Rosa's FloatVsDoubleBenchmark

Percentage Accurate: 70.1% → 99.5%

Time: 1.8min

Alternatives: 29

Speedup: 3.4×

• 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: 70.1% 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: 99.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(x1, x1 \cdot 3, 2 \cdot x2\right)\\ t_1 := x1 \cdot x1 + 1\\ t_2 := \frac{x1 - t\_0}{\mathsf{fma}\left(x1, x1, 1\right)}\\ t_3 := 3 \cdot \left(x1 \cdot x1\right)\\ t_4 := x1 \cdot \left(x1 \cdot 3\right)\\ t_5 := \frac{\left(t\_4 + 2 \cdot x2\right) - x1}{t\_1}\\ t_6 := \frac{t\_0 - x1}{\mathsf{fma}\left(x1, x1, 1\right)}\\ \mathbf{if}\;x1 + \left(\left(x1 + \left(\left(t\_1 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t\_5\right) \cdot \left(t\_5 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(t\_5 \cdot 4 - 6\right)\right) + t\_4 \cdot t\_5\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 3 \cdot \frac{x1 + \left(2 \cdot x2 - t\_4\right)}{-1 - x1 \cdot x1}\right) \leq \infty:\\ \;\;\;\;x1 + \mathsf{fma}\left(3, \frac{t\_3 - \mathsf{fma}\left(2, x2, x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}, x1 + \mathsf{fma}\left(\mathsf{fma}\left(x1, x1, 1\right), \mathsf{fma}\left(x1, x1 \cdot \mathsf{fma}\left(t\_6, 4, -6\right), \left(x1 \cdot \left(2 \cdot t\_2\right)\right) \cdot \left(t\_2 - -3\right)\right), \mathsf{fma}\left(t\_3, t\_6, {x1}^{3}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + 6 \cdot {x1}^{4}\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (fma x1 (* x1 3.0) (* 2.0 x2)))
        (t_1 (+ (* x1 x1) 1.0))
        (t_2 (/ (- x1 t_0) (fma x1 x1 1.0)))
        (t_3 (* 3.0 (* x1 x1)))
        (t_4 (* x1 (* x1 3.0)))
        (t_5 (/ (- (+ t_4 (* 2.0 x2)) x1) t_1))
        (t_6 (/ (- t_0 x1) (fma x1 x1 1.0))))
   (if (<=
        (+
         x1
         (+
          (+
           x1
           (+
            (+
             (*
              t_1
              (+
               (* (* (* x1 2.0) t_5) (- t_5 3.0))
               (* (* x1 x1) (- (* t_5 4.0) 6.0))))
             (* t_4 t_5))
            (* x1 (* x1 x1))))
          (* 3.0 (/ (+ x1 (- (* 2.0 x2) t_4)) (- -1.0 (* x1 x1))))))
        INFINITY)
     (+
      x1
      (fma
       3.0
       (/ (- t_3 (fma 2.0 x2 x1)) (fma x1 x1 1.0))
       (+
        x1
        (fma
         (fma x1 x1 1.0)
         (fma x1 (* x1 (fma t_6 4.0 -6.0)) (* (* x1 (* 2.0 t_2)) (- t_2 -3.0)))
         (fma t_3 t_6 (pow x1 3.0))))))
     (+ x1 (* 6.0 (pow x1 4.0))))))

C

double code(double x1, double x2) {
	double t_0 = fma(x1, (x1 * 3.0), (2.0 * x2));
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = (x1 - t_0) / fma(x1, x1, 1.0);
	double t_3 = 3.0 * (x1 * x1);
	double t_4 = x1 * (x1 * 3.0);
	double t_5 = ((t_4 + (2.0 * x2)) - x1) / t_1;
	double t_6 = (t_0 - x1) / fma(x1, x1, 1.0);
	double tmp;
	if ((x1 + ((x1 + (((t_1 * ((((x1 * 2.0) * t_5) * (t_5 - 3.0)) + ((x1 * x1) * ((t_5 * 4.0) - 6.0)))) + (t_4 * t_5)) + (x1 * (x1 * x1)))) + (3.0 * ((x1 + ((2.0 * x2) - t_4)) / (-1.0 - (x1 * x1)))))) <= ((double) INFINITY)) {
		tmp = x1 + fma(3.0, ((t_3 - fma(2.0, x2, x1)) / fma(x1, x1, 1.0)), (x1 + fma(fma(x1, x1, 1.0), fma(x1, (x1 * fma(t_6, 4.0, -6.0)), ((x1 * (2.0 * t_2)) * (t_2 - -3.0))), fma(t_3, t_6, pow(x1, 3.0)))));
	} else {
		tmp = x1 + (6.0 * pow(x1, 4.0));
	}
	return tmp;
}

Julia

function code(x1, x2)
	t_0 = fma(x1, Float64(x1 * 3.0), Float64(2.0 * x2))
	t_1 = Float64(Float64(x1 * x1) + 1.0)
	t_2 = Float64(Float64(x1 - t_0) / fma(x1, x1, 1.0))
	t_3 = Float64(3.0 * Float64(x1 * x1))
	t_4 = Float64(x1 * Float64(x1 * 3.0))
	t_5 = Float64(Float64(Float64(t_4 + Float64(2.0 * x2)) - x1) / t_1)
	t_6 = Float64(Float64(t_0 - x1) / fma(x1, x1, 1.0))
	tmp = 0.0
	if (Float64(x1 + Float64(Float64(x1 + Float64(Float64(Float64(t_1 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_5) * Float64(t_5 - 3.0)) + Float64(Float64(x1 * x1) * Float64(Float64(t_5 * 4.0) - 6.0)))) + Float64(t_4 * t_5)) + Float64(x1 * Float64(x1 * x1)))) + Float64(3.0 * Float64(Float64(x1 + Float64(Float64(2.0 * x2) - t_4)) / Float64(-1.0 - Float64(x1 * x1)))))) <= Inf)
		tmp = Float64(x1 + fma(3.0, Float64(Float64(t_3 - fma(2.0, x2, x1)) / fma(x1, x1, 1.0)), Float64(x1 + fma(fma(x1, x1, 1.0), fma(x1, Float64(x1 * fma(t_6, 4.0, -6.0)), Float64(Float64(x1 * Float64(2.0 * t_2)) * Float64(t_2 - -3.0))), fma(t_3, t_6, (x1 ^ 3.0))))));
	else
		tmp = Float64(x1 + Float64(6.0 * (x1 ^ 4.0)));
	end
	return tmp
end

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 99.4%

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

   3. Simplified 99.6%

      \[\leadsto \color{blue}{x1 + \mathsf{fma}\left(3, \frac{3 \cdot \left(x1 \cdot x1\right) - \mathsf{fma}\left(2, x2, x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}, x1 + \mathsf{fma}\left(\mathsf{fma}\left(x1, x1, 1\right), \mathsf{fma}\left(x1, x1 \cdot \mathsf{fma}\left(\frac{\mathsf{fma}\left(x1, x1 \cdot 3, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}, 4, -6\right), \left(x1 \cdot \left(2 \cdot \frac{\mathsf{fma}\left(x1, x1 \cdot 3, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}\right)\right) \cdot \left(\frac{\mathsf{fma}\left(x1, x1 \cdot 3, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)} + -3\right)\right), \mathsf{fma}\left(3 \cdot \left(x1 \cdot x1\right), \frac{\mathsf{fma}\left(x1, x1 \cdot 3, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}, {x1}^{3}\right)\right)\right)} \]
   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 0.0%

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

   4. Taylor expanded in x1 around 0 0.0%

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

      1. neg-mul-1 0.0%

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

      2. unsub-neg 0.0%

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

      3. *-commutative 0.0%

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

   6. Simplified 0.0%

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

   7. Taylor expanded in x1 around inf 100.0%

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

   8. Taylor expanded in x1 around inf 100.0%

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

4. Final simplification 99.7%

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

Alternative 2: 99.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot x1\right)\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := \left(t\_1 + 2 \cdot x2\right) - x1\\ t_3 := -1 - x1 \cdot x1\\ t_4 := x1 \cdot x1 + 1\\ t_5 := \frac{t\_2}{t\_4}\\ t_6 := \left(x1 \cdot 2\right) \cdot t\_5\\ t_7 := \left(x1 \cdot x1\right) \cdot \left(t\_5 \cdot 4 - 6\right)\\ \mathbf{if}\;x1 + \left(\left(x1 + \left(\left(t\_4 \cdot \left(t\_6 \cdot \left(t\_5 - 3\right) + t\_7\right) + t\_1 \cdot t\_5\right) + t\_0\right)\right) + 3 \cdot \frac{x1 + \left(2 \cdot x2 - t\_1\right)}{t\_3}\right) \leq \infty:\\ \;\;\;\;x1 + \left(\left(x1 + \left(t\_0 - \left(t\_4 \cdot \left(t\_6 \cdot \left(3 + \frac{t\_2}{t\_3}\right) - t\_7\right) - 3 \cdot t\_1\right)\right)\right) + 3 \cdot \left(x2 \cdot -2 - x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + 6 \cdot {x1}^{4}\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 x1)))
        (t_1 (* x1 (* x1 3.0)))
        (t_2 (- (+ t_1 (* 2.0 x2)) x1))
        (t_3 (- -1.0 (* x1 x1)))
        (t_4 (+ (* x1 x1) 1.0))
        (t_5 (/ t_2 t_4))
        (t_6 (* (* x1 2.0) t_5))
        (t_7 (* (* x1 x1) (- (* t_5 4.0) 6.0))))
   (if (<=
        (+
         x1
         (+
          (+ x1 (+ (+ (* t_4 (+ (* t_6 (- t_5 3.0)) t_7)) (* t_1 t_5)) t_0))
          (* 3.0 (/ (+ x1 (- (* 2.0 x2) t_1)) t_3))))
        INFINITY)
     (+
      x1
      (+
       (+
        x1
        (- t_0 (- (* t_4 (- (* t_6 (+ 3.0 (/ t_2 t_3))) t_7)) (* 3.0 t_1))))
       (* 3.0 (- (* x2 -2.0) x1))))
     (+ x1 (* 6.0 (pow x1 4.0))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * x1);
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = (t_1 + (2.0 * x2)) - x1;
	double t_3 = -1.0 - (x1 * x1);
	double t_4 = (x1 * x1) + 1.0;
	double t_5 = t_2 / t_4;
	double t_6 = (x1 * 2.0) * t_5;
	double t_7 = (x1 * x1) * ((t_5 * 4.0) - 6.0);
	double tmp;
	if ((x1 + ((x1 + (((t_4 * ((t_6 * (t_5 - 3.0)) + t_7)) + (t_1 * t_5)) + t_0)) + (3.0 * ((x1 + ((2.0 * x2) - t_1)) / t_3)))) <= ((double) INFINITY)) {
		tmp = x1 + ((x1 + (t_0 - ((t_4 * ((t_6 * (3.0 + (t_2 / t_3))) - t_7)) - (3.0 * t_1)))) + (3.0 * ((x2 * -2.0) - x1)));
	} else {
		tmp = x1 + (6.0 * pow(x1, 4.0));
	}
	return tmp;
}

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * x1);
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = (t_1 + (2.0 * x2)) - x1;
	double t_3 = -1.0 - (x1 * x1);
	double t_4 = (x1 * x1) + 1.0;
	double t_5 = t_2 / t_4;
	double t_6 = (x1 * 2.0) * t_5;
	double t_7 = (x1 * x1) * ((t_5 * 4.0) - 6.0);
	double tmp;
	if ((x1 + ((x1 + (((t_4 * ((t_6 * (t_5 - 3.0)) + t_7)) + (t_1 * t_5)) + t_0)) + (3.0 * ((x1 + ((2.0 * x2) - t_1)) / t_3)))) <= Double.POSITIVE_INFINITY) {
		tmp = x1 + ((x1 + (t_0 - ((t_4 * ((t_6 * (3.0 + (t_2 / t_3))) - t_7)) - (3.0 * t_1)))) + (3.0 * ((x2 * -2.0) - x1)));
	} else {
		tmp = x1 + (6.0 * Math.pow(x1, 4.0));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * x1)
	t_1 = x1 * (x1 * 3.0)
	t_2 = (t_1 + (2.0 * x2)) - x1
	t_3 = -1.0 - (x1 * x1)
	t_4 = (x1 * x1) + 1.0
	t_5 = t_2 / t_4
	t_6 = (x1 * 2.0) * t_5
	t_7 = (x1 * x1) * ((t_5 * 4.0) - 6.0)
	tmp = 0
	if (x1 + ((x1 + (((t_4 * ((t_6 * (t_5 - 3.0)) + t_7)) + (t_1 * t_5)) + t_0)) + (3.0 * ((x1 + ((2.0 * x2) - t_1)) / t_3)))) <= math.inf:
		tmp = x1 + ((x1 + (t_0 - ((t_4 * ((t_6 * (3.0 + (t_2 / t_3))) - t_7)) - (3.0 * t_1)))) + (3.0 * ((x2 * -2.0) - x1)))
	else:
		tmp = x1 + (6.0 * math.pow(x1, 4.0))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * x1))
	t_1 = Float64(x1 * Float64(x1 * 3.0))
	t_2 = Float64(Float64(t_1 + Float64(2.0 * x2)) - x1)
	t_3 = Float64(-1.0 - Float64(x1 * x1))
	t_4 = Float64(Float64(x1 * x1) + 1.0)
	t_5 = Float64(t_2 / t_4)
	t_6 = Float64(Float64(x1 * 2.0) * t_5)
	t_7 = Float64(Float64(x1 * x1) * Float64(Float64(t_5 * 4.0) - 6.0))
	tmp = 0.0
	if (Float64(x1 + Float64(Float64(x1 + Float64(Float64(Float64(t_4 * Float64(Float64(t_6 * Float64(t_5 - 3.0)) + t_7)) + Float64(t_1 * t_5)) + t_0)) + Float64(3.0 * Float64(Float64(x1 + Float64(Float64(2.0 * x2) - t_1)) / t_3)))) <= Inf)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(t_0 - Float64(Float64(t_4 * Float64(Float64(t_6 * Float64(3.0 + Float64(t_2 / t_3))) - t_7)) - Float64(3.0 * t_1)))) + Float64(3.0 * Float64(Float64(x2 * -2.0) - x1))));
	else
		tmp = Float64(x1 + Float64(6.0 * (x1 ^ 4.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * x1);
	t_1 = x1 * (x1 * 3.0);
	t_2 = (t_1 + (2.0 * x2)) - x1;
	t_3 = -1.0 - (x1 * x1);
	t_4 = (x1 * x1) + 1.0;
	t_5 = t_2 / t_4;
	t_6 = (x1 * 2.0) * t_5;
	t_7 = (x1 * x1) * ((t_5 * 4.0) - 6.0);
	tmp = 0.0;
	if ((x1 + ((x1 + (((t_4 * ((t_6 * (t_5 - 3.0)) + t_7)) + (t_1 * t_5)) + t_0)) + (3.0 * ((x1 + ((2.0 * x2) - t_1)) / t_3)))) <= Inf)
		tmp = x1 + ((x1 + (t_0 - ((t_4 * ((t_6 * (3.0 + (t_2 / t_3))) - t_7)) - (3.0 * t_1)))) + (3.0 * ((x2 * -2.0) - x1)));
	else
		tmp = x1 + (6.0 * (x1 ^ 4.0));
	end
	tmp_2 = tmp;
end

