

      \[\leadsto \color{blue}{{x1}^{4} \cdot \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)} \]
   9. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{4}\right), \color{blue}{\left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)}\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{\left(2 \cdot 2\right)}\right), \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)\right) \]

      3. pow-sqr N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{2} \cdot {x1}^{2}\right), \left(\color{blue}{6} + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left({x1}^{2}\right), \left({x1}^{2}\right)\right), \left(\color{blue}{6} + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)\right) \]

      5. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x1 \cdot x1\right), \left({x1}^{2}\right)\right), \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left({x1}^{2}\right)\right), \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left(x1 \cdot x1\right)\right), \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)\right) \]

      9. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \left(6 + \left(\mathsf{neg}\left(\frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)\right)\right)\right) \]

      10. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \left(6 - \color{blue}{\frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}}\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \color{blue}{\left(\frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)}\right)\right) \]

      12. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \mathsf{/.f64}\left(\left(3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}\right), \color{blue}{x1}\right)\right)\right) \]

   10. Simplified 94.9%

       \[\leadsto \color{blue}{\left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right)\right) \cdot \left(6 - \frac{3 - \frac{x2 \cdot 8 + -3}{x1}}{x1}\right)} \]

   11. Taylor expanded in x2 around inf

       \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \color{blue}{\left(-8 \cdot \frac{x2}{{x1}^{2}}\right)}\right)\right) \]
   12. Step-by-step derivation

       1. associate-*r/ N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \left(\frac{-8 \cdot x2}{\color{blue}{{x1}^{2}}}\right)\right)\right) \]

       2. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \left(\frac{\left(\mathsf{neg}\left(8\right)\right) \cdot x2}{{x1}^{2}}\right)\right)\right) \]

       3. distribute-lft-neg-in N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \left(\frac{\mathsf{neg}\left(8 \cdot x2\right)}{{\color{blue}{x1}}^{2}}\right)\right)\right) \]

       4. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \left(\frac{\mathsf{neg}\left(8 \cdot x2\right)}{x1 \cdot \color{blue}{x1}}\right)\right)\right) \]

       5. associate-/r* N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \left(\frac{\frac{\mathsf{neg}\left(8 \cdot x2\right)}{x1}}{\color{blue}{x1}}\right)\right)\right) \]

       6. distribute-neg-frac N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \left(\frac{\mathsf{neg}\left(\frac{8 \cdot x2}{x1}\right)}{x1}\right)\right)\right) \]

       7. associate-*r/ N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \left(\frac{\mathsf{neg}\left(8 \cdot \frac{x2}{x1}\right)}{x1}\right)\right)\right) \]

       8. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \mathsf{/.f64}\left(\left(\mathsf{neg}\left(8 \cdot \frac{x2}{x1}\right)\right), \color{blue}{x1}\right)\right)\right) \]

       9. associate-*r/ N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \mathsf{/.f64}\left(\left(\mathsf{neg}\left(\frac{8 \cdot x2}{x1}\right)\right), x1\right)\right)\right) \]

       10. distribute-neg-frac N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \mathsf{/.f64}\left(\left(\frac{\mathsf{neg}\left(8 \cdot x2\right)}{x1}\right), x1\right)\right)\right) \]

       11. /-lowering-/.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(\mathsf{neg}\left(8 \cdot x2\right)\right), x1\right), x1\right)\right)\right) \]

       12. *-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(\mathsf{neg}\left(x2 \cdot 8\right)\right), x1\right), x1\right)\right)\right) \]

       13. distribute-rgt-neg-in N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(x2 \cdot \left(\mathsf{neg}\left(8\right)\right)\right), x1\right), x1\right)\right)\right) \]

       14. metadata-eval N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(x2 \cdot -8\right), x1\right), x1\right)\right)\right) \]

       15. *-lowering-*.f64 94.9%

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x2, -8\right), x1\right), x1\right)\right)\right) \]

   13. Simplified 94.9%

       \[\leadsto \left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right)\right) \cdot \left(6 - \color{blue}{\frac{\frac{x2 \cdot -8}{x1}}{x1}}\right) \]

   if -2e14 < x1 < 15000

   1. Initial program 99.4%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x1 around 0

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

   7. Simplified 87.5%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(x2 \cdot 2\right) \cdot \left(x2 \cdot 4 + -6\right) + \left(x1 \cdot \left(\left(\left(\left(9 + 3 \cdot \left(x2 \cdot 2\right)\right) + x2 \cdot 10\right) - \left(x2 \cdot 4 + -6\right)\right) + -6\right) + -1\right)\right)} \]

   8. Taylor expanded in x2 around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right), \color{blue}{\left(9 \cdot x1 - 1\right)}\right)\right)\right) \]
   9. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right), \left(9 \cdot x1 + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right), \left(9 \cdot x1 + -1\right)\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right), \mathsf{+.f64}\left(\left(9 \cdot x1\right), \color{blue}{-1}\right)\right)\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right), \mathsf{+.f64}\left(\left(x1 \cdot 9\right), -1\right)\right)\right)\right) \]

      5. *-lowering-*.f64 87.5%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 9\right), -1\right)\right)\right)\right) \]

   10. Simplified 87.5%

       \[\leadsto -6 \cdot x2 + x1 \cdot \left(\left(x2 \cdot 2\right) \cdot \left(x2 \cdot 4 + -6\right) + \color{blue}{\left(x1 \cdot 9 + -1\right)}\right) \]

   11. Taylor expanded in x2 around 0

       \[\leadsto \color{blue}{x1 \cdot \left(9 \cdot x1 - 1\right) + x2 \cdot \left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right)} \]
   12. Step-by-step derivation

       1. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\left(x1 \cdot \left(9 \cdot x1 - 1\right)\right), \color{blue}{\left(x2 \cdot \left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right)\right)}\right) \]

       2. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \left(9 \cdot x1 - 1\right)\right), \left(\color{blue}{x2} \cdot \left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right)\right)\right) \]

       3. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \left(9 \cdot x1 + \left(\mathsf{neg}\left(1\right)\right)\right)\right), \left(x2 \cdot \left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right)\right)\right) \]

       4. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \left(9 \cdot x1 + -1\right)\right), \left(x2 \cdot \left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right)\right)\right) \]

       5. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\left(9 \cdot x1\right), -1\right)\right), \left(x2 \cdot \left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right)\right)\right) \]

       6. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\left(x1 \cdot 9\right), -1\right)\right), \left(x2 \cdot \left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right)\right)\right) \]

       7. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 9\right), -1\right)\right), \left(x2 \cdot \left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right)\right)\right) \]

       8. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 9\right), -1\right)\right), \mathsf{*.f64}\left(x2, \color{blue}{\left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right)}\right)\right) \]

       9. associate--l+ N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 9\right), -1\right)\right), \mathsf{*.f64}\left(x2, \left(-12 \cdot x1 + \color{blue}{\left(8 \cdot \left(x1 \cdot x2\right) - 6\right)}\right)\right)\right) \]

       10. +-lowering-+.f64 N/A

           \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 9\right), -1\right)\right), \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\left(-12 \cdot x1\right), \color{blue}{\left(8 \cdot \left(x1 \cdot x2\right) - 6\right)}\right)\right)\right) \]

       11. *-commutative N/A

           \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 9\right), -1\right)\right), \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\left(x1 \cdot -12\right), \left(\color{blue}{8 \cdot \left(x1 \cdot x2\right)} - 6\right)\right)\right)\right) \]

       12. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 9\right), -1\right)\right), \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, -12\right), \left(\color{blue}{8 \cdot \left(x1 \cdot x2\right)} - 6\right)\right)\right)\right) \]

       13. sub-neg N/A

           \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 9\right), -1\right)\right), \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, -12\right), \left(8 \cdot \left(x1 \cdot x2\right) + \color{blue}{\left(\mathsf{neg}\left(6\right)\right)}\right)\right)\right)\right) \]

       14. metadata-eval N/A

           \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 9\right), -1\right)\right), \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, -12\right), \left(8 \cdot \left(x1 \cdot x2\right) + -6\right)\right)\right)\right) \]

       15. +-lowering-+.f64 N/A

           \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 9\right), -1\right)\right), \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, -12\right), \mathsf{+.f64}\left(\left(8 \cdot \left(x1 \cdot x2\right)\right), \color{blue}{-6}\right)\right)\right)\right) \]

       16. *-commutative N/A

           \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 9\right), -1\right)\right), \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, -12\right), \mathsf{+.f64}\left(\left(\left(x1 \cdot x2\right) \cdot 8\right), -6\right)\right)\right)\right) \]

       17. associate-*l* N/A

           \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 9\right), -1\right)\right), \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, -12\right), \mathsf{+.f64}\left(\left(x1 \cdot \left(x2 \cdot 8\right)\right), -6\right)\right)\right)\right) \]

       18. *-commutative N/A

           \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 9\right), -1\right)\right), \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, -12\right), \mathsf{+.f64}\left(\left(x1 \cdot \left(8 \cdot x2\right)\right), -6\right)\right)\right)\right) \]

       19. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 9\right), -1\right)\right), \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, -12\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \left(8 \cdot x2\right)\right), -6\right)\right)\right)\right) \]

       20. *-commutative N/A

           \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 9\right), -1\right)\right), \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, -12\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \left(x2 \cdot 8\right)\right), -6\right)\right)\right)\right) \]

       21. *-lowering-*.f64 98.4%

           \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 9\right), -1\right)\right), \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, -12\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x2, 8\right)\right), -6\right)\right)\right)\right) \]

   13. Simplified 98.4%

       \[\leadsto \color{blue}{x1 \cdot \left(x1 \cdot 9 + -1\right) + x2 \cdot \left(x1 \cdot -12 + \left(x1 \cdot \left(x2 \cdot 8\right) + -6\right)\right)} \]
   14. Step-by-step derivation

       1. +-commutative N/A

          \[\leadsto x2 \cdot \left(x1 \cdot -12 + \left(x1 \cdot \left(x2 \cdot 8\right) + -6\right)\right) + \color{blue}{x1 \cdot \left(x1 \cdot 9 + -1\right)} \]

       2. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\left(x2 \cdot \left(x1 \cdot -12 + \left(x1 \cdot \left(x2 \cdot 8\right) + -6\right)\right)\right), \color{blue}{\left(x1 \cdot \left(x1 \cdot 9 + -1\right)\right)}\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, \left(x1 \cdot -12 + \left(x1 \cdot \left(x2 \cdot 8\right) + -6\right)\right)\right), \left(\color{blue}{x1} \cdot \left(x1 \cdot 9 + -1\right)\right)\right) \]

       4. associate-+r+ N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, \left(\left(x1 \cdot -12 + x1 \cdot \left(x2 \cdot 8\right)\right) + -6\right)\right), \left(x1 \cdot \left(x1 \cdot 9 + -1\right)\right)\right) \]

       5. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, \left(-6 + \left(x1 \cdot -12 + x1 \cdot \left(x2 \cdot 8\right)\right)\right)\right), \left(x1 \cdot \left(x1 \cdot 9 + -1\right)\right)\right) \]

       6. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(-6, \left(x1 \cdot -12 + x1 \cdot \left(x2 \cdot 8\right)\right)\right)\right), \left(x1 \cdot \left(x1 \cdot 9 + -1\right)\right)\right) \]

       7. distribute-lft-out N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(-6, \left(x1 \cdot \left(-12 + x2 \cdot 8\right)\right)\right)\right), \left(x1 \cdot \left(x1 \cdot 9 + -1\right)\right)\right) \]

       8. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(-6, \mathsf{*.f64}\left(x1, \left(-12 + x2 \cdot 8\right)\right)\right)\right), \left(x1 \cdot \left(x1 \cdot 9 + -1\right)\right)\right) \]

       9. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(-6, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-12, \left(x2 \cdot 8\right)\right)\right)\right)\right), \left(x1 \cdot \left(x1 \cdot 9 + -1\right)\right)\right) \]

       10. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(-6, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-12, \mathsf{*.f64}\left(x2, 8\right)\right)\right)\right)\right), \left(x1 \cdot \left(x1 \cdot 9 + -1\right)\right)\right) \]

       11. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(-6, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-12, \mathsf{*.f64}\left(x2, 8\right)\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \color{blue}{\left(x1 \cdot 9 + -1\right)}\right)\right) \]

       12. +-lowering-+.f64 N/A

           \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(-6, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-12, \mathsf{*.f64}\left(x2, 8\right)\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\left(x1 \cdot 9\right), \color{blue}{-1}\right)\right)\right) \]

       13. *-lowering-*.f64 98.4%

           \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(-6, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-12, \mathsf{*.f64}\left(x2, 8\right)\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 9\right), -1\right)\right)\right) \]

   15. Applied egg-rr 98.4%

       \[\leadsto \color{blue}{x2 \cdot \left(-6 + x1 \cdot \left(-12 + x2 \cdot 8\right)\right) + x1 \cdot \left(x1 \cdot 9 + -1\right)} \]

   if 15000 < x1

   1. Initial program 48.9%

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

   3. Simplified 49.0%

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

   5. Taylor expanded in x1 around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, -6\right)\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-6, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 4\right)\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \color{blue}{9}\right)\right)\right)\right)\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 49.0%

      \[\leadsto \frac{3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right)}{x1 \cdot x1 + 1} + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(x1 \cdot \left(x1 \cdot -6\right) + \frac{2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)}{x1 \cdot x1 + 1} \cdot \left(x1 \cdot \left(-6 + \left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right) \cdot \frac{2}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot 4\right)\right) + x1 \cdot \left(2 + x1 \cdot \left(x1 + \color{blue}{9}\right)\right)\right) \]

   8. Taylor expanded in x1 around -inf

      \[\leadsto \color{blue}{{x1}^{4} \cdot \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)} \]
   9. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{4}\right), \color{blue}{\left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)}\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{\left(2 \cdot 2\right)}\right), \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)\right) \]

      3. pow-sqr N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{2} \cdot {x1}^{2}\right), \left(\color{blue}{6} + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left({x1}^{2}\right), \left({x1}^{2}\right)\right), \left(\color{blue}{6} + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)\right) \]

      5. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x1 \cdot x1\right), \left({x1}^{2}\right)\right), \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left({x1}^{2}\right)\right), \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left(x1 \cdot x1\right)\right), \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)\right) \]

      9. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \left(6 + \left(\mathsf{neg}\left(\frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)\right)\right)\right) \]

      10. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \left(6 - \color{blue}{\frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}}\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \color{blue}{\left(\frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)}\right)\right) \]

      12. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \mathsf{/.f64}\left(\left(3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}\right), \color{blue}{x1}\right)\right)\right) \]

   10. Simplified 90.8%

       \[\leadsto \color{blue}{\left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right)\right) \cdot \left(6 - \frac{3 - \frac{x2 \cdot 8 + -3}{x1}}{x1}\right)} \]

   11. Taylor expanded in x1 around 0

       \[\leadsto \color{blue}{{x1}^{2} \cdot \left(\left(8 \cdot x2 + x1 \cdot \left(6 \cdot x1 - 3\right)\right) - 3\right)} \]
   12. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\left({x1}^{2}\right), \color{blue}{\left(\left(8 \cdot x2 + x1 \cdot \left(6 \cdot x1 - 3\right)\right) - 3\right)}\right) \]

       2. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(\left(x1 \cdot x1\right), \left(\color{blue}{\left(8 \cdot x2 + x1 \cdot \left(6 \cdot x1 - 3\right)\right)} - 3\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left(\color{blue}{\left(8 \cdot x2 + x1 \cdot \left(6 \cdot x1 - 3\right)\right)} - 3\right)\right) \]

       4. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left(\left(x1 \cdot \left(6 \cdot x1 - 3\right) + 8 \cdot x2\right) - 3\right)\right) \]

       5. associate--l+ N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left(x1 \cdot \left(6 \cdot x1 - 3\right) + \color{blue}{\left(8 \cdot x2 - 3\right)}\right)\right) \]

       6. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\left(x1 \cdot \left(6 \cdot x1 - 3\right)\right), \color{blue}{\left(8 \cdot x2 - 3\right)}\right)\right) \]

       7. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \left(6 \cdot x1 - 3\right)\right), \left(\color{blue}{8 \cdot x2} - 3\right)\right)\right) \]

       8. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \left(6 \cdot x1 + \left(\mathsf{neg}\left(3\right)\right)\right)\right), \left(8 \cdot \color{blue}{x2} - 3\right)\right)\right) \]

       9. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \left(6 \cdot x1 + -3\right)\right), \left(8 \cdot x2 - 3\right)\right)\right) \]

       10. +-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \left(-3 + 6 \cdot x1\right)\right), \left(8 \cdot \color{blue}{x2} - 3\right)\right)\right) \]

       11. +-lowering-+.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-3, \left(6 \cdot x1\right)\right)\right), \left(8 \cdot \color{blue}{x2} - 3\right)\right)\right) \]

       12. *-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-3, \left(x1 \cdot 6\right)\right)\right), \left(8 \cdot x2 - 3\right)\right)\right) \]

       13. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-3, \mathsf{*.f64}\left(x1, 6\right)\right)\right), \left(8 \cdot x2 - 3\right)\right)\right) \]

       14. sub-neg N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-3, \mathsf{*.f64}\left(x1, 6\right)\right)\right), \left(8 \cdot x2 + \color{blue}{\left(\mathsf{neg}\left(3\right)\right)}\right)\right)\right) \]

       15. metadata-eval N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-3, \mathsf{*.f64}\left(x1, 6\right)\right)\right), \left(8 \cdot x2 + -3\right)\right)\right) \]

       16. +-lowering-+.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-3, \mathsf{*.f64}\left(x1, 6\right)\right)\right), \mathsf{+.f64}\left(\left(8 \cdot x2\right), \color{blue}{-3}\right)\right)\right) \]

       17. *-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-3, \mathsf{*.f64}\left(x1, 6\right)\right)\right), \mathsf{+.f64}\left(\left(x2 \cdot 8\right), -3\right)\right)\right) \]

       18. *-lowering-*.f64 91.0%

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-3, \mathsf{*.f64}\left(x1, 6\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 8\right), -3\right)\right)\right) \]

   13. Simplified 91.0%

       \[\leadsto \color{blue}{\left(x1 \cdot x1\right) \cdot \left(x1 \cdot \left(-3 + x1 \cdot 6\right) + \left(x2 \cdot 8 + -3\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 95.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -2 \cdot 10^{+14}:\\ \;\;\;\;\left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right)\right) \cdot \left(6 - \frac{\frac{x2 \cdot -8}{x1}}{x1}\right)\\ \mathbf{elif}\;x1 \leq 15000:\\ \;\;\;\;x1 \cdot \left(-1 + x1 \cdot 9\right) + x2 \cdot \left(-6 + x1 \cdot \left(-12 + x2 \cdot 8\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x1 \cdot x1\right) \cdot \left(x1 \cdot \left(-3 + x1 \cdot 6\right) + \left(-3 + x2 \cdot 8\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 72.1% accurate, 4.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x2 \cdot \left(x1 \cdot \left(x2 \cdot 8\right)\right)\\ \mathbf{if}\;x1 \leq -8.8 \cdot 10^{+101}:\\ \;\;\;\;x1 \cdot \left(\left(x1 \cdot x1\right) \cdot -3\right)\\ \mathbf{elif}\;x1 \leq -1.8 \cdot 10^{-57}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x1 \leq 2.3 \cdot 10^{-13}:\\ \;\;\;\;x2 \cdot -6 - x1\\ \mathbf{elif}\;x1 \leq 8.2 \cdot 10^{+152}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot \left(x1 \cdot 9\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x2 (* x1 (* x2 8.0)))))
   (if (<= x1 -8.8e+101)
     (* x1 (* (* x1 x1) -3.0))
     (if (<= x1 -1.8e-57)
       t_0
       (if (<= x1 2.3e-13)
         (- (* x2 -6.0) x1)
         (if (<= x1 8.2e+152) t_0 (* x1 (* x1 9.0))))))))

C

double code(double x1, double x2) {
	double t_0 = x2 * (x1 * (x2 * 8.0));
	double tmp;
	if (x1 <= -8.8e+101) {
		tmp = x1 * ((x1 * x1) * -3.0);
	} else if (x1 <= -1.8e-57) {
		tmp = t_0;
	} else if (x1 <= 2.3e-13) {
		tmp = (x2 * -6.0) - x1;
	} else if (x1 <= 8.2e+152) {
		tmp = t_0;
	} else {
		tmp = x1 * (x1 * 9.0);
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x2 * (x1 * (x2 * 8.0d0))
    if (x1 <= (-8.8d+101)) then
        tmp = x1 * ((x1 * x1) * (-3.0d0))
    else if (x1 <= (-1.8d-57)) then
        tmp = t_0
    else if (x1 <= 2.3d-13) then
        tmp = (x2 * (-6.0d0)) - x1
    else if (x1 <= 8.2d+152) then
        tmp = t_0
    else
        tmp = x1 * (x1 * 9.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x2 * (x1 * (x2 * 8.0));
	double tmp;
	if (x1 <= -8.8e+101) {
		tmp = x1 * ((x1 * x1) * -3.0);
	} else if (x1 <= -1.8e-57) {
		tmp = t_0;
	} else if (x1 <= 2.3e-13) {
		tmp = (x2 * -6.0) - x1;
	} else if (x1 <= 8.2e+152) {
		tmp = t_0;
	} else {
		tmp = x1 * (x1 * 9.0);
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x2 * (x1 * (x2 * 8.0))
	tmp = 0
	if x1 <= -8.8e+101:
		tmp = x1 * ((x1 * x1) * -3.0)
	elif x1 <= -1.8e-57:
		tmp = t_0
	elif x1 <= 2.3e-13:
		tmp = (x2 * -6.0) - x1
	elif x1 <= 8.2e+152:
		tmp = t_0
	else:
		tmp = x1 * (x1 * 9.0)
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x2 * Float64(x1 * Float64(x2 * 8.0)))
	tmp = 0.0
	if (x1 <= -8.8e+101)
		tmp = Float64(x1 * Float64(Float64(x1 * x1) * -3.0));
	elseif (x1 <= -1.8e-57)
		tmp = t_0;
	elseif (x1 <= 2.3e-13)
		tmp = Float64(Float64(x2 * -6.0) - x1);
	elseif (x1 <= 8.2e+152)
		tmp = t_0;
	else
		tmp = Float64(x1 * Float64(x1 * 9.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x2 * (x1 * (x2 * 8.0));
	tmp = 0.0;
	if (x1 <= -8.8e+101)
		tmp = x1 * ((x1 * x1) * -3.0);
	elseif (x1 <= -1.8e-57)
		tmp = t_0;
	elseif (x1 <= 2.3e-13)
		tmp = (x2 * -6.0) - x1;
	elseif (x1 <= 8.2e+152)
		tmp = t_0;
	else
		tmp = x1 * (x1 * 9.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x2 * N[(x1 * N[(x2 * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -8.8e+101], N[(x1 * N[(N[(x1 * x1), $MachinePrecision] * -3.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -1.8e-57], t$95$0, If[LessEqual[x1, 2.3e-13], N[(N[(x2 * -6.0), $MachinePrecision] - x1), $MachinePrecision], If[LessEqual[x1, 8.2e+152], t$95$0, N[(x1 * N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -8.8000000000000003e101

   1. Initial program 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in x1 around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, -6\right)\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-6, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 4\right)\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \color{blue}{9}\right)\right)\right)\right)\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 0.0%

      \[\leadsto \frac{3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right)}{x1 \cdot x1 + 1} + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(x1 \cdot \left(x1 \cdot -6\right) + \frac{2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)}{x1 \cdot x1 + 1} \cdot \left(x1 \cdot \left(-6 + \left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right) \cdot \frac{2}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot 4\right)\right) + x1 \cdot \left(2 + x1 \cdot \left(x1 + \color{blue}{9}\right)\right)\right) \]

   8. Taylor expanded in x1 around inf

      \[\leadsto \color{blue}{{x1}^{4} \cdot \left(6 - 3 \cdot \frac{1}{x1}\right)} \]
   9. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{4}\right), \color{blue}{\left(6 - 3 \cdot \frac{1}{x1}\right)}\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{\left(2 \cdot 2\right)}\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      3. pow-sqr N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{2} \cdot {x1}^{2}\right), \left(\color{blue}{6} - 3 \cdot \frac{1}{x1}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left({x1}^{2}\right), \left({x1}^{2}\right)\right), \left(\color{blue}{6} - 3 \cdot \frac{1}{x1}\right)\right) \]

      5. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x1 \cdot x1\right), \left({x1}^{2}\right)\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left({x1}^{2}\right)\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left(x1 \cdot x1\right)\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \left(6 + \color{blue}{\left(\mathsf{neg}\left(3 \cdot \frac{1}{x1}\right)\right)}\right)\right) \]

      10. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \color{blue}{\left(\mathsf{neg}\left(3 \cdot \frac{1}{x1}\right)\right)}\right)\right) \]

      11. associate-*r/ N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \left(\mathsf{neg}\left(\frac{3 \cdot 1}{x1}\right)\right)\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \left(\mathsf{neg}\left(\frac{3}{x1}\right)\right)\right)\right) \]

      13. distribute-neg-frac N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \left(\frac{\mathsf{neg}\left(3\right)}{\color{blue}{x1}}\right)\right)\right) \]

      14. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \left(\frac{-3}{x1}\right)\right)\right) \]

      15. /-lowering-/.f64 100.0%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \mathsf{/.f64}\left(-3, \color{blue}{x1}\right)\right)\right) \]

   10. Simplified 100.0%

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

   11. Taylor expanded in x1 around 0

       \[\leadsto \color{blue}{-3 \cdot {x1}^{3}} \]
   12. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto {x1}^{3} \cdot \color{blue}{-3} \]

       2. cube-mult N/A

          \[\leadsto \left(x1 \cdot \left(x1 \cdot x1\right)\right) \cdot -3 \]

       3. unpow2 N/A

          \[\leadsto \left(x1 \cdot {x1}^{2}\right) \cdot -3 \]

       4. associate-*l* N/A

          \[\leadsto x1 \cdot \color{blue}{\left({x1}^{2} \cdot -3\right)} \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x1, \color{blue}{\left({x1}^{2} \cdot -3\right)}\right) \]

