Rosa's FloatVsDoubleBenchmark

Percentage Accurate: 70.3% → 99.4%

Time: 22.3s

Alternatives: 27

Speedup: 4.7×

• 46.6% 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: 70.3% 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: 99.4% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t$95$1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 / N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $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[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] - N[(N[(t$95$1 * t$95$3), $MachinePrecision] + N[(t$95$0 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 + N[(4.0 * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(t$95$2 / t$95$0), $MachinePrecision] * N[(x1 * 2.0), $MachinePrecision]), $MachinePrecision] * N[(3.0 + t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(N[(N[(t$95$1 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(3.0 * N[(N[(N[(x2 * -2.0), $MachinePrecision] + t$95$4), $MachinePrecision] / t$95$0), $MachinePrecision] + N[(N[(t$95$0 * N[(N[(N[(x1 * x1), $MachinePrecision] * -6.0), $MachinePrecision] + N[(N[(x1 * N[(N[(-6.0 + N[(t$95$5 / N[(t$95$0 / 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t$95$0 / t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(2.0 + N[(x1 * N[(x1 + N[(t$95$5 / N[(t$95$0 / 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(6.0 * N[Power[x1, 4.0], $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 99.5%

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

   3. Simplified 99.6%

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

   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%

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

   3. Taylor expanded in x1 around inf

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

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

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

      2. pow-lowering-pow.f64 96.8%

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

   5. Simplified 96.8%

      \[\leadsto \color{blue}{6 \cdot {x1}^{4}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.0%

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

Alternative 2: 99.3% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x1 * x1) + 1.0;
	t_1 = x1 * (x1 * 3.0);
	t_2 = (t_1 + (2.0 * x2)) - x1;
	t_3 = t_2 / (-1.0 - (x1 * x1));
	t_4 = x1 * ((x1 * 3.0) + -1.0);
	t_5 = (2.0 * x2) + t_4;
	tmp = 0.0;
	if ((x1 + ((x1 + ((x1 * (x1 * x1)) - ((t_1 * t_3) + (t_0 * (((x1 * x1) * (6.0 + (4.0 * t_3))) + (((t_2 / t_0) * (x1 * 2.0)) * (3.0 + t_3))))))) + (3.0 * (((t_1 - (2.0 * x2)) - x1) / t_0)))) <= Inf)
		tmp = ((3.0 * ((x2 * -2.0) + t_4)) / t_0) + ((t_0 * ((x1 * (x1 * -6.0)) + ((t_5 / t_0) * ((x1 * (-6.0 + (t_5 * (2.0 / t_0)))) + ((x1 * x1) * 4.0))))) + (x1 * (2.0 + (x1 * (x1 + (t_5 * (3.0 / t_0)))))));
	else
		tmp = 6.0 * (x1 ^ 4.0);
	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[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t$95$1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 / N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $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[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] - N[(N[(t$95$1 * t$95$3), $MachinePrecision] + N[(t$95$0 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 + N[(4.0 * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(t$95$2 / t$95$0), $MachinePrecision] * N[(x1 * 2.0), $MachinePrecision]), $MachinePrecision] * N[(3.0 + t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(N[(N[(t$95$1 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[(N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] + t$95$4), $MachinePrecision]), $MachinePrecision] / t$95$0), $MachinePrecision] + N[(N[(t$95$0 * N[(N[(x1 * N[(x1 * -6.0), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$5 / t$95$0), $MachinePrecision] * N[(N[(x1 * N[(-6.0 + N[(t$95$5 * 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 + N[(t$95$5 * N[(3.0 / t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(6.0 * N[Power[x1, 4.0], $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 99.5%

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

   3. Simplified 99.6%

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

   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%

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

   3. Taylor expanded in x1 around inf

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

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

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

      2. pow-lowering-pow.f64 96.8%

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

   5. Simplified 96.8%

      \[\leadsto \color{blue}{6 \cdot {x1}^{4}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.9%

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

Alternative 3: 98.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := x1 \cdot \left(x1 \cdot 3 + -1\right)\\ t_2 := 2 \cdot x2 + t\_1\\ \mathbf{if}\;x1 \leq -5.5 \cdot 10^{+102}:\\ \;\;\;\;x1 \cdot \left(-1 + x1 \cdot \left(9 + x1 \cdot -19\right)\right)\\ \mathbf{elif}\;x1 \leq 10^{+100}:\\ \;\;\;\;\frac{3}{\frac{t\_0}{x2 \cdot -2 + t\_1}} + \left(t\_0 \cdot \left(\frac{x1 \cdot \left(\left(-6 + \frac{t\_2}{\frac{t\_0}{2}}\right) + x1 \cdot 4\right)}{\frac{t\_0}{t\_2}} + x1 \cdot \left(x1 \cdot -6\right)\right) + x1 \cdot \left(2 + x1 \cdot \left(x1 + \frac{t\_2}{\frac{t\_0}{3}}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot \left(3 \cdot \left(x1 \cdot x1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ (* x1 x1) 1.0))
        (t_1 (* x1 (+ (* x1 3.0) -1.0)))
        (t_2 (+ (* 2.0 x2) t_1)))
   (if (<= x1 -5.5e+102)
     (* x1 (+ -1.0 (* x1 (+ 9.0 (* x1 -19.0)))))
     (if (<= x1 1e+100)
       (+
        (/ 3.0 (/ t_0 (+ (* x2 -2.0) t_1)))
        (+
         (*
          t_0
          (+
           (/ (* x1 (+ (+ -6.0 (/ t_2 (/ t_0 2.0))) (* x1 4.0))) (/ t_0 t_2))
           (* x1 (* x1 -6.0))))
         (* x1 (+ 2.0 (* x1 (+ x1 (/ t_2 (/ t_0 3.0))))))))
       (* x1 (* 3.0 (* x1 x1)))))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = x1 * ((x1 * 3.0) + -1.0);
	double t_2 = (2.0 * x2) + t_1;
	double tmp;
	if (x1 <= -5.5e+102) {
		tmp = x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0))));
	} else if (x1 <= 1e+100) {
		tmp = (3.0 / (t_0 / ((x2 * -2.0) + t_1))) + ((t_0 * (((x1 * ((-6.0 + (t_2 / (t_0 / 2.0))) + (x1 * 4.0))) / (t_0 / t_2)) + (x1 * (x1 * -6.0)))) + (x1 * (2.0 + (x1 * (x1 + (t_2 / (t_0 / 3.0)))))));
	} else {
		tmp = x1 * (3.0 * (x1 * x1));
	}
	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 * ((x1 * 3.0d0) + (-1.0d0))
    t_2 = (2.0d0 * x2) + t_1
    if (x1 <= (-5.5d+102)) then
        tmp = x1 * ((-1.0d0) + (x1 * (9.0d0 + (x1 * (-19.0d0)))))
    else if (x1 <= 1d+100) then
        tmp = (3.0d0 / (t_0 / ((x2 * (-2.0d0)) + t_1))) + ((t_0 * (((x1 * (((-6.0d0) + (t_2 / (t_0 / 2.0d0))) + (x1 * 4.0d0))) / (t_0 / t_2)) + (x1 * (x1 * (-6.0d0))))) + (x1 * (2.0d0 + (x1 * (x1 + (t_2 / (t_0 / 3.0d0)))))))
    else
        tmp = x1 * (3.0d0 * (x1 * x1))
    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 * ((x1 * 3.0) + -1.0);
	double t_2 = (2.0 * x2) + t_1;
	double tmp;
	if (x1 <= -5.5e+102) {
		tmp = x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0))));
	} else if (x1 <= 1e+100) {
		tmp = (3.0 / (t_0 / ((x2 * -2.0) + t_1))) + ((t_0 * (((x1 * ((-6.0 + (t_2 / (t_0 / 2.0))) + (x1 * 4.0))) / (t_0 / t_2)) + (x1 * (x1 * -6.0)))) + (x1 * (2.0 + (x1 * (x1 + (t_2 / (t_0 / 3.0)))))));
	} else {
		tmp = x1 * (3.0 * (x1 * x1));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x1 * x1) + 1.0
	t_1 = x1 * ((x1 * 3.0) + -1.0)
	t_2 = (2.0 * x2) + t_1
	tmp = 0
	if x1 <= -5.5e+102:
		tmp = x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0))))
	elif x1 <= 1e+100:
		tmp = (3.0 / (t_0 / ((x2 * -2.0) + t_1))) + ((t_0 * (((x1 * ((-6.0 + (t_2 / (t_0 / 2.0))) + (x1 * 4.0))) / (t_0 / t_2)) + (x1 * (x1 * -6.0)))) + (x1 * (2.0 + (x1 * (x1 + (t_2 / (t_0 / 3.0)))))))
	else:
		tmp = x1 * (3.0 * (x1 * x1))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * x1) + 1.0)
	t_1 = Float64(x1 * Float64(Float64(x1 * 3.0) + -1.0))
	t_2 = Float64(Float64(2.0 * x2) + t_1)
	tmp = 0.0
	if (x1 <= -5.5e+102)
		tmp = Float64(x1 * Float64(-1.0 + Float64(x1 * Float64(9.0 + Float64(x1 * -19.0)))));
	elseif (x1 <= 1e+100)
		tmp = Float64(Float64(3.0 / Float64(t_0 / Float64(Float64(x2 * -2.0) + t_1))) + Float64(Float64(t_0 * Float64(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(x1 * -6.0)))) + Float64(x1 * Float64(2.0 + Float64(x1 * Float64(x1 + Float64(t_2 / Float64(t_0 / 3.0))))))));
	else
		tmp = Float64(x1 * Float64(3.0 * Float64(x1 * x1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x1 * x1) + 1.0;
	t_1 = x1 * ((x1 * 3.0) + -1.0);
	t_2 = (2.0 * x2) + t_1;
	tmp = 0.0;
	if (x1 <= -5.5e+102)
		tmp = x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0))));
	elseif (x1 <= 1e+100)
		tmp = (3.0 / (t_0 / ((x2 * -2.0) + t_1))) + ((t_0 * (((x1 * ((-6.0 + (t_2 / (t_0 / 2.0))) + (x1 * 4.0))) / (t_0 / t_2)) + (x1 * (x1 * -6.0)))) + (x1 * (2.0 + (x1 * (x1 + (t_2 / (t_0 / 3.0)))))));
	else
		tmp = x1 * (3.0 * (x1 * x1));
	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[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(2.0 * x2), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[LessEqual[x1, -5.5e+102], N[(x1 * N[(-1.0 + N[(x1 * N[(9.0 + N[(x1 * -19.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1e+100], N[(N[(3.0 / N[(t$95$0 / N[(N[(x2 * -2.0), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$0 * N[(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] + N[(x1 * N[(x1 * -6.0), $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]), $MachinePrecision], N[(x1 * N[(3.0 * N[(x1 * x1), $MachinePrecision]), $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 0

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

   7. Simplified 76.5%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(2 \cdot \left(x2 \cdot \left(x2 \cdot 4 + -6\right)\right) + \left(x1 \cdot \left(\left(\left(\left(9 + 3 \cdot \left(x2 \cdot 2\right)\right) + \left(x2 \cdot 10 + x1 \cdot \left(\left(3 \cdot \left(x2 \cdot 4\right) + -18\right) + \left(4 \cdot \left(x2 \cdot \left(3 - x2 \cdot 2\right)\right) + -1\right)\right)\right)\right) - \left(x2 \cdot 4 + -6\right)\right) + -6\right) + -1\right)\right)} \]

   8. Taylor expanded in x2 around 0

      \[\leadsto \color{blue}{x1 \cdot \left(x1 \cdot \left(9 + -19 \cdot x1\right) - 1\right)} \]
   9. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(x1, \color{blue}{\left(x1 \cdot \left(9 + -19 \cdot x1\right) - 1\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x1, \left(x1 \cdot \left(9 + -19 \cdot x1\right) + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right) \]

      3. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(x1, \left(x1 \cdot \left(9 + -19 \cdot x1\right) + -1\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\left(x1 \cdot \left(9 + -19 \cdot x1\right)\right), \color{blue}{-1}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \left(9 + -19 \cdot x1\right)\right), -1\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(9, \left(-19 \cdot x1\right)\right)\right), -1\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(9, \left(x1 \cdot -19\right)\right)\right), -1\right)\right) \]

      8. *-lowering-*.f64 100.0%

         \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(9, \mathsf{*.f64}\left(x1, -19\right)\right)\right), -1\right)\right) \]

   10. Simplified 100.0%

       \[\leadsto \color{blue}{x1 \cdot \left(x1 \cdot \left(9 + x1 \cdot -19\right) + -1\right)} \]

   if -5.49999999999999981e102 < x1 < 1.00000000000000002e100

   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

   6. Applied egg-rr 99.7%

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

   8. Applied egg-rr 99.4%

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

   if 1.00000000000000002e100 < x1

   1. Initial program 34.1%

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

   3. Simplified 34.1%

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

   5. Taylor expanded in x1 around 0

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

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

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

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

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

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

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

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

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

      5. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + \color{blue}{\left(\mathsf{neg}\left(6\right)\right)}\right)\right)\right)\right)\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + -6\right)\right)\right)\right)\right)\right) \]

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

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

      8. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\left(x2 \cdot 4\right), -6\right)\right)\right)\right)\right)\right) \]

      9. *-lowering-*.f64 8.1%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right)\right)\right)\right)\right) \]

   7. Simplified 8.1%

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

   8. Taylor expanded in x1 around 0

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

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

         \[\leadsto \mathsf{+.f64}\left(\left(-6 \cdot x2\right), \color{blue}{\left(x1 \cdot \left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)\right) - 1\right)\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \left(\color{blue}{x1} \cdot \left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)\right) - 1\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \color{blue}{\left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)\right) - 1\right)}\right)\right) \]

      4. associate--l+ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + \color{blue}{\left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right) - 1\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)\right), \color{blue}{\left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right) - 1\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)\right), \left(\color{blue}{x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)} - 1\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 - 6\right)\right)\right), \left(x1 \cdot \color{blue}{\left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)} - 1\right)\right)\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + \left(\mathsf{neg}\left(6\right)\right)\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + \color{blue}{3 \cdot \left(3 - -2 \cdot x2\right)}\right) - 1\right)\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + -6\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \color{blue}{\left(3 - -2 \cdot x2\right)}\right) - 1\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\left(4 \cdot x2\right), -6\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + \color{blue}{3 \cdot \left(3 - -2 \cdot x2\right)}\right) - 1\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, x2\right), -6\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + \color{blue}{3} \cdot \left(3 - -2 \cdot x2\right)\right) - 1\right)\right)\right)\right) \]

      12. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, x2\right), -6\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right) + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, x2\right), -6\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right) + -1\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, x2\right), -6\right)\right)\right), \mathsf{+.f64}\left(\left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)\right), \color{blue}{-1}\right)\right)\right)\right) \]

   10. Simplified 88.6%

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

   11. Taylor expanded in x1 around inf

       \[\leadsto \color{blue}{3 \cdot {x1}^{3}} \]
   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. *-commutative N/A

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

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

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

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

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

       8. unpow2 N/A

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

       9. *-lowering-*.f64 95.5%

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

   13. Simplified 95.5%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.5 \cdot 10^{+102}:\\ \;\;\;\;x1 \cdot \left(-1 + x1 \cdot \left(9 + x1 \cdot -19\right)\right)\\ \mathbf{elif}\;x1 \leq 10^{+100}:\\ \;\;\;\;\frac{3}{\frac{x1 \cdot x1 + 1}{x2 \cdot -2 + x1 \cdot \left(x1 \cdot 3 + -1\right)}} + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(\frac{x1 \cdot \left(\left(-6 + \frac{2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)}{\frac{x1 \cdot x1 + 1}{2}}\right) + x1 \cdot 4\right)}{\frac{x1 \cdot x1 + 1}{2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)}} + x1 \cdot \left(x1 \cdot -6\right)\right) + x1 \cdot \left(2 + x1 \cdot \left(x1 + \frac{2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)}{\frac{x1 \cdot x1 + 1}{3}}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot \left(3 \cdot \left(x1 \cdot x1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 98.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3 + -1\right)\\ t_1 := 2 \cdot x2 + t\_0\\ t_2 := x1 \cdot x1 + 1\\ \mathbf{if}\;x1 \leq -5 \cdot 10^{+102}:\\ \;\;\;\;x1 \cdot \left(-1 + x1 \cdot \left(9 + x1 \cdot -19\right)\right)\\ \mathbf{elif}\;x1 \leq 10^{+100}:\\ \;\;\;\;\frac{3 \cdot \left(x2 \cdot -2 + t\_0\right)}{t\_2} + \left(t\_2 \cdot \left(x1 \cdot \left(x1 \cdot -6\right) + \frac{t\_1}{t\_2} \cdot \left(x1 \cdot \left(-6 + t\_1 \cdot \frac{2}{t\_2}\right) + \left(x1 \cdot x1\right) \cdot 4\right)\right) + x1 \cdot \left(2 + x1 \cdot \left(x1 + 9\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot \left(3 \cdot \left(x1 \cdot x1\right)\right)\\ \end{array} \end{array} \]

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 -5e+102)
     (* x1 (+ -1.0 (* x1 (+ 9.0 (* x1 -19.0)))))
     (if (<= x1 1e+100)
       (+
        (/ (* 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 (* 3.0 (* x1 x1)))))))

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 <= -5e+102) {
		tmp = x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0))));
	} else if (x1 <= 1e+100) {
		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 * (3.0 * (x1 * x1));
	}
	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 <= (-5d+102)) then
        tmp = x1 * ((-1.0d0) + (x1 * (9.0d0 + (x1 * (-19.0d0)))))
    else if (x1 <= 1d+100) 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 * (3.0d0 * (x1 * x1))
    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 <= -5e+102) {
		tmp = x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0))));
	} else if (x1 <= 1e+100) {
		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 * (3.0 * (x1 * x1));
	}
	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 <= -5e+102:
		tmp = x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0))))
	elif x1 <= 1e+100:
		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 * (3.0 * (x1 * x1))
	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 <= -5e+102)
		tmp = Float64(x1 * Float64(-1.0 + Float64(x1 * Float64(9.0 + Float64(x1 * -19.0)))));
	elseif (x1 <= 1e+100)
		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(3.0 * Float64(x1 * x1)));
	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 <= -5e+102)
		tmp = x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0))));
	elseif (x1 <= 1e+100)
		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 * (3.0 * (x1 * x1));
	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, -5e+102], N[(x1 * N[(-1.0 + N[(x1 * N[(9.0 + N[(x1 * -19.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1e+100], 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[(3.0 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -5e102

   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

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

   7. Simplified 76.5%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(2 \cdot \left(x2 \cdot \left(x2 \cdot 4 + -6\right)\right) + \left(x1 \cdot \left(\left(\left(\left(9 + 3 \cdot \left(x2 \cdot 2\right)\right) + \left(x2 \cdot 10 + x1 \cdot \left(\left(3 \cdot \left(x2 \cdot 4\right) + -18\right) + \left(4 \cdot \left(x2 \cdot \left(3 - x2 \cdot 2\right)\right) + -1\right)\right)\right)\right) - \left(x2 \cdot 4 + -6\right)\right) + -6\right) + -1\right)\right)} \]

   8. Taylor expanded in x2 around 0

      \[\leadsto \color{blue}{x1 \cdot \left(x1 \cdot \left(9 + -19 \cdot x1\right) - 1\right)} \]
   9. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(x1, \color{blue}{\left(x1 \cdot \left(9 + -19 \cdot x1\right) - 1\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x1, \left(x1 \cdot \left(9 + -19 \cdot x1\right) + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right) \]

      3. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(x1, \left(x1 \cdot \left(9 + -19 \cdot x1\right) + -1\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\left(x1 \cdot \left(9 + -19 \cdot x1\right)\right), \color{blue}{-1}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \left(9 + -19 \cdot x1\right)\right), -1\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(9, \left(-19 \cdot x1\right)\right)\right), -1\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(9, \left(x1 \cdot -19\right)\right)\right), -1\right)\right) \]

      8. *-lowering-*.f64 100.0%

         \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(9, \mathsf{*.f64}\left(x1, -19\right)\right)\right), -1\right)\right) \]

   10. Simplified 100.0%

       \[\leadsto \color{blue}{x1 \cdot \left(x1 \cdot \left(9 + x1 \cdot -19\right) + -1\right)} \]

   if -5e102 < x1 < 1.00000000000000002e100

   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 99.0%

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

   if 1.00000000000000002e100 < x1

   1. Initial program 34.1%

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

   3. Simplified 34.1%

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

   5. Taylor expanded in x1 around 0

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

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

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

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

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

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

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

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

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

      5. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + \color{blue}{\left(\mathsf{neg}\left(6\right)\right)}\right)\right)\right)\right)\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + -6\right)\right)\right)\right)\right)\right) \]

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

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

      8. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\left(x2 \cdot 4\right), -6\right)\right)\right)\right)\right)\right) \]

      9. *-lowering-*.f64 8.1%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right)\right)\right)\right)\right) \]

   7. Simplified 8.1%

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

   8. Taylor expanded in x1 around 0

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

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

         \[\leadsto \mathsf{+.f64}\left(\left(-6 \cdot x2\right), \color{blue}{\left(x1 \cdot \left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)\right) - 1\right)\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \left(\color{blue}{x1} \cdot \left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)\right) - 1\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \color{blue}{\left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)\right) - 1\right)}\right)\right) \]

      4. associate--l+ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + \color{blue}{\left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right) - 1\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)\right), \color{blue}{\left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right) - 1\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)\right), \left(\color{blue}{x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)} - 1\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 - 6\right)\right)\right), \left(x1 \cdot \color{blue}{\left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)} - 1\right)\right)\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + \left(\mathsf{neg}\left(6\right)\right)\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + \color{blue}{3 \cdot \left(3 - -2 \cdot x2\right)}\right) - 1\right)\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + -6\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \color{blue}{\left(3 - -2 \cdot x2\right)}\right) - 1\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\left(4 \cdot x2\right), -6\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + \color{blue}{3 \cdot \left(3 - -2 \cdot x2\right)}\right) - 1\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, x2\right), -6\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + \color{blue}{3} \cdot \left(3 - -2 \cdot x2\right)\right) - 1\right)\right)\right)\right) \]

      12. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, x2\right), -6\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right) + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, x2\right), -6\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right) + -1\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, x2\right), -6\right)\right)\right), \mathsf{+.f64}\left(\left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)\right), \color{blue}{-1}\right)\right)\right)\right) \]

   10. Simplified 88.6%

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

   11. Taylor expanded in x1 around inf

       \[\leadsto \color{blue}{3 \cdot {x1}^{3}} \]
   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. *-commutative N/A

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

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

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

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

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

       8. unpow2 N/A

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

       9. *-lowering-*.f64 95.5%

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

   13. Simplified 95.5%

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

4. Final simplification 98.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5 \cdot 10^{+102}:\\ \;\;\;\;x1 \cdot \left(-1 + x1 \cdot \left(9 + x1 \cdot -19\right)\right)\\ \mathbf{elif}\;x1 \leq 10^{+100}:\\ \;\;\;\;\frac{3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right)}{x1 \cdot x1 + 1} + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(x1 \cdot \left(x1 \cdot -6\right) + \frac{2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)}{x1 \cdot x1 + 1} \cdot \left(x1 \cdot \left(-6 + \left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right) \cdot \frac{2}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot 4\right)\right) + x1 \cdot \left(2 + x1 \cdot \left(x1 + 9\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot \left(3 \cdot \left(x1 \cdot x1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 93.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := x1 \cdot \left(x1 \cdot 3 + -1\right)\\ t_2 := 2 \cdot x2 + t\_1\\ t_3 := x2 \cdot -2 + t\_1\\ t_4 := \frac{3 \cdot t\_3}{t\_0}\\ \mathbf{if}\;x1 \leq -4.4 \cdot 10^{+102}:\\ \;\;\;\;x1 \cdot \left(-1 + x1 \cdot \left(9 + x1 \cdot -19\right)\right)\\ \mathbf{elif}\;x1 \leq -9.2 \cdot 10^{+21}:\\ \;\;\;\;\frac{3}{\frac{t\_0}{t\_3}} + \left(x1 \cdot \left(2 + x1 \cdot \left(x1 + \frac{t\_2}{\frac{t\_0}{3}}\right)\right) + t\_0 \cdot \left(x1 \cdot \left(x1 \cdot -6\right) + \frac{x1 \cdot \left(x1 \cdot 4 + \frac{-2}{x1}\right)}{\frac{t\_0}{t\_2}}\right)\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+42}:\\ \;\;\;\;t\_4 + \left(x1 \cdot 2 + x2 \cdot \left(x1 \cdot -12 + x2 \cdot \left(x1 \cdot 8\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 4 \cdot 10^{+102}:\\ \;\;\;\;t\_4 + \left(x1 \cdot \left(2 + x1 \cdot \left(x1 + t\_2 \cdot \frac{3}{t\_0}\right)\right) + t\_0 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 + \frac{\frac{x2 \cdot 8 + -18}{x1} - 4}{x1}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot \left(3 \cdot \left(x1 \cdot x1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ (* x1 x1) 1.0))
        (t_1 (* x1 (+ (* x1 3.0) -1.0)))
        (t_2 (+ (* 2.0 x2) t_1))
        (t_3 (+ (* x2 -2.0) t_1))
        (t_4 (/ (* 3.0 t_3) t_0)))
   (if (<= x1 -4.4e+102)
     (* x1 (+ -1.0 (* x1 (+ 9.0 (* x1 -19.0)))))
     (if (<= x1 -9.2e+21)
       (+
        (/ 3.0 (/ t_0 t_3))
        (+
         (* x1 (+ 2.0 (* x1 (+ x1 (/ t_2 (/ t_0 3.0))))))
         (*
          t_0
          (+
           (* x1 (* x1 -6.0))
           (/ (* x1 (+ (* x1 4.0) (/ -2.0 x1))) (/ t_0 t_2))))))
       (if (<= x1 1.35e+42)
         (+ t_4 (+ (* x1 2.0) (* x2 (+ (* x1 -12.0) (* x2 (* x1 8.0))))))
         (if (<= x1 4e+102)
           (+
            t_4
            (+
             (* x1 (+ 2.0 (* x1 (+ x1 (* t_2 (/ 3.0 t_0))))))
             (*
              t_0
              (*
               (* x1 x1)
               (+ 6.0 (/ (- (/ (+ (* x2 8.0) -18.0) x1) 4.0) x1))))))
           (* x1 (* 3.0 (* x1 x1)))))))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = x1 * ((x1 * 3.0) + -1.0);
	double t_2 = (2.0 * x2) + t_1;
	double t_3 = (x2 * -2.0) + t_1;
	double t_4 = (3.0 * t_3) / t_0;
	double tmp;
	if (x1 <= -4.4e+102) {
		tmp = x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0))));
	} else if (x1 <= -9.2e+21) {
		tmp = (3.0 / (t_0 / t_3)) + ((x1 * (2.0 + (x1 * (x1 + (t_2 / (t_0 / 3.0)))))) + (t_0 * ((x1 * (x1 * -6.0)) + ((x1 * ((x1 * 4.0) + (-2.0 / x1))) / (t_0 / t_2)))));
	} else if (x1 <= 1.35e+42) {
		tmp = t_4 + ((x1 * 2.0) + (x2 * ((x1 * -12.0) + (x2 * (x1 * 8.0)))));
	} else if (x1 <= 4e+102) {
		tmp = t_4 + ((x1 * (2.0 + (x1 * (x1 + (t_2 * (3.0 / t_0)))))) + (t_0 * ((x1 * x1) * (6.0 + (((((x2 * 8.0) + -18.0) / x1) - 4.0) / x1)))));
	} else {
		tmp = x1 * (3.0 * (x1 * x1));
	}
	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) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_0 = (x1 * x1) + 1.0d0
    t_1 = x1 * ((x1 * 3.0d0) + (-1.0d0))
    t_2 = (2.0d0 * x2) + t_1
    t_3 = (x2 * (-2.0d0)) + t_1
    t_4 = (3.0d0 * t_3) / t_0
    if (x1 <= (-4.4d+102)) then
        tmp = x1 * ((-1.0d0) + (x1 * (9.0d0 + (x1 * (-19.0d0)))))
    else if (x1 <= (-9.2d+21)) then
        tmp = (3.0d0 / (t_0 / t_3)) + ((x1 * (2.0d0 + (x1 * (x1 + (t_2 / (t_0 / 3.0d0)))))) + (t_0 * ((x1 * (x1 * (-6.0d0))) + ((x1 * ((x1 * 4.0d0) + ((-2.0d0) / x1))) / (t_0 / t_2)))))
    else if (x1 <= 1.35d+42) then
        tmp = t_4 + ((x1 * 2.0d0) + (x2 * ((x1 * (-12.0d0)) + (x2 * (x1 * 8.0d0)))))
    else if (x1 <= 4d+102) then
        tmp = t_4 + ((x1 * (2.0d0 + (x1 * (x1 + (t_2 * (3.0d0 / t_0)))))) + (t_0 * ((x1 * x1) * (6.0d0 + (((((x2 * 8.0d0) + (-18.0d0)) / x1) - 4.0d0) / x1)))))
    else
        tmp = x1 * (3.0d0 * (x1 * x1))
    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 * ((x1 * 3.0) + -1.0);
	double t_2 = (2.0 * x2) + t_1;
	double t_3 = (x2 * -2.0) + t_1;
	double t_4 = (3.0 * t_3) / t_0;
	double tmp;
	if (x1 <= -4.4e+102) {
		tmp = x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0))));
	} else if (x1 <= -9.2e+21) {
		tmp = (3.0 / (t_0 / t_3)) + ((x1 * (2.0 + (x1 * (x1 + (t_2 / (t_0 / 3.0)))))) + (t_0 * ((x1 * (x1 * -6.0)) + ((x1 * ((x1 * 4.0) + (-2.0 / x1))) / (t_0 / t_2)))));
	} else if (x1 <= 1.35e+42) {
		tmp = t_4 + ((x1 * 2.0) + (x2 * ((x1 * -12.0) + (x2 * (x1 * 8.0)))));
	} else if (x1 <= 4e+102) {
		tmp = t_4 + ((x1 * (2.0 + (x1 * (x1 + (t_2 * (3.0 / t_0)))))) + (t_0 * ((x1 * x1) * (6.0 + (((((x2 * 8.0) + -18.0) / x1) - 4.0) / x1)))));
	} else {
		tmp = x1 * (3.0 * (x1 * x1));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x1 * x1) + 1.0
	t_1 = x1 * ((x1 * 3.0) + -1.0)
	t_2 = (2.0 * x2) + t_1
	t_3 = (x2 * -2.0) + t_1
	t_4 = (3.0 * t_3) / t_0
	tmp = 0
	if x1 <= -4.4e+102:
		tmp = x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0))))
	elif x1 <= -9.2e+21:
		tmp = (3.0 / (t_0 / t_3)) + ((x1 * (2.0 + (x1 * (x1 + (t_2 / (t_0 / 3.0)))))) + (t_0 * ((x1 * (x1 * -6.0)) + ((x1 * ((x1 * 4.0) + (-2.0 / x1))) / (t_0 / t_2)))))
	elif x1 <= 1.35e+42:
		tmp = t_4 + ((x1 * 2.0) + (x2 * ((x1 * -12.0) + (x2 * (x1 * 8.0)))))
	elif x1 <= 4e+102:
		tmp = t_4 + ((x1 * (2.0 + (x1 * (x1 + (t_2 * (3.0 / t_0)))))) + (t_0 * ((x1 * x1) * (6.0 + (((((x2 * 8.0) + -18.0) / x1) - 4.0) / x1)))))
	else:
		tmp = x1 * (3.0 * (x1 * x1))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * x1) + 1.0)
	t_1 = Float64(x1 * Float64(Float64(x1 * 3.0) + -1.0))
	t_2 = Float64(Float64(2.0 * x2) + t_1)
	t_3 = Float64(Float64(x2 * -2.0) + t_1)
	t_4 = Float64(Float64(3.0 * t_3) / t_0)
	tmp = 0.0
	if (x1 <= -4.4e+102)
		tmp = Float64(x1 * Float64(-1.0 + Float64(x1 * Float64(9.0 + Float64(x1 * -19.0)))));
	elseif (x1 <= -9.2e+21)
		tmp = Float64(Float64(3.0 / Float64(t_0 / t_3)) + Float64(Float64(x1 * Float64(2.0 + Float64(x1 * Float64(x1 + Float64(t_2 / Float64(t_0 / 3.0)))))) + Float64(t_0 * Float64(Float64(x1 * Float64(x1 * -6.0)) + Float64(Float64(x1 * Float64(Float64(x1 * 4.0) + Float64(-2.0 / x1))) / Float64(t_0 / t_2))))));
	elseif (x1 <= 1.35e+42)
		tmp = Float64(t_4 + Float64(Float64(x1 * 2.0) + Float64(x2 * Float64(Float64(x1 * -12.0) + Float64(x2 * Float64(x1 * 8.0))))));
	elseif (x1 <= 4e+102)
		tmp = Float64(t_4 + Float64(Float64(x1 * Float64(2.0 + Float64(x1 * Float64(x1 + Float64(t_2 * Float64(3.0 / t_0)))))) + Float64(t_0 * Float64(Float64(x1 * x1) * Float64(6.0 + Float64(Float64(Float64(Float64(Float64(x2 * 8.0) + -18.0) / x1) - 4.0) / x1))))));
	else
		tmp = Float64(x1 * Float64(3.0 * Float64(x1 * x1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x1 * x1) + 1.0;
	t_1 = x1 * ((x1 * 3.0) + -1.0);
	t_2 = (2.0 * x2) + t_1;
	t_3 = (x2 * -2.0) + t_1;
	t_4 = (3.0 * t_3) / t_0;
	tmp = 0.0;
	if (x1 <= -4.4e+102)
		tmp = x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0))));
	elseif (x1 <= -9.2e+21)
		tmp = (3.0 / (t_0 / t_3)) + ((x1 * (2.0 + (x1 * (x1 + (t_2 / (t_0 / 3.0)))))) + (t_0 * ((x1 * (x1 * -6.0)) + ((x1 * ((x1 * 4.0) + (-2.0 / x1))) / (t_0 / t_2)))));
	elseif (x1 <= 1.35e+42)
		tmp = t_4 + ((x1 * 2.0) + (x2 * ((x1 * -12.0) + (x2 * (x1 * 8.0)))));
	elseif (x1 <= 4e+102)
		tmp = t_4 + ((x1 * (2.0 + (x1 * (x1 + (t_2 * (3.0 / t_0)))))) + (t_0 * ((x1 * x1) * (6.0 + (((((x2 * 8.0) + -18.0) / x1) - 4.0) / x1)))));
	else
		tmp = x1 * (3.0 * (x1 * x1));
	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[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(2.0 * x2), $MachinePrecision] + t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x2 * -2.0), $MachinePrecision] + t$95$1), $MachinePrecision]}, Block[{t$95$4 = N[(N[(3.0 * t$95$3), $MachinePrecision] / t$95$0), $MachinePrecision]}, If[LessEqual[x1, -4.4e+102], N[(x1 * N[(-1.0 + N[(x1 * N[(9.0 + N[(x1 * -19.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -9.2e+21], N[(N[(3.0 / N[(t$95$0 / t$95$3), $MachinePrecision]), $MachinePrecision] + N[(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] + N[(t$95$0 * N[(N[(x1 * N[(x1 * -6.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * N[(N[(x1 * 4.0), $MachinePrecision] + N[(-2.0 / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t$95$0 / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.35e+42], N[(t$95$4 + N[(N[(x1 * 2.0), $MachinePrecision] + N[(x2 * N[(N[(x1 * -12.0), $MachinePrecision] + N[(x2 * N[(x1 * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 4e+102], N[(t$95$4 + N[(N[(x1 * N[(2.0 + N[(x1 * N[(x1 + N[(t$95$2 * N[(3.0 / t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$0 * N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 + N[(N[(N[(N[(N[(x2 * 8.0), $MachinePrecision] + -18.0), $MachinePrecision] / x1), $MachinePrecision] - 4.0), $MachinePrecision] / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 * N[(3.0 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x1 < -4.40000000000000015e102

   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

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

   7. Simplified 76.5%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(2 \cdot \left(x2 \cdot \left(x2 \cdot 4 + -6\right)\right) + \left(x1 \cdot \left(\left(\left(\left(9 + 3 \cdot \left(x2 \cdot 2\right)\right) + \left(x2 \cdot 10 + x1 \cdot \left(\left(3 \cdot \left(x2 \cdot 4\right) + -18\right) + \left(4 \cdot \left(x2 \cdot \left(3 - x2 \cdot 2\right)\right) + -1\right)\right)\right)\right) - \left(x2 \cdot 4 + -6\right)\right) + -6\right) + -1\right)\right)} \]

   8. Taylor expanded in x2 around 0

      \[\leadsto \color{blue}{x1 \cdot \left(x1 \cdot \left(9 + -19 \cdot x1\right) - 1\right)} \]
   9. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(x1, \color{blue}{\left(x1 \cdot \left(9 + -19 \cdot x1\right) - 1\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x1, \left(x1 \cdot \left(9 + -19 \cdot x1\right) + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right) \]

      3. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(x1, \left(x1 \cdot \left(9 + -19 \cdot x1\right) + -1\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\left(x1 \cdot \left(9 + -19 \cdot x1\right)\right), \color{blue}{-1}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \left(9 + -19 \cdot x1\right)\right), -1\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(9, \left(-19 \cdot x1\right)\right)\right), -1\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(9, \left(x1 \cdot -19\right)\right)\right), -1\right)\right) \]

      8. *-lowering-*.f64 100.0%

         \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(9, \mathsf{*.f64}\left(x1, -19\right)\right)\right), -1\right)\right) \]

   10. Simplified 100.0%

       \[\leadsto \color{blue}{x1 \cdot \left(x1 \cdot \left(9 + x1 \cdot -19\right) + -1\right)} \]

   if -4.40000000000000015e102 < x1 < -9.2e21

   1. Initial program 99.6%

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

   3. Simplified 99.8%

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

   6. Applied egg-rr 99.5%

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

   8. Applied egg-rr 99.9%

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

   9. Taylor expanded in x1 around inf

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

       1. /-lowering-/.f64 95.7%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(3, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, x1\right), -1\right)\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, -6\right)\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{/.f64}\left(-2, x1\right), \mathsf{*.f64}\left(x1, 4\right)\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, x1\right), -1\right)\right), \mathsf{*.f64}\left(x2, 2\right)\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, x1\right), -1\right)\right), \mathsf{*.f64}\left(x2, 2\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), 3\right)\right)\right)\right)\right)\right)\right)\right) \]

   11. Simplified 95.7%

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

   if -9.2e21 < x1 < 1.35e42

   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

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

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

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

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

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

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

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

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

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

      5. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + \color{blue}{\left(\mathsf{neg}\left(6\right)\right)}\right)\right)\right)\right)\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + -6\right)\right)\right)\right)\right)\right) \]

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

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

      8. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\left(x2 \cdot 4\right), -6\right)\right)\right)\right)\right)\right) \]

      9. *-lowering-*.f64 88.6%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right)\right)\right)\right)\right) \]

   7. Simplified 88.6%

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

   8. Taylor expanded in x2 around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \color{blue}{\left(2 \cdot x1 + x2 \cdot \left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right)\right)}\right) \]
   9. Step-by-step derivation

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\left(2 \cdot x1\right), \color{blue}{\left(x2 \cdot \left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right)\right)}\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\left(x1 \cdot 2\right), \left(\color{blue}{x2} \cdot \left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 2\right), \left(\color{blue}{x2} \cdot \left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 2\right), \mathsf{*.f64}\left(x2, \color{blue}{\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 2\right), \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\left(-12 \cdot x1\right), \color{blue}{\left(8 \cdot \left(x1 \cdot x2\right)\right)}\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 2\right), \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\left(x1 \cdot -12\right), \left(\color{blue}{8} \cdot \left(x1 \cdot x2\right)\right)\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 2\right), \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, -12\right), \left(\color{blue}{8} \cdot \left(x1 \cdot x2\right)\right)\right)\right)\right)\right) \]

      8. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 2\right), \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, -12\right), \left(\left(8 \cdot x1\right) \cdot \color{blue}{x2}\right)\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 2\right), \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, -12\right), \mathsf{*.f64}\left(\left(8 \cdot x1\right), \color{blue}{x2}\right)\right)\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 2\right), \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, -12\right), \mathsf{*.f64}\left(\left(x1 \cdot 8\right), x2\right)\right)\right)\right)\right) \]

      11. *-lowering-*.f64 95.7%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 2\right), \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, -12\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, 8\right), x2\right)\right)\right)\right)\right) \]

   10. Simplified 95.7%

       \[\leadsto \frac{3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right)}{x1 \cdot x1 + 1} + \color{blue}{\left(x1 \cdot 2 + x2 \cdot \left(x1 \cdot -12 + \left(x1 \cdot 8\right) \cdot x2\right)\right)} \]

   if 1.35e42 < x1 < 3.99999999999999991e102

   1. Initial program 99.0%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in x1 around -inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \color{blue}{\left({x1}^{2} \cdot \left(6 + -1 \cdot \frac{4 + -1 \cdot \frac{8 \cdot x2 - 18}{x1}}{x1}\right)\right)}\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]
   6. Step-by-step derivation

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{*.f64}\left(\left({x1}^{2}\right), \left(6 + -1 \cdot \frac{4 + -1 \cdot \frac{8 \cdot x2 - 18}{x1}}{x1}\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      2. unpow2 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{*.f64}\left(\left(x1 \cdot x1\right), \left(6 + -1 \cdot \frac{4 + -1 \cdot \frac{8 \cdot x2 - 18}{x1}}{x1}\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left(6 + -1 \cdot \frac{4 + -1 \cdot \frac{8 \cdot x2 - 18}{x1}}{x1}\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      4. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left(6 + \left(\mathsf{neg}\left(\frac{4 + -1 \cdot \frac{8 \cdot x2 - 18}{x1}}{x1}\right)\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      5. unsub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left(6 - \frac{4 + -1 \cdot \frac{8 \cdot x2 - 18}{x1}}{x1}\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{\_.f64}\left(6, \left(\frac{4 + -1 \cdot \frac{8 \cdot x2 - 18}{x1}}{x1}\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{\_.f64}\left(6, \mathsf{/.f64}\left(\left(4 + -1 \cdot \frac{8 \cdot x2 - 18}{x1}\right), x1\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      8. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{\_.f64}\left(6, \mathsf{/.f64}\left(\left(4 + \left(\mathsf{neg}\left(\frac{8 \cdot x2 - 18}{x1}\right)\right)\right), x1\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      9. unsub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{\_.f64}\left(6, \mathsf{/.f64}\left(\left(4 - \frac{8 \cdot x2 - 18}{x1}\right), x1\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{\_.f64}\left(6, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(4, \left(\frac{8 \cdot x2 - 18}{x1}\right)\right), x1\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{\_.f64}\left(6, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(4, \mathsf{/.f64}\left(\left(8 \cdot x2 - 18\right), x1\right)\right), x1\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      12. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{\_.f64}\left(6, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(4, \mathsf{/.f64}\left(\left(8 \cdot x2 + \left(\mathsf{neg}\left(18\right)\right)\right), x1\right)\right), x1\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{\_.f64}\left(6, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(4, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(8 \cdot x2\right), \left(\mathsf{neg}\left(18\right)\right)\right), x1\right)\right), x1\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{\_.f64}\left(6, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(4, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(x2 \cdot 8\right), \left(\mathsf{neg}\left(18\right)\right)\right), x1\right)\right), x1\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{\_.f64}\left(6, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(4, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 8\right), \left(\mathsf{neg}\left(18\right)\right)\right), x1\right)\right), x1\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      16. metadata-eval 99.4%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{\_.f64}\left(6, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(4, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 8\right), -18\right), x1\right)\right), x1\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

   7. Simplified 99.4%

      \[\leadsto \frac{3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right)}{x1 \cdot x1 + 1} + \left(\left(x1 \cdot x1 + 1\right) \cdot \color{blue}{\left(\left(x1 \cdot x1\right) \cdot \left(6 - \frac{4 - \frac{x2 \cdot 8 + -18}{x1}}{x1}\right)\right)} + x1 \cdot \left(2 + x1 \cdot \left(x1 + \left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right) \cdot \frac{3}{x1 \cdot x1 + 1}\right)\right)\right) \]

   if 3.99999999999999991e102 < x1

   1. Initial program 34.1%

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

   3. Simplified 34.1%

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

   5. Taylor expanded in x1 around 0

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

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

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

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

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

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

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

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

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

      5. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + \color{blue}{\left(\mathsf{neg}\left(6\right)\right)}\right)\right)\right)\right)\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + -6\right)\right)\right)\right)\right)\right) \]

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

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

      8. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\left(x2 \cdot 4\right), -6\right)\right)\right)\right)\right)\right) \]

      9. *-lowering-*.f64 8.1%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right)\right)\right)\right)\right) \]