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 99.4%

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

   3. Taylor expanded in x1 around inf 98.4%

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

   4. Taylor expanded in x1 around 0 99.4%

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

      1. neg-mul-1 99.4%

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

      2. unsub-neg 99.4%

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

      3. *-commutative 99.4%

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

   6. Simplified 99.4%

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

   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 0.0%

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

   4. Taylor expanded in x1 around 0 0.0%

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

      1. neg-mul-1 0.0%

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

      2. unsub-neg 0.0%

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

      3. *-commutative 0.0%

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

   6. Simplified 0.0%

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

   7. Taylor expanded in x1 around inf 100.0%

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

   8. Taylor expanded in x1 around inf 100.0%

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

4. Final simplification 99.6%

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

Alternative 3: 95.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := 2 \cdot x2 - 3\\ t_2 := \left(t\_0 + 2 \cdot x2\right) - x1\\ t_3 := x2 \cdot \left(3 - 2 \cdot x2\right)\\ t_4 := 3 \cdot \left(x2 \cdot -2 - x1\right)\\ t_5 := x1 \cdot x1 + 1\\ t_6 := 4 \cdot t\_3\\ t_7 := \frac{t\_2}{t\_5}\\ \mathbf{if}\;x1 \leq -5.5 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(t\_4 + \left(x1 - x1 \cdot \left(x1 \cdot \left(\left(2 \cdot \left(t\_1 - x2 \cdot -2\right) + \left(x1 \cdot \left(3 + \left(t\_6 - 2 \cdot \left(\left(1 + \left(2 \cdot \left(x2 \cdot \left(3 + x2 \cdot -2\right)\right) + 3 \cdot t\_1\right)\right) + 2 \cdot t\_3\right)\right)\right) - x2 \cdot 8\right)\right) - 3\right) + t\_6\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 2.5 \cdot 10^{+152}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) - \left(t\_5 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t\_7\right) \cdot \left(3 + \frac{t\_2}{-1 - x1 \cdot x1}\right) - \left(x1 \cdot x1\right) \cdot \left(t\_7 \cdot 4 - 6\right)\right) - 3 \cdot t\_0\right)\right)\right) + t\_4\right)\\ \mathbf{else}:\\ \;\;\;\;x1 - \left(3 \cdot \left(x1 - x2 \cdot -2\right) + \left(x1 \cdot \left(t\_6 - x1 \cdot 9\right) - x1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (- (* 2.0 x2) 3.0))
        (t_2 (- (+ t_0 (* 2.0 x2)) x1))
        (t_3 (* x2 (- 3.0 (* 2.0 x2))))
        (t_4 (* 3.0 (- (* x2 -2.0) x1)))
        (t_5 (+ (* x1 x1) 1.0))
        (t_6 (* 4.0 t_3))
        (t_7 (/ t_2 t_5)))
   (if (<= x1 -5.5e+102)
     (+
      x1
      (+
       t_4
       (-
        x1
        (*
         x1
         (+
          (*
           x1
           (-
            (+
             (* 2.0 (- t_1 (* x2 -2.0)))
             (-
              (*
               x1
               (+
                3.0
                (-
                 t_6
                 (*
                  2.0
                  (+
                   (+ 1.0 (+ (* 2.0 (* x2 (+ 3.0 (* x2 -2.0)))) (* 3.0 t_1)))
                   (* 2.0 t_3))))))
              (* x2 8.0)))
            3.0))
          t_6)))))
     (if (<= x1 2.5e+152)
       (+
        x1
        (+
         (+
          x1
          (-
           (* x1 (* x1 x1))
           (-
            (*
             t_5
             (-
              (* (* (* x1 2.0) t_7) (+ 3.0 (/ t_2 (- -1.0 (* x1 x1)))))
              (* (* x1 x1) (- (* t_7 4.0) 6.0))))
            (* 3.0 t_0))))
         t_4))
       (-
        x1
        (+ (* 3.0 (- x1 (* x2 -2.0))) (- (* x1 (- t_6 (* x1 9.0))) x1)))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = (2.0 * x2) - 3.0;
	double t_2 = (t_0 + (2.0 * x2)) - x1;
	double t_3 = x2 * (3.0 - (2.0 * x2));
	double t_4 = 3.0 * ((x2 * -2.0) - x1);
	double t_5 = (x1 * x1) + 1.0;
	double t_6 = 4.0 * t_3;
	double t_7 = t_2 / t_5;
	double tmp;
	if (x1 <= -5.5e+102) {
		tmp = x1 + (t_4 + (x1 - (x1 * ((x1 * (((2.0 * (t_1 - (x2 * -2.0))) + ((x1 * (3.0 + (t_6 - (2.0 * ((1.0 + ((2.0 * (x2 * (3.0 + (x2 * -2.0)))) + (3.0 * t_1))) + (2.0 * t_3)))))) - (x2 * 8.0))) - 3.0)) + t_6))));
	} else if (x1 <= 2.5e+152) {
		tmp = x1 + ((x1 + ((x1 * (x1 * x1)) - ((t_5 * ((((x1 * 2.0) * t_7) * (3.0 + (t_2 / (-1.0 - (x1 * x1))))) - ((x1 * x1) * ((t_7 * 4.0) - 6.0)))) - (3.0 * t_0)))) + t_4);
	} else {
		tmp = x1 - ((3.0 * (x1 - (x2 * -2.0))) + ((x1 * (t_6 - (x1 * 9.0))) - 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) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: tmp
    t_0 = x1 * (x1 * 3.0d0)
    t_1 = (2.0d0 * x2) - 3.0d0
    t_2 = (t_0 + (2.0d0 * x2)) - x1
    t_3 = x2 * (3.0d0 - (2.0d0 * x2))
    t_4 = 3.0d0 * ((x2 * (-2.0d0)) - x1)
    t_5 = (x1 * x1) + 1.0d0
    t_6 = 4.0d0 * t_3
    t_7 = t_2 / t_5
    if (x1 <= (-5.5d+102)) then
        tmp = x1 + (t_4 + (x1 - (x1 * ((x1 * (((2.0d0 * (t_1 - (x2 * (-2.0d0)))) + ((x1 * (3.0d0 + (t_6 - (2.0d0 * ((1.0d0 + ((2.0d0 * (x2 * (3.0d0 + (x2 * (-2.0d0))))) + (3.0d0 * t_1))) + (2.0d0 * t_3)))))) - (x2 * 8.0d0))) - 3.0d0)) + t_6))))
    else if (x1 <= 2.5d+152) then
        tmp = x1 + ((x1 + ((x1 * (x1 * x1)) - ((t_5 * ((((x1 * 2.0d0) * t_7) * (3.0d0 + (t_2 / ((-1.0d0) - (x1 * x1))))) - ((x1 * x1) * ((t_7 * 4.0d0) - 6.0d0)))) - (3.0d0 * t_0)))) + t_4)
    else
        tmp = x1 - ((3.0d0 * (x1 - (x2 * (-2.0d0)))) + ((x1 * (t_6 - (x1 * 9.0d0))) - x1))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = (2.0 * x2) - 3.0;
	double t_2 = (t_0 + (2.0 * x2)) - x1;
	double t_3 = x2 * (3.0 - (2.0 * x2));
	double t_4 = 3.0 * ((x2 * -2.0) - x1);
	double t_5 = (x1 * x1) + 1.0;
	double t_6 = 4.0 * t_3;
	double t_7 = t_2 / t_5;
	double tmp;
	if (x1 <= -5.5e+102) {
		tmp = x1 + (t_4 + (x1 - (x1 * ((x1 * (((2.0 * (t_1 - (x2 * -2.0))) + ((x1 * (3.0 + (t_6 - (2.0 * ((1.0 + ((2.0 * (x2 * (3.0 + (x2 * -2.0)))) + (3.0 * t_1))) + (2.0 * t_3)))))) - (x2 * 8.0))) - 3.0)) + t_6))));
	} else if (x1 <= 2.5e+152) {
		tmp = x1 + ((x1 + ((x1 * (x1 * x1)) - ((t_5 * ((((x1 * 2.0) * t_7) * (3.0 + (t_2 / (-1.0 - (x1 * x1))))) - ((x1 * x1) * ((t_7 * 4.0) - 6.0)))) - (3.0 * t_0)))) + t_4);
	} else {
		tmp = x1 - ((3.0 * (x1 - (x2 * -2.0))) + ((x1 * (t_6 - (x1 * 9.0))) - x1));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = (2.0 * x2) - 3.0
	t_2 = (t_0 + (2.0 * x2)) - x1
	t_3 = x2 * (3.0 - (2.0 * x2))
	t_4 = 3.0 * ((x2 * -2.0) - x1)
	t_5 = (x1 * x1) + 1.0
	t_6 = 4.0 * t_3
	t_7 = t_2 / t_5
	tmp = 0
	if x1 <= -5.5e+102:
		tmp = x1 + (t_4 + (x1 - (x1 * ((x1 * (((2.0 * (t_1 - (x2 * -2.0))) + ((x1 * (3.0 + (t_6 - (2.0 * ((1.0 + ((2.0 * (x2 * (3.0 + (x2 * -2.0)))) + (3.0 * t_1))) + (2.0 * t_3)))))) - (x2 * 8.0))) - 3.0)) + t_6))))
	elif x1 <= 2.5e+152:
		tmp = x1 + ((x1 + ((x1 * (x1 * x1)) - ((t_5 * ((((x1 * 2.0) * t_7) * (3.0 + (t_2 / (-1.0 - (x1 * x1))))) - ((x1 * x1) * ((t_7 * 4.0) - 6.0)))) - (3.0 * t_0)))) + t_4)
	else:
		tmp = x1 - ((3.0 * (x1 - (x2 * -2.0))) + ((x1 * (t_6 - (x1 * 9.0))) - x1))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(Float64(2.0 * x2) - 3.0)
	t_2 = Float64(Float64(t_0 + Float64(2.0 * x2)) - x1)
	t_3 = Float64(x2 * Float64(3.0 - Float64(2.0 * x2)))
	t_4 = Float64(3.0 * Float64(Float64(x2 * -2.0) - x1))
	t_5 = Float64(Float64(x1 * x1) + 1.0)
	t_6 = Float64(4.0 * t_3)
	t_7 = Float64(t_2 / t_5)
	tmp = 0.0
	if (x1 <= -5.5e+102)
		tmp = Float64(x1 + Float64(t_4 + Float64(x1 - Float64(x1 * Float64(Float64(x1 * Float64(Float64(Float64(2.0 * Float64(t_1 - Float64(x2 * -2.0))) + Float64(Float64(x1 * Float64(3.0 + Float64(t_6 - Float64(2.0 * Float64(Float64(1.0 + Float64(Float64(2.0 * Float64(x2 * Float64(3.0 + Float64(x2 * -2.0)))) + Float64(3.0 * t_1))) + Float64(2.0 * t_3)))))) - Float64(x2 * 8.0))) - 3.0)) + t_6)))));
	elseif (x1 <= 2.5e+152)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) - Float64(Float64(t_5 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_7) * Float64(3.0 + Float64(t_2 / Float64(-1.0 - Float64(x1 * x1))))) - Float64(Float64(x1 * x1) * Float64(Float64(t_7 * 4.0) - 6.0)))) - Float64(3.0 * t_0)))) + t_4));
	else
		tmp = Float64(x1 - Float64(Float64(3.0 * Float64(x1 - Float64(x2 * -2.0))) + Float64(Float64(x1 * Float64(t_6 - Float64(x1 * 9.0))) - x1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * 3.0);
	t_1 = (2.0 * x2) - 3.0;
	t_2 = (t_0 + (2.0 * x2)) - x1;
	t_3 = x2 * (3.0 - (2.0 * x2));
	t_4 = 3.0 * ((x2 * -2.0) - x1);
	t_5 = (x1 * x1) + 1.0;
	t_6 = 4.0 * t_3;
	t_7 = t_2 / t_5;
	tmp = 0.0;
	if (x1 <= -5.5e+102)
		tmp = x1 + (t_4 + (x1 - (x1 * ((x1 * (((2.0 * (t_1 - (x2 * -2.0))) + ((x1 * (3.0 + (t_6 - (2.0 * ((1.0 + ((2.0 * (x2 * (3.0 + (x2 * -2.0)))) + (3.0 * t_1))) + (2.0 * t_3)))))) - (x2 * 8.0))) - 3.0)) + t_6))));
	elseif (x1 <= 2.5e+152)
		tmp = x1 + ((x1 + ((x1 * (x1 * x1)) - ((t_5 * ((((x1 * 2.0) * t_7) * (3.0 + (t_2 / (-1.0 - (x1 * x1))))) - ((x1 * x1) * ((t_7 * 4.0) - 6.0)))) - (3.0 * t_0)))) + t_4);
	else
		tmp = x1 - ((3.0 * (x1 - (x2 * -2.0))) + ((x1 * (t_6 - (x1 * 9.0))) - x1));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]}, Block[{t$95$3 = N[(x2 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$6 = N[(4.0 * t$95$3), $MachinePrecision]}, Block[{t$95$7 = N[(t$95$2 / t$95$5), $MachinePrecision]}, If[LessEqual[x1, -5.5e+102], N[(x1 + N[(t$95$4 + N[(x1 - N[(x1 * N[(N[(x1 * N[(N[(N[(2.0 * N[(t$95$1 - N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * N[(3.0 + N[(t$95$6 - N[(2.0 * N[(N[(1.0 + N[(N[(2.0 * N[(x2 * N[(3.0 + N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(2.0 * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x2 * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision] + t$95$6), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 2.5e+152], N[(x1 + N[(N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] - N[(N[(t$95$5 * N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$7), $MachinePrecision] * N[(3.0 + N[(t$95$2 / N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$7 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(3.0 * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$4), $MachinePrecision]), $MachinePrecision], N[(x1 - N[(N[(3.0 * N[(x1 - N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * N[(t$95$6 - N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -5.49999999999999981e102

   1. Initial program 0.0%

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

   3. Taylor expanded in x1 around inf 0.0%

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

   4. Taylor expanded in x1 around 0 0.0%

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

      1. neg-mul-1 0.0%

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

      2. unsub-neg 0.0%

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

      3. *-commutative 0.0%

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

   6. Simplified 0.0%

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

   7. Taylor expanded in x1 around 0 80.0%

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

   if -5.49999999999999981e102 < x1 < 2.5e152

   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 inf 98.4%

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

   4. Taylor expanded in x1 around 0 99.4%

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

      1. neg-mul-1 99.4%

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

      2. unsub-neg 99.4%

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

      3. *-commutative 99.4%

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

   6. Simplified 99.4%

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

   if 2.5e152 < x1

   1. Initial program 5.6%

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

   3. Taylor expanded in x1 around inf 5.6%

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

   4. Taylor expanded in x1 around 0 5.6%

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

      1. neg-mul-1 5.6%

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

      2. unsub-neg 5.6%

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

      3. *-commutative 5.6%

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

   6. Simplified 5.6%

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

   7. Taylor expanded in x1 around 0 97.7%

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

   8. Taylor expanded in x2 around 0 100.0%

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

4. Final simplification 96.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.5 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2 - x1\right) + \left(x1 - x1 \cdot \left(x1 \cdot \left(\left(2 \cdot \left(\left(2 \cdot x2 - 3\right) - x2 \cdot -2\right) + \left(x1 \cdot \left(3 + \left(4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right) - 2 \cdot \left(\left(1 + \left(2 \cdot \left(x2 \cdot \left(3 + x2 \cdot -2\right)\right) + 3 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + 2 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right)\right) - x2 \cdot 8\right)\right) - 3\right) + 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 2.5 \cdot 10^{+152}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) - \left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(3 + \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1}\right) - \left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right)\right) - 3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right)\right)\right)\right) + 3 \cdot \left(x2 \cdot -2 - x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 - \left(3 \cdot \left(x1 - x2 \cdot -2\right) + \left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right) - x1 \cdot 9\right) - x1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 92.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 2 \cdot x2 - 3\\ t_1 := 4 \cdot \left(x2 \cdot t\_0\right)\\ t_2 := 3 \cdot \left(x2 \cdot -2 - x1\right)\\ t_3 := x1 \cdot x1 + 1\\ t_4 := 3 - 2 \cdot x2\\ t_5 := x1 \cdot \left(x1 \cdot 3\right)\\ t_6 := \frac{\left(t\_5 + 2 \cdot x2\right) - x1}{t\_3}\\ \mathbf{if}\;x1 \leq -5.5 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(t\_2 + \left(x1 + x1 \cdot \left(t\_1 + x1 \cdot \left(3 + \left(2 \cdot \left(x2 \cdot -2 + t\_4\right) + \left(x2 \cdot 8 + x1 \cdot \left(\left(t\_1 + 2 \cdot \left(\left(1 + \left(2 \cdot \left(x2 \cdot \left(3 + x2 \cdot -2\right)\right) + 3 \cdot t\_0\right)\right) + 2 \cdot \left(x2 \cdot t\_4\right)\right)\right) - 3\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 2.5 \cdot 10^{+152}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t\_5 - 2 \cdot x2\right) - x1}{t\_3} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot t\_5 + t\_3 \cdot \left(\left(x1 \cdot x1\right) \cdot 6 - \left(\left(x1 \cdot 2\right) \cdot t\_6\right) \cdot \left(3 - t\_6\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(t\_2 + \left(x1 + x1 \cdot \left(t\_1 + x1 \cdot 9\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (- (* 2.0 x2) 3.0))
        (t_1 (* 4.0 (* x2 t_0)))
        (t_2 (* 3.0 (- (* x2 -2.0) x1)))
        (t_3 (+ (* x1 x1) 1.0))
        (t_4 (- 3.0 (* 2.0 x2)))
        (t_5 (* x1 (* x1 3.0)))
        (t_6 (/ (- (+ t_5 (* 2.0 x2)) x1) t_3)))
   (if (<= x1 -5.5e+102)
     (+
      x1
      (+
       t_2
       (+
        x1
        (*
         x1
         (+
          t_1
          (*
           x1
           (+
            3.0
            (+
             (* 2.0 (+ (* x2 -2.0) t_4))
             (+
              (* x2 8.0)
              (*
               x1
               (-
                (+
                 t_1
                 (*
                  2.0
                  (+
                   (+ 1.0 (+ (* 2.0 (* x2 (+ 3.0 (* x2 -2.0)))) (* 3.0 t_0)))
                   (* 2.0 (* x2 t_4)))))
                3.0)))))))))))
     (if (<= x1 2.5e+152)
       (+
        x1
        (+
         (* 3.0 (/ (- (- t_5 (* 2.0 x2)) x1) t_3))
         (+
          x1
          (+
           (* x1 (* x1 x1))
           (+
            (* 3.0 t_5)
            (*
             t_3
             (- (* (* x1 x1) 6.0) (* (* (* x1 2.0) t_6) (- 3.0 t_6)))))))))
       (+ x1 (+ t_2 (+ x1 (* x1 (+ t_1 (* x1 9.0))))))))))

C

double code(double x1, double x2) {
	double t_0 = (2.0 * x2) - 3.0;
	double t_1 = 4.0 * (x2 * t_0);
	double t_2 = 3.0 * ((x2 * -2.0) - x1);
	double t_3 = (x1 * x1) + 1.0;
	double t_4 = 3.0 - (2.0 * x2);
	double t_5 = x1 * (x1 * 3.0);
	double t_6 = ((t_5 + (2.0 * x2)) - x1) / t_3;
	double tmp;
	if (x1 <= -5.5e+102) {
		tmp = x1 + (t_2 + (x1 + (x1 * (t_1 + (x1 * (3.0 + ((2.0 * ((x2 * -2.0) + t_4)) + ((x2 * 8.0) + (x1 * ((t_1 + (2.0 * ((1.0 + ((2.0 * (x2 * (3.0 + (x2 * -2.0)))) + (3.0 * t_0))) + (2.0 * (x2 * t_4))))) - 3.0))))))))));
	} else if (x1 <= 2.5e+152) {
		tmp = x1 + ((3.0 * (((t_5 - (2.0 * x2)) - x1) / t_3)) + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_5) + (t_3 * (((x1 * x1) * 6.0) - (((x1 * 2.0) * t_6) * (3.0 - t_6))))))));
	} else {
		tmp = x1 + (t_2 + (x1 + (x1 * (t_1 + (x1 * 9.0)))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: tmp
    t_0 = (2.0d0 * x2) - 3.0d0
    t_1 = 4.0d0 * (x2 * t_0)
    t_2 = 3.0d0 * ((x2 * (-2.0d0)) - x1)
    t_3 = (x1 * x1) + 1.0d0
    t_4 = 3.0d0 - (2.0d0 * x2)
    t_5 = x1 * (x1 * 3.0d0)
    t_6 = ((t_5 + (2.0d0 * x2)) - x1) / t_3
    if (x1 <= (-5.5d+102)) then
        tmp = x1 + (t_2 + (x1 + (x1 * (t_1 + (x1 * (3.0d0 + ((2.0d0 * ((x2 * (-2.0d0)) + t_4)) + ((x2 * 8.0d0) + (x1 * ((t_1 + (2.0d0 * ((1.0d0 + ((2.0d0 * (x2 * (3.0d0 + (x2 * (-2.0d0))))) + (3.0d0 * t_0))) + (2.0d0 * (x2 * t_4))))) - 3.0d0))))))))))
    else if (x1 <= 2.5d+152) then
        tmp = x1 + ((3.0d0 * (((t_5 - (2.0d0 * x2)) - x1) / t_3)) + (x1 + ((x1 * (x1 * x1)) + ((3.0d0 * t_5) + (t_3 * (((x1 * x1) * 6.0d0) - (((x1 * 2.0d0) * t_6) * (3.0d0 - t_6))))))))
    else
        tmp = x1 + (t_2 + (x1 + (x1 * (t_1 + (x1 * 9.0d0)))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (2.0 * x2) - 3.0;
	double t_1 = 4.0 * (x2 * t_0);
	double t_2 = 3.0 * ((x2 * -2.0) - x1);
	double t_3 = (x1 * x1) + 1.0;
	double t_4 = 3.0 - (2.0 * x2);
	double t_5 = x1 * (x1 * 3.0);
	double t_6 = ((t_5 + (2.0 * x2)) - x1) / t_3;
	double tmp;
	if (x1 <= -5.5e+102) {
		tmp = x1 + (t_2 + (x1 + (x1 * (t_1 + (x1 * (3.0 + ((2.0 * ((x2 * -2.0) + t_4)) + ((x2 * 8.0) + (x1 * ((t_1 + (2.0 * ((1.0 + ((2.0 * (x2 * (3.0 + (x2 * -2.0)))) + (3.0 * t_0))) + (2.0 * (x2 * t_4))))) - 3.0))))))))));
	} else if (x1 <= 2.5e+152) {
		tmp = x1 + ((3.0 * (((t_5 - (2.0 * x2)) - x1) / t_3)) + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_5) + (t_3 * (((x1 * x1) * 6.0) - (((x1 * 2.0) * t_6) * (3.0 - t_6))))))));
	} else {
		tmp = x1 + (t_2 + (x1 + (x1 * (t_1 + (x1 * 9.0)))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (2.0 * x2) - 3.0
	t_1 = 4.0 * (x2 * t_0)
	t_2 = 3.0 * ((x2 * -2.0) - x1)
	t_3 = (x1 * x1) + 1.0
	t_4 = 3.0 - (2.0 * x2)
	t_5 = x1 * (x1 * 3.0)
	t_6 = ((t_5 + (2.0 * x2)) - x1) / t_3
	tmp = 0
	if x1 <= -5.5e+102:
		tmp = x1 + (t_2 + (x1 + (x1 * (t_1 + (x1 * (3.0 + ((2.0 * ((x2 * -2.0) + t_4)) + ((x2 * 8.0) + (x1 * ((t_1 + (2.0 * ((1.0 + ((2.0 * (x2 * (3.0 + (x2 * -2.0)))) + (3.0 * t_0))) + (2.0 * (x2 * t_4))))) - 3.0))))))))))
	elif x1 <= 2.5e+152:
		tmp = x1 + ((3.0 * (((t_5 - (2.0 * x2)) - x1) / t_3)) + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_5) + (t_3 * (((x1 * x1) * 6.0) - (((x1 * 2.0) * t_6) * (3.0 - t_6))))))))
	else:
		tmp = x1 + (t_2 + (x1 + (x1 * (t_1 + (x1 * 9.0)))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(2.0 * x2) - 3.0)
	t_1 = Float64(4.0 * Float64(x2 * t_0))
	t_2 = Float64(3.0 * Float64(Float64(x2 * -2.0) - x1))
	t_3 = Float64(Float64(x1 * x1) + 1.0)
	t_4 = Float64(3.0 - Float64(2.0 * x2))
	t_5 = Float64(x1 * Float64(x1 * 3.0))
	t_6 = Float64(Float64(Float64(t_5 + Float64(2.0 * x2)) - x1) / t_3)
	tmp = 0.0
	if (x1 <= -5.5e+102)
		tmp = Float64(x1 + Float64(t_2 + Float64(x1 + Float64(x1 * Float64(t_1 + Float64(x1 * Float64(3.0 + Float64(Float64(2.0 * Float64(Float64(x2 * -2.0) + t_4)) + Float64(Float64(x2 * 8.0) + Float64(x1 * Float64(Float64(t_1 + Float64(2.0 * Float64(Float64(1.0 + Float64(Float64(2.0 * Float64(x2 * Float64(3.0 + Float64(x2 * -2.0)))) + Float64(3.0 * t_0))) + Float64(2.0 * Float64(x2 * t_4))))) - 3.0)))))))))));
	elseif (x1 <= 2.5e+152)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_5 - Float64(2.0 * x2)) - x1) / t_3)) + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(3.0 * t_5) + Float64(t_3 * Float64(Float64(Float64(x1 * x1) * 6.0) - Float64(Float64(Float64(x1 * 2.0) * t_6) * Float64(3.0 - t_6)))))))));
	else
		tmp = Float64(x1 + Float64(t_2 + Float64(x1 + Float64(x1 * Float64(t_1 + Float64(x1 * 9.0))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (2.0 * x2) - 3.0;
	t_1 = 4.0 * (x2 * t_0);
	t_2 = 3.0 * ((x2 * -2.0) - x1);
	t_3 = (x1 * x1) + 1.0;
	t_4 = 3.0 - (2.0 * x2);
	t_5 = x1 * (x1 * 3.0);
	t_6 = ((t_5 + (2.0 * x2)) - x1) / t_3;
	tmp = 0.0;
	if (x1 <= -5.5e+102)
		tmp = x1 + (t_2 + (x1 + (x1 * (t_1 + (x1 * (3.0 + ((2.0 * ((x2 * -2.0) + t_4)) + ((x2 * 8.0) + (x1 * ((t_1 + (2.0 * ((1.0 + ((2.0 * (x2 * (3.0 + (x2 * -2.0)))) + (3.0 * t_0))) + (2.0 * (x2 * t_4))))) - 3.0))))))))));
	elseif (x1 <= 2.5e+152)
		tmp = x1 + ((3.0 * (((t_5 - (2.0 * x2)) - x1) / t_3)) + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_5) + (t_3 * (((x1 * x1) * 6.0) - (((x1 * 2.0) * t_6) * (3.0 - t_6))))))));
	else
		tmp = x1 + (t_2 + (x1 + (x1 * (t_1 + (x1 * 9.0)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]}, Block[{t$95$1 = N[(4.0 * N[(x2 * t$95$0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$4 = N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(N[(t$95$5 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$3), $MachinePrecision]}, If[LessEqual[x1, -5.5e+102], N[(x1 + N[(t$95$2 + N[(x1 + N[(x1 * N[(t$95$1 + N[(x1 * N[(3.0 + N[(N[(2.0 * N[(N[(x2 * -2.0), $MachinePrecision] + t$95$4), $MachinePrecision]), $MachinePrecision] + N[(N[(x2 * 8.0), $MachinePrecision] + N[(x1 * N[(N[(t$95$1 + N[(2.0 * N[(N[(1.0 + N[(N[(2.0 * N[(x2 * N[(3.0 + N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(2.0 * N[(x2 * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 2.5e+152], N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$5 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$3), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(3.0 * t$95$5), $MachinePrecision] + N[(t$95$3 * N[(N[(N[(x1 * x1), $MachinePrecision] * 6.0), $MachinePrecision] - N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$6), $MachinePrecision] * N[(3.0 - t$95$6), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(t$95$2 + N[(x1 + N[(x1 * N[(t$95$1 + N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -5.49999999999999981e102