       6. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(\left({x1}^{2}\right), \color{blue}{-3}\right)\right) \]

       7. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(\left(x1 \cdot x1\right), -3\right)\right) \]

       8. *-lowering-*.f64 100.0%

          \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), -3\right)\right) \]

   13. Simplified 100.0%

       \[\leadsto \color{blue}{x1 \cdot \left(\left(x1 \cdot x1\right) \cdot -3\right)} \]

   if -8.8000000000000003e101 < x1 < -1.8000000000000001e-57 or 2.29999999999999979e-13 < x1 < 8.1999999999999996e152

   1. Initial program 99.4%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x1 around 0

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

   7. Simplified 45.4%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(x2 \cdot 2\right) \cdot \left(x2 \cdot 4 + -6\right) + \left(x1 \cdot \left(\left(\left(\left(9 + 3 \cdot \left(x2 \cdot 2\right)\right) + x2 \cdot 10\right) - \left(x2 \cdot 4 + -6\right)\right) + -6\right) + -1\right)\right)} \]

   8. Taylor expanded in x2 around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right), \color{blue}{\left(9 \cdot x1 - 1\right)}\right)\right)\right) \]
   9. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right), \left(9 \cdot x1 + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right), \left(9 \cdot x1 + -1\right)\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right), \mathsf{+.f64}\left(\left(9 \cdot x1\right), \color{blue}{-1}\right)\right)\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right), \mathsf{+.f64}\left(\left(x1 \cdot 9\right), -1\right)\right)\right)\right) \]

      5. *-lowering-*.f64 48.4%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 9\right), -1\right)\right)\right)\right) \]

   10. Simplified 48.4%

       \[\leadsto -6 \cdot x2 + x1 \cdot \left(\left(x2 \cdot 2\right) \cdot \left(x2 \cdot 4 + -6\right) + \color{blue}{\left(x1 \cdot 9 + -1\right)}\right) \]

   11. Taylor expanded in x2 around inf

       \[\leadsto \color{blue}{8 \cdot \left(x1 \cdot {x2}^{2}\right)} \]
   12. Step-by-step derivation

       1. unpow2 N/A

          \[\leadsto 8 \cdot \left(x1 \cdot \left(x2 \cdot \color{blue}{x2}\right)\right) \]

       2. associate-*r* N/A

          \[\leadsto 8 \cdot \left(\left(x1 \cdot x2\right) \cdot \color{blue}{x2}\right) \]

       3. associate-*l* N/A

          \[\leadsto \left(8 \cdot \left(x1 \cdot x2\right)\right) \cdot \color{blue}{x2} \]

       4. *-commutative N/A

          \[\leadsto x2 \cdot \color{blue}{\left(8 \cdot \left(x1 \cdot x2\right)\right)} \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x2, \color{blue}{\left(8 \cdot \left(x1 \cdot x2\right)\right)}\right) \]

       6. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x2, \left(\left(x1 \cdot x2\right) \cdot \color{blue}{8}\right)\right) \]

       7. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(x2, \left(x1 \cdot \color{blue}{\left(x2 \cdot 8\right)}\right)\right) \]

       8. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x2, \left(x1 \cdot \left(8 \cdot \color{blue}{x2}\right)\right)\right) \]

       9. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x2, \mathsf{*.f64}\left(x1, \color{blue}{\left(8 \cdot x2\right)}\right)\right) \]

       10. *-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(x2, \mathsf{*.f64}\left(x1, \left(x2 \cdot \color{blue}{8}\right)\right)\right) \]

       11. *-lowering-*.f64 41.7%

           \[\leadsto \mathsf{*.f64}\left(x2, \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x2, \color{blue}{8}\right)\right)\right) \]

   13. Simplified 41.7%

       \[\leadsto \color{blue}{x2 \cdot \left(x1 \cdot \left(x2 \cdot 8\right)\right)} \]

   if -1.8000000000000001e-57 < x1 < 2.29999999999999979e-13

   1. Initial program 99.4%

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

   3. Simplified 99.5%

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

   6. Applied egg-rr 99.5%

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

   7. Taylor expanded in x1 around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(\color{blue}{\left(12 \cdot {x1}^{4}\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(-6, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]
   8. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(12, \left({x1}^{4}\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(-6, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(12, \left({x1}^{\left(2 \cdot 2\right)}\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(-6, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      3. pow-sqr N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(12, \left({x1}^{2} \cdot {x1}^{2}\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(-6, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(12, \mathsf{*.f64}\left(\left({x1}^{2}\right), \left({x1}^{2}\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(-6, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      5. unpow2 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(12, \mathsf{*.f64}\left(\left(x1 \cdot x1\right), \left({x1}^{2}\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(-6, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(12, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left({x1}^{2}\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(-6, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(12, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left(x1 \cdot x1\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(-6, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      8. *-lowering-*.f64 80.9%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(12, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(-6, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

   9. Simplified 80.9%

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

   10. Taylor expanded in x1 around 0

       \[\leadsto \color{blue}{-6 \cdot x2 + -1 \cdot x1} \]
   11. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto -6 \cdot x2 + \left(\mathsf{neg}\left(x1\right)\right) \]

       2. unsub-neg N/A

          \[\leadsto -6 \cdot x2 - \color{blue}{x1} \]

       3. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\left(-6 \cdot x2\right), \color{blue}{x1}\right) \]

       4. *-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(\left(x2 \cdot -6\right), x1\right) \]

       5. *-lowering-*.f64 81.1%

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x2, -6\right), x1\right) \]

   12. Simplified 81.1%

       \[\leadsto \color{blue}{x2 \cdot -6 - x1} \]

   if 8.1999999999999996e152 < x1

   1. Initial program 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in x1 around 0

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

   7. Simplified 69.0%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(x2 \cdot 2\right) \cdot \left(x2 \cdot 4 + -6\right) + \left(x1 \cdot \left(\left(\left(\left(9 + 3 \cdot \left(x2 \cdot 2\right)\right) + x2 \cdot 10\right) - \left(x2 \cdot 4 + -6\right)\right) + -6\right) + -1\right)\right)} \]

   8. Taylor expanded in x2 around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right), \color{blue}{\left(9 \cdot x1 - 1\right)}\right)\right)\right) \]
   9. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right), \left(9 \cdot x1 + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right), \left(9 \cdot x1 + -1\right)\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right), \mathsf{+.f64}\left(\left(9 \cdot x1\right), \color{blue}{-1}\right)\right)\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right), \mathsf{+.f64}\left(\left(x1 \cdot 9\right), -1\right)\right)\right)\right) \]

      5. *-lowering-*.f64 100.0%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 9\right), -1\right)\right)\right)\right) \]

   10. Simplified 100.0%

       \[\leadsto -6 \cdot x2 + x1 \cdot \left(\left(x2 \cdot 2\right) \cdot \left(x2 \cdot 4 + -6\right) + \color{blue}{\left(x1 \cdot 9 + -1\right)}\right) \]

   11. Taylor expanded in x1 around inf

       \[\leadsto \color{blue}{9 \cdot {x1}^{2}} \]
   12. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto {x1}^{2} \cdot \color{blue}{9} \]

       2. unpow2 N/A

          \[\leadsto \left(x1 \cdot x1\right) \cdot 9 \]

       3. associate-*l* N/A

          \[\leadsto x1 \cdot \color{blue}{\left(x1 \cdot 9\right)} \]

       4. *-commutative N/A

          \[\leadsto x1 \cdot \left(9 \cdot \color{blue}{x1}\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x1, \color{blue}{\left(9 \cdot x1\right)}\right) \]

       6. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x1, \left(x1 \cdot \color{blue}{9}\right)\right) \]

       7. *-lowering-*.f64 100.0%

          \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, \color{blue}{9}\right)\right) \]

   13. Simplified 100.0%

       \[\leadsto \color{blue}{x1 \cdot \left(x1 \cdot 9\right)} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 12: 72.0% accurate, 4.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 8 \cdot \left(x1 \cdot \left(x2 \cdot x2\right)\right)\\ \mathbf{if}\;x1 \leq -2.25 \cdot 10^{+102}:\\ \;\;\;\;x1 \cdot \left(\left(x1 \cdot x1\right) \cdot -3\right)\\ \mathbf{elif}\;x1 \leq -6.6 \cdot 10^{-58}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{-15}:\\ \;\;\;\;x2 \cdot -6 - x1\\ \mathbf{elif}\;x1 \leq 4.5 \cdot 10^{+153}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot \left(x1 \cdot 9\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* 8.0 (* x1 (* x2 x2)))))
   (if (<= x1 -2.25e+102)
     (* x1 (* (* x1 x1) -3.0))
     (if (<= x1 -6.6e-58)
       t_0
       (if (<= x1 5e-15)
         (- (* x2 -6.0) x1)
         (if (<= x1 4.5e+153) t_0 (* x1 (* x1 9.0))))))))

C

double code(double x1, double x2) {
	double t_0 = 8.0 * (x1 * (x2 * x2));
	double tmp;
	if (x1 <= -2.25e+102) {
		tmp = x1 * ((x1 * x1) * -3.0);
	} else if (x1 <= -6.6e-58) {
		tmp = t_0;
	} else if (x1 <= 5e-15) {
		tmp = (x2 * -6.0) - x1;
	} else if (x1 <= 4.5e+153) {
		tmp = t_0;
	} else {
		tmp = x1 * (x1 * 9.0);
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 8.0d0 * (x1 * (x2 * x2))
    if (x1 <= (-2.25d+102)) then
        tmp = x1 * ((x1 * x1) * (-3.0d0))
    else if (x1 <= (-6.6d-58)) then
        tmp = t_0
    else if (x1 <= 5d-15) then
        tmp = (x2 * (-6.0d0)) - x1
    else if (x1 <= 4.5d+153) then
        tmp = t_0
    else
        tmp = x1 * (x1 * 9.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = 8.0 * (x1 * (x2 * x2));
	double tmp;
	if (x1 <= -2.25e+102) {
		tmp = x1 * ((x1 * x1) * -3.0);
	} else if (x1 <= -6.6e-58) {
		tmp = t_0;
	} else if (x1 <= 5e-15) {
		tmp = (x2 * -6.0) - x1;
	} else if (x1 <= 4.5e+153) {
		tmp = t_0;
	} else {
		tmp = x1 * (x1 * 9.0);
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = 8.0 * (x1 * (x2 * x2))
	tmp = 0
	if x1 <= -2.25e+102:
		tmp = x1 * ((x1 * x1) * -3.0)
	elif x1 <= -6.6e-58:
		tmp = t_0
	elif x1 <= 5e-15:
		tmp = (x2 * -6.0) - x1
	elif x1 <= 4.5e+153:
		tmp = t_0
	else:
		tmp = x1 * (x1 * 9.0)
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(8.0 * Float64(x1 * Float64(x2 * x2)))
	tmp = 0.0
	if (x1 <= -2.25e+102)
		tmp = Float64(x1 * Float64(Float64(x1 * x1) * -3.0));
	elseif (x1 <= -6.6e-58)
		tmp = t_0;
	elseif (x1 <= 5e-15)
		tmp = Float64(Float64(x2 * -6.0) - x1);
	elseif (x1 <= 4.5e+153)
		tmp = t_0;
	else
		tmp = Float64(x1 * Float64(x1 * 9.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = 8.0 * (x1 * (x2 * x2));
	tmp = 0.0;
	if (x1 <= -2.25e+102)
		tmp = x1 * ((x1 * x1) * -3.0);
	elseif (x1 <= -6.6e-58)
		tmp = t_0;
	elseif (x1 <= 5e-15)
		tmp = (x2 * -6.0) - x1;
	elseif (x1 <= 4.5e+153)
		tmp = t_0;
	else
		tmp = x1 * (x1 * 9.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(8.0 * N[(x1 * N[(x2 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -2.25e+102], N[(x1 * N[(N[(x1 * x1), $MachinePrecision] * -3.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -6.6e-58], t$95$0, If[LessEqual[x1, 5e-15], N[(N[(x2 * -6.0), $MachinePrecision] - x1), $MachinePrecision], If[LessEqual[x1, 4.5e+153], t$95$0, N[(x1 * N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -2.2500000000000001e102

   1. Initial program 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in x1 around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, -6\right)\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-6, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 4\right)\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \color{blue}{9}\right)\right)\right)\right)\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 0.0%

      \[\leadsto \frac{3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right)}{x1 \cdot x1 + 1} + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(x1 \cdot \left(x1 \cdot -6\right) + \frac{2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)}{x1 \cdot x1 + 1} \cdot \left(x1 \cdot \left(-6 + \left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right) \cdot \frac{2}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot 4\right)\right) + x1 \cdot \left(2 + x1 \cdot \left(x1 + \color{blue}{9}\right)\right)\right) \]

   8. Taylor expanded in x1 around inf

      \[\leadsto \color{blue}{{x1}^{4} \cdot \left(6 - 3 \cdot \frac{1}{x1}\right)} \]
   9. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{4}\right), \color{blue}{\left(6 - 3 \cdot \frac{1}{x1}\right)}\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{\left(2 \cdot 2\right)}\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      3. pow-sqr N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{2} \cdot {x1}^{2}\right), \left(\color{blue}{6} - 3 \cdot \frac{1}{x1}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left({x1}^{2}\right), \left({x1}^{2}\right)\right), \left(\color{blue}{6} - 3 \cdot \frac{1}{x1}\right)\right) \]

      5. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x1 \cdot x1\right), \left({x1}^{2}\right)\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left({x1}^{2}\right)\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left(x1 \cdot x1\right)\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \left(6 + \color{blue}{\left(\mathsf{neg}\left(3 \cdot \frac{1}{x1}\right)\right)}\right)\right) \]

      10. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \color{blue}{\left(\mathsf{neg}\left(3 \cdot \frac{1}{x1}\right)\right)}\right)\right) \]

      11. associate-*r/ N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \left(\mathsf{neg}\left(\frac{3 \cdot 1}{x1}\right)\right)\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \left(\mathsf{neg}\left(\frac{3}{x1}\right)\right)\right)\right) \]

      13. distribute-neg-frac N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \left(\frac{\mathsf{neg}\left(3\right)}{\color{blue}{x1}}\right)\right)\right) \]

      14. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \left(\frac{-3}{x1}\right)\right)\right) \]

      15. /-lowering-/.f64 100.0%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \mathsf{/.f64}\left(-3, \color{blue}{x1}\right)\right)\right) \]

   10. Simplified 100.0%

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

   11. Taylor expanded in x1 around 0

       \[\leadsto \color{blue}{-3 \cdot {x1}^{3}} \]
   12. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto {x1}^{3} \cdot \color{blue}{-3} \]

       2. cube-mult N/A

          \[\leadsto \left(x1 \cdot \left(x1 \cdot x1\right)\right) \cdot -3 \]

       3. unpow2 N/A

          \[\leadsto \left(x1 \cdot {x1}^{2}\right) \cdot -3 \]

       4. associate-*l* N/A

          \[\leadsto x1 \cdot \color{blue}{\left({x1}^{2} \cdot -3\right)} \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x1, \color{blue}{\left({x1}^{2} \cdot -3\right)}\right) \]

       6. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(\left({x1}^{2}\right), \color{blue}{-3}\right)\right) \]

       7. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(\left(x1 \cdot x1\right), -3\right)\right) \]

       8. *-lowering-*.f64 100.0%

          \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), -3\right)\right) \]

   13. Simplified 100.0%

       \[\leadsto \color{blue}{x1 \cdot \left(\left(x1 \cdot x1\right) \cdot -3\right)} \]

   if -2.2500000000000001e102 < x1 < -6.60000000000000052e-58 or 4.99999999999999999e-15 < x1 < 4.5000000000000001e153

   1. Initial program 99.4%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x1 around 0

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

   7. Simplified 45.4%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(x2 \cdot 2\right) \cdot \left(x2 \cdot 4 + -6\right) + \left(x1 \cdot \left(\left(\left(\left(9 + 3 \cdot \left(x2 \cdot 2\right)\right) + x2 \cdot 10\right) - \left(x2 \cdot 4 + -6\right)\right) + -6\right) + -1\right)\right)} \]

   8. Taylor expanded in x2 around inf

      \[\leadsto \color{blue}{8 \cdot \left(x1 \cdot {x2}^{2}\right)} \]
   9. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(8, \color{blue}{\left(x1 \cdot {x2}^{2}\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(8, \mathsf{*.f64}\left(x1, \color{blue}{\left({x2}^{2}\right)}\right)\right) \]

      3. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(8, \mathsf{*.f64}\left(x1, \left(x2 \cdot \color{blue}{x2}\right)\right)\right) \]

      4. *-lowering-*.f64 41.7%

         \[\leadsto \mathsf{*.f64}\left(8, \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x2, \color{blue}{x2}\right)\right)\right) \]

   10. Simplified 41.7%

       \[\leadsto \color{blue}{8 \cdot \left(x1 \cdot \left(x2 \cdot x2\right)\right)} \]

   if -6.60000000000000052e-58 < x1 < 4.99999999999999999e-15

   1. Initial program 99.4%

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

   3. Simplified 99.5%

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

   6. Applied egg-rr 99.5%

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

   7. Taylor expanded in x1 around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(\color{blue}{\left(12 \cdot {x1}^{4}\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(-6, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]
   8. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(12, \left({x1}^{4}\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(-6, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(12, \left({x1}^{\left(2 \cdot 2\right)}\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(-6, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      3. pow-sqr N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(12, \left({x1}^{2} \cdot {x1}^{2}\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(-6, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(12, \mathsf{*.f64}\left(\left({x1}^{2}\right), \left({x1}^{2}\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(-6, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      5. unpow2 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(12, \mathsf{*.f64}\left(\left(x1 \cdot x1\right), \left({x1}^{2}\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(-6, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(12, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left({x1}^{2}\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(-6, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(12, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left(x1 \cdot x1\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(-6, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      8. *-lowering-*.f64 80.9%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(12, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(-6, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

   9. Simplified 80.9%

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

   10. Taylor expanded in x1 around 0

       \[\leadsto \color{blue}{-6 \cdot x2 + -1 \cdot x1} \]
   11. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto -6 \cdot x2 + \left(\mathsf{neg}\left(x1\right)\right) \]

       2. unsub-neg N/A

          \[\leadsto -6 \cdot x2 - \color{blue}{x1} \]

       3. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\left(-6 \cdot x2\right), \color{blue}{x1}\right) \]

       4. *-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(\left(x2 \cdot -6\right), x1\right) \]

       5. *-lowering-*.f64 81.1%

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x2, -6\right), x1\right) \]

   12. Simplified 81.1%

       \[\leadsto \color{blue}{x2 \cdot -6 - x1} \]

   if 4.5000000000000001e153 < x1

   1. Initial program 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in x1 around 0

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

   7. Simplified 69.0%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(x2 \cdot 2\right) \cdot \left(x2 \cdot 4 + -6\right) + \left(x1 \cdot \left(\left(\left(\left(9 + 3 \cdot \left(x2 \cdot 2\right)\right) + x2 \cdot 10\right) - \left(x2 \cdot 4 + -6\right)\right) + -6\right) + -1\right)\right)} \]

   8. Taylor expanded in x2 around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right), \color{blue}{\left(9 \cdot x1 - 1\right)}\right)\right)\right) \]
   9. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right), \left(9 \cdot x1 + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right), \left(9 \cdot x1 + -1\right)\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right), \mathsf{+.f64}\left(\left(9 \cdot x1\right), \color{blue}{-1}\right)\right)\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right), \mathsf{+.f64}\left(\left(x1 \cdot 9\right), -1\right)\right)\right)\right) \]

      5. *-lowering-*.f64 100.0%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 9\right), -1\right)\right)\right)\right) \]

   10. Simplified 100.0%

       \[\leadsto -6 \cdot x2 + x1 \cdot \left(\left(x2 \cdot 2\right) \cdot \left(x2 \cdot 4 + -6\right) + \color{blue}{\left(x1 \cdot 9 + -1\right)}\right) \]

   11. Taylor expanded in x1 around inf

       \[\leadsto \color{blue}{9 \cdot {x1}^{2}} \]
   12. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto {x1}^{2} \cdot \color{blue}{9} \]

       2. unpow2 N/A

          \[\leadsto \left(x1 \cdot x1\right) \cdot 9 \]

       3. associate-*l* N/A

          \[\leadsto x1 \cdot \color{blue}{\left(x1 \cdot 9\right)} \]

       4. *-commutative N/A

          \[\leadsto x1 \cdot \left(9 \cdot \color{blue}{x1}\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x1, \color{blue}{\left(9 \cdot x1\right)}\right) \]

       6. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x1, \left(x1 \cdot \color{blue}{9}\right)\right) \]

       7. *-lowering-*.f64 100.0%

          \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, \color{blue}{9}\right)\right) \]

   13. Simplified 100.0%

       \[\leadsto \color{blue}{x1 \cdot \left(x1 \cdot 9\right)} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 13: 68.1% accurate, 4.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 9\right)\\ t_1 := 8 \cdot \left(x1 \cdot \left(x2 \cdot x2\right)\right)\\ \mathbf{if}\;x1 \leq -3.3 \cdot 10^{+108}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x1 \leq -1.5 \cdot 10^{-57}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x1 \leq 3.1 \cdot 10^{-15}:\\ \;\;\;\;x2 \cdot -6 - x1\\ \mathbf{elif}\;x1 \leq 4.5 \cdot 10^{+153}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 9.0))) (t_1 (* 8.0 (* x1 (* x2 x2)))))
   (if (<= x1 -3.3e+108)
     t_0
     (if (<= x1 -1.5e-57)
       t_1
       (if (<= x1 3.1e-15)
         (- (* x2 -6.0) x1)
         (if (<= x1 4.5e+153) t_1 t_0))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 9.0);
	double t_1 = 8.0 * (x1 * (x2 * x2));
	double tmp;
	if (x1 <= -3.3e+108) {
		tmp = t_0;
	} else if (x1 <= -1.5e-57) {
		tmp = t_1;
	} else if (x1 <= 3.1e-15) {
		tmp = (x2 * -6.0) - x1;
	} else if (x1 <= 4.5e+153) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

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) :: tmp
    t_0 = x1 * (x1 * 9.0d0)
    t_1 = 8.0d0 * (x1 * (x2 * x2))
    if (x1 <= (-3.3d+108)) then
        tmp = t_0
    else if (x1 <= (-1.5d-57)) then
        tmp = t_1
    else if (x1 <= 3.1d-15) then
        tmp = (x2 * (-6.0d0)) - x1
    else if (x1 <= 4.5d+153) then
        tmp = t_1
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 9.0);
	double t_1 = 8.0 * (x1 * (x2 * x2));
	double tmp;
	if (x1 <= -3.3e+108) {
		tmp = t_0;
	} else if (x1 <= -1.5e-57) {
		tmp = t_1;
	} else if (x1 <= 3.1e-15) {
		tmp = (x2 * -6.0) - x1;
	} else if (x1 <= 4.5e+153) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 9.0)
	t_1 = 8.0 * (x1 * (x2 * x2))
	tmp = 0
	if x1 <= -3.3e+108:
		tmp = t_0
	elif x1 <= -1.5e-57:
		tmp = t_1
	elif x1 <= 3.1e-15:
		tmp = (x2 * -6.0) - x1
	elif x1 <= 4.5e+153:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 9.0))
	t_1 = Float64(8.0 * Float64(x1 * Float64(x2 * x2)))
	tmp = 0.0
	if (x1 <= -3.3e+108)
		tmp = t_0;
	elseif (x1 <= -1.5e-57)
		tmp = t_1;
	elseif (x1 <= 3.1e-15)
		tmp = Float64(Float64(x2 * -6.0) - x1);
	elseif (x1 <= 4.5e+153)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * 9.0);
	t_1 = 8.0 * (x1 * (x2 * x2));
	tmp = 0.0;
	if (x1 <= -3.3e+108)
		tmp = t_0;
	elseif (x1 <= -1.5e-57)
		tmp = t_1;
	elseif (x1 <= 3.1e-15)
		tmp = (x2 * -6.0) - x1;
	elseif (x1 <= 4.5e+153)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(8.0 * N[(x1 * N[(x2 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -3.3e+108], t$95$0, If[LessEqual[x1, -1.5e-57], t$95$1, If[LessEqual[x1, 3.1e-15], N[(N[(x2 * -6.0), $MachinePrecision] - x1), $MachinePrecision], If[LessEqual[x1, 4.5e+153], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -3.30000000000000019e108 or 4.5000000000000001e153 < x1

   1. Initial program 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in x1 around 0

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

   7. Simplified 59.4%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(x2 \cdot 2\right) \cdot \left(x2 \cdot 4 + -6\right) + \left(x1 \cdot \left(\left(\left(\left(9 + 3 \cdot \left(x2 \cdot 2\right)\right) + x2 \cdot 10\right) - \left(x2 \cdot 4 + -6\right)\right) + -6\right) + -1\right)\right)} \]

   8. Taylor expanded in x2 around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right), \color{blue}{\left(9 \cdot x1 - 1\right)}\right)\right)\right) \]
   9. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right), \left(9 \cdot x1 + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right), \left(9 \cdot x1 + -1\right)\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right), \mathsf{+.f64}\left(\left(9 \cdot x1\right), \color{blue}{-1}\right)\right)\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right), \mathsf{+.f64}\left(\left(x1 \cdot 9\right), -1\right)\right)\right)\right) \]

      5. *-lowering-*.f64 68.9%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 9\right), -1\right)\right)\right)\right) \]

   10. Simplified 68.9%

       \[\leadsto -6 \cdot x2 + x1 \cdot \left(\left(x2 \cdot 2\right) \cdot \left(x2 \cdot 4 + -6\right) + \color{blue}{\left(x1 \cdot 9 + -1\right)}\right) \]

   11. Taylor expanded in x1 around inf

       \[\leadsto \color{blue}{9 \cdot {x1}^{2}} \]
   12. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto {x1}^{2} \cdot \color{blue}{9} \]

       2. unpow2 N/A

          \[\leadsto \left(x1 \cdot x1\right) \cdot 9 \]