   7. Simplified 8.1%

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

   8. Taylor expanded in x1 around 0

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

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

         \[\leadsto \mathsf{+.f64}\left(\left(-6 \cdot x2\right), \color{blue}{\left(x1 \cdot \left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)\right) - 1\right)\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \left(\color{blue}{x1} \cdot \left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)\right) - 1\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \color{blue}{\left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)\right) - 1\right)}\right)\right) \]

      4. associate--l+ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + \color{blue}{\left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right) - 1\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)\right), \color{blue}{\left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right) - 1\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)\right), \left(\color{blue}{x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)} - 1\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 - 6\right)\right)\right), \left(x1 \cdot \color{blue}{\left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)} - 1\right)\right)\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + \left(\mathsf{neg}\left(6\right)\right)\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + \color{blue}{3 \cdot \left(3 - -2 \cdot x2\right)}\right) - 1\right)\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + -6\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \color{blue}{\left(3 - -2 \cdot x2\right)}\right) - 1\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\left(4 \cdot x2\right), -6\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + \color{blue}{3 \cdot \left(3 - -2 \cdot x2\right)}\right) - 1\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, x2\right), -6\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + \color{blue}{3} \cdot \left(3 - -2 \cdot x2\right)\right) - 1\right)\right)\right)\right) \]

      12. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, x2\right), -6\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right) + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, x2\right), -6\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right) + -1\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, x2\right), -6\right)\right)\right), \mathsf{+.f64}\left(\left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)\right), \color{blue}{-1}\right)\right)\right)\right) \]

   10. Simplified 88.6%

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

   11. Taylor expanded in x1 around inf

       \[\leadsto \color{blue}{3 \cdot {x1}^{3}} \]
   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. *-commutative N/A

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

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

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

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

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

       8. unpow2 N/A

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

       9. *-lowering-*.f64 95.5%

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

   13. Simplified 95.5%

       \[\leadsto \color{blue}{x1 \cdot \left(3 \cdot \left(x1 \cdot x1\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 96.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4.4 \cdot 10^{+102}:\\ \;\;\;\;x1 \cdot \left(-1 + x1 \cdot \left(9 + x1 \cdot -19\right)\right)\\ \mathbf{elif}\;x1 \leq -9.2 \cdot 10^{+21}:\\ \;\;\;\;\frac{3}{\frac{x1 \cdot x1 + 1}{x2 \cdot -2 + x1 \cdot \left(x1 \cdot 3 + -1\right)}} + \left(x1 \cdot \left(2 + x1 \cdot \left(x1 + \frac{2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)}{\frac{x1 \cdot x1 + 1}{3}}\right)\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(x1 \cdot \left(x1 \cdot -6\right) + \frac{x1 \cdot \left(x1 \cdot 4 + \frac{-2}{x1}\right)}{\frac{x1 \cdot x1 + 1}{2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)}}\right)\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+42}:\\ \;\;\;\;\frac{3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right)}{x1 \cdot x1 + 1} + \left(x1 \cdot 2 + x2 \cdot \left(x1 \cdot -12 + x2 \cdot \left(x1 \cdot 8\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 4 \cdot 10^{+102}:\\ \;\;\;\;\frac{3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right)}{x1 \cdot x1 + 1} + \left(x1 \cdot \left(2 + x1 \cdot \left(x1 + \left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right) \cdot \frac{3}{x1 \cdot x1 + 1}\right)\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 + \frac{\frac{x2 \cdot 8 + -18}{x1} - 4}{x1}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot \left(3 \cdot \left(x1 \cdot x1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 93.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3 + -1\right)\\ t_1 := x1 \cdot x1 + 1\\ t_2 := \frac{3 \cdot \left(x2 \cdot -2 + t\_0\right)}{t\_1}\\ t_3 := t\_2 + \left(x1 \cdot \left(2 + x1 \cdot \left(x1 + \left(2 \cdot x2 + t\_0\right) \cdot \frac{3}{t\_1}\right)\right) + t\_1 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 + \frac{\frac{x2 \cdot 8 + -18}{x1} - 4}{x1}\right)\right)\right)\\ \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 \cdot \left(-1 + x1 \cdot \left(9 + x1 \cdot -19\right)\right)\\ \mathbf{elif}\;x1 \leq -9.2 \cdot 10^{+21}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+42}:\\ \;\;\;\;t\_2 + \left(x1 \cdot 2 + x2 \cdot \left(x1 \cdot -12 + x2 \cdot \left(x1 \cdot 8\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 10^{+100}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot \left(3 \cdot \left(x1 \cdot x1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (+ (* x1 3.0) -1.0)))
        (t_1 (+ (* x1 x1) 1.0))
        (t_2 (/ (* 3.0 (+ (* x2 -2.0) t_0)) t_1))
        (t_3
         (+
          t_2
          (+
           (* x1 (+ 2.0 (* x1 (+ x1 (* (+ (* 2.0 x2) t_0) (/ 3.0 t_1))))))
           (*
            t_1
            (*
             (* x1 x1)
             (+ 6.0 (/ (- (/ (+ (* x2 8.0) -18.0) x1) 4.0) x1))))))))
   (if (<= x1 -5.6e+102)
     (* x1 (+ -1.0 (* x1 (+ 9.0 (* x1 -19.0)))))
     (if (<= x1 -9.2e+21)
       t_3
       (if (<= x1 1.35e+42)
         (+ t_2 (+ (* x1 2.0) (* x2 (+ (* x1 -12.0) (* x2 (* x1 8.0))))))
         (if (<= x1 1e+100) t_3 (* x1 (* 3.0 (* x1 x1)))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * ((x1 * 3.0) + -1.0);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = (3.0 * ((x2 * -2.0) + t_0)) / t_1;
	double t_3 = t_2 + ((x1 * (2.0 + (x1 * (x1 + (((2.0 * x2) + t_0) * (3.0 / t_1)))))) + (t_1 * ((x1 * x1) * (6.0 + (((((x2 * 8.0) + -18.0) / x1) - 4.0) / x1)))));
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0))));
	} else if (x1 <= -9.2e+21) {
		tmp = t_3;
	} else if (x1 <= 1.35e+42) {
		tmp = t_2 + ((x1 * 2.0) + (x2 * ((x1 * -12.0) + (x2 * (x1 * 8.0)))));
	} else if (x1 <= 1e+100) {
		tmp = t_3;
	} else {
		tmp = x1 * (3.0 * (x1 * x1));
	}
	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) :: t_3
    real(8) :: tmp
    t_0 = x1 * ((x1 * 3.0d0) + (-1.0d0))
    t_1 = (x1 * x1) + 1.0d0
    t_2 = (3.0d0 * ((x2 * (-2.0d0)) + t_0)) / t_1
    t_3 = t_2 + ((x1 * (2.0d0 + (x1 * (x1 + (((2.0d0 * x2) + t_0) * (3.0d0 / t_1)))))) + (t_1 * ((x1 * x1) * (6.0d0 + (((((x2 * 8.0d0) + (-18.0d0)) / x1) - 4.0d0) / x1)))))
    if (x1 <= (-5.6d+102)) then
        tmp = x1 * ((-1.0d0) + (x1 * (9.0d0 + (x1 * (-19.0d0)))))
    else if (x1 <= (-9.2d+21)) then
        tmp = t_3
    else if (x1 <= 1.35d+42) then
        tmp = t_2 + ((x1 * 2.0d0) + (x2 * ((x1 * (-12.0d0)) + (x2 * (x1 * 8.0d0)))))
    else if (x1 <= 1d+100) then
        tmp = t_3
    else
        tmp = x1 * (3.0d0 * (x1 * x1))
    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 = (x1 * x1) + 1.0;
	double t_2 = (3.0 * ((x2 * -2.0) + t_0)) / t_1;
	double t_3 = t_2 + ((x1 * (2.0 + (x1 * (x1 + (((2.0 * x2) + t_0) * (3.0 / t_1)))))) + (t_1 * ((x1 * x1) * (6.0 + (((((x2 * 8.0) + -18.0) / x1) - 4.0) / x1)))));
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0))));
	} else if (x1 <= -9.2e+21) {
		tmp = t_3;
	} else if (x1 <= 1.35e+42) {
		tmp = t_2 + ((x1 * 2.0) + (x2 * ((x1 * -12.0) + (x2 * (x1 * 8.0)))));
	} else if (x1 <= 1e+100) {
		tmp = t_3;
	} else {
		tmp = x1 * (3.0 * (x1 * x1));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * ((x1 * 3.0) + -1.0)
	t_1 = (x1 * x1) + 1.0
	t_2 = (3.0 * ((x2 * -2.0) + t_0)) / t_1
	t_3 = t_2 + ((x1 * (2.0 + (x1 * (x1 + (((2.0 * x2) + t_0) * (3.0 / t_1)))))) + (t_1 * ((x1 * x1) * (6.0 + (((((x2 * 8.0) + -18.0) / x1) - 4.0) / x1)))))
	tmp = 0
	if x1 <= -5.6e+102:
		tmp = x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0))))
	elif x1 <= -9.2e+21:
		tmp = t_3
	elif x1 <= 1.35e+42:
		tmp = t_2 + ((x1 * 2.0) + (x2 * ((x1 * -12.0) + (x2 * (x1 * 8.0)))))
	elif x1 <= 1e+100:
		tmp = t_3
	else:
		tmp = x1 * (3.0 * (x1 * x1))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(Float64(x1 * 3.0) + -1.0))
	t_1 = Float64(Float64(x1 * x1) + 1.0)
	t_2 = Float64(Float64(3.0 * Float64(Float64(x2 * -2.0) + t_0)) / t_1)
	t_3 = Float64(t_2 + Float64(Float64(x1 * Float64(2.0 + Float64(x1 * Float64(x1 + Float64(Float64(Float64(2.0 * x2) + t_0) * Float64(3.0 / t_1)))))) + Float64(t_1 * Float64(Float64(x1 * x1) * Float64(6.0 + Float64(Float64(Float64(Float64(Float64(x2 * 8.0) + -18.0) / x1) - 4.0) / x1))))))
	tmp = 0.0
	if (x1 <= -5.6e+102)
		tmp = Float64(x1 * Float64(-1.0 + Float64(x1 * Float64(9.0 + Float64(x1 * -19.0)))));
	elseif (x1 <= -9.2e+21)
		tmp = t_3;
	elseif (x1 <= 1.35e+42)
		tmp = Float64(t_2 + Float64(Float64(x1 * 2.0) + Float64(x2 * Float64(Float64(x1 * -12.0) + Float64(x2 * Float64(x1 * 8.0))))));
	elseif (x1 <= 1e+100)
		tmp = t_3;
	else
		tmp = Float64(x1 * Float64(3.0 * Float64(x1 * x1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * ((x1 * 3.0) + -1.0);
	t_1 = (x1 * x1) + 1.0;
	t_2 = (3.0 * ((x2 * -2.0) + t_0)) / t_1;
	t_3 = t_2 + ((x1 * (2.0 + (x1 * (x1 + (((2.0 * x2) + t_0) * (3.0 / t_1)))))) + (t_1 * ((x1 * x1) * (6.0 + (((((x2 * 8.0) + -18.0) / x1) - 4.0) / x1)))));
	tmp = 0.0;
	if (x1 <= -5.6e+102)
		tmp = x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0))));
	elseif (x1 <= -9.2e+21)
		tmp = t_3;
	elseif (x1 <= 1.35e+42)
		tmp = t_2 + ((x1 * 2.0) + (x2 * ((x1 * -12.0) + (x2 * (x1 * 8.0)))));
	elseif (x1 <= 1e+100)
		tmp = t_3;
	else
		tmp = x1 * (3.0 * (x1 * x1));
	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[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] + t$95$0), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 + N[(N[(x1 * N[(2.0 + N[(x1 * N[(x1 + N[(N[(N[(2.0 * x2), $MachinePrecision] + t$95$0), $MachinePrecision] * N[(3.0 / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$1 * N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 + N[(N[(N[(N[(N[(x2 * 8.0), $MachinePrecision] + -18.0), $MachinePrecision] / x1), $MachinePrecision] - 4.0), $MachinePrecision] / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -5.6e+102], N[(x1 * N[(-1.0 + N[(x1 * N[(9.0 + N[(x1 * -19.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -9.2e+21], t$95$3, If[LessEqual[x1, 1.35e+42], N[(t$95$2 + N[(N[(x1 * 2.0), $MachinePrecision] + N[(x2 * N[(N[(x1 * -12.0), $MachinePrecision] + N[(x2 * N[(x1 * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1e+100], t$95$3, N[(x1 * N[(3.0 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -5.60000000000000037e102

   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

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

   7. Simplified 76.5%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(2 \cdot \left(x2 \cdot \left(x2 \cdot 4 + -6\right)\right) + \left(x1 \cdot \left(\left(\left(\left(9 + 3 \cdot \left(x2 \cdot 2\right)\right) + \left(x2 \cdot 10 + x1 \cdot \left(\left(3 \cdot \left(x2 \cdot 4\right) + -18\right) + \left(4 \cdot \left(x2 \cdot \left(3 - x2 \cdot 2\right)\right) + -1\right)\right)\right)\right) - \left(x2 \cdot 4 + -6\right)\right) + -6\right) + -1\right)\right)} \]

   8. Taylor expanded in x2 around 0

      \[\leadsto \color{blue}{x1 \cdot \left(x1 \cdot \left(9 + -19 \cdot x1\right) - 1\right)} \]
   9. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(x1, \color{blue}{\left(x1 \cdot \left(9 + -19 \cdot x1\right) - 1\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x1, \left(x1 \cdot \left(9 + -19 \cdot x1\right) + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right) \]

      3. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(x1, \left(x1 \cdot \left(9 + -19 \cdot x1\right) + -1\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\left(x1 \cdot \left(9 + -19 \cdot x1\right)\right), \color{blue}{-1}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \left(9 + -19 \cdot x1\right)\right), -1\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(9, \left(-19 \cdot x1\right)\right)\right), -1\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(9, \left(x1 \cdot -19\right)\right)\right), -1\right)\right) \]

      8. *-lowering-*.f64 100.0%

         \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(9, \mathsf{*.f64}\left(x1, -19\right)\right)\right), -1\right)\right) \]

   10. Simplified 100.0%

       \[\leadsto \color{blue}{x1 \cdot \left(x1 \cdot \left(9 + x1 \cdot -19\right) + -1\right)} \]

   if -5.60000000000000037e102 < x1 < -9.2e21 or 1.35e42 < x1 < 1.00000000000000002e100

   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

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \color{blue}{\left({x1}^{2} \cdot \left(6 + -1 \cdot \frac{4 + -1 \cdot \frac{8 \cdot x2 - 18}{x1}}{x1}\right)\right)}\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]
   6. Step-by-step derivation

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{*.f64}\left(\left({x1}^{2}\right), \left(6 + -1 \cdot \frac{4 + -1 \cdot \frac{8 \cdot x2 - 18}{x1}}{x1}\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      2. unpow2 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{*.f64}\left(\left(x1 \cdot x1\right), \left(6 + -1 \cdot \frac{4 + -1 \cdot \frac{8 \cdot x2 - 18}{x1}}{x1}\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left(6 + -1 \cdot \frac{4 + -1 \cdot \frac{8 \cdot x2 - 18}{x1}}{x1}\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      4. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left(6 + \left(\mathsf{neg}\left(\frac{4 + -1 \cdot \frac{8 \cdot x2 - 18}{x1}}{x1}\right)\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      5. unsub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \left(6 - \frac{4 + -1 \cdot \frac{8 \cdot x2 - 18}{x1}}{x1}\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{\_.f64}\left(6, \left(\frac{4 + -1 \cdot \frac{8 \cdot x2 - 18}{x1}}{x1}\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{\_.f64}\left(6, \mathsf{/.f64}\left(\left(4 + -1 \cdot \frac{8 \cdot x2 - 18}{x1}\right), x1\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      8. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{\_.f64}\left(6, \mathsf{/.f64}\left(\left(4 + \left(\mathsf{neg}\left(\frac{8 \cdot x2 - 18}{x1}\right)\right)\right), x1\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      9. unsub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{\_.f64}\left(6, \mathsf{/.f64}\left(\left(4 - \frac{8 \cdot x2 - 18}{x1}\right), x1\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{\_.f64}\left(6, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(4, \left(\frac{8 \cdot x2 - 18}{x1}\right)\right), x1\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{\_.f64}\left(6, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(4, \mathsf{/.f64}\left(\left(8 \cdot x2 - 18\right), x1\right)\right), x1\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      12. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{\_.f64}\left(6, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(4, \mathsf{/.f64}\left(\left(8 \cdot x2 + \left(\mathsf{neg}\left(18\right)\right)\right), x1\right)\right), x1\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{\_.f64}\left(6, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(4, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(8 \cdot x2\right), \left(\mathsf{neg}\left(18\right)\right)\right), x1\right)\right), x1\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{\_.f64}\left(6, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(4, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(x2 \cdot 8\right), \left(\mathsf{neg}\left(18\right)\right)\right), x1\right)\right), x1\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{\_.f64}\left(6, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(4, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 8\right), \left(\mathsf{neg}\left(18\right)\right)\right), x1\right)\right), x1\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      16. metadata-eval 96.4%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), \mathsf{\_.f64}\left(6, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(4, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 8\right), -18\right), x1\right)\right), x1\right)\right)\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right), \mathsf{/.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

   7. Simplified 96.4%

      \[\leadsto \frac{3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right)}{x1 \cdot x1 + 1} + \left(\left(x1 \cdot x1 + 1\right) \cdot \color{blue}{\left(\left(x1 \cdot x1\right) \cdot \left(6 - \frac{4 - \frac{x2 \cdot 8 + -18}{x1}}{x1}\right)\right)} + x1 \cdot \left(2 + x1 \cdot \left(x1 + \left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right) \cdot \frac{3}{x1 \cdot x1 + 1}\right)\right)\right) \]

   if -9.2e21 < x1 < 1.35e42

   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

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

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

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

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

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

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

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

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

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

      5. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + \color{blue}{\left(\mathsf{neg}\left(6\right)\right)}\right)\right)\right)\right)\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + -6\right)\right)\right)\right)\right)\right) \]

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

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

      8. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\left(x2 \cdot 4\right), -6\right)\right)\right)\right)\right)\right) \]

      9. *-lowering-*.f64 88.6%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right)\right)\right)\right)\right) \]

   7. Simplified 88.6%

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

   8. Taylor expanded in x2 around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \color{blue}{\left(2 \cdot x1 + x2 \cdot \left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right)\right)}\right) \]
   9. Step-by-step derivation

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\left(2 \cdot x1\right), \color{blue}{\left(x2 \cdot \left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right)\right)}\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\left(x1 \cdot 2\right), \left(\color{blue}{x2} \cdot \left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 2\right), \left(\color{blue}{x2} \cdot \left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 2\right), \mathsf{*.f64}\left(x2, \color{blue}{\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 2\right), \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\left(-12 \cdot x1\right), \color{blue}{\left(8 \cdot \left(x1 \cdot x2\right)\right)}\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 2\right), \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\left(x1 \cdot -12\right), \left(\color{blue}{8} \cdot \left(x1 \cdot x2\right)\right)\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 2\right), \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, -12\right), \left(\color{blue}{8} \cdot \left(x1 \cdot x2\right)\right)\right)\right)\right)\right) \]

      8. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 2\right), \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, -12\right), \left(\left(8 \cdot x1\right) \cdot \color{blue}{x2}\right)\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 2\right), \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, -12\right), \mathsf{*.f64}\left(\left(8 \cdot x1\right), \color{blue}{x2}\right)\right)\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 2\right), \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, -12\right), \mathsf{*.f64}\left(\left(x1 \cdot 8\right), x2\right)\right)\right)\right)\right) \]

      11. *-lowering-*.f64 95.7%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 2\right), \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, -12\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, 8\right), x2\right)\right)\right)\right)\right) \]

   10. Simplified 95.7%

       \[\leadsto \frac{3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right)}{x1 \cdot x1 + 1} + \color{blue}{\left(x1 \cdot 2 + x2 \cdot \left(x1 \cdot -12 + \left(x1 \cdot 8\right) \cdot x2\right)\right)} \]

   if 1.00000000000000002e100 < x1

   1. Initial program 34.1%

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

   3. Simplified 34.1%

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

   5. Taylor expanded in x1 around 0

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

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

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

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

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

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

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

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

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

      5. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + \color{blue}{\left(\mathsf{neg}\left(6\right)\right)}\right)\right)\right)\right)\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + -6\right)\right)\right)\right)\right)\right) \]

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

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

      8. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\left(x2 \cdot 4\right), -6\right)\right)\right)\right)\right)\right) \]

      9. *-lowering-*.f64 8.1%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right)\right)\right)\right)\right) \]

   7. Simplified 8.1%

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

   8. Taylor expanded in x1 around 0

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

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

         \[\leadsto \mathsf{+.f64}\left(\left(-6 \cdot x2\right), \color{blue}{\left(x1 \cdot \left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)\right) - 1\right)\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \left(\color{blue}{x1} \cdot \left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)\right) - 1\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \color{blue}{\left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)\right) - 1\right)}\right)\right) \]

      4. associate--l+ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + \color{blue}{\left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right) - 1\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)\right), \color{blue}{\left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right) - 1\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)\right), \left(\color{blue}{x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)} - 1\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 - 6\right)\right)\right), \left(x1 \cdot \color{blue}{\left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)} - 1\right)\right)\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + \left(\mathsf{neg}\left(6\right)\right)\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + \color{blue}{3 \cdot \left(3 - -2 \cdot x2\right)}\right) - 1\right)\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + -6\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \color{blue}{\left(3 - -2 \cdot x2\right)}\right) - 1\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\left(4 \cdot x2\right), -6\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + \color{blue}{3 \cdot \left(3 - -2 \cdot x2\right)}\right) - 1\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, x2\right), -6\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + \color{blue}{3} \cdot \left(3 - -2 \cdot x2\right)\right) - 1\right)\right)\right)\right) \]

      12. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, x2\right), -6\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right) + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, x2\right), -6\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right) + -1\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, x2\right), -6\right)\right)\right), \mathsf{+.f64}\left(\left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)\right), \color{blue}{-1}\right)\right)\right)\right) \]

   10. Simplified 88.6%

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

   11. Taylor expanded in x1 around inf

       \[\leadsto \color{blue}{3 \cdot {x1}^{3}} \]
   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. *-commutative N/A

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

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

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

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

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

       8. unpow2 N/A

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

       9. *-lowering-*.f64 95.5%

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

   13. Simplified 95.5%

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

4. Final simplification 96.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 \cdot \left(-1 + x1 \cdot \left(9 + x1 \cdot -19\right)\right)\\ \mathbf{elif}\;x1 \leq -9.2 \cdot 10^{+21}:\\ \;\;\;\;\frac{3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right)}{x1 \cdot x1 + 1} + \left(x1 \cdot \left(2 + x1 \cdot \left(x1 + \left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right) \cdot \frac{3}{x1 \cdot x1 + 1}\right)\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 + \frac{\frac{x2 \cdot 8 + -18}{x1} - 4}{x1}\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+42}:\\ \;\;\;\;\frac{3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right)}{x1 \cdot x1 + 1} + \left(x1 \cdot 2 + x2 \cdot \left(x1 \cdot -12 + x2 \cdot \left(x1 \cdot 8\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 10^{+100}:\\ \;\;\;\;\frac{3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right)}{x1 \cdot x1 + 1} + \left(x1 \cdot \left(2 + x1 \cdot \left(x1 + \left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right) \cdot \frac{3}{x1 \cdot x1 + 1}\right)\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 + \frac{\frac{x2 \cdot 8 + -18}{x1} - 4}{x1}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot \left(3 \cdot \left(x1 \cdot x1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 91.7% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := x1 \cdot \left(x1 \cdot 3 + -1\right)\\ t_2 := x2 \cdot -2 + t\_1\\ t_3 := \frac{3}{\frac{t\_0}{t\_2}} + \left(x1 \cdot \left(2 + x1 \cdot \left(x1 + \frac{2 \cdot x2 + t\_1}{\frac{t\_0}{3}}\right)\right) + t\_0 \cdot \left(\left(x1 \cdot x1\right) \cdot 6\right)\right)\\ \mathbf{if}\;x1 \leq -5 \cdot 10^{+102}:\\ \;\;\;\;x1 \cdot \left(-1 + x1 \cdot \left(9 + x1 \cdot -19\right)\right)\\ \mathbf{elif}\;x1 \leq -9.2 \cdot 10^{+21}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+42}:\\ \;\;\;\;\frac{3 \cdot t\_2}{t\_0} + \left(x1 \cdot 2 + x2 \cdot \left(x1 \cdot -12 + x2 \cdot \left(x1 \cdot 8\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 10^{+100}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot \left(3 \cdot \left(x1 \cdot x1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ (* x1 x1) 1.0))
        (t_1 (* x1 (+ (* x1 3.0) -1.0)))
        (t_2 (+ (* x2 -2.0) t_1))
        (t_3
         (+
          (/ 3.0 (/ t_0 t_2))
          (+
           (* x1 (+ 2.0 (* x1 (+ x1 (/ (+ (* 2.0 x2) t_1) (/ t_0 3.0))))))
           (* t_0 (* (* x1 x1) 6.0))))))
   (if (<= x1 -5e+102)
     (* x1 (+ -1.0 (* x1 (+ 9.0 (* x1 -19.0)))))
     (if (<= x1 -9.2e+21)
       t_3
       (if (<= x1 1.35e+42)
         (+
          (/ (* 3.0 t_2) t_0)
          (+ (* x1 2.0) (* x2 (+ (* x1 -12.0) (* x2 (* x1 8.0))))))
         (if (<= x1 1e+100) t_3 (* x1 (* 3.0 (* x1 x1)))))))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = x1 * ((x1 * 3.0) + -1.0);
	double t_2 = (x2 * -2.0) + t_1;
	double t_3 = (3.0 / (t_0 / t_2)) + ((x1 * (2.0 + (x1 * (x1 + (((2.0 * x2) + t_1) / (t_0 / 3.0)))))) + (t_0 * ((x1 * x1) * 6.0)));
	double tmp;
	if (x1 <= -5e+102) {
		tmp = x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0))));
	} else if (x1 <= -9.2e+21) {
		tmp = t_3;
	} else if (x1 <= 1.35e+42) {
		tmp = ((3.0 * t_2) / t_0) + ((x1 * 2.0) + (x2 * ((x1 * -12.0) + (x2 * (x1 * 8.0)))));
	} else if (x1 <= 1e+100) {
		tmp = t_3;
	} else {
		tmp = x1 * (3.0 * (x1 * x1));
	}
	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) :: t_3
    real(8) :: tmp
    t_0 = (x1 * x1) + 1.0d0
    t_1 = x1 * ((x1 * 3.0d0) + (-1.0d0))
    t_2 = (x2 * (-2.0d0)) + t_1
    t_3 = (3.0d0 / (t_0 / t_2)) + ((x1 * (2.0d0 + (x1 * (x1 + (((2.0d0 * x2) + t_1) / (t_0 / 3.0d0)))))) + (t_0 * ((x1 * x1) * 6.0d0)))
    if (x1 <= (-5d+102)) then
        tmp = x1 * ((-1.0d0) + (x1 * (9.0d0 + (x1 * (-19.0d0)))))
    else if (x1 <= (-9.2d+21)) then
        tmp = t_3
    else if (x1 <= 1.35d+42) then
        tmp = ((3.0d0 * t_2) / t_0) + ((x1 * 2.0d0) + (x2 * ((x1 * (-12.0d0)) + (x2 * (x1 * 8.0d0)))))
    else if (x1 <= 1d+100) then
        tmp = t_3
    else
        tmp = x1 * (3.0d0 * (x1 * x1))
    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 * ((x1 * 3.0) + -1.0);
	double t_2 = (x2 * -2.0) + t_1;
	double t_3 = (3.0 / (t_0 / t_2)) + ((x1 * (2.0 + (x1 * (x1 + (((2.0 * x2) + t_1) / (t_0 / 3.0)))))) + (t_0 * ((x1 * x1) * 6.0)));
	double tmp;
	if (x1 <= -5e+102) {
		tmp = x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0))));
	} else if (x1 <= -9.2e+21) {
		tmp = t_3;
	} else if (x1 <= 1.35e+42) {
		tmp = ((3.0 * t_2) / t_0) + ((x1 * 2.0) + (x2 * ((x1 * -12.0) + (x2 * (x1 * 8.0)))));
	} else if (x1 <= 1e+100) {
		tmp = t_3;
	} else {
		tmp = x1 * (3.0 * (x1 * x1));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x1 * x1) + 1.0
	t_1 = x1 * ((x1 * 3.0) + -1.0)
	t_2 = (x2 * -2.0) + t_1
	t_3 = (3.0 / (t_0 / t_2)) + ((x1 * (2.0 + (x1 * (x1 + (((2.0 * x2) + t_1) / (t_0 / 3.0)))))) + (t_0 * ((x1 * x1) * 6.0)))
	tmp = 0
	if x1 <= -5e+102:
		tmp = x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0))))
	elif x1 <= -9.2e+21:
		tmp = t_3
	elif x1 <= 1.35e+42:
		tmp = ((3.0 * t_2) / t_0) + ((x1 * 2.0) + (x2 * ((x1 * -12.0) + (x2 * (x1 * 8.0)))))
	elif x1 <= 1e+100:
		tmp = t_3
	else:
		tmp = x1 * (3.0 * (x1 * x1))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * x1) + 1.0)
	t_1 = Float64(x1 * Float64(Float64(x1 * 3.0) + -1.0))
	t_2 = Float64(Float64(x2 * -2.0) + t_1)
	t_3 = Float64(Float64(3.0 / Float64(t_0 / t_2)) + Float64(Float64(x1 * Float64(2.0 + Float64(x1 * Float64(x1 + Float64(Float64(Float64(2.0 * x2) + t_1) / Float64(t_0 / 3.0)))))) + Float64(t_0 * Float64(Float64(x1 * x1) * 6.0))))
	tmp = 0.0
	if (x1 <= -5e+102)
		tmp = Float64(x1 * Float64(-1.0 + Float64(x1 * Float64(9.0 + Float64(x1 * -19.0)))));
	elseif (x1 <= -9.2e+21)
		tmp = t_3;
	elseif (x1 <= 1.35e+42)
		tmp = Float64(Float64(Float64(3.0 * t_2) / t_0) + Float64(Float64(x1 * 2.0) + Float64(x2 * Float64(Float64(x1 * -12.0) + Float64(x2 * Float64(x1 * 8.0))))));
	elseif (x1 <= 1e+100)
		tmp = t_3;
	else
		tmp = Float64(x1 * Float64(3.0 * Float64(x1 * x1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x1 * x1) + 1.0;
	t_1 = x1 * ((x1 * 3.0) + -1.0);
	t_2 = (x2 * -2.0) + t_1;
	t_3 = (3.0 / (t_0 / t_2)) + ((x1 * (2.0 + (x1 * (x1 + (((2.0 * x2) + t_1) / (t_0 / 3.0)))))) + (t_0 * ((x1 * x1) * 6.0)));
	tmp = 0.0;
	if (x1 <= -5e+102)
		tmp = x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0))));
	elseif (x1 <= -9.2e+21)
		tmp = t_3;
	elseif (x1 <= 1.35e+42)
		tmp = ((3.0 * t_2) / t_0) + ((x1 * 2.0) + (x2 * ((x1 * -12.0) + (x2 * (x1 * 8.0)))));
	elseif (x1 <= 1e+100)
		tmp = t_3;
	else
		tmp = x1 * (3.0 * (x1 * x1));
	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[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x2 * -2.0), $MachinePrecision] + t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(3.0 / N[(t$95$0 / t$95$2), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * N[(2.0 + N[(x1 * N[(x1 + N[(N[(N[(2.0 * x2), $MachinePrecision] + t$95$1), $MachinePrecision] / N[(t$95$0 / 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$0 * N[(N[(x1 * x1), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -5e+102], N[(x1 * N[(-1.0 + N[(x1 * N[(9.0 + N[(x1 * -19.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -9.2e+21], t$95$3, If[LessEqual[x1, 1.35e+42], N[(N[(N[(3.0 * t$95$2), $MachinePrecision] / t$95$0), $MachinePrecision] + N[(N[(x1 * 2.0), $MachinePrecision] + N[(x2 * N[(N[(x1 * -12.0), $MachinePrecision] + N[(x2 * N[(x1 * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1e+100], t$95$3, N[(x1 * N[(3.0 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -5e102

   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

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

   7. Simplified 76.5%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(2 \cdot \left(x2 \cdot \left(x2 \cdot 4 + -6\right)\right) + \left(x1 \cdot \left(\left(\left(\left(9 + 3 \cdot \left(x2 \cdot 2\right)\right) + \left(x2 \cdot 10 + x1 \cdot \left(\left(3 \cdot \left(x2 \cdot 4\right) + -18\right) + \left(4 \cdot \left(x2 \cdot \left(3 - x2 \cdot 2\right)\right) + -1\right)\right)\right)\right) - \left(x2 \cdot 4 + -6\right)\right) + -6\right) + -1\right)\right)} \]

   8. Taylor expanded in x2 around 0

      \[\leadsto \color{blue}{x1 \cdot \left(x1 \cdot \left(9 + -19 \cdot x1\right) - 1\right)} \]
   9. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(x1, \color{blue}{\left(x1 \cdot \left(9 + -19 \cdot x1\right) - 1\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x1, \left(x1 \cdot \left(9 + -19 \cdot x1\right) + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right) \]

      3. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(x1, \left(x1 \cdot \left(9 + -19 \cdot x1\right) + -1\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\left(x1 \cdot \left(9 + -19 \cdot x1\right)\right), \color{blue}{-1}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \left(9 + -19 \cdot x1\right)\right), -1\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(9, \left(-19 \cdot x1\right)\right)\right), -1\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(9, \left(x1 \cdot -19\right)\right)\right), -1\right)\right) \]

      8. *-lowering-*.f64 100.0%

         \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(9, \mathsf{*.f64}\left(x1, -19\right)\right)\right), -1\right)\right) \]

   10. Simplified 100.0%

       \[\leadsto \color{blue}{x1 \cdot \left(x1 \cdot \left(9 + x1 \cdot -19\right) + -1\right)} \]

   if -5e102 < x1 < -9.2e21 or 1.35e42 < x1 < 1.00000000000000002e100

   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

   6. Applied egg-rr 99.4%

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

   8. Applied egg-rr 99.7%

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

   9. Taylor expanded in x1 around inf

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

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

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

       2. unpow2 N/A

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

       3. *-lowering-*.f64 75.9%

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

   11. Simplified 75.9%

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

   if -9.2e21 < x1 < 1.35e42

   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

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

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

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

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

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

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

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

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

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

      5. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + \color{blue}{\left(\mathsf{neg}\left(6\right)\right)}\right)\right)\right)\right)\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + -6\right)\right)\right)\right)\right)\right) \]

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

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

      8. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\left(x2 \cdot 4\right), -6\right)\right)\right)\right)\right)\right) \]

      9. *-lowering-*.f64 88.6%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right)\right)\right)\right)\right) \]

   7. Simplified 88.6%

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

   8. Taylor expanded in x2 around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \color{blue}{\left(2 \cdot x1 + x2 \cdot \left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right)\right)}\right) \]
   9. Step-by-step derivation

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\left(2 \cdot x1\right), \color{blue}{\left(x2 \cdot \left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right)\right)}\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\left(x1 \cdot 2\right), \left(\color{blue}{x2} \cdot \left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 2\right), \left(\color{blue}{x2} \cdot \left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 2\right), \mathsf{*.f64}\left(x2, \color{blue}{\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 2\right), \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\left(-12 \cdot x1\right), \color{blue}{\left(8 \cdot \left(x1 \cdot x2\right)\right)}\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 2\right), \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\left(x1 \cdot -12\right), \left(\color{blue}{8} \cdot \left(x1 \cdot x2\right)\right)\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 2\right), \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, -12\right), \left(\color{blue}{8} \cdot \left(x1 \cdot x2\right)\right)\right)\right)\right)\right) \]

      8. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 2\right), \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, -12\right), \left(\left(8 \cdot x1\right) \cdot \color{blue}{x2}\right)\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 2\right), \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, -12\right), \mathsf{*.f64}\left(\left(8 \cdot x1\right), \color{blue}{x2}\right)\right)\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 2\right), \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, -12\right), \mathsf{*.f64}\left(\left(x1 \cdot 8\right), x2\right)\right)\right)\right)\right) \]

      11. *-lowering-*.f64 95.7%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 2\right), \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, -12\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, 8\right), x2\right)\right)\right)\right)\right) \]

   10. Simplified 95.7%

       \[\leadsto \frac{3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right)}{x1 \cdot x1 + 1} + \color{blue}{\left(x1 \cdot 2 + x2 \cdot \left(x1 \cdot -12 + \left(x1 \cdot 8\right) \cdot x2\right)\right)} \]

   if 1.00000000000000002e100 < x1

   1. Initial program 34.1%

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

   3. Simplified 34.1%

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

   5. Taylor expanded in x1 around 0

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

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

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

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

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

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

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

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

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

      5. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + \color{blue}{\left(\mathsf{neg}\left(6\right)\right)}\right)\right)\right)\right)\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + -6\right)\right)\right)\right)\right)\right) \]

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

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

      8. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\left(x2 \cdot 4\right), -6\right)\right)\right)\right)\right)\right) \]

      9. *-lowering-*.f64 8.1%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right)\right)\right)\right)\right) \]

   7. Simplified 8.1%

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

   8. Taylor expanded in x1 around 0

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

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

         \[\leadsto \mathsf{+.f64}\left(\left(-6 \cdot x2\right), \color{blue}{\left(x1 \cdot \left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)\right) - 1\right)\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \left(\color{blue}{x1} \cdot \left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)\right) - 1\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \color{blue}{\left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)\right) - 1\right)}\right)\right) \]

      4. associate--l+ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + \color{blue}{\left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right) - 1\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)\right), \color{blue}{\left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right) - 1\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)\right), \left(\color{blue}{x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)} - 1\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 - 6\right)\right)\right), \left(x1 \cdot \color{blue}{\left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)} - 1\right)\right)\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + \left(\mathsf{neg}\left(6\right)\right)\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + \color{blue}{3 \cdot \left(3 - -2 \cdot x2\right)}\right) - 1\right)\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + -6\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \color{blue}{\left(3 - -2 \cdot x2\right)}\right) - 1\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\left(4 \cdot x2\right), -6\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + \color{blue}{3 \cdot \left(3 - -2 \cdot x2\right)}\right) - 1\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, x2\right), -6\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + \color{blue}{3} \cdot \left(3 - -2 \cdot x2\right)\right) - 1\right)\right)\right)\right) \]

      12. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, x2\right), -6\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right) + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, x2\right), -6\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right) + -1\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, x2\right), -6\right)\right)\right), \mathsf{+.f64}\left(\left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)\right), \color{blue}{-1}\right)\right)\right)\right) \]

   10. Simplified 88.6%

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

   11. Taylor expanded in x1 around inf

       \[\leadsto \color{blue}{3 \cdot {x1}^{3}} \]
   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. *-commutative N/A

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

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

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

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

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

       8. unpow2 N/A

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

       9. *-lowering-*.f64 95.5%

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

   13. Simplified 95.5%

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

4. Final simplification 93.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5 \cdot 10^{+102}:\\ \;\;\;\;x1 \cdot \left(-1 + x1 \cdot \left(9 + x1 \cdot -19\right)\right)\\ \mathbf{elif}\;x1 \leq -9.2 \cdot 10^{+21}:\\ \;\;\;\;\frac{3}{\frac{x1 \cdot x1 + 1}{x2 \cdot -2 + x1 \cdot \left(x1 \cdot 3 + -1\right)}} + \left(x1 \cdot \left(2 + x1 \cdot \left(x1 + \frac{2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)}{\frac{x1 \cdot x1 + 1}{3}}\right)\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot 6\right)\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+42}:\\ \;\;\;\;\frac{3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right)}{x1 \cdot x1 + 1} + \left(x1 \cdot 2 + x2 \cdot \left(x1 \cdot -12 + x2 \cdot \left(x1 \cdot 8\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 10^{+100}:\\ \;\;\;\;\frac{3}{\frac{x1 \cdot x1 + 1}{x2 \cdot -2 + x1 \cdot \left(x1 \cdot 3 + -1\right)}} + \left(x1 \cdot \left(2 + x1 \cdot \left(x1 + \frac{2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)}{\frac{x1 \cdot x1 + 1}{3}}\right)\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot 6\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot \left(3 \cdot \left(x1 \cdot x1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 86.6% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot x1\right)\\ \mathbf{if}\;x1 \leq -6.2 \cdot 10^{+78}:\\ \;\;\;\;t\_0 \cdot \left(4 \cdot \left(x2 \cdot \left(3 + x2 \cdot -2\right)\right) + \left(-19 + x2 \cdot 12\right)\right)\\ \mathbf{elif}\;x1 \leq 2.5 \cdot 10^{+17}:\\ \;\;\;\;\frac{3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right)}{x1 \cdot x1 + 1} + \left(x1 \cdot 2 + x2 \cdot \left(x1 \cdot -12 + x2 \cdot \left(x1 \cdot 8\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0 \cdot \left(\frac{\left(9 + x2 \cdot 6\right) + \frac{-1 + \left(2 \cdot x2\right) \cdot \left(-6 + x2 \cdot 4\right)}{x1}}{x1} - -3\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 x1))))
   (if (<= x1 -6.2e+78)
     (* t_0 (+ (* 4.0 (* x2 (+ 3.0 (* x2 -2.0)))) (+ -19.0 (* x2 12.0))))
     (if (<= x1 2.5e+17)
       (+
        (/
         (* 3.0 (+ (* x2 -2.0) (* x1 (+ (* x1 3.0) -1.0))))
         (+ (* x1 x1) 1.0))
        (+ (* x1 2.0) (* x2 (+ (* x1 -12.0) (* x2 (* x1 8.0))))))
       (*
        t_0
        (-
         (/
          (+
           (+ 9.0 (* x2 6.0))
           (/ (+ -1.0 (* (* 2.0 x2) (+ -6.0 (* x2 4.0)))) x1))
          x1)
         -3.0))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * x1);
	double tmp;
	if (x1 <= -6.2e+78) {
		tmp = t_0 * ((4.0 * (x2 * (3.0 + (x2 * -2.0)))) + (-19.0 + (x2 * 12.0)));
	} else if (x1 <= 2.5e+17) {
		tmp = ((3.0 * ((x2 * -2.0) + (x1 * ((x1 * 3.0) + -1.0)))) / ((x1 * x1) + 1.0)) + ((x1 * 2.0) + (x2 * ((x1 * -12.0) + (x2 * (x1 * 8.0)))));
	} else {
		tmp = t_0 * ((((9.0 + (x2 * 6.0)) + ((-1.0 + ((2.0 * x2) * (-6.0 + (x2 * 4.0)))) / x1)) / x1) - -3.0);
	}
	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 * x1)
    if (x1 <= (-6.2d+78)) then
        tmp = t_0 * ((4.0d0 * (x2 * (3.0d0 + (x2 * (-2.0d0))))) + ((-19.0d0) + (x2 * 12.0d0)))
    else if (x1 <= 2.5d+17) then
        tmp = ((3.0d0 * ((x2 * (-2.0d0)) + (x1 * ((x1 * 3.0d0) + (-1.0d0))))) / ((x1 * x1) + 1.0d0)) + ((x1 * 2.0d0) + (x2 * ((x1 * (-12.0d0)) + (x2 * (x1 * 8.0d0)))))
    else
        tmp = t_0 * ((((9.0d0 + (x2 * 6.0d0)) + (((-1.0d0) + ((2.0d0 * x2) * ((-6.0d0) + (x2 * 4.0d0)))) / x1)) / x1) - (-3.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * x1);
	double tmp;
	if (x1 <= -6.2e+78) {
		tmp = t_0 * ((4.0 * (x2 * (3.0 + (x2 * -2.0)))) + (-19.0 + (x2 * 12.0)));
	} else if (x1 <= 2.5e+17) {
		tmp = ((3.0 * ((x2 * -2.0) + (x1 * ((x1 * 3.0) + -1.0)))) / ((x1 * x1) + 1.0)) + ((x1 * 2.0) + (x2 * ((x1 * -12.0) + (x2 * (x1 * 8.0)))));
	} else {
		tmp = t_0 * ((((9.0 + (x2 * 6.0)) + ((-1.0 + ((2.0 * x2) * (-6.0 + (x2 * 4.0)))) / x1)) / x1) - -3.0);
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * x1)
	tmp = 0
	if x1 <= -6.2e+78:
		tmp = t_0 * ((4.0 * (x2 * (3.0 + (x2 * -2.0)))) + (-19.0 + (x2 * 12.0)))
	elif x1 <= 2.5e+17:
		tmp = ((3.0 * ((x2 * -2.0) + (x1 * ((x1 * 3.0) + -1.0)))) / ((x1 * x1) + 1.0)) + ((x1 * 2.0) + (x2 * ((x1 * -12.0) + (x2 * (x1 * 8.0)))))
	else:
		tmp = t_0 * ((((9.0 + (x2 * 6.0)) + ((-1.0 + ((2.0 * x2) * (-6.0 + (x2 * 4.0)))) / x1)) / x1) - -3.0)
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * x1))
	tmp = 0.0
	if (x1 <= -6.2e+78)
		tmp = Float64(t_0 * Float64(Float64(4.0 * Float64(x2 * Float64(3.0 + Float64(x2 * -2.0)))) + Float64(-19.0 + Float64(x2 * 12.0))));
	elseif (x1 <= 2.5e+17)
		tmp = Float64(Float64(Float64(3.0 * Float64(Float64(x2 * -2.0) + Float64(x1 * Float64(Float64(x1 * 3.0) + -1.0)))) / Float64(Float64(x1 * x1) + 1.0)) + Float64(Float64(x1 * 2.0) + Float64(x2 * Float64(Float64(x1 * -12.0) + Float64(x2 * Float64(x1 * 8.0))))));
	else
		tmp = Float64(t_0 * Float64(Float64(Float64(Float64(9.0 + Float64(x2 * 6.0)) + Float64(Float64(-1.0 + Float64(Float64(2.0 * x2) * Float64(-6.0 + Float64(x2 * 4.0)))) / x1)) / x1) - -3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * x1);
	tmp = 0.0;
	if (x1 <= -6.2e+78)
		tmp = t_0 * ((4.0 * (x2 * (3.0 + (x2 * -2.0)))) + (-19.0 + (x2 * 12.0)));
	elseif (x1 <= 2.5e+17)
		tmp = ((3.0 * ((x2 * -2.0) + (x1 * ((x1 * 3.0) + -1.0)))) / ((x1 * x1) + 1.0)) + ((x1 * 2.0) + (x2 * ((x1 * -12.0) + (x2 * (x1 * 8.0)))));
	else
		tmp = t_0 * ((((9.0 + (x2 * 6.0)) + ((-1.0 + ((2.0 * x2) * (-6.0 + (x2 * 4.0)))) / x1)) / x1) - -3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -6.2e+78], N[(t$95$0 * N[(N[(4.0 * N[(x2 * N[(3.0 + N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-19.0 + N[(x2 * 12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 2.5e+17], N[(N[(N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] + N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * 2.0), $MachinePrecision] + N[(x2 * N[(N[(x1 * -12.0), $MachinePrecision] + N[(x2 * N[(x1 * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$0 * N[(N[(N[(N[(9.0 + N[(x2 * 6.0), $MachinePrecision]), $MachinePrecision] + N[(N[(-1.0 + N[(N[(2.0 * x2), $MachinePrecision] * N[(-6.0 + N[(x2 * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x1), $MachinePrecision]), $MachinePrecision] / x1), $MachinePrecision] - -3.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -6.2e78