   1. Initial program 0.0%

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

   3. Taylor expanded in x1 around inf 0.0%

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

   4. Taylor expanded in x1 around 0 0.0%

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

      1. neg-mul-1 0.0%

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

      2. unsub-neg 0.0%

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

      3. *-commutative 0.0%

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

   6. Simplified 0.0%

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

   7. Taylor expanded in x1 around 0 80.0%

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

   if -5.49999999999999981e102 < x1 < 2.5e152

   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 inf 98.4%

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

   4. Taylor expanded in x1 around inf 97.7%

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

   if 2.5e152 < x1

   1. Initial program 5.6%

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

   3. Taylor expanded in x1 around inf 5.6%

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

   4. Taylor expanded in x1 around 0 5.6%

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

      1. neg-mul-1 5.6%

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

      2. unsub-neg 5.6%

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

      3. *-commutative 5.6%

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

   6. Simplified 5.6%

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

   7. Taylor expanded in x1 around 0 97.7%

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

   8. Taylor expanded in x2 around 0 100.0%

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

4. Final simplification 94.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.5 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2 - x1\right) + \left(x1 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(3 + \left(2 \cdot \left(x2 \cdot -2 + \left(3 - 2 \cdot x2\right)\right) + \left(x2 \cdot 8 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + 2 \cdot \left(\left(1 + \left(2 \cdot \left(x2 \cdot \left(3 + x2 \cdot -2\right)\right) + 3 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + 2 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right) - 3\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 2.5 \cdot 10^{+152}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot 6 - \left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(3 - \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2 - x1\right) + \left(x1 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot 9\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 87.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 2 \cdot x2 - 3\\ t_1 := x1 \cdot x1 + 1\\ t_2 := 3 \cdot \left(x2 \cdot -2 - x1\right)\\ t_3 := x1 \cdot \left(x1 \cdot x1\right)\\ t_4 := x1 \cdot \left(x1 \cdot 3\right)\\ t_5 := \frac{\left(t\_4 + 2 \cdot x2\right) - x1}{t\_1}\\ t_6 := \left(x1 \cdot 2\right) \cdot t\_5\\ t_7 := 3 \cdot t\_4\\ \mathbf{if}\;x1 \leq -5.5 \cdot 10^{+102}:\\ \;\;\;\;x1 - \left(x2 \cdot \left(6 - -3 \cdot \frac{x1}{x2}\right) + \left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right) - x1 \cdot \left(3 + \left(x2 \cdot 8 - 2 \cdot \left(t\_0 - x2 \cdot -2\right)\right)\right)\right) - x1\right)\right)\\ \mathbf{elif}\;x1 \leq -0.106:\\ \;\;\;\;x1 + \left(\left(x1 + \left(t\_3 + \left(t\_7 + t\_1 \cdot \left(\left(x1 \cdot x1\right) \cdot 6 - t\_6 \cdot \left(3 - t\_5\right)\right)\right)\right)\right) + 3 \cdot \left(x2 \cdot -2\right)\right)\\ \mathbf{elif}\;x1 \leq 7.5 \cdot 10^{+138}:\\ \;\;\;\;x1 + \left(t\_2 + \left(x1 + \left(t\_3 + \left(t\_7 + t\_1 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(t\_5 \cdot 4 - 6\right) + t\_6 \cdot t\_0\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(t\_2 + \left(x1 + x1 \cdot \left(4 \cdot \left(x2 \cdot t\_0\right) + x1 \cdot 9\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (- (* 2.0 x2) 3.0))
        (t_1 (+ (* x1 x1) 1.0))
        (t_2 (* 3.0 (- (* x2 -2.0) x1)))
        (t_3 (* x1 (* x1 x1)))
        (t_4 (* x1 (* x1 3.0)))
        (t_5 (/ (- (+ t_4 (* 2.0 x2)) x1) t_1))
        (t_6 (* (* x1 2.0) t_5))
        (t_7 (* 3.0 t_4)))
   (if (<= x1 -5.5e+102)
     (-
      x1
      (+
       (* x2 (- 6.0 (* -3.0 (/ x1 x2))))
       (-
        (*
         x1
         (-
          (* 4.0 (* x2 (- 3.0 (* 2.0 x2))))
          (* x1 (+ 3.0 (- (* x2 8.0) (* 2.0 (- t_0 (* x2 -2.0))))))))
        x1)))
     (if (<= x1 -0.106)
       (+
        x1
        (+
         (+
          x1
          (+ t_3 (+ t_7 (* t_1 (- (* (* x1 x1) 6.0) (* t_6 (- 3.0 t_5)))))))
         (* 3.0 (* x2 -2.0))))
       (if (<= x1 7.5e+138)
         (+
          x1
          (+
           t_2
           (+
            x1
            (+
             t_3
             (+
              t_7
              (* t_1 (+ (* (* x1 x1) (- (* t_5 4.0) 6.0)) (* t_6 t_0))))))))
         (+ x1 (+ t_2 (+ x1 (* x1 (+ (* 4.0 (* x2 t_0)) (* x1 9.0)))))))))))

C

double code(double x1, double x2) {
	double t_0 = (2.0 * x2) - 3.0;
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = 3.0 * ((x2 * -2.0) - x1);
	double t_3 = x1 * (x1 * x1);
	double t_4 = x1 * (x1 * 3.0);
	double t_5 = ((t_4 + (2.0 * x2)) - x1) / t_1;
	double t_6 = (x1 * 2.0) * t_5;
	double t_7 = 3.0 * t_4;
	double tmp;
	if (x1 <= -5.5e+102) {
		tmp = x1 - ((x2 * (6.0 - (-3.0 * (x1 / x2)))) + ((x1 * ((4.0 * (x2 * (3.0 - (2.0 * x2)))) - (x1 * (3.0 + ((x2 * 8.0) - (2.0 * (t_0 - (x2 * -2.0)))))))) - x1));
	} else if (x1 <= -0.106) {
		tmp = x1 + ((x1 + (t_3 + (t_7 + (t_1 * (((x1 * x1) * 6.0) - (t_6 * (3.0 - t_5))))))) + (3.0 * (x2 * -2.0)));
	} else if (x1 <= 7.5e+138) {
		tmp = x1 + (t_2 + (x1 + (t_3 + (t_7 + (t_1 * (((x1 * x1) * ((t_5 * 4.0) - 6.0)) + (t_6 * t_0)))))));
	} else {
		tmp = x1 + (t_2 + (x1 + (x1 * ((4.0 * (x2 * t_0)) + (x1 * 9.0)))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: tmp
    t_0 = (2.0d0 * x2) - 3.0d0
    t_1 = (x1 * x1) + 1.0d0
    t_2 = 3.0d0 * ((x2 * (-2.0d0)) - x1)
    t_3 = x1 * (x1 * x1)
    t_4 = x1 * (x1 * 3.0d0)
    t_5 = ((t_4 + (2.0d0 * x2)) - x1) / t_1
    t_6 = (x1 * 2.0d0) * t_5
    t_7 = 3.0d0 * t_4
    if (x1 <= (-5.5d+102)) then
        tmp = x1 - ((x2 * (6.0d0 - ((-3.0d0) * (x1 / x2)))) + ((x1 * ((4.0d0 * (x2 * (3.0d0 - (2.0d0 * x2)))) - (x1 * (3.0d0 + ((x2 * 8.0d0) - (2.0d0 * (t_0 - (x2 * (-2.0d0))))))))) - x1))
    else if (x1 <= (-0.106d0)) then
        tmp = x1 + ((x1 + (t_3 + (t_7 + (t_1 * (((x1 * x1) * 6.0d0) - (t_6 * (3.0d0 - t_5))))))) + (3.0d0 * (x2 * (-2.0d0))))
    else if (x1 <= 7.5d+138) then
        tmp = x1 + (t_2 + (x1 + (t_3 + (t_7 + (t_1 * (((x1 * x1) * ((t_5 * 4.0d0) - 6.0d0)) + (t_6 * t_0)))))))
    else
        tmp = x1 + (t_2 + (x1 + (x1 * ((4.0d0 * (x2 * t_0)) + (x1 * 9.0d0)))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (2.0 * x2) - 3.0;
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = 3.0 * ((x2 * -2.0) - x1);
	double t_3 = x1 * (x1 * x1);
	double t_4 = x1 * (x1 * 3.0);
	double t_5 = ((t_4 + (2.0 * x2)) - x1) / t_1;
	double t_6 = (x1 * 2.0) * t_5;
	double t_7 = 3.0 * t_4;
	double tmp;
	if (x1 <= -5.5e+102) {
		tmp = x1 - ((x2 * (6.0 - (-3.0 * (x1 / x2)))) + ((x1 * ((4.0 * (x2 * (3.0 - (2.0 * x2)))) - (x1 * (3.0 + ((x2 * 8.0) - (2.0 * (t_0 - (x2 * -2.0)))))))) - x1));
	} else if (x1 <= -0.106) {
		tmp = x1 + ((x1 + (t_3 + (t_7 + (t_1 * (((x1 * x1) * 6.0) - (t_6 * (3.0 - t_5))))))) + (3.0 * (x2 * -2.0)));
	} else if (x1 <= 7.5e+138) {
		tmp = x1 + (t_2 + (x1 + (t_3 + (t_7 + (t_1 * (((x1 * x1) * ((t_5 * 4.0) - 6.0)) + (t_6 * t_0)))))));
	} else {
		tmp = x1 + (t_2 + (x1 + (x1 * ((4.0 * (x2 * t_0)) + (x1 * 9.0)))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (2.0 * x2) - 3.0
	t_1 = (x1 * x1) + 1.0
	t_2 = 3.0 * ((x2 * -2.0) - x1)
	t_3 = x1 * (x1 * x1)
	t_4 = x1 * (x1 * 3.0)
	t_5 = ((t_4 + (2.0 * x2)) - x1) / t_1
	t_6 = (x1 * 2.0) * t_5
	t_7 = 3.0 * t_4
	tmp = 0
	if x1 <= -5.5e+102:
		tmp = x1 - ((x2 * (6.0 - (-3.0 * (x1 / x2)))) + ((x1 * ((4.0 * (x2 * (3.0 - (2.0 * x2)))) - (x1 * (3.0 + ((x2 * 8.0) - (2.0 * (t_0 - (x2 * -2.0)))))))) - x1))
	elif x1 <= -0.106:
		tmp = x1 + ((x1 + (t_3 + (t_7 + (t_1 * (((x1 * x1) * 6.0) - (t_6 * (3.0 - t_5))))))) + (3.0 * (x2 * -2.0)))
	elif x1 <= 7.5e+138:
		tmp = x1 + (t_2 + (x1 + (t_3 + (t_7 + (t_1 * (((x1 * x1) * ((t_5 * 4.0) - 6.0)) + (t_6 * t_0)))))))
	else:
		tmp = x1 + (t_2 + (x1 + (x1 * ((4.0 * (x2 * t_0)) + (x1 * 9.0)))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(2.0 * x2) - 3.0)
	t_1 = Float64(Float64(x1 * x1) + 1.0)
	t_2 = Float64(3.0 * Float64(Float64(x2 * -2.0) - x1))
	t_3 = Float64(x1 * Float64(x1 * x1))
	t_4 = Float64(x1 * Float64(x1 * 3.0))
	t_5 = Float64(Float64(Float64(t_4 + Float64(2.0 * x2)) - x1) / t_1)
	t_6 = Float64(Float64(x1 * 2.0) * t_5)
	t_7 = Float64(3.0 * t_4)
	tmp = 0.0
	if (x1 <= -5.5e+102)
		tmp = Float64(x1 - Float64(Float64(x2 * Float64(6.0 - Float64(-3.0 * Float64(x1 / x2)))) + Float64(Float64(x1 * Float64(Float64(4.0 * Float64(x2 * Float64(3.0 - Float64(2.0 * x2)))) - Float64(x1 * Float64(3.0 + Float64(Float64(x2 * 8.0) - Float64(2.0 * Float64(t_0 - Float64(x2 * -2.0)))))))) - x1)));
	elseif (x1 <= -0.106)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(t_3 + Float64(t_7 + Float64(t_1 * Float64(Float64(Float64(x1 * x1) * 6.0) - Float64(t_6 * Float64(3.0 - t_5))))))) + Float64(3.0 * Float64(x2 * -2.0))));
	elseif (x1 <= 7.5e+138)
		tmp = Float64(x1 + Float64(t_2 + Float64(x1 + Float64(t_3 + Float64(t_7 + Float64(t_1 * Float64(Float64(Float64(x1 * x1) * Float64(Float64(t_5 * 4.0) - 6.0)) + Float64(t_6 * t_0))))))));
	else
		tmp = Float64(x1 + Float64(t_2 + Float64(x1 + Float64(x1 * Float64(Float64(4.0 * Float64(x2 * t_0)) + Float64(x1 * 9.0))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (2.0 * x2) - 3.0;
	t_1 = (x1 * x1) + 1.0;
	t_2 = 3.0 * ((x2 * -2.0) - x1);
	t_3 = x1 * (x1 * x1);
	t_4 = x1 * (x1 * 3.0);
	t_5 = ((t_4 + (2.0 * x2)) - x1) / t_1;
	t_6 = (x1 * 2.0) * t_5;
	t_7 = 3.0 * t_4;
	tmp = 0.0;
	if (x1 <= -5.5e+102)
		tmp = x1 - ((x2 * (6.0 - (-3.0 * (x1 / x2)))) + ((x1 * ((4.0 * (x2 * (3.0 - (2.0 * x2)))) - (x1 * (3.0 + ((x2 * 8.0) - (2.0 * (t_0 - (x2 * -2.0)))))))) - x1));
	elseif (x1 <= -0.106)
		tmp = x1 + ((x1 + (t_3 + (t_7 + (t_1 * (((x1 * x1) * 6.0) - (t_6 * (3.0 - t_5))))))) + (3.0 * (x2 * -2.0)));
	elseif (x1 <= 7.5e+138)
		tmp = x1 + (t_2 + (x1 + (t_3 + (t_7 + (t_1 * (((x1 * x1) * ((t_5 * 4.0) - 6.0)) + (t_6 * t_0)))))));
	else
		tmp = x1 + (t_2 + (x1 + (x1 * ((4.0 * (x2 * t_0)) + (x1 * 9.0)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$2 = N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(N[(t$95$4 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$6 = N[(N[(x1 * 2.0), $MachinePrecision] * t$95$5), $MachinePrecision]}, Block[{t$95$7 = N[(3.0 * t$95$4), $MachinePrecision]}, If[LessEqual[x1, -5.5e+102], N[(x1 - N[(N[(x2 * N[(6.0 - N[(-3.0 * N[(x1 / x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * N[(N[(4.0 * N[(x2 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x1 * N[(3.0 + N[(N[(x2 * 8.0), $MachinePrecision] - N[(2.0 * N[(t$95$0 - N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -0.106], N[(x1 + N[(N[(x1 + N[(t$95$3 + N[(t$95$7 + N[(t$95$1 * N[(N[(N[(x1 * x1), $MachinePrecision] * 6.0), $MachinePrecision] - N[(t$95$6 * N[(3.0 - t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 7.5e+138], N[(x1 + N[(t$95$2 + N[(x1 + N[(t$95$3 + N[(t$95$7 + N[(t$95$1 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$5 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] + N[(t$95$6 * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(t$95$2 + N[(x1 + N[(x1 * N[(N[(4.0 * N[(x2 * t$95$0), $MachinePrecision]), $MachinePrecision] + N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -5.49999999999999981e102

   1. Initial program 0.0%

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

   3. Taylor expanded in x1 around inf 0.0%

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

   4. Taylor expanded in x1 around 0 0.0%

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

      1. neg-mul-1 0.0%

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

      2. unsub-neg 0.0%

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

      3. *-commutative 0.0%

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

   6. Simplified 0.0%

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

   7. Taylor expanded in x1 around 0 48.8%

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

   8. Taylor expanded in x2 around inf 59.1%

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

   if -5.49999999999999981e102 < x1 < -0.105999999999999997

   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 inf 99.5%

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

   4. Taylor expanded in x1 around inf 96.1%

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

   5. Taylor expanded in x1 around 0 96.1%

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

      1. *-commutative 96.1%

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

   7. Simplified 96.1%

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

   if -0.105999999999999997 < x1 < 7.4999999999999999e138

   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 inf 98.2%

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

   4. Taylor expanded in x1 around 0 99.4%

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

      1. neg-mul-1 99.4%

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

      2. unsub-neg 99.4%

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

      3. *-commutative 99.4%

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

   6. Simplified 99.4%

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

   7. Taylor expanded in x1 around 0 97.2%

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

   if 7.4999999999999999e138 < x1

   1. Initial program 12.8%

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

   3. Taylor expanded in x1 around inf 12.8%

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

   4. Taylor expanded in x1 around 0 12.8%

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

      1. neg-mul-1 12.8%

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

      2. unsub-neg 12.8%

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

      3. *-commutative 12.8%

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

   6. Simplified 12.8%

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

   7. Taylor expanded in x1 around 0 95.6%

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

   8. Taylor expanded in x2 around 0 97.7%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.5 \cdot 10^{+102}:\\ \;\;\;\;x1 - \left(x2 \cdot \left(6 - -3 \cdot \frac{x1}{x2}\right) + \left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right) - x1 \cdot \left(3 + \left(x2 \cdot 8 - 2 \cdot \left(\left(2 \cdot x2 - 3\right) - x2 \cdot -2\right)\right)\right)\right) - x1\right)\right)\\ \mathbf{elif}\;x1 \leq -0.106:\\ \;\;\;\;x1 + \left(\left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot 6 - \left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(3 - \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right)\right)\right)\right)\right) + 3 \cdot \left(x2 \cdot -2\right)\right)\\ \mathbf{elif}\;x1 \leq 7.5 \cdot 10^{+138}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2 - x1\right) + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right) + \left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2 - x1\right) + \left(x1 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot 9\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 90.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 2 \cdot x2 - 3\\ t_1 := 4 \cdot \left(x2 \cdot t\_0\right)\\ t_2 := 3 \cdot \left(x2 \cdot -2 - x1\right)\\ t_3 := x1 \cdot \left(x1 \cdot 3\right)\\ t_4 := 3 - 2 \cdot x2\\ t_5 := x1 \cdot x1 + 1\\ t_6 := \frac{\left(t\_3 + 2 \cdot x2\right) - x1}{t\_5}\\ \mathbf{if}\;x1 \leq -5 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(t\_2 + \left(x1 + x1 \cdot \left(t\_1 + x1 \cdot \left(3 + \left(2 \cdot \left(x2 \cdot -2 + t\_4\right) + \left(x2 \cdot 8 + x1 \cdot \left(\left(t\_1 + 2 \cdot \left(\left(1 + \left(2 \cdot \left(x2 \cdot \left(3 + x2 \cdot -2\right)\right) + 3 \cdot t\_0\right)\right) + 2 \cdot \left(x2 \cdot t\_4\right)\right)\right) - 3\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 7.5 \cdot 10^{+138}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot t\_3 + t\_5 \cdot \left(\left(x1 \cdot x1\right) \cdot 6 - \left(\left(x1 \cdot 2\right) \cdot t\_6\right) \cdot \left(3 - t\_6\right)\right)\right)\right)\right) + 3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(-1 + x1 \cdot \left(3 - x2 \cdot -2\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(t\_2 + \left(x1 + x1 \cdot \left(t\_1 + x1 \cdot 9\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (- (* 2.0 x2) 3.0))
        (t_1 (* 4.0 (* x2 t_0)))
        (t_2 (* 3.0 (- (* x2 -2.0) x1)))
        (t_3 (* x1 (* x1 3.0)))
        (t_4 (- 3.0 (* 2.0 x2)))
        (t_5 (+ (* x1 x1) 1.0))
        (t_6 (/ (- (+ t_3 (* 2.0 x2)) x1) t_5)))
   (if (<= x1 -5e+102)
     (+
      x1
      (+
       t_2
       (+
        x1
        (*
         x1
         (+
          t_1
          (*
           x1
           (+
            3.0
            (+
             (* 2.0 (+ (* x2 -2.0) t_4))
             (+
              (* x2 8.0)
              (*
               x1
               (-
                (+
                 t_1
                 (*
                  2.0
                  (+
                   (+ 1.0 (+ (* 2.0 (* x2 (+ 3.0 (* x2 -2.0)))) (* 3.0 t_0)))
                   (* 2.0 (* x2 t_4)))))
                3.0)))))))))))
     (if (<= x1 7.5e+138)
       (+
        x1
        (+
         (+
          x1
          (+
           (* x1 (* x1 x1))
           (+
            (* 3.0 t_3)
            (* t_5 (- (* (* x1 x1) 6.0) (* (* (* x1 2.0) t_6) (- 3.0 t_6)))))))
         (* 3.0 (+ (* x2 -2.0) (* x1 (+ -1.0 (* x1 (- 3.0 (* x2 -2.0)))))))))
       (+ x1 (+ t_2 (+ x1 (* x1 (+ t_1 (* x1 9.0))))))))))