       3. associate-*l* N/A

          \[\leadsto x1 \cdot \color{blue}{\left(x1 \cdot 9\right)} \]

       4. *-commutative N/A

          \[\leadsto x1 \cdot \left(9 \cdot \color{blue}{x1}\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x1, \color{blue}{\left(9 \cdot x1\right)}\right) \]

       6. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x1, \left(x1 \cdot \color{blue}{9}\right)\right) \]

       7. *-lowering-*.f64 90.4%

          \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, \color{blue}{9}\right)\right) \]

   13. Simplified 90.4%

       \[\leadsto \color{blue}{x1 \cdot \left(x1 \cdot 9\right)} \]

   if -3.30000000000000019e108 < x1 < -1.5e-57 or 3.0999999999999999e-15 < x1 < 4.5000000000000001e153

   1. Initial program 99.4%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x1 around 0

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

   7. Simplified 45.4%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(x2 \cdot 2\right) \cdot \left(x2 \cdot 4 + -6\right) + \left(x1 \cdot \left(\left(\left(\left(9 + 3 \cdot \left(x2 \cdot 2\right)\right) + x2 \cdot 10\right) - \left(x2 \cdot 4 + -6\right)\right) + -6\right) + -1\right)\right)} \]

   8. Taylor expanded in x2 around inf

      \[\leadsto \color{blue}{8 \cdot \left(x1 \cdot {x2}^{2}\right)} \]
   9. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(8, \color{blue}{\left(x1 \cdot {x2}^{2}\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(8, \mathsf{*.f64}\left(x1, \color{blue}{\left({x2}^{2}\right)}\right)\right) \]

      3. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(8, \mathsf{*.f64}\left(x1, \left(x2 \cdot \color{blue}{x2}\right)\right)\right) \]

      4. *-lowering-*.f64 41.7%

         \[\leadsto \mathsf{*.f64}\left(8, \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x2, \color{blue}{x2}\right)\right)\right) \]

   10. Simplified 41.7%

       \[\leadsto \color{blue}{8 \cdot \left(x1 \cdot \left(x2 \cdot x2\right)\right)} \]

   if -1.5e-57 < x1 < 3.0999999999999999e-15

   1. Initial program 99.4%

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

   3. Simplified 99.5%

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

   6. Applied egg-rr 99.5%

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

   7. Taylor expanded in x1 around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(\color{blue}{\left(12 \cdot {x1}^{4}\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(-6, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]
   8. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(12, \left({x1}^{4}\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(-6, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(12, \left({x1}^{\left(2 \cdot 2\right)}\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(-6, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      3. pow-sqr N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(12, \left({x1}^{2} \cdot {x1}^{2}\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(-6, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(12, \mathsf{*.f64}\left(\left({x1}^{2}\right), \left({x1}^{2}\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(-6, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      5. unpow2 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(12, \mathsf{*.f64}\left(\left(x1 \cdot x1\right), \left({x1}^{2}\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(-6, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(12, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left({x1}^{2}\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(-6, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(12, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left(x1 \cdot x1\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(-6, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      8. *-lowering-*.f64 80.9%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(12, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(-6, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

   9. Simplified 80.9%

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

   10. Taylor expanded in x1 around 0

       \[\leadsto \color{blue}{-6 \cdot x2 + -1 \cdot x1} \]
   11. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto -6 \cdot x2 + \left(\mathsf{neg}\left(x1\right)\right) \]

       2. unsub-neg N/A

          \[\leadsto -6 \cdot x2 - \color{blue}{x1} \]

       3. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\left(-6 \cdot x2\right), \color{blue}{x1}\right) \]

       4. *-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(\left(x2 \cdot -6\right), x1\right) \]

       5. *-lowering-*.f64 81.1%

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x2, -6\right), x1\right) \]

   12. Simplified 81.1%

       \[\leadsto \color{blue}{x2 \cdot -6 - x1} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 14: 95.7% accurate, 4.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -8.5 \cdot 10^{+14}:\\ \;\;\;\;\left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right)\right) \cdot \left(6 - \frac{\frac{x2 \cdot -8}{x1}}{x1}\right)\\ \mathbf{elif}\;x1 \leq 820:\\ \;\;\;\;x2 \cdot \left(x1 \cdot -12 + \left(-6 + x1 \cdot \left(x2 \cdot 8\right)\right)\right) - x1\\ \mathbf{else}:\\ \;\;\;\;\left(x1 \cdot x1\right) \cdot \left(x1 \cdot \left(-3 + x1 \cdot 6\right) + \left(-3 + x2 \cdot 8\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -8.5e+14)
   (* (* (* x1 x1) (* x1 x1)) (- 6.0 (/ (/ (* x2 -8.0) x1) x1)))
   (if (<= x1 820.0)
     (- (* x2 (+ (* x1 -12.0) (+ -6.0 (* x1 (* x2 8.0))))) x1)
     (* (* x1 x1) (+ (* x1 (+ -3.0 (* x1 6.0))) (+ -3.0 (* x2 8.0)))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -8.5e+14) {
		tmp = ((x1 * x1) * (x1 * x1)) * (6.0 - (((x2 * -8.0) / x1) / x1));
	} else if (x1 <= 820.0) {
		tmp = (x2 * ((x1 * -12.0) + (-6.0 + (x1 * (x2 * 8.0))))) - x1;
	} else {
		tmp = (x1 * x1) * ((x1 * (-3.0 + (x1 * 6.0))) + (-3.0 + (x2 * 8.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x1 <= (-8.5d+14)) then
        tmp = ((x1 * x1) * (x1 * x1)) * (6.0d0 - (((x2 * (-8.0d0)) / x1) / x1))
    else if (x1 <= 820.0d0) then
        tmp = (x2 * ((x1 * (-12.0d0)) + ((-6.0d0) + (x1 * (x2 * 8.0d0))))) - x1
    else
        tmp = (x1 * x1) * ((x1 * ((-3.0d0) + (x1 * 6.0d0))) + ((-3.0d0) + (x2 * 8.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= -8.5e+14) {
		tmp = ((x1 * x1) * (x1 * x1)) * (6.0 - (((x2 * -8.0) / x1) / x1));
	} else if (x1 <= 820.0) {
		tmp = (x2 * ((x1 * -12.0) + (-6.0 + (x1 * (x2 * 8.0))))) - x1;
	} else {
		tmp = (x1 * x1) * ((x1 * (-3.0 + (x1 * 6.0))) + (-3.0 + (x2 * 8.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -8.5e+14:
		tmp = ((x1 * x1) * (x1 * x1)) * (6.0 - (((x2 * -8.0) / x1) / x1))
	elif x1 <= 820.0:
		tmp = (x2 * ((x1 * -12.0) + (-6.0 + (x1 * (x2 * 8.0))))) - x1
	else:
		tmp = (x1 * x1) * ((x1 * (-3.0 + (x1 * 6.0))) + (-3.0 + (x2 * 8.0)))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -8.5e+14)
		tmp = Float64(Float64(Float64(x1 * x1) * Float64(x1 * x1)) * Float64(6.0 - Float64(Float64(Float64(x2 * -8.0) / x1) / x1)));
	elseif (x1 <= 820.0)
		tmp = Float64(Float64(x2 * Float64(Float64(x1 * -12.0) + Float64(-6.0 + Float64(x1 * Float64(x2 * 8.0))))) - x1);
	else
		tmp = Float64(Float64(x1 * x1) * Float64(Float64(x1 * Float64(-3.0 + Float64(x1 * 6.0))) + Float64(-3.0 + Float64(x2 * 8.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -8.5e+14)
		tmp = ((x1 * x1) * (x1 * x1)) * (6.0 - (((x2 * -8.0) / x1) / x1));
	elseif (x1 <= 820.0)
		tmp = (x2 * ((x1 * -12.0) + (-6.0 + (x1 * (x2 * 8.0))))) - x1;
	else
		tmp = (x1 * x1) * ((x1 * (-3.0 + (x1 * 6.0))) + (-3.0 + (x2 * 8.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -8.5e+14], N[(N[(N[(x1 * x1), $MachinePrecision] * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] * N[(6.0 - N[(N[(N[(x2 * -8.0), $MachinePrecision] / x1), $MachinePrecision] / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 820.0], N[(N[(x2 * N[(N[(x1 * -12.0), $MachinePrecision] + N[(-6.0 + N[(x1 * N[(x2 * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision], N[(N[(x1 * x1), $MachinePrecision] * N[(N[(x1 * N[(-3.0 + N[(x1 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-3.0 + N[(x2 * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -8.5e14

   1. Initial program 27.1%

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

   3. Simplified 27.1%

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

   5. Taylor expanded in x1 around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, -6\right)\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-6, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 4\right)\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \color{blue}{9}\right)\right)\right)\right)\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 27.1%

      \[\leadsto \frac{3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right)}{x1 \cdot x1 + 1} + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(x1 \cdot \left(x1 \cdot -6\right) + \frac{2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)}{x1 \cdot x1 + 1} \cdot \left(x1 \cdot \left(-6 + \left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right) \cdot \frac{2}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot 4\right)\right) + x1 \cdot \left(2 + x1 \cdot \left(x1 + \color{blue}{9}\right)\right)\right) \]

   8. Taylor expanded in x1 around -inf

      \[\leadsto \color{blue}{{x1}^{4} \cdot \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)} \]
   9. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{4}\right), \color{blue}{\left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)}\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{\left(2 \cdot 2\right)}\right), \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)\right) \]

      3. pow-sqr N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{2} \cdot {x1}^{2}\right), \left(\color{blue}{6} + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left({x1}^{2}\right), \left({x1}^{2}\right)\right), \left(\color{blue}{6} + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)\right) \]

      5. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x1 \cdot x1\right), \left({x1}^{2}\right)\right), \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left({x1}^{2}\right)\right), \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left(x1 \cdot x1\right)\right), \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)\right) \]

      9. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \left(6 + \left(\mathsf{neg}\left(\frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)\right)\right)\right) \]

      10. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \left(6 - \color{blue}{\frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}}\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \color{blue}{\left(\frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)}\right)\right) \]

      12. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \mathsf{/.f64}\left(\left(3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}\right), \color{blue}{x1}\right)\right)\right) \]

   10. Simplified 94.9%

       \[\leadsto \color{blue}{\left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right)\right) \cdot \left(6 - \frac{3 - \frac{x2 \cdot 8 + -3}{x1}}{x1}\right)} \]

   11. Taylor expanded in x2 around inf

       \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \color{blue}{\left(-8 \cdot \frac{x2}{{x1}^{2}}\right)}\right)\right) \]
   12. Step-by-step derivation

       1. associate-*r/ N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \left(\frac{-8 \cdot x2}{\color{blue}{{x1}^{2}}}\right)\right)\right) \]

       2. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \left(\frac{\left(\mathsf{neg}\left(8\right)\right) \cdot x2}{{x1}^{2}}\right)\right)\right) \]

       3. distribute-lft-neg-in N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \left(\frac{\mathsf{neg}\left(8 \cdot x2\right)}{{\color{blue}{x1}}^{2}}\right)\right)\right) \]

       4. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \left(\frac{\mathsf{neg}\left(8 \cdot x2\right)}{x1 \cdot \color{blue}{x1}}\right)\right)\right) \]

       5. associate-/r* N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \left(\frac{\frac{\mathsf{neg}\left(8 \cdot x2\right)}{x1}}{\color{blue}{x1}}\right)\right)\right) \]

       6. distribute-neg-frac N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \left(\frac{\mathsf{neg}\left(\frac{8 \cdot x2}{x1}\right)}{x1}\right)\right)\right) \]

       7. associate-*r/ N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \left(\frac{\mathsf{neg}\left(8 \cdot \frac{x2}{x1}\right)}{x1}\right)\right)\right) \]

       8. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \mathsf{/.f64}\left(\left(\mathsf{neg}\left(8 \cdot \frac{x2}{x1}\right)\right), \color{blue}{x1}\right)\right)\right) \]

       9. associate-*r/ N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \mathsf{/.f64}\left(\left(\mathsf{neg}\left(\frac{8 \cdot x2}{x1}\right)\right), x1\right)\right)\right) \]

       10. distribute-neg-frac N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \mathsf{/.f64}\left(\left(\frac{\mathsf{neg}\left(8 \cdot x2\right)}{x1}\right), x1\right)\right)\right) \]

       11. /-lowering-/.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(\mathsf{neg}\left(8 \cdot x2\right)\right), x1\right), x1\right)\right)\right) \]

       12. *-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(\mathsf{neg}\left(x2 \cdot 8\right)\right), x1\right), x1\right)\right)\right) \]

       13. distribute-rgt-neg-in N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(x2 \cdot \left(\mathsf{neg}\left(8\right)\right)\right), x1\right), x1\right)\right)\right) \]

       14. metadata-eval N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(x2 \cdot -8\right), x1\right), x1\right)\right)\right) \]

       15. *-lowering-*.f64 94.9%

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x2, -8\right), x1\right), x1\right)\right)\right) \]

   13. Simplified 94.9%

       \[\leadsto \left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right)\right) \cdot \left(6 - \color{blue}{\frac{\frac{x2 \cdot -8}{x1}}{x1}}\right) \]

   if -8.5e14 < x1 < 820

   1. Initial program 99.4%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x1 around 0

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

   7. Simplified 87.5%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(x2 \cdot 2\right) \cdot \left(x2 \cdot 4 + -6\right) + \left(x1 \cdot \left(\left(\left(\left(9 + 3 \cdot \left(x2 \cdot 2\right)\right) + x2 \cdot 10\right) - \left(x2 \cdot 4 + -6\right)\right) + -6\right) + -1\right)\right)} \]

   8. Taylor expanded in x2 around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right), \color{blue}{\left(9 \cdot x1 - 1\right)}\right)\right)\right) \]
   9. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right), \left(9 \cdot x1 + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right), \left(9 \cdot x1 + -1\right)\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right), \mathsf{+.f64}\left(\left(9 \cdot x1\right), \color{blue}{-1}\right)\right)\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right), \mathsf{+.f64}\left(\left(x1 \cdot 9\right), -1\right)\right)\right)\right) \]

      5. *-lowering-*.f64 87.5%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 9\right), -1\right)\right)\right)\right) \]

   10. Simplified 87.5%

       \[\leadsto -6 \cdot x2 + x1 \cdot \left(\left(x2 \cdot 2\right) \cdot \left(x2 \cdot 4 + -6\right) + \color{blue}{\left(x1 \cdot 9 + -1\right)}\right) \]

   11. Taylor expanded in x2 around 0

       \[\leadsto \color{blue}{x1 \cdot \left(9 \cdot x1 - 1\right) + x2 \cdot \left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right)} \]
   12. Step-by-step derivation

       1. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\left(x1 \cdot \left(9 \cdot x1 - 1\right)\right), \color{blue}{\left(x2 \cdot \left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right)\right)}\right) \]

       2. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \left(9 \cdot x1 - 1\right)\right), \left(\color{blue}{x2} \cdot \left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right)\right)\right) \]

       3. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \left(9 \cdot x1 + \left(\mathsf{neg}\left(1\right)\right)\right)\right), \left(x2 \cdot \left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right)\right)\right) \]

       4. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \left(9 \cdot x1 + -1\right)\right), \left(x2 \cdot \left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right)\right)\right) \]

       5. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\left(9 \cdot x1\right), -1\right)\right), \left(x2 \cdot \left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right)\right)\right) \]

       6. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\left(x1 \cdot 9\right), -1\right)\right), \left(x2 \cdot \left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right)\right)\right) \]

       7. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 9\right), -1\right)\right), \left(x2 \cdot \left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right)\right)\right) \]

       8. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 9\right), -1\right)\right), \mathsf{*.f64}\left(x2, \color{blue}{\left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right)}\right)\right) \]

       9. associate--l+ N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 9\right), -1\right)\right), \mathsf{*.f64}\left(x2, \left(-12 \cdot x1 + \color{blue}{\left(8 \cdot \left(x1 \cdot x2\right) - 6\right)}\right)\right)\right) \]

       10. +-lowering-+.f64 N/A

           \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 9\right), -1\right)\right), \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\left(-12 \cdot x1\right), \color{blue}{\left(8 \cdot \left(x1 \cdot x2\right) - 6\right)}\right)\right)\right) \]

       11. *-commutative N/A

           \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 9\right), -1\right)\right), \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\left(x1 \cdot -12\right), \left(\color{blue}{8 \cdot \left(x1 \cdot x2\right)} - 6\right)\right)\right)\right) \]

       12. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 9\right), -1\right)\right), \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, -12\right), \left(\color{blue}{8 \cdot \left(x1 \cdot x2\right)} - 6\right)\right)\right)\right) \]

       13. sub-neg N/A

           \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 9\right), -1\right)\right), \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, -12\right), \left(8 \cdot \left(x1 \cdot x2\right) + \color{blue}{\left(\mathsf{neg}\left(6\right)\right)}\right)\right)\right)\right) \]

       14. metadata-eval N/A

           \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 9\right), -1\right)\right), \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, -12\right), \left(8 \cdot \left(x1 \cdot x2\right) + -6\right)\right)\right)\right) \]

       15. +-lowering-+.f64 N/A

           \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 9\right), -1\right)\right), \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, -12\right), \mathsf{+.f64}\left(\left(8 \cdot \left(x1 \cdot x2\right)\right), \color{blue}{-6}\right)\right)\right)\right) \]

       16. *-commutative N/A

           \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 9\right), -1\right)\right), \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, -12\right), \mathsf{+.f64}\left(\left(\left(x1 \cdot x2\right) \cdot 8\right), -6\right)\right)\right)\right) \]

       17. associate-*l* N/A

           \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 9\right), -1\right)\right), \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, -12\right), \mathsf{+.f64}\left(\left(x1 \cdot \left(x2 \cdot 8\right)\right), -6\right)\right)\right)\right) \]

       18. *-commutative N/A

           \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 9\right), -1\right)\right), \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, -12\right), \mathsf{+.f64}\left(\left(x1 \cdot \left(8 \cdot x2\right)\right), -6\right)\right)\right)\right) \]

       19. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 9\right), -1\right)\right), \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, -12\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \left(8 \cdot x2\right)\right), -6\right)\right)\right)\right) \]

       20. *-commutative N/A

           \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 9\right), -1\right)\right), \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, -12\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \left(x2 \cdot 8\right)\right), -6\right)\right)\right)\right) \]

       21. *-lowering-*.f64 98.4%

           \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 9\right), -1\right)\right), \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, -12\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x2, 8\right)\right), -6\right)\right)\right)\right) \]

   13. Simplified 98.4%

       \[\leadsto \color{blue}{x1 \cdot \left(x1 \cdot 9 + -1\right) + x2 \cdot \left(x1 \cdot -12 + \left(x1 \cdot \left(x2 \cdot 8\right) + -6\right)\right)} \]

   14. Taylor expanded in x1 around 0

       \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(-1 \cdot x1\right)}, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, -12\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x2, 8\right)\right), -6\right)\right)\right)\right) \]
   15. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\mathsf{neg}\left(x1\right)\right), \mathsf{*.f64}\left(\color{blue}{x2}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, -12\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x2, 8\right)\right), -6\right)\right)\right)\right) \]

       2. neg-sub0 N/A

          \[\leadsto \mathsf{+.f64}\left(\left(0 - x1\right), \mathsf{*.f64}\left(\color{blue}{x2}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, -12\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x2, 8\right)\right), -6\right)\right)\right)\right) \]

       3. --lowering--.f64 97.9%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(0, x1\right), \mathsf{*.f64}\left(\color{blue}{x2}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, -12\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x2, 8\right)\right), -6\right)\right)\right)\right) \]

   16. Simplified 97.9%

       \[\leadsto \color{blue}{\left(0 - x1\right)} + x2 \cdot \left(x1 \cdot -12 + \left(x1 \cdot \left(x2 \cdot 8\right) + -6\right)\right) \]

   if 820 < x1

   1. Initial program 48.9%

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

   3. Simplified 49.0%

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

   5. Taylor expanded in x1 around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, -6\right)\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-6, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 4\right)\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \color{blue}{9}\right)\right)\right)\right)\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 49.0%

      \[\leadsto \frac{3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right)}{x1 \cdot x1 + 1} + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(x1 \cdot \left(x1 \cdot -6\right) + \frac{2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)}{x1 \cdot x1 + 1} \cdot \left(x1 \cdot \left(-6 + \left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right) \cdot \frac{2}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot 4\right)\right) + x1 \cdot \left(2 + x1 \cdot \left(x1 + \color{blue}{9}\right)\right)\right) \]

   8. Taylor expanded in x1 around -inf

      \[\leadsto \color{blue}{{x1}^{4} \cdot \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)} \]
   9. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{4}\right), \color{blue}{\left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)}\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{\left(2 \cdot 2\right)}\right), \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)\right) \]

      3. pow-sqr N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{2} \cdot {x1}^{2}\right), \left(\color{blue}{6} + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left({x1}^{2}\right), \left({x1}^{2}\right)\right), \left(\color{blue}{6} + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)\right) \]

      5. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x1 \cdot x1\right), \left({x1}^{2}\right)\right), \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left({x1}^{2}\right)\right), \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left(x1 \cdot x1\right)\right), \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)\right) \]

      9. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \left(6 + \left(\mathsf{neg}\left(\frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)\right)\right)\right) \]

      10. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \left(6 - \color{blue}{\frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}}\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \color{blue}{\left(\frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)}\right)\right) \]

      12. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \mathsf{/.f64}\left(\left(3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}\right), \color{blue}{x1}\right)\right)\right) \]

   10. Simplified 90.8%

       \[\leadsto \color{blue}{\left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right)\right) \cdot \left(6 - \frac{3 - \frac{x2 \cdot 8 + -3}{x1}}{x1}\right)} \]

   11. Taylor expanded in x1 around 0

       \[\leadsto \color{blue}{{x1}^{2} \cdot \left(\left(8 \cdot x2 + x1 \cdot \left(6 \cdot x1 - 3\right)\right) - 3\right)} \]
   12. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\left({x1}^{2}\right), \color{blue}{\left(\left(8 \cdot x2 + x1 \cdot \left(6 \cdot x1 - 3\right)\right) - 3\right)}\right) \]

       2. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(\left(x1 \cdot x1\right), \left(\color{blue}{\left(8 \cdot x2 + x1 \cdot \left(6 \cdot x1 - 3\right)\right)} - 3\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left(\color{blue}{\left(8 \cdot x2 + x1 \cdot \left(6 \cdot x1 - 3\right)\right)} - 3\right)\right) \]

       4. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left(\left(x1 \cdot \left(6 \cdot x1 - 3\right) + 8 \cdot x2\right) - 3\right)\right) \]

       5. associate--l+ N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left(x1 \cdot \left(6 \cdot x1 - 3\right) + \color{blue}{\left(8 \cdot x2 - 3\right)}\right)\right) \]

       6. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\left(x1 \cdot \left(6 \cdot x1 - 3\right)\right), \color{blue}{\left(8 \cdot x2 - 3\right)}\right)\right) \]

       7. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \left(6 \cdot x1 - 3\right)\right), \left(\color{blue}{8 \cdot x2} - 3\right)\right)\right) \]

       8. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \left(6 \cdot x1 + \left(\mathsf{neg}\left(3\right)\right)\right)\right), \left(8 \cdot \color{blue}{x2} - 3\right)\right)\right) \]

       9. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \left(6 \cdot x1 + -3\right)\right), \left(8 \cdot x2 - 3\right)\right)\right) \]

       10. +-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \left(-3 + 6 \cdot x1\right)\right), \left(8 \cdot \color{blue}{x2} - 3\right)\right)\right) \]

       11. +-lowering-+.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-3, \left(6 \cdot x1\right)\right)\right), \left(8 \cdot \color{blue}{x2} - 3\right)\right)\right) \]

       12. *-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-3, \left(x1 \cdot 6\right)\right)\right), \left(8 \cdot x2 - 3\right)\right)\right) \]

       13. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-3, \mathsf{*.f64}\left(x1, 6\right)\right)\right), \left(8 \cdot x2 - 3\right)\right)\right) \]

       14. sub-neg N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-3, \mathsf{*.f64}\left(x1, 6\right)\right)\right), \left(8 \cdot x2 + \color{blue}{\left(\mathsf{neg}\left(3\right)\right)}\right)\right)\right) \]

       15. metadata-eval N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-3, \mathsf{*.f64}\left(x1, 6\right)\right)\right), \left(8 \cdot x2 + -3\right)\right)\right) \]

       16. +-lowering-+.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-3, \mathsf{*.f64}\left(x1, 6\right)\right)\right), \mathsf{+.f64}\left(\left(8 \cdot x2\right), \color{blue}{-3}\right)\right)\right) \]

       17. *-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-3, \mathsf{*.f64}\left(x1, 6\right)\right)\right), \mathsf{+.f64}\left(\left(x2 \cdot 8\right), -3\right)\right)\right) \]

       18. *-lowering-*.f64 91.0%

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-3, \mathsf{*.f64}\left(x1, 6\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 8\right), -3\right)\right)\right) \]