   1. Initial program 19.0%

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

   3. Simplified 19.0%

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

   5. Taylor expanded in x1 around 0

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

   7. Simplified 69.7%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(2 \cdot \left(x2 \cdot \left(x2 \cdot 4 + -6\right)\right) + \left(x1 \cdot \left(\left(\left(\left(9 + 3 \cdot \left(x2 \cdot 2\right)\right) + \left(x2 \cdot 10 + x1 \cdot \left(\left(3 \cdot \left(x2 \cdot 4\right) + -18\right) + \left(4 \cdot \left(x2 \cdot \left(3 - x2 \cdot 2\right)\right) + -1\right)\right)\right)\right) - \left(x2 \cdot 4 + -6\right)\right) + -6\right) + -1\right)\right)} \]

   8. Taylor expanded in x1 around inf

      \[\leadsto \color{blue}{{x1}^{3} \cdot \left(\left(4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right) + 12 \cdot x2\right) - 19\right)} \]
   9. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{3}\right), \color{blue}{\left(\left(4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right) + 12 \cdot x2\right) - 19\right)}\right) \]

      2. cube-mult N/A

         \[\leadsto \mathsf{*.f64}\left(\left(x1 \cdot \left(x1 \cdot x1\right)\right), \left(\color{blue}{\left(4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right) + 12 \cdot x2\right)} - 19\right)\right) \]

      3. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(x1 \cdot {x1}^{2}\right), \left(\left(4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right) + \color{blue}{12 \cdot x2}\right) - 19\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \left({x1}^{2}\right)\right), \left(\color{blue}{\left(4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right) + 12 \cdot x2\right)} - 19\right)\right) \]

      5. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \left(x1 \cdot x1\right)\right), \left(\left(4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right) + \color{blue}{12 \cdot x2}\right) - 19\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, x1\right)\right), \left(\left(4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right) + \color{blue}{12 \cdot x2}\right) - 19\right)\right) \]

      7. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, x1\right)\right), \left(4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right) + \color{blue}{\left(12 \cdot x2 - 19\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(\left(4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right), \color{blue}{\left(12 \cdot x2 - 19\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right), \left(\color{blue}{12 \cdot x2} - 19\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, \mathsf{*.f64}\left(x2, \left(3 - 2 \cdot x2\right)\right)\right), \left(12 \cdot \color{blue}{x2} - 19\right)\right)\right) \]

      11. cancel-sign-sub-inv N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, \mathsf{*.f64}\left(x2, \left(3 + \left(\mathsf{neg}\left(2\right)\right) \cdot x2\right)\right)\right), \left(12 \cdot x2 - 19\right)\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, \mathsf{*.f64}\left(x2, \left(3 + -2 \cdot x2\right)\right)\right), \left(12 \cdot x2 - 19\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(3, \left(-2 \cdot x2\right)\right)\right)\right), \left(12 \cdot x2 - 19\right)\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(3, \left(x2 \cdot -2\right)\right)\right)\right), \left(12 \cdot x2 - 19\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(3, \mathsf{*.f64}\left(x2, -2\right)\right)\right)\right), \left(12 \cdot x2 - 19\right)\right)\right) \]

      16. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(3, \mathsf{*.f64}\left(x2, -2\right)\right)\right)\right), \left(12 \cdot x2 + \color{blue}{\left(\mathsf{neg}\left(19\right)\right)}\right)\right)\right) \]

      17. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(3, \mathsf{*.f64}\left(x2, -2\right)\right)\right)\right), \left(12 \cdot x2 + -19\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(3, \mathsf{*.f64}\left(x2, -2\right)\right)\right)\right), \mathsf{+.f64}\left(\left(12 \cdot x2\right), \color{blue}{-19}\right)\right)\right) \]

      19. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(3, \mathsf{*.f64}\left(x2, -2\right)\right)\right)\right), \mathsf{+.f64}\left(\left(x2 \cdot 12\right), -19\right)\right)\right) \]

      20. *-lowering-*.f64 88.8%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(3, \mathsf{*.f64}\left(x2, -2\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 12\right), -19\right)\right)\right) \]

   10. Simplified 88.8%

       \[\leadsto \color{blue}{\left(x1 \cdot \left(x1 \cdot x1\right)\right) \cdot \left(4 \cdot \left(x2 \cdot \left(3 + x2 \cdot -2\right)\right) + \left(x2 \cdot 12 + -19\right)\right)} \]

   if -6.2e78 < x1 < 2.5e17

   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

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

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

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

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

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

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

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

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

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

      5. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + \color{blue}{\left(\mathsf{neg}\left(6\right)\right)}\right)\right)\right)\right)\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + -6\right)\right)\right)\right)\right)\right) \]

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

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

      8. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\left(x2 \cdot 4\right), -6\right)\right)\right)\right)\right)\right) \]

      9. *-lowering-*.f64 85.3%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right)\right)\right)\right)\right) \]

   7. Simplified 85.3%

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

   8. Taylor expanded in x2 around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \color{blue}{\left(2 \cdot x1 + x2 \cdot \left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right)\right)}\right) \]
   9. Step-by-step derivation

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\left(2 \cdot x1\right), \color{blue}{\left(x2 \cdot \left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right)\right)}\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\left(x1 \cdot 2\right), \left(\color{blue}{x2} \cdot \left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 2\right), \left(\color{blue}{x2} \cdot \left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 2\right), \mathsf{*.f64}\left(x2, \color{blue}{\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 2\right), \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\left(-12 \cdot x1\right), \color{blue}{\left(8 \cdot \left(x1 \cdot x2\right)\right)}\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 2\right), \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\left(x1 \cdot -12\right), \left(\color{blue}{8} \cdot \left(x1 \cdot x2\right)\right)\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 2\right), \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, -12\right), \left(\color{blue}{8} \cdot \left(x1 \cdot x2\right)\right)\right)\right)\right)\right) \]

      8. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 2\right), \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, -12\right), \left(\left(8 \cdot x1\right) \cdot \color{blue}{x2}\right)\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 2\right), \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, -12\right), \mathsf{*.f64}\left(\left(8 \cdot x1\right), \color{blue}{x2}\right)\right)\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 2\right), \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, -12\right), \mathsf{*.f64}\left(\left(x1 \cdot 8\right), x2\right)\right)\right)\right)\right) \]

      11. *-lowering-*.f64 92.0%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 2\right), \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, -12\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, 8\right), x2\right)\right)\right)\right)\right) \]

   10. Simplified 92.0%

       \[\leadsto \frac{3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right)}{x1 \cdot x1 + 1} + \color{blue}{\left(x1 \cdot 2 + x2 \cdot \left(x1 \cdot -12 + \left(x1 \cdot 8\right) \cdot x2\right)\right)} \]

   if 2.5e17 < 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 0

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

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

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

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

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

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

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

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

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

      5. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + \color{blue}{\left(\mathsf{neg}\left(6\right)\right)}\right)\right)\right)\right)\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + -6\right)\right)\right)\right)\right)\right) \]

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

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

      8. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\left(x2 \cdot 4\right), -6\right)\right)\right)\right)\right)\right) \]

      9. *-lowering-*.f64 12.2%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right)\right)\right)\right)\right) \]

   7. Simplified 12.2%

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

   8. Taylor expanded in x1 around 0

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

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

         \[\leadsto \mathsf{+.f64}\left(\left(-6 \cdot x2\right), \color{blue}{\left(x1 \cdot \left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)\right) - 1\right)\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \left(\color{blue}{x1} \cdot \left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)\right) - 1\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \color{blue}{\left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)\right) - 1\right)}\right)\right) \]

      4. associate--l+ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + \color{blue}{\left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right) - 1\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)\right), \color{blue}{\left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right) - 1\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)\right), \left(\color{blue}{x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)} - 1\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 - 6\right)\right)\right), \left(x1 \cdot \color{blue}{\left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)} - 1\right)\right)\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + \left(\mathsf{neg}\left(6\right)\right)\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + \color{blue}{3 \cdot \left(3 - -2 \cdot x2\right)}\right) - 1\right)\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + -6\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \color{blue}{\left(3 - -2 \cdot x2\right)}\right) - 1\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\left(4 \cdot x2\right), -6\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + \color{blue}{3 \cdot \left(3 - -2 \cdot x2\right)}\right) - 1\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, x2\right), -6\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + \color{blue}{3} \cdot \left(3 - -2 \cdot x2\right)\right) - 1\right)\right)\right)\right) \]

      12. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, x2\right), -6\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right) + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, x2\right), -6\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right) + -1\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, x2\right), -6\right)\right)\right), \mathsf{+.f64}\left(\left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)\right), \color{blue}{-1}\right)\right)\right)\right) \]

   10. Simplified 72.7%

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

   11. Taylor expanded in x1 around -inf

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

   13. Simplified 77.8%

       \[\leadsto \color{blue}{\left(-3 - \frac{\left(9 + x2 \cdot 6\right) + \frac{-1 + \left(-6 + x2 \cdot 4\right) \cdot \left(x2 \cdot 2\right)}{x1}}{x1}\right) \cdot \left(0 - x1 \cdot \left(x1 \cdot x1\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -6.2 \cdot 10^{+78}:\\ \;\;\;\;\left(x1 \cdot \left(x1 \cdot x1\right)\right) \cdot \left(4 \cdot \left(x2 \cdot \left(3 + x2 \cdot -2\right)\right) + \left(-19 + x2 \cdot 12\right)\right)\\ \mathbf{elif}\;x1 \leq 2.5 \cdot 10^{+17}:\\ \;\;\;\;\frac{3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right)}{x1 \cdot x1 + 1} + \left(x1 \cdot 2 + x2 \cdot \left(x1 \cdot -12 + x2 \cdot \left(x1 \cdot 8\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x1 \cdot \left(x1 \cdot x1\right)\right) \cdot \left(\frac{\left(9 + x2 \cdot 6\right) + \frac{-1 + \left(2 \cdot x2\right) \cdot \left(-6 + x2 \cdot 4\right)}{x1}}{x1} - -3\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 80.2% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -6.2 \cdot 10^{+78}:\\ \;\;\;\;\left(x1 \cdot \left(x1 \cdot x1\right)\right) \cdot \left(4 \cdot \left(x2 \cdot \left(3 + x2 \cdot -2\right)\right) + \left(-19 + x2 \cdot 12\right)\right)\\ \mathbf{elif}\;x1 \leq 2.2 \cdot 10^{+59}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(2 \cdot \left(x2 \cdot \left(-6 + x2 \cdot 4\right)\right) + \left(-1 + 3 \cdot \left(x1 \cdot \left(3 + 2 \cdot x2\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot \left(3 \cdot \left(x1 \cdot x1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -6.2e+78)
   (*
    (* x1 (* x1 x1))
    (+ (* 4.0 (* x2 (+ 3.0 (* x2 -2.0)))) (+ -19.0 (* x2 12.0))))
   (if (<= x1 2.2e+59)
     (+
      (* x2 -6.0)
      (*
       x1
       (+
        (* 2.0 (* x2 (+ -6.0 (* x2 4.0))))
        (+ -1.0 (* 3.0 (* x1 (+ 3.0 (* 2.0 x2))))))))
     (* x1 (* 3.0 (* x1 x1))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -6.2e+78) {
		tmp = (x1 * (x1 * x1)) * ((4.0 * (x2 * (3.0 + (x2 * -2.0)))) + (-19.0 + (x2 * 12.0)));
	} else if (x1 <= 2.2e+59) {
		tmp = (x2 * -6.0) + (x1 * ((2.0 * (x2 * (-6.0 + (x2 * 4.0)))) + (-1.0 + (3.0 * (x1 * (3.0 + (2.0 * x2)))))));
	} else {
		tmp = x1 * (3.0 * (x1 * x1));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x1 <= (-6.2d+78)) then
        tmp = (x1 * (x1 * x1)) * ((4.0d0 * (x2 * (3.0d0 + (x2 * (-2.0d0))))) + ((-19.0d0) + (x2 * 12.0d0)))
    else if (x1 <= 2.2d+59) then
        tmp = (x2 * (-6.0d0)) + (x1 * ((2.0d0 * (x2 * ((-6.0d0) + (x2 * 4.0d0)))) + ((-1.0d0) + (3.0d0 * (x1 * (3.0d0 + (2.0d0 * x2)))))))
    else
        tmp = x1 * (3.0d0 * (x1 * x1))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= -6.2e+78) {
		tmp = (x1 * (x1 * x1)) * ((4.0 * (x2 * (3.0 + (x2 * -2.0)))) + (-19.0 + (x2 * 12.0)));
	} else if (x1 <= 2.2e+59) {
		tmp = (x2 * -6.0) + (x1 * ((2.0 * (x2 * (-6.0 + (x2 * 4.0)))) + (-1.0 + (3.0 * (x1 * (3.0 + (2.0 * x2)))))));
	} else {
		tmp = x1 * (3.0 * (x1 * x1));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -6.2e+78:
		tmp = (x1 * (x1 * x1)) * ((4.0 * (x2 * (3.0 + (x2 * -2.0)))) + (-19.0 + (x2 * 12.0)))
	elif x1 <= 2.2e+59:
		tmp = (x2 * -6.0) + (x1 * ((2.0 * (x2 * (-6.0 + (x2 * 4.0)))) + (-1.0 + (3.0 * (x1 * (3.0 + (2.0 * x2)))))))
	else:
		tmp = x1 * (3.0 * (x1 * x1))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -6.2e+78)
		tmp = Float64(Float64(x1 * Float64(x1 * x1)) * Float64(Float64(4.0 * Float64(x2 * Float64(3.0 + Float64(x2 * -2.0)))) + Float64(-19.0 + Float64(x2 * 12.0))));
	elseif (x1 <= 2.2e+59)
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(2.0 * Float64(x2 * Float64(-6.0 + Float64(x2 * 4.0)))) + Float64(-1.0 + Float64(3.0 * Float64(x1 * Float64(3.0 + Float64(2.0 * x2))))))));
	else
		tmp = Float64(x1 * Float64(3.0 * Float64(x1 * x1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -6.2e+78)
		tmp = (x1 * (x1 * x1)) * ((4.0 * (x2 * (3.0 + (x2 * -2.0)))) + (-19.0 + (x2 * 12.0)));
	elseif (x1 <= 2.2e+59)
		tmp = (x2 * -6.0) + (x1 * ((2.0 * (x2 * (-6.0 + (x2 * 4.0)))) + (-1.0 + (3.0 * (x1 * (3.0 + (2.0 * x2)))))));
	else
		tmp = x1 * (3.0 * (x1 * x1));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -6.2e+78], N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] * N[(N[(4.0 * N[(x2 * N[(3.0 + N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-19.0 + N[(x2 * 12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 2.2e+59], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(2.0 * N[(x2 * N[(-6.0 + N[(x2 * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-1.0 + N[(3.0 * N[(x1 * N[(3.0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 * N[(3.0 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -6.2e78

   1. Initial program 19.0%

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

   3. Simplified 19.0%

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

   5. Taylor expanded in x1 around 0

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

   7. Simplified 69.7%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(2 \cdot \left(x2 \cdot \left(x2 \cdot 4 + -6\right)\right) + \left(x1 \cdot \left(\left(\left(\left(9 + 3 \cdot \left(x2 \cdot 2\right)\right) + \left(x2 \cdot 10 + x1 \cdot \left(\left(3 \cdot \left(x2 \cdot 4\right) + -18\right) + \left(4 \cdot \left(x2 \cdot \left(3 - x2 \cdot 2\right)\right) + -1\right)\right)\right)\right) - \left(x2 \cdot 4 + -6\right)\right) + -6\right) + -1\right)\right)} \]

   8. Taylor expanded in x1 around inf

      \[\leadsto \color{blue}{{x1}^{3} \cdot \left(\left(4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right) + 12 \cdot x2\right) - 19\right)} \]
   9. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{3}\right), \color{blue}{\left(\left(4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right) + 12 \cdot x2\right) - 19\right)}\right) \]

      2. cube-mult N/A

         \[\leadsto \mathsf{*.f64}\left(\left(x1 \cdot \left(x1 \cdot x1\right)\right), \left(\color{blue}{\left(4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right) + 12 \cdot x2\right)} - 19\right)\right) \]

      3. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(x1 \cdot {x1}^{2}\right), \left(\left(4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right) + \color{blue}{12 \cdot x2}\right) - 19\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \left({x1}^{2}\right)\right), \left(\color{blue}{\left(4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right) + 12 \cdot x2\right)} - 19\right)\right) \]

      5. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \left(x1 \cdot x1\right)\right), \left(\left(4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right) + \color{blue}{12 \cdot x2}\right) - 19\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, x1\right)\right), \left(\left(4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right) + \color{blue}{12 \cdot x2}\right) - 19\right)\right) \]

      7. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, x1\right)\right), \left(4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right) + \color{blue}{\left(12 \cdot x2 - 19\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(\left(4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right), \color{blue}{\left(12 \cdot x2 - 19\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right), \left(\color{blue}{12 \cdot x2} - 19\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, \mathsf{*.f64}\left(x2, \left(3 - 2 \cdot x2\right)\right)\right), \left(12 \cdot \color{blue}{x2} - 19\right)\right)\right) \]

      11. cancel-sign-sub-inv N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, \mathsf{*.f64}\left(x2, \left(3 + \left(\mathsf{neg}\left(2\right)\right) \cdot x2\right)\right)\right), \left(12 \cdot x2 - 19\right)\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, \mathsf{*.f64}\left(x2, \left(3 + -2 \cdot x2\right)\right)\right), \left(12 \cdot x2 - 19\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(3, \left(-2 \cdot x2\right)\right)\right)\right), \left(12 \cdot x2 - 19\right)\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(3, \left(x2 \cdot -2\right)\right)\right)\right), \left(12 \cdot x2 - 19\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(3, \mathsf{*.f64}\left(x2, -2\right)\right)\right)\right), \left(12 \cdot x2 - 19\right)\right)\right) \]

      16. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(3, \mathsf{*.f64}\left(x2, -2\right)\right)\right)\right), \left(12 \cdot x2 + \color{blue}{\left(\mathsf{neg}\left(19\right)\right)}\right)\right)\right) \]

      17. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(3, \mathsf{*.f64}\left(x2, -2\right)\right)\right)\right), \left(12 \cdot x2 + -19\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(3, \mathsf{*.f64}\left(x2, -2\right)\right)\right)\right), \mathsf{+.f64}\left(\left(12 \cdot x2\right), \color{blue}{-19}\right)\right)\right) \]

      19. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(3, \mathsf{*.f64}\left(x2, -2\right)\right)\right)\right), \mathsf{+.f64}\left(\left(x2 \cdot 12\right), -19\right)\right)\right) \]

      20. *-lowering-*.f64 88.8%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(3, \mathsf{*.f64}\left(x2, -2\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 12\right), -19\right)\right)\right) \]

   10. Simplified 88.8%

       \[\leadsto \color{blue}{\left(x1 \cdot \left(x1 \cdot x1\right)\right) \cdot \left(4 \cdot \left(x2 \cdot \left(3 + x2 \cdot -2\right)\right) + \left(x2 \cdot 12 + -19\right)\right)} \]

   if -6.2e78 < x1 < 2.2e59

   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

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

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

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

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

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

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

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

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

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

      5. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + \color{blue}{\left(\mathsf{neg}\left(6\right)\right)}\right)\right)\right)\right)\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + -6\right)\right)\right)\right)\right)\right) \]

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

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

      8. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\left(x2 \cdot 4\right), -6\right)\right)\right)\right)\right)\right) \]

      9. *-lowering-*.f64 83.6%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right)\right)\right)\right)\right) \]

   7. Simplified 83.6%

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

   8. Taylor expanded in x1 around 0

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

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

         \[\leadsto \mathsf{+.f64}\left(\left(-6 \cdot x2\right), \color{blue}{\left(x1 \cdot \left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + 3 \cdot \left(x1 \cdot \left(3 - -2 \cdot x2\right)\right)\right) - 1\right)\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \left(\color{blue}{x1} \cdot \left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + 3 \cdot \left(x1 \cdot \left(3 - -2 \cdot x2\right)\right)\right) - 1\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \color{blue}{\left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + 3 \cdot \left(x1 \cdot \left(3 - -2 \cdot x2\right)\right)\right) - 1\right)}\right)\right) \]

      4. associate--l+ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + \color{blue}{\left(3 \cdot \left(x1 \cdot \left(3 - -2 \cdot x2\right)\right) - 1\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)\right), \color{blue}{\left(3 \cdot \left(x1 \cdot \left(3 - -2 \cdot x2\right)\right) - 1\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)\right), \left(\color{blue}{3 \cdot \left(x1 \cdot \left(3 - -2 \cdot x2\right)\right)} - 1\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 - 6\right)\right)\right), \left(3 \cdot \color{blue}{\left(x1 \cdot \left(3 - -2 \cdot x2\right)\right)} - 1\right)\right)\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + \left(\mathsf{neg}\left(6\right)\right)\right)\right)\right), \left(3 \cdot \left(x1 \cdot \color{blue}{\left(3 - -2 \cdot x2\right)}\right) - 1\right)\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + -6\right)\right)\right), \left(3 \cdot \left(x1 \cdot \left(3 - \color{blue}{-2 \cdot x2}\right)\right) - 1\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\left(4 \cdot x2\right), -6\right)\right)\right), \left(3 \cdot \left(x1 \cdot \color{blue}{\left(3 - -2 \cdot x2\right)}\right) - 1\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, x2\right), -6\right)\right)\right), \left(3 \cdot \left(x1 \cdot \left(\color{blue}{3} - -2 \cdot x2\right)\right) - 1\right)\right)\right)\right) \]

      12. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, x2\right), -6\right)\right)\right), \left(3 \cdot \left(x1 \cdot \left(3 - -2 \cdot x2\right)\right) + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, x2\right), -6\right)\right)\right), \left(3 \cdot \left(x1 \cdot \left(3 - -2 \cdot x2\right)\right) + -1\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, x2\right), -6\right)\right)\right), \mathsf{+.f64}\left(\left(3 \cdot \left(x1 \cdot \left(3 - -2 \cdot x2\right)\right)\right), \color{blue}{-1}\right)\right)\right)\right) \]

   10. Simplified 84.1%

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

   if 2.2e59 < x1

   1. Initial program 44.1%

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

   3. Simplified 44.1%

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

   5. Taylor expanded in x1 around 0

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

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

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

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

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

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

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

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

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

      5. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + \color{blue}{\left(\mathsf{neg}\left(6\right)\right)}\right)\right)\right)\right)\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + -6\right)\right)\right)\right)\right)\right) \]

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

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

      8. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\left(x2 \cdot 4\right), -6\right)\right)\right)\right)\right)\right) \]

      9. *-lowering-*.f64 7.6%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right)\right)\right)\right)\right) \]

   7. Simplified 7.6%

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

   8. Taylor expanded in x1 around 0

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

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

         \[\leadsto \mathsf{+.f64}\left(\left(-6 \cdot x2\right), \color{blue}{\left(x1 \cdot \left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)\right) - 1\right)\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \left(\color{blue}{x1} \cdot \left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)\right) - 1\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \color{blue}{\left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)\right) - 1\right)}\right)\right) \]

      4. associate--l+ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + \color{blue}{\left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right) - 1\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)\right), \color{blue}{\left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right) - 1\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)\right), \left(\color{blue}{x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)} - 1\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 - 6\right)\right)\right), \left(x1 \cdot \color{blue}{\left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)} - 1\right)\right)\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + \left(\mathsf{neg}\left(6\right)\right)\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + \color{blue}{3 \cdot \left(3 - -2 \cdot x2\right)}\right) - 1\right)\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + -6\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \color{blue}{\left(3 - -2 \cdot x2\right)}\right) - 1\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\left(4 \cdot x2\right), -6\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + \color{blue}{3 \cdot \left(3 - -2 \cdot x2\right)}\right) - 1\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, x2\right), -6\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + \color{blue}{3} \cdot \left(3 - -2 \cdot x2\right)\right) - 1\right)\right)\right)\right) \]

      12. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, x2\right), -6\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right) + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, x2\right), -6\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right) + -1\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, x2\right), -6\right)\right)\right), \mathsf{+.f64}\left(\left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)\right), \color{blue}{-1}\right)\right)\right)\right) \]

   10. Simplified 76.1%

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

   11. Taylor expanded in x1 around inf

       \[\leadsto \color{blue}{3 \cdot {x1}^{3}} \]
   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. *-commutative N/A

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

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

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

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

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

       8. unpow2 N/A

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

       9. *-lowering-*.f64 81.8%

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

   13. Simplified 81.8%

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

4. Final simplification 84.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -6.2 \cdot 10^{+78}:\\ \;\;\;\;\left(x1 \cdot \left(x1 \cdot x1\right)\right) \cdot \left(4 \cdot \left(x2 \cdot \left(3 + x2 \cdot -2\right)\right) + \left(-19 + x2 \cdot 12\right)\right)\\ \mathbf{elif}\;x1 \leq 2.2 \cdot 10^{+59}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(2 \cdot \left(x2 \cdot \left(-6 + x2 \cdot 4\right)\right) + \left(-1 + 3 \cdot \left(x1 \cdot \left(3 + 2 \cdot x2\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot \left(3 \cdot \left(x1 \cdot x1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 74.1% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(-1 + x1 \cdot \left(9 + x1 \cdot -19\right)\right)\\ \mathbf{if}\;x1 \leq -2.1 \cdot 10^{+90}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x1 \leq -2.05 \cdot 10^{-66}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(x2 \cdot \left(x2 \cdot 8\right)\right)\\ \mathbf{elif}\;x1 \leq 7.4 \cdot 10^{-184}:\\ \;\;\;\;t\_0 + x2 \cdot -6\\ \mathbf{elif}\;x1 \leq 3.9 \cdot 10^{+102}:\\ \;\;\;\;x2 \cdot \left(x2 \cdot \left(x1 \cdot \left(8 + \frac{-12}{x2}\right) + \frac{-6}{x2}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot \left(3 \cdot \left(x1 \cdot x1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (+ -1.0 (* x1 (+ 9.0 (* x1 -19.0)))))))
   (if (<= x1 -2.1e+90)
     t_0
     (if (<= x1 -2.05e-66)
       (+ (* x2 -6.0) (* x1 (* x2 (* x2 8.0))))
       (if (<= x1 7.4e-184)
         (+ t_0 (* x2 -6.0))
         (if (<= x1 3.9e+102)
           (* x2 (* x2 (+ (* x1 (+ 8.0 (/ -12.0 x2))) (/ -6.0 x2))))
           (* x1 (* 3.0 (* x1 x1)))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0))));
	double tmp;
	if (x1 <= -2.1e+90) {
		tmp = t_0;
	} else if (x1 <= -2.05e-66) {
		tmp = (x2 * -6.0) + (x1 * (x2 * (x2 * 8.0)));
	} else if (x1 <= 7.4e-184) {
		tmp = t_0 + (x2 * -6.0);
	} else if (x1 <= 3.9e+102) {
		tmp = x2 * (x2 * ((x1 * (8.0 + (-12.0 / x2))) + (-6.0 / x2)));
	} else {
		tmp = x1 * (3.0 * (x1 * x1));
	}
	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 * ((-1.0d0) + (x1 * (9.0d0 + (x1 * (-19.0d0)))))
    if (x1 <= (-2.1d+90)) then
        tmp = t_0
    else if (x1 <= (-2.05d-66)) then
        tmp = (x2 * (-6.0d0)) + (x1 * (x2 * (x2 * 8.0d0)))
    else if (x1 <= 7.4d-184) then
        tmp = t_0 + (x2 * (-6.0d0))
    else if (x1 <= 3.9d+102) then
        tmp = x2 * (x2 * ((x1 * (8.0d0 + ((-12.0d0) / x2))) + ((-6.0d0) / x2)))
    else
        tmp = x1 * (3.0d0 * (x1 * x1))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0))));
	double tmp;
	if (x1 <= -2.1e+90) {
		tmp = t_0;
	} else if (x1 <= -2.05e-66) {
		tmp = (x2 * -6.0) + (x1 * (x2 * (x2 * 8.0)));
	} else if (x1 <= 7.4e-184) {
		tmp = t_0 + (x2 * -6.0);
	} else if (x1 <= 3.9e+102) {
		tmp = x2 * (x2 * ((x1 * (8.0 + (-12.0 / x2))) + (-6.0 / x2)));
	} else {
		tmp = x1 * (3.0 * (x1 * x1));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0))))
	tmp = 0
	if x1 <= -2.1e+90:
		tmp = t_0
	elif x1 <= -2.05e-66:
		tmp = (x2 * -6.0) + (x1 * (x2 * (x2 * 8.0)))
	elif x1 <= 7.4e-184:
		tmp = t_0 + (x2 * -6.0)
	elif x1 <= 3.9e+102:
		tmp = x2 * (x2 * ((x1 * (8.0 + (-12.0 / x2))) + (-6.0 / x2)))
	else:
		tmp = x1 * (3.0 * (x1 * x1))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(-1.0 + Float64(x1 * Float64(9.0 + Float64(x1 * -19.0)))))
	tmp = 0.0
	if (x1 <= -2.1e+90)
		tmp = t_0;
	elseif (x1 <= -2.05e-66)
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(x2 * Float64(x2 * 8.0))));
	elseif (x1 <= 7.4e-184)
		tmp = Float64(t_0 + Float64(x2 * -6.0));
	elseif (x1 <= 3.9e+102)
		tmp = Float64(x2 * Float64(x2 * Float64(Float64(x1 * Float64(8.0 + Float64(-12.0 / x2))) + Float64(-6.0 / x2))));
	else
		tmp = Float64(x1 * Float64(3.0 * Float64(x1 * x1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0))));
	tmp = 0.0;
	if (x1 <= -2.1e+90)
		tmp = t_0;
	elseif (x1 <= -2.05e-66)
		tmp = (x2 * -6.0) + (x1 * (x2 * (x2 * 8.0)));
	elseif (x1 <= 7.4e-184)
		tmp = t_0 + (x2 * -6.0);
	elseif (x1 <= 3.9e+102)
		tmp = x2 * (x2 * ((x1 * (8.0 + (-12.0 / x2))) + (-6.0 / x2)));
	else
		tmp = x1 * (3.0 * (x1 * x1));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(-1.0 + N[(x1 * N[(9.0 + N[(x1 * -19.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -2.1e+90], t$95$0, If[LessEqual[x1, -2.05e-66], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(x2 * N[(x2 * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 7.4e-184], N[(t$95$0 + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 3.9e+102], N[(x2 * N[(x2 * N[(N[(x1 * N[(8.0 + N[(-12.0 / x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-6.0 / x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 * N[(3.0 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if x1 < -2.09999999999999981e90

   1. Initial program 5.6%

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

   3. Simplified 5.6%

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

   5. Taylor expanded in x1 around 0

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

   7. Simplified 77.8%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(2 \cdot \left(x2 \cdot \left(x2 \cdot 4 + -6\right)\right) + \left(x1 \cdot \left(\left(\left(\left(9 + 3 \cdot \left(x2 \cdot 2\right)\right) + \left(x2 \cdot 10 + x1 \cdot \left(\left(3 \cdot \left(x2 \cdot 4\right) + -18\right) + \left(4 \cdot \left(x2 \cdot \left(3 - x2 \cdot 2\right)\right) + -1\right)\right)\right)\right) - \left(x2 \cdot 4 + -6\right)\right) + -6\right) + -1\right)\right)} \]

   8. Taylor expanded in x2 around 0

      \[\leadsto \color{blue}{x1 \cdot \left(x1 \cdot \left(9 + -19 \cdot x1\right) - 1\right)} \]
   9. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(x1, \color{blue}{\left(x1 \cdot \left(9 + -19 \cdot x1\right) - 1\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x1, \left(x1 \cdot \left(9 + -19 \cdot x1\right) + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right) \]

      3. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(x1, \left(x1 \cdot \left(9 + -19 \cdot x1\right) + -1\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\left(x1 \cdot \left(9 + -19 \cdot x1\right)\right), \color{blue}{-1}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \left(9 + -19 \cdot x1\right)\right), -1\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(9, \left(-19 \cdot x1\right)\right)\right), -1\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(9, \left(x1 \cdot -19\right)\right)\right), -1\right)\right) \]

      8. *-lowering-*.f64 94.9%

         \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(9, \mathsf{*.f64}\left(x1, -19\right)\right)\right), -1\right)\right) \]

   10. Simplified 94.9%

       \[\leadsto \color{blue}{x1 \cdot \left(x1 \cdot \left(9 + x1 \cdot -19\right) + -1\right)} \]

   if -2.09999999999999981e90 < x1 < -2.04999999999999999e-66

   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 99.5%

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

   5. Taylor expanded in x1 around 0

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

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

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

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

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

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

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

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

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

      5. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + \color{blue}{\left(\mathsf{neg}\left(6\right)\right)}\right)\right)\right)\right)\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + -6\right)\right)\right)\right)\right)\right) \]

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

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

      8. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\left(x2 \cdot 4\right), -6\right)\right)\right)\right)\right)\right) \]

      9. *-lowering-*.f64 64.3%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right)\right)\right)\right)\right) \]

   7. Simplified 64.3%

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

   8. Taylor expanded in x1 around 0

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

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

         \[\leadsto \mathsf{+.f64}\left(\left(-6 \cdot x2\right), \color{blue}{\left(x1 \cdot \left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + 3 \cdot \left(x1 \cdot \left(3 - -2 \cdot x2\right)\right)\right) - 1\right)\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \left(\color{blue}{x1} \cdot \left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + 3 \cdot \left(x1 \cdot \left(3 - -2 \cdot x2\right)\right)\right) - 1\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \color{blue}{\left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + 3 \cdot \left(x1 \cdot \left(3 - -2 \cdot x2\right)\right)\right) - 1\right)}\right)\right) \]

      4. associate--l+ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + \color{blue}{\left(3 \cdot \left(x1 \cdot \left(3 - -2 \cdot x2\right)\right) - 1\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)\right), \color{blue}{\left(3 \cdot \left(x1 \cdot \left(3 - -2 \cdot x2\right)\right) - 1\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)\right), \left(\color{blue}{3 \cdot \left(x1 \cdot \left(3 - -2 \cdot x2\right)\right)} - 1\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 - 6\right)\right)\right), \left(3 \cdot \color{blue}{\left(x1 \cdot \left(3 - -2 \cdot x2\right)\right)} - 1\right)\right)\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + \left(\mathsf{neg}\left(6\right)\right)\right)\right)\right), \left(3 \cdot \left(x1 \cdot \color{blue}{\left(3 - -2 \cdot x2\right)}\right) - 1\right)\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + -6\right)\right)\right), \left(3 \cdot \left(x1 \cdot \left(3 - \color{blue}{-2 \cdot x2}\right)\right) - 1\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\left(4 \cdot x2\right), -6\right)\right)\right), \left(3 \cdot \left(x1 \cdot \color{blue}{\left(3 - -2 \cdot x2\right)}\right) - 1\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, x2\right), -6\right)\right)\right), \left(3 \cdot \left(x1 \cdot \left(\color{blue}{3} - -2 \cdot x2\right)\right) - 1\right)\right)\right)\right) \]

      12. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, x2\right), -6\right)\right)\right), \left(3 \cdot \left(x1 \cdot \left(3 - -2 \cdot x2\right)\right) + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, x2\right), -6\right)\right)\right), \left(3 \cdot \left(x1 \cdot \left(3 - -2 \cdot x2\right)\right) + -1\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, x2\right), -6\right)\right)\right), \mathsf{+.f64}\left(\left(3 \cdot \left(x1 \cdot \left(3 - -2 \cdot x2\right)\right)\right), \color{blue}{-1}\right)\right)\right)\right) \]

   10. Simplified 65.9%

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

   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. *-commutative N/A

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

       2. associate-*l* N/A

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

       3. *-commutative N/A

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

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

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

       5. *-commutative N/A

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

       6. unpow2 N/A

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

       7. associate-*l* N/A

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

       8. *-commutative N/A

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

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

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

       10. *-commutative N/A

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

       11. *-lowering-*.f64 50.9%

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

   13. Simplified 50.9%

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

   if -2.04999999999999999e-66 < x1 < 7.3999999999999997e-184

   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

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

   7. Simplified 85.4%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(2 \cdot \left(x2 \cdot \left(x2 \cdot 4 + -6\right)\right) + \left(x1 \cdot \left(\left(\left(\left(9 + 3 \cdot \left(x2 \cdot 2\right)\right) + \left(x2 \cdot 10 + x1 \cdot \left(\left(3 \cdot \left(x2 \cdot 4\right) + -18\right) + \left(4 \cdot \left(x2 \cdot \left(3 - x2 \cdot 2\right)\right) + -1\right)\right)\right)\right) - \left(x2 \cdot 4 + -6\right)\right) + -6\right) + -1\right)\right)} \]

   8. Taylor expanded in x2 around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \color{blue}{\left(x1 \cdot \left(x1 \cdot \left(9 + -19 \cdot x1\right) - 1\right)\right)}\right) \]
   9. Step-by-step derivation

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \color{blue}{\left(x1 \cdot \left(9 + -19 \cdot x1\right) - 1\right)}\right)\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \left(x1 \cdot \left(9 + -19 \cdot x1\right) + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right) \]

      3. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \left(x1 \cdot \left(9 + -19 \cdot x1\right) + -1\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\left(x1 \cdot \left(9 + -19 \cdot x1\right)\right), \color{blue}{-1}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \left(9 + -19 \cdot x1\right)\right), -1\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(9, \left(-19 \cdot x1\right)\right)\right), -1\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(9, \left(x1 \cdot -19\right)\right)\right), -1\right)\right)\right) \]

      8. *-lowering-*.f64 93.9%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(9, \mathsf{*.f64}\left(x1, -19\right)\right)\right), -1\right)\right)\right) \]

   10. Simplified 93.9%

       \[\leadsto -6 \cdot x2 + \color{blue}{x1 \cdot \left(x1 \cdot \left(9 + x1 \cdot -19\right) + -1\right)} \]

   if 7.3999999999999997e-184 < x1 < 3.8999999999999998e102

   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 99.6%

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

   5. Taylor expanded in x2 around -inf

      \[\leadsto \color{blue}{{x2}^{2} \cdot \left(-1 \cdot \frac{-6 \cdot \frac{{x1}^{2}}{1 + {x1}^{2}} + \left(6 \cdot \frac{1}{1 + {x1}^{2}} + \left(1 + {x1}^{2}\right) \cdot \left(-4 \cdot \frac{{x1}^{2} \cdot \left(3 \cdot x1 - 1\right)}{{\left(1 + {x1}^{2}\right)}^{2}} + -2 \cdot \frac{4 \cdot {x1}^{2} + x1 \cdot \left(2 \cdot \frac{x1 \cdot \left(3 \cdot x1 - 1\right)}{1 + {x1}^{2}} - 6\right)}{1 + {x1}^{2}}\right)\right)}{x2} + 8 \cdot \frac{x1}{1 + {x1}^{2}}\right)} \]

   7. Simplified 63.5%

      \[\leadsto \color{blue}{\left(x2 \cdot x2\right) \cdot \left(\frac{8 \cdot x1}{1 + x1 \cdot x1} - \frac{\frac{-6 \cdot \left(x1 \cdot x1\right)}{1 + x1 \cdot x1} + \left(\frac{6}{1 + x1 \cdot x1} + \left(1 + x1 \cdot x1\right) \cdot \left(\frac{-4 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot 3 + -1\right)\right)}{\left(1 + x1 \cdot x1\right) \cdot \left(1 + x1 \cdot x1\right)} + \frac{-2 \cdot \left(4 \cdot \left(x1 \cdot x1\right) + x1 \cdot \left(\frac{2 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)}{1 + x1 \cdot x1} + -6\right)\right)}{1 + x1 \cdot x1}\right)\right)}{x2}\right)} \]

   8. Taylor expanded in x1 around 0

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

      1. sub-neg N/A

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

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

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

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

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

      4. sub-neg N/A

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

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

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

      6. associate-*r/ N/A

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

      7. metadata-eval N/A

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

      8. distribute-neg-frac N/A

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

      9. metadata-eval N/A

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

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

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

      11. associate-*r/ N/A

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

      12. metadata-eval N/A

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

      13. distribute-neg-frac N/A

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

      14. metadata-eval N/A

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

      15. /-lowering-/.f64 58.7%

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

   10. Simplified 58.7%

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

       1. associate-*l* N/A

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

       2. *-commutative N/A

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

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

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

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

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

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

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

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

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

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

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

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

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

       9. /-lowering-/.f64 65.3%

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

   12. Applied egg-rr 65.3%

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

   if 3.8999999999999998e102 < x1

   1. Initial program 34.1%

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

   3. Simplified 34.1%

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

   5. Taylor expanded in x1 around 0

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

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

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

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

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

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

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

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

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

      5. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + \color{blue}{\left(\mathsf{neg}\left(6\right)\right)}\right)\right)\right)\right)\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + -6\right)\right)\right)\right)\right)\right) \]

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

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

      8. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\left(x2 \cdot 4\right), -6\right)\right)\right)\right)\right)\right) \]

      9. *-lowering-*.f64 8.1%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right)\right)\right)\right)\right) \]

   7. Simplified 8.1%

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

   8. Taylor expanded in x1 around 0

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

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

         \[\leadsto \mathsf{+.f64}\left(\left(-6 \cdot x2\right), \color{blue}{\left(x1 \cdot \left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)\right) - 1\right)\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \left(\color{blue}{x1} \cdot \left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)\right) - 1\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \color{blue}{\left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)\right) - 1\right)}\right)\right) \]

      4. associate--l+ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + \color{blue}{\left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right) - 1\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)\right), \color{blue}{\left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right) - 1\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)\right), \left(\color{blue}{x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)} - 1\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 - 6\right)\right)\right), \left(x1 \cdot \color{blue}{\left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)} - 1\right)\right)\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + \left(\mathsf{neg}\left(6\right)\right)\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + \color{blue}{3 \cdot \left(3 - -2 \cdot x2\right)}\right) - 1\right)\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + -6\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \color{blue}{\left(3 - -2 \cdot x2\right)}\right) - 1\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\left(4 \cdot x2\right), -6\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + \color{blue}{3 \cdot \left(3 - -2 \cdot x2\right)}\right) - 1\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, x2\right), -6\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + \color{blue}{3} \cdot \left(3 - -2 \cdot x2\right)\right) - 1\right)\right)\right)\right) \]