C

double code(double x1, double x2) {
	double t_0 = (2.0 * x2) - 3.0;
	double t_1 = 4.0 * (x2 * t_0);
	double t_2 = 3.0 * ((x2 * -2.0) - x1);
	double t_3 = x1 * (x1 * 3.0);
	double t_4 = 3.0 - (2.0 * x2);
	double t_5 = (x1 * x1) + 1.0;
	double t_6 = ((t_3 + (2.0 * x2)) - x1) / t_5;
	double tmp;
	if (x1 <= -5e+102) {
		tmp = x1 + (t_2 + (x1 + (x1 * (t_1 + (x1 * (3.0 + ((2.0 * ((x2 * -2.0) + t_4)) + ((x2 * 8.0) + (x1 * ((t_1 + (2.0 * ((1.0 + ((2.0 * (x2 * (3.0 + (x2 * -2.0)))) + (3.0 * t_0))) + (2.0 * (x2 * t_4))))) - 3.0))))))))));
	} else if (x1 <= 7.5e+138) {
		tmp = x1 + ((x1 + ((x1 * (x1 * x1)) + ((3.0 * t_3) + (t_5 * (((x1 * x1) * 6.0) - (((x1 * 2.0) * t_6) * (3.0 - t_6))))))) + (3.0 * ((x2 * -2.0) + (x1 * (-1.0 + (x1 * (3.0 - (x2 * -2.0))))))));
	} else {
		tmp = x1 + (t_2 + (x1 + (x1 * (t_1 + (x1 * 9.0)))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: tmp
    t_0 = (2.0d0 * x2) - 3.0d0
    t_1 = 4.0d0 * (x2 * t_0)
    t_2 = 3.0d0 * ((x2 * (-2.0d0)) - x1)
    t_3 = x1 * (x1 * 3.0d0)
    t_4 = 3.0d0 - (2.0d0 * x2)
    t_5 = (x1 * x1) + 1.0d0
    t_6 = ((t_3 + (2.0d0 * x2)) - x1) / t_5
    if (x1 <= (-5d+102)) then
        tmp = x1 + (t_2 + (x1 + (x1 * (t_1 + (x1 * (3.0d0 + ((2.0d0 * ((x2 * (-2.0d0)) + t_4)) + ((x2 * 8.0d0) + (x1 * ((t_1 + (2.0d0 * ((1.0d0 + ((2.0d0 * (x2 * (3.0d0 + (x2 * (-2.0d0))))) + (3.0d0 * t_0))) + (2.0d0 * (x2 * t_4))))) - 3.0d0))))))))))
    else if (x1 <= 7.5d+138) then
        tmp = x1 + ((x1 + ((x1 * (x1 * x1)) + ((3.0d0 * t_3) + (t_5 * (((x1 * x1) * 6.0d0) - (((x1 * 2.0d0) * t_6) * (3.0d0 - t_6))))))) + (3.0d0 * ((x2 * (-2.0d0)) + (x1 * ((-1.0d0) + (x1 * (3.0d0 - (x2 * (-2.0d0)))))))))
    else
        tmp = x1 + (t_2 + (x1 + (x1 * (t_1 + (x1 * 9.0d0)))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (2.0 * x2) - 3.0;
	double t_1 = 4.0 * (x2 * t_0);
	double t_2 = 3.0 * ((x2 * -2.0) - x1);
	double t_3 = x1 * (x1 * 3.0);
	double t_4 = 3.0 - (2.0 * x2);
	double t_5 = (x1 * x1) + 1.0;
	double t_6 = ((t_3 + (2.0 * x2)) - x1) / t_5;
	double tmp;
	if (x1 <= -5e+102) {
		tmp = x1 + (t_2 + (x1 + (x1 * (t_1 + (x1 * (3.0 + ((2.0 * ((x2 * -2.0) + t_4)) + ((x2 * 8.0) + (x1 * ((t_1 + (2.0 * ((1.0 + ((2.0 * (x2 * (3.0 + (x2 * -2.0)))) + (3.0 * t_0))) + (2.0 * (x2 * t_4))))) - 3.0))))))))));
	} else if (x1 <= 7.5e+138) {
		tmp = x1 + ((x1 + ((x1 * (x1 * x1)) + ((3.0 * t_3) + (t_5 * (((x1 * x1) * 6.0) - (((x1 * 2.0) * t_6) * (3.0 - t_6))))))) + (3.0 * ((x2 * -2.0) + (x1 * (-1.0 + (x1 * (3.0 - (x2 * -2.0))))))));
	} else {
		tmp = x1 + (t_2 + (x1 + (x1 * (t_1 + (x1 * 9.0)))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (2.0 * x2) - 3.0
	t_1 = 4.0 * (x2 * t_0)
	t_2 = 3.0 * ((x2 * -2.0) - x1)
	t_3 = x1 * (x1 * 3.0)
	t_4 = 3.0 - (2.0 * x2)
	t_5 = (x1 * x1) + 1.0
	t_6 = ((t_3 + (2.0 * x2)) - x1) / t_5
	tmp = 0
	if x1 <= -5e+102:
		tmp = x1 + (t_2 + (x1 + (x1 * (t_1 + (x1 * (3.0 + ((2.0 * ((x2 * -2.0) + t_4)) + ((x2 * 8.0) + (x1 * ((t_1 + (2.0 * ((1.0 + ((2.0 * (x2 * (3.0 + (x2 * -2.0)))) + (3.0 * t_0))) + (2.0 * (x2 * t_4))))) - 3.0))))))))))
	elif x1 <= 7.5e+138:
		tmp = x1 + ((x1 + ((x1 * (x1 * x1)) + ((3.0 * t_3) + (t_5 * (((x1 * x1) * 6.0) - (((x1 * 2.0) * t_6) * (3.0 - t_6))))))) + (3.0 * ((x2 * -2.0) + (x1 * (-1.0 + (x1 * (3.0 - (x2 * -2.0))))))))
	else:
		tmp = x1 + (t_2 + (x1 + (x1 * (t_1 + (x1 * 9.0)))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(2.0 * x2) - 3.0)
	t_1 = Float64(4.0 * Float64(x2 * t_0))
	t_2 = Float64(3.0 * Float64(Float64(x2 * -2.0) - x1))
	t_3 = Float64(x1 * Float64(x1 * 3.0))
	t_4 = Float64(3.0 - Float64(2.0 * x2))
	t_5 = Float64(Float64(x1 * x1) + 1.0)
	t_6 = Float64(Float64(Float64(t_3 + Float64(2.0 * x2)) - x1) / t_5)
	tmp = 0.0
	if (x1 <= -5e+102)
		tmp = Float64(x1 + Float64(t_2 + Float64(x1 + Float64(x1 * Float64(t_1 + Float64(x1 * Float64(3.0 + Float64(Float64(2.0 * Float64(Float64(x2 * -2.0) + t_4)) + Float64(Float64(x2 * 8.0) + Float64(x1 * Float64(Float64(t_1 + Float64(2.0 * Float64(Float64(1.0 + Float64(Float64(2.0 * Float64(x2 * Float64(3.0 + Float64(x2 * -2.0)))) + Float64(3.0 * t_0))) + Float64(2.0 * Float64(x2 * t_4))))) - 3.0)))))))))));
	elseif (x1 <= 7.5e+138)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(3.0 * t_3) + Float64(t_5 * Float64(Float64(Float64(x1 * x1) * 6.0) - Float64(Float64(Float64(x1 * 2.0) * t_6) * Float64(3.0 - t_6))))))) + Float64(3.0 * Float64(Float64(x2 * -2.0) + Float64(x1 * Float64(-1.0 + Float64(x1 * Float64(3.0 - Float64(x2 * -2.0)))))))));
	else
		tmp = Float64(x1 + Float64(t_2 + Float64(x1 + Float64(x1 * Float64(t_1 + Float64(x1 * 9.0))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (2.0 * x2) - 3.0;
	t_1 = 4.0 * (x2 * t_0);
	t_2 = 3.0 * ((x2 * -2.0) - x1);
	t_3 = x1 * (x1 * 3.0);
	t_4 = 3.0 - (2.0 * x2);
	t_5 = (x1 * x1) + 1.0;
	t_6 = ((t_3 + (2.0 * x2)) - x1) / t_5;
	tmp = 0.0;
	if (x1 <= -5e+102)
		tmp = x1 + (t_2 + (x1 + (x1 * (t_1 + (x1 * (3.0 + ((2.0 * ((x2 * -2.0) + t_4)) + ((x2 * 8.0) + (x1 * ((t_1 + (2.0 * ((1.0 + ((2.0 * (x2 * (3.0 + (x2 * -2.0)))) + (3.0 * t_0))) + (2.0 * (x2 * t_4))))) - 3.0))))))))));
	elseif (x1 <= 7.5e+138)
		tmp = x1 + ((x1 + ((x1 * (x1 * x1)) + ((3.0 * t_3) + (t_5 * (((x1 * x1) * 6.0) - (((x1 * 2.0) * t_6) * (3.0 - t_6))))))) + (3.0 * ((x2 * -2.0) + (x1 * (-1.0 + (x1 * (3.0 - (x2 * -2.0))))))));
	else
		tmp = x1 + (t_2 + (x1 + (x1 * (t_1 + (x1 * 9.0)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]}, Block[{t$95$1 = N[(4.0 * N[(x2 * t$95$0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$6 = N[(N[(N[(t$95$3 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$5), $MachinePrecision]}, If[LessEqual[x1, -5e+102], N[(x1 + N[(t$95$2 + N[(x1 + N[(x1 * N[(t$95$1 + N[(x1 * N[(3.0 + N[(N[(2.0 * N[(N[(x2 * -2.0), $MachinePrecision] + t$95$4), $MachinePrecision]), $MachinePrecision] + N[(N[(x2 * 8.0), $MachinePrecision] + N[(x1 * N[(N[(t$95$1 + N[(2.0 * N[(N[(1.0 + N[(N[(2.0 * N[(x2 * N[(3.0 + N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(2.0 * N[(x2 * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 7.5e+138], N[(x1 + N[(N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(3.0 * t$95$3), $MachinePrecision] + N[(t$95$5 * N[(N[(N[(x1 * x1), $MachinePrecision] * 6.0), $MachinePrecision] - N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$6), $MachinePrecision] * N[(3.0 - t$95$6), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] + N[(x1 * N[(-1.0 + N[(x1 * N[(3.0 - N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(t$95$2 + N[(x1 + N[(x1 * N[(t$95$1 + N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -5e102

   1. Initial program 0.0%

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

   3. Taylor expanded in x1 around inf 0.0%

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

   4. Taylor expanded in x1 around 0 0.0%

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

      1. neg-mul-1 0.0%

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

      2. unsub-neg 0.0%

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

      3. *-commutative 0.0%

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

   6. Simplified 0.0%

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

   7. Taylor expanded in x1 around 0 80.0%

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

   if -5e102 < x1 < 7.4999999999999999e138

   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 inf 98.4%

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

   4. Taylor expanded in x1 around inf 97.7%

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

   5. Taylor expanded in x1 around 0 96.0%

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

   if 7.4999999999999999e138 < x1

   1. Initial program 12.8%

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

   3. Taylor expanded in x1 around inf 12.8%

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

   4. Taylor expanded in x1 around 0 12.8%

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

      1. neg-mul-1 12.8%

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

      2. unsub-neg 12.8%

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

      3. *-commutative 12.8%

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

   6. Simplified 12.8%

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

   7. Taylor expanded in x1 around 0 95.6%

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

   8. Taylor expanded in x2 around 0 97.7%

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

4. Final simplification 93.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2 - x1\right) + \left(x1 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(3 + \left(2 \cdot \left(x2 \cdot -2 + \left(3 - 2 \cdot x2\right)\right) + \left(x2 \cdot 8 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + 2 \cdot \left(\left(1 + \left(2 \cdot \left(x2 \cdot \left(3 + x2 \cdot -2\right)\right) + 3 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + 2 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right) - 3\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 7.5 \cdot 10^{+138}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot 6 - \left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(3 - \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right)\right)\right)\right)\right) + 3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(-1 + x1 \cdot \left(3 - x2 \cdot -2\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2 - x1\right) + \left(x1 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot 9\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 88.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 2 \cdot x2 - 3\\ t_1 := x1 \cdot x1 + 1\\ t_2 := x1 \cdot \left(x1 \cdot 3\right)\\ t_3 := \frac{\left(t\_2 + 2 \cdot x2\right) - x1}{t\_1}\\ t_4 := x1 + \left(\left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot t\_2 + t\_1 \cdot \left(\left(x1 \cdot x1\right) \cdot 6 - \left(\left(x1 \cdot 2\right) \cdot t\_3\right) \cdot \left(3 - t\_3\right)\right)\right)\right)\right) + 3 \cdot \left(x2 \cdot -2\right)\right)\\ \mathbf{if}\;x1 \leq -5.5 \cdot 10^{+102}:\\ \;\;\;\;x1 - \left(x2 \cdot \left(6 - -3 \cdot \frac{x1}{x2}\right) + \left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right) - x1 \cdot \left(3 + \left(x2 \cdot 8 - 2 \cdot \left(t\_0 - x2 \cdot -2\right)\right)\right)\right) - x1\right)\right)\\ \mathbf{elif}\;x1 \leq -0.085:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;x1 \leq 3.1 \cdot 10^{-32}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t\_2 - 2 \cdot x2\right) - x1}{t\_1} + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot -3 + 2 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 2.5 \cdot 10^{+152}:\\ \;\;\;\;t\_4\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2 - x1\right) + \left(x1 + x1 \cdot \left(4 \cdot \left(x2 \cdot t\_0\right) + x1 \cdot 9\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (- (* 2.0 x2) 3.0))
        (t_1 (+ (* x1 x1) 1.0))
        (t_2 (* x1 (* x1 3.0)))
        (t_3 (/ (- (+ t_2 (* 2.0 x2)) x1) t_1))
        (t_4
         (+
          x1
          (+
           (+
            x1
            (+
             (* x1 (* x1 x1))
             (+
              (* 3.0 t_2)
              (*
               t_1
               (- (* (* x1 x1) 6.0) (* (* (* x1 2.0) t_3) (- 3.0 t_3)))))))
           (* 3.0 (* x2 -2.0))))))
   (if (<= x1 -5.5e+102)
     (-
      x1
      (+
       (* x2 (- 6.0 (* -3.0 (/ x1 x2))))
       (-
        (*
         x1
         (-
          (* 4.0 (* x2 (- 3.0 (* 2.0 x2))))
          (* x1 (+ 3.0 (- (* x2 8.0) (* 2.0 (- t_0 (* x2 -2.0))))))))
        x1)))
     (if (<= x1 -0.085)
       t_4
       (if (<= x1 3.1e-32)
         (+
          x1
          (+
           (* 3.0 (/ (- (- t_2 (* 2.0 x2)) x1) t_1))
           (+ x1 (* 4.0 (* x2 (+ (* x1 -3.0) (* 2.0 (* x1 x2))))))))
         (if (<= x1 2.5e+152)
           t_4
           (+
            x1
            (+
             (* 3.0 (- (* x2 -2.0) x1))
             (+ x1 (* x1 (+ (* 4.0 (* x2 t_0)) (* x1 9.0))))))))))))