   13. Simplified 91.0%

       \[\leadsto \color{blue}{\left(x1 \cdot x1\right) \cdot \left(x1 \cdot \left(-3 + x1 \cdot 6\right) + \left(x2 \cdot 8 + -3\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 95.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -8.5 \cdot 10^{+14}:\\ \;\;\;\;\left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right)\right) \cdot \left(6 - \frac{\frac{x2 \cdot -8}{x1}}{x1}\right)\\ \mathbf{elif}\;x1 \leq 820:\\ \;\;\;\;x2 \cdot \left(x1 \cdot -12 + \left(-6 + x1 \cdot \left(x2 \cdot 8\right)\right)\right) - x1\\ \mathbf{else}:\\ \;\;\;\;\left(x1 \cdot x1\right) \cdot \left(x1 \cdot \left(-3 + x1 \cdot 6\right) + \left(-3 + x2 \cdot 8\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 90.1% accurate, 4.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -4.8 \cdot 10^{+15}:\\ \;\;\;\;\left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right)\right) \cdot \left(6 - \frac{\frac{x2 \cdot -8}{x1}}{x1}\right)\\ \mathbf{elif}\;x1 \leq 16000:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + \left(x2 \cdot 4\right) \cdot \left(2 \cdot x2 + -3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x1 \cdot x1\right) \cdot \left(x1 \cdot \left(-3 + x1 \cdot 6\right) + \left(-3 + x2 \cdot 8\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -4.8e+15)
   (* (* (* x1 x1) (* x1 x1)) (- 6.0 (/ (/ (* x2 -8.0) x1) x1)))
   (if (<= x1 16000.0)
     (+ (* x2 -6.0) (* x1 (+ -1.0 (* (* x2 4.0) (+ (* 2.0 x2) -3.0)))))
     (* (* x1 x1) (+ (* x1 (+ -3.0 (* x1 6.0))) (+ -3.0 (* x2 8.0)))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -4.8e+15) {
		tmp = ((x1 * x1) * (x1 * x1)) * (6.0 - (((x2 * -8.0) / x1) / x1));
	} else if (x1 <= 16000.0) {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + ((x2 * 4.0) * ((2.0 * x2) + -3.0))));
	} else {
		tmp = (x1 * x1) * ((x1 * (-3.0 + (x1 * 6.0))) + (-3.0 + (x2 * 8.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x1 <= (-4.8d+15)) then
        tmp = ((x1 * x1) * (x1 * x1)) * (6.0d0 - (((x2 * (-8.0d0)) / x1) / x1))
    else if (x1 <= 16000.0d0) then
        tmp = (x2 * (-6.0d0)) + (x1 * ((-1.0d0) + ((x2 * 4.0d0) * ((2.0d0 * x2) + (-3.0d0)))))
    else
        tmp = (x1 * x1) * ((x1 * ((-3.0d0) + (x1 * 6.0d0))) + ((-3.0d0) + (x2 * 8.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= -4.8e+15) {
		tmp = ((x1 * x1) * (x1 * x1)) * (6.0 - (((x2 * -8.0) / x1) / x1));
	} else if (x1 <= 16000.0) {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + ((x2 * 4.0) * ((2.0 * x2) + -3.0))));
	} else {
		tmp = (x1 * x1) * ((x1 * (-3.0 + (x1 * 6.0))) + (-3.0 + (x2 * 8.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -4.8e+15:
		tmp = ((x1 * x1) * (x1 * x1)) * (6.0 - (((x2 * -8.0) / x1) / x1))
	elif x1 <= 16000.0:
		tmp = (x2 * -6.0) + (x1 * (-1.0 + ((x2 * 4.0) * ((2.0 * x2) + -3.0))))
	else:
		tmp = (x1 * x1) * ((x1 * (-3.0 + (x1 * 6.0))) + (-3.0 + (x2 * 8.0)))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -4.8e+15)
		tmp = Float64(Float64(Float64(x1 * x1) * Float64(x1 * x1)) * Float64(6.0 - Float64(Float64(Float64(x2 * -8.0) / x1) / x1)));
	elseif (x1 <= 16000.0)
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(-1.0 + Float64(Float64(x2 * 4.0) * Float64(Float64(2.0 * x2) + -3.0)))));
	else
		tmp = Float64(Float64(x1 * x1) * Float64(Float64(x1 * Float64(-3.0 + Float64(x1 * 6.0))) + Float64(-3.0 + Float64(x2 * 8.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -4.8e+15)
		tmp = ((x1 * x1) * (x1 * x1)) * (6.0 - (((x2 * -8.0) / x1) / x1));
	elseif (x1 <= 16000.0)
		tmp = (x2 * -6.0) + (x1 * (-1.0 + ((x2 * 4.0) * ((2.0 * x2) + -3.0))));
	else
		tmp = (x1 * x1) * ((x1 * (-3.0 + (x1 * 6.0))) + (-3.0 + (x2 * 8.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -4.8e+15], N[(N[(N[(x1 * x1), $MachinePrecision] * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] * N[(6.0 - N[(N[(N[(x2 * -8.0), $MachinePrecision] / x1), $MachinePrecision] / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 16000.0], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(-1.0 + N[(N[(x2 * 4.0), $MachinePrecision] * N[(N[(2.0 * x2), $MachinePrecision] + -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x1 * x1), $MachinePrecision] * N[(N[(x1 * N[(-3.0 + N[(x1 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-3.0 + N[(x2 * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -4.8e15

   1. Initial program 27.1%

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

   3. Simplified 27.1%

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

   5. Taylor expanded in x1 around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, -6\right)\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-6, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 4\right)\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \color{blue}{9}\right)\right)\right)\right)\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 27.1%

      \[\leadsto \frac{3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right)}{x1 \cdot x1 + 1} + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(x1 \cdot \left(x1 \cdot -6\right) + \frac{2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)}{x1 \cdot x1 + 1} \cdot \left(x1 \cdot \left(-6 + \left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right) \cdot \frac{2}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot 4\right)\right) + x1 \cdot \left(2 + x1 \cdot \left(x1 + \color{blue}{9}\right)\right)\right) \]

   8. Taylor expanded in x1 around -inf

      \[\leadsto \color{blue}{{x1}^{4} \cdot \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)} \]
   9. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{4}\right), \color{blue}{\left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)}\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{\left(2 \cdot 2\right)}\right), \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)\right) \]

      3. pow-sqr N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{2} \cdot {x1}^{2}\right), \left(\color{blue}{6} + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left({x1}^{2}\right), \left({x1}^{2}\right)\right), \left(\color{blue}{6} + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)\right) \]

      5. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x1 \cdot x1\right), \left({x1}^{2}\right)\right), \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left({x1}^{2}\right)\right), \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left(x1 \cdot x1\right)\right), \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)\right) \]

      9. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \left(6 + \left(\mathsf{neg}\left(\frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)\right)\right)\right) \]

      10. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \left(6 - \color{blue}{\frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}}\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \color{blue}{\left(\frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)}\right)\right) \]

      12. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \mathsf{/.f64}\left(\left(3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}\right), \color{blue}{x1}\right)\right)\right) \]

   10. Simplified 94.9%

       \[\leadsto \color{blue}{\left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right)\right) \cdot \left(6 - \frac{3 - \frac{x2 \cdot 8 + -3}{x1}}{x1}\right)} \]

   11. Taylor expanded in x2 around inf

       \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \color{blue}{\left(-8 \cdot \frac{x2}{{x1}^{2}}\right)}\right)\right) \]
   12. Step-by-step derivation

       1. associate-*r/ N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \left(\frac{-8 \cdot x2}{\color{blue}{{x1}^{2}}}\right)\right)\right) \]

       2. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \left(\frac{\left(\mathsf{neg}\left(8\right)\right) \cdot x2}{{x1}^{2}}\right)\right)\right) \]

       3. distribute-lft-neg-in N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \left(\frac{\mathsf{neg}\left(8 \cdot x2\right)}{{\color{blue}{x1}}^{2}}\right)\right)\right) \]

       4. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \left(\frac{\mathsf{neg}\left(8 \cdot x2\right)}{x1 \cdot \color{blue}{x1}}\right)\right)\right) \]

       5. associate-/r* N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \left(\frac{\frac{\mathsf{neg}\left(8 \cdot x2\right)}{x1}}{\color{blue}{x1}}\right)\right)\right) \]

       6. distribute-neg-frac N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \left(\frac{\mathsf{neg}\left(\frac{8 \cdot x2}{x1}\right)}{x1}\right)\right)\right) \]

       7. associate-*r/ N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \left(\frac{\mathsf{neg}\left(8 \cdot \frac{x2}{x1}\right)}{x1}\right)\right)\right) \]

       8. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \mathsf{/.f64}\left(\left(\mathsf{neg}\left(8 \cdot \frac{x2}{x1}\right)\right), \color{blue}{x1}\right)\right)\right) \]

       9. associate-*r/ N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \mathsf{/.f64}\left(\left(\mathsf{neg}\left(\frac{8 \cdot x2}{x1}\right)\right), x1\right)\right)\right) \]

       10. distribute-neg-frac N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \mathsf{/.f64}\left(\left(\frac{\mathsf{neg}\left(8 \cdot x2\right)}{x1}\right), x1\right)\right)\right) \]

       11. /-lowering-/.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(\mathsf{neg}\left(8 \cdot x2\right)\right), x1\right), x1\right)\right)\right) \]

       12. *-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(\mathsf{neg}\left(x2 \cdot 8\right)\right), x1\right), x1\right)\right)\right) \]

       13. distribute-rgt-neg-in N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(x2 \cdot \left(\mathsf{neg}\left(8\right)\right)\right), x1\right), x1\right)\right)\right) \]

       14. metadata-eval N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(x2 \cdot -8\right), x1\right), x1\right)\right)\right) \]

       15. *-lowering-*.f64 94.9%

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x2, -8\right), x1\right), x1\right)\right)\right) \]

   13. Simplified 94.9%

       \[\leadsto \left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right)\right) \cdot \left(6 - \color{blue}{\frac{\frac{x2 \cdot -8}{x1}}{x1}}\right) \]

   if -4.8e15 < x1 < 16000

   1. Initial program 99.4%

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

   3. Taylor expanded in x1 around 0

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 1\right)} \]
   4. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(-6 \cdot x2\right), \color{blue}{\left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 1\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \left(\color{blue}{x1} \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 1\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \color{blue}{\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 1\right)}\right)\right) \]

      4. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + -1\right)\right)\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right), \color{blue}{-1}\right)\right)\right) \]

      7. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\left(\left(4 \cdot x2\right) \cdot \left(2 \cdot x2 - 3\right)\right), -1\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(4 \cdot x2\right), \left(2 \cdot x2 - 3\right)\right), -1\right)\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(x2 \cdot 4\right), \left(2 \cdot x2 - 3\right)\right), -1\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 4\right), \left(2 \cdot x2 - 3\right)\right), -1\right)\right)\right) \]

      11. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 4\right), \left(2 \cdot x2 + \left(\mathsf{neg}\left(3\right)\right)\right)\right), -1\right)\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 4\right), \left(2 \cdot x2 + -3\right)\right), -1\right)\right)\right) \]

      13. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 4\right), \mathsf{+.f64}\left(\left(2 \cdot x2\right), -3\right)\right), -1\right)\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 4\right), \mathsf{+.f64}\left(\left(x2 \cdot 2\right), -3\right)\right), -1\right)\right)\right) \]

      15. *-lowering-*.f64 87.1%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 4\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 2\right), -3\right)\right), -1\right)\right)\right) \]

   5. Simplified 87.1%

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

   if 16000 < x1

   1. Initial program 48.9%

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

   3. Simplified 49.0%

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

   5. Taylor expanded in x1 around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, -6\right)\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-6, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 4\right)\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \color{blue}{9}\right)\right)\right)\right)\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 49.0%

      \[\leadsto \frac{3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right)}{x1 \cdot x1 + 1} + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(x1 \cdot \left(x1 \cdot -6\right) + \frac{2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)}{x1 \cdot x1 + 1} \cdot \left(x1 \cdot \left(-6 + \left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right) \cdot \frac{2}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot 4\right)\right) + x1 \cdot \left(2 + x1 \cdot \left(x1 + \color{blue}{9}\right)\right)\right) \]

   8. Taylor expanded in x1 around -inf

      \[\leadsto \color{blue}{{x1}^{4} \cdot \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)} \]
   9. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{4}\right), \color{blue}{\left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)}\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{\left(2 \cdot 2\right)}\right), \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)\right) \]

      3. pow-sqr N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{2} \cdot {x1}^{2}\right), \left(\color{blue}{6} + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left({x1}^{2}\right), \left({x1}^{2}\right)\right), \left(\color{blue}{6} + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)\right) \]

      5. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x1 \cdot x1\right), \left({x1}^{2}\right)\right), \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left({x1}^{2}\right)\right), \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left(x1 \cdot x1\right)\right), \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)\right) \]

      9. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \left(6 + \left(\mathsf{neg}\left(\frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)\right)\right)\right) \]

      10. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \left(6 - \color{blue}{\frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}}\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \color{blue}{\left(\frac{3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}}{x1}\right)}\right)\right) \]

      12. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{\_.f64}\left(6, \mathsf{/.f64}\left(\left(3 + -1 \cdot \frac{8 \cdot x2 - 3}{x1}\right), \color{blue}{x1}\right)\right)\right) \]

   10. Simplified 90.8%

       \[\leadsto \color{blue}{\left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right)\right) \cdot \left(6 - \frac{3 - \frac{x2 \cdot 8 + -3}{x1}}{x1}\right)} \]

   11. Taylor expanded in x1 around 0

       \[\leadsto \color{blue}{{x1}^{2} \cdot \left(\left(8 \cdot x2 + x1 \cdot \left(6 \cdot x1 - 3\right)\right) - 3\right)} \]
   12. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\left({x1}^{2}\right), \color{blue}{\left(\left(8 \cdot x2 + x1 \cdot \left(6 \cdot x1 - 3\right)\right) - 3\right)}\right) \]

       2. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(\left(x1 \cdot x1\right), \left(\color{blue}{\left(8 \cdot x2 + x1 \cdot \left(6 \cdot x1 - 3\right)\right)} - 3\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left(\color{blue}{\left(8 \cdot x2 + x1 \cdot \left(6 \cdot x1 - 3\right)\right)} - 3\right)\right) \]

       4. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left(\left(x1 \cdot \left(6 \cdot x1 - 3\right) + 8 \cdot x2\right) - 3\right)\right) \]

       5. associate--l+ N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left(x1 \cdot \left(6 \cdot x1 - 3\right) + \color{blue}{\left(8 \cdot x2 - 3\right)}\right)\right) \]

       6. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\left(x1 \cdot \left(6 \cdot x1 - 3\right)\right), \color{blue}{\left(8 \cdot x2 - 3\right)}\right)\right) \]

       7. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \left(6 \cdot x1 - 3\right)\right), \left(\color{blue}{8 \cdot x2} - 3\right)\right)\right) \]

       8. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \left(6 \cdot x1 + \left(\mathsf{neg}\left(3\right)\right)\right)\right), \left(8 \cdot \color{blue}{x2} - 3\right)\right)\right) \]

       9. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \left(6 \cdot x1 + -3\right)\right), \left(8 \cdot x2 - 3\right)\right)\right) \]

       10. +-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \left(-3 + 6 \cdot x1\right)\right), \left(8 \cdot \color{blue}{x2} - 3\right)\right)\right) \]

       11. +-lowering-+.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-3, \left(6 \cdot x1\right)\right)\right), \left(8 \cdot \color{blue}{x2} - 3\right)\right)\right) \]

       12. *-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-3, \left(x1 \cdot 6\right)\right)\right), \left(8 \cdot x2 - 3\right)\right)\right) \]

       13. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-3, \mathsf{*.f64}\left(x1, 6\right)\right)\right), \left(8 \cdot x2 - 3\right)\right)\right) \]

       14. sub-neg N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-3, \mathsf{*.f64}\left(x1, 6\right)\right)\right), \left(8 \cdot x2 + \color{blue}{\left(\mathsf{neg}\left(3\right)\right)}\right)\right)\right) \]

       15. metadata-eval N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-3, \mathsf{*.f64}\left(x1, 6\right)\right)\right), \left(8 \cdot x2 + -3\right)\right)\right) \]

       16. +-lowering-+.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-3, \mathsf{*.f64}\left(x1, 6\right)\right)\right), \mathsf{+.f64}\left(\left(8 \cdot x2\right), \color{blue}{-3}\right)\right)\right) \]

       17. *-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-3, \mathsf{*.f64}\left(x1, 6\right)\right)\right), \mathsf{+.f64}\left(\left(x2 \cdot 8\right), -3\right)\right)\right) \]

       18. *-lowering-*.f64 91.0%

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-3, \mathsf{*.f64}\left(x1, 6\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 8\right), -3\right)\right)\right) \]

   13. Simplified 91.0%

       \[\leadsto \color{blue}{\left(x1 \cdot x1\right) \cdot \left(x1 \cdot \left(-3 + x1 \cdot 6\right) + \left(x2 \cdot 8 + -3\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4.8 \cdot 10^{+15}:\\ \;\;\;\;\left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right)\right) \cdot \left(6 - \frac{\frac{x2 \cdot -8}{x1}}{x1}\right)\\ \mathbf{elif}\;x1 \leq 16000:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + \left(x2 \cdot 4\right) \cdot \left(2 \cdot x2 + -3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x1 \cdot x1\right) \cdot \left(x1 \cdot \left(-3 + x1 \cdot 6\right) + \left(-3 + x2 \cdot 8\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 81.5% accurate, 4.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -4.1 \cdot 10^{+14}:\\ \;\;\;\;6 \cdot \left(x1 \cdot \left(x1 \cdot \left(x1 \cdot x1\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 5.5 \cdot 10^{-279}:\\ \;\;\;\;x2 \cdot -6 + x2 \cdot \left(x1 \cdot \left(x2 \cdot 8\right)\right)\\ \mathbf{elif}\;x1 \leq 0.07:\\ \;\;\;\;x1 \cdot \left(-1 + x1 \cdot 9\right) + x2 \cdot -6\\ \mathbf{else}:\\ \;\;\;\;\left(x1 \cdot x1\right) \cdot \left(x1 \cdot \left(-3 + x1 \cdot 6\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -4.1e+14)
   (* 6.0 (* x1 (* x1 (* x1 x1))))
   (if (<= x1 5.5e-279)
     (+ (* x2 -6.0) (* x2 (* x1 (* x2 8.0))))
     (if (<= x1 0.07)
       (+ (* x1 (+ -1.0 (* x1 9.0))) (* x2 -6.0))
       (* (* x1 x1) (* x1 (+ -3.0 (* x1 6.0))))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -4.1e+14) {
		tmp = 6.0 * (x1 * (x1 * (x1 * x1)));
	} else if (x1 <= 5.5e-279) {
		tmp = (x2 * -6.0) + (x2 * (x1 * (x2 * 8.0)));
	} else if (x1 <= 0.07) {
		tmp = (x1 * (-1.0 + (x1 * 9.0))) + (x2 * -6.0);
	} else {
		tmp = (x1 * x1) * (x1 * (-3.0 + (x1 * 6.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x1 <= (-4.1d+14)) then
        tmp = 6.0d0 * (x1 * (x1 * (x1 * x1)))
    else if (x1 <= 5.5d-279) then
        tmp = (x2 * (-6.0d0)) + (x2 * (x1 * (x2 * 8.0d0)))
    else if (x1 <= 0.07d0) then
        tmp = (x1 * ((-1.0d0) + (x1 * 9.0d0))) + (x2 * (-6.0d0))
    else
        tmp = (x1 * x1) * (x1 * ((-3.0d0) + (x1 * 6.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= -4.1e+14) {
		tmp = 6.0 * (x1 * (x1 * (x1 * x1)));
	} else if (x1 <= 5.5e-279) {
		tmp = (x2 * -6.0) + (x2 * (x1 * (x2 * 8.0)));
	} else if (x1 <= 0.07) {
		tmp = (x1 * (-1.0 + (x1 * 9.0))) + (x2 * -6.0);
	} else {
		tmp = (x1 * x1) * (x1 * (-3.0 + (x1 * 6.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -4.1e+14:
		tmp = 6.0 * (x1 * (x1 * (x1 * x1)))
	elif x1 <= 5.5e-279:
		tmp = (x2 * -6.0) + (x2 * (x1 * (x2 * 8.0)))
	elif x1 <= 0.07:
		tmp = (x1 * (-1.0 + (x1 * 9.0))) + (x2 * -6.0)
	else:
		tmp = (x1 * x1) * (x1 * (-3.0 + (x1 * 6.0)))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -4.1e+14)
		tmp = Float64(6.0 * Float64(x1 * Float64(x1 * Float64(x1 * x1))));
	elseif (x1 <= 5.5e-279)
		tmp = Float64(Float64(x2 * -6.0) + Float64(x2 * Float64(x1 * Float64(x2 * 8.0))));
	elseif (x1 <= 0.07)
		tmp = Float64(Float64(x1 * Float64(-1.0 + Float64(x1 * 9.0))) + Float64(x2 * -6.0));
	else
		tmp = Float64(Float64(x1 * x1) * Float64(x1 * Float64(-3.0 + Float64(x1 * 6.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -4.1e+14)
		tmp = 6.0 * (x1 * (x1 * (x1 * x1)));
	elseif (x1 <= 5.5e-279)
		tmp = (x2 * -6.0) + (x2 * (x1 * (x2 * 8.0)));
	elseif (x1 <= 0.07)
		tmp = (x1 * (-1.0 + (x1 * 9.0))) + (x2 * -6.0);
	else
		tmp = (x1 * x1) * (x1 * (-3.0 + (x1 * 6.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -4.1e+14], N[(6.0 * N[(x1 * N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 5.5e-279], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x2 * N[(x1 * N[(x2 * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 0.07], N[(N[(x1 * N[(-1.0 + N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision], N[(N[(x1 * x1), $MachinePrecision] * N[(x1 * N[(-3.0 + N[(x1 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -4.1e14

   1. Initial program 27.1%

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

   3. Simplified 27.1%

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

   5. Taylor expanded in x1 around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, -6\right)\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-6, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 4\right)\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \color{blue}{9}\right)\right)\right)\right)\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 27.1%

      \[\leadsto \frac{3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right)}{x1 \cdot x1 + 1} + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(x1 \cdot \left(x1 \cdot -6\right) + \frac{2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)}{x1 \cdot x1 + 1} \cdot \left(x1 \cdot \left(-6 + \left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right) \cdot \frac{2}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot 4\right)\right) + x1 \cdot \left(2 + x1 \cdot \left(x1 + \color{blue}{9}\right)\right)\right) \]

   8. Taylor expanded in x1 around inf

      \[\leadsto \color{blue}{{x1}^{4} \cdot \left(6 - 3 \cdot \frac{1}{x1}\right)} \]
   9. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{4}\right), \color{blue}{\left(6 - 3 \cdot \frac{1}{x1}\right)}\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{\left(2 \cdot 2\right)}\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      3. pow-sqr N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{2} \cdot {x1}^{2}\right), \left(\color{blue}{6} - 3 \cdot \frac{1}{x1}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left({x1}^{2}\right), \left({x1}^{2}\right)\right), \left(\color{blue}{6} - 3 \cdot \frac{1}{x1}\right)\right) \]

      5. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x1 \cdot x1\right), \left({x1}^{2}\right)\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left({x1}^{2}\right)\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left(x1 \cdot x1\right)\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \left(6 + \color{blue}{\left(\mathsf{neg}\left(3 \cdot \frac{1}{x1}\right)\right)}\right)\right) \]

      10. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \color{blue}{\left(\mathsf{neg}\left(3 \cdot \frac{1}{x1}\right)\right)}\right)\right) \]

      11. associate-*r/ N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \left(\mathsf{neg}\left(\frac{3 \cdot 1}{x1}\right)\right)\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \left(\mathsf{neg}\left(\frac{3}{x1}\right)\right)\right)\right) \]

      13. distribute-neg-frac N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \left(\frac{\mathsf{neg}\left(3\right)}{\color{blue}{x1}}\right)\right)\right) \]

      14. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \left(\frac{-3}{x1}\right)\right)\right) \]

      15. /-lowering-/.f64 92.1%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \mathsf{/.f64}\left(-3, \color{blue}{x1}\right)\right)\right) \]

   10. Simplified 92.1%

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

   11. Taylor expanded in x1 around inf

       \[\leadsto \color{blue}{6 \cdot {x1}^{4}} \]
   12. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(6, \color{blue}{\left({x1}^{4}\right)}\right) \]

       2. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(6, \left({x1}^{\left(2 \cdot \color{blue}{2}\right)}\right)\right) \]

       3. pow-sqr N/A

          \[\leadsto \mathsf{*.f64}\left(6, \left({x1}^{2} \cdot \color{blue}{{x1}^{2}}\right)\right) \]

       4. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(6, \left(\left(x1 \cdot x1\right) \cdot {\color{blue}{x1}}^{2}\right)\right) \]

       5. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(6, \left(x1 \cdot \color{blue}{\left(x1 \cdot {x1}^{2}\right)}\right)\right) \]

       6. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(6, \left(x1 \cdot \left(x1 \cdot \left(x1 \cdot \color{blue}{x1}\right)\right)\right)\right) \]

       7. cube-mult N/A

          \[\leadsto \mathsf{*.f64}\left(6, \left(x1 \cdot {x1}^{\color{blue}{3}}\right)\right) \]

       8. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(x1, \color{blue}{\left({x1}^{3}\right)}\right)\right) \]

       9. cube-mult N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(x1, \left(x1 \cdot \color{blue}{\left(x1 \cdot x1\right)}\right)\right)\right) \]

       10. unpow2 N/A

           \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(x1, \left(x1 \cdot {x1}^{\color{blue}{2}}\right)\right)\right) \]

       11. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, \color{blue}{\left({x1}^{2}\right)}\right)\right)\right) \]

       12. unpow2 N/A

           \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, \left(x1 \cdot \color{blue}{x1}\right)\right)\right)\right) \]

       13. *-lowering-*.f64 92.1%

           \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, \color{blue}{x1}\right)\right)\right)\right) \]

   13. Simplified 92.1%

       \[\leadsto \color{blue}{6 \cdot \left(x1 \cdot \left(x1 \cdot \left(x1 \cdot x1\right)\right)\right)} \]

   if -4.1e14 < x1 < 5.5000000000000002e-279

   1. Initial program 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x1 around 0

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

   7. Simplified 83.4%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(x2 \cdot 2\right) \cdot \left(x2 \cdot 4 + -6\right) + \left(x1 \cdot \left(\left(\left(\left(9 + 3 \cdot \left(x2 \cdot 2\right)\right) + x2 \cdot 10\right) - \left(x2 \cdot 4 + -6\right)\right) + -6\right) + -1\right)\right)} \]

   8. Taylor expanded in x2 around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right), \color{blue}{\left(9 \cdot x1 - 1\right)}\right)\right)\right) \]
   9. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right), \left(9 \cdot x1 + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right), \left(9 \cdot x1 + -1\right)\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right), \mathsf{+.f64}\left(\left(9 \cdot x1\right), \color{blue}{-1}\right)\right)\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right), \mathsf{+.f64}\left(\left(x1 \cdot 9\right), -1\right)\right)\right)\right) \]