      12. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, x2\right), -6\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right) + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, x2\right), -6\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right) + -1\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, x2\right), -6\right)\right)\right), \mathsf{+.f64}\left(\left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)\right), \color{blue}{-1}\right)\right)\right)\right) \]

   10. Simplified 88.6%

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

   11. Taylor expanded in x1 around inf

       \[\leadsto \color{blue}{3 \cdot {x1}^{3}} \]
   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. *-commutative N/A

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

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

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

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

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

       8. unpow2 N/A

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

       9. *-lowering-*.f64 95.5%

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

   13. Simplified 95.5%

       \[\leadsto \color{blue}{x1 \cdot \left(3 \cdot \left(x1 \cdot x1\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -2.1 \cdot 10^{+90}:\\ \;\;\;\;x1 \cdot \left(-1 + x1 \cdot \left(9 + x1 \cdot -19\right)\right)\\ \mathbf{elif}\;x1 \leq -2.05 \cdot 10^{-66}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(x2 \cdot \left(x2 \cdot 8\right)\right)\\ \mathbf{elif}\;x1 \leq 7.4 \cdot 10^{-184}:\\ \;\;\;\;x1 \cdot \left(-1 + x1 \cdot \left(9 + x1 \cdot -19\right)\right) + x2 \cdot -6\\ \mathbf{elif}\;x1 \leq 3.9 \cdot 10^{+102}:\\ \;\;\;\;x2 \cdot \left(x2 \cdot \left(x1 \cdot \left(8 + \frac{-12}{x2}\right) + \frac{-6}{x2}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot \left(3 \cdot \left(x1 \cdot x1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 74.1% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -3.65 \cdot 10^{+90}:\\ \;\;\;\;x1 \cdot \left(-1 + x1 \cdot \left(9 + x1 \cdot -19\right)\right)\\ \mathbf{elif}\;x1 \leq -1.05 \cdot 10^{-68}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(x2 \cdot \left(x2 \cdot 8\right)\right)\\ \mathbf{elif}\;x1 \leq 6.2 \cdot 10^{-184}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + x2 \cdot -12\right)\\ \mathbf{elif}\;x1 \leq 3.9 \cdot 10^{+102}:\\ \;\;\;\;x2 \cdot \left(x2 \cdot \left(x1 \cdot \left(8 + \frac{-12}{x2}\right) + \frac{-6}{x2}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot \left(3 \cdot \left(x1 \cdot x1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -3.65e+90)
   (* x1 (+ -1.0 (* x1 (+ 9.0 (* x1 -19.0)))))
   (if (<= x1 -1.05e-68)
     (+ (* x2 -6.0) (* x1 (* x2 (* x2 8.0))))
     (if (<= x1 6.2e-184)
       (+ (* x2 -6.0) (* x1 (+ -1.0 (* x2 -12.0))))
       (if (<= x1 3.9e+102)
         (* x2 (* x2 (+ (* x1 (+ 8.0 (/ -12.0 x2))) (/ -6.0 x2))))
         (* x1 (* 3.0 (* x1 x1))))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -3.65e+90) {
		tmp = x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0))));
	} else if (x1 <= -1.05e-68) {
		tmp = (x2 * -6.0) + (x1 * (x2 * (x2 * 8.0)));
	} else if (x1 <= 6.2e-184) {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x2 * -12.0)));
	} else if (x1 <= 3.9e+102) {
		tmp = x2 * (x2 * ((x1 * (8.0 + (-12.0 / x2))) + (-6.0 / x2)));
	} else {
		tmp = x1 * (3.0 * (x1 * x1));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x1 <= (-3.65d+90)) then
        tmp = x1 * ((-1.0d0) + (x1 * (9.0d0 + (x1 * (-19.0d0)))))
    else if (x1 <= (-1.05d-68)) then
        tmp = (x2 * (-6.0d0)) + (x1 * (x2 * (x2 * 8.0d0)))
    else if (x1 <= 6.2d-184) then
        tmp = (x2 * (-6.0d0)) + (x1 * ((-1.0d0) + (x2 * (-12.0d0))))
    else if (x1 <= 3.9d+102) then
        tmp = x2 * (x2 * ((x1 * (8.0d0 + ((-12.0d0) / x2))) + ((-6.0d0) / x2)))
    else
        tmp = x1 * (3.0d0 * (x1 * x1))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= -3.65e+90) {
		tmp = x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0))));
	} else if (x1 <= -1.05e-68) {
		tmp = (x2 * -6.0) + (x1 * (x2 * (x2 * 8.0)));
	} else if (x1 <= 6.2e-184) {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x2 * -12.0)));
	} else if (x1 <= 3.9e+102) {
		tmp = x2 * (x2 * ((x1 * (8.0 + (-12.0 / x2))) + (-6.0 / x2)));
	} else {
		tmp = x1 * (3.0 * (x1 * x1));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -3.65e+90:
		tmp = x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0))))
	elif x1 <= -1.05e-68:
		tmp = (x2 * -6.0) + (x1 * (x2 * (x2 * 8.0)))
	elif x1 <= 6.2e-184:
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x2 * -12.0)))
	elif x1 <= 3.9e+102:
		tmp = x2 * (x2 * ((x1 * (8.0 + (-12.0 / x2))) + (-6.0 / x2)))
	else:
		tmp = x1 * (3.0 * (x1 * x1))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -3.65e+90)
		tmp = Float64(x1 * Float64(-1.0 + Float64(x1 * Float64(9.0 + Float64(x1 * -19.0)))));
	elseif (x1 <= -1.05e-68)
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(x2 * Float64(x2 * 8.0))));
	elseif (x1 <= 6.2e-184)
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(-1.0 + Float64(x2 * -12.0))));
	elseif (x1 <= 3.9e+102)
		tmp = Float64(x2 * Float64(x2 * Float64(Float64(x1 * Float64(8.0 + Float64(-12.0 / x2))) + Float64(-6.0 / x2))));
	else
		tmp = Float64(x1 * Float64(3.0 * Float64(x1 * x1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -3.65e+90)
		tmp = x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0))));
	elseif (x1 <= -1.05e-68)
		tmp = (x2 * -6.0) + (x1 * (x2 * (x2 * 8.0)));
	elseif (x1 <= 6.2e-184)
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x2 * -12.0)));
	elseif (x1 <= 3.9e+102)
		tmp = x2 * (x2 * ((x1 * (8.0 + (-12.0 / x2))) + (-6.0 / x2)));
	else
		tmp = x1 * (3.0 * (x1 * x1));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -3.65e+90], N[(x1 * N[(-1.0 + N[(x1 * N[(9.0 + N[(x1 * -19.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -1.05e-68], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(x2 * N[(x2 * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 6.2e-184], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(-1.0 + N[(x2 * -12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 3.9e+102], N[(x2 * N[(x2 * N[(N[(x1 * N[(8.0 + N[(-12.0 / x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-6.0 / x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 * N[(3.0 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if x1 < -3.64999999999999997e90

   1. Initial program 5.6%

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

   3. Simplified 5.6%

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

   5. Taylor expanded in x1 around 0

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

   7. Simplified 77.8%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(2 \cdot \left(x2 \cdot \left(x2 \cdot 4 + -6\right)\right) + \left(x1 \cdot \left(\left(\left(\left(9 + 3 \cdot \left(x2 \cdot 2\right)\right) + \left(x2 \cdot 10 + x1 \cdot \left(\left(3 \cdot \left(x2 \cdot 4\right) + -18\right) + \left(4 \cdot \left(x2 \cdot \left(3 - x2 \cdot 2\right)\right) + -1\right)\right)\right)\right) - \left(x2 \cdot 4 + -6\right)\right) + -6\right) + -1\right)\right)} \]

   8. Taylor expanded in x2 around 0

      \[\leadsto \color{blue}{x1 \cdot \left(x1 \cdot \left(9 + -19 \cdot x1\right) - 1\right)} \]
   9. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(x1, \color{blue}{\left(x1 \cdot \left(9 + -19 \cdot x1\right) - 1\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x1, \left(x1 \cdot \left(9 + -19 \cdot x1\right) + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right) \]

      3. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(x1, \left(x1 \cdot \left(9 + -19 \cdot x1\right) + -1\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\left(x1 \cdot \left(9 + -19 \cdot x1\right)\right), \color{blue}{-1}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \left(9 + -19 \cdot x1\right)\right), -1\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(9, \left(-19 \cdot x1\right)\right)\right), -1\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(9, \left(x1 \cdot -19\right)\right)\right), -1\right)\right) \]

      8. *-lowering-*.f64 94.9%

         \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(9, \mathsf{*.f64}\left(x1, -19\right)\right)\right), -1\right)\right) \]

   10. Simplified 94.9%

       \[\leadsto \color{blue}{x1 \cdot \left(x1 \cdot \left(9 + x1 \cdot -19\right) + -1\right)} \]

   if -3.64999999999999997e90 < x1 < -1.05000000000000004e-68

   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 99.5%

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

   5. Taylor expanded in x1 around 0

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

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

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

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

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

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

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

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

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

      5. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + \color{blue}{\left(\mathsf{neg}\left(6\right)\right)}\right)\right)\right)\right)\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + -6\right)\right)\right)\right)\right)\right) \]

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

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

      8. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\left(x2 \cdot 4\right), -6\right)\right)\right)\right)\right)\right) \]

      9. *-lowering-*.f64 64.3%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right)\right)\right)\right)\right) \]

   7. Simplified 64.3%

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

   8. Taylor expanded in x1 around 0

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

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

         \[\leadsto \mathsf{+.f64}\left(\left(-6 \cdot x2\right), \color{blue}{\left(x1 \cdot \left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + 3 \cdot \left(x1 \cdot \left(3 - -2 \cdot x2\right)\right)\right) - 1\right)\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \left(\color{blue}{x1} \cdot \left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + 3 \cdot \left(x1 \cdot \left(3 - -2 \cdot x2\right)\right)\right) - 1\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \color{blue}{\left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + 3 \cdot \left(x1 \cdot \left(3 - -2 \cdot x2\right)\right)\right) - 1\right)}\right)\right) \]

      4. associate--l+ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + \color{blue}{\left(3 \cdot \left(x1 \cdot \left(3 - -2 \cdot x2\right)\right) - 1\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)\right), \color{blue}{\left(3 \cdot \left(x1 \cdot \left(3 - -2 \cdot x2\right)\right) - 1\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)\right), \left(\color{blue}{3 \cdot \left(x1 \cdot \left(3 - -2 \cdot x2\right)\right)} - 1\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 - 6\right)\right)\right), \left(3 \cdot \color{blue}{\left(x1 \cdot \left(3 - -2 \cdot x2\right)\right)} - 1\right)\right)\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + \left(\mathsf{neg}\left(6\right)\right)\right)\right)\right), \left(3 \cdot \left(x1 \cdot \color{blue}{\left(3 - -2 \cdot x2\right)}\right) - 1\right)\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + -6\right)\right)\right), \left(3 \cdot \left(x1 \cdot \left(3 - \color{blue}{-2 \cdot x2}\right)\right) - 1\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\left(4 \cdot x2\right), -6\right)\right)\right), \left(3 \cdot \left(x1 \cdot \color{blue}{\left(3 - -2 \cdot x2\right)}\right) - 1\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, x2\right), -6\right)\right)\right), \left(3 \cdot \left(x1 \cdot \left(\color{blue}{3} - -2 \cdot x2\right)\right) - 1\right)\right)\right)\right) \]

      12. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, x2\right), -6\right)\right)\right), \left(3 \cdot \left(x1 \cdot \left(3 - -2 \cdot x2\right)\right) + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, x2\right), -6\right)\right)\right), \left(3 \cdot \left(x1 \cdot \left(3 - -2 \cdot x2\right)\right) + -1\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, x2\right), -6\right)\right)\right), \mathsf{+.f64}\left(\left(3 \cdot \left(x1 \cdot \left(3 - -2 \cdot x2\right)\right)\right), \color{blue}{-1}\right)\right)\right)\right) \]

   10. Simplified 65.9%

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

   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. *-commutative N/A

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

       2. associate-*l* N/A

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

       3. *-commutative N/A

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

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

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

       5. *-commutative N/A

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

       6. unpow2 N/A

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

       7. associate-*l* N/A

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

       8. *-commutative N/A

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

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

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

       10. *-commutative N/A

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

       11. *-lowering-*.f64 50.9%

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

   13. Simplified 50.9%

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

   if -1.05000000000000004e-68 < x1 < 6.2000000000000004e-184

   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

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

   7. Simplified 85.4%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(2 \cdot \left(x2 \cdot \left(x2 \cdot 4 + -6\right)\right) + \left(x1 \cdot \left(\left(\left(\left(9 + 3 \cdot \left(x2 \cdot 2\right)\right) + \left(x2 \cdot 10 + x1 \cdot \left(\left(3 \cdot \left(x2 \cdot 4\right) + -18\right) + \left(4 \cdot \left(x2 \cdot \left(3 - x2 \cdot 2\right)\right) + -1\right)\right)\right)\right) - \left(x2 \cdot 4 + -6\right)\right) + -6\right) + -1\right)\right)} \]

   8. Taylor expanded in x2 around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \color{blue}{\left(x1 \cdot \left(x2 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right) + x1 \cdot \left(x1 \cdot \left(9 + -19 \cdot x1\right) - 1\right)\right)}\right) \]
   9. Step-by-step derivation

      1. distribute-lft-out N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \left(x1 \cdot \color{blue}{\left(x2 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right) + \left(x1 \cdot \left(9 + -19 \cdot x1\right) - 1\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \color{blue}{\left(x2 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right) + \left(x1 \cdot \left(9 + -19 \cdot x1\right) - 1\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\left(x2 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right), \color{blue}{\left(x1 \cdot \left(9 + -19 \cdot x1\right) - 1\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right), \left(\color{blue}{x1 \cdot \left(9 + -19 \cdot x1\right)} - 1\right)\right)\right)\right) \]

      5. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, \left(x1 \cdot \left(12 + 24 \cdot x1\right) + \left(\mathsf{neg}\left(12\right)\right)\right)\right), \left(x1 \cdot \color{blue}{\left(9 + -19 \cdot x1\right)} - 1\right)\right)\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, \left(x1 \cdot \left(12 + 24 \cdot x1\right) + -12\right)\right), \left(x1 \cdot \left(9 + \color{blue}{-19 \cdot x1}\right) - 1\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\left(x1 \cdot \left(12 + 24 \cdot x1\right)\right), -12\right)\right), \left(x1 \cdot \color{blue}{\left(9 + -19 \cdot x1\right)} - 1\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \left(12 + 24 \cdot x1\right)\right), -12\right)\right), \left(x1 \cdot \left(\color{blue}{9} + -19 \cdot x1\right) - 1\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(12, \left(24 \cdot x1\right)\right)\right), -12\right)\right), \left(x1 \cdot \left(9 + -19 \cdot x1\right) - 1\right)\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(12, \left(x1 \cdot 24\right)\right)\right), -12\right)\right), \left(x1 \cdot \left(9 + -19 \cdot x1\right) - 1\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(12, \mathsf{*.f64}\left(x1, 24\right)\right)\right), -12\right)\right), \left(x1 \cdot \left(9 + -19 \cdot x1\right) - 1\right)\right)\right)\right) \]

      12. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(12, \mathsf{*.f64}\left(x1, 24\right)\right)\right), -12\right)\right), \left(x1 \cdot \left(9 + -19 \cdot x1\right) + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(12, \mathsf{*.f64}\left(x1, 24\right)\right)\right), -12\right)\right), \left(x1 \cdot \left(9 + -19 \cdot x1\right) + -1\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(12, \mathsf{*.f64}\left(x1, 24\right)\right)\right), -12\right)\right), \mathsf{+.f64}\left(\left(x1 \cdot \left(9 + -19 \cdot x1\right)\right), \color{blue}{-1}\right)\right)\right)\right) \]

   10. Simplified 93.9%

       \[\leadsto -6 \cdot x2 + \color{blue}{x1 \cdot \left(x2 \cdot \left(x1 \cdot \left(12 + x1 \cdot 24\right) + -12\right) + \left(x1 \cdot \left(9 + x1 \cdot -19\right) + -1\right)\right)} \]

   11. Taylor expanded in x1 around 0

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

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

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

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

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

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

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

       4. sub-neg N/A

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

       5. metadata-eval N/A

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

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

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

       7. *-commutative N/A

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

       8. *-lowering-*.f64 93.9%

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

   13. Simplified 93.9%

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

   if 6.2000000000000004e-184 < x1 < 3.8999999999999998e102

   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 99.6%

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

   5. Taylor expanded in x2 around -inf

      \[\leadsto \color{blue}{{x2}^{2} \cdot \left(-1 \cdot \frac{-6 \cdot \frac{{x1}^{2}}{1 + {x1}^{2}} + \left(6 \cdot \frac{1}{1 + {x1}^{2}} + \left(1 + {x1}^{2}\right) \cdot \left(-4 \cdot \frac{{x1}^{2} \cdot \left(3 \cdot x1 - 1\right)}{{\left(1 + {x1}^{2}\right)}^{2}} + -2 \cdot \frac{4 \cdot {x1}^{2} + x1 \cdot \left(2 \cdot \frac{x1 \cdot \left(3 \cdot x1 - 1\right)}{1 + {x1}^{2}} - 6\right)}{1 + {x1}^{2}}\right)\right)}{x2} + 8 \cdot \frac{x1}{1 + {x1}^{2}}\right)} \]

   7. Simplified 63.5%

      \[\leadsto \color{blue}{\left(x2 \cdot x2\right) \cdot \left(\frac{8 \cdot x1}{1 + x1 \cdot x1} - \frac{\frac{-6 \cdot \left(x1 \cdot x1\right)}{1 + x1 \cdot x1} + \left(\frac{6}{1 + x1 \cdot x1} + \left(1 + x1 \cdot x1\right) \cdot \left(\frac{-4 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot 3 + -1\right)\right)}{\left(1 + x1 \cdot x1\right) \cdot \left(1 + x1 \cdot x1\right)} + \frac{-2 \cdot \left(4 \cdot \left(x1 \cdot x1\right) + x1 \cdot \left(\frac{2 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)}{1 + x1 \cdot x1} + -6\right)\right)}{1 + x1 \cdot x1}\right)\right)}{x2}\right)} \]

   8. Taylor expanded in x1 around 0

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

      1. sub-neg N/A

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

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

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

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

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

      4. sub-neg N/A

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

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

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

      6. associate-*r/ N/A

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

      7. metadata-eval N/A

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

      8. distribute-neg-frac N/A

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

      9. metadata-eval N/A

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

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

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

      11. associate-*r/ N/A

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

      12. metadata-eval N/A

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

      13. distribute-neg-frac N/A

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

      14. metadata-eval N/A

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

      15. /-lowering-/.f64 58.7%

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

   10. Simplified 58.7%

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

       1. associate-*l* N/A

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

       2. *-commutative N/A

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

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

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

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

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

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

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

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

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

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

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

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

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

       9. /-lowering-/.f64 65.3%

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

   12. Applied egg-rr 65.3%

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

   if 3.8999999999999998e102 < x1

   1. Initial program 34.1%

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

   3. Simplified 34.1%

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

   5. Taylor expanded in x1 around 0

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

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

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

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

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

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

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

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

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

      5. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + \color{blue}{\left(\mathsf{neg}\left(6\right)\right)}\right)\right)\right)\right)\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + -6\right)\right)\right)\right)\right)\right) \]

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

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

      8. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\left(x2 \cdot 4\right), -6\right)\right)\right)\right)\right)\right) \]

      9. *-lowering-*.f64 8.1%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right)\right)\right)\right)\right) \]

   7. Simplified 8.1%

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

   8. Taylor expanded in x1 around 0

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

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

         \[\leadsto \mathsf{+.f64}\left(\left(-6 \cdot x2\right), \color{blue}{\left(x1 \cdot \left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)\right) - 1\right)\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \left(\color{blue}{x1} \cdot \left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)\right) - 1\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \color{blue}{\left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)\right) - 1\right)}\right)\right) \]

      4. associate--l+ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + \color{blue}{\left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right) - 1\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)\right), \color{blue}{\left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right) - 1\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)\right), \left(\color{blue}{x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)} - 1\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 - 6\right)\right)\right), \left(x1 \cdot \color{blue}{\left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)} - 1\right)\right)\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + \left(\mathsf{neg}\left(6\right)\right)\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + \color{blue}{3 \cdot \left(3 - -2 \cdot x2\right)}\right) - 1\right)\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + -6\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \color{blue}{\left(3 - -2 \cdot x2\right)}\right) - 1\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\left(4 \cdot x2\right), -6\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + \color{blue}{3 \cdot \left(3 - -2 \cdot x2\right)}\right) - 1\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, x2\right), -6\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + \color{blue}{3} \cdot \left(3 - -2 \cdot x2\right)\right) - 1\right)\right)\right)\right) \]

      12. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, x2\right), -6\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right) + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, x2\right), -6\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right) + -1\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, x2\right), -6\right)\right)\right), \mathsf{+.f64}\left(\left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)\right), \color{blue}{-1}\right)\right)\right)\right) \]

   10. Simplified 88.6%

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

   11. Taylor expanded in x1 around inf

       \[\leadsto \color{blue}{3 \cdot {x1}^{3}} \]
   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. *-commutative N/A

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

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

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

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

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

       8. unpow2 N/A

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

       9. *-lowering-*.f64 95.5%

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

   13. Simplified 95.5%

       \[\leadsto \color{blue}{x1 \cdot \left(3 \cdot \left(x1 \cdot x1\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -3.65 \cdot 10^{+90}:\\ \;\;\;\;x1 \cdot \left(-1 + x1 \cdot \left(9 + x1 \cdot -19\right)\right)\\ \mathbf{elif}\;x1 \leq -1.05 \cdot 10^{-68}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(x2 \cdot \left(x2 \cdot 8\right)\right)\\ \mathbf{elif}\;x1 \leq 6.2 \cdot 10^{-184}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + x2 \cdot -12\right)\\ \mathbf{elif}\;x1 \leq 3.9 \cdot 10^{+102}:\\ \;\;\;\;x2 \cdot \left(x2 \cdot \left(x1 \cdot \left(8 + \frac{-12}{x2}\right) + \frac{-6}{x2}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot \left(3 \cdot \left(x1 \cdot x1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 79.8% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -6.2 \cdot 10^{+78}:\\ \;\;\;\;\left(x1 \cdot \left(x1 \cdot x1\right)\right) \cdot \left(4 \cdot \left(x2 \cdot \left(3 + x2 \cdot -2\right)\right) + \left(-19 + x2 \cdot 12\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(2 \cdot \left(x2 \cdot \left(-6 + x2 \cdot 4\right)\right) + \left(-1 + x1 \cdot \left(3 \cdot \left(x1 + \left(3 + 2 \cdot x2\right)\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -6.2e+78)
   (*
    (* x1 (* x1 x1))
    (+ (* 4.0 (* x2 (+ 3.0 (* x2 -2.0)))) (+ -19.0 (* x2 12.0))))
   (+
    (* x2 -6.0)
    (*
     x1
     (+
      (* 2.0 (* x2 (+ -6.0 (* x2 4.0))))
      (+ -1.0 (* x1 (* 3.0 (+ x1 (+ 3.0 (* 2.0 x2)))))))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -6.2e+78) {
		tmp = (x1 * (x1 * x1)) * ((4.0 * (x2 * (3.0 + (x2 * -2.0)))) + (-19.0 + (x2 * 12.0)));
	} else {
		tmp = (x2 * -6.0) + (x1 * ((2.0 * (x2 * (-6.0 + (x2 * 4.0)))) + (-1.0 + (x1 * (3.0 * (x1 + (3.0 + (2.0 * x2))))))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x1 <= (-6.2d+78)) then
        tmp = (x1 * (x1 * x1)) * ((4.0d0 * (x2 * (3.0d0 + (x2 * (-2.0d0))))) + ((-19.0d0) + (x2 * 12.0d0)))
    else
        tmp = (x2 * (-6.0d0)) + (x1 * ((2.0d0 * (x2 * ((-6.0d0) + (x2 * 4.0d0)))) + ((-1.0d0) + (x1 * (3.0d0 * (x1 + (3.0d0 + (2.0d0 * x2))))))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= -6.2e+78) {
		tmp = (x1 * (x1 * x1)) * ((4.0 * (x2 * (3.0 + (x2 * -2.0)))) + (-19.0 + (x2 * 12.0)));
	} else {
		tmp = (x2 * -6.0) + (x1 * ((2.0 * (x2 * (-6.0 + (x2 * 4.0)))) + (-1.0 + (x1 * (3.0 * (x1 + (3.0 + (2.0 * x2))))))));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -6.2e+78:
		tmp = (x1 * (x1 * x1)) * ((4.0 * (x2 * (3.0 + (x2 * -2.0)))) + (-19.0 + (x2 * 12.0)))
	else:
		tmp = (x2 * -6.0) + (x1 * ((2.0 * (x2 * (-6.0 + (x2 * 4.0)))) + (-1.0 + (x1 * (3.0 * (x1 + (3.0 + (2.0 * x2))))))))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -6.2e+78)
		tmp = Float64(Float64(x1 * Float64(x1 * x1)) * Float64(Float64(4.0 * Float64(x2 * Float64(3.0 + Float64(x2 * -2.0)))) + Float64(-19.0 + Float64(x2 * 12.0))));
	else
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(2.0 * Float64(x2 * Float64(-6.0 + Float64(x2 * 4.0)))) + Float64(-1.0 + Float64(x1 * Float64(3.0 * Float64(x1 + Float64(3.0 + Float64(2.0 * x2)))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -6.2e+78)
		tmp = (x1 * (x1 * x1)) * ((4.0 * (x2 * (3.0 + (x2 * -2.0)))) + (-19.0 + (x2 * 12.0)));
	else
		tmp = (x2 * -6.0) + (x1 * ((2.0 * (x2 * (-6.0 + (x2 * 4.0)))) + (-1.0 + (x1 * (3.0 * (x1 + (3.0 + (2.0 * x2))))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -6.2e+78], N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] * N[(N[(4.0 * N[(x2 * N[(3.0 + N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-19.0 + N[(x2 * 12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(2.0 * N[(x2 * N[(-6.0 + N[(x2 * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-1.0 + N[(x1 * N[(3.0 * N[(x1 + N[(3.0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x1 < -6.2e78

   1. Initial program 19.0%

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

   3. Simplified 19.0%

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

   5. Taylor expanded in x1 around 0

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

   7. Simplified 69.7%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(2 \cdot \left(x2 \cdot \left(x2 \cdot 4 + -6\right)\right) + \left(x1 \cdot \left(\left(\left(\left(9 + 3 \cdot \left(x2 \cdot 2\right)\right) + \left(x2 \cdot 10 + x1 \cdot \left(\left(3 \cdot \left(x2 \cdot 4\right) + -18\right) + \left(4 \cdot \left(x2 \cdot \left(3 - x2 \cdot 2\right)\right) + -1\right)\right)\right)\right) - \left(x2 \cdot 4 + -6\right)\right) + -6\right) + -1\right)\right)} \]

   8. Taylor expanded in x1 around inf

      \[\leadsto \color{blue}{{x1}^{3} \cdot \left(\left(4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right) + 12 \cdot x2\right) - 19\right)} \]
   9. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{3}\right), \color{blue}{\left(\left(4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right) + 12 \cdot x2\right) - 19\right)}\right) \]

      2. cube-mult N/A

         \[\leadsto \mathsf{*.f64}\left(\left(x1 \cdot \left(x1 \cdot x1\right)\right), \left(\color{blue}{\left(4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right) + 12 \cdot x2\right)} - 19\right)\right) \]

      3. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(x1 \cdot {x1}^{2}\right), \left(\left(4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right) + \color{blue}{12 \cdot x2}\right) - 19\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \left({x1}^{2}\right)\right), \left(\color{blue}{\left(4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right) + 12 \cdot x2\right)} - 19\right)\right) \]

      5. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \left(x1 \cdot x1\right)\right), \left(\left(4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right) + \color{blue}{12 \cdot x2}\right) - 19\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, x1\right)\right), \left(\left(4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right) + \color{blue}{12 \cdot x2}\right) - 19\right)\right) \]

      7. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, x1\right)\right), \left(4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right) + \color{blue}{\left(12 \cdot x2 - 19\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(\left(4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right), \color{blue}{\left(12 \cdot x2 - 19\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right), \left(\color{blue}{12 \cdot x2} - 19\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, \mathsf{*.f64}\left(x2, \left(3 - 2 \cdot x2\right)\right)\right), \left(12 \cdot \color{blue}{x2} - 19\right)\right)\right) \]

      11. cancel-sign-sub-inv N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, \mathsf{*.f64}\left(x2, \left(3 + \left(\mathsf{neg}\left(2\right)\right) \cdot x2\right)\right)\right), \left(12 \cdot x2 - 19\right)\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, \mathsf{*.f64}\left(x2, \left(3 + -2 \cdot x2\right)\right)\right), \left(12 \cdot x2 - 19\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(3, \left(-2 \cdot x2\right)\right)\right)\right), \left(12 \cdot x2 - 19\right)\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(3, \left(x2 \cdot -2\right)\right)\right)\right), \left(12 \cdot x2 - 19\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(3, \mathsf{*.f64}\left(x2, -2\right)\right)\right)\right), \left(12 \cdot x2 - 19\right)\right)\right) \]

      16. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(3, \mathsf{*.f64}\left(x2, -2\right)\right)\right)\right), \left(12 \cdot x2 + \color{blue}{\left(\mathsf{neg}\left(19\right)\right)}\right)\right)\right) \]

      17. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(3, \mathsf{*.f64}\left(x2, -2\right)\right)\right)\right), \left(12 \cdot x2 + -19\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(3, \mathsf{*.f64}\left(x2, -2\right)\right)\right)\right), \mathsf{+.f64}\left(\left(12 \cdot x2\right), \color{blue}{-19}\right)\right)\right) \]

      19. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(3, \mathsf{*.f64}\left(x2, -2\right)\right)\right)\right), \mathsf{+.f64}\left(\left(x2 \cdot 12\right), -19\right)\right)\right) \]

      20. *-lowering-*.f64 88.8%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(3, \mathsf{*.f64}\left(x2, -2\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 12\right), -19\right)\right)\right) \]

   10. Simplified 88.8%

       \[\leadsto \color{blue}{\left(x1 \cdot \left(x1 \cdot x1\right)\right) \cdot \left(4 \cdot \left(x2 \cdot \left(3 + x2 \cdot -2\right)\right) + \left(x2 \cdot 12 + -19\right)\right)} \]

   if -6.2e78 < x1

   1. Initial program 86.0%

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

   3. Simplified 86.1%

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

   5. Taylor expanded in x1 around 0

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

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

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

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

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

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

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

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

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

      5. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + \color{blue}{\left(\mathsf{neg}\left(6\right)\right)}\right)\right)\right)\right)\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + -6\right)\right)\right)\right)\right)\right) \]

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

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

      8. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\left(x2 \cdot 4\right), -6\right)\right)\right)\right)\right)\right) \]

      9. *-lowering-*.f64 65.1%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right)\right)\right)\right)\right) \]

   7. Simplified 65.1%

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

   8. Taylor expanded in x1 around 0

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

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

         \[\leadsto \mathsf{+.f64}\left(\left(-6 \cdot x2\right), \color{blue}{\left(x1 \cdot \left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)\right) - 1\right)\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \left(\color{blue}{x1} \cdot \left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)\right) - 1\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \color{blue}{\left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)\right) - 1\right)}\right)\right) \]

      4. associate--l+ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + \color{blue}{\left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right) - 1\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)\right), \color{blue}{\left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right) - 1\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)\right), \left(\color{blue}{x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)} - 1\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 - 6\right)\right)\right), \left(x1 \cdot \color{blue}{\left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)} - 1\right)\right)\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + \left(\mathsf{neg}\left(6\right)\right)\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + \color{blue}{3 \cdot \left(3 - -2 \cdot x2\right)}\right) - 1\right)\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + -6\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \color{blue}{\left(3 - -2 \cdot x2\right)}\right) - 1\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\left(4 \cdot x2\right), -6\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + \color{blue}{3 \cdot \left(3 - -2 \cdot x2\right)}\right) - 1\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, x2\right), -6\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + \color{blue}{3} \cdot \left(3 - -2 \cdot x2\right)\right) - 1\right)\right)\right)\right) \]

      12. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, x2\right), -6\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right) + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, x2\right), -6\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right) + -1\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, x2\right), -6\right)\right)\right), \mathsf{+.f64}\left(\left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)\right), \color{blue}{-1}\right)\right)\right)\right) \]

   10. Simplified 82.0%

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

4. Final simplification 83.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -6.2 \cdot 10^{+78}:\\ \;\;\;\;\left(x1 \cdot \left(x1 \cdot x1\right)\right) \cdot \left(4 \cdot \left(x2 \cdot \left(3 + x2 \cdot -2\right)\right) + \left(-19 + x2 \cdot 12\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(2 \cdot \left(x2 \cdot \left(-6 + x2 \cdot 4\right)\right) + \left(-1 + x1 \cdot \left(3 \cdot \left(x1 + \left(3 + 2 \cdot x2\right)\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 73.3% accurate, 3.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -3.2 \cdot 10^{+90}:\\ \;\;\;\;x1 \cdot \left(-1 + x1 \cdot \left(9 + x1 \cdot -19\right)\right)\\ \mathbf{elif}\;x1 \leq -4.5 \cdot 10^{-65}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(x2 \cdot \left(x2 \cdot 8\right)\right)\\ \mathbf{elif}\;x1 \leq 2.3 \cdot 10^{-183}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + x2 \cdot -12\right)\\ \mathbf{elif}\;x1 \leq 1.9 \cdot 10^{+59}:\\ \;\;\;\;x2 \cdot \left(x1 \cdot -12 + \left(-6 + 8 \cdot \left(x1 \cdot x2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot \left(3 \cdot \left(x1 \cdot x1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -3.2e+90)
   (* x1 (+ -1.0 (* x1 (+ 9.0 (* x1 -19.0)))))
   (if (<= x1 -4.5e-65)
     (+ (* x2 -6.0) (* x1 (* x2 (* x2 8.0))))
     (if (<= x1 2.3e-183)
       (+ (* x2 -6.0) (* x1 (+ -1.0 (* x2 -12.0))))
       (if (<= x1 1.9e+59)
         (* x2 (+ (* x1 -12.0) (+ -6.0 (* 8.0 (* x1 x2)))))
         (* x1 (* 3.0 (* x1 x1))))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -3.2e+90) {
		tmp = x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0))));
	} else if (x1 <= -4.5e-65) {
		tmp = (x2 * -6.0) + (x1 * (x2 * (x2 * 8.0)));
	} else if (x1 <= 2.3e-183) {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x2 * -12.0)));
	} else if (x1 <= 1.9e+59) {
		tmp = x2 * ((x1 * -12.0) + (-6.0 + (8.0 * (x1 * x2))));
	} else {
		tmp = x1 * (3.0 * (x1 * x1));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x1 <= (-3.2d+90)) then
        tmp = x1 * ((-1.0d0) + (x1 * (9.0d0 + (x1 * (-19.0d0)))))
    else if (x1 <= (-4.5d-65)) then
        tmp = (x2 * (-6.0d0)) + (x1 * (x2 * (x2 * 8.0d0)))
    else if (x1 <= 2.3d-183) then
        tmp = (x2 * (-6.0d0)) + (x1 * ((-1.0d0) + (x2 * (-12.0d0))))
    else if (x1 <= 1.9d+59) then
        tmp = x2 * ((x1 * (-12.0d0)) + ((-6.0d0) + (8.0d0 * (x1 * x2))))
    else
        tmp = x1 * (3.0d0 * (x1 * x1))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= -3.2e+90) {
		tmp = x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0))));
	} else if (x1 <= -4.5e-65) {
		tmp = (x2 * -6.0) + (x1 * (x2 * (x2 * 8.0)));
	} else if (x1 <= 2.3e-183) {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x2 * -12.0)));
	} else if (x1 <= 1.9e+59) {
		tmp = x2 * ((x1 * -12.0) + (-6.0 + (8.0 * (x1 * x2))));
	} else {
		tmp = x1 * (3.0 * (x1 * x1));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -3.2e+90:
		tmp = x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0))))
	elif x1 <= -4.5e-65:
		tmp = (x2 * -6.0) + (x1 * (x2 * (x2 * 8.0)))
	elif x1 <= 2.3e-183:
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x2 * -12.0)))
	elif x1 <= 1.9e+59:
		tmp = x2 * ((x1 * -12.0) + (-6.0 + (8.0 * (x1 * x2))))
	else:
		tmp = x1 * (3.0 * (x1 * x1))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -3.2e+90)
		tmp = Float64(x1 * Float64(-1.0 + Float64(x1 * Float64(9.0 + Float64(x1 * -19.0)))));
	elseif (x1 <= -4.5e-65)
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(x2 * Float64(x2 * 8.0))));
	elseif (x1 <= 2.3e-183)
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(-1.0 + Float64(x2 * -12.0))));
	elseif (x1 <= 1.9e+59)
		tmp = Float64(x2 * Float64(Float64(x1 * -12.0) + Float64(-6.0 + Float64(8.0 * Float64(x1 * x2)))));
	else
		tmp = Float64(x1 * Float64(3.0 * Float64(x1 * x1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -3.2e+90)
		tmp = x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0))));
	elseif (x1 <= -4.5e-65)
		tmp = (x2 * -6.0) + (x1 * (x2 * (x2 * 8.0)));
	elseif (x1 <= 2.3e-183)
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x2 * -12.0)));
	elseif (x1 <= 1.9e+59)
		tmp = x2 * ((x1 * -12.0) + (-6.0 + (8.0 * (x1 * x2))));
	else
		tmp = x1 * (3.0 * (x1 * x1));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -3.2e+90], N[(x1 * N[(-1.0 + N[(x1 * N[(9.0 + N[(x1 * -19.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -4.5e-65], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(x2 * N[(x2 * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 2.3e-183], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(-1.0 + N[(x2 * -12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.9e+59], N[(x2 * N[(N[(x1 * -12.0), $MachinePrecision] + N[(-6.0 + N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 * N[(3.0 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if x1 < -3.19999999999999998e90

   1. Initial program 5.6%

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

   3. Simplified 5.6%

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

   5. Taylor expanded in x1 around 0

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

   7. Simplified 77.8%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(2 \cdot \left(x2 \cdot \left(x2 \cdot 4 + -6\right)\right) + \left(x1 \cdot \left(\left(\left(\left(9 + 3 \cdot \left(x2 \cdot 2\right)\right) + \left(x2 \cdot 10 + x1 \cdot \left(\left(3 \cdot \left(x2 \cdot 4\right) + -18\right) + \left(4 \cdot \left(x2 \cdot \left(3 - x2 \cdot 2\right)\right) + -1\right)\right)\right)\right) - \left(x2 \cdot 4 + -6\right)\right) + -6\right) + -1\right)\right)} \]

   8. Taylor expanded in x2 around 0

      \[\leadsto \color{blue}{x1 \cdot \left(x1 \cdot \left(9 + -19 \cdot x1\right) - 1\right)} \]
   9. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(x1, \color{blue}{\left(x1 \cdot \left(9 + -19 \cdot x1\right) - 1\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x1, \left(x1 \cdot \left(9 + -19 \cdot x1\right) + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right) \]

      3. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(x1, \left(x1 \cdot \left(9 + -19 \cdot x1\right) + -1\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\left(x1 \cdot \left(9 + -19 \cdot x1\right)\right), \color{blue}{-1}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \left(9 + -19 \cdot x1\right)\right), -1\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(9, \left(-19 \cdot x1\right)\right)\right), -1\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(9, \left(x1 \cdot -19\right)\right)\right), -1\right)\right) \]

      8. *-lowering-*.f64 94.9%

         \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(9, \mathsf{*.f64}\left(x1, -19\right)\right)\right), -1\right)\right) \]

   10. Simplified 94.9%

       \[\leadsto \color{blue}{x1 \cdot \left(x1 \cdot \left(9 + x1 \cdot -19\right) + -1\right)} \]

   if -3.19999999999999998e90 < x1 < -4.4999999999999998e-65

   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 99.5%

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

   5. Taylor expanded in x1 around 0

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

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

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

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

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

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

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

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

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

      5. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + \color{blue}{\left(\mathsf{neg}\left(6\right)\right)}\right)\right)\right)\right)\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + -6\right)\right)\right)\right)\right)\right) \]

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

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

      8. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\left(x2 \cdot 4\right), -6\right)\right)\right)\right)\right)\right) \]

      9. *-lowering-*.f64 64.3%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right)\right)\right)\right)\right) \]

   7. Simplified 64.3%

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

   8. Taylor expanded in x1 around 0

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

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

         \[\leadsto \mathsf{+.f64}\left(\left(-6 \cdot x2\right), \color{blue}{\left(x1 \cdot \left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + 3 \cdot \left(x1 \cdot \left(3 - -2 \cdot x2\right)\right)\right) - 1\right)\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \left(\color{blue}{x1} \cdot \left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + 3 \cdot \left(x1 \cdot \left(3 - -2 \cdot x2\right)\right)\right) - 1\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \color{blue}{\left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + 3 \cdot \left(x1 \cdot \left(3 - -2 \cdot x2\right)\right)\right) - 1\right)}\right)\right) \]

      4. associate--l+ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + \color{blue}{\left(3 \cdot \left(x1 \cdot \left(3 - -2 \cdot x2\right)\right) - 1\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)\right), \color{blue}{\left(3 \cdot \left(x1 \cdot \left(3 - -2 \cdot x2\right)\right) - 1\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)\right), \left(\color{blue}{3 \cdot \left(x1 \cdot \left(3 - -2 \cdot x2\right)\right)} - 1\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 - 6\right)\right)\right), \left(3 \cdot \color{blue}{\left(x1 \cdot \left(3 - -2 \cdot x2\right)\right)} - 1\right)\right)\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + \left(\mathsf{neg}\left(6\right)\right)\right)\right)\right), \left(3 \cdot \left(x1 \cdot \color{blue}{\left(3 - -2 \cdot x2\right)}\right) - 1\right)\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + -6\right)\right)\right), \left(3 \cdot \left(x1 \cdot \left(3 - \color{blue}{-2 \cdot x2}\right)\right) - 1\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\left(4 \cdot x2\right), -6\right)\right)\right), \left(3 \cdot \left(x1 \cdot \color{blue}{\left(3 - -2 \cdot x2\right)}\right) - 1\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, x2\right), -6\right)\right)\right), \left(3 \cdot \left(x1 \cdot \left(\color{blue}{3} - -2 \cdot x2\right)\right) - 1\right)\right)\right)\right) \]

      12. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, x2\right), -6\right)\right)\right), \left(3 \cdot \left(x1 \cdot \left(3 - -2 \cdot x2\right)\right) + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, x2\right), -6\right)\right)\right), \left(3 \cdot \left(x1 \cdot \left(3 - -2 \cdot x2\right)\right) + -1\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, x2\right), -6\right)\right)\right), \mathsf{+.f64}\left(\left(3 \cdot \left(x1 \cdot \left(3 - -2 \cdot x2\right)\right)\right), \color{blue}{-1}\right)\right)\right)\right) \]

   10. Simplified 65.9%

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

   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. *-commutative N/A

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

       2. associate-*l* N/A

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

       3. *-commutative N/A

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

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

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

       5. *-commutative N/A

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

       6. unpow2 N/A

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

       7. associate-*l* N/A

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

       8. *-commutative N/A

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

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

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

       10. *-commutative N/A

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

       11. *-lowering-*.f64 50.9%

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

   13. Simplified 50.9%

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

   if -4.4999999999999998e-65 < x1 < 2.30000000000000016e-183

   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

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

   7. Simplified 85.4%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(2 \cdot \left(x2 \cdot \left(x2 \cdot 4 + -6\right)\right) + \left(x1 \cdot \left(\left(\left(\left(9 + 3 \cdot \left(x2 \cdot 2\right)\right) + \left(x2 \cdot 10 + x1 \cdot \left(\left(3 \cdot \left(x2 \cdot 4\right) + -18\right) + \left(4 \cdot \left(x2 \cdot \left(3 - x2 \cdot 2\right)\right) + -1\right)\right)\right)\right) - \left(x2 \cdot 4 + -6\right)\right) + -6\right) + -1\right)\right)} \]

   8. Taylor expanded in x2 around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \color{blue}{\left(x1 \cdot \left(x2 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right) + x1 \cdot \left(x1 \cdot \left(9 + -19 \cdot x1\right) - 1\right)\right)}\right) \]
   9. Step-by-step derivation

      1. distribute-lft-out N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \left(x1 \cdot \color{blue}{\left(x2 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right) + \left(x1 \cdot \left(9 + -19 \cdot x1\right) - 1\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \color{blue}{\left(x2 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right) + \left(x1 \cdot \left(9 + -19 \cdot x1\right) - 1\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\left(x2 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right), \color{blue}{\left(x1 \cdot \left(9 + -19 \cdot x1\right) - 1\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right), \left(\color{blue}{x1 \cdot \left(9 + -19 \cdot x1\right)} - 1\right)\right)\right)\right) \]