C

double code(double x1, double x2) {
	double t_0 = (2.0 * x2) - 3.0;
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = ((t_2 + (2.0 * x2)) - x1) / t_1;
	double t_4 = x1 + ((x1 + ((x1 * (x1 * x1)) + ((3.0 * t_2) + (t_1 * (((x1 * x1) * 6.0) - (((x1 * 2.0) * t_3) * (3.0 - t_3))))))) + (3.0 * (x2 * -2.0)));
	double tmp;
	if (x1 <= -5.5e+102) {
		tmp = x1 - ((x2 * (6.0 - (-3.0 * (x1 / x2)))) + ((x1 * ((4.0 * (x2 * (3.0 - (2.0 * x2)))) - (x1 * (3.0 + ((x2 * 8.0) - (2.0 * (t_0 - (x2 * -2.0)))))))) - x1));
	} else if (x1 <= -0.085) {
		tmp = t_4;
	} else if (x1 <= 3.1e-32) {
		tmp = x1 + ((3.0 * (((t_2 - (2.0 * x2)) - x1) / t_1)) + (x1 + (4.0 * (x2 * ((x1 * -3.0) + (2.0 * (x1 * x2)))))));
	} else if (x1 <= 2.5e+152) {
		tmp = t_4;
	} else {
		tmp = x1 + ((3.0 * ((x2 * -2.0) - x1)) + (x1 + (x1 * ((4.0 * (x2 * t_0)) + (x1 * 9.0)))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_0 = (2.0d0 * x2) - 3.0d0
    t_1 = (x1 * x1) + 1.0d0
    t_2 = x1 * (x1 * 3.0d0)
    t_3 = ((t_2 + (2.0d0 * x2)) - x1) / t_1
    t_4 = x1 + ((x1 + ((x1 * (x1 * x1)) + ((3.0d0 * t_2) + (t_1 * (((x1 * x1) * 6.0d0) - (((x1 * 2.0d0) * t_3) * (3.0d0 - t_3))))))) + (3.0d0 * (x2 * (-2.0d0))))
    if (x1 <= (-5.5d+102)) then
        tmp = x1 - ((x2 * (6.0d0 - ((-3.0d0) * (x1 / x2)))) + ((x1 * ((4.0d0 * (x2 * (3.0d0 - (2.0d0 * x2)))) - (x1 * (3.0d0 + ((x2 * 8.0d0) - (2.0d0 * (t_0 - (x2 * (-2.0d0))))))))) - x1))
    else if (x1 <= (-0.085d0)) then
        tmp = t_4
    else if (x1 <= 3.1d-32) then
        tmp = x1 + ((3.0d0 * (((t_2 - (2.0d0 * x2)) - x1) / t_1)) + (x1 + (4.0d0 * (x2 * ((x1 * (-3.0d0)) + (2.0d0 * (x1 * x2)))))))
    else if (x1 <= 2.5d+152) then
        tmp = t_4
    else
        tmp = x1 + ((3.0d0 * ((x2 * (-2.0d0)) - x1)) + (x1 + (x1 * ((4.0d0 * (x2 * t_0)) + (x1 * 9.0d0)))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (2.0 * x2) - 3.0;
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = ((t_2 + (2.0 * x2)) - x1) / t_1;
	double t_4 = x1 + ((x1 + ((x1 * (x1 * x1)) + ((3.0 * t_2) + (t_1 * (((x1 * x1) * 6.0) - (((x1 * 2.0) * t_3) * (3.0 - t_3))))))) + (3.0 * (x2 * -2.0)));
	double tmp;
	if (x1 <= -5.5e+102) {
		tmp = x1 - ((x2 * (6.0 - (-3.0 * (x1 / x2)))) + ((x1 * ((4.0 * (x2 * (3.0 - (2.0 * x2)))) - (x1 * (3.0 + ((x2 * 8.0) - (2.0 * (t_0 - (x2 * -2.0)))))))) - x1));
	} else if (x1 <= -0.085) {
		tmp = t_4;
	} else if (x1 <= 3.1e-32) {
		tmp = x1 + ((3.0 * (((t_2 - (2.0 * x2)) - x1) / t_1)) + (x1 + (4.0 * (x2 * ((x1 * -3.0) + (2.0 * (x1 * x2)))))));
	} else if (x1 <= 2.5e+152) {
		tmp = t_4;
	} else {
		tmp = x1 + ((3.0 * ((x2 * -2.0) - x1)) + (x1 + (x1 * ((4.0 * (x2 * t_0)) + (x1 * 9.0)))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (2.0 * x2) - 3.0
	t_1 = (x1 * x1) + 1.0
	t_2 = x1 * (x1 * 3.0)
	t_3 = ((t_2 + (2.0 * x2)) - x1) / t_1
	t_4 = x1 + ((x1 + ((x1 * (x1 * x1)) + ((3.0 * t_2) + (t_1 * (((x1 * x1) * 6.0) - (((x1 * 2.0) * t_3) * (3.0 - t_3))))))) + (3.0 * (x2 * -2.0)))
	tmp = 0
	if x1 <= -5.5e+102:
		tmp = x1 - ((x2 * (6.0 - (-3.0 * (x1 / x2)))) + ((x1 * ((4.0 * (x2 * (3.0 - (2.0 * x2)))) - (x1 * (3.0 + ((x2 * 8.0) - (2.0 * (t_0 - (x2 * -2.0)))))))) - x1))
	elif x1 <= -0.085:
		tmp = t_4
	elif x1 <= 3.1e-32:
		tmp = x1 + ((3.0 * (((t_2 - (2.0 * x2)) - x1) / t_1)) + (x1 + (4.0 * (x2 * ((x1 * -3.0) + (2.0 * (x1 * x2)))))))
	elif x1 <= 2.5e+152:
		tmp = t_4
	else:
		tmp = x1 + ((3.0 * ((x2 * -2.0) - x1)) + (x1 + (x1 * ((4.0 * (x2 * t_0)) + (x1 * 9.0)))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(2.0 * x2) - 3.0)
	t_1 = Float64(Float64(x1 * x1) + 1.0)
	t_2 = Float64(x1 * Float64(x1 * 3.0))
	t_3 = Float64(Float64(Float64(t_2 + Float64(2.0 * x2)) - x1) / t_1)
	t_4 = Float64(x1 + Float64(Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(3.0 * t_2) + Float64(t_1 * Float64(Float64(Float64(x1 * x1) * 6.0) - Float64(Float64(Float64(x1 * 2.0) * t_3) * Float64(3.0 - t_3))))))) + Float64(3.0 * Float64(x2 * -2.0))))
	tmp = 0.0
	if (x1 <= -5.5e+102)
		tmp = Float64(x1 - Float64(Float64(x2 * Float64(6.0 - Float64(-3.0 * Float64(x1 / x2)))) + Float64(Float64(x1 * Float64(Float64(4.0 * Float64(x2 * Float64(3.0 - Float64(2.0 * x2)))) - Float64(x1 * Float64(3.0 + Float64(Float64(x2 * 8.0) - Float64(2.0 * Float64(t_0 - Float64(x2 * -2.0)))))))) - x1)));
	elseif (x1 <= -0.085)
		tmp = t_4;
	elseif (x1 <= 3.1e-32)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_2 - Float64(2.0 * x2)) - x1) / t_1)) + Float64(x1 + Float64(4.0 * Float64(x2 * Float64(Float64(x1 * -3.0) + Float64(2.0 * Float64(x1 * x2))))))));
	elseif (x1 <= 2.5e+152)
		tmp = t_4;
	else
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(x2 * -2.0) - x1)) + Float64(x1 + Float64(x1 * Float64(Float64(4.0 * Float64(x2 * t_0)) + Float64(x1 * 9.0))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (2.0 * x2) - 3.0;
	t_1 = (x1 * x1) + 1.0;
	t_2 = x1 * (x1 * 3.0);
	t_3 = ((t_2 + (2.0 * x2)) - x1) / t_1;
	t_4 = x1 + ((x1 + ((x1 * (x1 * x1)) + ((3.0 * t_2) + (t_1 * (((x1 * x1) * 6.0) - (((x1 * 2.0) * t_3) * (3.0 - t_3))))))) + (3.0 * (x2 * -2.0)));
	tmp = 0.0;
	if (x1 <= -5.5e+102)
		tmp = x1 - ((x2 * (6.0 - (-3.0 * (x1 / x2)))) + ((x1 * ((4.0 * (x2 * (3.0 - (2.0 * x2)))) - (x1 * (3.0 + ((x2 * 8.0) - (2.0 * (t_0 - (x2 * -2.0)))))))) - x1));
	elseif (x1 <= -0.085)
		tmp = t_4;
	elseif (x1 <= 3.1e-32)
		tmp = x1 + ((3.0 * (((t_2 - (2.0 * x2)) - x1) / t_1)) + (x1 + (4.0 * (x2 * ((x1 * -3.0) + (2.0 * (x1 * x2)))))));
	elseif (x1 <= 2.5e+152)
		tmp = t_4;
	else
		tmp = x1 + ((3.0 * ((x2 * -2.0) - x1)) + (x1 + (x1 * ((4.0 * (x2 * t_0)) + (x1 * 9.0)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$2 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(t$95$2 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$4 = N[(x1 + N[(N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(3.0 * t$95$2), $MachinePrecision] + N[(t$95$1 * N[(N[(N[(x1 * x1), $MachinePrecision] * 6.0), $MachinePrecision] - N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$3), $MachinePrecision] * N[(3.0 - t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -5.5e+102], N[(x1 - N[(N[(x2 * N[(6.0 - N[(-3.0 * N[(x1 / x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * N[(N[(4.0 * N[(x2 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x1 * N[(3.0 + N[(N[(x2 * 8.0), $MachinePrecision] - N[(2.0 * N[(t$95$0 - N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -0.085], t$95$4, If[LessEqual[x1, 3.1e-32], N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$2 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(4.0 * N[(x2 * N[(N[(x1 * -3.0), $MachinePrecision] + N[(2.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 2.5e+152], t$95$4, N[(x1 + N[(N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(x1 * N[(N[(4.0 * N[(x2 * t$95$0), $MachinePrecision]), $MachinePrecision] + N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -5.49999999999999981e102

   1. Initial program 0.0%

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

   3. Taylor expanded in x1 around inf 0.0%

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

   4. Taylor expanded in x1 around 0 0.0%

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

      1. neg-mul-1 0.0%

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

      2. unsub-neg 0.0%

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

      3. *-commutative 0.0%

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

   6. Simplified 0.0%

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

   7. Taylor expanded in x1 around 0 48.8%

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

   8. Taylor expanded in x2 around inf 59.1%

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

   if -5.49999999999999981e102 < x1 < -0.0850000000000000061 or 3.10000000000000011e-32 < x1 < 2.5e152

   1. Initial program 99.6%

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

   3. Taylor expanded in x1 around inf 99.6%

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

   4. Taylor expanded in x1 around inf 97.5%

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

   5. Taylor expanded in x1 around 0 97.5%

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

      1. *-commutative 97.5%

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

   7. Simplified 97.5%

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

   if -0.0850000000000000061 < x1 < 3.10000000000000011e-32

   1. Initial program 99.3%

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

   3. Taylor expanded in x1 around 0 88.4%

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

   4. Taylor expanded in x2 around 0 98.6%

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

   if 2.5e152 < x1

   1. Initial program 5.6%

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

   3. Taylor expanded in x1 around inf 5.6%

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

   4. Taylor expanded in x1 around 0 5.6%

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

      1. neg-mul-1 5.6%

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

      2. unsub-neg 5.6%

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

      3. *-commutative 5.6%

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

   6. Simplified 5.6%

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

   7. Taylor expanded in x1 around 0 97.7%

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

   8. Taylor expanded in x2 around 0 100.0%

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

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.5 \cdot 10^{+102}:\\ \;\;\;\;x1 - \left(x2 \cdot \left(6 - -3 \cdot \frac{x1}{x2}\right) + \left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right) - x1 \cdot \left(3 + \left(x2 \cdot 8 - 2 \cdot \left(\left(2 \cdot x2 - 3\right) - x2 \cdot -2\right)\right)\right)\right) - x1\right)\right)\\ \mathbf{elif}\;x1 \leq -0.085:\\ \;\;\;\;x1 + \left(\left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot 6 - \left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(3 - \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right)\right)\right)\right)\right) + 3 \cdot \left(x2 \cdot -2\right)\right)\\ \mathbf{elif}\;x1 \leq 3.1 \cdot 10^{-32}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot -3 + 2 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 2.5 \cdot 10^{+152}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot 6 - \left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(3 - \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right)\right)\right)\right)\right) + 3 \cdot \left(x2 \cdot -2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2 - x1\right) + \left(x1 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot 9\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 87.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := 3 \cdot \left(x2 \cdot -2 - x1\right)\\ t_2 := 2 \cdot x2 - 3\\ t_3 := x1 \cdot \left(x1 \cdot 3\right)\\ t_4 := \frac{\left(t\_3 + 2 \cdot x2\right) - x1}{t\_0}\\ \mathbf{if}\;x1 \leq -5.5 \cdot 10^{+102}:\\ \;\;\;\;x1 - \left(x2 \cdot \left(6 - -3 \cdot \frac{x1}{x2}\right) + \left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right) - x1 \cdot \left(3 + \left(x2 \cdot 8 - 2 \cdot \left(t\_2 - x2 \cdot -2\right)\right)\right)\right) - x1\right)\right)\\ \mathbf{elif}\;x1 \leq 7.5 \cdot 10^{+138}:\\ \;\;\;\;x1 + \left(t\_1 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot t\_3 + t\_0 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(t\_4 \cdot 4 - 6\right) + \left(t\_4 - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(2 \cdot x2 - x1\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(t\_1 + \left(x1 + x1 \cdot \left(4 \cdot \left(x2 \cdot t\_2\right) + x1 \cdot 9\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ (* x1 x1) 1.0))
        (t_1 (* 3.0 (- (* x2 -2.0) x1)))
        (t_2 (- (* 2.0 x2) 3.0))
        (t_3 (* x1 (* x1 3.0)))
        (t_4 (/ (- (+ t_3 (* 2.0 x2)) x1) t_0)))
   (if (<= x1 -5.5e+102)
     (-
      x1
      (+
       (* x2 (- 6.0 (* -3.0 (/ x1 x2))))
       (-
        (*
         x1
         (-
          (* 4.0 (* x2 (- 3.0 (* 2.0 x2))))
          (* x1 (+ 3.0 (- (* x2 8.0) (* 2.0 (- t_2 (* x2 -2.0))))))))
        x1)))
     (if (<= x1 7.5e+138)
       (+
        x1
        (+
         t_1
         (+
          x1
          (+
           (* x1 (* x1 x1))
           (+
            (* 3.0 t_3)
            (*
             t_0
             (+
              (* (* x1 x1) (- (* t_4 4.0) 6.0))
              (* (- t_4 3.0) (* (* x1 2.0) (- (* 2.0 x2) x1))))))))))
       (+ x1 (+ t_1 (+ x1 (* x1 (+ (* 4.0 (* x2 t_2)) (* x1 9.0))))))))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = 3.0 * ((x2 * -2.0) - x1);
	double t_2 = (2.0 * x2) - 3.0;
	double t_3 = x1 * (x1 * 3.0);
	double t_4 = ((t_3 + (2.0 * x2)) - x1) / t_0;
	double tmp;
	if (x1 <= -5.5e+102) {
		tmp = x1 - ((x2 * (6.0 - (-3.0 * (x1 / x2)))) + ((x1 * ((4.0 * (x2 * (3.0 - (2.0 * x2)))) - (x1 * (3.0 + ((x2 * 8.0) - (2.0 * (t_2 - (x2 * -2.0)))))))) - x1));
	} else if (x1 <= 7.5e+138) {
		tmp = x1 + (t_1 + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_3) + (t_0 * (((x1 * x1) * ((t_4 * 4.0) - 6.0)) + ((t_4 - 3.0) * ((x1 * 2.0) * ((2.0 * x2) - x1)))))))));
	} else {
		tmp = x1 + (t_1 + (x1 + (x1 * ((4.0 * (x2 * t_2)) + (x1 * 9.0)))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_0 = (x1 * x1) + 1.0d0
    t_1 = 3.0d0 * ((x2 * (-2.0d0)) - x1)
    t_2 = (2.0d0 * x2) - 3.0d0
    t_3 = x1 * (x1 * 3.0d0)
    t_4 = ((t_3 + (2.0d0 * x2)) - x1) / t_0
    if (x1 <= (-5.5d+102)) then
        tmp = x1 - ((x2 * (6.0d0 - ((-3.0d0) * (x1 / x2)))) + ((x1 * ((4.0d0 * (x2 * (3.0d0 - (2.0d0 * x2)))) - (x1 * (3.0d0 + ((x2 * 8.0d0) - (2.0d0 * (t_2 - (x2 * (-2.0d0))))))))) - x1))
    else if (x1 <= 7.5d+138) then
        tmp = x1 + (t_1 + (x1 + ((x1 * (x1 * x1)) + ((3.0d0 * t_3) + (t_0 * (((x1 * x1) * ((t_4 * 4.0d0) - 6.0d0)) + ((t_4 - 3.0d0) * ((x1 * 2.0d0) * ((2.0d0 * x2) - x1)))))))))
    else
        tmp = x1 + (t_1 + (x1 + (x1 * ((4.0d0 * (x2 * t_2)) + (x1 * 9.0d0)))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = 3.0 * ((x2 * -2.0) - x1);
	double t_2 = (2.0 * x2) - 3.0;
	double t_3 = x1 * (x1 * 3.0);
	double t_4 = ((t_3 + (2.0 * x2)) - x1) / t_0;
	double tmp;
	if (x1 <= -5.5e+102) {
		tmp = x1 - ((x2 * (6.0 - (-3.0 * (x1 / x2)))) + ((x1 * ((4.0 * (x2 * (3.0 - (2.0 * x2)))) - (x1 * (3.0 + ((x2 * 8.0) - (2.0 * (t_2 - (x2 * -2.0)))))))) - x1));
	} else if (x1 <= 7.5e+138) {
		tmp = x1 + (t_1 + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_3) + (t_0 * (((x1 * x1) * ((t_4 * 4.0) - 6.0)) + ((t_4 - 3.0) * ((x1 * 2.0) * ((2.0 * x2) - x1)))))))));
	} else {
		tmp = x1 + (t_1 + (x1 + (x1 * ((4.0 * (x2 * t_2)) + (x1 * 9.0)))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x1 * x1) + 1.0
	t_1 = 3.0 * ((x2 * -2.0) - x1)
	t_2 = (2.0 * x2) - 3.0
	t_3 = x1 * (x1 * 3.0)
	t_4 = ((t_3 + (2.0 * x2)) - x1) / t_0
	tmp = 0
	if x1 <= -5.5e+102:
		tmp = x1 - ((x2 * (6.0 - (-3.0 * (x1 / x2)))) + ((x1 * ((4.0 * (x2 * (3.0 - (2.0 * x2)))) - (x1 * (3.0 + ((x2 * 8.0) - (2.0 * (t_2 - (x2 * -2.0)))))))) - x1))
	elif x1 <= 7.5e+138:
		tmp = x1 + (t_1 + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_3) + (t_0 * (((x1 * x1) * ((t_4 * 4.0) - 6.0)) + ((t_4 - 3.0) * ((x1 * 2.0) * ((2.0 * x2) - x1)))))))))
	else:
		tmp = x1 + (t_1 + (x1 + (x1 * ((4.0 * (x2 * t_2)) + (x1 * 9.0)))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * x1) + 1.0)
	t_1 = Float64(3.0 * Float64(Float64(x2 * -2.0) - x1))
	t_2 = Float64(Float64(2.0 * x2) - 3.0)
	t_3 = Float64(x1 * Float64(x1 * 3.0))
	t_4 = Float64(Float64(Float64(t_3 + Float64(2.0 * x2)) - x1) / t_0)
	tmp = 0.0
	if (x1 <= -5.5e+102)
		tmp = Float64(x1 - Float64(Float64(x2 * Float64(6.0 - Float64(-3.0 * Float64(x1 / x2)))) + Float64(Float64(x1 * Float64(Float64(4.0 * Float64(x2 * Float64(3.0 - Float64(2.0 * x2)))) - Float64(x1 * Float64(3.0 + Float64(Float64(x2 * 8.0) - Float64(2.0 * Float64(t_2 - Float64(x2 * -2.0)))))))) - x1)));
	elseif (x1 <= 7.5e+138)
		tmp = Float64(x1 + Float64(t_1 + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(3.0 * t_3) + Float64(t_0 * Float64(Float64(Float64(x1 * x1) * Float64(Float64(t_4 * 4.0) - 6.0)) + Float64(Float64(t_4 - 3.0) * Float64(Float64(x1 * 2.0) * Float64(Float64(2.0 * x2) - x1))))))))));
	else
		tmp = Float64(x1 + Float64(t_1 + Float64(x1 + Float64(x1 * Float64(Float64(4.0 * Float64(x2 * t_2)) + Float64(x1 * 9.0))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x1 * x1) + 1.0;
	t_1 = 3.0 * ((x2 * -2.0) - x1);
	t_2 = (2.0 * x2) - 3.0;
	t_3 = x1 * (x1 * 3.0);
	t_4 = ((t_3 + (2.0 * x2)) - x1) / t_0;
	tmp = 0.0;
	if (x1 <= -5.5e+102)
		tmp = x1 - ((x2 * (6.0 - (-3.0 * (x1 / x2)))) + ((x1 * ((4.0 * (x2 * (3.0 - (2.0 * x2)))) - (x1 * (3.0 + ((x2 * 8.0) - (2.0 * (t_2 - (x2 * -2.0)))))))) - x1));
	elseif (x1 <= 7.5e+138)
		tmp = x1 + (t_1 + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_3) + (t_0 * (((x1 * x1) * ((t_4 * 4.0) - 6.0)) + ((t_4 - 3.0) * ((x1 * 2.0) * ((2.0 * x2) - x1)))))))));
	else
		tmp = x1 + (t_1 + (x1 + (x1 * ((4.0 * (x2 * t_2)) + (x1 * 9.0)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$1 = N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]}, Block[{t$95$3 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(t$95$3 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]}, If[LessEqual[x1, -5.5e+102], N[(x1 - N[(N[(x2 * N[(6.0 - N[(-3.0 * N[(x1 / x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * N[(N[(4.0 * N[(x2 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x1 * N[(3.0 + N[(N[(x2 * 8.0), $MachinePrecision] - N[(2.0 * N[(t$95$2 - N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 7.5e+138], N[(x1 + N[(t$95$1 + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(3.0 * t$95$3), $MachinePrecision] + N[(t$95$0 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$4 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$4 - 3.0), $MachinePrecision] * N[(N[(x1 * 2.0), $MachinePrecision] * N[(N[(2.0 * x2), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(t$95$1 + N[(x1 + N[(x1 * N[(N[(4.0 * N[(x2 * t$95$2), $MachinePrecision]), $MachinePrecision] + N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -5.49999999999999981e102