      5. *-lowering-*.f64 83.4%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 9\right), -1\right)\right)\right)\right) \]

   10. Simplified 83.4%

       \[\leadsto -6 \cdot x2 + x1 \cdot \left(\left(x2 \cdot 2\right) \cdot \left(x2 \cdot 4 + -6\right) + \color{blue}{\left(x1 \cdot 9 + -1\right)}\right) \]

   11. Taylor expanded in x2 around inf

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \color{blue}{\left(8 \cdot \left(x1 \cdot {x2}^{2}\right)\right)}\right) \]
   12. Step-by-step derivation

       1. unpow2 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \left(8 \cdot \left(x1 \cdot \left(x2 \cdot \color{blue}{x2}\right)\right)\right)\right) \]

       2. associate-*r* N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \left(8 \cdot \left(\left(x1 \cdot x2\right) \cdot \color{blue}{x2}\right)\right)\right) \]

       3. associate-*l* N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \left(\left(8 \cdot \left(x1 \cdot x2\right)\right) \cdot \color{blue}{x2}\right)\right) \]

       4. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \left(x2 \cdot \color{blue}{\left(8 \cdot \left(x1 \cdot x2\right)\right)}\right)\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x2, \color{blue}{\left(8 \cdot \left(x1 \cdot x2\right)\right)}\right)\right) \]

       6. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x2, \left(\left(x1 \cdot x2\right) \cdot \color{blue}{8}\right)\right)\right) \]

       7. associate-*l* N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x2, \left(x1 \cdot \color{blue}{\left(x2 \cdot 8\right)}\right)\right)\right) \]

       8. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x2, \left(x1 \cdot \left(8 \cdot \color{blue}{x2}\right)\right)\right)\right) \]

       9. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x2, \mathsf{*.f64}\left(x1, \color{blue}{\left(8 \cdot x2\right)}\right)\right)\right) \]

       10. *-commutative N/A

           \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x2, \mathsf{*.f64}\left(x1, \left(x2 \cdot \color{blue}{8}\right)\right)\right)\right) \]

       11. *-lowering-*.f64 81.4%

           \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x2, \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x2, \color{blue}{8}\right)\right)\right)\right) \]

   13. Simplified 81.4%

       \[\leadsto -6 \cdot x2 + \color{blue}{x2 \cdot \left(x1 \cdot \left(x2 \cdot 8\right)\right)} \]

   if 5.5000000000000002e-279 < x1 < 0.070000000000000007

   1. Initial program 99.3%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in x1 around 0

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

   7. Simplified 95.7%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(x2 \cdot 2\right) \cdot \left(x2 \cdot 4 + -6\right) + \left(x1 \cdot \left(\left(\left(\left(9 + 3 \cdot \left(x2 \cdot 2\right)\right) + x2 \cdot 10\right) - \left(x2 \cdot 4 + -6\right)\right) + -6\right) + -1\right)\right)} \]

   8. Taylor expanded in x2 around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \color{blue}{\left(x1 \cdot \left(9 \cdot x1 - 1\right)\right)}\right) \]
   9. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \color{blue}{\left(9 \cdot x1 - 1\right)}\right)\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \left(9 \cdot x1 + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right) \]

      3. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \left(9 \cdot x1 + -1\right)\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\left(9 \cdot x1\right), \color{blue}{-1}\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\left(x1 \cdot 9\right), -1\right)\right)\right) \]

      6. *-lowering-*.f64 82.8%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 9\right), -1\right)\right)\right) \]

   10. Simplified 82.8%

       \[\leadsto -6 \cdot x2 + \color{blue}{x1 \cdot \left(x1 \cdot 9 + -1\right)} \]

   if 0.070000000000000007 < x1

   1. Initial program 50.6%

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

   3. Simplified 50.7%

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

   5. Taylor expanded in x1 around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, -6\right)\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-6, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 4\right)\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \color{blue}{9}\right)\right)\right)\right)\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 50.7%

      \[\leadsto \frac{3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right)}{x1 \cdot x1 + 1} + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(x1 \cdot \left(x1 \cdot -6\right) + \frac{2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)}{x1 \cdot x1 + 1} \cdot \left(x1 \cdot \left(-6 + \left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right) \cdot \frac{2}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot 4\right)\right) + x1 \cdot \left(2 + x1 \cdot \left(x1 + \color{blue}{9}\right)\right)\right) \]

   8. Taylor expanded in x1 around inf

      \[\leadsto \color{blue}{{x1}^{4} \cdot \left(6 - 3 \cdot \frac{1}{x1}\right)} \]
   9. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{4}\right), \color{blue}{\left(6 - 3 \cdot \frac{1}{x1}\right)}\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{\left(2 \cdot 2\right)}\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      3. pow-sqr N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{2} \cdot {x1}^{2}\right), \left(\color{blue}{6} - 3 \cdot \frac{1}{x1}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left({x1}^{2}\right), \left({x1}^{2}\right)\right), \left(\color{blue}{6} - 3 \cdot \frac{1}{x1}\right)\right) \]

      5. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x1 \cdot x1\right), \left({x1}^{2}\right)\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left({x1}^{2}\right)\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left(x1 \cdot x1\right)\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \left(6 + \color{blue}{\left(\mathsf{neg}\left(3 \cdot \frac{1}{x1}\right)\right)}\right)\right) \]

      10. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \color{blue}{\left(\mathsf{neg}\left(3 \cdot \frac{1}{x1}\right)\right)}\right)\right) \]

      11. associate-*r/ N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \left(\mathsf{neg}\left(\frac{3 \cdot 1}{x1}\right)\right)\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \left(\mathsf{neg}\left(\frac{3}{x1}\right)\right)\right)\right) \]

      13. distribute-neg-frac N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \left(\frac{\mathsf{neg}\left(3\right)}{\color{blue}{x1}}\right)\right)\right) \]

      14. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \left(\frac{-3}{x1}\right)\right)\right) \]

      15. /-lowering-/.f64 82.2%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \mathsf{/.f64}\left(-3, \color{blue}{x1}\right)\right)\right) \]

   10. Simplified 82.2%

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

   11. Taylor expanded in x1 around 0

       \[\leadsto \color{blue}{{x1}^{3} \cdot \left(6 \cdot x1 - 3\right)} \]
   12. Step-by-step derivation

       1. unpow3 N/A

          \[\leadsto \left(\left(x1 \cdot x1\right) \cdot x1\right) \cdot \left(\color{blue}{6 \cdot x1} - 3\right) \]

       2. unpow2 N/A

          \[\leadsto \left({x1}^{2} \cdot x1\right) \cdot \left(\color{blue}{6} \cdot x1 - 3\right) \]

       3. associate-*l* N/A

          \[\leadsto {x1}^{2} \cdot \color{blue}{\left(x1 \cdot \left(6 \cdot x1 - 3\right)\right)} \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\left({x1}^{2}\right), \color{blue}{\left(x1 \cdot \left(6 \cdot x1 - 3\right)\right)}\right) \]

       5. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(\left(x1 \cdot x1\right), \left(\color{blue}{x1} \cdot \left(6 \cdot x1 - 3\right)\right)\right) \]

       6. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left(\color{blue}{x1} \cdot \left(6 \cdot x1 - 3\right)\right)\right) \]

       7. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, \color{blue}{\left(6 \cdot x1 - 3\right)}\right)\right) \]

       8. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, \left(6 \cdot x1 + \color{blue}{\left(\mathsf{neg}\left(3\right)\right)}\right)\right)\right) \]

       9. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, \left(6 \cdot x1 + -3\right)\right)\right) \]

       10. +-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, \left(-3 + \color{blue}{6 \cdot x1}\right)\right)\right) \]

       11. +-lowering-+.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-3, \color{blue}{\left(6 \cdot x1\right)}\right)\right)\right) \]

       12. *-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-3, \left(x1 \cdot \color{blue}{6}\right)\right)\right)\right) \]

       13. *-lowering-*.f64 82.4%

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-3, \mathsf{*.f64}\left(x1, \color{blue}{6}\right)\right)\right)\right) \]

   13. Simplified 82.4%

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

4. Final simplification 85.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4.1 \cdot 10^{+14}:\\ \;\;\;\;6 \cdot \left(x1 \cdot \left(x1 \cdot \left(x1 \cdot x1\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 5.5 \cdot 10^{-279}:\\ \;\;\;\;x2 \cdot -6 + x2 \cdot \left(x1 \cdot \left(x2 \cdot 8\right)\right)\\ \mathbf{elif}\;x1 \leq 0.07:\\ \;\;\;\;x1 \cdot \left(-1 + x1 \cdot 9\right) + x2 \cdot -6\\ \mathbf{else}:\\ \;\;\;\;\left(x1 \cdot x1\right) \cdot \left(x1 \cdot \left(-3 + x1 \cdot 6\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 81.1% accurate, 4.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -3.5 \cdot 10^{+15}:\\ \;\;\;\;6 \cdot \left(x1 \cdot \left(x1 \cdot \left(x1 \cdot x1\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -9.4 \cdot 10^{-101}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(8 \cdot \left(x2 \cdot x2\right)\right)\\ \mathbf{elif}\;x1 \leq 0.07:\\ \;\;\;\;x1 \cdot \left(-1 + x1 \cdot 9\right) + x2 \cdot -6\\ \mathbf{else}:\\ \;\;\;\;\left(x1 \cdot x1\right) \cdot \left(x1 \cdot \left(-3 + x1 \cdot 6\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -3.5e+15)
   (* 6.0 (* x1 (* x1 (* x1 x1))))
   (if (<= x1 -9.4e-101)
     (+ (* x2 -6.0) (* x1 (* 8.0 (* x2 x2))))
     (if (<= x1 0.07)
       (+ (* x1 (+ -1.0 (* x1 9.0))) (* x2 -6.0))
       (* (* x1 x1) (* x1 (+ -3.0 (* x1 6.0))))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -3.5e+15) {
		tmp = 6.0 * (x1 * (x1 * (x1 * x1)));
	} else if (x1 <= -9.4e-101) {
		tmp = (x2 * -6.0) + (x1 * (8.0 * (x2 * x2)));
	} else if (x1 <= 0.07) {
		tmp = (x1 * (-1.0 + (x1 * 9.0))) + (x2 * -6.0);
	} else {
		tmp = (x1 * x1) * (x1 * (-3.0 + (x1 * 6.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x1 <= (-3.5d+15)) then
        tmp = 6.0d0 * (x1 * (x1 * (x1 * x1)))
    else if (x1 <= (-9.4d-101)) then
        tmp = (x2 * (-6.0d0)) + (x1 * (8.0d0 * (x2 * x2)))
    else if (x1 <= 0.07d0) then
        tmp = (x1 * ((-1.0d0) + (x1 * 9.0d0))) + (x2 * (-6.0d0))
    else
        tmp = (x1 * x1) * (x1 * ((-3.0d0) + (x1 * 6.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= -3.5e+15) {
		tmp = 6.0 * (x1 * (x1 * (x1 * x1)));
	} else if (x1 <= -9.4e-101) {
		tmp = (x2 * -6.0) + (x1 * (8.0 * (x2 * x2)));
	} else if (x1 <= 0.07) {
		tmp = (x1 * (-1.0 + (x1 * 9.0))) + (x2 * -6.0);
	} else {
		tmp = (x1 * x1) * (x1 * (-3.0 + (x1 * 6.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -3.5e+15:
		tmp = 6.0 * (x1 * (x1 * (x1 * x1)))
	elif x1 <= -9.4e-101:
		tmp = (x2 * -6.0) + (x1 * (8.0 * (x2 * x2)))
	elif x1 <= 0.07:
		tmp = (x1 * (-1.0 + (x1 * 9.0))) + (x2 * -6.0)
	else:
		tmp = (x1 * x1) * (x1 * (-3.0 + (x1 * 6.0)))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -3.5e+15)
		tmp = Float64(6.0 * Float64(x1 * Float64(x1 * Float64(x1 * x1))));
	elseif (x1 <= -9.4e-101)
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(8.0 * Float64(x2 * x2))));
	elseif (x1 <= 0.07)
		tmp = Float64(Float64(x1 * Float64(-1.0 + Float64(x1 * 9.0))) + Float64(x2 * -6.0));
	else
		tmp = Float64(Float64(x1 * x1) * Float64(x1 * Float64(-3.0 + Float64(x1 * 6.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -3.5e+15)
		tmp = 6.0 * (x1 * (x1 * (x1 * x1)));
	elseif (x1 <= -9.4e-101)
		tmp = (x2 * -6.0) + (x1 * (8.0 * (x2 * x2)));
	elseif (x1 <= 0.07)
		tmp = (x1 * (-1.0 + (x1 * 9.0))) + (x2 * -6.0);
	else
		tmp = (x1 * x1) * (x1 * (-3.0 + (x1 * 6.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -3.5e+15], N[(6.0 * N[(x1 * N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -9.4e-101], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(8.0 * N[(x2 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 0.07], N[(N[(x1 * N[(-1.0 + N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision], N[(N[(x1 * x1), $MachinePrecision] * N[(x1 * N[(-3.0 + N[(x1 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -3.5e15

   1. Initial program 27.1%

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

   3. Simplified 27.1%

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

   5. Taylor expanded in x1 around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, -6\right)\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-6, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 4\right)\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \color{blue}{9}\right)\right)\right)\right)\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 27.1%

      \[\leadsto \frac{3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right)}{x1 \cdot x1 + 1} + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(x1 \cdot \left(x1 \cdot -6\right) + \frac{2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)}{x1 \cdot x1 + 1} \cdot \left(x1 \cdot \left(-6 + \left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right) \cdot \frac{2}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot 4\right)\right) + x1 \cdot \left(2 + x1 \cdot \left(x1 + \color{blue}{9}\right)\right)\right) \]

   8. Taylor expanded in x1 around inf

      \[\leadsto \color{blue}{{x1}^{4} \cdot \left(6 - 3 \cdot \frac{1}{x1}\right)} \]
   9. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{4}\right), \color{blue}{\left(6 - 3 \cdot \frac{1}{x1}\right)}\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{\left(2 \cdot 2\right)}\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      3. pow-sqr N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{2} \cdot {x1}^{2}\right), \left(\color{blue}{6} - 3 \cdot \frac{1}{x1}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left({x1}^{2}\right), \left({x1}^{2}\right)\right), \left(\color{blue}{6} - 3 \cdot \frac{1}{x1}\right)\right) \]

      5. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x1 \cdot x1\right), \left({x1}^{2}\right)\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left({x1}^{2}\right)\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left(x1 \cdot x1\right)\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \left(6 + \color{blue}{\left(\mathsf{neg}\left(3 \cdot \frac{1}{x1}\right)\right)}\right)\right) \]

      10. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \color{blue}{\left(\mathsf{neg}\left(3 \cdot \frac{1}{x1}\right)\right)}\right)\right) \]

      11. associate-*r/ N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \left(\mathsf{neg}\left(\frac{3 \cdot 1}{x1}\right)\right)\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \left(\mathsf{neg}\left(\frac{3}{x1}\right)\right)\right)\right) \]

      13. distribute-neg-frac N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \left(\frac{\mathsf{neg}\left(3\right)}{\color{blue}{x1}}\right)\right)\right) \]

      14. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \left(\frac{-3}{x1}\right)\right)\right) \]

      15. /-lowering-/.f64 92.1%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \mathsf{/.f64}\left(-3, \color{blue}{x1}\right)\right)\right) \]

   10. Simplified 92.1%

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

   11. Taylor expanded in x1 around inf

       \[\leadsto \color{blue}{6 \cdot {x1}^{4}} \]
   12. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(6, \color{blue}{\left({x1}^{4}\right)}\right) \]

       2. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(6, \left({x1}^{\left(2 \cdot \color{blue}{2}\right)}\right)\right) \]

       3. pow-sqr N/A

          \[\leadsto \mathsf{*.f64}\left(6, \left({x1}^{2} \cdot \color{blue}{{x1}^{2}}\right)\right) \]

       4. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(6, \left(\left(x1 \cdot x1\right) \cdot {\color{blue}{x1}}^{2}\right)\right) \]

       5. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(6, \left(x1 \cdot \color{blue}{\left(x1 \cdot {x1}^{2}\right)}\right)\right) \]

       6. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(6, \left(x1 \cdot \left(x1 \cdot \left(x1 \cdot \color{blue}{x1}\right)\right)\right)\right) \]

       7. cube-mult N/A

          \[\leadsto \mathsf{*.f64}\left(6, \left(x1 \cdot {x1}^{\color{blue}{3}}\right)\right) \]

       8. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(x1, \color{blue}{\left({x1}^{3}\right)}\right)\right) \]

       9. cube-mult N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(x1, \left(x1 \cdot \color{blue}{\left(x1 \cdot x1\right)}\right)\right)\right) \]

       10. unpow2 N/A

           \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(x1, \left(x1 \cdot {x1}^{\color{blue}{2}}\right)\right)\right) \]

       11. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, \color{blue}{\left({x1}^{2}\right)}\right)\right)\right) \]

       12. unpow2 N/A

           \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, \left(x1 \cdot \color{blue}{x1}\right)\right)\right)\right) \]

       13. *-lowering-*.f64 92.1%

           \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, \color{blue}{x1}\right)\right)\right)\right) \]

   13. Simplified 92.1%

       \[\leadsto \color{blue}{6 \cdot \left(x1 \cdot \left(x1 \cdot \left(x1 \cdot x1\right)\right)\right)} \]

   if -3.5e15 < x1 < -9.3999999999999999e-101

   1. Initial program 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x1 around 0

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

   7. Simplified 91.2%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(x2 \cdot 2\right) \cdot \left(x2 \cdot 4 + -6\right) + \left(x1 \cdot \left(\left(\left(\left(9 + 3 \cdot \left(x2 \cdot 2\right)\right) + x2 \cdot 10\right) - \left(x2 \cdot 4 + -6\right)\right) + -6\right) + -1\right)\right)} \]

   8. Taylor expanded in x2 around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \color{blue}{\left(8 \cdot {x2}^{2}\right)}\right)\right) \]
   9. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(8, \color{blue}{\left({x2}^{2}\right)}\right)\right)\right) \]

      2. unpow2 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(8, \left(x2 \cdot \color{blue}{x2}\right)\right)\right)\right) \]

      3. *-lowering-*.f64 65.4%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(8, \mathsf{*.f64}\left(x2, \color{blue}{x2}\right)\right)\right)\right) \]

   10. Simplified 65.4%

       \[\leadsto -6 \cdot x2 + x1 \cdot \color{blue}{\left(8 \cdot \left(x2 \cdot x2\right)\right)} \]

   if -9.3999999999999999e-101 < x1 < 0.070000000000000007

   1. Initial program 99.4%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x1 around 0

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

   7. Simplified 87.4%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(x2 \cdot 2\right) \cdot \left(x2 \cdot 4 + -6\right) + \left(x1 \cdot \left(\left(\left(\left(9 + 3 \cdot \left(x2 \cdot 2\right)\right) + x2 \cdot 10\right) - \left(x2 \cdot 4 + -6\right)\right) + -6\right) + -1\right)\right)} \]

   8. Taylor expanded in x2 around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \color{blue}{\left(x1 \cdot \left(9 \cdot x1 - 1\right)\right)}\right) \]
   9. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \color{blue}{\left(9 \cdot x1 - 1\right)}\right)\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \left(9 \cdot x1 + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right) \]

      3. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \left(9 \cdot x1 + -1\right)\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\left(9 \cdot x1\right), \color{blue}{-1}\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\left(x1 \cdot 9\right), -1\right)\right)\right) \]

      6. *-lowering-*.f64 82.7%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 9\right), -1\right)\right)\right) \]

   10. Simplified 82.7%

       \[\leadsto -6 \cdot x2 + \color{blue}{x1 \cdot \left(x1 \cdot 9 + -1\right)} \]

   if 0.070000000000000007 < x1

   1. Initial program 50.6%

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

   3. Simplified 50.7%

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

   5. Taylor expanded in x1 around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, -6\right)\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-6, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 4\right)\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \color{blue}{9}\right)\right)\right)\right)\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 50.7%

      \[\leadsto \frac{3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right)}{x1 \cdot x1 + 1} + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(x1 \cdot \left(x1 \cdot -6\right) + \frac{2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)}{x1 \cdot x1 + 1} \cdot \left(x1 \cdot \left(-6 + \left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right) \cdot \frac{2}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot 4\right)\right) + x1 \cdot \left(2 + x1 \cdot \left(x1 + \color{blue}{9}\right)\right)\right) \]

   8. Taylor expanded in x1 around inf

      \[\leadsto \color{blue}{{x1}^{4} \cdot \left(6 - 3 \cdot \frac{1}{x1}\right)} \]
   9. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{4}\right), \color{blue}{\left(6 - 3 \cdot \frac{1}{x1}\right)}\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{\left(2 \cdot 2\right)}\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      3. pow-sqr N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{2} \cdot {x1}^{2}\right), \left(\color{blue}{6} - 3 \cdot \frac{1}{x1}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left({x1}^{2}\right), \left({x1}^{2}\right)\right), \left(\color{blue}{6} - 3 \cdot \frac{1}{x1}\right)\right) \]

      5. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x1 \cdot x1\right), \left({x1}^{2}\right)\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left({x1}^{2}\right)\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left(x1 \cdot x1\right)\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \left(6 + \color{blue}{\left(\mathsf{neg}\left(3 \cdot \frac{1}{x1}\right)\right)}\right)\right) \]

      10. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \color{blue}{\left(\mathsf{neg}\left(3 \cdot \frac{1}{x1}\right)\right)}\right)\right) \]

      11. associate-*r/ N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \left(\mathsf{neg}\left(\frac{3 \cdot 1}{x1}\right)\right)\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \left(\mathsf{neg}\left(\frac{3}{x1}\right)\right)\right)\right) \]

      13. distribute-neg-frac N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \left(\frac{\mathsf{neg}\left(3\right)}{\color{blue}{x1}}\right)\right)\right) \]

      14. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \left(\frac{-3}{x1}\right)\right)\right) \]

      15. /-lowering-/.f64 82.2%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \mathsf{/.f64}\left(-3, \color{blue}{x1}\right)\right)\right) \]

   10. Simplified 82.2%

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

   11. Taylor expanded in x1 around 0

       \[\leadsto \color{blue}{{x1}^{3} \cdot \left(6 \cdot x1 - 3\right)} \]
   12. Step-by-step derivation

       1. unpow3 N/A

          \[\leadsto \left(\left(x1 \cdot x1\right) \cdot x1\right) \cdot \left(\color{blue}{6 \cdot x1} - 3\right) \]

       2. unpow2 N/A

          \[\leadsto \left({x1}^{2} \cdot x1\right) \cdot \left(\color{blue}{6} \cdot x1 - 3\right) \]

       3. associate-*l* N/A

          \[\leadsto {x1}^{2} \cdot \color{blue}{\left(x1 \cdot \left(6 \cdot x1 - 3\right)\right)} \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\left({x1}^{2}\right), \color{blue}{\left(x1 \cdot \left(6 \cdot x1 - 3\right)\right)}\right) \]

       5. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(\left(x1 \cdot x1\right), \left(\color{blue}{x1} \cdot \left(6 \cdot x1 - 3\right)\right)\right) \]

       6. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left(\color{blue}{x1} \cdot \left(6 \cdot x1 - 3\right)\right)\right) \]

       7. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, \color{blue}{\left(6 \cdot x1 - 3\right)}\right)\right) \]

       8. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, \left(6 \cdot x1 + \color{blue}{\left(\mathsf{neg}\left(3\right)\right)}\right)\right)\right) \]

       9. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, \left(6 \cdot x1 + -3\right)\right)\right) \]

       10. +-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, \left(-3 + \color{blue}{6 \cdot x1}\right)\right)\right) \]

       11. +-lowering-+.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-3, \color{blue}{\left(6 \cdot x1\right)}\right)\right)\right) \]

       12. *-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-3, \left(x1 \cdot \color{blue}{6}\right)\right)\right)\right) \]

       13. *-lowering-*.f64 82.4%

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-3, \mathsf{*.f64}\left(x1, \color{blue}{6}\right)\right)\right)\right) \]