      5. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, \left(x1 \cdot \left(12 + 24 \cdot x1\right) + \left(\mathsf{neg}\left(12\right)\right)\right)\right), \left(x1 \cdot \color{blue}{\left(9 + -19 \cdot x1\right)} - 1\right)\right)\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, \left(x1 \cdot \left(12 + 24 \cdot x1\right) + -12\right)\right), \left(x1 \cdot \left(9 + \color{blue}{-19 \cdot x1}\right) - 1\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\left(x1 \cdot \left(12 + 24 \cdot x1\right)\right), -12\right)\right), \left(x1 \cdot \color{blue}{\left(9 + -19 \cdot x1\right)} - 1\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \left(12 + 24 \cdot x1\right)\right), -12\right)\right), \left(x1 \cdot \left(\color{blue}{9} + -19 \cdot x1\right) - 1\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(12, \left(24 \cdot x1\right)\right)\right), -12\right)\right), \left(x1 \cdot \left(9 + -19 \cdot x1\right) - 1\right)\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(12, \left(x1 \cdot 24\right)\right)\right), -12\right)\right), \left(x1 \cdot \left(9 + -19 \cdot x1\right) - 1\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(12, \mathsf{*.f64}\left(x1, 24\right)\right)\right), -12\right)\right), \left(x1 \cdot \left(9 + -19 \cdot x1\right) - 1\right)\right)\right)\right) \]

      12. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(12, \mathsf{*.f64}\left(x1, 24\right)\right)\right), -12\right)\right), \left(x1 \cdot \left(9 + -19 \cdot x1\right) + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(12, \mathsf{*.f64}\left(x1, 24\right)\right)\right), -12\right)\right), \left(x1 \cdot \left(9 + -19 \cdot x1\right) + -1\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(12, \mathsf{*.f64}\left(x1, 24\right)\right)\right), -12\right)\right), \mathsf{+.f64}\left(\left(x1 \cdot \left(9 + -19 \cdot x1\right)\right), \color{blue}{-1}\right)\right)\right)\right) \]

   10. Simplified 93.9%

       \[\leadsto -6 \cdot x2 + \color{blue}{x1 \cdot \left(x2 \cdot \left(x1 \cdot \left(12 + x1 \cdot 24\right) + -12\right) + \left(x1 \cdot \left(9 + x1 \cdot -19\right) + -1\right)\right)} \]

   11. Taylor expanded in x1 around 0

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

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

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

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

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

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

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

       4. sub-neg N/A

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

       5. metadata-eval N/A

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

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

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

       7. *-commutative N/A

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

       8. *-lowering-*.f64 93.9%

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

   13. Simplified 93.9%

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

   if 2.30000000000000016e-183 < x1 < 1.9e59

   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 99.7%

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

   5. Taylor expanded in x2 around -inf

      \[\leadsto \color{blue}{{x2}^{2} \cdot \left(-1 \cdot \frac{-6 \cdot \frac{{x1}^{2}}{1 + {x1}^{2}} + \left(6 \cdot \frac{1}{1 + {x1}^{2}} + \left(1 + {x1}^{2}\right) \cdot \left(-4 \cdot \frac{{x1}^{2} \cdot \left(3 \cdot x1 - 1\right)}{{\left(1 + {x1}^{2}\right)}^{2}} + -2 \cdot \frac{4 \cdot {x1}^{2} + x1 \cdot \left(2 \cdot \frac{x1 \cdot \left(3 \cdot x1 - 1\right)}{1 + {x1}^{2}} - 6\right)}{1 + {x1}^{2}}\right)\right)}{x2} + 8 \cdot \frac{x1}{1 + {x1}^{2}}\right)} \]

   7. Simplified 73.2%

      \[\leadsto \color{blue}{\left(x2 \cdot x2\right) \cdot \left(\frac{8 \cdot x1}{1 + x1 \cdot x1} - \frac{\frac{-6 \cdot \left(x1 \cdot x1\right)}{1 + x1 \cdot x1} + \left(\frac{6}{1 + x1 \cdot x1} + \left(1 + x1 \cdot x1\right) \cdot \left(\frac{-4 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot 3 + -1\right)\right)}{\left(1 + x1 \cdot x1\right) \cdot \left(1 + x1 \cdot x1\right)} + \frac{-2 \cdot \left(4 \cdot \left(x1 \cdot x1\right) + x1 \cdot \left(\frac{2 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)}{1 + x1 \cdot x1} + -6\right)\right)}{1 + x1 \cdot x1}\right)\right)}{x2}\right)} \]

   8. Taylor expanded in x1 around 0

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

      1. sub-neg N/A

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

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

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

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

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

      4. sub-neg N/A

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

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

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

      6. associate-*r/ N/A

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

      7. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, x2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(8, \left(\mathsf{neg}\left(\frac{12}{x2}\right)\right)\right)\right), \left(\mathsf{neg}\left(6 \cdot \frac{1}{x2}\right)\right)\right)\right) \]

      8. distribute-neg-frac N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, x2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(8, \left(\frac{\mathsf{neg}\left(12\right)}{x2}\right)\right)\right), \left(\mathsf{neg}\left(6 \cdot \frac{1}{\color{blue}{x2}}\right)\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, x2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(8, \left(\frac{-12}{x2}\right)\right)\right), \left(\mathsf{neg}\left(6 \cdot \frac{1}{x2}\right)\right)\right)\right) \]

      10. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, x2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(8, \mathsf{/.f64}\left(-12, x2\right)\right)\right), \left(\mathsf{neg}\left(6 \cdot \frac{1}{\color{blue}{x2}}\right)\right)\right)\right) \]

      11. associate-*r/ N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, x2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(8, \mathsf{/.f64}\left(-12, x2\right)\right)\right), \left(\mathsf{neg}\left(\frac{6 \cdot 1}{x2}\right)\right)\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, x2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(8, \mathsf{/.f64}\left(-12, x2\right)\right)\right), \left(\mathsf{neg}\left(\frac{6}{x2}\right)\right)\right)\right) \]

      13. distribute-neg-frac N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, x2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(8, \mathsf{/.f64}\left(-12, x2\right)\right)\right), \left(\frac{\mathsf{neg}\left(6\right)}{\color{blue}{x2}}\right)\right)\right) \]

      14. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, x2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(8, \mathsf{/.f64}\left(-12, x2\right)\right)\right), \left(\frac{-6}{x2}\right)\right)\right) \]

      15. /-lowering-/.f64 67.7%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, x2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(8, \mathsf{/.f64}\left(-12, x2\right)\right)\right), \mathsf{/.f64}\left(-6, \color{blue}{x2}\right)\right)\right) \]

   10. Simplified 67.7%

       \[\leadsto \left(x2 \cdot x2\right) \cdot \color{blue}{\left(x1 \cdot \left(8 + \frac{-12}{x2}\right) + \frac{-6}{x2}\right)} \]

   11. Taylor expanded in x2 around 0

       \[\leadsto \color{blue}{x2 \cdot \left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right)} \]
   12. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x2, \color{blue}{\left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right)}\right) \]

       2. associate--l+ N/A

          \[\leadsto \mathsf{*.f64}\left(x2, \left(-12 \cdot x1 + \color{blue}{\left(8 \cdot \left(x1 \cdot x2\right) - 6\right)}\right)\right) \]

       3. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\left(-12 \cdot x1\right), \color{blue}{\left(8 \cdot \left(x1 \cdot x2\right) - 6\right)}\right)\right) \]

       4. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\left(x1 \cdot -12\right), \left(\color{blue}{8 \cdot \left(x1 \cdot x2\right)} - 6\right)\right)\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, -12\right), \left(\color{blue}{8 \cdot \left(x1 \cdot x2\right)} - 6\right)\right)\right) \]

       6. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, -12\right), \left(8 \cdot \left(x1 \cdot x2\right) + \color{blue}{\left(\mathsf{neg}\left(6\right)\right)}\right)\right)\right) \]

       7. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, -12\right), \left(8 \cdot \left(x1 \cdot x2\right) + -6\right)\right)\right) \]

       8. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, -12\right), \mathsf{+.f64}\left(\left(8 \cdot \left(x1 \cdot x2\right)\right), \color{blue}{-6}\right)\right)\right) \]

       9. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, -12\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(8, \left(x1 \cdot x2\right)\right), -6\right)\right)\right) \]

       10. *-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, -12\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(8, \left(x2 \cdot x1\right)\right), -6\right)\right)\right) \]

       11. *-lowering-*.f64 73.4%

           \[\leadsto \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, -12\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(8, \mathsf{*.f64}\left(x2, x1\right)\right), -6\right)\right)\right) \]

   13. Simplified 73.4%

       \[\leadsto \color{blue}{x2 \cdot \left(x1 \cdot -12 + \left(8 \cdot \left(x2 \cdot x1\right) + -6\right)\right)} \]

   if 1.9e59 < x1

   1. Initial program 44.1%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Simplified 44.1%

      \[\leadsto \color{blue}{\frac{3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right)}{x1 \cdot x1 + 1} + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(x1 \cdot \left(x1 \cdot -6\right) + \frac{2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)}{x1 \cdot x1 + 1} \cdot \left(x1 \cdot \left(-6 + \left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right) \cdot \frac{2}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot 4\right)\right) + x1 \cdot \left(2 + x1 \cdot \left(x1 + \left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right) \cdot \frac{3}{x1 \cdot x1 + 1}\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x1 around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \color{blue}{\left(x1 \cdot \left(2 + 2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)\right)\right)}\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \color{blue}{\left(2 + 2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)\right)}\right)\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \color{blue}{\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \color{blue}{\left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)}\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \color{blue}{\left(4 \cdot x2 - 6\right)}\right)\right)\right)\right)\right) \]

      5. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + \color{blue}{\left(\mathsf{neg}\left(6\right)\right)}\right)\right)\right)\right)\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + -6\right)\right)\right)\right)\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\left(4 \cdot x2\right), \color{blue}{-6}\right)\right)\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\left(x2 \cdot 4\right), -6\right)\right)\right)\right)\right)\right) \]

      9. *-lowering-*.f64 7.6%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right)\right)\right)\right)\right) \]

   7. Simplified 7.6%

      \[\leadsto \frac{3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right)}{x1 \cdot x1 + 1} + \color{blue}{x1 \cdot \left(2 + 2 \cdot \left(x2 \cdot \left(x2 \cdot 4 + -6\right)\right)\right)} \]

   8. Taylor expanded in x1 around 0

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)\right) - 1\right)} \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(-6 \cdot x2\right), \color{blue}{\left(x1 \cdot \left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)\right) - 1\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \left(\color{blue}{x1} \cdot \left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)\right) - 1\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \color{blue}{\left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)\right) - 1\right)}\right)\right) \]

      4. associate--l+ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + \color{blue}{\left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right) - 1\right)}\right)\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)\right), \color{blue}{\left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right) - 1\right)}\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)\right), \left(\color{blue}{x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)} - 1\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 - 6\right)\right)\right), \left(x1 \cdot \color{blue}{\left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)} - 1\right)\right)\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + \left(\mathsf{neg}\left(6\right)\right)\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + \color{blue}{3 \cdot \left(3 - -2 \cdot x2\right)}\right) - 1\right)\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + -6\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \color{blue}{\left(3 - -2 \cdot x2\right)}\right) - 1\right)\right)\right)\right) \]

      10. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\left(4 \cdot x2\right), -6\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + \color{blue}{3 \cdot \left(3 - -2 \cdot x2\right)}\right) - 1\right)\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, x2\right), -6\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + \color{blue}{3} \cdot \left(3 - -2 \cdot x2\right)\right) - 1\right)\right)\right)\right) \]

      12. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, x2\right), -6\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right) + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, x2\right), -6\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right) + -1\right)\right)\right)\right) \]

      14. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, x2\right), -6\right)\right)\right), \mathsf{+.f64}\left(\left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)\right), \color{blue}{-1}\right)\right)\right)\right) \]

   10. Simplified 76.1%

       \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 + -6\right)\right) + \left(x1 \cdot \left(3 \cdot \left(x1 + \left(3 + 2 \cdot x2\right)\right)\right) + -1\right)\right)} \]

   11. Taylor expanded in x1 around inf

       \[\leadsto \color{blue}{3 \cdot {x1}^{3}} \]
   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. *-commutative N/A

          \[\leadsto x1 \cdot \left(3 \cdot \color{blue}{{x1}^{2}}\right) \]

       6. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x1, \color{blue}{\left(3 \cdot {x1}^{2}\right)}\right) \]

       7. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(3, \color{blue}{\left({x1}^{2}\right)}\right)\right) \]

       8. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(3, \left(x1 \cdot \color{blue}{x1}\right)\right)\right) \]

       9. *-lowering-*.f64 81.8%

          \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(3, \mathsf{*.f64}\left(x1, \color{blue}{x1}\right)\right)\right) \]

   13. Simplified 81.8%

       \[\leadsto \color{blue}{x1 \cdot \left(3 \cdot \left(x1 \cdot x1\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -3.2 \cdot 10^{+90}:\\ \;\;\;\;x1 \cdot \left(-1 + x1 \cdot \left(9 + x1 \cdot -19\right)\right)\\ \mathbf{elif}\;x1 \leq -4.5 \cdot 10^{-65}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(x2 \cdot \left(x2 \cdot 8\right)\right)\\ \mathbf{elif}\;x1 \leq 2.3 \cdot 10^{-183}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + x2 \cdot -12\right)\\ \mathbf{elif}\;x1 \leq 1.9 \cdot 10^{+59}:\\ \;\;\;\;x2 \cdot \left(x1 \cdot -12 + \left(-6 + 8 \cdot \left(x1 \cdot x2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot \left(3 \cdot \left(x1 \cdot x1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 72.3% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x2 \cdot -6 + x1 \cdot \left(x2 \cdot \left(x2 \cdot 8\right)\right)\\ \mathbf{if}\;x1 \leq -1.75 \cdot 10^{+89}:\\ \;\;\;\;x1 \cdot \left(-1 + x1 \cdot \left(9 + x1 \cdot -19\right)\right)\\ \mathbf{elif}\;x1 \leq -5.5 \cdot 10^{-67}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x1 \leq 9.5 \cdot 10^{-161}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + x2 \cdot -12\right)\\ \mathbf{elif}\;x1 \leq 2.2 \cdot 10^{+59}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot \left(3 \cdot \left(x1 \cdot x1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ (* x2 -6.0) (* x1 (* x2 (* x2 8.0))))))
   (if (<= x1 -1.75e+89)
     (* x1 (+ -1.0 (* x1 (+ 9.0 (* x1 -19.0)))))
     (if (<= x1 -5.5e-67)
       t_0
       (if (<= x1 9.5e-161)
         (+ (* x2 -6.0) (* x1 (+ -1.0 (* x2 -12.0))))
         (if (<= x1 2.2e+59) t_0 (* x1 (* 3.0 (* x1 x1)))))))))

C

double code(double x1, double x2) {
	double t_0 = (x2 * -6.0) + (x1 * (x2 * (x2 * 8.0)));
	double tmp;
	if (x1 <= -1.75e+89) {
		tmp = x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0))));
	} else if (x1 <= -5.5e-67) {
		tmp = t_0;
	} else if (x1 <= 9.5e-161) {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x2 * -12.0)));
	} else if (x1 <= 2.2e+59) {
		tmp = t_0;
	} else {
		tmp = x1 * (3.0 * (x1 * x1));
	}
	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 * (-6.0d0)) + (x1 * (x2 * (x2 * 8.0d0)))
    if (x1 <= (-1.75d+89)) then
        tmp = x1 * ((-1.0d0) + (x1 * (9.0d0 + (x1 * (-19.0d0)))))
    else if (x1 <= (-5.5d-67)) then
        tmp = t_0
    else if (x1 <= 9.5d-161) then
        tmp = (x2 * (-6.0d0)) + (x1 * ((-1.0d0) + (x2 * (-12.0d0))))
    else if (x1 <= 2.2d+59) then
        tmp = t_0
    else
        tmp = x1 * (3.0d0 * (x1 * x1))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (x2 * -6.0) + (x1 * (x2 * (x2 * 8.0)));
	double tmp;
	if (x1 <= -1.75e+89) {
		tmp = x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0))));
	} else if (x1 <= -5.5e-67) {
		tmp = t_0;
	} else if (x1 <= 9.5e-161) {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x2 * -12.0)));
	} else if (x1 <= 2.2e+59) {
		tmp = t_0;
	} else {
		tmp = x1 * (3.0 * (x1 * x1));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x2 * -6.0) + (x1 * (x2 * (x2 * 8.0)))
	tmp = 0
	if x1 <= -1.75e+89:
		tmp = x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0))))
	elif x1 <= -5.5e-67:
		tmp = t_0
	elif x1 <= 9.5e-161:
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x2 * -12.0)))
	elif x1 <= 2.2e+59:
		tmp = t_0
	else:
		tmp = x1 * (3.0 * (x1 * x1))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(x2 * Float64(x2 * 8.0))))
	tmp = 0.0
	if (x1 <= -1.75e+89)
		tmp = Float64(x1 * Float64(-1.0 + Float64(x1 * Float64(9.0 + Float64(x1 * -19.0)))));
	elseif (x1 <= -5.5e-67)
		tmp = t_0;
	elseif (x1 <= 9.5e-161)
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(-1.0 + Float64(x2 * -12.0))));
	elseif (x1 <= 2.2e+59)
		tmp = t_0;
	else
		tmp = Float64(x1 * Float64(3.0 * Float64(x1 * x1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x2 * -6.0) + (x1 * (x2 * (x2 * 8.0)));
	tmp = 0.0;
	if (x1 <= -1.75e+89)
		tmp = x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0))));
	elseif (x1 <= -5.5e-67)
		tmp = t_0;
	elseif (x1 <= 9.5e-161)
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x2 * -12.0)));
	elseif (x1 <= 2.2e+59)
		tmp = t_0;
	else
		tmp = x1 * (3.0 * (x1 * x1));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(x2 * N[(x2 * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -1.75e+89], N[(x1 * N[(-1.0 + N[(x1 * N[(9.0 + N[(x1 * -19.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -5.5e-67], t$95$0, If[LessEqual[x1, 9.5e-161], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(-1.0 + N[(x2 * -12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 2.2e+59], t$95$0, N[(x1 * N[(3.0 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -1.75e89

   1. Initial program 5.6%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Simplified 5.6%

      \[\leadsto \color{blue}{\frac{3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right)}{x1 \cdot x1 + 1} + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(x1 \cdot \left(x1 \cdot -6\right) + \frac{2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)}{x1 \cdot x1 + 1} \cdot \left(x1 \cdot \left(-6 + \left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right) \cdot \frac{2}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot 4\right)\right) + x1 \cdot \left(2 + x1 \cdot \left(x1 + \left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right) \cdot \frac{3}{x1 \cdot x1 + 1}\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x1 around 0

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + x1 \cdot \left(\left(-1 \cdot \left(4 \cdot x2 - 6\right) + \left(3 \cdot \left(3 - -2 \cdot x2\right) + \left(4 \cdot x2 + \left(6 \cdot x2 + x1 \cdot \left(\left(3 \cdot \left(4 \cdot x2 - 6\right) + 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right) - 1\right)\right)\right)\right)\right) - 6\right)\right) - 1\right)} \]

   7. Simplified 77.8%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(2 \cdot \left(x2 \cdot \left(x2 \cdot 4 + -6\right)\right) + \left(x1 \cdot \left(\left(\left(\left(9 + 3 \cdot \left(x2 \cdot 2\right)\right) + \left(x2 \cdot 10 + x1 \cdot \left(\left(3 \cdot \left(x2 \cdot 4\right) + -18\right) + \left(4 \cdot \left(x2 \cdot \left(3 - x2 \cdot 2\right)\right) + -1\right)\right)\right)\right) - \left(x2 \cdot 4 + -6\right)\right) + -6\right) + -1\right)\right)} \]

   8. Taylor expanded in x2 around 0

      \[\leadsto \color{blue}{x1 \cdot \left(x1 \cdot \left(9 + -19 \cdot x1\right) - 1\right)} \]
   9. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x1, \color{blue}{\left(x1 \cdot \left(9 + -19 \cdot x1\right) - 1\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x1, \left(x1 \cdot \left(9 + -19 \cdot x1\right) + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right) \]

      3. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(x1, \left(x1 \cdot \left(9 + -19 \cdot x1\right) + -1\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\left(x1 \cdot \left(9 + -19 \cdot x1\right)\right), \color{blue}{-1}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \left(9 + -19 \cdot x1\right)\right), -1\right)\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(9, \left(-19 \cdot x1\right)\right)\right), -1\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(9, \left(x1 \cdot -19\right)\right)\right), -1\right)\right) \]

      8. *-lowering-*.f64 94.9%

         \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(9, \mathsf{*.f64}\left(x1, -19\right)\right)\right), -1\right)\right) \]

   10. Simplified 94.9%

       \[\leadsto \color{blue}{x1 \cdot \left(x1 \cdot \left(9 + x1 \cdot -19\right) + -1\right)} \]

   if -1.75e89 < x1 < -5.5000000000000003e-67 or 9.4999999999999996e-161 < x1 < 2.2e59

   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

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \color{blue}{\left(x1 \cdot \left(2 + 2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)\right)\right)}\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \color{blue}{\left(2 + 2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)\right)}\right)\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \color{blue}{\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \color{blue}{\left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)}\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \color{blue}{\left(4 \cdot x2 - 6\right)}\right)\right)\right)\right)\right) \]

      5. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + \color{blue}{\left(\mathsf{neg}\left(6\right)\right)}\right)\right)\right)\right)\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + -6\right)\right)\right)\right)\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\left(4 \cdot x2\right), \color{blue}{-6}\right)\right)\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\left(x2 \cdot 4\right), -6\right)\right)\right)\right)\right)\right) \]

      9. *-lowering-*.f64 74.8%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right)\right)\right)\right)\right) \]

   7. Simplified 74.8%

      \[\leadsto \frac{3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right)}{x1 \cdot x1 + 1} + \color{blue}{x1 \cdot \left(2 + 2 \cdot \left(x2 \cdot \left(x2 \cdot 4 + -6\right)\right)\right)} \]

   8. Taylor expanded in x1 around 0

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + 3 \cdot \left(x1 \cdot \left(3 - -2 \cdot x2\right)\right)\right) - 1\right)} \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(-6 \cdot x2\right), \color{blue}{\left(x1 \cdot \left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + 3 \cdot \left(x1 \cdot \left(3 - -2 \cdot x2\right)\right)\right) - 1\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \left(\color{blue}{x1} \cdot \left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + 3 \cdot \left(x1 \cdot \left(3 - -2 \cdot x2\right)\right)\right) - 1\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \color{blue}{\left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + 3 \cdot \left(x1 \cdot \left(3 - -2 \cdot x2\right)\right)\right) - 1\right)}\right)\right) \]

      4. associate--l+ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + \color{blue}{\left(3 \cdot \left(x1 \cdot \left(3 - -2 \cdot x2\right)\right) - 1\right)}\right)\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)\right), \color{blue}{\left(3 \cdot \left(x1 \cdot \left(3 - -2 \cdot x2\right)\right) - 1\right)}\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)\right), \left(\color{blue}{3 \cdot \left(x1 \cdot \left(3 - -2 \cdot x2\right)\right)} - 1\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 - 6\right)\right)\right), \left(3 \cdot \color{blue}{\left(x1 \cdot \left(3 - -2 \cdot x2\right)\right)} - 1\right)\right)\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + \left(\mathsf{neg}\left(6\right)\right)\right)\right)\right), \left(3 \cdot \left(x1 \cdot \color{blue}{\left(3 - -2 \cdot x2\right)}\right) - 1\right)\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + -6\right)\right)\right), \left(3 \cdot \left(x1 \cdot \left(3 - \color{blue}{-2 \cdot x2}\right)\right) - 1\right)\right)\right)\right) \]

      10. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\left(4 \cdot x2\right), -6\right)\right)\right), \left(3 \cdot \left(x1 \cdot \color{blue}{\left(3 - -2 \cdot x2\right)}\right) - 1\right)\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, x2\right), -6\right)\right)\right), \left(3 \cdot \left(x1 \cdot \left(\color{blue}{3} - -2 \cdot x2\right)\right) - 1\right)\right)\right)\right) \]

      12. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, x2\right), -6\right)\right)\right), \left(3 \cdot \left(x1 \cdot \left(3 - -2 \cdot x2\right)\right) + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, x2\right), -6\right)\right)\right), \left(3 \cdot \left(x1 \cdot \left(3 - -2 \cdot x2\right)\right) + -1\right)\right)\right)\right) \]

      14. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, x2\right), -6\right)\right)\right), \mathsf{+.f64}\left(\left(3 \cdot \left(x1 \cdot \left(3 - -2 \cdot x2\right)\right)\right), \color{blue}{-1}\right)\right)\right)\right) \]

   10. Simplified 75.7%

       \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 + -6\right)\right) + \left(3 \cdot \left(x1 \cdot \left(3 + 2 \cdot x2\right)\right) + -1\right)\right)} \]

   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. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \left(\left(x1 \cdot {x2}^{2}\right) \cdot \color{blue}{8}\right)\right) \]

       2. associate-*l* N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \left(x1 \cdot \color{blue}{\left({x2}^{2} \cdot 8\right)}\right)\right) \]

       3. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \left(x1 \cdot \left(8 \cdot \color{blue}{{x2}^{2}}\right)\right)\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \color{blue}{\left(8 \cdot {x2}^{2}\right)}\right)\right) \]

       5. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \left({x2}^{2} \cdot \color{blue}{8}\right)\right)\right) \]

       6. unpow2 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \left(\left(x2 \cdot x2\right) \cdot 8\right)\right)\right) \]

       7. associate-*l* N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \left(x2 \cdot \color{blue}{\left(x2 \cdot 8\right)}\right)\right)\right) \]

       8. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \left(x2 \cdot \left(8 \cdot \color{blue}{x2}\right)\right)\right)\right) \]

       9. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x2, \color{blue}{\left(8 \cdot x2\right)}\right)\right)\right) \]

       10. *-commutative N/A

           \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x2, \left(x2 \cdot \color{blue}{8}\right)\right)\right)\right) \]

       11. *-lowering-*.f64 60.6%

           \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x2, \mathsf{*.f64}\left(x2, \color{blue}{8}\right)\right)\right)\right) \]

   13. Simplified 60.6%

       \[\leadsto -6 \cdot x2 + \color{blue}{x1 \cdot \left(x2 \cdot \left(x2 \cdot 8\right)\right)} \]

   if -5.5000000000000003e-67 < x1 < 9.4999999999999996e-161

   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 99.6%

      \[\leadsto \color{blue}{\frac{3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right)}{x1 \cdot x1 + 1} + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(x1 \cdot \left(x1 \cdot -6\right) + \frac{2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)}{x1 \cdot x1 + 1} \cdot \left(x1 \cdot \left(-6 + \left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right) \cdot \frac{2}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot 4\right)\right) + x1 \cdot \left(2 + x1 \cdot \left(x1 + \left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right) \cdot \frac{3}{x1 \cdot x1 + 1}\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x1 around 0

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + x1 \cdot \left(\left(-1 \cdot \left(4 \cdot x2 - 6\right) + \left(3 \cdot \left(3 - -2 \cdot x2\right) + \left(4 \cdot x2 + \left(6 \cdot x2 + x1 \cdot \left(\left(3 \cdot \left(4 \cdot x2 - 6\right) + 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right) - 1\right)\right)\right)\right)\right) - 6\right)\right) - 1\right)} \]

   7. Simplified 82.8%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(2 \cdot \left(x2 \cdot \left(x2 \cdot 4 + -6\right)\right) + \left(x1 \cdot \left(\left(\left(\left(9 + 3 \cdot \left(x2 \cdot 2\right)\right) + \left(x2 \cdot 10 + x1 \cdot \left(\left(3 \cdot \left(x2 \cdot 4\right) + -18\right) + \left(4 \cdot \left(x2 \cdot \left(3 - x2 \cdot 2\right)\right) + -1\right)\right)\right)\right) - \left(x2 \cdot 4 + -6\right)\right) + -6\right) + -1\right)\right)} \]

   8. Taylor expanded in x2 around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \color{blue}{\left(x1 \cdot \left(x2 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right) + x1 \cdot \left(x1 \cdot \left(9 + -19 \cdot x1\right) - 1\right)\right)}\right) \]
   9. Step-by-step derivation

      1. distribute-lft-out N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \left(x1 \cdot \color{blue}{\left(x2 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right) + \left(x1 \cdot \left(9 + -19 \cdot x1\right) - 1\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \color{blue}{\left(x2 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right) + \left(x1 \cdot \left(9 + -19 \cdot x1\right) - 1\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\left(x2 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right), \color{blue}{\left(x1 \cdot \left(9 + -19 \cdot x1\right) - 1\right)}\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right), \left(\color{blue}{x1 \cdot \left(9 + -19 \cdot x1\right)} - 1\right)\right)\right)\right) \]

      5. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, \left(x1 \cdot \left(12 + 24 \cdot x1\right) + \left(\mathsf{neg}\left(12\right)\right)\right)\right), \left(x1 \cdot \color{blue}{\left(9 + -19 \cdot x1\right)} - 1\right)\right)\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, \left(x1 \cdot \left(12 + 24 \cdot x1\right) + -12\right)\right), \left(x1 \cdot \left(9 + \color{blue}{-19 \cdot x1}\right) - 1\right)\right)\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\left(x1 \cdot \left(12 + 24 \cdot x1\right)\right), -12\right)\right), \left(x1 \cdot \color{blue}{\left(9 + -19 \cdot x1\right)} - 1\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \left(12 + 24 \cdot x1\right)\right), -12\right)\right), \left(x1 \cdot \left(\color{blue}{9} + -19 \cdot x1\right) - 1\right)\right)\right)\right) \]

      9. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(12, \left(24 \cdot x1\right)\right)\right), -12\right)\right), \left(x1 \cdot \left(9 + -19 \cdot x1\right) - 1\right)\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(12, \left(x1 \cdot 24\right)\right)\right), -12\right)\right), \left(x1 \cdot \left(9 + -19 \cdot x1\right) - 1\right)\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(12, \mathsf{*.f64}\left(x1, 24\right)\right)\right), -12\right)\right), \left(x1 \cdot \left(9 + -19 \cdot x1\right) - 1\right)\right)\right)\right) \]

      12. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(12, \mathsf{*.f64}\left(x1, 24\right)\right)\right), -12\right)\right), \left(x1 \cdot \left(9 + -19 \cdot x1\right) + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(12, \mathsf{*.f64}\left(x1, 24\right)\right)\right), -12\right)\right), \left(x1 \cdot \left(9 + -19 \cdot x1\right) + -1\right)\right)\right)\right) \]

      14. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(12, \mathsf{*.f64}\left(x1, 24\right)\right)\right), -12\right)\right), \mathsf{+.f64}\left(\left(x1 \cdot \left(9 + -19 \cdot x1\right)\right), \color{blue}{-1}\right)\right)\right)\right) \]

   10. Simplified 91.9%

       \[\leadsto -6 \cdot x2 + \color{blue}{x1 \cdot \left(x2 \cdot \left(x1 \cdot \left(12 + x1 \cdot 24\right) + -12\right) + \left(x1 \cdot \left(9 + x1 \cdot -19\right) + -1\right)\right)} \]

   11. Taylor expanded in x1 around 0

       \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(-12 \cdot x2 - 1\right)} \]
   12. Step-by-step derivation

       1. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\left(-6 \cdot x2\right), \color{blue}{\left(x1 \cdot \left(-12 \cdot x2 - 1\right)\right)}\right) \]

       2. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \left(\color{blue}{x1} \cdot \left(-12 \cdot x2 - 1\right)\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \color{blue}{\left(-12 \cdot x2 - 1\right)}\right)\right) \]

       4. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \left(-12 \cdot x2 + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right) \]

       5. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \left(-12 \cdot x2 + -1\right)\right)\right) \]

       6. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\left(-12 \cdot x2\right), \color{blue}{-1}\right)\right)\right) \]

       7. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\left(x2 \cdot -12\right), -1\right)\right)\right) \]

       8. *-lowering-*.f64 91.9%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -12\right), -1\right)\right)\right) \]

   13. Simplified 91.9%

       \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(x2 \cdot -12 + -1\right)} \]

   if 2.2e59 < x1

   1. Initial program 44.1%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Simplified 44.1%

      \[\leadsto \color{blue}{\frac{3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right)}{x1 \cdot x1 + 1} + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(x1 \cdot \left(x1 \cdot -6\right) + \frac{2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)}{x1 \cdot x1 + 1} \cdot \left(x1 \cdot \left(-6 + \left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right) \cdot \frac{2}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot 4\right)\right) + x1 \cdot \left(2 + x1 \cdot \left(x1 + \left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right) \cdot \frac{3}{x1 \cdot x1 + 1}\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x1 around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \color{blue}{\left(x1 \cdot \left(2 + 2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)\right)\right)}\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \color{blue}{\left(2 + 2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)\right)}\right)\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \color{blue}{\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \color{blue}{\left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)}\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \color{blue}{\left(4 \cdot x2 - 6\right)}\right)\right)\right)\right)\right) \]

      5. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + \color{blue}{\left(\mathsf{neg}\left(6\right)\right)}\right)\right)\right)\right)\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + -6\right)\right)\right)\right)\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\left(4 \cdot x2\right), \color{blue}{-6}\right)\right)\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\left(x2 \cdot 4\right), -6\right)\right)\right)\right)\right)\right) \]

      9. *-lowering-*.f64 7.6%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right)\right)\right)\right)\right) \]

   7. Simplified 7.6%

      \[\leadsto \frac{3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right)}{x1 \cdot x1 + 1} + \color{blue}{x1 \cdot \left(2 + 2 \cdot \left(x2 \cdot \left(x2 \cdot 4 + -6\right)\right)\right)} \]

   8. Taylor expanded in x1 around 0

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)\right) - 1\right)} \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(-6 \cdot x2\right), \color{blue}{\left(x1 \cdot \left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)\right) - 1\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \left(\color{blue}{x1} \cdot \left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)\right) - 1\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \color{blue}{\left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)\right) - 1\right)}\right)\right) \]

      4. associate--l+ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + \color{blue}{\left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right) - 1\right)}\right)\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)\right), \color{blue}{\left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right) - 1\right)}\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)\right), \left(\color{blue}{x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)} - 1\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 - 6\right)\right)\right), \left(x1 \cdot \color{blue}{\left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)} - 1\right)\right)\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + \left(\mathsf{neg}\left(6\right)\right)\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + \color{blue}{3 \cdot \left(3 - -2 \cdot x2\right)}\right) - 1\right)\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + -6\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \color{blue}{\left(3 - -2 \cdot x2\right)}\right) - 1\right)\right)\right)\right) \]

      10. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\left(4 \cdot x2\right), -6\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + \color{blue}{3 \cdot \left(3 - -2 \cdot x2\right)}\right) - 1\right)\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, x2\right), -6\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + \color{blue}{3} \cdot \left(3 - -2 \cdot x2\right)\right) - 1\right)\right)\right)\right) \]

      12. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, x2\right), -6\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right) + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, x2\right), -6\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right) + -1\right)\right)\right)\right) \]

      14. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, x2\right), -6\right)\right)\right), \mathsf{+.f64}\left(\left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)\right), \color{blue}{-1}\right)\right)\right)\right) \]

   10. Simplified 76.1%

       \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 + -6\right)\right) + \left(x1 \cdot \left(3 \cdot \left(x1 + \left(3 + 2 \cdot x2\right)\right)\right) + -1\right)\right)} \]

   11. Taylor expanded in x1 around inf

       \[\leadsto \color{blue}{3 \cdot {x1}^{3}} \]
   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. *-commutative N/A

          \[\leadsto x1 \cdot \left(3 \cdot \color{blue}{{x1}^{2}}\right) \]

       6. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x1, \color{blue}{\left(3 \cdot {x1}^{2}\right)}\right) \]

       7. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(3, \color{blue}{\left({x1}^{2}\right)}\right)\right) \]

       8. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(3, \left(x1 \cdot \color{blue}{x1}\right)\right)\right) \]

       9. *-lowering-*.f64 81.8%

          \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(3, \mathsf{*.f64}\left(x1, \color{blue}{x1}\right)\right)\right) \]

   13. Simplified 81.8%

       \[\leadsto \color{blue}{x1 \cdot \left(3 \cdot \left(x1 \cdot x1\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.75 \cdot 10^{+89}:\\ \;\;\;\;x1 \cdot \left(-1 + x1 \cdot \left(9 + x1 \cdot -19\right)\right)\\ \mathbf{elif}\;x1 \leq -5.5 \cdot 10^{-67}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(x2 \cdot \left(x2 \cdot 8\right)\right)\\ \mathbf{elif}\;x1 \leq 9.5 \cdot 10^{-161}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + x2 \cdot -12\right)\\ \mathbf{elif}\;x1 \leq 2.2 \cdot 10^{+59}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(x2 \cdot \left(x2 \cdot 8\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot \left(3 \cdot \left(x1 \cdot x1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 69.4% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(x2 \cdot x2\right) \cdot \left(x1 \cdot 8 + \frac{-6}{x2}\right)\\ \mathbf{if}\;x1 \leq -2 \cdot 10^{+90}:\\ \;\;\;\;x1 \cdot \left(-1 + x1 \cdot \left(9 + x1 \cdot -19\right)\right)\\ \mathbf{elif}\;x1 \leq -2.2 \cdot 10^{-196}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x1 \leq 1.65 \cdot 10^{-181}:\\ \;\;\;\;x2 \cdot -6\\ \mathbf{elif}\;x1 \leq 1.9 \cdot 10^{+58}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot \left(3 \cdot \left(x1 \cdot x1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* (* x2 x2) (+ (* x1 8.0) (/ -6.0 x2)))))
   (if (<= x1 -2e+90)
     (* x1 (+ -1.0 (* x1 (+ 9.0 (* x1 -19.0)))))
     (if (<= x1 -2.2e-196)
       t_0
       (if (<= x1 1.65e-181)
         (* x2 -6.0)
         (if (<= x1 1.9e+58) t_0 (* x1 (* 3.0 (* x1 x1)))))))))

C

double code(double x1, double x2) {
	double t_0 = (x2 * x2) * ((x1 * 8.0) + (-6.0 / x2));
	double tmp;
	if (x1 <= -2e+90) {
		tmp = x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0))));
	} else if (x1 <= -2.2e-196) {
		tmp = t_0;
	} else if (x1 <= 1.65e-181) {
		tmp = x2 * -6.0;
	} else if (x1 <= 1.9e+58) {
		tmp = t_0;
	} else {
		tmp = x1 * (3.0 * (x1 * x1));
	}
	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 * x2) * ((x1 * 8.0d0) + ((-6.0d0) / x2))
    if (x1 <= (-2d+90)) then
        tmp = x1 * ((-1.0d0) + (x1 * (9.0d0 + (x1 * (-19.0d0)))))
    else if (x1 <= (-2.2d-196)) then
        tmp = t_0
    else if (x1 <= 1.65d-181) then
        tmp = x2 * (-6.0d0)
    else if (x1 <= 1.9d+58) then
        tmp = t_0
    else
        tmp = x1 * (3.0d0 * (x1 * x1))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (x2 * x2) * ((x1 * 8.0) + (-6.0 / x2));
	double tmp;
	if (x1 <= -2e+90) {
		tmp = x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0))));
	} else if (x1 <= -2.2e-196) {
		tmp = t_0;
	} else if (x1 <= 1.65e-181) {
		tmp = x2 * -6.0;
	} else if (x1 <= 1.9e+58) {
		tmp = t_0;
	} else {
		tmp = x1 * (3.0 * (x1 * x1));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x2 * x2) * ((x1 * 8.0) + (-6.0 / x2))
	tmp = 0
	if x1 <= -2e+90:
		tmp = x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0))))
	elif x1 <= -2.2e-196:
		tmp = t_0
	elif x1 <= 1.65e-181:
		tmp = x2 * -6.0
	elif x1 <= 1.9e+58:
		tmp = t_0
	else:
		tmp = x1 * (3.0 * (x1 * x1))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x2 * x2) * Float64(Float64(x1 * 8.0) + Float64(-6.0 / x2)))
	tmp = 0.0
	if (x1 <= -2e+90)
		tmp = Float64(x1 * Float64(-1.0 + Float64(x1 * Float64(9.0 + Float64(x1 * -19.0)))));
	elseif (x1 <= -2.2e-196)
		tmp = t_0;
	elseif (x1 <= 1.65e-181)
		tmp = Float64(x2 * -6.0);
	elseif (x1 <= 1.9e+58)
		tmp = t_0;
	else
		tmp = Float64(x1 * Float64(3.0 * Float64(x1 * x1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x2 * x2) * ((x1 * 8.0) + (-6.0 / x2));
	tmp = 0.0;
	if (x1 <= -2e+90)
		tmp = x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0))));
	elseif (x1 <= -2.2e-196)
		tmp = t_0;
	elseif (x1 <= 1.65e-181)
		tmp = x2 * -6.0;
	elseif (x1 <= 1.9e+58)
		tmp = t_0;
	else
		tmp = x1 * (3.0 * (x1 * x1));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x2 * x2), $MachinePrecision] * N[(N[(x1 * 8.0), $MachinePrecision] + N[(-6.0 / x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -2e+90], N[(x1 * N[(-1.0 + N[(x1 * N[(9.0 + N[(x1 * -19.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -2.2e-196], t$95$0, If[LessEqual[x1, 1.65e-181], N[(x2 * -6.0), $MachinePrecision], If[LessEqual[x1, 1.9e+58], t$95$0, N[(x1 * N[(3.0 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -1.99999999999999993e90

   1. Initial program 5.6%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Simplified 5.6%

      \[\leadsto \color{blue}{\frac{3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right)}{x1 \cdot x1 + 1} + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(x1 \cdot \left(x1 \cdot -6\right) + \frac{2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)}{x1 \cdot x1 + 1} \cdot \left(x1 \cdot \left(-6 + \left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right) \cdot \frac{2}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot 4\right)\right) + x1 \cdot \left(2 + x1 \cdot \left(x1 + \left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right) \cdot \frac{3}{x1 \cdot x1 + 1}\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x1 around 0

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + x1 \cdot \left(\left(-1 \cdot \left(4 \cdot x2 - 6\right) + \left(3 \cdot \left(3 - -2 \cdot x2\right) + \left(4 \cdot x2 + \left(6 \cdot x2 + x1 \cdot \left(\left(3 \cdot \left(4 \cdot x2 - 6\right) + 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right) - 1\right)\right)\right)\right)\right) - 6\right)\right) - 1\right)} \]

   7. Simplified 77.8%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(2 \cdot \left(x2 \cdot \left(x2 \cdot 4 + -6\right)\right) + \left(x1 \cdot \left(\left(\left(\left(9 + 3 \cdot \left(x2 \cdot 2\right)\right) + \left(x2 \cdot 10 + x1 \cdot \left(\left(3 \cdot \left(x2 \cdot 4\right) + -18\right) + \left(4 \cdot \left(x2 \cdot \left(3 - x2 \cdot 2\right)\right) + -1\right)\right)\right)\right) - \left(x2 \cdot 4 + -6\right)\right) + -6\right) + -1\right)\right)} \]

   8. Taylor expanded in x2 around 0

      \[\leadsto \color{blue}{x1 \cdot \left(x1 \cdot \left(9 + -19 \cdot x1\right) - 1\right)} \]
   9. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x1, \color{blue}{\left(x1 \cdot \left(9 + -19 \cdot x1\right) - 1\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x1, \left(x1 \cdot \left(9 + -19 \cdot x1\right) + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right) \]

      3. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(x1, \left(x1 \cdot \left(9 + -19 \cdot x1\right) + -1\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\left(x1 \cdot \left(9 + -19 \cdot x1\right)\right), \color{blue}{-1}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \left(9 + -19 \cdot x1\right)\right), -1\right)\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(9, \left(-19 \cdot x1\right)\right)\right), -1\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(9, \left(x1 \cdot -19\right)\right)\right), -1\right)\right) \]

      8. *-lowering-*.f64 94.9%

         \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(9, \mathsf{*.f64}\left(x1, -19\right)\right)\right), -1\right)\right) \]

   10. Simplified 94.9%

       \[\leadsto \color{blue}{x1 \cdot \left(x1 \cdot \left(9 + x1 \cdot -19\right) + -1\right)} \]

   if -1.99999999999999993e90 < x1 < -2.20000000000000015e-196 or 1.65000000000000004e-181 < x1 < 1.8999999999999999e58

   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 x2 around -inf

      \[\leadsto \color{blue}{{x2}^{2} \cdot \left(-1 \cdot \frac{-6 \cdot \frac{{x1}^{2}}{1 + {x1}^{2}} + \left(6 \cdot \frac{1}{1 + {x1}^{2}} + \left(1 + {x1}^{2}\right) \cdot \left(-4 \cdot \frac{{x1}^{2} \cdot \left(3 \cdot x1 - 1\right)}{{\left(1 + {x1}^{2}\right)}^{2}} + -2 \cdot \frac{4 \cdot {x1}^{2} + x1 \cdot \left(2 \cdot \frac{x1 \cdot \left(3 \cdot x1 - 1\right)}{1 + {x1}^{2}} - 6\right)}{1 + {x1}^{2}}\right)\right)}{x2} + 8 \cdot \frac{x1}{1 + {x1}^{2}}\right)} \]