   1. Initial program 0.0%

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

   3. Taylor expanded in x1 around inf 0.0%

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

   4. Taylor expanded in x1 around 0 0.0%

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

      1. neg-mul-1 0.0%

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

      2. unsub-neg 0.0%

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

      3. *-commutative 0.0%

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

   6. Simplified 0.0%

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

   7. Taylor expanded in x1 around 0 48.8%

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

   8. Taylor expanded in x2 around inf 59.1%

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

   if -5.49999999999999981e102 < x1 < 7.4999999999999999e138

   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 inf 98.4%

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

   4. Taylor expanded in x1 around 0 99.4%

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

      1. neg-mul-1 99.4%

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

      2. unsub-neg 99.4%

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

      3. *-commutative 99.4%

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

   6. Simplified 99.4%

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

   7. Taylor expanded in x1 around 0 95.5%

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

      1. neg-mul-1 95.5%

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

      2. +-commutative 95.5%

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

      3. unsub-neg 95.5%

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

   9. Simplified 95.5%

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

   if 7.4999999999999999e138 < x1

   1. Initial program 12.8%

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

   3. Taylor expanded in x1 around inf 12.8%

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

   4. Taylor expanded in x1 around 0 12.8%

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

      1. neg-mul-1 12.8%

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

      2. unsub-neg 12.8%

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

      3. *-commutative 12.8%

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

   6. Simplified 12.8%

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

   7. Taylor expanded in x1 around 0 95.6%

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

   8. Taylor expanded in x2 around 0 97.7%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.5 \cdot 10^{+102}:\\ \;\;\;\;x1 - \left(x2 \cdot \left(6 - -3 \cdot \frac{x1}{x2}\right) + \left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right) - x1 \cdot \left(3 + \left(x2 \cdot 8 - 2 \cdot \left(\left(2 \cdot x2 - 3\right) - x2 \cdot -2\right)\right)\right)\right) - x1\right)\right)\\ \mathbf{elif}\;x1 \leq 7.5 \cdot 10^{+138}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2 - x1\right) + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right) + \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(2 \cdot x2 - x1\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2 - x1\right) + \left(x1 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot 9\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 90.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 2 \cdot x2 - 3\\ t_1 := x1 \cdot x1 + 1\\ t_2 := 3 \cdot \left(x2 \cdot -2 - x1\right)\\ t_3 := x1 \cdot \left(x1 \cdot 3\right)\\ t_4 := x2 \cdot \left(3 - 2 \cdot x2\right)\\ t_5 := 4 \cdot t\_4\\ t_6 := \frac{\left(t\_3 + 2 \cdot x2\right) - x1}{t\_1}\\ \mathbf{if}\;x1 \leq -5.5 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(t\_2 + \left(x1 - x1 \cdot \left(x1 \cdot \left(\left(2 \cdot \left(t\_0 - x2 \cdot -2\right) + \left(x1 \cdot \left(3 + \left(t\_5 - 2 \cdot \left(\left(1 + \left(2 \cdot \left(x2 \cdot \left(3 + x2 \cdot -2\right)\right) + 3 \cdot t\_0\right)\right) + 2 \cdot t\_4\right)\right)\right) - x2 \cdot 8\right)\right) - 3\right) + t\_5\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 7.5 \cdot 10^{+138}:\\ \;\;\;\;x1 + \left(t\_2 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot t\_3 - t\_1 \cdot \left(\left(t\_6 - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(x1 - 2 \cdot x2\right)\right) - \left(x1 \cdot x1\right) \cdot \left(t\_6 \cdot 4 - 6\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 - \left(3 \cdot \left(x1 - x2 \cdot -2\right) + \left(x1 \cdot \left(t\_5 - x1 \cdot 9\right) - x1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (- (* 2.0 x2) 3.0))
        (t_1 (+ (* x1 x1) 1.0))
        (t_2 (* 3.0 (- (* x2 -2.0) x1)))
        (t_3 (* x1 (* x1 3.0)))
        (t_4 (* x2 (- 3.0 (* 2.0 x2))))
        (t_5 (* 4.0 t_4))
        (t_6 (/ (- (+ t_3 (* 2.0 x2)) x1) t_1)))
   (if (<= x1 -5.5e+102)
     (+
      x1
      (+
       t_2
       (-
        x1
        (*
         x1
         (+
          (*
           x1
           (-
            (+
             (* 2.0 (- t_0 (* x2 -2.0)))
             (-
              (*
               x1
               (+
                3.0
                (-
                 t_5
                 (*
                  2.0
                  (+
                   (+ 1.0 (+ (* 2.0 (* x2 (+ 3.0 (* x2 -2.0)))) (* 3.0 t_0)))
                   (* 2.0 t_4))))))
              (* x2 8.0)))
            3.0))
          t_5)))))
     (if (<= x1 7.5e+138)
       (+
        x1
        (+
         t_2
         (+
          x1
          (+
           (* x1 (* x1 x1))
           (-
            (* 3.0 t_3)
            (*
             t_1
             (-
              (* (- t_6 3.0) (* (* x1 2.0) (- x1 (* 2.0 x2))))
              (* (* x1 x1) (- (* t_6 4.0) 6.0)))))))))
       (-
        x1
        (+ (* 3.0 (- x1 (* x2 -2.0))) (- (* x1 (- t_5 (* x1 9.0))) x1)))))))

C

double code(double x1, double x2) {
	double t_0 = (2.0 * x2) - 3.0;
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = 3.0 * ((x2 * -2.0) - x1);
	double t_3 = x1 * (x1 * 3.0);
	double t_4 = x2 * (3.0 - (2.0 * x2));
	double t_5 = 4.0 * t_4;
	double t_6 = ((t_3 + (2.0 * x2)) - x1) / t_1;
	double tmp;
	if (x1 <= -5.5e+102) {
		tmp = x1 + (t_2 + (x1 - (x1 * ((x1 * (((2.0 * (t_0 - (x2 * -2.0))) + ((x1 * (3.0 + (t_5 - (2.0 * ((1.0 + ((2.0 * (x2 * (3.0 + (x2 * -2.0)))) + (3.0 * t_0))) + (2.0 * t_4)))))) - (x2 * 8.0))) - 3.0)) + t_5))));
	} else if (x1 <= 7.5e+138) {
		tmp = x1 + (t_2 + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_3) - (t_1 * (((t_6 - 3.0) * ((x1 * 2.0) * (x1 - (2.0 * x2)))) - ((x1 * x1) * ((t_6 * 4.0) - 6.0))))))));
	} else {
		tmp = x1 - ((3.0 * (x1 - (x2 * -2.0))) + ((x1 * (t_5 - (x1 * 9.0))) - 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) :: t_5
    real(8) :: t_6
    real(8) :: tmp
    t_0 = (2.0d0 * x2) - 3.0d0
    t_1 = (x1 * x1) + 1.0d0
    t_2 = 3.0d0 * ((x2 * (-2.0d0)) - x1)
    t_3 = x1 * (x1 * 3.0d0)
    t_4 = x2 * (3.0d0 - (2.0d0 * x2))
    t_5 = 4.0d0 * t_4
    t_6 = ((t_3 + (2.0d0 * x2)) - x1) / t_1
    if (x1 <= (-5.5d+102)) then
        tmp = x1 + (t_2 + (x1 - (x1 * ((x1 * (((2.0d0 * (t_0 - (x2 * (-2.0d0)))) + ((x1 * (3.0d0 + (t_5 - (2.0d0 * ((1.0d0 + ((2.0d0 * (x2 * (3.0d0 + (x2 * (-2.0d0))))) + (3.0d0 * t_0))) + (2.0d0 * t_4)))))) - (x2 * 8.0d0))) - 3.0d0)) + t_5))))
    else if (x1 <= 7.5d+138) then
        tmp = x1 + (t_2 + (x1 + ((x1 * (x1 * x1)) + ((3.0d0 * t_3) - (t_1 * (((t_6 - 3.0d0) * ((x1 * 2.0d0) * (x1 - (2.0d0 * x2)))) - ((x1 * x1) * ((t_6 * 4.0d0) - 6.0d0))))))))
    else
        tmp = x1 - ((3.0d0 * (x1 - (x2 * (-2.0d0)))) + ((x1 * (t_5 - (x1 * 9.0d0))) - x1))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (2.0 * x2) - 3.0;
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = 3.0 * ((x2 * -2.0) - x1);
	double t_3 = x1 * (x1 * 3.0);
	double t_4 = x2 * (3.0 - (2.0 * x2));
	double t_5 = 4.0 * t_4;
	double t_6 = ((t_3 + (2.0 * x2)) - x1) / t_1;
	double tmp;
	if (x1 <= -5.5e+102) {
		tmp = x1 + (t_2 + (x1 - (x1 * ((x1 * (((2.0 * (t_0 - (x2 * -2.0))) + ((x1 * (3.0 + (t_5 - (2.0 * ((1.0 + ((2.0 * (x2 * (3.0 + (x2 * -2.0)))) + (3.0 * t_0))) + (2.0 * t_4)))))) - (x2 * 8.0))) - 3.0)) + t_5))));
	} else if (x1 <= 7.5e+138) {
		tmp = x1 + (t_2 + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_3) - (t_1 * (((t_6 - 3.0) * ((x1 * 2.0) * (x1 - (2.0 * x2)))) - ((x1 * x1) * ((t_6 * 4.0) - 6.0))))))));
	} else {
		tmp = x1 - ((3.0 * (x1 - (x2 * -2.0))) + ((x1 * (t_5 - (x1 * 9.0))) - x1));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (2.0 * x2) - 3.0
	t_1 = (x1 * x1) + 1.0
	t_2 = 3.0 * ((x2 * -2.0) - x1)
	t_3 = x1 * (x1 * 3.0)
	t_4 = x2 * (3.0 - (2.0 * x2))
	t_5 = 4.0 * t_4
	t_6 = ((t_3 + (2.0 * x2)) - x1) / t_1
	tmp = 0
	if x1 <= -5.5e+102:
		tmp = x1 + (t_2 + (x1 - (x1 * ((x1 * (((2.0 * (t_0 - (x2 * -2.0))) + ((x1 * (3.0 + (t_5 - (2.0 * ((1.0 + ((2.0 * (x2 * (3.0 + (x2 * -2.0)))) + (3.0 * t_0))) + (2.0 * t_4)))))) - (x2 * 8.0))) - 3.0)) + t_5))))
	elif x1 <= 7.5e+138:
		tmp = x1 + (t_2 + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_3) - (t_1 * (((t_6 - 3.0) * ((x1 * 2.0) * (x1 - (2.0 * x2)))) - ((x1 * x1) * ((t_6 * 4.0) - 6.0))))))))
	else:
		tmp = x1 - ((3.0 * (x1 - (x2 * -2.0))) + ((x1 * (t_5 - (x1 * 9.0))) - x1))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(2.0 * x2) - 3.0)
	t_1 = Float64(Float64(x1 * x1) + 1.0)
	t_2 = Float64(3.0 * Float64(Float64(x2 * -2.0) - x1))
	t_3 = Float64(x1 * Float64(x1 * 3.0))
	t_4 = Float64(x2 * Float64(3.0 - Float64(2.0 * x2)))
	t_5 = Float64(4.0 * t_4)
	t_6 = Float64(Float64(Float64(t_3 + Float64(2.0 * x2)) - x1) / t_1)
	tmp = 0.0
	if (x1 <= -5.5e+102)
		tmp = Float64(x1 + Float64(t_2 + Float64(x1 - Float64(x1 * Float64(Float64(x1 * Float64(Float64(Float64(2.0 * Float64(t_0 - Float64(x2 * -2.0))) + Float64(Float64(x1 * Float64(3.0 + Float64(t_5 - Float64(2.0 * Float64(Float64(1.0 + Float64(Float64(2.0 * Float64(x2 * Float64(3.0 + Float64(x2 * -2.0)))) + Float64(3.0 * t_0))) + Float64(2.0 * t_4)))))) - Float64(x2 * 8.0))) - 3.0)) + t_5)))));
	elseif (x1 <= 7.5e+138)
		tmp = Float64(x1 + Float64(t_2 + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(3.0 * t_3) - Float64(t_1 * Float64(Float64(Float64(t_6 - 3.0) * Float64(Float64(x1 * 2.0) * Float64(x1 - Float64(2.0 * x2)))) - Float64(Float64(x1 * x1) * Float64(Float64(t_6 * 4.0) - 6.0)))))))));
	else
		tmp = Float64(x1 - Float64(Float64(3.0 * Float64(x1 - Float64(x2 * -2.0))) + Float64(Float64(x1 * Float64(t_5 - Float64(x1 * 9.0))) - x1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (2.0 * x2) - 3.0;
	t_1 = (x1 * x1) + 1.0;
	t_2 = 3.0 * ((x2 * -2.0) - x1);
	t_3 = x1 * (x1 * 3.0);
	t_4 = x2 * (3.0 - (2.0 * x2));
	t_5 = 4.0 * t_4;
	t_6 = ((t_3 + (2.0 * x2)) - x1) / t_1;
	tmp = 0.0;
	if (x1 <= -5.5e+102)
		tmp = x1 + (t_2 + (x1 - (x1 * ((x1 * (((2.0 * (t_0 - (x2 * -2.0))) + ((x1 * (3.0 + (t_5 - (2.0 * ((1.0 + ((2.0 * (x2 * (3.0 + (x2 * -2.0)))) + (3.0 * t_0))) + (2.0 * t_4)))))) - (x2 * 8.0))) - 3.0)) + t_5))));
	elseif (x1 <= 7.5e+138)
		tmp = x1 + (t_2 + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_3) - (t_1 * (((t_6 - 3.0) * ((x1 * 2.0) * (x1 - (2.0 * x2)))) - ((x1 * x1) * ((t_6 * 4.0) - 6.0))))))));
	else
		tmp = x1 - ((3.0 * (x1 - (x2 * -2.0))) + ((x1 * (t_5 - (x1 * 9.0))) - x1));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$2 = N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(x2 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(4.0 * t$95$4), $MachinePrecision]}, Block[{t$95$6 = N[(N[(N[(t$95$3 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[x1, -5.5e+102], N[(x1 + N[(t$95$2 + N[(x1 - N[(x1 * N[(N[(x1 * N[(N[(N[(2.0 * N[(t$95$0 - N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * N[(3.0 + N[(t$95$5 - N[(2.0 * N[(N[(1.0 + N[(N[(2.0 * N[(x2 * N[(3.0 + N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(2.0 * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x2 * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision] + t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 7.5e+138], N[(x1 + N[(t$95$2 + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(3.0 * t$95$3), $MachinePrecision] - N[(t$95$1 * N[(N[(N[(t$95$6 - 3.0), $MachinePrecision] * N[(N[(x1 * 2.0), $MachinePrecision] * N[(x1 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$6 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 - N[(N[(3.0 * N[(x1 - N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * N[(t$95$5 - N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -5.49999999999999981e102

   1. Initial program 0.0%

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

   3. Taylor expanded in x1 around inf 0.0%

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

   4. Taylor expanded in x1 around 0 0.0%

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

      1. neg-mul-1 0.0%

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

      2. unsub-neg 0.0%

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

      3. *-commutative 0.0%

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

   6. Simplified 0.0%

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

   7. Taylor expanded in x1 around 0 80.0%

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

   if -5.49999999999999981e102 < x1 < 7.4999999999999999e138

   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 inf 98.4%

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

   4. Taylor expanded in x1 around 0 99.4%

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

      1. neg-mul-1 99.4%

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

      2. unsub-neg 99.4%

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

      3. *-commutative 99.4%

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

   6. Simplified 99.4%

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

   7. Taylor expanded in x1 around 0 95.5%

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

      1. neg-mul-1 95.5%

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

      2. +-commutative 95.5%

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

      3. unsub-neg 95.5%

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

   9. Simplified 95.5%

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

   if 7.4999999999999999e138 < x1

   1. Initial program 12.8%

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

   3. Taylor expanded in x1 around inf 12.8%

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

   4. Taylor expanded in x1 around 0 12.8%

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

      1. neg-mul-1 12.8%

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

      2. unsub-neg 12.8%

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

      3. *-commutative 12.8%

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

   6. Simplified 12.8%

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

   7. Taylor expanded in x1 around 0 95.6%

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

   8. Taylor expanded in x2 around 0 97.7%

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

4. Final simplification 93.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.5 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2 - x1\right) + \left(x1 - x1 \cdot \left(x1 \cdot \left(\left(2 \cdot \left(\left(2 \cdot x2 - 3\right) - x2 \cdot -2\right) + \left(x1 \cdot \left(3 + \left(4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right) - 2 \cdot \left(\left(1 + \left(2 \cdot \left(x2 \cdot \left(3 + x2 \cdot -2\right)\right) + 3 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + 2 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right)\right) - x2 \cdot 8\right)\right) - 3\right) + 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 7.5 \cdot 10^{+138}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2 - x1\right) + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) - \left(x1 \cdot x1 + 1\right) \cdot \left(\left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(x1 - 2 \cdot x2\right)\right) - \left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 - \left(3 \cdot \left(x1 - x2 \cdot -2\right) + \left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right) - x1 \cdot 9\right) - x1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 86.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 2 \cdot x2 - 3\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := x1 \cdot x1 + 1\\ t_3 := x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot t\_1 + t\_2 \cdot \left(\left(x1 \cdot x1\right) \cdot 6 + \left(\left(x1 \cdot 2\right) \cdot \frac{\left(t\_1 + 2 \cdot x2\right) - x1}{t\_2}\right) \cdot 0\right)\right)\right)\\ t_4 := 3 \cdot \frac{\left(t\_1 - 2 \cdot x2\right) - x1}{t\_2}\\ \mathbf{if}\;x1 \leq -5.5 \cdot 10^{+102}:\\ \;\;\;\;x1 - \left(x2 \cdot \left(6 - -3 \cdot \frac{x1}{x2}\right) + \left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right) - x1 \cdot \left(3 + \left(x2 \cdot 8 - 2 \cdot \left(t\_0 - x2 \cdot -2\right)\right)\right)\right) - x1\right)\right)\\ \mathbf{elif}\;x1 \leq -2.4 \cdot 10^{+18}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(-1 + x1 \cdot \left(3 - x2 \cdot -2\right)\right)\right) + t\_3\right)\\ \mathbf{elif}\;x1 \leq 40000000:\\ \;\;\;\;x1 + \left(t\_4 + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot -3 + 2 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 2.5 \cdot 10^{+152}:\\ \;\;\;\;x1 + \left(t\_4 + t\_3\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2 - x1\right) + \left(x1 + x1 \cdot \left(4 \cdot \left(x2 \cdot t\_0\right) + x1 \cdot 9\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (- (* 2.0 x2) 3.0))
        (t_1 (* x1 (* x1 3.0)))
        (t_2 (+ (* x1 x1) 1.0))
        (t_3
         (+
          x1
          (+
           (* x1 (* x1 x1))
           (+
            (* 3.0 t_1)
            (*
             t_2
             (+
              (* (* x1 x1) 6.0)
              (* (* (* x1 2.0) (/ (- (+ t_1 (* 2.0 x2)) x1) t_2)) 0.0)))))))
        (t_4 (* 3.0 (/ (- (- t_1 (* 2.0 x2)) x1) t_2))))
   (if (<= x1 -5.5e+102)
     (-
      x1
      (+
       (* x2 (- 6.0 (* -3.0 (/ x1 x2))))
       (-
        (*
         x1
         (-
          (* 4.0 (* x2 (- 3.0 (* 2.0 x2))))
          (* x1 (+ 3.0 (- (* x2 8.0) (* 2.0 (- t_0 (* x2 -2.0))))))))
        x1)))
     (if (<= x1 -2.4e+18)
       (+
        x1
        (+
         (* 3.0 (+ (* x2 -2.0) (* x1 (+ -1.0 (* x1 (- 3.0 (* x2 -2.0)))))))
         t_3))
       (if (<= x1 40000000.0)
         (+ x1 (+ t_4 (+ x1 (* 4.0 (* x2 (+ (* x1 -3.0) (* 2.0 (* x1 x2))))))))
         (if (<= x1 2.5e+152)
           (+ x1 (+ t_4 t_3))
           (+
            x1
            (+
             (* 3.0 (- (* x2 -2.0) x1))
             (+ x1 (* x1 (+ (* 4.0 (* x2 t_0)) (* x1 9.0))))))))))))