   13. Simplified 82.4%

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

4. Final simplification 84.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -3.5 \cdot 10^{+15}:\\ \;\;\;\;6 \cdot \left(x1 \cdot \left(x1 \cdot \left(x1 \cdot x1\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -9.4 \cdot 10^{-101}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(8 \cdot \left(x2 \cdot x2\right)\right)\\ \mathbf{elif}\;x1 \leq 0.07:\\ \;\;\;\;x1 \cdot \left(-1 + x1 \cdot 9\right) + x2 \cdot -6\\ \mathbf{else}:\\ \;\;\;\;\left(x1 \cdot x1\right) \cdot \left(x1 \cdot \left(-3 + x1 \cdot 6\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 80.9% accurate, 4.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -3.55 \cdot 10^{+15}:\\ \;\;\;\;6 \cdot \left(x1 \cdot \left(x1 \cdot \left(x1 \cdot x1\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -2.2 \cdot 10^{-102}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(8 \cdot \left(x2 \cdot x2\right)\right)\\ \mathbf{elif}\;x1 \leq 0.07:\\ \;\;\;\;x2 \cdot -6 - x1\\ \mathbf{else}:\\ \;\;\;\;\left(x1 \cdot x1\right) \cdot \left(x1 \cdot \left(-3 + x1 \cdot 6\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -3.55e+15)
   (* 6.0 (* x1 (* x1 (* x1 x1))))
   (if (<= x1 -2.2e-102)
     (+ (* x2 -6.0) (* x1 (* 8.0 (* x2 x2))))
     (if (<= x1 0.07)
       (- (* x2 -6.0) x1)
       (* (* x1 x1) (* x1 (+ -3.0 (* x1 6.0))))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -3.55e+15) {
		tmp = 6.0 * (x1 * (x1 * (x1 * x1)));
	} else if (x1 <= -2.2e-102) {
		tmp = (x2 * -6.0) + (x1 * (8.0 * (x2 * x2)));
	} else if (x1 <= 0.07) {
		tmp = (x2 * -6.0) - x1;
	} else {
		tmp = (x1 * x1) * (x1 * (-3.0 + (x1 * 6.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x1 <= (-3.55d+15)) then
        tmp = 6.0d0 * (x1 * (x1 * (x1 * x1)))
    else if (x1 <= (-2.2d-102)) then
        tmp = (x2 * (-6.0d0)) + (x1 * (8.0d0 * (x2 * x2)))
    else if (x1 <= 0.07d0) then
        tmp = (x2 * (-6.0d0)) - x1
    else
        tmp = (x1 * x1) * (x1 * ((-3.0d0) + (x1 * 6.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= -3.55e+15) {
		tmp = 6.0 * (x1 * (x1 * (x1 * x1)));
	} else if (x1 <= -2.2e-102) {
		tmp = (x2 * -6.0) + (x1 * (8.0 * (x2 * x2)));
	} else if (x1 <= 0.07) {
		tmp = (x2 * -6.0) - x1;
	} else {
		tmp = (x1 * x1) * (x1 * (-3.0 + (x1 * 6.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -3.55e+15:
		tmp = 6.0 * (x1 * (x1 * (x1 * x1)))
	elif x1 <= -2.2e-102:
		tmp = (x2 * -6.0) + (x1 * (8.0 * (x2 * x2)))
	elif x1 <= 0.07:
		tmp = (x2 * -6.0) - x1
	else:
		tmp = (x1 * x1) * (x1 * (-3.0 + (x1 * 6.0)))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -3.55e+15)
		tmp = Float64(6.0 * Float64(x1 * Float64(x1 * Float64(x1 * x1))));
	elseif (x1 <= -2.2e-102)
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(8.0 * Float64(x2 * x2))));
	elseif (x1 <= 0.07)
		tmp = Float64(Float64(x2 * -6.0) - x1);
	else
		tmp = Float64(Float64(x1 * x1) * Float64(x1 * Float64(-3.0 + Float64(x1 * 6.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -3.55e+15)
		tmp = 6.0 * (x1 * (x1 * (x1 * x1)));
	elseif (x1 <= -2.2e-102)
		tmp = (x2 * -6.0) + (x1 * (8.0 * (x2 * x2)));
	elseif (x1 <= 0.07)
		tmp = (x2 * -6.0) - x1;
	else
		tmp = (x1 * x1) * (x1 * (-3.0 + (x1 * 6.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -3.55e+15], N[(6.0 * N[(x1 * N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -2.2e-102], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(8.0 * N[(x2 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 0.07], N[(N[(x2 * -6.0), $MachinePrecision] - x1), $MachinePrecision], N[(N[(x1 * x1), $MachinePrecision] * N[(x1 * N[(-3.0 + N[(x1 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -3.55e15

   1. Initial program 27.1%

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

   3. Simplified 27.1%

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

   5. Taylor expanded in x1 around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, -6\right)\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-6, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 4\right)\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \color{blue}{9}\right)\right)\right)\right)\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 27.1%

      \[\leadsto \frac{3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right)}{x1 \cdot x1 + 1} + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(x1 \cdot \left(x1 \cdot -6\right) + \frac{2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)}{x1 \cdot x1 + 1} \cdot \left(x1 \cdot \left(-6 + \left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right) \cdot \frac{2}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot 4\right)\right) + x1 \cdot \left(2 + x1 \cdot \left(x1 + \color{blue}{9}\right)\right)\right) \]

   8. Taylor expanded in x1 around inf

      \[\leadsto \color{blue}{{x1}^{4} \cdot \left(6 - 3 \cdot \frac{1}{x1}\right)} \]
   9. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{4}\right), \color{blue}{\left(6 - 3 \cdot \frac{1}{x1}\right)}\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{\left(2 \cdot 2\right)}\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      3. pow-sqr N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{2} \cdot {x1}^{2}\right), \left(\color{blue}{6} - 3 \cdot \frac{1}{x1}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left({x1}^{2}\right), \left({x1}^{2}\right)\right), \left(\color{blue}{6} - 3 \cdot \frac{1}{x1}\right)\right) \]

      5. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x1 \cdot x1\right), \left({x1}^{2}\right)\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left({x1}^{2}\right)\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left(x1 \cdot x1\right)\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \left(6 + \color{blue}{\left(\mathsf{neg}\left(3 \cdot \frac{1}{x1}\right)\right)}\right)\right) \]

      10. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \color{blue}{\left(\mathsf{neg}\left(3 \cdot \frac{1}{x1}\right)\right)}\right)\right) \]

      11. associate-*r/ N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \left(\mathsf{neg}\left(\frac{3 \cdot 1}{x1}\right)\right)\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \left(\mathsf{neg}\left(\frac{3}{x1}\right)\right)\right)\right) \]

      13. distribute-neg-frac N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \left(\frac{\mathsf{neg}\left(3\right)}{\color{blue}{x1}}\right)\right)\right) \]

      14. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \left(\frac{-3}{x1}\right)\right)\right) \]

      15. /-lowering-/.f64 92.1%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \mathsf{/.f64}\left(-3, \color{blue}{x1}\right)\right)\right) \]

   10. Simplified 92.1%

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

   11. Taylor expanded in x1 around inf

       \[\leadsto \color{blue}{6 \cdot {x1}^{4}} \]
   12. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(6, \color{blue}{\left({x1}^{4}\right)}\right) \]

       2. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(6, \left({x1}^{\left(2 \cdot \color{blue}{2}\right)}\right)\right) \]

       3. pow-sqr N/A

          \[\leadsto \mathsf{*.f64}\left(6, \left({x1}^{2} \cdot \color{blue}{{x1}^{2}}\right)\right) \]

       4. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(6, \left(\left(x1 \cdot x1\right) \cdot {\color{blue}{x1}}^{2}\right)\right) \]

       5. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(6, \left(x1 \cdot \color{blue}{\left(x1 \cdot {x1}^{2}\right)}\right)\right) \]

       6. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(6, \left(x1 \cdot \left(x1 \cdot \left(x1 \cdot \color{blue}{x1}\right)\right)\right)\right) \]

       7. cube-mult N/A

          \[\leadsto \mathsf{*.f64}\left(6, \left(x1 \cdot {x1}^{\color{blue}{3}}\right)\right) \]

       8. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(x1, \color{blue}{\left({x1}^{3}\right)}\right)\right) \]

       9. cube-mult N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(x1, \left(x1 \cdot \color{blue}{\left(x1 \cdot x1\right)}\right)\right)\right) \]

       10. unpow2 N/A

           \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(x1, \left(x1 \cdot {x1}^{\color{blue}{2}}\right)\right)\right) \]

       11. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, \color{blue}{\left({x1}^{2}\right)}\right)\right)\right) \]

       12. unpow2 N/A

           \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, \left(x1 \cdot \color{blue}{x1}\right)\right)\right)\right) \]

       13. *-lowering-*.f64 92.1%

           \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, \color{blue}{x1}\right)\right)\right)\right) \]

   13. Simplified 92.1%

       \[\leadsto \color{blue}{6 \cdot \left(x1 \cdot \left(x1 \cdot \left(x1 \cdot x1\right)\right)\right)} \]

   if -3.55e15 < x1 < -2.20000000000000013e-102

   1. Initial program 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x1 around 0

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

   7. Simplified 91.2%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(x2 \cdot 2\right) \cdot \left(x2 \cdot 4 + -6\right) + \left(x1 \cdot \left(\left(\left(\left(9 + 3 \cdot \left(x2 \cdot 2\right)\right) + x2 \cdot 10\right) - \left(x2 \cdot 4 + -6\right)\right) + -6\right) + -1\right)\right)} \]

   8. Taylor expanded in x2 around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \color{blue}{\left(8 \cdot {x2}^{2}\right)}\right)\right) \]
   9. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(8, \color{blue}{\left({x2}^{2}\right)}\right)\right)\right) \]

      2. unpow2 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(8, \left(x2 \cdot \color{blue}{x2}\right)\right)\right)\right) \]

      3. *-lowering-*.f64 65.4%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(8, \mathsf{*.f64}\left(x2, \color{blue}{x2}\right)\right)\right)\right) \]

   10. Simplified 65.4%

       \[\leadsto -6 \cdot x2 + x1 \cdot \color{blue}{\left(8 \cdot \left(x2 \cdot x2\right)\right)} \]

   if -2.20000000000000013e-102 < x1 < 0.070000000000000007

   1. Initial program 99.4%

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

   3. Simplified 99.5%

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

   6. Applied egg-rr 99.5%

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

   7. Taylor expanded in x1 around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(\color{blue}{\left(12 \cdot {x1}^{4}\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(-6, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]
   8. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(12, \left({x1}^{4}\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(-6, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(12, \left({x1}^{\left(2 \cdot 2\right)}\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(-6, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      3. pow-sqr N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(12, \left({x1}^{2} \cdot {x1}^{2}\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(-6, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(12, \mathsf{*.f64}\left(\left({x1}^{2}\right), \left({x1}^{2}\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(-6, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      5. unpow2 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(12, \mathsf{*.f64}\left(\left(x1 \cdot x1\right), \left({x1}^{2}\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(-6, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(12, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left({x1}^{2}\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(-6, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(12, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left(x1 \cdot x1\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(-6, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      8. *-lowering-*.f64 82.3%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(12, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(-6, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

   9. Simplified 82.3%

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

   10. Taylor expanded in x1 around 0

       \[\leadsto \color{blue}{-6 \cdot x2 + -1 \cdot x1} \]
   11. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto -6 \cdot x2 + \left(\mathsf{neg}\left(x1\right)\right) \]

       2. unsub-neg N/A

          \[\leadsto -6 \cdot x2 - \color{blue}{x1} \]

       3. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\left(-6 \cdot x2\right), \color{blue}{x1}\right) \]

       4. *-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(\left(x2 \cdot -6\right), x1\right) \]

       5. *-lowering-*.f64 82.6%

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x2, -6\right), x1\right) \]

   12. Simplified 82.6%

       \[\leadsto \color{blue}{x2 \cdot -6 - x1} \]

   if 0.070000000000000007 < x1

   1. Initial program 50.6%

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

   3. Simplified 50.7%

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

   5. Taylor expanded in x1 around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, -6\right)\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-6, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 4\right)\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \color{blue}{9}\right)\right)\right)\right)\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 50.7%

      \[\leadsto \frac{3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right)}{x1 \cdot x1 + 1} + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(x1 \cdot \left(x1 \cdot -6\right) + \frac{2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)}{x1 \cdot x1 + 1} \cdot \left(x1 \cdot \left(-6 + \left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right) \cdot \frac{2}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot 4\right)\right) + x1 \cdot \left(2 + x1 \cdot \left(x1 + \color{blue}{9}\right)\right)\right) \]

   8. Taylor expanded in x1 around inf

      \[\leadsto \color{blue}{{x1}^{4} \cdot \left(6 - 3 \cdot \frac{1}{x1}\right)} \]
   9. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{4}\right), \color{blue}{\left(6 - 3 \cdot \frac{1}{x1}\right)}\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{\left(2 \cdot 2\right)}\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      3. pow-sqr N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{2} \cdot {x1}^{2}\right), \left(\color{blue}{6} - 3 \cdot \frac{1}{x1}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left({x1}^{2}\right), \left({x1}^{2}\right)\right), \left(\color{blue}{6} - 3 \cdot \frac{1}{x1}\right)\right) \]

      5. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x1 \cdot x1\right), \left({x1}^{2}\right)\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left({x1}^{2}\right)\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left(x1 \cdot x1\right)\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \left(6 + \color{blue}{\left(\mathsf{neg}\left(3 \cdot \frac{1}{x1}\right)\right)}\right)\right) \]

      10. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \color{blue}{\left(\mathsf{neg}\left(3 \cdot \frac{1}{x1}\right)\right)}\right)\right) \]

      11. associate-*r/ N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \left(\mathsf{neg}\left(\frac{3 \cdot 1}{x1}\right)\right)\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \left(\mathsf{neg}\left(\frac{3}{x1}\right)\right)\right)\right) \]

      13. distribute-neg-frac N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \left(\frac{\mathsf{neg}\left(3\right)}{\color{blue}{x1}}\right)\right)\right) \]

      14. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \left(\frac{-3}{x1}\right)\right)\right) \]

      15. /-lowering-/.f64 82.2%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \mathsf{/.f64}\left(-3, \color{blue}{x1}\right)\right)\right) \]

   10. Simplified 82.2%

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

   11. Taylor expanded in x1 around 0

       \[\leadsto \color{blue}{{x1}^{3} \cdot \left(6 \cdot x1 - 3\right)} \]
   12. Step-by-step derivation

       1. unpow3 N/A

          \[\leadsto \left(\left(x1 \cdot x1\right) \cdot x1\right) \cdot \left(\color{blue}{6 \cdot x1} - 3\right) \]

       2. unpow2 N/A

          \[\leadsto \left({x1}^{2} \cdot x1\right) \cdot \left(\color{blue}{6} \cdot x1 - 3\right) \]

       3. associate-*l* N/A

          \[\leadsto {x1}^{2} \cdot \color{blue}{\left(x1 \cdot \left(6 \cdot x1 - 3\right)\right)} \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\left({x1}^{2}\right), \color{blue}{\left(x1 \cdot \left(6 \cdot x1 - 3\right)\right)}\right) \]

       5. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(\left(x1 \cdot x1\right), \left(\color{blue}{x1} \cdot \left(6 \cdot x1 - 3\right)\right)\right) \]

       6. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left(\color{blue}{x1} \cdot \left(6 \cdot x1 - 3\right)\right)\right) \]

       7. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, \color{blue}{\left(6 \cdot x1 - 3\right)}\right)\right) \]

       8. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, \left(6 \cdot x1 + \color{blue}{\left(\mathsf{neg}\left(3\right)\right)}\right)\right)\right) \]

       9. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, \left(6 \cdot x1 + -3\right)\right)\right) \]

       10. +-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, \left(-3 + \color{blue}{6 \cdot x1}\right)\right)\right) \]

       11. +-lowering-+.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-3, \color{blue}{\left(6 \cdot x1\right)}\right)\right)\right) \]

       12. *-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-3, \left(x1 \cdot \color{blue}{6}\right)\right)\right)\right) \]

       13. *-lowering-*.f64 82.4%

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-3, \mathsf{*.f64}\left(x1, \color{blue}{6}\right)\right)\right)\right) \]

   13. Simplified 82.4%

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

4. Final simplification 84.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -3.55 \cdot 10^{+15}:\\ \;\;\;\;6 \cdot \left(x1 \cdot \left(x1 \cdot \left(x1 \cdot x1\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -2.2 \cdot 10^{-102}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(8 \cdot \left(x2 \cdot x2\right)\right)\\ \mathbf{elif}\;x1 \leq 0.07:\\ \;\;\;\;x2 \cdot -6 - x1\\ \mathbf{else}:\\ \;\;\;\;\left(x1 \cdot x1\right) \cdot \left(x1 \cdot \left(-3 + x1 \cdot 6\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 80.6% accurate, 4.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -3.5 \cdot 10^{+15}:\\ \;\;\;\;6 \cdot \left(x1 \cdot \left(x1 \cdot \left(x1 \cdot x1\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -1.85 \cdot 10^{-63}:\\ \;\;\;\;x2 \cdot \left(x1 \cdot \left(x2 \cdot 8\right)\right)\\ \mathbf{elif}\;x1 \leq 0.07:\\ \;\;\;\;x2 \cdot -6 - x1\\ \mathbf{else}:\\ \;\;\;\;\left(x1 \cdot x1\right) \cdot \left(x1 \cdot \left(-3 + x1 \cdot 6\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -3.5e+15)
   (* 6.0 (* x1 (* x1 (* x1 x1))))
   (if (<= x1 -1.85e-63)
     (* x2 (* x1 (* x2 8.0)))
     (if (<= x1 0.07)
       (- (* x2 -6.0) x1)
       (* (* x1 x1) (* x1 (+ -3.0 (* x1 6.0))))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -3.5e+15) {
		tmp = 6.0 * (x1 * (x1 * (x1 * x1)));
	} else if (x1 <= -1.85e-63) {
		tmp = x2 * (x1 * (x2 * 8.0));
	} else if (x1 <= 0.07) {
		tmp = (x2 * -6.0) - x1;
	} else {
		tmp = (x1 * x1) * (x1 * (-3.0 + (x1 * 6.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x1 <= (-3.5d+15)) then
        tmp = 6.0d0 * (x1 * (x1 * (x1 * x1)))
    else if (x1 <= (-1.85d-63)) then
        tmp = x2 * (x1 * (x2 * 8.0d0))
    else if (x1 <= 0.07d0) then
        tmp = (x2 * (-6.0d0)) - x1
    else
        tmp = (x1 * x1) * (x1 * ((-3.0d0) + (x1 * 6.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= -3.5e+15) {
		tmp = 6.0 * (x1 * (x1 * (x1 * x1)));
	} else if (x1 <= -1.85e-63) {
		tmp = x2 * (x1 * (x2 * 8.0));
	} else if (x1 <= 0.07) {
		tmp = (x2 * -6.0) - x1;
	} else {
		tmp = (x1 * x1) * (x1 * (-3.0 + (x1 * 6.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -3.5e+15:
		tmp = 6.0 * (x1 * (x1 * (x1 * x1)))
	elif x1 <= -1.85e-63:
		tmp = x2 * (x1 * (x2 * 8.0))
	elif x1 <= 0.07:
		tmp = (x2 * -6.0) - x1
	else:
		tmp = (x1 * x1) * (x1 * (-3.0 + (x1 * 6.0)))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -3.5e+15)
		tmp = Float64(6.0 * Float64(x1 * Float64(x1 * Float64(x1 * x1))));
	elseif (x1 <= -1.85e-63)
		tmp = Float64(x2 * Float64(x1 * Float64(x2 * 8.0)));
	elseif (x1 <= 0.07)
		tmp = Float64(Float64(x2 * -6.0) - x1);
	else
		tmp = Float64(Float64(x1 * x1) * Float64(x1 * Float64(-3.0 + Float64(x1 * 6.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -3.5e+15)
		tmp = 6.0 * (x1 * (x1 * (x1 * x1)));
	elseif (x1 <= -1.85e-63)
		tmp = x2 * (x1 * (x2 * 8.0));
	elseif (x1 <= 0.07)
		tmp = (x2 * -6.0) - x1;
	else
		tmp = (x1 * x1) * (x1 * (-3.0 + (x1 * 6.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -3.5e+15], N[(6.0 * N[(x1 * N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -1.85e-63], N[(x2 * N[(x1 * N[(x2 * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 0.07], N[(N[(x2 * -6.0), $MachinePrecision] - x1), $MachinePrecision], N[(N[(x1 * x1), $MachinePrecision] * N[(x1 * N[(-3.0 + N[(x1 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -3.5e15

   1. Initial program 27.1%

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

   3. Simplified 27.1%

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

   5. Taylor expanded in x1 around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, -6\right)\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-6, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 4\right)\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \color{blue}{9}\right)\right)\right)\right)\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 27.1%

      \[\leadsto \frac{3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right)}{x1 \cdot x1 + 1} + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(x1 \cdot \left(x1 \cdot -6\right) + \frac{2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)}{x1 \cdot x1 + 1} \cdot \left(x1 \cdot \left(-6 + \left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right) \cdot \frac{2}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot 4\right)\right) + x1 \cdot \left(2 + x1 \cdot \left(x1 + \color{blue}{9}\right)\right)\right) \]

   8. Taylor expanded in x1 around inf

      \[\leadsto \color{blue}{{x1}^{4} \cdot \left(6 - 3 \cdot \frac{1}{x1}\right)} \]
   9. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{4}\right), \color{blue}{\left(6 - 3 \cdot \frac{1}{x1}\right)}\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{\left(2 \cdot 2\right)}\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      3. pow-sqr N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{2} \cdot {x1}^{2}\right), \left(\color{blue}{6} - 3 \cdot \frac{1}{x1}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left({x1}^{2}\right), \left({x1}^{2}\right)\right), \left(\color{blue}{6} - 3 \cdot \frac{1}{x1}\right)\right) \]

      5. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x1 \cdot x1\right), \left({x1}^{2}\right)\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left({x1}^{2}\right)\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left(x1 \cdot x1\right)\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \left(6 + \color{blue}{\left(\mathsf{neg}\left(3 \cdot \frac{1}{x1}\right)\right)}\right)\right) \]

      10. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \color{blue}{\left(\mathsf{neg}\left(3 \cdot \frac{1}{x1}\right)\right)}\right)\right) \]

      11. associate-*r/ N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \left(\mathsf{neg}\left(\frac{3 \cdot 1}{x1}\right)\right)\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \left(\mathsf{neg}\left(\frac{3}{x1}\right)\right)\right)\right) \]

      13. distribute-neg-frac N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \left(\frac{\mathsf{neg}\left(3\right)}{\color{blue}{x1}}\right)\right)\right) \]

      14. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \left(\frac{-3}{x1}\right)\right)\right) \]

      15. /-lowering-/.f64 92.1%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \mathsf{/.f64}\left(-3, \color{blue}{x1}\right)\right)\right) \]

   10. Simplified 92.1%

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

   11. Taylor expanded in x1 around inf

       \[\leadsto \color{blue}{6 \cdot {x1}^{4}} \]
   12. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(6, \color{blue}{\left({x1}^{4}\right)}\right) \]

       2. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(6, \left({x1}^{\left(2 \cdot \color{blue}{2}\right)}\right)\right) \]

       3. pow-sqr N/A

          \[\leadsto \mathsf{*.f64}\left(6, \left({x1}^{2} \cdot \color{blue}{{x1}^{2}}\right)\right) \]

       4. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(6, \left(\left(x1 \cdot x1\right) \cdot {\color{blue}{x1}}^{2}\right)\right) \]

       5. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(6, \left(x1 \cdot \color{blue}{\left(x1 \cdot {x1}^{2}\right)}\right)\right) \]

       6. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(6, \left(x1 \cdot \left(x1 \cdot \left(x1 \cdot \color{blue}{x1}\right)\right)\right)\right) \]

       7. cube-mult N/A

          \[\leadsto \mathsf{*.f64}\left(6, \left(x1 \cdot {x1}^{\color{blue}{3}}\right)\right) \]

       8. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(x1, \color{blue}{\left({x1}^{3}\right)}\right)\right) \]

       9. cube-mult N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(x1, \left(x1 \cdot \color{blue}{\left(x1 \cdot x1\right)}\right)\right)\right) \]

       10. unpow2 N/A

           \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(x1, \left(x1 \cdot {x1}^{\color{blue}{2}}\right)\right)\right) \]

       11. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, \color{blue}{\left({x1}^{2}\right)}\right)\right)\right) \]

       12. unpow2 N/A

           \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, \left(x1 \cdot \color{blue}{x1}\right)\right)\right)\right) \]

       13. *-lowering-*.f64 92.1%

           \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, \color{blue}{x1}\right)\right)\right)\right) \]

   13. Simplified 92.1%

       \[\leadsto \color{blue}{6 \cdot \left(x1 \cdot \left(x1 \cdot \left(x1 \cdot x1\right)\right)\right)} \]

   if -3.5e15 < x1 < -1.85000000000000006e-63

   1. Initial program 99.4%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x1 around 0

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

   7. Simplified 86.0%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(x2 \cdot 2\right) \cdot \left(x2 \cdot 4 + -6\right) + \left(x1 \cdot \left(\left(\left(\left(9 + 3 \cdot \left(x2 \cdot 2\right)\right) + x2 \cdot 10\right) - \left(x2 \cdot 4 + -6\right)\right) + -6\right) + -1\right)\right)} \]

   8. Taylor expanded in x2 around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right), \color{blue}{\left(9 \cdot x1 - 1\right)}\right)\right)\right) \]
   9. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right), \left(9 \cdot x1 + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right), \left(9 \cdot x1 + -1\right)\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right), \mathsf{+.f64}\left(\left(9 \cdot x1\right), \color{blue}{-1}\right)\right)\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right), \mathsf{+.f64}\left(\left(x1 \cdot 9\right), -1\right)\right)\right)\right) \]

      5. *-lowering-*.f64 85.8%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 9\right), -1\right)\right)\right)\right) \]

   10. Simplified 85.8%

       \[\leadsto -6 \cdot x2 + x1 \cdot \left(\left(x2 \cdot 2\right) \cdot \left(x2 \cdot 4 + -6\right) + \color{blue}{\left(x1 \cdot 9 + -1\right)}\right) \]

   11. Taylor expanded in x2 around inf

       \[\leadsto \color{blue}{8 \cdot \left(x1 \cdot {x2}^{2}\right)} \]
   12. Step-by-step derivation

       1. unpow2 N/A

          \[\leadsto 8 \cdot \left(x1 \cdot \left(x2 \cdot \color{blue}{x2}\right)\right) \]

       2. associate-*r* N/A

          \[\leadsto 8 \cdot \left(\left(x1 \cdot x2\right) \cdot \color{blue}{x2}\right) \]

       3. associate-*l* N/A

          \[\leadsto \left(8 \cdot \left(x1 \cdot x2\right)\right) \cdot \color{blue}{x2} \]

       4. *-commutative N/A

          \[\leadsto x2 \cdot \color{blue}{\left(8 \cdot \left(x1 \cdot x2\right)\right)} \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x2, \color{blue}{\left(8 \cdot \left(x1 \cdot x2\right)\right)}\right) \]

       6. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x2, \left(\left(x1 \cdot x2\right) \cdot \color{blue}{8}\right)\right) \]

       7. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(x2, \left(x1 \cdot \color{blue}{\left(x2 \cdot 8\right)}\right)\right) \]

       8. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x2, \left(x1 \cdot \left(8 \cdot \color{blue}{x2}\right)\right)\right) \]

       9. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x2, \mathsf{*.f64}\left(x1, \color{blue}{\left(8 \cdot x2\right)}\right)\right) \]

       10. *-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(x2, \mathsf{*.f64}\left(x1, \left(x2 \cdot \color{blue}{8}\right)\right)\right) \]

       11. *-lowering-*.f64 60.0%

           \[\leadsto \mathsf{*.f64}\left(x2, \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x2, \color{blue}{8}\right)\right)\right) \]