   7. Simplified 63.1%

      \[\leadsto \color{blue}{\left(x2 \cdot x2\right) \cdot \left(\frac{8 \cdot x1}{1 + x1 \cdot x1} - \frac{\frac{-6 \cdot \left(x1 \cdot x1\right)}{1 + x1 \cdot x1} + \left(\frac{6}{1 + x1 \cdot x1} + \left(1 + x1 \cdot x1\right) \cdot \left(\frac{-4 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot 3 + -1\right)\right)}{\left(1 + x1 \cdot x1\right) \cdot \left(1 + x1 \cdot x1\right)} + \frac{-2 \cdot \left(4 \cdot \left(x1 \cdot x1\right) + x1 \cdot \left(\frac{2 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)}{1 + x1 \cdot x1} + -6\right)\right)}{1 + x1 \cdot x1}\right)\right)}{x2}\right)} \]

   8. Taylor expanded in x1 around 0

      \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, x2\right), \color{blue}{\left(x1 \cdot \left(8 - 12 \cdot \frac{1}{x2}\right) - 6 \cdot \frac{1}{x2}\right)}\right) \]
   9. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, x2\right), \left(x1 \cdot \left(8 - 12 \cdot \frac{1}{x2}\right) + \color{blue}{\left(\mathsf{neg}\left(6 \cdot \frac{1}{x2}\right)\right)}\right)\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, x2\right), \mathsf{+.f64}\left(\left(x1 \cdot \left(8 - 12 \cdot \frac{1}{x2}\right)\right), \color{blue}{\left(\mathsf{neg}\left(6 \cdot \frac{1}{x2}\right)\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, x2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \left(8 - 12 \cdot \frac{1}{x2}\right)\right), \left(\mathsf{neg}\left(\color{blue}{6 \cdot \frac{1}{x2}}\right)\right)\right)\right) \]

      4. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, x2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \left(8 + \left(\mathsf{neg}\left(12 \cdot \frac{1}{x2}\right)\right)\right)\right), \left(\mathsf{neg}\left(6 \cdot \color{blue}{\frac{1}{x2}}\right)\right)\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, x2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(8, \left(\mathsf{neg}\left(12 \cdot \frac{1}{x2}\right)\right)\right)\right), \left(\mathsf{neg}\left(6 \cdot \color{blue}{\frac{1}{x2}}\right)\right)\right)\right) \]

      6. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, x2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(8, \left(\mathsf{neg}\left(\frac{12 \cdot 1}{x2}\right)\right)\right)\right), \left(\mathsf{neg}\left(6 \cdot \frac{1}{x2}\right)\right)\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, x2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(8, \left(\mathsf{neg}\left(\frac{12}{x2}\right)\right)\right)\right), \left(\mathsf{neg}\left(6 \cdot \frac{1}{x2}\right)\right)\right)\right) \]

      8. distribute-neg-frac N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, x2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(8, \left(\frac{\mathsf{neg}\left(12\right)}{x2}\right)\right)\right), \left(\mathsf{neg}\left(6 \cdot \frac{1}{\color{blue}{x2}}\right)\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, x2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(8, \left(\frac{-12}{x2}\right)\right)\right), \left(\mathsf{neg}\left(6 \cdot \frac{1}{x2}\right)\right)\right)\right) \]

      10. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, x2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(8, \mathsf{/.f64}\left(-12, x2\right)\right)\right), \left(\mathsf{neg}\left(6 \cdot \frac{1}{\color{blue}{x2}}\right)\right)\right)\right) \]

      11. associate-*r/ N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, x2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(8, \mathsf{/.f64}\left(-12, x2\right)\right)\right), \left(\mathsf{neg}\left(\frac{6 \cdot 1}{x2}\right)\right)\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, x2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(8, \mathsf{/.f64}\left(-12, x2\right)\right)\right), \left(\mathsf{neg}\left(\frac{6}{x2}\right)\right)\right)\right) \]

      13. distribute-neg-frac N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, x2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(8, \mathsf{/.f64}\left(-12, x2\right)\right)\right), \left(\frac{\mathsf{neg}\left(6\right)}{\color{blue}{x2}}\right)\right)\right) \]

      14. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, x2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(8, \mathsf{/.f64}\left(-12, x2\right)\right)\right), \left(\frac{-6}{x2}\right)\right)\right) \]

      15. /-lowering-/.f64 60.5%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, x2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(8, \mathsf{/.f64}\left(-12, x2\right)\right)\right), \mathsf{/.f64}\left(-6, \color{blue}{x2}\right)\right)\right) \]

   10. Simplified 60.5%

       \[\leadsto \left(x2 \cdot x2\right) \cdot \color{blue}{\left(x1 \cdot \left(8 + \frac{-12}{x2}\right) + \frac{-6}{x2}\right)} \]

   11. Taylor expanded in x2 around inf

       \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, x2\right), \mathsf{+.f64}\left(\color{blue}{\left(8 \cdot x1\right)}, \mathsf{/.f64}\left(-6, x2\right)\right)\right) \]
   12. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, x2\right), \mathsf{+.f64}\left(\left(x1 \cdot 8\right), \mathsf{/.f64}\left(\color{blue}{-6}, x2\right)\right)\right) \]

       2. *-lowering-*.f64 60.5%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, x2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 8\right), \mathsf{/.f64}\left(\color{blue}{-6}, x2\right)\right)\right) \]

   13. Simplified 60.5%

       \[\leadsto \left(x2 \cdot x2\right) \cdot \left(\color{blue}{x1 \cdot 8} + \frac{-6}{x2}\right) \]

   if -2.20000000000000015e-196 < x1 < 1.65000000000000004e-181

   1. Initial program 99.5%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x1 around 0

      \[\leadsto \color{blue}{-6 \cdot x2} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 80.9%

         \[\leadsto \mathsf{*.f64}\left(-6, \color{blue}{x2}\right) \]

   5. Simplified 80.9%

      \[\leadsto \color{blue}{-6 \cdot x2} \]

   if 1.8999999999999999e58 < x1

   1. Initial program 44.1%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Simplified 44.1%

      \[\leadsto \color{blue}{\frac{3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right)}{x1 \cdot x1 + 1} + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(x1 \cdot \left(x1 \cdot -6\right) + \frac{2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)}{x1 \cdot x1 + 1} \cdot \left(x1 \cdot \left(-6 + \left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right) \cdot \frac{2}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot 4\right)\right) + x1 \cdot \left(2 + x1 \cdot \left(x1 + \left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right) \cdot \frac{3}{x1 \cdot x1 + 1}\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x1 around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \color{blue}{\left(x1 \cdot \left(2 + 2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)\right)\right)}\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \color{blue}{\left(2 + 2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)\right)}\right)\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \color{blue}{\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \color{blue}{\left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)}\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \color{blue}{\left(4 \cdot x2 - 6\right)}\right)\right)\right)\right)\right) \]

      5. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + \color{blue}{\left(\mathsf{neg}\left(6\right)\right)}\right)\right)\right)\right)\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + -6\right)\right)\right)\right)\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\left(4 \cdot x2\right), \color{blue}{-6}\right)\right)\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\left(x2 \cdot 4\right), -6\right)\right)\right)\right)\right)\right) \]

      9. *-lowering-*.f64 7.6%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right)\right)\right)\right)\right) \]

   7. Simplified 7.6%

      \[\leadsto \frac{3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right)}{x1 \cdot x1 + 1} + \color{blue}{x1 \cdot \left(2 + 2 \cdot \left(x2 \cdot \left(x2 \cdot 4 + -6\right)\right)\right)} \]

   8. Taylor expanded in x1 around 0

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)\right) - 1\right)} \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(-6 \cdot x2\right), \color{blue}{\left(x1 \cdot \left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)\right) - 1\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \left(\color{blue}{x1} \cdot \left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)\right) - 1\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \color{blue}{\left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)\right) - 1\right)}\right)\right) \]

      4. associate--l+ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + \color{blue}{\left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right) - 1\right)}\right)\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)\right), \color{blue}{\left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right) - 1\right)}\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)\right), \left(\color{blue}{x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)} - 1\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 - 6\right)\right)\right), \left(x1 \cdot \color{blue}{\left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)} - 1\right)\right)\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + \left(\mathsf{neg}\left(6\right)\right)\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + \color{blue}{3 \cdot \left(3 - -2 \cdot x2\right)}\right) - 1\right)\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + -6\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \color{blue}{\left(3 - -2 \cdot x2\right)}\right) - 1\right)\right)\right)\right) \]

      10. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\left(4 \cdot x2\right), -6\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + \color{blue}{3 \cdot \left(3 - -2 \cdot x2\right)}\right) - 1\right)\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, x2\right), -6\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + \color{blue}{3} \cdot \left(3 - -2 \cdot x2\right)\right) - 1\right)\right)\right)\right) \]

      12. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, x2\right), -6\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right) + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, x2\right), -6\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right) + -1\right)\right)\right)\right) \]

      14. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, x2\right), -6\right)\right)\right), \mathsf{+.f64}\left(\left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)\right), \color{blue}{-1}\right)\right)\right)\right) \]

   10. Simplified 76.1%

       \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 + -6\right)\right) + \left(x1 \cdot \left(3 \cdot \left(x1 + \left(3 + 2 \cdot x2\right)\right)\right) + -1\right)\right)} \]

   11. Taylor expanded in x1 around inf

       \[\leadsto \color{blue}{3 \cdot {x1}^{3}} \]
   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. *-commutative N/A

          \[\leadsto x1 \cdot \left(3 \cdot \color{blue}{{x1}^{2}}\right) \]

       6. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x1, \color{blue}{\left(3 \cdot {x1}^{2}\right)}\right) \]

       7. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(3, \color{blue}{\left({x1}^{2}\right)}\right)\right) \]

       8. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(3, \left(x1 \cdot \color{blue}{x1}\right)\right)\right) \]

       9. *-lowering-*.f64 81.8%

          \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(3, \mathsf{*.f64}\left(x1, \color{blue}{x1}\right)\right)\right) \]

   13. Simplified 81.8%

       \[\leadsto \color{blue}{x1 \cdot \left(3 \cdot \left(x1 \cdot x1\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 74.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -2 \cdot 10^{+90}:\\ \;\;\;\;x1 \cdot \left(-1 + x1 \cdot \left(9 + x1 \cdot -19\right)\right)\\ \mathbf{elif}\;x1 \leq -2.2 \cdot 10^{-196}:\\ \;\;\;\;\left(x2 \cdot x2\right) \cdot \left(x1 \cdot 8 + \frac{-6}{x2}\right)\\ \mathbf{elif}\;x1 \leq 1.65 \cdot 10^{-181}:\\ \;\;\;\;x2 \cdot -6\\ \mathbf{elif}\;x1 \leq 1.9 \cdot 10^{+58}:\\ \;\;\;\;\left(x2 \cdot x2\right) \cdot \left(x1 \cdot 8 + \frac{-6}{x2}\right)\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot \left(3 \cdot \left(x1 \cdot x1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 64.6% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(x1 \cdot \left(8 + \frac{-12}{x2}\right)\right) \cdot \left(x2 \cdot x2\right)\\ \mathbf{if}\;x1 \leq -3.45 \cdot 10^{+90}:\\ \;\;\;\;x1 \cdot \left(-1 + x1 \cdot \left(9 + x1 \cdot -19\right)\right)\\ \mathbf{elif}\;x1 \leq -2 \cdot 10^{-71}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x1 \leq 2.1 \cdot 10^{-113}:\\ \;\;\;\;x2 \cdot -6\\ \mathbf{elif}\;x1 \leq 6.5 \cdot 10^{+58}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot \left(3 \cdot \left(x1 \cdot x1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* (* x1 (+ 8.0 (/ -12.0 x2))) (* x2 x2))))
   (if (<= x1 -3.45e+90)
     (* x1 (+ -1.0 (* x1 (+ 9.0 (* x1 -19.0)))))
     (if (<= x1 -2e-71)
       t_0
       (if (<= x1 2.1e-113)
         (* x2 -6.0)
         (if (<= x1 6.5e+58) t_0 (* x1 (* 3.0 (* x1 x1)))))))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * (8.0 + (-12.0 / x2))) * (x2 * x2);
	double tmp;
	if (x1 <= -3.45e+90) {
		tmp = x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0))));
	} else if (x1 <= -2e-71) {
		tmp = t_0;
	} else if (x1 <= 2.1e-113) {
		tmp = x2 * -6.0;
	} else if (x1 <= 6.5e+58) {
		tmp = t_0;
	} else {
		tmp = x1 * (3.0 * (x1 * x1));
	}
	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 * (8.0d0 + ((-12.0d0) / x2))) * (x2 * x2)
    if (x1 <= (-3.45d+90)) then
        tmp = x1 * ((-1.0d0) + (x1 * (9.0d0 + (x1 * (-19.0d0)))))
    else if (x1 <= (-2d-71)) then
        tmp = t_0
    else if (x1 <= 2.1d-113) then
        tmp = x2 * (-6.0d0)
    else if (x1 <= 6.5d+58) then
        tmp = t_0
    else
        tmp = x1 * (3.0d0 * (x1 * x1))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (x1 * (8.0 + (-12.0 / x2))) * (x2 * x2);
	double tmp;
	if (x1 <= -3.45e+90) {
		tmp = x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0))));
	} else if (x1 <= -2e-71) {
		tmp = t_0;
	} else if (x1 <= 2.1e-113) {
		tmp = x2 * -6.0;
	} else if (x1 <= 6.5e+58) {
		tmp = t_0;
	} else {
		tmp = x1 * (3.0 * (x1 * x1));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x1 * (8.0 + (-12.0 / x2))) * (x2 * x2)
	tmp = 0
	if x1 <= -3.45e+90:
		tmp = x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0))))
	elif x1 <= -2e-71:
		tmp = t_0
	elif x1 <= 2.1e-113:
		tmp = x2 * -6.0
	elif x1 <= 6.5e+58:
		tmp = t_0
	else:
		tmp = x1 * (3.0 * (x1 * x1))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * Float64(8.0 + Float64(-12.0 / x2))) * Float64(x2 * x2))
	tmp = 0.0
	if (x1 <= -3.45e+90)
		tmp = Float64(x1 * Float64(-1.0 + Float64(x1 * Float64(9.0 + Float64(x1 * -19.0)))));
	elseif (x1 <= -2e-71)
		tmp = t_0;
	elseif (x1 <= 2.1e-113)
		tmp = Float64(x2 * -6.0);
	elseif (x1 <= 6.5e+58)
		tmp = t_0;
	else
		tmp = Float64(x1 * Float64(3.0 * Float64(x1 * x1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x1 * (8.0 + (-12.0 / x2))) * (x2 * x2);
	tmp = 0.0;
	if (x1 <= -3.45e+90)
		tmp = x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0))));
	elseif (x1 <= -2e-71)
		tmp = t_0;
	elseif (x1 <= 2.1e-113)
		tmp = x2 * -6.0;
	elseif (x1 <= 6.5e+58)
		tmp = t_0;
	else
		tmp = x1 * (3.0 * (x1 * x1));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x1 * N[(8.0 + N[(-12.0 / x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x2 * x2), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -3.45e+90], N[(x1 * N[(-1.0 + N[(x1 * N[(9.0 + N[(x1 * -19.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -2e-71], t$95$0, If[LessEqual[x1, 2.1e-113], N[(x2 * -6.0), $MachinePrecision], If[LessEqual[x1, 6.5e+58], t$95$0, N[(x1 * N[(3.0 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -3.44999999999999978e90

   1. Initial program 5.6%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Simplified 5.6%

      \[\leadsto \color{blue}{\frac{3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right)}{x1 \cdot x1 + 1} + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(x1 \cdot \left(x1 \cdot -6\right) + \frac{2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)}{x1 \cdot x1 + 1} \cdot \left(x1 \cdot \left(-6 + \left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right) \cdot \frac{2}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot 4\right)\right) + x1 \cdot \left(2 + x1 \cdot \left(x1 + \left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right) \cdot \frac{3}{x1 \cdot x1 + 1}\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x1 around 0

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + x1 \cdot \left(\left(-1 \cdot \left(4 \cdot x2 - 6\right) + \left(3 \cdot \left(3 - -2 \cdot x2\right) + \left(4 \cdot x2 + \left(6 \cdot x2 + x1 \cdot \left(\left(3 \cdot \left(4 \cdot x2 - 6\right) + 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right) - 1\right)\right)\right)\right)\right) - 6\right)\right) - 1\right)} \]

   7. Simplified 77.8%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(2 \cdot \left(x2 \cdot \left(x2 \cdot 4 + -6\right)\right) + \left(x1 \cdot \left(\left(\left(\left(9 + 3 \cdot \left(x2 \cdot 2\right)\right) + \left(x2 \cdot 10 + x1 \cdot \left(\left(3 \cdot \left(x2 \cdot 4\right) + -18\right) + \left(4 \cdot \left(x2 \cdot \left(3 - x2 \cdot 2\right)\right) + -1\right)\right)\right)\right) - \left(x2 \cdot 4 + -6\right)\right) + -6\right) + -1\right)\right)} \]

   8. Taylor expanded in x2 around 0

      \[\leadsto \color{blue}{x1 \cdot \left(x1 \cdot \left(9 + -19 \cdot x1\right) - 1\right)} \]
   9. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x1, \color{blue}{\left(x1 \cdot \left(9 + -19 \cdot x1\right) - 1\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x1, \left(x1 \cdot \left(9 + -19 \cdot x1\right) + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right) \]

      3. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(x1, \left(x1 \cdot \left(9 + -19 \cdot x1\right) + -1\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\left(x1 \cdot \left(9 + -19 \cdot x1\right)\right), \color{blue}{-1}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \left(9 + -19 \cdot x1\right)\right), -1\right)\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(9, \left(-19 \cdot x1\right)\right)\right), -1\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(9, \left(x1 \cdot -19\right)\right)\right), -1\right)\right) \]

      8. *-lowering-*.f64 94.9%

         \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(9, \mathsf{*.f64}\left(x1, -19\right)\right)\right), -1\right)\right) \]

   10. Simplified 94.9%

       \[\leadsto \color{blue}{x1 \cdot \left(x1 \cdot \left(9 + x1 \cdot -19\right) + -1\right)} \]

   if -3.44999999999999978e90 < x1 < -1.9999999999999998e-71 or 2.1e-113 < x1 < 6.49999999999999998e58

   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 99.6%

      \[\leadsto \color{blue}{\frac{3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right)}{x1 \cdot x1 + 1} + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(x1 \cdot \left(x1 \cdot -6\right) + \frac{2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)}{x1 \cdot x1 + 1} \cdot \left(x1 \cdot \left(-6 + \left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right) \cdot \frac{2}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot 4\right)\right) + x1 \cdot \left(2 + x1 \cdot \left(x1 + \left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right) \cdot \frac{3}{x1 \cdot x1 + 1}\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x2 around -inf

      \[\leadsto \color{blue}{{x2}^{2} \cdot \left(-1 \cdot \frac{-6 \cdot \frac{{x1}^{2}}{1 + {x1}^{2}} + \left(6 \cdot \frac{1}{1 + {x1}^{2}} + \left(1 + {x1}^{2}\right) \cdot \left(-4 \cdot \frac{{x1}^{2} \cdot \left(3 \cdot x1 - 1\right)}{{\left(1 + {x1}^{2}\right)}^{2}} + -2 \cdot \frac{4 \cdot {x1}^{2} + x1 \cdot \left(2 \cdot \frac{x1 \cdot \left(3 \cdot x1 - 1\right)}{1 + {x1}^{2}} - 6\right)}{1 + {x1}^{2}}\right)\right)}{x2} + 8 \cdot \frac{x1}{1 + {x1}^{2}}\right)} \]

   7. Simplified 61.7%

      \[\leadsto \color{blue}{\left(x2 \cdot x2\right) \cdot \left(\frac{8 \cdot x1}{1 + x1 \cdot x1} - \frac{\frac{-6 \cdot \left(x1 \cdot x1\right)}{1 + x1 \cdot x1} + \left(\frac{6}{1 + x1 \cdot x1} + \left(1 + x1 \cdot x1\right) \cdot \left(\frac{-4 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot 3 + -1\right)\right)}{\left(1 + x1 \cdot x1\right) \cdot \left(1 + x1 \cdot x1\right)} + \frac{-2 \cdot \left(4 \cdot \left(x1 \cdot x1\right) + x1 \cdot \left(\frac{2 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)}{1 + x1 \cdot x1} + -6\right)\right)}{1 + x1 \cdot x1}\right)\right)}{x2}\right)} \]

   8. Taylor expanded in x1 around 0

      \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, x2\right), \color{blue}{\left(x1 \cdot \left(8 - 12 \cdot \frac{1}{x2}\right) - 6 \cdot \frac{1}{x2}\right)}\right) \]
   9. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, x2\right), \left(x1 \cdot \left(8 - 12 \cdot \frac{1}{x2}\right) + \color{blue}{\left(\mathsf{neg}\left(6 \cdot \frac{1}{x2}\right)\right)}\right)\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, x2\right), \mathsf{+.f64}\left(\left(x1 \cdot \left(8 - 12 \cdot \frac{1}{x2}\right)\right), \color{blue}{\left(\mathsf{neg}\left(6 \cdot \frac{1}{x2}\right)\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, x2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \left(8 - 12 \cdot \frac{1}{x2}\right)\right), \left(\mathsf{neg}\left(\color{blue}{6 \cdot \frac{1}{x2}}\right)\right)\right)\right) \]

      4. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, x2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \left(8 + \left(\mathsf{neg}\left(12 \cdot \frac{1}{x2}\right)\right)\right)\right), \left(\mathsf{neg}\left(6 \cdot \color{blue}{\frac{1}{x2}}\right)\right)\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, x2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(8, \left(\mathsf{neg}\left(12 \cdot \frac{1}{x2}\right)\right)\right)\right), \left(\mathsf{neg}\left(6 \cdot \color{blue}{\frac{1}{x2}}\right)\right)\right)\right) \]

      6. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, x2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(8, \left(\mathsf{neg}\left(\frac{12 \cdot 1}{x2}\right)\right)\right)\right), \left(\mathsf{neg}\left(6 \cdot \frac{1}{x2}\right)\right)\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, x2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(8, \left(\mathsf{neg}\left(\frac{12}{x2}\right)\right)\right)\right), \left(\mathsf{neg}\left(6 \cdot \frac{1}{x2}\right)\right)\right)\right) \]

      8. distribute-neg-frac N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, x2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(8, \left(\frac{\mathsf{neg}\left(12\right)}{x2}\right)\right)\right), \left(\mathsf{neg}\left(6 \cdot \frac{1}{\color{blue}{x2}}\right)\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, x2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(8, \left(\frac{-12}{x2}\right)\right)\right), \left(\mathsf{neg}\left(6 \cdot \frac{1}{x2}\right)\right)\right)\right) \]

      10. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, x2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(8, \mathsf{/.f64}\left(-12, x2\right)\right)\right), \left(\mathsf{neg}\left(6 \cdot \frac{1}{\color{blue}{x2}}\right)\right)\right)\right) \]

      11. associate-*r/ N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, x2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(8, \mathsf{/.f64}\left(-12, x2\right)\right)\right), \left(\mathsf{neg}\left(\frac{6 \cdot 1}{x2}\right)\right)\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, x2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(8, \mathsf{/.f64}\left(-12, x2\right)\right)\right), \left(\mathsf{neg}\left(\frac{6}{x2}\right)\right)\right)\right) \]

      13. distribute-neg-frac N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, x2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(8, \mathsf{/.f64}\left(-12, x2\right)\right)\right), \left(\frac{\mathsf{neg}\left(6\right)}{\color{blue}{x2}}\right)\right)\right) \]

      14. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, x2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(8, \mathsf{/.f64}\left(-12, x2\right)\right)\right), \left(\frac{-6}{x2}\right)\right)\right) \]

      15. /-lowering-/.f64 57.9%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, x2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(8, \mathsf{/.f64}\left(-12, x2\right)\right)\right), \mathsf{/.f64}\left(-6, \color{blue}{x2}\right)\right)\right) \]

   10. Simplified 57.9%

       \[\leadsto \left(x2 \cdot x2\right) \cdot \color{blue}{\left(x1 \cdot \left(8 + \frac{-12}{x2}\right) + \frac{-6}{x2}\right)} \]

   11. Taylor expanded in x1 around inf

       \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, x2\right), \color{blue}{\left(x1 \cdot \left(8 - 12 \cdot \frac{1}{x2}\right)\right)}\right) \]
   12. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, x2\right), \mathsf{*.f64}\left(x1, \color{blue}{\left(8 - 12 \cdot \frac{1}{x2}\right)}\right)\right) \]

       2. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, x2\right), \mathsf{*.f64}\left(x1, \left(8 + \color{blue}{\left(\mathsf{neg}\left(12 \cdot \frac{1}{x2}\right)\right)}\right)\right)\right) \]

       3. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(8, \color{blue}{\left(\mathsf{neg}\left(12 \cdot \frac{1}{x2}\right)\right)}\right)\right)\right) \]

       4. associate-*r/ N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(8, \left(\mathsf{neg}\left(\frac{12 \cdot 1}{x2}\right)\right)\right)\right)\right) \]

       5. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(8, \left(\mathsf{neg}\left(\frac{12}{x2}\right)\right)\right)\right)\right) \]

       6. distribute-neg-frac N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(8, \left(\frac{\mathsf{neg}\left(12\right)}{\color{blue}{x2}}\right)\right)\right)\right) \]

       7. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(8, \left(\frac{-12}{x2}\right)\right)\right)\right) \]

       8. /-lowering-/.f64 47.9%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(8, \mathsf{/.f64}\left(-12, \color{blue}{x2}\right)\right)\right)\right) \]

   13. Simplified 47.9%

       \[\leadsto \left(x2 \cdot x2\right) \cdot \color{blue}{\left(x1 \cdot \left(8 + \frac{-12}{x2}\right)\right)} \]

   if -1.9999999999999998e-71 < x1 < 2.1e-113

   1. Initial program 99.5%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x1 around 0

      \[\leadsto \color{blue}{-6 \cdot x2} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 71.4%

         \[\leadsto \mathsf{*.f64}\left(-6, \color{blue}{x2}\right) \]

   5. Simplified 71.4%

      \[\leadsto \color{blue}{-6 \cdot x2} \]

   if 6.49999999999999998e58 < x1

   1. Initial program 44.1%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Simplified 44.1%

      \[\leadsto \color{blue}{\frac{3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right)}{x1 \cdot x1 + 1} + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(x1 \cdot \left(x1 \cdot -6\right) + \frac{2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)}{x1 \cdot x1 + 1} \cdot \left(x1 \cdot \left(-6 + \left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right) \cdot \frac{2}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot 4\right)\right) + x1 \cdot \left(2 + x1 \cdot \left(x1 + \left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right) \cdot \frac{3}{x1 \cdot x1 + 1}\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x1 around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \color{blue}{\left(x1 \cdot \left(2 + 2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)\right)\right)}\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \color{blue}{\left(2 + 2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)\right)}\right)\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \color{blue}{\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \color{blue}{\left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)}\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \color{blue}{\left(4 \cdot x2 - 6\right)}\right)\right)\right)\right)\right) \]

      5. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + \color{blue}{\left(\mathsf{neg}\left(6\right)\right)}\right)\right)\right)\right)\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + -6\right)\right)\right)\right)\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\left(4 \cdot x2\right), \color{blue}{-6}\right)\right)\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\left(x2 \cdot 4\right), -6\right)\right)\right)\right)\right)\right) \]

      9. *-lowering-*.f64 7.6%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right)\right)\right)\right)\right) \]

   7. Simplified 7.6%

      \[\leadsto \frac{3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right)}{x1 \cdot x1 + 1} + \color{blue}{x1 \cdot \left(2 + 2 \cdot \left(x2 \cdot \left(x2 \cdot 4 + -6\right)\right)\right)} \]

   8. Taylor expanded in x1 around 0

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)\right) - 1\right)} \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(-6 \cdot x2\right), \color{blue}{\left(x1 \cdot \left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)\right) - 1\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \left(\color{blue}{x1} \cdot \left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)\right) - 1\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \color{blue}{\left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)\right) - 1\right)}\right)\right) \]

      4. associate--l+ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + \color{blue}{\left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right) - 1\right)}\right)\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)\right), \color{blue}{\left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right) - 1\right)}\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)\right), \left(\color{blue}{x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)} - 1\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 - 6\right)\right)\right), \left(x1 \cdot \color{blue}{\left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)} - 1\right)\right)\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + \left(\mathsf{neg}\left(6\right)\right)\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + \color{blue}{3 \cdot \left(3 - -2 \cdot x2\right)}\right) - 1\right)\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + -6\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \color{blue}{\left(3 - -2 \cdot x2\right)}\right) - 1\right)\right)\right)\right) \]

      10. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\left(4 \cdot x2\right), -6\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + \color{blue}{3 \cdot \left(3 - -2 \cdot x2\right)}\right) - 1\right)\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, x2\right), -6\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + \color{blue}{3} \cdot \left(3 - -2 \cdot x2\right)\right) - 1\right)\right)\right)\right) \]

      12. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, x2\right), -6\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right) + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, x2\right), -6\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right) + -1\right)\right)\right)\right) \]

      14. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, x2\right), -6\right)\right)\right), \mathsf{+.f64}\left(\left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)\right), \color{blue}{-1}\right)\right)\right)\right) \]

   10. Simplified 76.1%

       \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 + -6\right)\right) + \left(x1 \cdot \left(3 \cdot \left(x1 + \left(3 + 2 \cdot x2\right)\right)\right) + -1\right)\right)} \]

   11. Taylor expanded in x1 around inf

       \[\leadsto \color{blue}{3 \cdot {x1}^{3}} \]
   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. *-commutative N/A

          \[\leadsto x1 \cdot \left(3 \cdot \color{blue}{{x1}^{2}}\right) \]

       6. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x1, \color{blue}{\left(3 \cdot {x1}^{2}\right)}\right) \]

       7. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(3, \color{blue}{\left({x1}^{2}\right)}\right)\right) \]

       8. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(3, \left(x1 \cdot \color{blue}{x1}\right)\right)\right) \]

       9. *-lowering-*.f64 81.8%

          \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(3, \mathsf{*.f64}\left(x1, \color{blue}{x1}\right)\right)\right) \]

   13. Simplified 81.8%

       \[\leadsto \color{blue}{x1 \cdot \left(3 \cdot \left(x1 \cdot x1\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -3.45 \cdot 10^{+90}:\\ \;\;\;\;x1 \cdot \left(-1 + x1 \cdot \left(9 + x1 \cdot -19\right)\right)\\ \mathbf{elif}\;x1 \leq -2 \cdot 10^{-71}:\\ \;\;\;\;\left(x1 \cdot \left(8 + \frac{-12}{x2}\right)\right) \cdot \left(x2 \cdot x2\right)\\ \mathbf{elif}\;x1 \leq 2.1 \cdot 10^{-113}:\\ \;\;\;\;x2 \cdot -6\\ \mathbf{elif}\;x1 \leq 6.5 \cdot 10^{+58}:\\ \;\;\;\;\left(x1 \cdot \left(8 + \frac{-12}{x2}\right)\right) \cdot \left(x2 \cdot x2\right)\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot \left(3 \cdot \left(x1 \cdot x1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 64.6% accurate, 4.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 8 \cdot \left(x1 \cdot \left(x2 \cdot x2\right)\right)\\ \mathbf{if}\;x1 \leq -2.9 \cdot 10^{+88}:\\ \;\;\;\;x1 \cdot \left(-1 + x1 \cdot \left(9 + x1 \cdot -19\right)\right)\\ \mathbf{elif}\;x1 \leq -2.55 \cdot 10^{-67}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x1 \leq 2.1 \cdot 10^{-113}:\\ \;\;\;\;x2 \cdot -6\\ \mathbf{elif}\;x1 \leq 2.2 \cdot 10^{+59}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot \left(3 \cdot \left(x1 \cdot x1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* 8.0 (* x1 (* x2 x2)))))
   (if (<= x1 -2.9e+88)
     (* x1 (+ -1.0 (* x1 (+ 9.0 (* x1 -19.0)))))
     (if (<= x1 -2.55e-67)
       t_0
       (if (<= x1 2.1e-113)
         (* x2 -6.0)
         (if (<= x1 2.2e+59) t_0 (* x1 (* 3.0 (* x1 x1)))))))))

C

double code(double x1, double x2) {
	double t_0 = 8.0 * (x1 * (x2 * x2));
	double tmp;
	if (x1 <= -2.9e+88) {
		tmp = x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0))));
	} else if (x1 <= -2.55e-67) {
		tmp = t_0;
	} else if (x1 <= 2.1e-113) {
		tmp = x2 * -6.0;
	} else if (x1 <= 2.2e+59) {
		tmp = t_0;
	} else {
		tmp = x1 * (3.0 * (x1 * x1));
	}
	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 <= (-2.9d+88)) then
        tmp = x1 * ((-1.0d0) + (x1 * (9.0d0 + (x1 * (-19.0d0)))))
    else if (x1 <= (-2.55d-67)) then
        tmp = t_0
    else if (x1 <= 2.1d-113) then
        tmp = x2 * (-6.0d0)
    else if (x1 <= 2.2d+59) then
        tmp = t_0
    else
        tmp = x1 * (3.0d0 * (x1 * x1))
    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 <= -2.9e+88) {
		tmp = x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0))));
	} else if (x1 <= -2.55e-67) {
		tmp = t_0;
	} else if (x1 <= 2.1e-113) {
		tmp = x2 * -6.0;
	} else if (x1 <= 2.2e+59) {
		tmp = t_0;
	} else {
		tmp = x1 * (3.0 * (x1 * x1));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = 8.0 * (x1 * (x2 * x2))
	tmp = 0
	if x1 <= -2.9e+88:
		tmp = x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0))))
	elif x1 <= -2.55e-67:
		tmp = t_0
	elif x1 <= 2.1e-113:
		tmp = x2 * -6.0
	elif x1 <= 2.2e+59:
		tmp = t_0
	else:
		tmp = x1 * (3.0 * (x1 * x1))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(8.0 * Float64(x1 * Float64(x2 * x2)))
	tmp = 0.0
	if (x1 <= -2.9e+88)
		tmp = Float64(x1 * Float64(-1.0 + Float64(x1 * Float64(9.0 + Float64(x1 * -19.0)))));
	elseif (x1 <= -2.55e-67)
		tmp = t_0;
	elseif (x1 <= 2.1e-113)
		tmp = Float64(x2 * -6.0);
	elseif (x1 <= 2.2e+59)
		tmp = t_0;
	else
		tmp = Float64(x1 * Float64(3.0 * Float64(x1 * x1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = 8.0 * (x1 * (x2 * x2));
	tmp = 0.0;
	if (x1 <= -2.9e+88)
		tmp = x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0))));
	elseif (x1 <= -2.55e-67)
		tmp = t_0;
	elseif (x1 <= 2.1e-113)
		tmp = x2 * -6.0;
	elseif (x1 <= 2.2e+59)
		tmp = t_0;
	else
		tmp = x1 * (3.0 * (x1 * x1));
	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, -2.9e+88], N[(x1 * N[(-1.0 + N[(x1 * N[(9.0 + N[(x1 * -19.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -2.55e-67], t$95$0, If[LessEqual[x1, 2.1e-113], N[(x2 * -6.0), $MachinePrecision], If[LessEqual[x1, 2.2e+59], t$95$0, N[(x1 * N[(3.0 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -2.9e88

   1. Initial program 5.6%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Simplified 5.6%

      \[\leadsto \color{blue}{\frac{3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right)}{x1 \cdot x1 + 1} + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(x1 \cdot \left(x1 \cdot -6\right) + \frac{2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)}{x1 \cdot x1 + 1} \cdot \left(x1 \cdot \left(-6 + \left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right) \cdot \frac{2}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot 4\right)\right) + x1 \cdot \left(2 + x1 \cdot \left(x1 + \left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right) \cdot \frac{3}{x1 \cdot x1 + 1}\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x1 around 0

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + x1 \cdot \left(\left(-1 \cdot \left(4 \cdot x2 - 6\right) + \left(3 \cdot \left(3 - -2 \cdot x2\right) + \left(4 \cdot x2 + \left(6 \cdot x2 + x1 \cdot \left(\left(3 \cdot \left(4 \cdot x2 - 6\right) + 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right) - 1\right)\right)\right)\right)\right) - 6\right)\right) - 1\right)} \]

   7. Simplified 77.8%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(2 \cdot \left(x2 \cdot \left(x2 \cdot 4 + -6\right)\right) + \left(x1 \cdot \left(\left(\left(\left(9 + 3 \cdot \left(x2 \cdot 2\right)\right) + \left(x2 \cdot 10 + x1 \cdot \left(\left(3 \cdot \left(x2 \cdot 4\right) + -18\right) + \left(4 \cdot \left(x2 \cdot \left(3 - x2 \cdot 2\right)\right) + -1\right)\right)\right)\right) - \left(x2 \cdot 4 + -6\right)\right) + -6\right) + -1\right)\right)} \]

   8. Taylor expanded in x2 around 0

      \[\leadsto \color{blue}{x1 \cdot \left(x1 \cdot \left(9 + -19 \cdot x1\right) - 1\right)} \]
   9. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x1, \color{blue}{\left(x1 \cdot \left(9 + -19 \cdot x1\right) - 1\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x1, \left(x1 \cdot \left(9 + -19 \cdot x1\right) + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right) \]

      3. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(x1, \left(x1 \cdot \left(9 + -19 \cdot x1\right) + -1\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\left(x1 \cdot \left(9 + -19 \cdot x1\right)\right), \color{blue}{-1}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \left(9 + -19 \cdot x1\right)\right), -1\right)\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(9, \left(-19 \cdot x1\right)\right)\right), -1\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(9, \left(x1 \cdot -19\right)\right)\right), -1\right)\right) \]

      8. *-lowering-*.f64 94.9%

         \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(9, \mathsf{*.f64}\left(x1, -19\right)\right)\right), -1\right)\right) \]

   10. Simplified 94.9%

       \[\leadsto \color{blue}{x1 \cdot \left(x1 \cdot \left(9 + x1 \cdot -19\right) + -1\right)} \]

   if -2.9e88 < x1 < -2.54999999999999991e-67 or 2.1e-113 < x1 < 2.2e59

   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 99.6%

      \[\leadsto \color{blue}{\frac{3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right)}{x1 \cdot x1 + 1} + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(x1 \cdot \left(x1 \cdot -6\right) + \frac{2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)}{x1 \cdot x1 + 1} \cdot \left(x1 \cdot \left(-6 + \left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right) \cdot \frac{2}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot 4\right)\right) + x1 \cdot \left(2 + x1 \cdot \left(x1 + \left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right) \cdot \frac{3}{x1 \cdot x1 + 1}\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x1 around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \color{blue}{\left(x1 \cdot \left(2 + 2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)\right)\right)}\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \color{blue}{\left(2 + 2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)\right)}\right)\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \color{blue}{\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \color{blue}{\left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)}\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \color{blue}{\left(4 \cdot x2 - 6\right)}\right)\right)\right)\right)\right) \]

      5. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + \color{blue}{\left(\mathsf{neg}\left(6\right)\right)}\right)\right)\right)\right)\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + -6\right)\right)\right)\right)\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\left(4 \cdot x2\right), \color{blue}{-6}\right)\right)\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\left(x2 \cdot 4\right), -6\right)\right)\right)\right)\right)\right) \]

      9. *-lowering-*.f64 71.5%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right)\right)\right)\right)\right) \]

   7. Simplified 71.5%

      \[\leadsto \frac{3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right)}{x1 \cdot x1 + 1} + \color{blue}{x1 \cdot \left(2 + 2 \cdot \left(x2 \cdot \left(x2 \cdot 4 + -6\right)\right)\right)} \]

   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 47.7%

         \[\leadsto \mathsf{*.f64}\left(8, \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x2, \color{blue}{x2}\right)\right)\right) \]

   10. Simplified 47.7%

       \[\leadsto \color{blue}{8 \cdot \left(x1 \cdot \left(x2 \cdot x2\right)\right)} \]

   if -2.54999999999999991e-67 < x1 < 2.1e-113

   1. Initial program 99.5%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x1 around 0

      \[\leadsto \color{blue}{-6 \cdot x2} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 71.4%

         \[\leadsto \mathsf{*.f64}\left(-6, \color{blue}{x2}\right) \]

   5. Simplified 71.4%

      \[\leadsto \color{blue}{-6 \cdot x2} \]

   if 2.2e59 < x1

   1. Initial program 44.1%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Simplified 44.1%

      \[\leadsto \color{blue}{\frac{3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right)}{x1 \cdot x1 + 1} + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(x1 \cdot \left(x1 \cdot -6\right) + \frac{2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)}{x1 \cdot x1 + 1} \cdot \left(x1 \cdot \left(-6 + \left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right) \cdot \frac{2}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot 4\right)\right) + x1 \cdot \left(2 + x1 \cdot \left(x1 + \left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right) \cdot \frac{3}{x1 \cdot x1 + 1}\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x1 around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \color{blue}{\left(x1 \cdot \left(2 + 2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)\right)\right)}\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \color{blue}{\left(2 + 2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)\right)}\right)\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \color{blue}{\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \color{blue}{\left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)}\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \color{blue}{\left(4 \cdot x2 - 6\right)}\right)\right)\right)\right)\right) \]

      5. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + \color{blue}{\left(\mathsf{neg}\left(6\right)\right)}\right)\right)\right)\right)\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + -6\right)\right)\right)\right)\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\left(4 \cdot x2\right), \color{blue}{-6}\right)\right)\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\left(x2 \cdot 4\right), -6\right)\right)\right)\right)\right)\right) \]

      9. *-lowering-*.f64 7.6%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right)\right)\right)\right)\right) \]

   7. Simplified 7.6%

      \[\leadsto \frac{3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right)}{x1 \cdot x1 + 1} + \color{blue}{x1 \cdot \left(2 + 2 \cdot \left(x2 \cdot \left(x2 \cdot 4 + -6\right)\right)\right)} \]

   8. Taylor expanded in x1 around 0

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)\right) - 1\right)} \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(-6 \cdot x2\right), \color{blue}{\left(x1 \cdot \left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)\right) - 1\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \left(\color{blue}{x1} \cdot \left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)\right) - 1\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \color{blue}{\left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)\right) - 1\right)}\right)\right) \]

      4. associate--l+ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + \color{blue}{\left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right) - 1\right)}\right)\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)\right), \color{blue}{\left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right) - 1\right)}\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)\right), \left(\color{blue}{x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)} - 1\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 - 6\right)\right)\right), \left(x1 \cdot \color{blue}{\left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)} - 1\right)\right)\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + \left(\mathsf{neg}\left(6\right)\right)\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + \color{blue}{3 \cdot \left(3 - -2 \cdot x2\right)}\right) - 1\right)\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + -6\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \color{blue}{\left(3 - -2 \cdot x2\right)}\right) - 1\right)\right)\right)\right) \]

      10. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\left(4 \cdot x2\right), -6\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + \color{blue}{3 \cdot \left(3 - -2 \cdot x2\right)}\right) - 1\right)\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, x2\right), -6\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + \color{blue}{3} \cdot \left(3 - -2 \cdot x2\right)\right) - 1\right)\right)\right)\right) \]

      12. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, x2\right), -6\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right) + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, x2\right), -6\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right) + -1\right)\right)\right)\right) \]

      14. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, x2\right), -6\right)\right)\right), \mathsf{+.f64}\left(\left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)\right), \color{blue}{-1}\right)\right)\right)\right) \]

   10. Simplified 76.1%

       \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 + -6\right)\right) + \left(x1 \cdot \left(3 \cdot \left(x1 + \left(3 + 2 \cdot x2\right)\right)\right) + -1\right)\right)} \]

   11. Taylor expanded in x1 around inf

       \[\leadsto \color{blue}{3 \cdot {x1}^{3}} \]
   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. *-commutative N/A

          \[\leadsto x1 \cdot \left(3 \cdot \color{blue}{{x1}^{2}}\right) \]

       6. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x1, \color{blue}{\left(3 \cdot {x1}^{2}\right)}\right) \]

       7. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(3, \color{blue}{\left({x1}^{2}\right)}\right)\right) \]

       8. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(3, \left(x1 \cdot \color{blue}{x1}\right)\right)\right) \]

       9. *-lowering-*.f64 81.8%

          \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(3, \mathsf{*.f64}\left(x1, \color{blue}{x1}\right)\right)\right) \]