C

double code(double x1, double x2) {
	double t_0 = (2.0 * x2) - 3.0;
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = x1 + ((x1 * (x1 * x1)) + ((3.0 * t_1) + (t_2 * (((x1 * x1) * 6.0) + (((x1 * 2.0) * (((t_1 + (2.0 * x2)) - x1) / t_2)) * 0.0)))));
	double t_4 = 3.0 * (((t_1 - (2.0 * x2)) - x1) / t_2);
	double tmp;
	if (x1 <= -5.5e+102) {
		tmp = x1 - ((x2 * (6.0 - (-3.0 * (x1 / x2)))) + ((x1 * ((4.0 * (x2 * (3.0 - (2.0 * x2)))) - (x1 * (3.0 + ((x2 * 8.0) - (2.0 * (t_0 - (x2 * -2.0)))))))) - x1));
	} else if (x1 <= -2.4e+18) {
		tmp = x1 + ((3.0 * ((x2 * -2.0) + (x1 * (-1.0 + (x1 * (3.0 - (x2 * -2.0))))))) + t_3);
	} else if (x1 <= 40000000.0) {
		tmp = x1 + (t_4 + (x1 + (4.0 * (x2 * ((x1 * -3.0) + (2.0 * (x1 * x2)))))));
	} else if (x1 <= 2.5e+152) {
		tmp = x1 + (t_4 + t_3);
	} else {
		tmp = x1 + ((3.0 * ((x2 * -2.0) - x1)) + (x1 + (x1 * ((4.0 * (x2 * t_0)) + (x1 * 9.0)))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_0 = (2.0d0 * x2) - 3.0d0
    t_1 = x1 * (x1 * 3.0d0)
    t_2 = (x1 * x1) + 1.0d0
    t_3 = x1 + ((x1 * (x1 * x1)) + ((3.0d0 * t_1) + (t_2 * (((x1 * x1) * 6.0d0) + (((x1 * 2.0d0) * (((t_1 + (2.0d0 * x2)) - x1) / t_2)) * 0.0d0)))))
    t_4 = 3.0d0 * (((t_1 - (2.0d0 * x2)) - x1) / t_2)
    if (x1 <= (-5.5d+102)) then
        tmp = x1 - ((x2 * (6.0d0 - ((-3.0d0) * (x1 / x2)))) + ((x1 * ((4.0d0 * (x2 * (3.0d0 - (2.0d0 * x2)))) - (x1 * (3.0d0 + ((x2 * 8.0d0) - (2.0d0 * (t_0 - (x2 * (-2.0d0))))))))) - x1))
    else if (x1 <= (-2.4d+18)) then
        tmp = x1 + ((3.0d0 * ((x2 * (-2.0d0)) + (x1 * ((-1.0d0) + (x1 * (3.0d0 - (x2 * (-2.0d0)))))))) + t_3)
    else if (x1 <= 40000000.0d0) then
        tmp = x1 + (t_4 + (x1 + (4.0d0 * (x2 * ((x1 * (-3.0d0)) + (2.0d0 * (x1 * x2)))))))
    else if (x1 <= 2.5d+152) then
        tmp = x1 + (t_4 + t_3)
    else
        tmp = x1 + ((3.0d0 * ((x2 * (-2.0d0)) - x1)) + (x1 + (x1 * ((4.0d0 * (x2 * t_0)) + (x1 * 9.0d0)))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (2.0 * x2) - 3.0;
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = x1 + ((x1 * (x1 * x1)) + ((3.0 * t_1) + (t_2 * (((x1 * x1) * 6.0) + (((x1 * 2.0) * (((t_1 + (2.0 * x2)) - x1) / t_2)) * 0.0)))));
	double t_4 = 3.0 * (((t_1 - (2.0 * x2)) - x1) / t_2);
	double tmp;
	if (x1 <= -5.5e+102) {
		tmp = x1 - ((x2 * (6.0 - (-3.0 * (x1 / x2)))) + ((x1 * ((4.0 * (x2 * (3.0 - (2.0 * x2)))) - (x1 * (3.0 + ((x2 * 8.0) - (2.0 * (t_0 - (x2 * -2.0)))))))) - x1));
	} else if (x1 <= -2.4e+18) {
		tmp = x1 + ((3.0 * ((x2 * -2.0) + (x1 * (-1.0 + (x1 * (3.0 - (x2 * -2.0))))))) + t_3);
	} else if (x1 <= 40000000.0) {
		tmp = x1 + (t_4 + (x1 + (4.0 * (x2 * ((x1 * -3.0) + (2.0 * (x1 * x2)))))));
	} else if (x1 <= 2.5e+152) {
		tmp = x1 + (t_4 + t_3);
	} else {
		tmp = x1 + ((3.0 * ((x2 * -2.0) - x1)) + (x1 + (x1 * ((4.0 * (x2 * t_0)) + (x1 * 9.0)))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (2.0 * x2) - 3.0
	t_1 = x1 * (x1 * 3.0)
	t_2 = (x1 * x1) + 1.0
	t_3 = x1 + ((x1 * (x1 * x1)) + ((3.0 * t_1) + (t_2 * (((x1 * x1) * 6.0) + (((x1 * 2.0) * (((t_1 + (2.0 * x2)) - x1) / t_2)) * 0.0)))))
	t_4 = 3.0 * (((t_1 - (2.0 * x2)) - x1) / t_2)
	tmp = 0
	if x1 <= -5.5e+102:
		tmp = x1 - ((x2 * (6.0 - (-3.0 * (x1 / x2)))) + ((x1 * ((4.0 * (x2 * (3.0 - (2.0 * x2)))) - (x1 * (3.0 + ((x2 * 8.0) - (2.0 * (t_0 - (x2 * -2.0)))))))) - x1))
	elif x1 <= -2.4e+18:
		tmp = x1 + ((3.0 * ((x2 * -2.0) + (x1 * (-1.0 + (x1 * (3.0 - (x2 * -2.0))))))) + t_3)
	elif x1 <= 40000000.0:
		tmp = x1 + (t_4 + (x1 + (4.0 * (x2 * ((x1 * -3.0) + (2.0 * (x1 * x2)))))))
	elif x1 <= 2.5e+152:
		tmp = x1 + (t_4 + t_3)
	else:
		tmp = x1 + ((3.0 * ((x2 * -2.0) - x1)) + (x1 + (x1 * ((4.0 * (x2 * t_0)) + (x1 * 9.0)))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(2.0 * x2) - 3.0)
	t_1 = Float64(x1 * Float64(x1 * 3.0))
	t_2 = Float64(Float64(x1 * x1) + 1.0)
	t_3 = Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(3.0 * t_1) + Float64(t_2 * Float64(Float64(Float64(x1 * x1) * 6.0) + Float64(Float64(Float64(x1 * 2.0) * Float64(Float64(Float64(t_1 + Float64(2.0 * x2)) - x1) / t_2)) * 0.0))))))
	t_4 = Float64(3.0 * Float64(Float64(Float64(t_1 - Float64(2.0 * x2)) - x1) / t_2))
	tmp = 0.0
	if (x1 <= -5.5e+102)
		tmp = Float64(x1 - Float64(Float64(x2 * Float64(6.0 - Float64(-3.0 * Float64(x1 / x2)))) + Float64(Float64(x1 * Float64(Float64(4.0 * Float64(x2 * Float64(3.0 - Float64(2.0 * x2)))) - Float64(x1 * Float64(3.0 + Float64(Float64(x2 * 8.0) - Float64(2.0 * Float64(t_0 - Float64(x2 * -2.0)))))))) - x1)));
	elseif (x1 <= -2.4e+18)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(x2 * -2.0) + Float64(x1 * Float64(-1.0 + Float64(x1 * Float64(3.0 - Float64(x2 * -2.0))))))) + t_3));
	elseif (x1 <= 40000000.0)
		tmp = Float64(x1 + Float64(t_4 + Float64(x1 + Float64(4.0 * Float64(x2 * Float64(Float64(x1 * -3.0) + Float64(2.0 * Float64(x1 * x2))))))));
	elseif (x1 <= 2.5e+152)
		tmp = Float64(x1 + Float64(t_4 + t_3));
	else
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(x2 * -2.0) - x1)) + Float64(x1 + Float64(x1 * Float64(Float64(4.0 * Float64(x2 * t_0)) + Float64(x1 * 9.0))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (2.0 * x2) - 3.0;
	t_1 = x1 * (x1 * 3.0);
	t_2 = (x1 * x1) + 1.0;
	t_3 = x1 + ((x1 * (x1 * x1)) + ((3.0 * t_1) + (t_2 * (((x1 * x1) * 6.0) + (((x1 * 2.0) * (((t_1 + (2.0 * x2)) - x1) / t_2)) * 0.0)))));
	t_4 = 3.0 * (((t_1 - (2.0 * x2)) - x1) / t_2);
	tmp = 0.0;
	if (x1 <= -5.5e+102)
		tmp = x1 - ((x2 * (6.0 - (-3.0 * (x1 / x2)))) + ((x1 * ((4.0 * (x2 * (3.0 - (2.0 * x2)))) - (x1 * (3.0 + ((x2 * 8.0) - (2.0 * (t_0 - (x2 * -2.0)))))))) - x1));
	elseif (x1 <= -2.4e+18)
		tmp = x1 + ((3.0 * ((x2 * -2.0) + (x1 * (-1.0 + (x1 * (3.0 - (x2 * -2.0))))))) + t_3);
	elseif (x1 <= 40000000.0)
		tmp = x1 + (t_4 + (x1 + (4.0 * (x2 * ((x1 * -3.0) + (2.0 * (x1 * x2)))))));
	elseif (x1 <= 2.5e+152)
		tmp = x1 + (t_4 + t_3);
	else
		tmp = x1 + ((3.0 * ((x2 * -2.0) - x1)) + (x1 + (x1 * ((4.0 * (x2 * t_0)) + (x1 * 9.0)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$3 = N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(3.0 * t$95$1), $MachinePrecision] + N[(t$95$2 * N[(N[(N[(x1 * x1), $MachinePrecision] * 6.0), $MachinePrecision] + N[(N[(N[(x1 * 2.0), $MachinePrecision] * N[(N[(N[(t$95$1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision] * 0.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(3.0 * N[(N[(N[(t$95$1 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -5.5e+102], N[(x1 - N[(N[(x2 * N[(6.0 - N[(-3.0 * N[(x1 / x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * N[(N[(4.0 * N[(x2 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x1 * N[(3.0 + N[(N[(x2 * 8.0), $MachinePrecision] - N[(2.0 * N[(t$95$0 - N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -2.4e+18], N[(x1 + N[(N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] + N[(x1 * N[(-1.0 + N[(x1 * N[(3.0 - N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$3), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 40000000.0], N[(x1 + N[(t$95$4 + N[(x1 + N[(4.0 * N[(x2 * N[(N[(x1 * -3.0), $MachinePrecision] + N[(2.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 2.5e+152], N[(x1 + N[(t$95$4 + t$95$3), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(x1 * N[(N[(4.0 * N[(x2 * t$95$0), $MachinePrecision]), $MachinePrecision] + N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x1 < -5.49999999999999981e102

   1. Initial program 0.0%

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

   3. Taylor expanded in x1 around inf 0.0%

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

   4. Taylor expanded in x1 around 0 0.0%

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

      1. neg-mul-1 0.0%

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

      2. unsub-neg 0.0%

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

      3. *-commutative 0.0%

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

   6. Simplified 0.0%

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

   7. Taylor expanded in x1 around 0 48.8%

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

   8. Taylor expanded in x2 around inf 59.1%

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

   if -5.49999999999999981e102 < x1 < -2.4e18

   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 inf 99.5%

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

   4. Taylor expanded in x1 around inf 97.7%

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

   5. Taylor expanded in x1 around 0 98.0%

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

   6. Taylor expanded in x1 around inf 85.9%

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

   if -2.4e18 < x1 < 4e7

   1. Initial program 99.3%

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

   3. Taylor expanded in x1 around 0 88.4%

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

   4. Taylor expanded in x2 around 0 97.9%

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

   if 4e7 < x1 < 2.5e152

   1. Initial program 99.7%

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

   3. Taylor expanded in x1 around inf 99.7%

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

   4. Taylor expanded in x1 around inf 98.4%

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

   5. Taylor expanded in x1 around inf 94.0%

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

   if 2.5e152 < x1

   1. Initial program 5.6%

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

   3. Taylor expanded in x1 around inf 5.6%

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

   4. Taylor expanded in x1 around 0 5.6%

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

      1. neg-mul-1 5.6%

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

      2. unsub-neg 5.6%

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

      3. *-commutative 5.6%

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

   6. Simplified 5.6%

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

   7. Taylor expanded in x1 around 0 97.7%

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

   8. Taylor expanded in x2 around 0 100.0%

      \[\leadsto x1 + \left(\left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(3 + \color{blue}{6}\right)\right) + x1\right) + 3 \cdot \left(x2 \cdot -2 - x1\right)\right) \]
3. Recombined 5 regimes into one program.

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.5 \cdot 10^{+102}:\\ \;\;\;\;x1 - \left(x2 \cdot \left(6 - -3 \cdot \frac{x1}{x2}\right) + \left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right) - x1 \cdot \left(3 + \left(x2 \cdot 8 - 2 \cdot \left(\left(2 \cdot x2 - 3\right) - x2 \cdot -2\right)\right)\right)\right) - x1\right)\right)\\ \mathbf{elif}\;x1 \leq -2.4 \cdot 10^{+18}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(-1 + x1 \cdot \left(3 - x2 \cdot -2\right)\right)\right) + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot 6 + \left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot 0\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 40000000:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot -3 + 2 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 2.5 \cdot 10^{+152}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot 6 + \left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot 0\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2 - x1\right) + \left(x1 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot 9\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 85.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 2 \cdot x2 - 3\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := x1 \cdot x1 + 1\\ t_3 := x1 + \left(3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(-1 + x1 \cdot \left(3 - x2 \cdot -2\right)\right)\right) + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot t\_1 + t\_2 \cdot \left(\left(x1 \cdot x1\right) \cdot 6 + \left(\left(x1 \cdot 2\right) \cdot \frac{\left(t\_1 + 2 \cdot x2\right) - x1}{t\_2}\right) \cdot 0\right)\right)\right)\right)\right)\\ \mathbf{if}\;x1 \leq -5.5 \cdot 10^{+102}:\\ \;\;\;\;x1 - \left(x2 \cdot \left(6 - -3 \cdot \frac{x1}{x2}\right) + \left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right) - x1 \cdot \left(3 + \left(x2 \cdot 8 - 2 \cdot \left(t\_0 - x2 \cdot -2\right)\right)\right)\right) - x1\right)\right)\\ \mathbf{elif}\;x1 \leq -2.4 \cdot 10^{+18}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x1 \leq 36000000:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t\_1 - 2 \cdot x2\right) - x1}{t\_2} + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot -3 + 2 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 7.5 \cdot 10^{+138}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2 - x1\right) + \left(x1 + x1 \cdot \left(4 \cdot \left(x2 \cdot t\_0\right) + x1 \cdot 9\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (- (* 2.0 x2) 3.0))
        (t_1 (* x1 (* x1 3.0)))
        (t_2 (+ (* x1 x1) 1.0))
        (t_3
         (+
          x1
          (+
           (* 3.0 (+ (* x2 -2.0) (* x1 (+ -1.0 (* x1 (- 3.0 (* x2 -2.0)))))))
           (+
            x1
            (+
             (* x1 (* x1 x1))
             (+
              (* 3.0 t_1)
              (*
               t_2
               (+
                (* (* x1 x1) 6.0)
                (*
                 (* (* x1 2.0) (/ (- (+ t_1 (* 2.0 x2)) x1) t_2))
                 0.0))))))))))
   (if (<= x1 -5.5e+102)
     (-
      x1
      (+
       (* x2 (- 6.0 (* -3.0 (/ x1 x2))))
       (-
        (*
         x1
         (-
          (* 4.0 (* x2 (- 3.0 (* 2.0 x2))))
          (* x1 (+ 3.0 (- (* x2 8.0) (* 2.0 (- t_0 (* x2 -2.0))))))))
        x1)))
     (if (<= x1 -2.4e+18)
       t_3
       (if (<= x1 36000000.0)
         (+
          x1
          (+
           (* 3.0 (/ (- (- t_1 (* 2.0 x2)) x1) t_2))
           (+ x1 (* 4.0 (* x2 (+ (* x1 -3.0) (* 2.0 (* x1 x2))))))))
         (if (<= x1 7.5e+138)
           t_3
           (+
            x1
            (+
             (* 3.0 (- (* x2 -2.0) x1))
             (+ x1 (* x1 (+ (* 4.0 (* x2 t_0)) (* x1 9.0))))))))))))

C

double code(double x1, double x2) {
	double t_0 = (2.0 * x2) - 3.0;
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = x1 + ((3.0 * ((x2 * -2.0) + (x1 * (-1.0 + (x1 * (3.0 - (x2 * -2.0))))))) + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_1) + (t_2 * (((x1 * x1) * 6.0) + (((x1 * 2.0) * (((t_1 + (2.0 * x2)) - x1) / t_2)) * 0.0)))))));
	double tmp;
	if (x1 <= -5.5e+102) {
		tmp = x1 - ((x2 * (6.0 - (-3.0 * (x1 / x2)))) + ((x1 * ((4.0 * (x2 * (3.0 - (2.0 * x2)))) - (x1 * (3.0 + ((x2 * 8.0) - (2.0 * (t_0 - (x2 * -2.0)))))))) - x1));
	} else if (x1 <= -2.4e+18) {
		tmp = t_3;
	} else if (x1 <= 36000000.0) {
		tmp = x1 + ((3.0 * (((t_1 - (2.0 * x2)) - x1) / t_2)) + (x1 + (4.0 * (x2 * ((x1 * -3.0) + (2.0 * (x1 * x2)))))));
	} else if (x1 <= 7.5e+138) {
		tmp = t_3;
	} else {
		tmp = x1 + ((3.0 * ((x2 * -2.0) - x1)) + (x1 + (x1 * ((4.0 * (x2 * t_0)) + (x1 * 9.0)))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_0 = (2.0d0 * x2) - 3.0d0
    t_1 = x1 * (x1 * 3.0d0)
    t_2 = (x1 * x1) + 1.0d0
    t_3 = x1 + ((3.0d0 * ((x2 * (-2.0d0)) + (x1 * ((-1.0d0) + (x1 * (3.0d0 - (x2 * (-2.0d0)))))))) + (x1 + ((x1 * (x1 * x1)) + ((3.0d0 * t_1) + (t_2 * (((x1 * x1) * 6.0d0) + (((x1 * 2.0d0) * (((t_1 + (2.0d0 * x2)) - x1) / t_2)) * 0.0d0)))))))
    if (x1 <= (-5.5d+102)) then
        tmp = x1 - ((x2 * (6.0d0 - ((-3.0d0) * (x1 / x2)))) + ((x1 * ((4.0d0 * (x2 * (3.0d0 - (2.0d0 * x2)))) - (x1 * (3.0d0 + ((x2 * 8.0d0) - (2.0d0 * (t_0 - (x2 * (-2.0d0))))))))) - x1))
    else if (x1 <= (-2.4d+18)) then
        tmp = t_3
    else if (x1 <= 36000000.0d0) then
        tmp = x1 + ((3.0d0 * (((t_1 - (2.0d0 * x2)) - x1) / t_2)) + (x1 + (4.0d0 * (x2 * ((x1 * (-3.0d0)) + (2.0d0 * (x1 * x2)))))))
    else if (x1 <= 7.5d+138) then
        tmp = t_3
    else
        tmp = x1 + ((3.0d0 * ((x2 * (-2.0d0)) - x1)) + (x1 + (x1 * ((4.0d0 * (x2 * t_0)) + (x1 * 9.0d0)))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (2.0 * x2) - 3.0;
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = x1 + ((3.0 * ((x2 * -2.0) + (x1 * (-1.0 + (x1 * (3.0 - (x2 * -2.0))))))) + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_1) + (t_2 * (((x1 * x1) * 6.0) + (((x1 * 2.0) * (((t_1 + (2.0 * x2)) - x1) / t_2)) * 0.0)))))));
	double tmp;
	if (x1 <= -5.5e+102) {
		tmp = x1 - ((x2 * (6.0 - (-3.0 * (x1 / x2)))) + ((x1 * ((4.0 * (x2 * (3.0 - (2.0 * x2)))) - (x1 * (3.0 + ((x2 * 8.0) - (2.0 * (t_0 - (x2 * -2.0)))))))) - x1));
	} else if (x1 <= -2.4e+18) {
		tmp = t_3;
	} else if (x1 <= 36000000.0) {
		tmp = x1 + ((3.0 * (((t_1 - (2.0 * x2)) - x1) / t_2)) + (x1 + (4.0 * (x2 * ((x1 * -3.0) + (2.0 * (x1 * x2)))))));
	} else if (x1 <= 7.5e+138) {
		tmp = t_3;
	} else {
		tmp = x1 + ((3.0 * ((x2 * -2.0) - x1)) + (x1 + (x1 * ((4.0 * (x2 * t_0)) + (x1 * 9.0)))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (2.0 * x2) - 3.0
	t_1 = x1 * (x1 * 3.0)
	t_2 = (x1 * x1) + 1.0
	t_3 = x1 + ((3.0 * ((x2 * -2.0) + (x1 * (-1.0 + (x1 * (3.0 - (x2 * -2.0))))))) + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_1) + (t_2 * (((x1 * x1) * 6.0) + (((x1 * 2.0) * (((t_1 + (2.0 * x2)) - x1) / t_2)) * 0.0)))))))
	tmp = 0
	if x1 <= -5.5e+102:
		tmp = x1 - ((x2 * (6.0 - (-3.0 * (x1 / x2)))) + ((x1 * ((4.0 * (x2 * (3.0 - (2.0 * x2)))) - (x1 * (3.0 + ((x2 * 8.0) - (2.0 * (t_0 - (x2 * -2.0)))))))) - x1))
	elif x1 <= -2.4e+18:
		tmp = t_3
	elif x1 <= 36000000.0:
		tmp = x1 + ((3.0 * (((t_1 - (2.0 * x2)) - x1) / t_2)) + (x1 + (4.0 * (x2 * ((x1 * -3.0) + (2.0 * (x1 * x2)))))))
	elif x1 <= 7.5e+138:
		tmp = t_3
	else:
		tmp = x1 + ((3.0 * ((x2 * -2.0) - x1)) + (x1 + (x1 * ((4.0 * (x2 * t_0)) + (x1 * 9.0)))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(2.0 * x2) - 3.0)
	t_1 = Float64(x1 * Float64(x1 * 3.0))
	t_2 = Float64(Float64(x1 * x1) + 1.0)
	t_3 = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(x2 * -2.0) + Float64(x1 * Float64(-1.0 + Float64(x1 * Float64(3.0 - Float64(x2 * -2.0))))))) + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(3.0 * t_1) + Float64(t_2 * Float64(Float64(Float64(x1 * x1) * 6.0) + Float64(Float64(Float64(x1 * 2.0) * Float64(Float64(Float64(t_1 + Float64(2.0 * x2)) - x1) / t_2)) * 0.0))))))))
	tmp = 0.0
	if (x1 <= -5.5e+102)
		tmp = Float64(x1 - Float64(Float64(x2 * Float64(6.0 - Float64(-3.0 * Float64(x1 / x2)))) + Float64(Float64(x1 * Float64(Float64(4.0 * Float64(x2 * Float64(3.0 - Float64(2.0 * x2)))) - Float64(x1 * Float64(3.0 + Float64(Float64(x2 * 8.0) - Float64(2.0 * Float64(t_0 - Float64(x2 * -2.0)))))))) - x1)));
	elseif (x1 <= -2.4e+18)
		tmp = t_3;
	elseif (x1 <= 36000000.0)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_1 - Float64(2.0 * x2)) - x1) / t_2)) + Float64(x1 + Float64(4.0 * Float64(x2 * Float64(Float64(x1 * -3.0) + Float64(2.0 * Float64(x1 * x2))))))));
	elseif (x1 <= 7.5e+138)
		tmp = t_3;
	else
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(x2 * -2.0) - x1)) + Float64(x1 + Float64(x1 * Float64(Float64(4.0 * Float64(x2 * t_0)) + Float64(x1 * 9.0))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (2.0 * x2) - 3.0;
	t_1 = x1 * (x1 * 3.0);
	t_2 = (x1 * x1) + 1.0;
	t_3 = x1 + ((3.0 * ((x2 * -2.0) + (x1 * (-1.0 + (x1 * (3.0 - (x2 * -2.0))))))) + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_1) + (t_2 * (((x1 * x1) * 6.0) + (((x1 * 2.0) * (((t_1 + (2.0 * x2)) - x1) / t_2)) * 0.0)))))));
	tmp = 0.0;
	if (x1 <= -5.5e+102)
		tmp = x1 - ((x2 * (6.0 - (-3.0 * (x1 / x2)))) + ((x1 * ((4.0 * (x2 * (3.0 - (2.0 * x2)))) - (x1 * (3.0 + ((x2 * 8.0) - (2.0 * (t_0 - (x2 * -2.0)))))))) - x1));
	elseif (x1 <= -2.4e+18)
		tmp = t_3;
	elseif (x1 <= 36000000.0)
		tmp = x1 + ((3.0 * (((t_1 - (2.0 * x2)) - x1) / t_2)) + (x1 + (4.0 * (x2 * ((x1 * -3.0) + (2.0 * (x1 * x2)))))));
	elseif (x1 <= 7.5e+138)
		tmp = t_3;
	else
		tmp = x1 + ((3.0 * ((x2 * -2.0) - x1)) + (x1 + (x1 * ((4.0 * (x2 * t_0)) + (x1 * 9.0)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$3 = N[(x1 + N[(N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] + N[(x1 * N[(-1.0 + N[(x1 * N[(3.0 - N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(3.0 * t$95$1), $MachinePrecision] + N[(t$95$2 * N[(N[(N[(x1 * x1), $MachinePrecision] * 6.0), $MachinePrecision] + N[(N[(N[(x1 * 2.0), $MachinePrecision] * N[(N[(N[(t$95$1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision] * 0.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -5.5e+102], N[(x1 - N[(N[(x2 * N[(6.0 - N[(-3.0 * N[(x1 / x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * N[(N[(4.0 * N[(x2 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x1 * N[(3.0 + N[(N[(x2 * 8.0), $MachinePrecision] - N[(2.0 * N[(t$95$0 - N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -2.4e+18], t$95$3, If[LessEqual[x1, 36000000.0], N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$1 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(4.0 * N[(x2 * N[(N[(x1 * -3.0), $MachinePrecision] + N[(2.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 7.5e+138], t$95$3, N[(x1 + N[(N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(x1 * N[(N[(4.0 * N[(x2 * t$95$0), $MachinePrecision]), $MachinePrecision] + N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -5.49999999999999981e102