   13. Simplified 60.0%

       \[\leadsto \color{blue}{x2 \cdot \left(x1 \cdot \left(x2 \cdot 8\right)\right)} \]

   if -1.85000000000000006e-63 < x1 < 0.070000000000000007

   1. Initial program 99.4%

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

   3. Simplified 99.5%

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

   6. Applied egg-rr 99.5%

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

   7. Taylor expanded in x1 around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(\color{blue}{\left(12 \cdot {x1}^{4}\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(-6, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]
   8. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(12, \left({x1}^{4}\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(-6, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(12, \left({x1}^{\left(2 \cdot 2\right)}\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(-6, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      3. pow-sqr N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(12, \left({x1}^{2} \cdot {x1}^{2}\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(-6, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(12, \mathsf{*.f64}\left(\left({x1}^{2}\right), \left({x1}^{2}\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(-6, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      5. unpow2 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(12, \mathsf{*.f64}\left(\left(x1 \cdot x1\right), \left({x1}^{2}\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(-6, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(12, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left({x1}^{2}\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(-6, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(12, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left(x1 \cdot x1\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(-6, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      8. *-lowering-*.f64 80.9%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(12, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(-6, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

   9. Simplified 80.9%

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

   10. Taylor expanded in x1 around 0

       \[\leadsto \color{blue}{-6 \cdot x2 + -1 \cdot x1} \]
   11. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto -6 \cdot x2 + \left(\mathsf{neg}\left(x1\right)\right) \]

       2. unsub-neg N/A

          \[\leadsto -6 \cdot x2 - \color{blue}{x1} \]

       3. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\left(-6 \cdot x2\right), \color{blue}{x1}\right) \]

       4. *-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(\left(x2 \cdot -6\right), x1\right) \]

       5. *-lowering-*.f64 81.1%

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x2, -6\right), x1\right) \]

   12. Simplified 81.1%

       \[\leadsto \color{blue}{x2 \cdot -6 - x1} \]

   if 0.070000000000000007 < x1

   1. Initial program 50.6%

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

   3. Simplified 50.7%

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

   5. Taylor expanded in x1 around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, -6\right)\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-6, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 4\right)\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \color{blue}{9}\right)\right)\right)\right)\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 50.7%

      \[\leadsto \frac{3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right)}{x1 \cdot x1 + 1} + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(x1 \cdot \left(x1 \cdot -6\right) + \frac{2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)}{x1 \cdot x1 + 1} \cdot \left(x1 \cdot \left(-6 + \left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right) \cdot \frac{2}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot 4\right)\right) + x1 \cdot \left(2 + x1 \cdot \left(x1 + \color{blue}{9}\right)\right)\right) \]

   8. Taylor expanded in x1 around inf

      \[\leadsto \color{blue}{{x1}^{4} \cdot \left(6 - 3 \cdot \frac{1}{x1}\right)} \]
   9. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{4}\right), \color{blue}{\left(6 - 3 \cdot \frac{1}{x1}\right)}\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{\left(2 \cdot 2\right)}\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      3. pow-sqr N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{2} \cdot {x1}^{2}\right), \left(\color{blue}{6} - 3 \cdot \frac{1}{x1}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left({x1}^{2}\right), \left({x1}^{2}\right)\right), \left(\color{blue}{6} - 3 \cdot \frac{1}{x1}\right)\right) \]

      5. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x1 \cdot x1\right), \left({x1}^{2}\right)\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left({x1}^{2}\right)\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left(x1 \cdot x1\right)\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \left(6 + \color{blue}{\left(\mathsf{neg}\left(3 \cdot \frac{1}{x1}\right)\right)}\right)\right) \]

      10. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \color{blue}{\left(\mathsf{neg}\left(3 \cdot \frac{1}{x1}\right)\right)}\right)\right) \]

      11. associate-*r/ N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \left(\mathsf{neg}\left(\frac{3 \cdot 1}{x1}\right)\right)\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \left(\mathsf{neg}\left(\frac{3}{x1}\right)\right)\right)\right) \]

      13. distribute-neg-frac N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \left(\frac{\mathsf{neg}\left(3\right)}{\color{blue}{x1}}\right)\right)\right) \]

      14. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \left(\frac{-3}{x1}\right)\right)\right) \]

      15. /-lowering-/.f64 82.2%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \mathsf{/.f64}\left(-3, \color{blue}{x1}\right)\right)\right) \]

   10. Simplified 82.2%

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

   11. Taylor expanded in x1 around 0

       \[\leadsto \color{blue}{{x1}^{3} \cdot \left(6 \cdot x1 - 3\right)} \]
   12. Step-by-step derivation

       1. unpow3 N/A

          \[\leadsto \left(\left(x1 \cdot x1\right) \cdot x1\right) \cdot \left(\color{blue}{6 \cdot x1} - 3\right) \]

       2. unpow2 N/A

          \[\leadsto \left({x1}^{2} \cdot x1\right) \cdot \left(\color{blue}{6} \cdot x1 - 3\right) \]

       3. associate-*l* N/A

          \[\leadsto {x1}^{2} \cdot \color{blue}{\left(x1 \cdot \left(6 \cdot x1 - 3\right)\right)} \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\left({x1}^{2}\right), \color{blue}{\left(x1 \cdot \left(6 \cdot x1 - 3\right)\right)}\right) \]

       5. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(\left(x1 \cdot x1\right), \left(\color{blue}{x1} \cdot \left(6 \cdot x1 - 3\right)\right)\right) \]

       6. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left(\color{blue}{x1} \cdot \left(6 \cdot x1 - 3\right)\right)\right) \]

       7. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, \color{blue}{\left(6 \cdot x1 - 3\right)}\right)\right) \]

       8. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, \left(6 \cdot x1 + \color{blue}{\left(\mathsf{neg}\left(3\right)\right)}\right)\right)\right) \]

       9. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, \left(6 \cdot x1 + -3\right)\right)\right) \]

       10. +-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, \left(-3 + \color{blue}{6 \cdot x1}\right)\right)\right) \]

       11. +-lowering-+.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-3, \color{blue}{\left(6 \cdot x1\right)}\right)\right)\right) \]

       12. *-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-3, \left(x1 \cdot \color{blue}{6}\right)\right)\right)\right) \]

       13. *-lowering-*.f64 82.4%

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-3, \mathsf{*.f64}\left(x1, \color{blue}{6}\right)\right)\right)\right) \]

   13. Simplified 82.4%

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

Alternative 20: 80.5% accurate, 5.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -2.8 \cdot 10^{+14}:\\ \;\;\;\;6 \cdot \left(x1 \cdot \left(x1 \cdot \left(x1 \cdot x1\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -3.8 \cdot 10^{-62}:\\ \;\;\;\;x2 \cdot \left(x1 \cdot \left(x2 \cdot 8\right)\right)\\ \mathbf{elif}\;x1 \leq 0.07:\\ \;\;\;\;x2 \cdot -6 - x1\\ \mathbf{else}:\\ \;\;\;\;\left(x1 \cdot x1\right) \cdot \left(x1 \cdot \left(x1 \cdot 6\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -2.8e+14)
   (* 6.0 (* x1 (* x1 (* x1 x1))))
   (if (<= x1 -3.8e-62)
     (* x2 (* x1 (* x2 8.0)))
     (if (<= x1 0.07) (- (* x2 -6.0) x1) (* (* x1 x1) (* x1 (* x1 6.0)))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -2.8e+14) {
		tmp = 6.0 * (x1 * (x1 * (x1 * x1)));
	} else if (x1 <= -3.8e-62) {
		tmp = x2 * (x1 * (x2 * 8.0));
	} else if (x1 <= 0.07) {
		tmp = (x2 * -6.0) - x1;
	} else {
		tmp = (x1 * x1) * (x1 * (x1 * 6.0));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x1 <= (-2.8d+14)) then
        tmp = 6.0d0 * (x1 * (x1 * (x1 * x1)))
    else if (x1 <= (-3.8d-62)) then
        tmp = x2 * (x1 * (x2 * 8.0d0))
    else if (x1 <= 0.07d0) then
        tmp = (x2 * (-6.0d0)) - x1
    else
        tmp = (x1 * x1) * (x1 * (x1 * 6.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= -2.8e+14) {
		tmp = 6.0 * (x1 * (x1 * (x1 * x1)));
	} else if (x1 <= -3.8e-62) {
		tmp = x2 * (x1 * (x2 * 8.0));
	} else if (x1 <= 0.07) {
		tmp = (x2 * -6.0) - x1;
	} else {
		tmp = (x1 * x1) * (x1 * (x1 * 6.0));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -2.8e+14:
		tmp = 6.0 * (x1 * (x1 * (x1 * x1)))
	elif x1 <= -3.8e-62:
		tmp = x2 * (x1 * (x2 * 8.0))
	elif x1 <= 0.07:
		tmp = (x2 * -6.0) - x1
	else:
		tmp = (x1 * x1) * (x1 * (x1 * 6.0))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -2.8e+14)
		tmp = Float64(6.0 * Float64(x1 * Float64(x1 * Float64(x1 * x1))));
	elseif (x1 <= -3.8e-62)
		tmp = Float64(x2 * Float64(x1 * Float64(x2 * 8.0)));
	elseif (x1 <= 0.07)
		tmp = Float64(Float64(x2 * -6.0) - x1);
	else
		tmp = Float64(Float64(x1 * x1) * Float64(x1 * Float64(x1 * 6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -2.8e+14)
		tmp = 6.0 * (x1 * (x1 * (x1 * x1)));
	elseif (x1 <= -3.8e-62)
		tmp = x2 * (x1 * (x2 * 8.0));
	elseif (x1 <= 0.07)
		tmp = (x2 * -6.0) - x1;
	else
		tmp = (x1 * x1) * (x1 * (x1 * 6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -2.8e+14], N[(6.0 * N[(x1 * N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -3.8e-62], N[(x2 * N[(x1 * N[(x2 * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 0.07], N[(N[(x2 * -6.0), $MachinePrecision] - x1), $MachinePrecision], N[(N[(x1 * x1), $MachinePrecision] * N[(x1 * N[(x1 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -2.8e14

   1. Initial program 27.1%

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

   3. Simplified 27.1%

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

   5. Taylor expanded in x1 around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, -6\right)\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-6, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 4\right)\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \color{blue}{9}\right)\right)\right)\right)\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 27.1%

      \[\leadsto \frac{3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right)}{x1 \cdot x1 + 1} + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(x1 \cdot \left(x1 \cdot -6\right) + \frac{2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)}{x1 \cdot x1 + 1} \cdot \left(x1 \cdot \left(-6 + \left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right) \cdot \frac{2}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot 4\right)\right) + x1 \cdot \left(2 + x1 \cdot \left(x1 + \color{blue}{9}\right)\right)\right) \]

   8. Taylor expanded in x1 around inf

      \[\leadsto \color{blue}{{x1}^{4} \cdot \left(6 - 3 \cdot \frac{1}{x1}\right)} \]
   9. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{4}\right), \color{blue}{\left(6 - 3 \cdot \frac{1}{x1}\right)}\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{\left(2 \cdot 2\right)}\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      3. pow-sqr N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{2} \cdot {x1}^{2}\right), \left(\color{blue}{6} - 3 \cdot \frac{1}{x1}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left({x1}^{2}\right), \left({x1}^{2}\right)\right), \left(\color{blue}{6} - 3 \cdot \frac{1}{x1}\right)\right) \]

      5. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x1 \cdot x1\right), \left({x1}^{2}\right)\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left({x1}^{2}\right)\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left(x1 \cdot x1\right)\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \left(6 + \color{blue}{\left(\mathsf{neg}\left(3 \cdot \frac{1}{x1}\right)\right)}\right)\right) \]

      10. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \color{blue}{\left(\mathsf{neg}\left(3 \cdot \frac{1}{x1}\right)\right)}\right)\right) \]

      11. associate-*r/ N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \left(\mathsf{neg}\left(\frac{3 \cdot 1}{x1}\right)\right)\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \left(\mathsf{neg}\left(\frac{3}{x1}\right)\right)\right)\right) \]

      13. distribute-neg-frac N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \left(\frac{\mathsf{neg}\left(3\right)}{\color{blue}{x1}}\right)\right)\right) \]

      14. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \left(\frac{-3}{x1}\right)\right)\right) \]

      15. /-lowering-/.f64 92.1%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \mathsf{/.f64}\left(-3, \color{blue}{x1}\right)\right)\right) \]

   10. Simplified 92.1%

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

   11. Taylor expanded in x1 around inf

       \[\leadsto \color{blue}{6 \cdot {x1}^{4}} \]
   12. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(6, \color{blue}{\left({x1}^{4}\right)}\right) \]

       2. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(6, \left({x1}^{\left(2 \cdot \color{blue}{2}\right)}\right)\right) \]

       3. pow-sqr N/A

          \[\leadsto \mathsf{*.f64}\left(6, \left({x1}^{2} \cdot \color{blue}{{x1}^{2}}\right)\right) \]

       4. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(6, \left(\left(x1 \cdot x1\right) \cdot {\color{blue}{x1}}^{2}\right)\right) \]

       5. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(6, \left(x1 \cdot \color{blue}{\left(x1 \cdot {x1}^{2}\right)}\right)\right) \]

       6. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(6, \left(x1 \cdot \left(x1 \cdot \left(x1 \cdot \color{blue}{x1}\right)\right)\right)\right) \]

       7. cube-mult N/A

          \[\leadsto \mathsf{*.f64}\left(6, \left(x1 \cdot {x1}^{\color{blue}{3}}\right)\right) \]

       8. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(x1, \color{blue}{\left({x1}^{3}\right)}\right)\right) \]

       9. cube-mult N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(x1, \left(x1 \cdot \color{blue}{\left(x1 \cdot x1\right)}\right)\right)\right) \]

       10. unpow2 N/A

           \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(x1, \left(x1 \cdot {x1}^{\color{blue}{2}}\right)\right)\right) \]

       11. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, \color{blue}{\left({x1}^{2}\right)}\right)\right)\right) \]

       12. unpow2 N/A

           \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, \left(x1 \cdot \color{blue}{x1}\right)\right)\right)\right) \]

       13. *-lowering-*.f64 92.1%

           \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, \color{blue}{x1}\right)\right)\right)\right) \]

   13. Simplified 92.1%

       \[\leadsto \color{blue}{6 \cdot \left(x1 \cdot \left(x1 \cdot \left(x1 \cdot x1\right)\right)\right)} \]

   if -2.8e14 < x1 < -3.80000000000000006e-62

   1. Initial program 99.4%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x1 around 0

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

   7. Simplified 86.0%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(x2 \cdot 2\right) \cdot \left(x2 \cdot 4 + -6\right) + \left(x1 \cdot \left(\left(\left(\left(9 + 3 \cdot \left(x2 \cdot 2\right)\right) + x2 \cdot 10\right) - \left(x2 \cdot 4 + -6\right)\right) + -6\right) + -1\right)\right)} \]

   8. Taylor expanded in x2 around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right), \color{blue}{\left(9 \cdot x1 - 1\right)}\right)\right)\right) \]
   9. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right), \left(9 \cdot x1 + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right), \left(9 \cdot x1 + -1\right)\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right), \mathsf{+.f64}\left(\left(9 \cdot x1\right), \color{blue}{-1}\right)\right)\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right), \mathsf{+.f64}\left(\left(x1 \cdot 9\right), -1\right)\right)\right)\right) \]

      5. *-lowering-*.f64 85.8%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 9\right), -1\right)\right)\right)\right) \]

   10. Simplified 85.8%

       \[\leadsto -6 \cdot x2 + x1 \cdot \left(\left(x2 \cdot 2\right) \cdot \left(x2 \cdot 4 + -6\right) + \color{blue}{\left(x1 \cdot 9 + -1\right)}\right) \]

   11. Taylor expanded in x2 around inf

       \[\leadsto \color{blue}{8 \cdot \left(x1 \cdot {x2}^{2}\right)} \]
   12. Step-by-step derivation

       1. unpow2 N/A

          \[\leadsto 8 \cdot \left(x1 \cdot \left(x2 \cdot \color{blue}{x2}\right)\right) \]

       2. associate-*r* N/A

          \[\leadsto 8 \cdot \left(\left(x1 \cdot x2\right) \cdot \color{blue}{x2}\right) \]

       3. associate-*l* N/A

          \[\leadsto \left(8 \cdot \left(x1 \cdot x2\right)\right) \cdot \color{blue}{x2} \]

       4. *-commutative N/A

          \[\leadsto x2 \cdot \color{blue}{\left(8 \cdot \left(x1 \cdot x2\right)\right)} \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x2, \color{blue}{\left(8 \cdot \left(x1 \cdot x2\right)\right)}\right) \]

       6. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x2, \left(\left(x1 \cdot x2\right) \cdot \color{blue}{8}\right)\right) \]

       7. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(x2, \left(x1 \cdot \color{blue}{\left(x2 \cdot 8\right)}\right)\right) \]

       8. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x2, \left(x1 \cdot \left(8 \cdot \color{blue}{x2}\right)\right)\right) \]

       9. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x2, \mathsf{*.f64}\left(x1, \color{blue}{\left(8 \cdot x2\right)}\right)\right) \]

       10. *-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(x2, \mathsf{*.f64}\left(x1, \left(x2 \cdot \color{blue}{8}\right)\right)\right) \]

       11. *-lowering-*.f64 60.0%

           \[\leadsto \mathsf{*.f64}\left(x2, \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x2, \color{blue}{8}\right)\right)\right) \]

   13. Simplified 60.0%

       \[\leadsto \color{blue}{x2 \cdot \left(x1 \cdot \left(x2 \cdot 8\right)\right)} \]

   if -3.80000000000000006e-62 < x1 < 0.070000000000000007

   1. Initial program 99.4%

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

   3. Simplified 99.5%

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

   6. Applied egg-rr 99.5%

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

   7. Taylor expanded in x1 around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(\color{blue}{\left(12 \cdot {x1}^{4}\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(-6, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]
   8. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(12, \left({x1}^{4}\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(-6, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(12, \left({x1}^{\left(2 \cdot 2\right)}\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(-6, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      3. pow-sqr N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(12, \left({x1}^{2} \cdot {x1}^{2}\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(-6, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(12, \mathsf{*.f64}\left(\left({x1}^{2}\right), \left({x1}^{2}\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(-6, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      5. unpow2 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(12, \mathsf{*.f64}\left(\left(x1 \cdot x1\right), \left({x1}^{2}\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(-6, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(12, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left({x1}^{2}\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(-6, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(12, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left(x1 \cdot x1\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(-6, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      8. *-lowering-*.f64 80.9%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(12, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(-6, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

   9. Simplified 80.9%

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

   10. Taylor expanded in x1 around 0

       \[\leadsto \color{blue}{-6 \cdot x2 + -1 \cdot x1} \]
   11. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto -6 \cdot x2 + \left(\mathsf{neg}\left(x1\right)\right) \]

       2. unsub-neg N/A

          \[\leadsto -6 \cdot x2 - \color{blue}{x1} \]

       3. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\left(-6 \cdot x2\right), \color{blue}{x1}\right) \]

       4. *-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(\left(x2 \cdot -6\right), x1\right) \]

       5. *-lowering-*.f64 81.1%

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x2, -6\right), x1\right) \]

   12. Simplified 81.1%

       \[\leadsto \color{blue}{x2 \cdot -6 - x1} \]

   if 0.070000000000000007 < x1

   1. Initial program 50.6%

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

   3. Simplified 50.7%

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

   5. Taylor expanded in x1 around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, -6\right)\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-6, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 4\right)\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \color{blue}{9}\right)\right)\right)\right)\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 50.7%

      \[\leadsto \frac{3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right)}{x1 \cdot x1 + 1} + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(x1 \cdot \left(x1 \cdot -6\right) + \frac{2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)}{x1 \cdot x1 + 1} \cdot \left(x1 \cdot \left(-6 + \left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right) \cdot \frac{2}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot 4\right)\right) + x1 \cdot \left(2 + x1 \cdot \left(x1 + \color{blue}{9}\right)\right)\right) \]

   8. Taylor expanded in x1 around inf

      \[\leadsto \color{blue}{{x1}^{4} \cdot \left(6 - 3 \cdot \frac{1}{x1}\right)} \]
   9. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{4}\right), \color{blue}{\left(6 - 3 \cdot \frac{1}{x1}\right)}\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{\left(2 \cdot 2\right)}\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      3. pow-sqr N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{2} \cdot {x1}^{2}\right), \left(\color{blue}{6} - 3 \cdot \frac{1}{x1}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left({x1}^{2}\right), \left({x1}^{2}\right)\right), \left(\color{blue}{6} - 3 \cdot \frac{1}{x1}\right)\right) \]

      5. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x1 \cdot x1\right), \left({x1}^{2}\right)\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left({x1}^{2}\right)\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left(x1 \cdot x1\right)\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \left(6 + \color{blue}{\left(\mathsf{neg}\left(3 \cdot \frac{1}{x1}\right)\right)}\right)\right) \]

      10. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \color{blue}{\left(\mathsf{neg}\left(3 \cdot \frac{1}{x1}\right)\right)}\right)\right) \]

      11. associate-*r/ N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \left(\mathsf{neg}\left(\frac{3 \cdot 1}{x1}\right)\right)\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \left(\mathsf{neg}\left(\frac{3}{x1}\right)\right)\right)\right) \]

      13. distribute-neg-frac N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \left(\frac{\mathsf{neg}\left(3\right)}{\color{blue}{x1}}\right)\right)\right) \]

      14. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \left(\frac{-3}{x1}\right)\right)\right) \]

      15. /-lowering-/.f64 82.2%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \mathsf{/.f64}\left(-3, \color{blue}{x1}\right)\right)\right) \]

   10. Simplified 82.2%

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

   11. Taylor expanded in x1 around 0

       \[\leadsto \color{blue}{{x1}^{3} \cdot \left(6 \cdot x1 - 3\right)} \]
   12. Step-by-step derivation

       1. unpow3 N/A

          \[\leadsto \left(\left(x1 \cdot x1\right) \cdot x1\right) \cdot \left(\color{blue}{6 \cdot x1} - 3\right) \]

       2. unpow2 N/A

          \[\leadsto \left({x1}^{2} \cdot x1\right) \cdot \left(\color{blue}{6} \cdot x1 - 3\right) \]

       3. associate-*l* N/A

          \[\leadsto {x1}^{2} \cdot \color{blue}{\left(x1 \cdot \left(6 \cdot x1 - 3\right)\right)} \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\left({x1}^{2}\right), \color{blue}{\left(x1 \cdot \left(6 \cdot x1 - 3\right)\right)}\right) \]

       5. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(\left(x1 \cdot x1\right), \left(\color{blue}{x1} \cdot \left(6 \cdot x1 - 3\right)\right)\right) \]

       6. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left(\color{blue}{x1} \cdot \left(6 \cdot x1 - 3\right)\right)\right) \]

       7. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, \color{blue}{\left(6 \cdot x1 - 3\right)}\right)\right) \]

       8. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, \left(6 \cdot x1 + \color{blue}{\left(\mathsf{neg}\left(3\right)\right)}\right)\right)\right) \]

       9. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, \left(6 \cdot x1 + -3\right)\right)\right) \]

       10. +-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, \left(-3 + \color{blue}{6 \cdot x1}\right)\right)\right) \]

       11. +-lowering-+.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-3, \color{blue}{\left(6 \cdot x1\right)}\right)\right)\right) \]

       12. *-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-3, \left(x1 \cdot \color{blue}{6}\right)\right)\right)\right) \]

       13. *-lowering-*.f64 82.4%

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-3, \mathsf{*.f64}\left(x1, \color{blue}{6}\right)\right)\right)\right) \]

   13. Simplified 82.4%

       \[\leadsto \color{blue}{\left(x1 \cdot x1\right) \cdot \left(x1 \cdot \left(-3 + x1 \cdot 6\right)\right)} \]

   14. Taylor expanded in x1 around inf

       \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \color{blue}{\left(6 \cdot {x1}^{2}\right)}\right) \]
   15. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left({x1}^{2} \cdot \color{blue}{6}\right)\right) \]

       2. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left(\left(x1 \cdot x1\right) \cdot 6\right)\right) \]

       3. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left(x1 \cdot \color{blue}{\left(x1 \cdot 6\right)}\right)\right) \]

       4. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left(x1 \cdot \left(6 \cdot \color{blue}{x1}\right)\right)\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, \color{blue}{\left(6 \cdot x1\right)}\right)\right) \]

       6. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, \left(x1 \cdot \color{blue}{6}\right)\right)\right) \]

       7. *-lowering-*.f64 82.1%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, \color{blue}{6}\right)\right)\right) \]

   16. Simplified 82.1%

       \[\leadsto \left(x1 \cdot x1\right) \cdot \color{blue}{\left(x1 \cdot \left(x1 \cdot 6\right)\right)} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 21: 80.7% accurate, 5.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(x1 \cdot \left(x1 \cdot \left(x1 \cdot x1\right)\right)\right)\\ \mathbf{if}\;x1 \leq -2 \cdot 10^{+14}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x1 \leq -1.7 \cdot 10^{-57}:\\ \;\;\;\;x2 \cdot \left(x1 \cdot \left(x2 \cdot 8\right)\right)\\ \mathbf{elif}\;x1 \leq 0.07:\\ \;\;\;\;x2 \cdot -6 - x1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* 6.0 (* x1 (* x1 (* x1 x1))))))
   (if (<= x1 -2e+14)
     t_0
     (if (<= x1 -1.7e-57)
       (* x2 (* x1 (* x2 8.0)))
       (if (<= x1 0.07) (- (* x2 -6.0) x1) t_0)))))