   13. Simplified 81.8%

       \[\leadsto \color{blue}{x1 \cdot \left(3 \cdot \left(x1 \cdot x1\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 69.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -2.9 \cdot 10^{+88}:\\ \;\;\;\;x1 \cdot \left(-1 + x1 \cdot \left(9 + x1 \cdot -19\right)\right)\\ \mathbf{elif}\;x1 \leq -2.55 \cdot 10^{-67}:\\ \;\;\;\;8 \cdot \left(x1 \cdot \left(x2 \cdot x2\right)\right)\\ \mathbf{elif}\;x1 \leq 2.1 \cdot 10^{-113}:\\ \;\;\;\;x2 \cdot -6\\ \mathbf{elif}\;x1 \leq 2.2 \cdot 10^{+59}:\\ \;\;\;\;8 \cdot \left(x1 \cdot \left(x2 \cdot x2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot \left(3 \cdot \left(x1 \cdot x1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 60.9% accurate, 4.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 8 \cdot \left(x1 \cdot \left(x2 \cdot x2\right)\right)\\ \mathbf{if}\;x1 \leq -3.8 \cdot 10^{+90}:\\ \;\;\;\;x1 \cdot \left(-1 + x1 \cdot 9\right)\\ \mathbf{elif}\;x1 \leq -3.4 \cdot 10^{-69}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x1 \leq 2.6 \cdot 10^{-113}:\\ \;\;\;\;x2 \cdot -6\\ \mathbf{elif}\;x1 \leq 2.2 \cdot 10^{+59}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot \left(3 \cdot \left(x1 \cdot x1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* 8.0 (* x1 (* x2 x2)))))
   (if (<= x1 -3.8e+90)
     (* x1 (+ -1.0 (* x1 9.0)))
     (if (<= x1 -3.4e-69)
       t_0
       (if (<= x1 2.6e-113)
         (* x2 -6.0)
         (if (<= x1 2.2e+59) t_0 (* x1 (* 3.0 (* x1 x1)))))))))

C

double code(double x1, double x2) {
	double t_0 = 8.0 * (x1 * (x2 * x2));
	double tmp;
	if (x1 <= -3.8e+90) {
		tmp = x1 * (-1.0 + (x1 * 9.0));
	} else if (x1 <= -3.4e-69) {
		tmp = t_0;
	} else if (x1 <= 2.6e-113) {
		tmp = x2 * -6.0;
	} else if (x1 <= 2.2e+59) {
		tmp = t_0;
	} else {
		tmp = x1 * (3.0 * (x1 * x1));
	}
	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 <= (-3.8d+90)) then
        tmp = x1 * ((-1.0d0) + (x1 * 9.0d0))
    else if (x1 <= (-3.4d-69)) then
        tmp = t_0
    else if (x1 <= 2.6d-113) then
        tmp = x2 * (-6.0d0)
    else if (x1 <= 2.2d+59) then
        tmp = t_0
    else
        tmp = x1 * (3.0d0 * (x1 * x1))
    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 <= -3.8e+90) {
		tmp = x1 * (-1.0 + (x1 * 9.0));
	} else if (x1 <= -3.4e-69) {
		tmp = t_0;
	} else if (x1 <= 2.6e-113) {
		tmp = x2 * -6.0;
	} else if (x1 <= 2.2e+59) {
		tmp = t_0;
	} else {
		tmp = x1 * (3.0 * (x1 * x1));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = 8.0 * (x1 * (x2 * x2))
	tmp = 0
	if x1 <= -3.8e+90:
		tmp = x1 * (-1.0 + (x1 * 9.0))
	elif x1 <= -3.4e-69:
		tmp = t_0
	elif x1 <= 2.6e-113:
		tmp = x2 * -6.0
	elif x1 <= 2.2e+59:
		tmp = t_0
	else:
		tmp = x1 * (3.0 * (x1 * x1))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(8.0 * Float64(x1 * Float64(x2 * x2)))
	tmp = 0.0
	if (x1 <= -3.8e+90)
		tmp = Float64(x1 * Float64(-1.0 + Float64(x1 * 9.0)));
	elseif (x1 <= -3.4e-69)
		tmp = t_0;
	elseif (x1 <= 2.6e-113)
		tmp = Float64(x2 * -6.0);
	elseif (x1 <= 2.2e+59)
		tmp = t_0;
	else
		tmp = Float64(x1 * Float64(3.0 * Float64(x1 * x1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = 8.0 * (x1 * (x2 * x2));
	tmp = 0.0;
	if (x1 <= -3.8e+90)
		tmp = x1 * (-1.0 + (x1 * 9.0));
	elseif (x1 <= -3.4e-69)
		tmp = t_0;
	elseif (x1 <= 2.6e-113)
		tmp = x2 * -6.0;
	elseif (x1 <= 2.2e+59)
		tmp = t_0;
	else
		tmp = x1 * (3.0 * (x1 * x1));
	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, -3.8e+90], N[(x1 * N[(-1.0 + N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -3.4e-69], t$95$0, If[LessEqual[x1, 2.6e-113], N[(x2 * -6.0), $MachinePrecision], If[LessEqual[x1, 2.2e+59], t$95$0, N[(x1 * N[(3.0 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -3.8000000000000001e90

   1. Initial program 5.6%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Simplified 5.6%

      \[\leadsto \color{blue}{\frac{3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right)}{x1 \cdot x1 + 1} + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(x1 \cdot \left(x1 \cdot -6\right) + \frac{2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)}{x1 \cdot x1 + 1} \cdot \left(x1 \cdot \left(-6 + \left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right) \cdot \frac{2}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot 4\right)\right) + x1 \cdot \left(2 + x1 \cdot \left(x1 + \left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right) \cdot \frac{3}{x1 \cdot x1 + 1}\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x1 around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \color{blue}{\left(x1 \cdot \left(2 + 2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)\right)\right)}\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \color{blue}{\left(2 + 2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)\right)}\right)\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \color{blue}{\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \color{blue}{\left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)}\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \color{blue}{\left(4 \cdot x2 - 6\right)}\right)\right)\right)\right)\right) \]

      5. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + \color{blue}{\left(\mathsf{neg}\left(6\right)\right)}\right)\right)\right)\right)\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + -6\right)\right)\right)\right)\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\left(4 \cdot x2\right), \color{blue}{-6}\right)\right)\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\left(x2 \cdot 4\right), -6\right)\right)\right)\right)\right)\right) \]

      9. *-lowering-*.f64 0.0%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right)\right)\right)\right)\right) \]

   7. Simplified 0.0%

      \[\leadsto \frac{3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right)}{x1 \cdot x1 + 1} + \color{blue}{x1 \cdot \left(2 + 2 \cdot \left(x2 \cdot \left(x2 \cdot 4 + -6\right)\right)\right)} \]

   8. Taylor expanded in x1 around 0

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + 3 \cdot \left(x1 \cdot \left(3 - -2 \cdot x2\right)\right)\right) - 1\right)} \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(-6 \cdot x2\right), \color{blue}{\left(x1 \cdot \left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + 3 \cdot \left(x1 \cdot \left(3 - -2 \cdot x2\right)\right)\right) - 1\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \left(\color{blue}{x1} \cdot \left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + 3 \cdot \left(x1 \cdot \left(3 - -2 \cdot x2\right)\right)\right) - 1\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \color{blue}{\left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + 3 \cdot \left(x1 \cdot \left(3 - -2 \cdot x2\right)\right)\right) - 1\right)}\right)\right) \]

      4. associate--l+ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + \color{blue}{\left(3 \cdot \left(x1 \cdot \left(3 - -2 \cdot x2\right)\right) - 1\right)}\right)\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)\right), \color{blue}{\left(3 \cdot \left(x1 \cdot \left(3 - -2 \cdot x2\right)\right) - 1\right)}\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)\right), \left(\color{blue}{3 \cdot \left(x1 \cdot \left(3 - -2 \cdot x2\right)\right)} - 1\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 - 6\right)\right)\right), \left(3 \cdot \color{blue}{\left(x1 \cdot \left(3 - -2 \cdot x2\right)\right)} - 1\right)\right)\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + \left(\mathsf{neg}\left(6\right)\right)\right)\right)\right), \left(3 \cdot \left(x1 \cdot \color{blue}{\left(3 - -2 \cdot x2\right)}\right) - 1\right)\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + -6\right)\right)\right), \left(3 \cdot \left(x1 \cdot \left(3 - \color{blue}{-2 \cdot x2}\right)\right) - 1\right)\right)\right)\right) \]

      10. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\left(4 \cdot x2\right), -6\right)\right)\right), \left(3 \cdot \left(x1 \cdot \color{blue}{\left(3 - -2 \cdot x2\right)}\right) - 1\right)\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, x2\right), -6\right)\right)\right), \left(3 \cdot \left(x1 \cdot \left(\color{blue}{3} - -2 \cdot x2\right)\right) - 1\right)\right)\right)\right) \]

      12. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, x2\right), -6\right)\right)\right), \left(3 \cdot \left(x1 \cdot \left(3 - -2 \cdot x2\right)\right) + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, x2\right), -6\right)\right)\right), \left(3 \cdot \left(x1 \cdot \left(3 - -2 \cdot x2\right)\right) + -1\right)\right)\right)\right) \]

      14. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, x2\right), -6\right)\right)\right), \mathsf{+.f64}\left(\left(3 \cdot \left(x1 \cdot \left(3 - -2 \cdot x2\right)\right)\right), \color{blue}{-1}\right)\right)\right)\right) \]

   10. Simplified 51.8%

       \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 + -6\right)\right) + \left(3 \cdot \left(x1 \cdot \left(3 + 2 \cdot x2\right)\right) + -1\right)\right)} \]

   11. Taylor expanded in x2 around 0

       \[\leadsto \color{blue}{x1 \cdot \left(9 \cdot x1 - 1\right)} \]
   12. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x1, \color{blue}{\left(9 \cdot x1 - 1\right)}\right) \]

       2. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(x1, \left(9 \cdot x1 + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right) \]

       3. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(x1, \left(9 \cdot x1 + -1\right)\right) \]

       4. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\left(9 \cdot x1\right), \color{blue}{-1}\right)\right) \]

       5. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\left(x1 \cdot 9\right), -1\right)\right) \]

       6. *-lowering-*.f64 69.2%

          \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 9\right), -1\right)\right) \]

   13. Simplified 69.2%

       \[\leadsto \color{blue}{x1 \cdot \left(x1 \cdot 9 + -1\right)} \]

   if -3.8000000000000001e90 < x1 < -3.40000000000000008e-69 or 2.5999999999999999e-113 < x1 < 2.2e59

   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 99.6%

      \[\leadsto \color{blue}{\frac{3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right)}{x1 \cdot x1 + 1} + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(x1 \cdot \left(x1 \cdot -6\right) + \frac{2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)}{x1 \cdot x1 + 1} \cdot \left(x1 \cdot \left(-6 + \left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right) \cdot \frac{2}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot 4\right)\right) + x1 \cdot \left(2 + x1 \cdot \left(x1 + \left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right) \cdot \frac{3}{x1 \cdot x1 + 1}\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x1 around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \color{blue}{\left(x1 \cdot \left(2 + 2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)\right)\right)}\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \color{blue}{\left(2 + 2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)\right)}\right)\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \color{blue}{\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \color{blue}{\left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)}\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \color{blue}{\left(4 \cdot x2 - 6\right)}\right)\right)\right)\right)\right) \]

      5. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + \color{blue}{\left(\mathsf{neg}\left(6\right)\right)}\right)\right)\right)\right)\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + -6\right)\right)\right)\right)\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\left(4 \cdot x2\right), \color{blue}{-6}\right)\right)\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\left(x2 \cdot 4\right), -6\right)\right)\right)\right)\right)\right) \]

      9. *-lowering-*.f64 71.5%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right)\right)\right)\right)\right) \]

   7. Simplified 71.5%

      \[\leadsto \frac{3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right)}{x1 \cdot x1 + 1} + \color{blue}{x1 \cdot \left(2 + 2 \cdot \left(x2 \cdot \left(x2 \cdot 4 + -6\right)\right)\right)} \]

   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 47.7%

         \[\leadsto \mathsf{*.f64}\left(8, \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x2, \color{blue}{x2}\right)\right)\right) \]

   10. Simplified 47.7%

       \[\leadsto \color{blue}{8 \cdot \left(x1 \cdot \left(x2 \cdot x2\right)\right)} \]

   if -3.40000000000000008e-69 < x1 < 2.5999999999999999e-113

   1. Initial program 99.5%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x1 around 0

      \[\leadsto \color{blue}{-6 \cdot x2} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 71.4%

         \[\leadsto \mathsf{*.f64}\left(-6, \color{blue}{x2}\right) \]

   5. Simplified 71.4%

      \[\leadsto \color{blue}{-6 \cdot x2} \]

   if 2.2e59 < x1

   1. Initial program 44.1%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Simplified 44.1%

      \[\leadsto \color{blue}{\frac{3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right)}{x1 \cdot x1 + 1} + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(x1 \cdot \left(x1 \cdot -6\right) + \frac{2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)}{x1 \cdot x1 + 1} \cdot \left(x1 \cdot \left(-6 + \left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right) \cdot \frac{2}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot 4\right)\right) + x1 \cdot \left(2 + x1 \cdot \left(x1 + \left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right) \cdot \frac{3}{x1 \cdot x1 + 1}\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x1 around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \color{blue}{\left(x1 \cdot \left(2 + 2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)\right)\right)}\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \color{blue}{\left(2 + 2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)\right)}\right)\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \color{blue}{\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \color{blue}{\left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)}\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \color{blue}{\left(4 \cdot x2 - 6\right)}\right)\right)\right)\right)\right) \]

      5. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + \color{blue}{\left(\mathsf{neg}\left(6\right)\right)}\right)\right)\right)\right)\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + -6\right)\right)\right)\right)\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\left(4 \cdot x2\right), \color{blue}{-6}\right)\right)\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\left(x2 \cdot 4\right), -6\right)\right)\right)\right)\right)\right) \]

      9. *-lowering-*.f64 7.6%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right)\right)\right)\right)\right) \]

   7. Simplified 7.6%

      \[\leadsto \frac{3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right)}{x1 \cdot x1 + 1} + \color{blue}{x1 \cdot \left(2 + 2 \cdot \left(x2 \cdot \left(x2 \cdot 4 + -6\right)\right)\right)} \]

   8. Taylor expanded in x1 around 0

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)\right) - 1\right)} \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(-6 \cdot x2\right), \color{blue}{\left(x1 \cdot \left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)\right) - 1\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \left(\color{blue}{x1} \cdot \left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)\right) - 1\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \color{blue}{\left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)\right) - 1\right)}\right)\right) \]

      4. associate--l+ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + \color{blue}{\left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right) - 1\right)}\right)\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)\right), \color{blue}{\left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right) - 1\right)}\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)\right), \left(\color{blue}{x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)} - 1\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 - 6\right)\right)\right), \left(x1 \cdot \color{blue}{\left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)} - 1\right)\right)\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + \left(\mathsf{neg}\left(6\right)\right)\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + \color{blue}{3 \cdot \left(3 - -2 \cdot x2\right)}\right) - 1\right)\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + -6\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \color{blue}{\left(3 - -2 \cdot x2\right)}\right) - 1\right)\right)\right)\right) \]

      10. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\left(4 \cdot x2\right), -6\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + \color{blue}{3 \cdot \left(3 - -2 \cdot x2\right)}\right) - 1\right)\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, x2\right), -6\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + \color{blue}{3} \cdot \left(3 - -2 \cdot x2\right)\right) - 1\right)\right)\right)\right) \]

      12. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, x2\right), -6\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right) + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, x2\right), -6\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right) + -1\right)\right)\right)\right) \]

      14. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, x2\right), -6\right)\right)\right), \mathsf{+.f64}\left(\left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)\right), \color{blue}{-1}\right)\right)\right)\right) \]

   10. Simplified 76.1%

       \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 + -6\right)\right) + \left(x1 \cdot \left(3 \cdot \left(x1 + \left(3 + 2 \cdot x2\right)\right)\right) + -1\right)\right)} \]

   11. Taylor expanded in x1 around inf

       \[\leadsto \color{blue}{3 \cdot {x1}^{3}} \]
   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. *-commutative N/A

          \[\leadsto x1 \cdot \left(3 \cdot \color{blue}{{x1}^{2}}\right) \]

       6. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x1, \color{blue}{\left(3 \cdot {x1}^{2}\right)}\right) \]

       7. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(3, \color{blue}{\left({x1}^{2}\right)}\right)\right) \]

       8. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(3, \left(x1 \cdot \color{blue}{x1}\right)\right)\right) \]

       9. *-lowering-*.f64 81.8%

          \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(3, \mathsf{*.f64}\left(x1, \color{blue}{x1}\right)\right)\right) \]

   13. Simplified 81.8%

       \[\leadsto \color{blue}{x1 \cdot \left(3 \cdot \left(x1 \cdot x1\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 66.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -3.8 \cdot 10^{+90}:\\ \;\;\;\;x1 \cdot \left(-1 + x1 \cdot 9\right)\\ \mathbf{elif}\;x1 \leq -3.4 \cdot 10^{-69}:\\ \;\;\;\;8 \cdot \left(x1 \cdot \left(x2 \cdot x2\right)\right)\\ \mathbf{elif}\;x1 \leq 2.6 \cdot 10^{-113}:\\ \;\;\;\;x2 \cdot -6\\ \mathbf{elif}\;x1 \leq 2.2 \cdot 10^{+59}:\\ \;\;\;\;8 \cdot \left(x1 \cdot \left(x2 \cdot x2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot \left(3 \cdot \left(x1 \cdot x1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 55.8% accurate, 4.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 8 \cdot \left(x1 \cdot \left(x2 \cdot x2\right)\right)\\ \mathbf{if}\;x1 \leq -3.1 \cdot 10^{+38}:\\ \;\;\;\;8 \cdot \left(x2 \cdot \left(x1 \cdot x1\right)\right)\\ \mathbf{elif}\;x1 \leq -9.5 \cdot 10^{-70}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x1 \leq 4.9 \cdot 10^{-113}:\\ \;\;\;\;x2 \cdot -6\\ \mathbf{elif}\;x1 \leq 2.1 \cdot 10^{+59}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot \left(3 \cdot \left(x1 \cdot x1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* 8.0 (* x1 (* x2 x2)))))
   (if (<= x1 -3.1e+38)
     (* 8.0 (* x2 (* x1 x1)))
     (if (<= x1 -9.5e-70)
       t_0
       (if (<= x1 4.9e-113)
         (* x2 -6.0)
         (if (<= x1 2.1e+59) t_0 (* x1 (* 3.0 (* x1 x1)))))))))

C

double code(double x1, double x2) {
	double t_0 = 8.0 * (x1 * (x2 * x2));
	double tmp;
	if (x1 <= -3.1e+38) {
		tmp = 8.0 * (x2 * (x1 * x1));
	} else if (x1 <= -9.5e-70) {
		tmp = t_0;
	} else if (x1 <= 4.9e-113) {
		tmp = x2 * -6.0;
	} else if (x1 <= 2.1e+59) {
		tmp = t_0;
	} else {
		tmp = x1 * (3.0 * (x1 * x1));
	}
	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 <= (-3.1d+38)) then
        tmp = 8.0d0 * (x2 * (x1 * x1))
    else if (x1 <= (-9.5d-70)) then
        tmp = t_0
    else if (x1 <= 4.9d-113) then
        tmp = x2 * (-6.0d0)
    else if (x1 <= 2.1d+59) then
        tmp = t_0
    else
        tmp = x1 * (3.0d0 * (x1 * x1))
    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 <= -3.1e+38) {
		tmp = 8.0 * (x2 * (x1 * x1));
	} else if (x1 <= -9.5e-70) {
		tmp = t_0;
	} else if (x1 <= 4.9e-113) {
		tmp = x2 * -6.0;
	} else if (x1 <= 2.1e+59) {
		tmp = t_0;
	} else {
		tmp = x1 * (3.0 * (x1 * x1));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = 8.0 * (x1 * (x2 * x2))
	tmp = 0
	if x1 <= -3.1e+38:
		tmp = 8.0 * (x2 * (x1 * x1))
	elif x1 <= -9.5e-70:
		tmp = t_0
	elif x1 <= 4.9e-113:
		tmp = x2 * -6.0
	elif x1 <= 2.1e+59:
		tmp = t_0
	else:
		tmp = x1 * (3.0 * (x1 * x1))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(8.0 * Float64(x1 * Float64(x2 * x2)))
	tmp = 0.0
	if (x1 <= -3.1e+38)
		tmp = Float64(8.0 * Float64(x2 * Float64(x1 * x1)));
	elseif (x1 <= -9.5e-70)
		tmp = t_0;
	elseif (x1 <= 4.9e-113)
		tmp = Float64(x2 * -6.0);
	elseif (x1 <= 2.1e+59)
		tmp = t_0;
	else
		tmp = Float64(x1 * Float64(3.0 * Float64(x1 * x1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = 8.0 * (x1 * (x2 * x2));
	tmp = 0.0;
	if (x1 <= -3.1e+38)
		tmp = 8.0 * (x2 * (x1 * x1));
	elseif (x1 <= -9.5e-70)
		tmp = t_0;
	elseif (x1 <= 4.9e-113)
		tmp = x2 * -6.0;
	elseif (x1 <= 2.1e+59)
		tmp = t_0;
	else
		tmp = x1 * (3.0 * (x1 * x1));
	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, -3.1e+38], N[(8.0 * N[(x2 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -9.5e-70], t$95$0, If[LessEqual[x1, 4.9e-113], N[(x2 * -6.0), $MachinePrecision], If[LessEqual[x1, 2.1e+59], t$95$0, N[(x1 * N[(3.0 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -3.10000000000000018e38

   1. Initial program 35.7%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Simplified 35.8%

      \[\leadsto \color{blue}{\frac{3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right)}{x1 \cdot x1 + 1} + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(x1 \cdot \left(x1 \cdot -6\right) + \frac{2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)}{x1 \cdot x1 + 1} \cdot \left(x1 \cdot \left(-6 + \left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right) \cdot \frac{2}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot 4\right)\right) + x1 \cdot \left(2 + x1 \cdot \left(x1 + \left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right) \cdot \frac{3}{x1 \cdot x1 + 1}\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x2 around -inf

      \[\leadsto \color{blue}{{x2}^{2} \cdot \left(-1 \cdot \frac{-6 \cdot \frac{{x1}^{2}}{1 + {x1}^{2}} + \left(6 \cdot \frac{1}{1 + {x1}^{2}} + \left(1 + {x1}^{2}\right) \cdot \left(-4 \cdot \frac{{x1}^{2} \cdot \left(3 \cdot x1 - 1\right)}{{\left(1 + {x1}^{2}\right)}^{2}} + -2 \cdot \frac{4 \cdot {x1}^{2} + x1 \cdot \left(2 \cdot \frac{x1 \cdot \left(3 \cdot x1 - 1\right)}{1 + {x1}^{2}} - 6\right)}{1 + {x1}^{2}}\right)\right)}{x2} + 8 \cdot \frac{x1}{1 + {x1}^{2}}\right)} \]

   7. Simplified 9.9%

      \[\leadsto \color{blue}{\left(x2 \cdot x2\right) \cdot \left(\frac{8 \cdot x1}{1 + x1 \cdot x1} - \frac{\frac{-6 \cdot \left(x1 \cdot x1\right)}{1 + x1 \cdot x1} + \left(\frac{6}{1 + x1 \cdot x1} + \left(1 + x1 \cdot x1\right) \cdot \left(\frac{-4 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot 3 + -1\right)\right)}{\left(1 + x1 \cdot x1\right) \cdot \left(1 + x1 \cdot x1\right)} + \frac{-2 \cdot \left(4 \cdot \left(x1 \cdot x1\right) + x1 \cdot \left(\frac{2 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)}{1 + x1 \cdot x1} + -6\right)\right)}{1 + x1 \cdot x1}\right)\right)}{x2}\right)} \]

   8. Taylor expanded in x1 around inf

      \[\leadsto \color{blue}{8 \cdot \left({x1}^{2} \cdot x2\right)} \]
   9. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(8, \color{blue}{\left({x1}^{2} \cdot x2\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(8, \mathsf{*.f64}\left(\left({x1}^{2}\right), \color{blue}{x2}\right)\right) \]

      3. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(8, \mathsf{*.f64}\left(\left(x1 \cdot x1\right), x2\right)\right) \]

      4. *-lowering-*.f64 41.1%

         \[\leadsto \mathsf{*.f64}\left(8, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), x2\right)\right) \]

   10. Simplified 41.1%

       \[\leadsto \color{blue}{8 \cdot \left(\left(x1 \cdot x1\right) \cdot x2\right)} \]

   if -3.10000000000000018e38 < x1 < -9.4999999999999994e-70 or 4.9000000000000003e-113 < x1 < 2.09999999999999984e59

   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 99.5%

      \[\leadsto \color{blue}{\frac{3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right)}{x1 \cdot x1 + 1} + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(x1 \cdot \left(x1 \cdot -6\right) + \frac{2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)}{x1 \cdot x1 + 1} \cdot \left(x1 \cdot \left(-6 + \left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right) \cdot \frac{2}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot 4\right)\right) + x1 \cdot \left(2 + x1 \cdot \left(x1 + \left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right) \cdot \frac{3}{x1 \cdot x1 + 1}\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x1 around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \color{blue}{\left(x1 \cdot \left(2 + 2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)\right)\right)}\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \color{blue}{\left(2 + 2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)\right)}\right)\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \color{blue}{\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \color{blue}{\left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)}\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \color{blue}{\left(4 \cdot x2 - 6\right)}\right)\right)\right)\right)\right) \]

      5. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + \color{blue}{\left(\mathsf{neg}\left(6\right)\right)}\right)\right)\right)\right)\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + -6\right)\right)\right)\right)\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\left(4 \cdot x2\right), \color{blue}{-6}\right)\right)\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\left(x2 \cdot 4\right), -6\right)\right)\right)\right)\right)\right) \]

      9. *-lowering-*.f64 83.5%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right)\right)\right)\right)\right) \]

   7. Simplified 83.5%

      \[\leadsto \frac{3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right)}{x1 \cdot x1 + 1} + \color{blue}{x1 \cdot \left(2 + 2 \cdot \left(x2 \cdot \left(x2 \cdot 4 + -6\right)\right)\right)} \]

   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 52.8%

         \[\leadsto \mathsf{*.f64}\left(8, \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x2, \color{blue}{x2}\right)\right)\right) \]

   10. Simplified 52.8%

       \[\leadsto \color{blue}{8 \cdot \left(x1 \cdot \left(x2 \cdot x2\right)\right)} \]

   if -9.4999999999999994e-70 < x1 < 4.9000000000000003e-113

   1. Initial program 99.5%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x1 around 0

      \[\leadsto \color{blue}{-6 \cdot x2} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 71.4%

         \[\leadsto \mathsf{*.f64}\left(-6, \color{blue}{x2}\right) \]

   5. Simplified 71.4%

      \[\leadsto \color{blue}{-6 \cdot x2} \]

   if 2.09999999999999984e59 < x1

   1. Initial program 44.1%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Simplified 44.1%

      \[\leadsto \color{blue}{\frac{3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right)}{x1 \cdot x1 + 1} + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(x1 \cdot \left(x1 \cdot -6\right) + \frac{2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)}{x1 \cdot x1 + 1} \cdot \left(x1 \cdot \left(-6 + \left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right) \cdot \frac{2}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot 4\right)\right) + x1 \cdot \left(2 + x1 \cdot \left(x1 + \left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right) \cdot \frac{3}{x1 \cdot x1 + 1}\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x1 around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \color{blue}{\left(x1 \cdot \left(2 + 2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)\right)\right)}\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \color{blue}{\left(2 + 2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)\right)}\right)\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \color{blue}{\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \color{blue}{\left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)}\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \color{blue}{\left(4 \cdot x2 - 6\right)}\right)\right)\right)\right)\right) \]

      5. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + \color{blue}{\left(\mathsf{neg}\left(6\right)\right)}\right)\right)\right)\right)\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + -6\right)\right)\right)\right)\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\left(4 \cdot x2\right), \color{blue}{-6}\right)\right)\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\left(x2 \cdot 4\right), -6\right)\right)\right)\right)\right)\right) \]

      9. *-lowering-*.f64 7.6%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right)\right)\right)\right)\right) \]

   7. Simplified 7.6%

      \[\leadsto \frac{3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right)}{x1 \cdot x1 + 1} + \color{blue}{x1 \cdot \left(2 + 2 \cdot \left(x2 \cdot \left(x2 \cdot 4 + -6\right)\right)\right)} \]

   8. Taylor expanded in x1 around 0

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)\right) - 1\right)} \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(-6 \cdot x2\right), \color{blue}{\left(x1 \cdot \left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)\right) - 1\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \left(\color{blue}{x1} \cdot \left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)\right) - 1\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \color{blue}{\left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)\right) - 1\right)}\right)\right) \]

      4. associate--l+ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + \color{blue}{\left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right) - 1\right)}\right)\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)\right), \color{blue}{\left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right) - 1\right)}\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)\right), \left(\color{blue}{x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)} - 1\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 - 6\right)\right)\right), \left(x1 \cdot \color{blue}{\left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)} - 1\right)\right)\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + \left(\mathsf{neg}\left(6\right)\right)\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + \color{blue}{3 \cdot \left(3 - -2 \cdot x2\right)}\right) - 1\right)\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + -6\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \color{blue}{\left(3 - -2 \cdot x2\right)}\right) - 1\right)\right)\right)\right) \]

      10. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\left(4 \cdot x2\right), -6\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + \color{blue}{3 \cdot \left(3 - -2 \cdot x2\right)}\right) - 1\right)\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, x2\right), -6\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + \color{blue}{3} \cdot \left(3 - -2 \cdot x2\right)\right) - 1\right)\right)\right)\right) \]

      12. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, x2\right), -6\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right) + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, x2\right), -6\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right) + -1\right)\right)\right)\right) \]

      14. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, x2\right), -6\right)\right)\right), \mathsf{+.f64}\left(\left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)\right), \color{blue}{-1}\right)\right)\right)\right) \]

   10. Simplified 76.1%

       \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 + -6\right)\right) + \left(x1 \cdot \left(3 \cdot \left(x1 + \left(3 + 2 \cdot x2\right)\right)\right) + -1\right)\right)} \]

   11. Taylor expanded in x1 around inf

       \[\leadsto \color{blue}{3 \cdot {x1}^{3}} \]
   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. *-commutative N/A

          \[\leadsto x1 \cdot \left(3 \cdot \color{blue}{{x1}^{2}}\right) \]

       6. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x1, \color{blue}{\left(3 \cdot {x1}^{2}\right)}\right) \]

       7. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(3, \color{blue}{\left({x1}^{2}\right)}\right)\right) \]

       8. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(3, \left(x1 \cdot \color{blue}{x1}\right)\right)\right) \]

       9. *-lowering-*.f64 81.8%

          \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(3, \mathsf{*.f64}\left(x1, \color{blue}{x1}\right)\right)\right) \]

   13. Simplified 81.8%

       \[\leadsto \color{blue}{x1 \cdot \left(3 \cdot \left(x1 \cdot x1\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -3.1 \cdot 10^{+38}:\\ \;\;\;\;8 \cdot \left(x2 \cdot \left(x1 \cdot x1\right)\right)\\ \mathbf{elif}\;x1 \leq -9.5 \cdot 10^{-70}:\\ \;\;\;\;8 \cdot \left(x1 \cdot \left(x2 \cdot x2\right)\right)\\ \mathbf{elif}\;x1 \leq 4.9 \cdot 10^{-113}:\\ \;\;\;\;x2 \cdot -6\\ \mathbf{elif}\;x1 \leq 2.1 \cdot 10^{+59}:\\ \;\;\;\;8 \cdot \left(x1 \cdot \left(x2 \cdot x2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot \left(3 \cdot \left(x1 \cdot x1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 47.3% accurate, 4.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 8 \cdot \left(x2 \cdot \left(x1 \cdot x1\right)\right)\\ t_1 := 8 \cdot \left(x1 \cdot \left(x2 \cdot x2\right)\right)\\ \mathbf{if}\;x1 \leq -5.1 \cdot 10^{+38}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x1 \leq -3.9 \cdot 10^{-72}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x1 \leq 4.5 \cdot 10^{-113}:\\ \;\;\;\;x2 \cdot -6\\ \mathbf{elif}\;x1 \leq 1.46 \cdot 10^{+63}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* 8.0 (* x2 (* x1 x1)))) (t_1 (* 8.0 (* x1 (* x2 x2)))))
   (if (<= x1 -5.1e+38)
     t_0
     (if (<= x1 -3.9e-72)
       t_1
       (if (<= x1 4.5e-113) (* x2 -6.0) (if (<= x1 1.46e+63) t_1 t_0))))))

C

double code(double x1, double x2) {
	double t_0 = 8.0 * (x2 * (x1 * x1));
	double t_1 = 8.0 * (x1 * (x2 * x2));
	double tmp;
	if (x1 <= -5.1e+38) {
		tmp = t_0;
	} else if (x1 <= -3.9e-72) {
		tmp = t_1;
	} else if (x1 <= 4.5e-113) {
		tmp = x2 * -6.0;
	} else if (x1 <= 1.46e+63) {
		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 = 8.0d0 * (x2 * (x1 * x1))
    t_1 = 8.0d0 * (x1 * (x2 * x2))
    if (x1 <= (-5.1d+38)) then
        tmp = t_0
    else if (x1 <= (-3.9d-72)) then
        tmp = t_1
    else if (x1 <= 4.5d-113) then
        tmp = x2 * (-6.0d0)
    else if (x1 <= 1.46d+63) 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 = 8.0 * (x2 * (x1 * x1));
	double t_1 = 8.0 * (x1 * (x2 * x2));
	double tmp;
	if (x1 <= -5.1e+38) {
		tmp = t_0;
	} else if (x1 <= -3.9e-72) {
		tmp = t_1;
	} else if (x1 <= 4.5e-113) {
		tmp = x2 * -6.0;
	} else if (x1 <= 1.46e+63) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = 8.0 * (x2 * (x1 * x1))
	t_1 = 8.0 * (x1 * (x2 * x2))
	tmp = 0
	if x1 <= -5.1e+38:
		tmp = t_0
	elif x1 <= -3.9e-72:
		tmp = t_1
	elif x1 <= 4.5e-113:
		tmp = x2 * -6.0
	elif x1 <= 1.46e+63:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(8.0 * Float64(x2 * Float64(x1 * x1)))
	t_1 = Float64(8.0 * Float64(x1 * Float64(x2 * x2)))
	tmp = 0.0
	if (x1 <= -5.1e+38)
		tmp = t_0;
	elseif (x1 <= -3.9e-72)
		tmp = t_1;
	elseif (x1 <= 4.5e-113)
		tmp = Float64(x2 * -6.0);
	elseif (x1 <= 1.46e+63)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = 8.0 * (x2 * (x1 * x1));
	t_1 = 8.0 * (x1 * (x2 * x2));
	tmp = 0.0;
	if (x1 <= -5.1e+38)
		tmp = t_0;
	elseif (x1 <= -3.9e-72)
		tmp = t_1;
	elseif (x1 <= 4.5e-113)
		tmp = x2 * -6.0;
	elseif (x1 <= 1.46e+63)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(8.0 * N[(x2 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(8.0 * N[(x1 * N[(x2 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -5.1e+38], t$95$0, If[LessEqual[x1, -3.9e-72], t$95$1, If[LessEqual[x1, 4.5e-113], N[(x2 * -6.0), $MachinePrecision], If[LessEqual[x1, 1.46e+63], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -5.1000000000000001e38 or 1.4599999999999999e63 < x1

   1. Initial program 39.3%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Simplified 39.3%

      \[\leadsto \color{blue}{\frac{3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right)}{x1 \cdot x1 + 1} + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(x1 \cdot \left(x1 \cdot -6\right) + \frac{2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)}{x1 \cdot x1 + 1} \cdot \left(x1 \cdot \left(-6 + \left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right) \cdot \frac{2}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot 4\right)\right) + x1 \cdot \left(2 + x1 \cdot \left(x1 + \left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right) \cdot \frac{3}{x1 \cdot x1 + 1}\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x2 around -inf

      \[\leadsto \color{blue}{{x2}^{2} \cdot \left(-1 \cdot \frac{-6 \cdot \frac{{x1}^{2}}{1 + {x1}^{2}} + \left(6 \cdot \frac{1}{1 + {x1}^{2}} + \left(1 + {x1}^{2}\right) \cdot \left(-4 \cdot \frac{{x1}^{2} \cdot \left(3 \cdot x1 - 1\right)}{{\left(1 + {x1}^{2}\right)}^{2}} + -2 \cdot \frac{4 \cdot {x1}^{2} + x1 \cdot \left(2 \cdot \frac{x1 \cdot \left(3 \cdot x1 - 1\right)}{1 + {x1}^{2}} - 6\right)}{1 + {x1}^{2}}\right)\right)}{x2} + 8 \cdot \frac{x1}{1 + {x1}^{2}}\right)} \]

   7. Simplified 5.3%

      \[\leadsto \color{blue}{\left(x2 \cdot x2\right) \cdot \left(\frac{8 \cdot x1}{1 + x1 \cdot x1} - \frac{\frac{-6 \cdot \left(x1 \cdot x1\right)}{1 + x1 \cdot x1} + \left(\frac{6}{1 + x1 \cdot x1} + \left(1 + x1 \cdot x1\right) \cdot \left(\frac{-4 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot 3 + -1\right)\right)}{\left(1 + x1 \cdot x1\right) \cdot \left(1 + x1 \cdot x1\right)} + \frac{-2 \cdot \left(4 \cdot \left(x1 \cdot x1\right) + x1 \cdot \left(\frac{2 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)}{1 + x1 \cdot x1} + -6\right)\right)}{1 + x1 \cdot x1}\right)\right)}{x2}\right)} \]

   8. Taylor expanded in x1 around inf

      \[\leadsto \color{blue}{8 \cdot \left({x1}^{2} \cdot x2\right)} \]
   9. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(8, \color{blue}{\left({x1}^{2} \cdot x2\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(8, \mathsf{*.f64}\left(\left({x1}^{2}\right), \color{blue}{x2}\right)\right) \]

      3. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(8, \mathsf{*.f64}\left(\left(x1 \cdot x1\right), x2\right)\right) \]

      4. *-lowering-*.f64 41.6%

         \[\leadsto \mathsf{*.f64}\left(8, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, x1\right), x2\right)\right) \]

   10. Simplified 41.6%

       \[\leadsto \color{blue}{8 \cdot \left(\left(x1 \cdot x1\right) \cdot x2\right)} \]

   if -5.1000000000000001e38 < x1 < -3.9e-72 or 4.5000000000000001e-113 < x1 < 1.4599999999999999e63

   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 99.5%

      \[\leadsto \color{blue}{\frac{3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right)}{x1 \cdot x1 + 1} + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(x1 \cdot \left(x1 \cdot -6\right) + \frac{2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)}{x1 \cdot x1 + 1} \cdot \left(x1 \cdot \left(-6 + \left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right) \cdot \frac{2}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot 4\right)\right) + x1 \cdot \left(2 + x1 \cdot \left(x1 + \left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right) \cdot \frac{3}{x1 \cdot x1 + 1}\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x1 around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \color{blue}{\left(x1 \cdot \left(2 + 2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)\right)\right)}\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \color{blue}{\left(2 + 2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)\right)}\right)\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \color{blue}{\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \color{blue}{\left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)}\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \color{blue}{\left(4 \cdot x2 - 6\right)}\right)\right)\right)\right)\right) \]

      5. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + \color{blue}{\left(\mathsf{neg}\left(6\right)\right)}\right)\right)\right)\right)\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + -6\right)\right)\right)\right)\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\left(4 \cdot x2\right), \color{blue}{-6}\right)\right)\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\left(x2 \cdot 4\right), -6\right)\right)\right)\right)\right)\right) \]

      9. *-lowering-*.f64 82.2%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right)\right)\right)\right)\right) \]

   7. Simplified 82.2%

      \[\leadsto \frac{3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right)}{x1 \cdot x1 + 1} + \color{blue}{x1 \cdot \left(2 + 2 \cdot \left(x2 \cdot \left(x2 \cdot 4 + -6\right)\right)\right)} \]

   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 52.0%

         \[\leadsto \mathsf{*.f64}\left(8, \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x2, \color{blue}{x2}\right)\right)\right) \]

   10. Simplified 52.0%

       \[\leadsto \color{blue}{8 \cdot \left(x1 \cdot \left(x2 \cdot x2\right)\right)} \]

   if -3.9e-72 < x1 < 4.5000000000000001e-113

   1. Initial program 99.5%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x1 around 0

      \[\leadsto \color{blue}{-6 \cdot x2} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 71.4%

         \[\leadsto \mathsf{*.f64}\left(-6, \color{blue}{x2}\right) \]

   5. Simplified 71.4%

      \[\leadsto \color{blue}{-6 \cdot x2} \]
3. Recombined 3 regimes into one program.

4. Final simplification 54.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.1 \cdot 10^{+38}:\\ \;\;\;\;8 \cdot \left(x2 \cdot \left(x1 \cdot x1\right)\right)\\ \mathbf{elif}\;x1 \leq -3.9 \cdot 10^{-72}:\\ \;\;\;\;8 \cdot \left(x1 \cdot \left(x2 \cdot x2\right)\right)\\ \mathbf{elif}\;x1 \leq 4.5 \cdot 10^{-113}:\\ \;\;\;\;x2 \cdot -6\\ \mathbf{elif}\;x1 \leq 1.46 \cdot 10^{+63}:\\ \;\;\;\;8 \cdot \left(x1 \cdot \left(x2 \cdot x2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;8 \cdot \left(x2 \cdot \left(x1 \cdot x1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 80.0% accurate, 4.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -6.8 \cdot 10^{+78}:\\ \;\;\;\;\left(x1 \cdot \left(x1 \cdot x1\right)\right) \cdot \left(4 \cdot \left(x2 \cdot \left(3 + x2 \cdot -2\right)\right) + \left(-19 + x2 \cdot 12\right)\right)\\ \mathbf{elif}\;x1 \leq 2.2 \cdot 10^{+59}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + \left(x2 \cdot 4\right) \cdot \left(2 \cdot x2 + -3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot \left(3 \cdot \left(x1 \cdot x1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -6.8e+78)
   (*
    (* x1 (* x1 x1))
    (+ (* 4.0 (* x2 (+ 3.0 (* x2 -2.0)))) (+ -19.0 (* x2 12.0))))
   (if (<= x1 2.2e+59)
     (+ (* x2 -6.0) (* x1 (+ -1.0 (* (* x2 4.0) (+ (* 2.0 x2) -3.0)))))
     (* x1 (* 3.0 (* x1 x1))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -6.8e+78) {
		tmp = (x1 * (x1 * x1)) * ((4.0 * (x2 * (3.0 + (x2 * -2.0)))) + (-19.0 + (x2 * 12.0)));
	} else if (x1 <= 2.2e+59) {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + ((x2 * 4.0) * ((2.0 * x2) + -3.0))));
	} else {
		tmp = x1 * (3.0 * (x1 * x1));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x1 <= (-6.8d+78)) then
        tmp = (x1 * (x1 * x1)) * ((4.0d0 * (x2 * (3.0d0 + (x2 * (-2.0d0))))) + ((-19.0d0) + (x2 * 12.0d0)))
    else if (x1 <= 2.2d+59) then
        tmp = (x2 * (-6.0d0)) + (x1 * ((-1.0d0) + ((x2 * 4.0d0) * ((2.0d0 * x2) + (-3.0d0)))))
    else
        tmp = x1 * (3.0d0 * (x1 * x1))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= -6.8e+78) {
		tmp = (x1 * (x1 * x1)) * ((4.0 * (x2 * (3.0 + (x2 * -2.0)))) + (-19.0 + (x2 * 12.0)));
	} else if (x1 <= 2.2e+59) {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + ((x2 * 4.0) * ((2.0 * x2) + -3.0))));
	} else {
		tmp = x1 * (3.0 * (x1 * x1));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -6.8e+78:
		tmp = (x1 * (x1 * x1)) * ((4.0 * (x2 * (3.0 + (x2 * -2.0)))) + (-19.0 + (x2 * 12.0)))
	elif x1 <= 2.2e+59:
		tmp = (x2 * -6.0) + (x1 * (-1.0 + ((x2 * 4.0) * ((2.0 * x2) + -3.0))))
	else:
		tmp = x1 * (3.0 * (x1 * x1))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -6.8e+78)
		tmp = Float64(Float64(x1 * Float64(x1 * x1)) * Float64(Float64(4.0 * Float64(x2 * Float64(3.0 + Float64(x2 * -2.0)))) + Float64(-19.0 + Float64(x2 * 12.0))));
	elseif (x1 <= 2.2e+59)
		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(x1 * Float64(3.0 * Float64(x1 * x1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -6.8e+78)
		tmp = (x1 * (x1 * x1)) * ((4.0 * (x2 * (3.0 + (x2 * -2.0)))) + (-19.0 + (x2 * 12.0)));
	elseif (x1 <= 2.2e+59)
		tmp = (x2 * -6.0) + (x1 * (-1.0 + ((x2 * 4.0) * ((2.0 * x2) + -3.0))));
	else
		tmp = x1 * (3.0 * (x1 * x1));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -6.8e+78], N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] * N[(N[(4.0 * N[(x2 * N[(3.0 + N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-19.0 + N[(x2 * 12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 2.2e+59], 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[(x1 * N[(3.0 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -6.80000000000000014e78

   1. Initial program 19.0%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Simplified 19.0%

      \[\leadsto \color{blue}{\frac{3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right)}{x1 \cdot x1 + 1} + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(x1 \cdot \left(x1 \cdot -6\right) + \frac{2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)}{x1 \cdot x1 + 1} \cdot \left(x1 \cdot \left(-6 + \left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right) \cdot \frac{2}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot 4\right)\right) + x1 \cdot \left(2 + x1 \cdot \left(x1 + \left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right) \cdot \frac{3}{x1 \cdot x1 + 1}\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x1 around 0

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + x1 \cdot \left(\left(-1 \cdot \left(4 \cdot x2 - 6\right) + \left(3 \cdot \left(3 - -2 \cdot x2\right) + \left(4 \cdot x2 + \left(6 \cdot x2 + x1 \cdot \left(\left(3 \cdot \left(4 \cdot x2 - 6\right) + 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right) - 1\right)\right)\right)\right)\right) - 6\right)\right) - 1\right)} \]

   7. Simplified 69.7%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(2 \cdot \left(x2 \cdot \left(x2 \cdot 4 + -6\right)\right) + \left(x1 \cdot \left(\left(\left(\left(9 + 3 \cdot \left(x2 \cdot 2\right)\right) + \left(x2 \cdot 10 + x1 \cdot \left(\left(3 \cdot \left(x2 \cdot 4\right) + -18\right) + \left(4 \cdot \left(x2 \cdot \left(3 - x2 \cdot 2\right)\right) + -1\right)\right)\right)\right) - \left(x2 \cdot 4 + -6\right)\right) + -6\right) + -1\right)\right)} \]

   8. Taylor expanded in x1 around inf

      \[\leadsto \color{blue}{{x1}^{3} \cdot \left(\left(4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right) + 12 \cdot x2\right) - 19\right)} \]
   9. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x1}^{3}\right), \color{blue}{\left(\left(4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right) + 12 \cdot x2\right) - 19\right)}\right) \]

      2. cube-mult N/A

         \[\leadsto \mathsf{*.f64}\left(\left(x1 \cdot \left(x1 \cdot x1\right)\right), \left(\color{blue}{\left(4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right) + 12 \cdot x2\right)} - 19\right)\right) \]

      3. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(x1 \cdot {x1}^{2}\right), \left(\left(4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right) + \color{blue}{12 \cdot x2}\right) - 19\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \left({x1}^{2}\right)\right), \left(\color{blue}{\left(4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right) + 12 \cdot x2\right)} - 19\right)\right) \]

      5. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \left(x1 \cdot x1\right)\right), \left(\left(4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right) + \color{blue}{12 \cdot x2}\right) - 19\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, x1\right)\right), \left(\left(4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right) + \color{blue}{12 \cdot x2}\right) - 19\right)\right) \]

      7. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, x1\right)\right), \left(4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right) + \color{blue}{\left(12 \cdot x2 - 19\right)}\right)\right) \]

      8. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(\left(4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right), \color{blue}{\left(12 \cdot x2 - 19\right)}\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right), \left(\color{blue}{12 \cdot x2} - 19\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, \mathsf{*.f64}\left(x2, \left(3 - 2 \cdot x2\right)\right)\right), \left(12 \cdot \color{blue}{x2} - 19\right)\right)\right) \]

      11. cancel-sign-sub-inv N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, \mathsf{*.f64}\left(x2, \left(3 + \left(\mathsf{neg}\left(2\right)\right) \cdot x2\right)\right)\right), \left(12 \cdot x2 - 19\right)\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, \mathsf{*.f64}\left(x2, \left(3 + -2 \cdot x2\right)\right)\right), \left(12 \cdot x2 - 19\right)\right)\right) \]

      13. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(3, \left(-2 \cdot x2\right)\right)\right)\right), \left(12 \cdot x2 - 19\right)\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(3, \left(x2 \cdot -2\right)\right)\right)\right), \left(12 \cdot x2 - 19\right)\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(3, \mathsf{*.f64}\left(x2, -2\right)\right)\right)\right), \left(12 \cdot x2 - 19\right)\right)\right) \]

      16. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(3, \mathsf{*.f64}\left(x2, -2\right)\right)\right)\right), \left(12 \cdot x2 + \color{blue}{\left(\mathsf{neg}\left(19\right)\right)}\right)\right)\right) \]

      17. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(3, \mathsf{*.f64}\left(x2, -2\right)\right)\right)\right), \left(12 \cdot x2 + -19\right)\right)\right) \]

      18. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(3, \mathsf{*.f64}\left(x2, -2\right)\right)\right)\right), \mathsf{+.f64}\left(\left(12 \cdot x2\right), \color{blue}{-19}\right)\right)\right) \]

      19. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(3, \mathsf{*.f64}\left(x2, -2\right)\right)\right)\right), \mathsf{+.f64}\left(\left(x2 \cdot 12\right), -19\right)\right)\right) \]

      20. *-lowering-*.f64 88.8%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x1, x1\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(3, \mathsf{*.f64}\left(x2, -2\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 12\right), -19\right)\right)\right) \]

   10. Simplified 88.8%

       \[\leadsto \color{blue}{\left(x1 \cdot \left(x1 \cdot x1\right)\right) \cdot \left(4 \cdot \left(x2 \cdot \left(3 + x2 \cdot -2\right)\right) + \left(x2 \cdot 12 + -19\right)\right)} \]

   if -6.80000000000000014e78 < x1 < 2.2e59

   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 84.0%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 4\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 2\right), -3\right)\right), -1\right)\right)\right) \]

   5. Simplified 84.0%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(x2 \cdot 4\right) \cdot \left(x2 \cdot 2 + -3\right) + -1\right)} \]

   if 2.2e59 < x1

   1. Initial program 44.1%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Simplified 44.1%

      \[\leadsto \color{blue}{\frac{3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right)}{x1 \cdot x1 + 1} + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(x1 \cdot \left(x1 \cdot -6\right) + \frac{2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)}{x1 \cdot x1 + 1} \cdot \left(x1 \cdot \left(-6 + \left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right) \cdot \frac{2}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot 4\right)\right) + x1 \cdot \left(2 + x1 \cdot \left(x1 + \left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right) \cdot \frac{3}{x1 \cdot x1 + 1}\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x1 around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \color{blue}{\left(x1 \cdot \left(2 + 2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)\right)\right)}\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \color{blue}{\left(2 + 2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)\right)}\right)\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \color{blue}{\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \color{blue}{\left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)}\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \color{blue}{\left(4 \cdot x2 - 6\right)}\right)\right)\right)\right)\right) \]

      5. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + \color{blue}{\left(\mathsf{neg}\left(6\right)\right)}\right)\right)\right)\right)\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + -6\right)\right)\right)\right)\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\left(4 \cdot x2\right), \color{blue}{-6}\right)\right)\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\left(x2 \cdot 4\right), -6\right)\right)\right)\right)\right)\right) \]

      9. *-lowering-*.f64 7.6%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right)\right)\right)\right)\right) \]

   7. Simplified 7.6%

      \[\leadsto \frac{3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right)}{x1 \cdot x1 + 1} + \color{blue}{x1 \cdot \left(2 + 2 \cdot \left(x2 \cdot \left(x2 \cdot 4 + -6\right)\right)\right)} \]

   8. Taylor expanded in x1 around 0

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)\right) - 1\right)} \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(-6 \cdot x2\right), \color{blue}{\left(x1 \cdot \left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)\right) - 1\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \left(\color{blue}{x1} \cdot \left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)\right) - 1\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \color{blue}{\left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)\right) - 1\right)}\right)\right) \]

      4. associate--l+ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + \color{blue}{\left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right) - 1\right)}\right)\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)\right), \color{blue}{\left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right) - 1\right)}\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)\right), \left(\color{blue}{x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)} - 1\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 - 6\right)\right)\right), \left(x1 \cdot \color{blue}{\left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)} - 1\right)\right)\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + \left(\mathsf{neg}\left(6\right)\right)\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + \color{blue}{3 \cdot \left(3 - -2 \cdot x2\right)}\right) - 1\right)\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + -6\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \color{blue}{\left(3 - -2 \cdot x2\right)}\right) - 1\right)\right)\right)\right) \]

      10. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\left(4 \cdot x2\right), -6\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + \color{blue}{3 \cdot \left(3 - -2 \cdot x2\right)}\right) - 1\right)\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, x2\right), -6\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + \color{blue}{3} \cdot \left(3 - -2 \cdot x2\right)\right) - 1\right)\right)\right)\right) \]

      12. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, x2\right), -6\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right) + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, x2\right), -6\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right) + -1\right)\right)\right)\right) \]

      14. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, x2\right), -6\right)\right)\right), \mathsf{+.f64}\left(\left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)\right), \color{blue}{-1}\right)\right)\right)\right) \]

   10. Simplified 76.1%

       \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 + -6\right)\right) + \left(x1 \cdot \left(3 \cdot \left(x1 + \left(3 + 2 \cdot x2\right)\right)\right) + -1\right)\right)} \]

   11. Taylor expanded in x1 around inf

       \[\leadsto \color{blue}{3 \cdot {x1}^{3}} \]
   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. *-commutative N/A

          \[\leadsto x1 \cdot \left(3 \cdot \color{blue}{{x1}^{2}}\right) \]

       6. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x1, \color{blue}{\left(3 \cdot {x1}^{2}\right)}\right) \]

       7. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(3, \color{blue}{\left({x1}^{2}\right)}\right)\right) \]

       8. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(3, \left(x1 \cdot \color{blue}{x1}\right)\right)\right) \]

       9. *-lowering-*.f64 81.8%

          \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(3, \mathsf{*.f64}\left(x1, \color{blue}{x1}\right)\right)\right) \]

   13. Simplified 81.8%

       \[\leadsto \color{blue}{x1 \cdot \left(3 \cdot \left(x1 \cdot x1\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 84.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -6.8 \cdot 10^{+78}:\\ \;\;\;\;\left(x1 \cdot \left(x1 \cdot x1\right)\right) \cdot \left(4 \cdot \left(x2 \cdot \left(3 + x2 \cdot -2\right)\right) + \left(-19 + x2 \cdot 12\right)\right)\\ \mathbf{elif}\;x1 \leq 2.2 \cdot 10^{+59}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + \left(x2 \cdot 4\right) \cdot \left(2 \cdot x2 + -3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot \left(3 \cdot \left(x1 \cdot x1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 79.6% accurate, 4.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -2.65 \cdot 10^{+90}:\\ \;\;\;\;x1 \cdot \left(-1 + x1 \cdot \left(9 + x1 \cdot -19\right)\right)\\ \mathbf{elif}\;x1 \leq 2.2 \cdot 10^{+59}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + \left(x2 \cdot 4\right) \cdot \left(2 \cdot x2 + -3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot \left(3 \cdot \left(x1 \cdot x1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -2.65e+90)
   (* x1 (+ -1.0 (* x1 (+ 9.0 (* x1 -19.0)))))
   (if (<= x1 2.2e+59)
     (+ (* x2 -6.0) (* x1 (+ -1.0 (* (* x2 4.0) (+ (* 2.0 x2) -3.0)))))
     (* x1 (* 3.0 (* x1 x1))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -2.65e+90) {
		tmp = x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0))));
	} else if (x1 <= 2.2e+59) {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + ((x2 * 4.0) * ((2.0 * x2) + -3.0))));
	} else {
		tmp = x1 * (3.0 * (x1 * x1));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x1 <= (-2.65d+90)) then
        tmp = x1 * ((-1.0d0) + (x1 * (9.0d0 + (x1 * (-19.0d0)))))
    else if (x1 <= 2.2d+59) then
        tmp = (x2 * (-6.0d0)) + (x1 * ((-1.0d0) + ((x2 * 4.0d0) * ((2.0d0 * x2) + (-3.0d0)))))
    else
        tmp = x1 * (3.0d0 * (x1 * x1))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= -2.65e+90) {
		tmp = x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0))));
	} else if (x1 <= 2.2e+59) {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + ((x2 * 4.0) * ((2.0 * x2) + -3.0))));
	} else {
		tmp = x1 * (3.0 * (x1 * x1));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -2.65e+90:
		tmp = x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0))))
	elif x1 <= 2.2e+59:
		tmp = (x2 * -6.0) + (x1 * (-1.0 + ((x2 * 4.0) * ((2.0 * x2) + -3.0))))
	else:
		tmp = x1 * (3.0 * (x1 * x1))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -2.65e+90)
		tmp = Float64(x1 * Float64(-1.0 + Float64(x1 * Float64(9.0 + Float64(x1 * -19.0)))));
	elseif (x1 <= 2.2e+59)
		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(x1 * Float64(3.0 * Float64(x1 * x1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -2.65e+90)
		tmp = x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0))));
	elseif (x1 <= 2.2e+59)
		tmp = (x2 * -6.0) + (x1 * (-1.0 + ((x2 * 4.0) * ((2.0 * x2) + -3.0))));
	else
		tmp = x1 * (3.0 * (x1 * x1));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -2.65e+90], N[(x1 * N[(-1.0 + N[(x1 * N[(9.0 + N[(x1 * -19.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 2.2e+59], 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[(x1 * N[(3.0 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -2.64999999999999989e90

   1. Initial program 5.6%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Simplified 5.6%

      \[\leadsto \color{blue}{\frac{3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right)}{x1 \cdot x1 + 1} + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(x1 \cdot \left(x1 \cdot -6\right) + \frac{2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)}{x1 \cdot x1 + 1} \cdot \left(x1 \cdot \left(-6 + \left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right) \cdot \frac{2}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot 4\right)\right) + x1 \cdot \left(2 + x1 \cdot \left(x1 + \left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right) \cdot \frac{3}{x1 \cdot x1 + 1}\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x1 around 0

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + x1 \cdot \left(\left(-1 \cdot \left(4 \cdot x2 - 6\right) + \left(3 \cdot \left(3 - -2 \cdot x2\right) + \left(4 \cdot x2 + \left(6 \cdot x2 + x1 \cdot \left(\left(3 \cdot \left(4 \cdot x2 - 6\right) + 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right) - 1\right)\right)\right)\right)\right) - 6\right)\right) - 1\right)} \]

   7. Simplified 77.8%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(2 \cdot \left(x2 \cdot \left(x2 \cdot 4 + -6\right)\right) + \left(x1 \cdot \left(\left(\left(\left(9 + 3 \cdot \left(x2 \cdot 2\right)\right) + \left(x2 \cdot 10 + x1 \cdot \left(\left(3 \cdot \left(x2 \cdot 4\right) + -18\right) + \left(4 \cdot \left(x2 \cdot \left(3 - x2 \cdot 2\right)\right) + -1\right)\right)\right)\right) - \left(x2 \cdot 4 + -6\right)\right) + -6\right) + -1\right)\right)} \]

   8. Taylor expanded in x2 around 0

      \[\leadsto \color{blue}{x1 \cdot \left(x1 \cdot \left(9 + -19 \cdot x1\right) - 1\right)} \]
   9. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x1, \color{blue}{\left(x1 \cdot \left(9 + -19 \cdot x1\right) - 1\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x1, \left(x1 \cdot \left(9 + -19 \cdot x1\right) + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right) \]

      3. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(x1, \left(x1 \cdot \left(9 + -19 \cdot x1\right) + -1\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\left(x1 \cdot \left(9 + -19 \cdot x1\right)\right), \color{blue}{-1}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \left(9 + -19 \cdot x1\right)\right), -1\right)\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(9, \left(-19 \cdot x1\right)\right)\right), -1\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(9, \left(x1 \cdot -19\right)\right)\right), -1\right)\right) \]

      8. *-lowering-*.f64 94.9%

         \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(9, \mathsf{*.f64}\left(x1, -19\right)\right)\right), -1\right)\right) \]

   10. Simplified 94.9%

       \[\leadsto \color{blue}{x1 \cdot \left(x1 \cdot \left(9 + x1 \cdot -19\right) + -1\right)} \]

   if -2.64999999999999989e90 < x1 < 2.2e59

   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 81.7%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x2, 4\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 2\right), -3\right)\right), -1\right)\right)\right) \]

   5. Simplified 81.7%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(x2 \cdot 4\right) \cdot \left(x2 \cdot 2 + -3\right) + -1\right)} \]

   if 2.2e59 < x1

   1. Initial program 44.1%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Simplified 44.1%

      \[\leadsto \color{blue}{\frac{3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right)}{x1 \cdot x1 + 1} + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(x1 \cdot \left(x1 \cdot -6\right) + \frac{2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)}{x1 \cdot x1 + 1} \cdot \left(x1 \cdot \left(-6 + \left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right) \cdot \frac{2}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot 4\right)\right) + x1 \cdot \left(2 + x1 \cdot \left(x1 + \left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right) \cdot \frac{3}{x1 \cdot x1 + 1}\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x1 around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \color{blue}{\left(x1 \cdot \left(2 + 2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)\right)\right)}\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \color{blue}{\left(2 + 2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)\right)}\right)\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \color{blue}{\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \color{blue}{\left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)}\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \color{blue}{\left(4 \cdot x2 - 6\right)}\right)\right)\right)\right)\right) \]

      5. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + \color{blue}{\left(\mathsf{neg}\left(6\right)\right)}\right)\right)\right)\right)\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + -6\right)\right)\right)\right)\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\left(4 \cdot x2\right), \color{blue}{-6}\right)\right)\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\left(x2 \cdot 4\right), -6\right)\right)\right)\right)\right)\right) \]

      9. *-lowering-*.f64 7.6%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right)\right)\right)\right)\right) \]

   7. Simplified 7.6%

      \[\leadsto \frac{3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right)}{x1 \cdot x1 + 1} + \color{blue}{x1 \cdot \left(2 + 2 \cdot \left(x2 \cdot \left(x2 \cdot 4 + -6\right)\right)\right)} \]

   8. Taylor expanded in x1 around 0

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)\right) - 1\right)} \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(-6 \cdot x2\right), \color{blue}{\left(x1 \cdot \left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)\right) - 1\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \left(\color{blue}{x1} \cdot \left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)\right) - 1\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \color{blue}{\left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)\right) - 1\right)}\right)\right) \]

      4. associate--l+ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + \color{blue}{\left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right) - 1\right)}\right)\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)\right), \color{blue}{\left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right) - 1\right)}\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)\right), \left(\color{blue}{x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)} - 1\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 - 6\right)\right)\right), \left(x1 \cdot \color{blue}{\left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)} - 1\right)\right)\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + \left(\mathsf{neg}\left(6\right)\right)\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + \color{blue}{3 \cdot \left(3 - -2 \cdot x2\right)}\right) - 1\right)\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + -6\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \color{blue}{\left(3 - -2 \cdot x2\right)}\right) - 1\right)\right)\right)\right) \]

      10. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\left(4 \cdot x2\right), -6\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + \color{blue}{3 \cdot \left(3 - -2 \cdot x2\right)}\right) - 1\right)\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, x2\right), -6\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + \color{blue}{3} \cdot \left(3 - -2 \cdot x2\right)\right) - 1\right)\right)\right)\right) \]

      12. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, x2\right), -6\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right) + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, x2\right), -6\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right) + -1\right)\right)\right)\right) \]

      14. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, x2\right), -6\right)\right)\right), \mathsf{+.f64}\left(\left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)\right), \color{blue}{-1}\right)\right)\right)\right) \]

   10. Simplified 76.1%

       \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 + -6\right)\right) + \left(x1 \cdot \left(3 \cdot \left(x1 + \left(3 + 2 \cdot x2\right)\right)\right) + -1\right)\right)} \]

   11. Taylor expanded in x1 around inf

       \[\leadsto \color{blue}{3 \cdot {x1}^{3}} \]
   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. *-commutative N/A

          \[\leadsto x1 \cdot \left(3 \cdot \color{blue}{{x1}^{2}}\right) \]

       6. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x1, \color{blue}{\left(3 \cdot {x1}^{2}\right)}\right) \]

       7. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(3, \color{blue}{\left({x1}^{2}\right)}\right)\right) \]

       8. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(3, \left(x1 \cdot \color{blue}{x1}\right)\right)\right) \]

       9. *-lowering-*.f64 81.8%

          \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(3, \mathsf{*.f64}\left(x1, \color{blue}{x1}\right)\right)\right) \]

   13. Simplified 81.8%

       \[\leadsto \color{blue}{x1 \cdot \left(3 \cdot \left(x1 \cdot x1\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 83.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -2.65 \cdot 10^{+90}:\\ \;\;\;\;x1 \cdot \left(-1 + x1 \cdot \left(9 + x1 \cdot -19\right)\right)\\ \mathbf{elif}\;x1 \leq 2.2 \cdot 10^{+59}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + \left(x2 \cdot 4\right) \cdot \left(2 \cdot x2 + -3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot \left(3 \cdot \left(x1 \cdot x1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 67.9% accurate, 6.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -1.65 \cdot 10^{+90}:\\ \;\;\;\;x1 \cdot \left(-1 + x1 \cdot \left(9 + x1 \cdot -19\right)\right)\\ \mathbf{elif}\;x1 \leq 1.65 \cdot 10^{+59}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(x2 \cdot \left(x2 \cdot 8\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot \left(3 \cdot \left(x1 \cdot x1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -1.65e+90)
   (* x1 (+ -1.0 (* x1 (+ 9.0 (* x1 -19.0)))))
   (if (<= x1 1.65e+59)
     (+ (* x2 -6.0) (* x1 (* x2 (* x2 8.0))))
     (* x1 (* 3.0 (* x1 x1))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -1.65e+90) {
		tmp = x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0))));
	} else if (x1 <= 1.65e+59) {
		tmp = (x2 * -6.0) + (x1 * (x2 * (x2 * 8.0)));
	} else {
		tmp = x1 * (3.0 * (x1 * x1));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x1 <= (-1.65d+90)) then
        tmp = x1 * ((-1.0d0) + (x1 * (9.0d0 + (x1 * (-19.0d0)))))
    else if (x1 <= 1.65d+59) then
        tmp = (x2 * (-6.0d0)) + (x1 * (x2 * (x2 * 8.0d0)))
    else
        tmp = x1 * (3.0d0 * (x1 * x1))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= -1.65e+90) {
		tmp = x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0))));
	} else if (x1 <= 1.65e+59) {
		tmp = (x2 * -6.0) + (x1 * (x2 * (x2 * 8.0)));
	} else {
		tmp = x1 * (3.0 * (x1 * x1));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -1.65e+90:
		tmp = x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0))))
	elif x1 <= 1.65e+59:
		tmp = (x2 * -6.0) + (x1 * (x2 * (x2 * 8.0)))
	else:
		tmp = x1 * (3.0 * (x1 * x1))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -1.65e+90)
		tmp = Float64(x1 * Float64(-1.0 + Float64(x1 * Float64(9.0 + Float64(x1 * -19.0)))));
	elseif (x1 <= 1.65e+59)
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(x2 * Float64(x2 * 8.0))));
	else
		tmp = Float64(x1 * Float64(3.0 * Float64(x1 * x1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -1.65e+90)
		tmp = x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0))));
	elseif (x1 <= 1.65e+59)
		tmp = (x2 * -6.0) + (x1 * (x2 * (x2 * 8.0)));
	else
		tmp = x1 * (3.0 * (x1 * x1));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -1.65e+90], N[(x1 * N[(-1.0 + N[(x1 * N[(9.0 + N[(x1 * -19.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.65e+59], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(x2 * N[(x2 * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 * N[(3.0 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -1.65000000000000004e90

   1. Initial program 5.6%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Simplified 5.6%

      \[\leadsto \color{blue}{\frac{3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right)}{x1 \cdot x1 + 1} + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(x1 \cdot \left(x1 \cdot -6\right) + \frac{2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)}{x1 \cdot x1 + 1} \cdot \left(x1 \cdot \left(-6 + \left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right) \cdot \frac{2}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot 4\right)\right) + x1 \cdot \left(2 + x1 \cdot \left(x1 + \left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right) \cdot \frac{3}{x1 \cdot x1 + 1}\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x1 around 0

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + x1 \cdot \left(\left(-1 \cdot \left(4 \cdot x2 - 6\right) + \left(3 \cdot \left(3 - -2 \cdot x2\right) + \left(4 \cdot x2 + \left(6 \cdot x2 + x1 \cdot \left(\left(3 \cdot \left(4 \cdot x2 - 6\right) + 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right) - 1\right)\right)\right)\right)\right) - 6\right)\right) - 1\right)} \]

   7. Simplified 77.8%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(2 \cdot \left(x2 \cdot \left(x2 \cdot 4 + -6\right)\right) + \left(x1 \cdot \left(\left(\left(\left(9 + 3 \cdot \left(x2 \cdot 2\right)\right) + \left(x2 \cdot 10 + x1 \cdot \left(\left(3 \cdot \left(x2 \cdot 4\right) + -18\right) + \left(4 \cdot \left(x2 \cdot \left(3 - x2 \cdot 2\right)\right) + -1\right)\right)\right)\right) - \left(x2 \cdot 4 + -6\right)\right) + -6\right) + -1\right)\right)} \]

   8. Taylor expanded in x2 around 0

      \[\leadsto \color{blue}{x1 \cdot \left(x1 \cdot \left(9 + -19 \cdot x1\right) - 1\right)} \]
   9. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x1, \color{blue}{\left(x1 \cdot \left(9 + -19 \cdot x1\right) - 1\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x1, \left(x1 \cdot \left(9 + -19 \cdot x1\right) + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right) \]

      3. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(x1, \left(x1 \cdot \left(9 + -19 \cdot x1\right) + -1\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\left(x1 \cdot \left(9 + -19 \cdot x1\right)\right), \color{blue}{-1}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \left(9 + -19 \cdot x1\right)\right), -1\right)\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(9, \left(-19 \cdot x1\right)\right)\right), -1\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(9, \left(x1 \cdot -19\right)\right)\right), -1\right)\right) \]

      8. *-lowering-*.f64 94.9%

         \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(9, \mathsf{*.f64}\left(x1, -19\right)\right)\right), -1\right)\right) \]

   10. Simplified 94.9%

       \[\leadsto \color{blue}{x1 \cdot \left(x1 \cdot \left(9 + x1 \cdot -19\right) + -1\right)} \]

   if -1.65000000000000004e90 < x1 < 1.65e59

   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

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \color{blue}{\left(x1 \cdot \left(2 + 2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)\right)\right)}\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \color{blue}{\left(2 + 2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)\right)}\right)\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \color{blue}{\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \color{blue}{\left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)}\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \color{blue}{\left(4 \cdot x2 - 6\right)}\right)\right)\right)\right)\right) \]

      5. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + \color{blue}{\left(\mathsf{neg}\left(6\right)\right)}\right)\right)\right)\right)\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + -6\right)\right)\right)\right)\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\left(4 \cdot x2\right), \color{blue}{-6}\right)\right)\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\left(x2 \cdot 4\right), -6\right)\right)\right)\right)\right)\right) \]

      9. *-lowering-*.f64 81.2%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right)\right)\right)\right)\right) \]

   7. Simplified 81.2%

      \[\leadsto \frac{3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right)}{x1 \cdot x1 + 1} + \color{blue}{x1 \cdot \left(2 + 2 \cdot \left(x2 \cdot \left(x2 \cdot 4 + -6\right)\right)\right)} \]

   8. Taylor expanded in x1 around 0

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + 3 \cdot \left(x1 \cdot \left(3 - -2 \cdot x2\right)\right)\right) - 1\right)} \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(-6 \cdot x2\right), \color{blue}{\left(x1 \cdot \left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + 3 \cdot \left(x1 \cdot \left(3 - -2 \cdot x2\right)\right)\right) - 1\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \left(\color{blue}{x1} \cdot \left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + 3 \cdot \left(x1 \cdot \left(3 - -2 \cdot x2\right)\right)\right) - 1\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \color{blue}{\left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + 3 \cdot \left(x1 \cdot \left(3 - -2 \cdot x2\right)\right)\right) - 1\right)}\right)\right) \]

      4. associate--l+ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + \color{blue}{\left(3 \cdot \left(x1 \cdot \left(3 - -2 \cdot x2\right)\right) - 1\right)}\right)\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)\right), \color{blue}{\left(3 \cdot \left(x1 \cdot \left(3 - -2 \cdot x2\right)\right) - 1\right)}\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)\right), \left(\color{blue}{3 \cdot \left(x1 \cdot \left(3 - -2 \cdot x2\right)\right)} - 1\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 - 6\right)\right)\right), \left(3 \cdot \color{blue}{\left(x1 \cdot \left(3 - -2 \cdot x2\right)\right)} - 1\right)\right)\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + \left(\mathsf{neg}\left(6\right)\right)\right)\right)\right), \left(3 \cdot \left(x1 \cdot \color{blue}{\left(3 - -2 \cdot x2\right)}\right) - 1\right)\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + -6\right)\right)\right), \left(3 \cdot \left(x1 \cdot \left(3 - \color{blue}{-2 \cdot x2}\right)\right) - 1\right)\right)\right)\right) \]

      10. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\left(4 \cdot x2\right), -6\right)\right)\right), \left(3 \cdot \left(x1 \cdot \color{blue}{\left(3 - -2 \cdot x2\right)}\right) - 1\right)\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, x2\right), -6\right)\right)\right), \left(3 \cdot \left(x1 \cdot \left(\color{blue}{3} - -2 \cdot x2\right)\right) - 1\right)\right)\right)\right) \]

      12. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, x2\right), -6\right)\right)\right), \left(3 \cdot \left(x1 \cdot \left(3 - -2 \cdot x2\right)\right) + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, x2\right), -6\right)\right)\right), \left(3 \cdot \left(x1 \cdot \left(3 - -2 \cdot x2\right)\right) + -1\right)\right)\right)\right) \]

      14. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, x2\right), -6\right)\right)\right), \mathsf{+.f64}\left(\left(3 \cdot \left(x1 \cdot \left(3 - -2 \cdot x2\right)\right)\right), \color{blue}{-1}\right)\right)\right)\right) \]

   10. Simplified 81.8%

       \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 + -6\right)\right) + \left(3 \cdot \left(x1 \cdot \left(3 + 2 \cdot x2\right)\right) + -1\right)\right)} \]

   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. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \left(\left(x1 \cdot {x2}^{2}\right) \cdot \color{blue}{8}\right)\right) \]

       2. associate-*l* N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \left(x1 \cdot \color{blue}{\left({x2}^{2} \cdot 8\right)}\right)\right) \]

       3. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \left(x1 \cdot \left(8 \cdot \color{blue}{{x2}^{2}}\right)\right)\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \color{blue}{\left(8 \cdot {x2}^{2}\right)}\right)\right) \]

       5. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \left({x2}^{2} \cdot \color{blue}{8}\right)\right)\right) \]

       6. unpow2 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \left(\left(x2 \cdot x2\right) \cdot 8\right)\right)\right) \]

       7. associate-*l* N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \left(x2 \cdot \color{blue}{\left(x2 \cdot 8\right)}\right)\right)\right) \]

       8. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \left(x2 \cdot \left(8 \cdot \color{blue}{x2}\right)\right)\right)\right) \]

       9. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x2, \color{blue}{\left(8 \cdot x2\right)}\right)\right)\right) \]

       10. *-commutative N/A

           \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x2, \left(x2 \cdot \color{blue}{8}\right)\right)\right)\right) \]

       11. *-lowering-*.f64 64.7%

           \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x2, \mathsf{*.f64}\left(x2, \color{blue}{8}\right)\right)\right)\right) \]

   13. Simplified 64.7%

       \[\leadsto -6 \cdot x2 + \color{blue}{x1 \cdot \left(x2 \cdot \left(x2 \cdot 8\right)\right)} \]

   if 1.65e59 < x1

   1. Initial program 44.1%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Simplified 44.1%

      \[\leadsto \color{blue}{\frac{3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right)}{x1 \cdot x1 + 1} + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(x1 \cdot \left(x1 \cdot -6\right) + \frac{2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)}{x1 \cdot x1 + 1} \cdot \left(x1 \cdot \left(-6 + \left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right) \cdot \frac{2}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot 4\right)\right) + x1 \cdot \left(2 + x1 \cdot \left(x1 + \left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right) \cdot \frac{3}{x1 \cdot x1 + 1}\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x1 around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \color{blue}{\left(x1 \cdot \left(2 + 2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)\right)\right)}\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \color{blue}{\left(2 + 2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)\right)}\right)\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \color{blue}{\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \color{blue}{\left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)}\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \color{blue}{\left(4 \cdot x2 - 6\right)}\right)\right)\right)\right)\right) \]

      5. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + \color{blue}{\left(\mathsf{neg}\left(6\right)\right)}\right)\right)\right)\right)\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + -6\right)\right)\right)\right)\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\left(4 \cdot x2\right), \color{blue}{-6}\right)\right)\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\left(x2 \cdot 4\right), -6\right)\right)\right)\right)\right)\right) \]

      9. *-lowering-*.f64 7.6%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right)\right)\right)\right)\right) \]

   7. Simplified 7.6%

      \[\leadsto \frac{3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right)}{x1 \cdot x1 + 1} + \color{blue}{x1 \cdot \left(2 + 2 \cdot \left(x2 \cdot \left(x2 \cdot 4 + -6\right)\right)\right)} \]

   8. Taylor expanded in x1 around 0

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)\right) - 1\right)} \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(-6 \cdot x2\right), \color{blue}{\left(x1 \cdot \left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)\right) - 1\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \left(\color{blue}{x1} \cdot \left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)\right) - 1\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \color{blue}{\left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)\right) - 1\right)}\right)\right) \]

      4. associate--l+ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right) + \color{blue}{\left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right) - 1\right)}\right)\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)\right), \color{blue}{\left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right) - 1\right)}\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)\right), \left(\color{blue}{x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)} - 1\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 - 6\right)\right)\right), \left(x1 \cdot \color{blue}{\left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)} - 1\right)\right)\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + \left(\mathsf{neg}\left(6\right)\right)\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + \color{blue}{3 \cdot \left(3 - -2 \cdot x2\right)}\right) - 1\right)\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + -6\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \color{blue}{\left(3 - -2 \cdot x2\right)}\right) - 1\right)\right)\right)\right) \]

      10. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\left(4 \cdot x2\right), -6\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + \color{blue}{3 \cdot \left(3 - -2 \cdot x2\right)}\right) - 1\right)\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, x2\right), -6\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + \color{blue}{3} \cdot \left(3 - -2 \cdot x2\right)\right) - 1\right)\right)\right)\right) \]

      12. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, x2\right), -6\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right) + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, x2\right), -6\right)\right)\right), \left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right) + -1\right)\right)\right)\right) \]

      14. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-6, x2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(4, x2\right), -6\right)\right)\right), \mathsf{+.f64}\left(\left(x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)\right), \color{blue}{-1}\right)\right)\right)\right) \]

   10. Simplified 76.1%

       \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 + -6\right)\right) + \left(x1 \cdot \left(3 \cdot \left(x1 + \left(3 + 2 \cdot x2\right)\right)\right) + -1\right)\right)} \]

   11. Taylor expanded in x1 around inf

       \[\leadsto \color{blue}{3 \cdot {x1}^{3}} \]
   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. *-commutative N/A

          \[\leadsto x1 \cdot \left(3 \cdot \color{blue}{{x1}^{2}}\right) \]

       6. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x1, \color{blue}{\left(3 \cdot {x1}^{2}\right)}\right) \]

       7. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(3, \color{blue}{\left({x1}^{2}\right)}\right)\right) \]

       8. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(3, \left(x1 \cdot \color{blue}{x1}\right)\right)\right) \]

       9. *-lowering-*.f64 81.8%

          \[\leadsto \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(3, \mathsf{*.f64}\left(x1, \color{blue}{x1}\right)\right)\right) \]

   13. Simplified 81.8%

       \[\leadsto \color{blue}{x1 \cdot \left(3 \cdot \left(x1 \cdot x1\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 72.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.65 \cdot 10^{+90}:\\ \;\;\;\;x1 \cdot \left(-1 + x1 \cdot \left(9 + x1 \cdot -19\right)\right)\\ \mathbf{elif}\;x1 \leq 1.65 \cdot 10^{+59}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(x2 \cdot \left(x2 \cdot 8\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot \left(3 \cdot \left(x1 \cdot x1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 40.0% accurate, 7.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 8 \cdot \left(x1 \cdot \left(x2 \cdot x2\right)\right)\\ \mathbf{if}\;x1 \leq -7.2 \cdot 10^{-72}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x1 \leq 3.8 \cdot 10^{-113}:\\ \;\;\;\;x2 \cdot -6\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* 8.0 (* x1 (* x2 x2)))))
   (if (<= x1 -7.2e-72) t_0 (if (<= x1 3.8e-113) (* x2 -6.0) t_0))))

C

double code(double x1, double x2) {
	double t_0 = 8.0 * (x1 * (x2 * x2));
	double tmp;
	if (x1 <= -7.2e-72) {
		tmp = t_0;
	} else if (x1 <= 3.8e-113) {
		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 = 8.0d0 * (x1 * (x2 * x2))
    if (x1 <= (-7.2d-72)) then
        tmp = t_0
    else if (x1 <= 3.8d-113) 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 = 8.0 * (x1 * (x2 * x2));
	double tmp;
	if (x1 <= -7.2e-72) {
		tmp = t_0;
	} else if (x1 <= 3.8e-113) {
		tmp = x2 * -6.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = 8.0 * (x1 * (x2 * x2))
	tmp = 0
	if x1 <= -7.2e-72:
		tmp = t_0
	elif x1 <= 3.8e-113:
		tmp = x2 * -6.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(8.0 * Float64(x1 * Float64(x2 * x2)))
	tmp = 0.0
	if (x1 <= -7.2e-72)
		tmp = t_0;
	elseif (x1 <= 3.8e-113)
		tmp = Float64(x2 * -6.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = 8.0 * (x1 * (x2 * x2));
	tmp = 0.0;
	if (x1 <= -7.2e-72)
		tmp = t_0;
	elseif (x1 <= 3.8e-113)
		tmp = x2 * -6.0;
	else
		tmp = t_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, -7.2e-72], t$95$0, If[LessEqual[x1, 3.8e-113], N[(x2 * -6.0), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x1 < -7.2e-72 or 3.79999999999999983e-113 < x1

   1. Initial program 61.2%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Simplified 61.3%

      \[\leadsto \color{blue}{\frac{3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right)}{x1 \cdot x1 + 1} + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(x1 \cdot \left(x1 \cdot -6\right) + \frac{2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)}{x1 \cdot x1 + 1} \cdot \left(x1 \cdot \left(-6 + \left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right) \cdot \frac{2}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot 4\right)\right) + x1 \cdot \left(2 + x1 \cdot \left(x1 + \left(2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right) \cdot \frac{3}{x1 \cdot x1 + 1}\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x1 around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \color{blue}{\left(x1 \cdot \left(2 + 2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)\right)\right)}\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \color{blue}{\left(2 + 2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)\right)}\right)\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \color{blue}{\left(2 \cdot \left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \color{blue}{\left(x2 \cdot \left(4 \cdot x2 - 6\right)\right)}\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \color{blue}{\left(4 \cdot x2 - 6\right)}\right)\right)\right)\right)\right) \]

      5. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + \color{blue}{\left(\mathsf{neg}\left(6\right)\right)}\right)\right)\right)\right)\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \left(4 \cdot x2 + -6\right)\right)\right)\right)\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\left(4 \cdot x2\right), \color{blue}{-6}\right)\right)\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\left(x2 \cdot 4\right), -6\right)\right)\right)\right)\right)\right) \]

      9. *-lowering-*.f64 35.5%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(3, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, -2\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, 3\right), -1\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x1, x1\right), 1\right)\right), \mathsf{*.f64}\left(x1, \mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x2, 4\right), -6\right)\right)\right)\right)\right)\right) \]

   7. Simplified 35.5%

      \[\leadsto \frac{3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(x1 \cdot 3 + -1\right)\right)}{x1 \cdot x1 + 1} + \color{blue}{x1 \cdot \left(2 + 2 \cdot \left(x2 \cdot \left(x2 \cdot 4 + -6\right)\right)\right)} \]

   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 32.1%

         \[\leadsto \mathsf{*.f64}\left(8, \mathsf{*.f64}\left(x1, \mathsf{*.f64}\left(x2, \color{blue}{x2}\right)\right)\right) \]

   10. Simplified 32.1%

       \[\leadsto \color{blue}{8 \cdot \left(x1 \cdot \left(x2 \cdot x2\right)\right)} \]

   if -7.2e-72 < x1 < 3.79999999999999983e-113

   1. Initial program 99.5%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x1 around 0

      \[\leadsto \color{blue}{-6 \cdot x2} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 71.4%

         \[\leadsto \mathsf{*.f64}\left(-6, \color{blue}{x2}\right) \]

   5. Simplified 71.4%

      \[\leadsto \color{blue}{-6 \cdot x2} \]
3. Recombined 2 regimes into one program.

4. Final simplification 46.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -7.2 \cdot 10^{-72}:\\ \;\;\;\;8 \cdot \left(x1 \cdot \left(x2 \cdot x2\right)\right)\\ \mathbf{elif}\;x1 \leq 3.8 \cdot 10^{-113}:\\ \;\;\;\;x2 \cdot -6\\ \mathbf{else}:\\ \;\;\;\;8 \cdot \left(x1 \cdot \left(x2 \cdot x2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 26.4% accurate, 25.4× speedup

Math

\[\begin{array}{l} \\ x1 + x2 \cdot -6 \end{array} \]

FPCore

(FPCore (x1 x2) :precision binary64 (+ x1 (* x2 -6.0)))

C

double code(double x1, double x2) {
	return x1 + (x2 * -6.0);
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    code = x1 + (x2 * (-6.0d0))
end function

Java

public static double code(double x1, double x2) {
	return x1 + (x2 * -6.0);
}

Python

def code(x1, x2):
	return x1 + (x2 * -6.0)

Julia

function code(x1, x2)
	return Float64(x1 + Float64(x2 * -6.0))
end

MATLAB

function tmp = code(x1, x2)
	tmp = x1 + (x2 * -6.0);
end

Wolfram

code[x1_, x2_] := N[(x1 + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 75.0%

   \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
2. Add Preprocessing

3. Taylor expanded in x1 around 0

   \[\leadsto \mathsf{+.f64}\left(x1, \color{blue}{\left(-6 \cdot x2\right)}\right) \]
4. Step-by-step derivation

   1. *-lowering-*.f64 29.6%

      \[\leadsto \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(-6, \color{blue}{x2}\right)\right) \]

5. Simplified 29.6%

   \[\leadsto x1 + \color{blue}{-6 \cdot x2} \]

6. Final simplification 29.6%

   \[\leadsto x1 + x2 \cdot -6 \]
7. Add Preprocessing

Alternative 26: 26.2% 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 75.0%

   \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
2. Add Preprocessing

3. Taylor expanded in x1 around 0

   \[\leadsto \color{blue}{-6 \cdot x2} \]
4. Step-by-step derivation

   1. *-lowering-*.f64 29.4%

      \[\leadsto \mathsf{*.f64}\left(-6, \color{blue}{x2}\right) \]

5. Simplified 29.4%

   \[\leadsto \color{blue}{-6 \cdot x2} \]

6. Final simplification 29.4%

   \[\leadsto x2 \cdot -6 \]
7. Add Preprocessing

Alternative 27: 3.3% accurate, 127.0× speedup

Math

\[\begin{array}{l} \\ x1 \end{array} \]

FPCore

(FPCore (x1 x2) :precision binary64 x1)

C

double code(double x1, double x2) {
	return x1;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    code = x1
end function

Java

public static double code(double x1, double x2) {
	return x1;
}

Python

def code(x1, x2):
	return x1

Julia

function code(x1, x2)
	return x1
end

MATLAB

function tmp = code(x1, x2)
	tmp = x1;
end

Wolfram

code[x1_, x2_] := x1

Derivation

1. Initial program 75.0%

   \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
2. Add Preprocessing

3. Taylor expanded in x1 around 0

   \[\leadsto \mathsf{+.f64}\left(x1, \color{blue}{\left(-6 \cdot x2\right)}\right) \]
4. Step-by-step derivation

   1. *-lowering-*.f64 29.6%

      \[\leadsto \mathsf{+.f64}\left(x1, \mathsf{*.f64}\left(-6, \color{blue}{x2}\right)\right) \]

5. Simplified 29.6%

   \[\leadsto x1 + \color{blue}{-6 \cdot x2} \]

6. Taylor expanded in x1 around inf

   \[\leadsto \color{blue}{x1} \]
7. Step-by-step derivation

8. Simplified 3.3%

   \[\leadsto \color{blue}{x1} \]
9. Add Preprocessing

Reproduce

herbie shell --seed 2024155 
(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))))))