C

double code(double x1, double x2) {
	double t_0 = 6.0 * (x1 * (x1 * (x1 * x1)));
	double tmp;
	if (x1 <= -2e+14) {
		tmp = t_0;
	} else if (x1 <= -1.7e-57) {
		tmp = x2 * (x1 * (x2 * 8.0));
	} else if (x1 <= 0.07) {
		tmp = (x2 * -6.0) - x1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 6.0d0 * (x1 * (x1 * (x1 * x1)))
    if (x1 <= (-2d+14)) then
        tmp = t_0
    else if (x1 <= (-1.7d-57)) then
        tmp = x2 * (x1 * (x2 * 8.0d0))
    else if (x1 <= 0.07d0) then
        tmp = (x2 * (-6.0d0)) - x1
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = 6.0 * (x1 * (x1 * (x1 * x1)));
	double tmp;
	if (x1 <= -2e+14) {
		tmp = t_0;
	} else if (x1 <= -1.7e-57) {
		tmp = x2 * (x1 * (x2 * 8.0));
	} else if (x1 <= 0.07) {
		tmp = (x2 * -6.0) - x1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = 6.0 * (x1 * (x1 * (x1 * x1)))
	tmp = 0
	if x1 <= -2e+14:
		tmp = t_0
	elif x1 <= -1.7e-57:
		tmp = x2 * (x1 * (x2 * 8.0))
	elif x1 <= 0.07:
		tmp = (x2 * -6.0) - x1
	else:
		tmp = t_0
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(6.0 * Float64(x1 * Float64(x1 * Float64(x1 * x1))))
	tmp = 0.0
	if (x1 <= -2e+14)
		tmp = t_0;
	elseif (x1 <= -1.7e-57)
		tmp = Float64(x2 * Float64(x1 * Float64(x2 * 8.0)));
	elseif (x1 <= 0.07)
		tmp = Float64(Float64(x2 * -6.0) - x1);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = 6.0 * (x1 * (x1 * (x1 * x1)));
	tmp = 0.0;
	if (x1 <= -2e+14)
		tmp = t_0;
	elseif (x1 <= -1.7e-57)
		tmp = x2 * (x1 * (x2 * 8.0));
	elseif (x1 <= 0.07)
		tmp = (x2 * -6.0) - x1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(6.0 * N[(x1 * N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -2e+14], t$95$0, If[LessEqual[x1, -1.7e-57], N[(x2 * N[(x1 * N[(x2 * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 0.07], N[(N[(x2 * -6.0), $MachinePrecision] - x1), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -2e14 or 0.070000000000000007 < x1

   1. Initial program 37.3%

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

   3. Simplified 37.4%

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

   5. Taylor expanded in x1 around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, -6\right)\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(-6, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 4\right)\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \color{blue}{9}\right)\right)\right)\right)\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 37.4%

      \[\leadsto \frac{3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right)}{x1 \cdot x1 + 1} + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(x1 \cdot \left(x1 \cdot -6\right) + \frac{2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)}{x1 \cdot x1 + 1} \cdot \left(x1 \cdot \left(-6 + \left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right) \cdot \frac{2}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot 4\right)\right) + x1 \cdot \left(2 + x1 \cdot \left(x1 + \color{blue}{9}\right)\right)\right) \]

   8. Taylor expanded in x1 around inf

      \[\leadsto \color{blue}{{x1}^{4} \cdot \left(6 - 3 \cdot \frac{1}{x1}\right)} \]
   9. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{4}\right), \color{blue}{\left(6 - 3 \cdot \frac{1}{x1}\right)}\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{\left(2 \cdot 2\right)}\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      3. pow-sqr N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{2} \cdot {x1}^{2}\right), \left(\color{blue}{6} - 3 \cdot \frac{1}{x1}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left({x1}^{2}\right), \left({x1}^{2}\right)\right), \left(\color{blue}{6} - 3 \cdot \frac{1}{x1}\right)\right) \]

      5. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x1 \cdot x1\right), \left({x1}^{2}\right)\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left({x1}^{2}\right)\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left(x1 \cdot x1\right)\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \left(6 - 3 \cdot \frac{1}{x1}\right)\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \left(6 + \color{blue}{\left(\mathsf{neg}\left(3 \cdot \frac{1}{x1}\right)\right)}\right)\right) \]

      10. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \color{blue}{\left(\mathsf{neg}\left(3 \cdot \frac{1}{x1}\right)\right)}\right)\right) \]

      11. associate-*r/ N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \left(\mathsf{neg}\left(\frac{3 \cdot 1}{x1}\right)\right)\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \left(\mathsf{neg}\left(\frac{3}{x1}\right)\right)\right)\right) \]

      13. distribute-neg-frac N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \left(\frac{\mathsf{neg}\left(3\right)}{\color{blue}{x1}}\right)\right)\right) \]

      14. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \left(\frac{-3}{x1}\right)\right)\right) \]

      15. /-lowering-/.f64 87.8%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(6, \mathsf{/.f64}\left(-3, \color{blue}{x1}\right)\right)\right) \]

   10. Simplified 87.8%

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

   11. Taylor expanded in x1 around inf

       \[\leadsto \color{blue}{6 \cdot {x1}^{4}} \]
   12. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(6, \color{blue}{\left({x1}^{4}\right)}\right) \]

       2. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(6, \left({x1}^{\left(2 \cdot \color{blue}{2}\right)}\right)\right) \]

       3. pow-sqr N/A

          \[\leadsto \mathsf{*.f64}\left(6, \left({x1}^{2} \cdot \color{blue}{{x1}^{2}}\right)\right) \]

       4. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(6, \left(\left(x1 \cdot x1\right) \cdot {\color{blue}{x1}}^{2}\right)\right) \]

       5. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(6, \left(x1 \cdot \color{blue}{\left(x1 \cdot {x1}^{2}\right)}\right)\right) \]

       6. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(6, \left(x1 \cdot \left(x1 \cdot \left(x1 \cdot \color{blue}{x1}\right)\right)\right)\right) \]

       7. cube-mult N/A

          \[\leadsto \mathsf{*.f64}\left(6, \left(x1 \cdot {x1}^{\color{blue}{3}}\right)\right) \]

       8. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(x1, \color{blue}{\left({x1}^{3}\right)}\right)\right) \]

       9. cube-mult N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(x1, \left(x1 \cdot \color{blue}{\left(x1 \cdot x1\right)}\right)\right)\right) \]

       10. unpow2 N/A

           \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(x1, \left(x1 \cdot {x1}^{\color{blue}{2}}\right)\right)\right) \]

       11. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, \color{blue}{\left({x1}^{2}\right)}\right)\right)\right) \]

       12. unpow2 N/A

           \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, \left(x1 \cdot \color{blue}{x1}\right)\right)\right)\right) \]

       13. *-lowering-*.f64 87.8%

           \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, \color{blue}{x1}\right)\right)\right)\right) \]

   13. Simplified 87.8%

       \[\leadsto \color{blue}{6 \cdot \left(x1 \cdot \left(x1 \cdot \left(x1 \cdot x1\right)\right)\right)} \]

   if -2e14 < x1 < -1.70000000000000008e-57

   1. Initial program 99.4%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x1 around 0

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

   7. Simplified 86.0%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(x2 \cdot 2\right) \cdot \left(x2 \cdot 4 + -6\right) + \left(x1 \cdot \left(\left(\left(\left(9 + 3 \cdot \left(x2 \cdot 2\right)\right) + x2 \cdot 10\right) - \left(x2 \cdot 4 + -6\right)\right) + -6\right) + -1\right)\right)} \]

   8. Taylor expanded in x2 around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right), \color{blue}{\left(9 \cdot x1 - 1\right)}\right)\right)\right) \]
   9. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right), \left(9 \cdot x1 + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right), \left(9 \cdot x1 + -1\right)\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right), \mathsf{+.f64}\left(\left(9 \cdot x1\right), \color{blue}{-1}\right)\right)\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right), \mathsf{+.f64}\left(\left(x1 \cdot 9\right), -1\right)\right)\right)\right) \]

      5. *-lowering-*.f64 85.8%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 9\right), -1\right)\right)\right)\right) \]

   10. Simplified 85.8%

       \[\leadsto -6 \cdot x2 + x1 \cdot \left(\left(x2 \cdot 2\right) \cdot \left(x2 \cdot 4 + -6\right) + \color{blue}{\left(x1 \cdot 9 + -1\right)}\right) \]

   11. Taylor expanded in x2 around inf

       \[\leadsto \color{blue}{8 \cdot \left(x1 \cdot {x2}^{2}\right)} \]
   12. Step-by-step derivation

       1. unpow2 N/A

          \[\leadsto 8 \cdot \left(x1 \cdot \left(x2 \cdot \color{blue}{x2}\right)\right) \]

       2. associate-*r* N/A

          \[\leadsto 8 \cdot \left(\left(x1 \cdot x2\right) \cdot \color{blue}{x2}\right) \]

       3. associate-*l* N/A

          \[\leadsto \left(8 \cdot \left(x1 \cdot x2\right)\right) \cdot \color{blue}{x2} \]

       4. *-commutative N/A

          \[\leadsto x2 \cdot \color{blue}{\left(8 \cdot \left(x1 \cdot x2\right)\right)} \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x2, \color{blue}{\left(8 \cdot \left(x1 \cdot x2\right)\right)}\right) \]

       6. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x2, \left(\left(x1 \cdot x2\right) \cdot \color{blue}{8}\right)\right) \]

       7. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(x2, \left(x1 \cdot \color{blue}{\left(x2 \cdot 8\right)}\right)\right) \]

       8. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x2, \left(x1 \cdot \left(8 \cdot \color{blue}{x2}\right)\right)\right) \]

       9. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x2, \mathsf{*.f64}\left(x1, \color{blue}{\left(8 \cdot x2\right)}\right)\right) \]

       10. *-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(x2, \mathsf{*.f64}\left(x1, \left(x2 \cdot \color{blue}{8}\right)\right)\right) \]

       11. *-lowering-*.f64 60.0%

           \[\leadsto \mathsf{*.f64}\left(x2, \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x2, \color{blue}{8}\right)\right)\right) \]

   13. Simplified 60.0%

       \[\leadsto \color{blue}{x2 \cdot \left(x1 \cdot \left(x2 \cdot 8\right)\right)} \]

   if -1.70000000000000008e-57 < x1 < 0.070000000000000007

   1. Initial program 99.4%

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

   3. Simplified 99.5%

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

   6. Applied egg-rr 99.5%

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

   7. Taylor expanded in x1 around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(\color{blue}{\left(12 \cdot {x1}^{4}\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(-6, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]
   8. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(12, \left({x1}^{4}\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(-6, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(12, \left({x1}^{\left(2 \cdot 2\right)}\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(-6, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      3. pow-sqr N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(12, \left({x1}^{2} \cdot {x1}^{2}\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(-6, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(12, \mathsf{*.f64}\left(\left({x1}^{2}\right), \left({x1}^{2}\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(-6, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      5. unpow2 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(12, \mathsf{*.f64}\left(\left(x1 \cdot x1\right), \left({x1}^{2}\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(-6, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(12, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left({x1}^{2}\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(-6, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(12, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left(x1 \cdot x1\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(-6, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      8. *-lowering-*.f64 80.9%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(12, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(-6, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

   9. Simplified 80.9%

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

   10. Taylor expanded in x1 around 0

       \[\leadsto \color{blue}{-6 \cdot x2 + -1 \cdot x1} \]
   11. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto -6 \cdot x2 + \left(\mathsf{neg}\left(x1\right)\right) \]

       2. unsub-neg N/A

          \[\leadsto -6 \cdot x2 - \color{blue}{x1} \]

       3. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\left(-6 \cdot x2\right), \color{blue}{x1}\right) \]

       4. *-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(\left(x2 \cdot -6\right), x1\right) \]

       5. *-lowering-*.f64 81.1%

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x2, -6\right), x1\right) \]

   12. Simplified 81.1%

       \[\leadsto \color{blue}{x2 \cdot -6 - x1} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 22: 64.0% accurate, 8.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 9\right)\\ \mathbf{if}\;x1 \leq -5.2 \cdot 10^{+47}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x1 \leq 0.07:\\ \;\;\;\;x2 \cdot -6 - x1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 9.0))))
   (if (<= x1 -5.2e+47) t_0 (if (<= x1 0.07) (- (* x2 -6.0) x1) t_0))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 9.0);
	double tmp;
	if (x1 <= -5.2e+47) {
		tmp = t_0;
	} else if (x1 <= 0.07) {
		tmp = (x2 * -6.0) - x1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x1 * (x1 * 9.0d0)
    if (x1 <= (-5.2d+47)) then
        tmp = t_0
    else if (x1 <= 0.07d0) then
        tmp = (x2 * (-6.0d0)) - x1
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 9.0);
	double tmp;
	if (x1 <= -5.2e+47) {
		tmp = t_0;
	} else if (x1 <= 0.07) {
		tmp = (x2 * -6.0) - x1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 9.0)
	tmp = 0
	if x1 <= -5.2e+47:
		tmp = t_0
	elif x1 <= 0.07:
		tmp = (x2 * -6.0) - x1
	else:
		tmp = t_0
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 9.0))
	tmp = 0.0
	if (x1 <= -5.2e+47)
		tmp = t_0;
	elseif (x1 <= 0.07)
		tmp = Float64(Float64(x2 * -6.0) - x1);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * 9.0);
	tmp = 0.0;
	if (x1 <= -5.2e+47)
		tmp = t_0;
	elseif (x1 <= 0.07)
		tmp = (x2 * -6.0) - x1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -5.2e+47], t$95$0, If[LessEqual[x1, 0.07], N[(N[(x2 * -6.0), $MachinePrecision] - x1), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x1 < -5.20000000000000007e47 or 0.070000000000000007 < x1

   1. Initial program 32.9%

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

   3. Simplified 33.0%

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

   5. Taylor expanded in x1 around 0

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

   7. Simplified 51.9%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(x2 \cdot 2\right) \cdot \left(x2 \cdot 4 + -6\right) + \left(x1 \cdot \left(\left(\left(\left(9 + 3 \cdot \left(x2 \cdot 2\right)\right) + x2 \cdot 10\right) - \left(x2 \cdot 4 + -6\right)\right) + -6\right) + -1\right)\right)} \]

   8. Taylor expanded in x2 around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right), \color{blue}{\left(9 \cdot x1 - 1\right)}\right)\right)\right) \]
   9. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right), \left(9 \cdot x1 + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right), \left(9 \cdot x1 + -1\right)\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right), \mathsf{+.f64}\left(\left(9 \cdot x1\right), \color{blue}{-1}\right)\right)\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right), \mathsf{+.f64}\left(\left(x1 \cdot 9\right), -1\right)\right)\right)\right) \]

      5. *-lowering-*.f64 59.0%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 9\right), -1\right)\right)\right)\right) \]

   10. Simplified 59.0%

       \[\leadsto -6 \cdot x2 + x1 \cdot \left(\left(x2 \cdot 2\right) \cdot \left(x2 \cdot 4 + -6\right) + \color{blue}{\left(x1 \cdot 9 + -1\right)}\right) \]

   11. Taylor expanded in x1 around inf

       \[\leadsto \color{blue}{9 \cdot {x1}^{2}} \]
   12. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto {x1}^{2} \cdot \color{blue}{9} \]

       2. unpow2 N/A

          \[\leadsto \left(x1 \cdot x1\right) \cdot 9 \]

       3. associate-*l* N/A

          \[\leadsto x1 \cdot \color{blue}{\left(x1 \cdot 9\right)} \]

       4. *-commutative N/A

          \[\leadsto x1 \cdot \left(9 \cdot \color{blue}{x1}\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x1, \color{blue}{\left(9 \cdot x1\right)}\right) \]

       6. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x1, \left(x1 \cdot \color{blue}{9}\right)\right) \]

       7. *-lowering-*.f64 62.2%

          \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, \color{blue}{9}\right)\right) \]

   13. Simplified 62.2%

       \[\leadsto \color{blue}{x1 \cdot \left(x1 \cdot 9\right)} \]

   if -5.20000000000000007e47 < x1 < 0.070000000000000007

   1. Initial program 99.4%

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

   3. Simplified 99.5%

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

   6. Applied egg-rr 99.5%

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

   7. Taylor expanded in x1 around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(\color{blue}{\left(12 \cdot {x1}^{4}\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(-6, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]
   8. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(12, \left({x1}^{4}\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(-6, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(12, \left({x1}^{\left(2 \cdot 2\right)}\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(-6, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      3. pow-sqr N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(12, \left({x1}^{2} \cdot {x1}^{2}\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(-6, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(12, \mathsf{*.f64}\left(\left({x1}^{2}\right), \left({x1}^{2}\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(-6, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      5. unpow2 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(12, \mathsf{*.f64}\left(\left(x1 \cdot x1\right), \left({x1}^{2}\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(-6, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(12, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left({x1}^{2}\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(-6, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(12, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left(x1 \cdot x1\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(-6, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      8. *-lowering-*.f64 74.7%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(12, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(x1, x1\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{*.f64}\left(-6, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

   9. Simplified 74.7%

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

   10. Taylor expanded in x1 around 0

       \[\leadsto \color{blue}{-6 \cdot x2 + -1 \cdot x1} \]
   11. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto -6 \cdot x2 + \left(\mathsf{neg}\left(x1\right)\right) \]

       2. unsub-neg N/A

          \[\leadsto -6 \cdot x2 - \color{blue}{x1} \]

       3. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\left(-6 \cdot x2\right), \color{blue}{x1}\right) \]

       4. *-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(\left(x2 \cdot -6\right), x1\right) \]

       5. *-lowering-*.f64 70.6%

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x2, -6\right), x1\right) \]

   12. Simplified 70.6%

       \[\leadsto \color{blue}{x2 \cdot -6 - x1} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 23: 51.7% accurate, 8.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 9\right)\\ \mathbf{if}\;x1 \leq -2 \cdot 10^{+14}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x1 \leq 2.4 \cdot 10^{-5}:\\ \;\;\;\;x2 \cdot -6\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 9.0))))
   (if (<= x1 -2e+14) t_0 (if (<= x1 2.4e-5) (* x2 -6.0) t_0))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 9.0);
	double tmp;
	if (x1 <= -2e+14) {
		tmp = t_0;
	} else if (x1 <= 2.4e-5) {
		tmp = x2 * -6.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x1 * (x1 * 9.0d0)
    if (x1 <= (-2d+14)) then
        tmp = t_0
    else if (x1 <= 2.4d-5) then
        tmp = x2 * (-6.0d0)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 9.0);
	double tmp;
	if (x1 <= -2e+14) {
		tmp = t_0;
	} else if (x1 <= 2.4e-5) {
		tmp = x2 * -6.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 9.0)
	tmp = 0
	if x1 <= -2e+14:
		tmp = t_0
	elif x1 <= 2.4e-5:
		tmp = x2 * -6.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 9.0))
	tmp = 0.0
	if (x1 <= -2e+14)
		tmp = t_0;
	elseif (x1 <= 2.4e-5)
		tmp = Float64(x2 * -6.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * 9.0);
	tmp = 0.0;
	if (x1 <= -2e+14)
		tmp = t_0;
	elseif (x1 <= 2.4e-5)
		tmp = x2 * -6.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -2e+14], t$95$0, If[LessEqual[x1, 2.4e-5], N[(x2 * -6.0), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x1 < -2e14 or 2.4000000000000001e-5 < x1

   1. Initial program 37.3%

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

   3. Simplified 37.4%

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

   5. Taylor expanded in x1 around 0

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

   7. Simplified 50.2%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(x2 \cdot 2\right) \cdot \left(x2 \cdot 4 + -6\right) + \left(x1 \cdot \left(\left(\left(\left(9 + 3 \cdot \left(x2 \cdot 2\right)\right) + x2 \cdot 10\right) - \left(x2 \cdot 4 + -6\right)\right) + -6\right) + -1\right)\right)} \]

   8. Taylor expanded in x2 around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right), \color{blue}{\left(9 \cdot x1 - 1\right)}\right)\right)\right) \]
   9. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right), \left(9 \cdot x1 + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right), \left(9 \cdot x1 + -1\right)\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right), \mathsf{+.f64}\left(\left(9 \cdot x1\right), \color{blue}{-1}\right)\right)\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right), \mathsf{+.f64}\left(\left(x1 \cdot 9\right), -1\right)\right)\right)\right) \]

      5. *-lowering-*.f64 57.6%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 9\right), -1\right)\right)\right)\right) \]

   10. Simplified 57.6%

       \[\leadsto -6 \cdot x2 + x1 \cdot \left(\left(x2 \cdot 2\right) \cdot \left(x2 \cdot 4 + -6\right) + \color{blue}{\left(x1 \cdot 9 + -1\right)}\right) \]

   11. Taylor expanded in x1 around inf

       \[\leadsto \color{blue}{9 \cdot {x1}^{2}} \]
   12. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto {x1}^{2} \cdot \color{blue}{9} \]

       2. unpow2 N/A

          \[\leadsto \left(x1 \cdot x1\right) \cdot 9 \]

       3. associate-*l* N/A

          \[\leadsto x1 \cdot \color{blue}{\left(x1 \cdot 9\right)} \]

       4. *-commutative N/A

          \[\leadsto x1 \cdot \left(9 \cdot \color{blue}{x1}\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x1, \color{blue}{\left(9 \cdot x1\right)}\right) \]

       6. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x1, \left(x1 \cdot \color{blue}{9}\right)\right) \]

       7. *-lowering-*.f64 58.4%

          \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, \color{blue}{9}\right)\right) \]

   13. Simplified 58.4%

       \[\leadsto \color{blue}{x1 \cdot \left(x1 \cdot 9\right)} \]

   if -2e14 < x1 < 2.4000000000000001e-5

   1. Initial program 99.4%

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

   3. Taylor expanded in x1 around 0

      \[\leadsto \color{blue}{-6 \cdot x2} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 51.9%

         \[\leadsto \mathsf{*.f64}\left(-6, \color{blue}{x2}\right) \]

   5. Simplified 51.9%

      \[\leadsto \color{blue}{-6 \cdot x2} \]
3. Recombined 2 regimes into one program.

4. Final simplification 55.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -2 \cdot 10^{+14}:\\ \;\;\;\;x1 \cdot \left(x1 \cdot 9\right)\\ \mathbf{elif}\;x1 \leq 2.4 \cdot 10^{-5}:\\ \;\;\;\;x2 \cdot -6\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot \left(x1 \cdot 9\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 26.6% accurate, 42.3× speedup

Math

\[\begin{array}{l} \\ x2 \cdot -6 \end{array} \]

FPCore

(FPCore (x1 x2) :precision binary64 (* x2 -6.0))

C

double code(double x1, double x2) {
	return x2 * -6.0;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    code = x2 * (-6.0d0)
end function

Java

public static double code(double x1, double x2) {
	return x2 * -6.0;
}

Python

def code(x1, x2):
	return x2 * -6.0

Julia

function code(x1, x2)
	return Float64(x2 * -6.0)
end

MATLAB

function tmp = code(x1, x2)
	tmp = x2 * -6.0;
end

Wolfram

code[x1_, x2_] := N[(x2 * -6.0), $MachinePrecision]

Derivation

1. Initial program 66.4%

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

3. Taylor expanded in x1 around 0

   \[\leadsto \color{blue}{-6 \cdot x2} \]
4. Step-by-step derivation

   1. *-lowering-*.f64 25.6%

      \[\leadsto \mathsf{*.f64}\left(-6, \color{blue}{x2}\right) \]

5. Simplified 25.6%

   \[\leadsto \color{blue}{-6 \cdot x2} \]

6. Final simplification 25.6%

   \[\leadsto x2 \cdot -6 \]
7. Add Preprocessing

Alternative 25: 3.5% accurate, 127.0× speedup

Math

\[\begin{array}{l} \\ 9 \end{array} \]

FPCore

(FPCore (x1 x2) :precision binary64 9.0)

C

double code(double x1, double x2) {
	return 9.0;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    code = 9.0d0
end function

Java

public static double code(double x1, double x2) {
	return 9.0;
}

Python

def code(x1, x2):
	return 9.0

Julia

function code(x1, x2)
	return 9.0
end

MATLAB

function tmp = code(x1, x2)
	tmp = 9.0;
end

Wolfram

code[x1_, x2_] := 9.0

Derivation

1. Initial program 66.4%

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

3. Simplified 66.5%

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

5. Taylor expanded in x2 around inf

   \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \color{blue}{\left(8 \cdot \frac{x1 \cdot {x2}^{2}}{1 + {x1}^{2}}\right)}\right) \]
6. Step-by-step derivation

   1. associate-*r/ N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \left(\frac{8 \cdot \left(x1 \cdot {x2}^{2}\right)}{\color{blue}{1 + {x1}^{2}}}\right)\right) \]

   2. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{/.f64}\left(\left(8 \cdot \left(x1 \cdot {x2}^{2}\right)\right), \color{blue}{\left(1 + {x1}^{2}\right)}\right)\right) \]

   3. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(8, \left(x1 \cdot {x2}^{2}\right)\right), \left(\color{blue}{1} + {x1}^{2}\right)\right)\right) \]

   4. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(8, \mathsf{*.f64}\left(x1, \left({x2}^{2}\right)\right)\right), \left(1 + {x1}^{2}\right)\right)\right) \]

   5. unpow2 N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(8, \mathsf{*.f64}\left(x1, \left(x2 \cdot x2\right)\right)\right), \left(1 + {x1}^{2}\right)\right)\right) \]

   6. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(8, \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x2, x2\right)\right)\right), \left(1 + {x1}^{2}\right)\right)\right) \]

   7. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(8, \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x2, x2\right)\right)\right), \mathsf{+.f64}\left(1, \color{blue}{\left({x1}^{2}\right)}\right)\right)\right) \]

   8. unpow2 N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(8, \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x2, x2\right)\right)\right), \mathsf{+.f64}\left(1, \left(x1 \cdot \color{blue}{x1}\right)\right)\right)\right) \]

   9. *-lowering-*.f64 40.3%

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(8, \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x2, x2\right)\right)\right), \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x1, \color{blue}{x1}\right)\right)\right)\right) \]

7. Simplified 40.3%

   \[\leadsto \frac{3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right)}{x1 \cdot x1 + 1} + \color{blue}{\frac{8 \cdot \left(x1 \cdot \left(x2 \cdot x2\right)\right)}{1 + x1 \cdot x1}} \]

8. Taylor expanded in x1 around inf

   \[\leadsto \color{blue}{9} \]
9. Step-by-step derivation

10. Simplified 3.5%

    \[\leadsto \color{blue}{9} \]
11. Add Preprocessing

Reproduce

herbie shell --seed 2024152 
(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))))))