   1. Initial program 0.0%

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

   3. Taylor expanded in x1 around inf 0.0%

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

   4. Taylor expanded in x1 around 0 0.0%

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

      1. neg-mul-1 0.0%

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

      2. unsub-neg 0.0%

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

      3. *-commutative 0.0%

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

   6. Simplified 0.0%

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

   7. Taylor expanded in x1 around 0 48.8%

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

   8. Taylor expanded in x2 around inf 59.1%

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

   if -5.49999999999999981e102 < x1 < -2.4e18 or 3.6e7 < x1 < 7.4999999999999999e138

   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 inf 99.5%

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

   4. Taylor expanded in x1 around inf 97.9%

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

   5. Taylor expanded in x1 around 0 93.4%

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

   6. Taylor expanded in x1 around inf 86.5%

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

   if -2.4e18 < x1 < 3.6e7

   1. Initial program 99.3%

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

   3. Taylor expanded in x1 around 0 88.4%

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

   4. Taylor expanded in x2 around 0 97.9%

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

   if 7.4999999999999999e138 < x1

   1. Initial program 12.8%

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

   3. Taylor expanded in x1 around inf 12.8%

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

   4. Taylor expanded in x1 around 0 12.8%

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

      1. neg-mul-1 12.8%

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

      2. unsub-neg 12.8%

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

      3. *-commutative 12.8%

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

   6. Simplified 12.8%

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

   7. Taylor expanded in x1 around 0 95.6%

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

   8. Taylor expanded in x2 around 0 97.7%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.5 \cdot 10^{+102}:\\ \;\;\;\;x1 - \left(x2 \cdot \left(6 - -3 \cdot \frac{x1}{x2}\right) + \left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right) - x1 \cdot \left(3 + \left(x2 \cdot 8 - 2 \cdot \left(\left(2 \cdot x2 - 3\right) - x2 \cdot -2\right)\right)\right)\right) - x1\right)\right)\\ \mathbf{elif}\;x1 \leq -2.4 \cdot 10^{+18}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(-1 + x1 \cdot \left(3 - x2 \cdot -2\right)\right)\right) + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot 6 + \left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot 0\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 36000000:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot -3 + 2 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 7.5 \cdot 10^{+138}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(-1 + x1 \cdot \left(3 - x2 \cdot -2\right)\right)\right) + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot 6 + \left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot 0\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2 - x1\right) + \left(x1 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot 9\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 78.5% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -2.7 \cdot 10^{+161}:\\ \;\;\;\;x1 - \left(3 \cdot \left(x1 - x2 \cdot -2\right) + \left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right) - x1 \cdot 9\right) - x1\right)\right)\\ \mathbf{elif}\;x1 \leq -8.8 \cdot 10^{+29}:\\ \;\;\;\;x1 + x2 \cdot \left(\left(\frac{x1 + x1 \cdot -3}{x2} - x1 \cdot 12\right) - 6\right)\\ \mathbf{elif}\;x1 \leq 6.5 \cdot 10^{+108}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{x1 + \left(2 \cdot x2 - x1 \cdot \left(x1 \cdot 3\right)\right)}{-1 - x1 \cdot x1} + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot -3 + 2 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 - \left(x1 \cdot \left(2 - \left(x2 \cdot -12 + x1 \cdot \left(x1 \cdot 3 + 3 \cdot \left(3 - x2 \cdot -2\right)\right)\right)\right) - x2 \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -2.7e+161)
   (-
    x1
    (+
     (* 3.0 (- x1 (* x2 -2.0)))
     (- (* x1 (- (* 4.0 (* x2 (- 3.0 (* 2.0 x2)))) (* x1 9.0))) x1)))
   (if (<= x1 -8.8e+29)
     (+ x1 (* x2 (- (- (/ (+ x1 (* x1 -3.0)) x2) (* x1 12.0)) 6.0)))
     (if (<= x1 6.5e+108)
       (+
        x1
        (+
         (* 3.0 (/ (+ x1 (- (* 2.0 x2) (* x1 (* x1 3.0)))) (- -1.0 (* x1 x1))))
         (+ x1 (* 4.0 (* x2 (+ (* x1 -3.0) (* 2.0 (* x1 x2))))))))
       (-
        x1
        (-
         (*
          x1
          (-
           2.0
           (+ (* x2 -12.0) (* x1 (+ (* x1 3.0) (* 3.0 (- 3.0 (* x2 -2.0))))))))
         (* x2 -6.0)))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -2.7e+161) {
		tmp = x1 - ((3.0 * (x1 - (x2 * -2.0))) + ((x1 * ((4.0 * (x2 * (3.0 - (2.0 * x2)))) - (x1 * 9.0))) - x1));
	} else if (x1 <= -8.8e+29) {
		tmp = x1 + (x2 * ((((x1 + (x1 * -3.0)) / x2) - (x1 * 12.0)) - 6.0));
	} else if (x1 <= 6.5e+108) {
		tmp = x1 + ((3.0 * ((x1 + ((2.0 * x2) - (x1 * (x1 * 3.0)))) / (-1.0 - (x1 * x1)))) + (x1 + (4.0 * (x2 * ((x1 * -3.0) + (2.0 * (x1 * x2)))))));
	} else {
		tmp = x1 - ((x1 * (2.0 - ((x2 * -12.0) + (x1 * ((x1 * 3.0) + (3.0 * (3.0 - (x2 * -2.0)))))))) - (x2 * -6.0));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x1 <= (-2.7d+161)) then
        tmp = x1 - ((3.0d0 * (x1 - (x2 * (-2.0d0)))) + ((x1 * ((4.0d0 * (x2 * (3.0d0 - (2.0d0 * x2)))) - (x1 * 9.0d0))) - x1))
    else if (x1 <= (-8.8d+29)) then
        tmp = x1 + (x2 * ((((x1 + (x1 * (-3.0d0))) / x2) - (x1 * 12.0d0)) - 6.0d0))
    else if (x1 <= 6.5d+108) then
        tmp = x1 + ((3.0d0 * ((x1 + ((2.0d0 * x2) - (x1 * (x1 * 3.0d0)))) / ((-1.0d0) - (x1 * x1)))) + (x1 + (4.0d0 * (x2 * ((x1 * (-3.0d0)) + (2.0d0 * (x1 * x2)))))))
    else
        tmp = x1 - ((x1 * (2.0d0 - ((x2 * (-12.0d0)) + (x1 * ((x1 * 3.0d0) + (3.0d0 * (3.0d0 - (x2 * (-2.0d0))))))))) - (x2 * (-6.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= -2.7e+161) {
		tmp = x1 - ((3.0 * (x1 - (x2 * -2.0))) + ((x1 * ((4.0 * (x2 * (3.0 - (2.0 * x2)))) - (x1 * 9.0))) - x1));
	} else if (x1 <= -8.8e+29) {
		tmp = x1 + (x2 * ((((x1 + (x1 * -3.0)) / x2) - (x1 * 12.0)) - 6.0));
	} else if (x1 <= 6.5e+108) {
		tmp = x1 + ((3.0 * ((x1 + ((2.0 * x2) - (x1 * (x1 * 3.0)))) / (-1.0 - (x1 * x1)))) + (x1 + (4.0 * (x2 * ((x1 * -3.0) + (2.0 * (x1 * x2)))))));
	} else {
		tmp = x1 - ((x1 * (2.0 - ((x2 * -12.0) + (x1 * ((x1 * 3.0) + (3.0 * (3.0 - (x2 * -2.0)))))))) - (x2 * -6.0));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -2.7e+161:
		tmp = x1 - ((3.0 * (x1 - (x2 * -2.0))) + ((x1 * ((4.0 * (x2 * (3.0 - (2.0 * x2)))) - (x1 * 9.0))) - x1))
	elif x1 <= -8.8e+29:
		tmp = x1 + (x2 * ((((x1 + (x1 * -3.0)) / x2) - (x1 * 12.0)) - 6.0))
	elif x1 <= 6.5e+108:
		tmp = x1 + ((3.0 * ((x1 + ((2.0 * x2) - (x1 * (x1 * 3.0)))) / (-1.0 - (x1 * x1)))) + (x1 + (4.0 * (x2 * ((x1 * -3.0) + (2.0 * (x1 * x2)))))))
	else:
		tmp = x1 - ((x1 * (2.0 - ((x2 * -12.0) + (x1 * ((x1 * 3.0) + (3.0 * (3.0 - (x2 * -2.0)))))))) - (x2 * -6.0))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -2.7e+161)
		tmp = Float64(x1 - Float64(Float64(3.0 * Float64(x1 - Float64(x2 * -2.0))) + Float64(Float64(x1 * Float64(Float64(4.0 * Float64(x2 * Float64(3.0 - Float64(2.0 * x2)))) - Float64(x1 * 9.0))) - x1)));
	elseif (x1 <= -8.8e+29)
		tmp = Float64(x1 + Float64(x2 * Float64(Float64(Float64(Float64(x1 + Float64(x1 * -3.0)) / x2) - Float64(x1 * 12.0)) - 6.0)));
	elseif (x1 <= 6.5e+108)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(x1 + Float64(Float64(2.0 * x2) - Float64(x1 * Float64(x1 * 3.0)))) / Float64(-1.0 - Float64(x1 * x1)))) + Float64(x1 + Float64(4.0 * Float64(x2 * Float64(Float64(x1 * -3.0) + Float64(2.0 * Float64(x1 * x2))))))));
	else
		tmp = Float64(x1 - Float64(Float64(x1 * Float64(2.0 - Float64(Float64(x2 * -12.0) + Float64(x1 * Float64(Float64(x1 * 3.0) + Float64(3.0 * Float64(3.0 - Float64(x2 * -2.0)))))))) - Float64(x2 * -6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -2.7e+161)
		tmp = x1 - ((3.0 * (x1 - (x2 * -2.0))) + ((x1 * ((4.0 * (x2 * (3.0 - (2.0 * x2)))) - (x1 * 9.0))) - x1));
	elseif (x1 <= -8.8e+29)
		tmp = x1 + (x2 * ((((x1 + (x1 * -3.0)) / x2) - (x1 * 12.0)) - 6.0));
	elseif (x1 <= 6.5e+108)
		tmp = x1 + ((3.0 * ((x1 + ((2.0 * x2) - (x1 * (x1 * 3.0)))) / (-1.0 - (x1 * x1)))) + (x1 + (4.0 * (x2 * ((x1 * -3.0) + (2.0 * (x1 * x2)))))));
	else
		tmp = x1 - ((x1 * (2.0 - ((x2 * -12.0) + (x1 * ((x1 * 3.0) + (3.0 * (3.0 - (x2 * -2.0)))))))) - (x2 * -6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -2.7e+161], N[(x1 - N[(N[(3.0 * N[(x1 - N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * N[(N[(4.0 * N[(x2 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -8.8e+29], N[(x1 + N[(x2 * N[(N[(N[(N[(x1 + N[(x1 * -3.0), $MachinePrecision]), $MachinePrecision] / x2), $MachinePrecision] - N[(x1 * 12.0), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 6.5e+108], N[(x1 + N[(N[(3.0 * N[(N[(x1 + N[(N[(2.0 * x2), $MachinePrecision] - N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(4.0 * N[(x2 * N[(N[(x1 * -3.0), $MachinePrecision] + N[(2.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 - N[(N[(x1 * N[(2.0 - N[(N[(x2 * -12.0), $MachinePrecision] + N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + N[(3.0 * N[(3.0 - N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -2.6999999999999998e161

   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 0.0%

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

   4. Taylor expanded in x1 around 0 0.0%

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

      1. neg-mul-1 0.0%

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

      2. unsub-neg 0.0%

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

      3. *-commutative 0.0%

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

   6. Simplified 0.0%

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

   7. Taylor expanded in x1 around 0 70.4%

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

   8. Taylor expanded in x2 around 0 70.4%

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

   if -2.6999999999999998e161 < x1 < -8.8000000000000005e29

   1. Initial program 54.7%

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

   3. Taylor expanded in x1 around 0 5.6%

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

   4. Taylor expanded in x2 around 0 8.9%

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

      1. *-commutative 8.9%

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

      2. associate-*l* 8.9%

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

   6. Simplified 8.9%

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

   7. Taylor expanded in x1 around 0 11.5%

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

      1. neg-mul-1 54.7%

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

      2. unsub-neg 54.7%

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

      3. *-commutative 54.7%

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

   9. Simplified 11.5%

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

   10. Taylor expanded in x2 around -inf 33.0%

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

   if -8.8000000000000005e29 < x1 < 6.4999999999999996e108

   1. Initial program 99.3%

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

   3. Taylor expanded in x1 around 0 81.1%

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

   4. Taylor expanded in x2 around 0 89.6%

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

   if 6.4999999999999996e108 < x1

   1. Initial program 22.7%

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

   3. Taylor expanded in x1 around 0 9.8%

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

   4. Taylor expanded in x2 around 0 2.8%

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

      1. *-commutative 2.8%

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

      2. associate-*l* 2.8%

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

   6. Simplified 2.8%

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

   7. Taylor expanded in x1 around 0 95.5%

      \[\leadsto x1 + \color{blue}{\left(-6 \cdot x2 + x1 \cdot \left(\left(-12 \cdot x2 + x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)\right) - 2\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -2.7 \cdot 10^{+161}:\\ \;\;\;\;x1 - \left(3 \cdot \left(x1 - x2 \cdot -2\right) + \left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right) - x1 \cdot 9\right) - x1\right)\right)\\ \mathbf{elif}\;x1 \leq -8.8 \cdot 10^{+29}:\\ \;\;\;\;x1 + x2 \cdot \left(\left(\frac{x1 + x1 \cdot -3}{x2} - x1 \cdot 12\right) - 6\right)\\ \mathbf{elif}\;x1 \leq 6.5 \cdot 10^{+108}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{x1 + \left(2 \cdot x2 - x1 \cdot \left(x1 \cdot 3\right)\right)}{-1 - x1 \cdot x1} + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot -3 + 2 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 - \left(x1 \cdot \left(2 - \left(x2 \cdot -12 + x1 \cdot \left(x1 \cdot 3 + 3 \cdot \left(3 - x2 \cdot -2\right)\right)\right)\right) - x2 \cdot -6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 78.9% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -3 \cdot 10^{-25}:\\ \;\;\;\;x1 - \left(x2 \cdot \left(6 - -3 \cdot \frac{x1}{x2}\right) + \left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right) - x1 \cdot \left(3 + \left(x2 \cdot 8 - 2 \cdot \left(\left(2 \cdot x2 - 3\right) - x2 \cdot -2\right)\right)\right)\right) - x1\right)\right)\\ \mathbf{elif}\;x1 \leq 6.5 \cdot 10^{+108}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot -3 + 2 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(\left(x2 \cdot -12 + x1 \cdot \left(x1 \cdot 3 + 3 \cdot \left(3 - x2 \cdot -2\right)\right)\right) - 2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -3e-25)
   (-
    x1
    (+
     (* x2 (- 6.0 (* -3.0 (/ x1 x2))))
     (-
      (*
       x1
       (-
        (* 4.0 (* x2 (- 3.0 (* 2.0 x2))))
        (*
         x1
         (+ 3.0 (- (* x2 8.0) (* 2.0 (- (- (* 2.0 x2) 3.0) (* x2 -2.0))))))))
      x1)))
   (if (<= x1 6.5e+108)
     (+
      x1
      (+
       (* 3.0 (/ (- (- (* x1 (* x1 3.0)) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0)))
       (+ x1 (* 4.0 (* x2 (+ (* x1 -3.0) (* 2.0 (* x1 x2))))))))
     (+
      x1
      (+
       (* x2 -6.0)
       (*
        x1
        (-
         (+ (* x2 -12.0) (* x1 (+ (* x1 3.0) (* 3.0 (- 3.0 (* x2 -2.0))))))
         2.0)))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -3e-25) {
		tmp = x1 - ((x2 * (6.0 - (-3.0 * (x1 / x2)))) + ((x1 * ((4.0 * (x2 * (3.0 - (2.0 * x2)))) - (x1 * (3.0 + ((x2 * 8.0) - (2.0 * (((2.0 * x2) - 3.0) - (x2 * -2.0)))))))) - x1));
	} else if (x1 <= 6.5e+108) {
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / ((x1 * x1) + 1.0))) + (x1 + (4.0 * (x2 * ((x1 * -3.0) + (2.0 * (x1 * x2)))))));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * (((x2 * -12.0) + (x1 * ((x1 * 3.0) + (3.0 * (3.0 - (x2 * -2.0)))))) - 2.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x1 <= (-3d-25)) then
        tmp = x1 - ((x2 * (6.0d0 - ((-3.0d0) * (x1 / x2)))) + ((x1 * ((4.0d0 * (x2 * (3.0d0 - (2.0d0 * x2)))) - (x1 * (3.0d0 + ((x2 * 8.0d0) - (2.0d0 * (((2.0d0 * x2) - 3.0d0) - (x2 * (-2.0d0))))))))) - x1))
    else if (x1 <= 6.5d+108) then
        tmp = x1 + ((3.0d0 * ((((x1 * (x1 * 3.0d0)) - (2.0d0 * x2)) - x1) / ((x1 * x1) + 1.0d0))) + (x1 + (4.0d0 * (x2 * ((x1 * (-3.0d0)) + (2.0d0 * (x1 * x2)))))))
    else
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * (((x2 * (-12.0d0)) + (x1 * ((x1 * 3.0d0) + (3.0d0 * (3.0d0 - (x2 * (-2.0d0))))))) - 2.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= -3e-25) {
		tmp = x1 - ((x2 * (6.0 - (-3.0 * (x1 / x2)))) + ((x1 * ((4.0 * (x2 * (3.0 - (2.0 * x2)))) - (x1 * (3.0 + ((x2 * 8.0) - (2.0 * (((2.0 * x2) - 3.0) - (x2 * -2.0)))))))) - x1));
	} else if (x1 <= 6.5e+108) {
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / ((x1 * x1) + 1.0))) + (x1 + (4.0 * (x2 * ((x1 * -3.0) + (2.0 * (x1 * x2)))))));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * (((x2 * -12.0) + (x1 * ((x1 * 3.0) + (3.0 * (3.0 - (x2 * -2.0)))))) - 2.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -3e-25:
		tmp = x1 - ((x2 * (6.0 - (-3.0 * (x1 / x2)))) + ((x1 * ((4.0 * (x2 * (3.0 - (2.0 * x2)))) - (x1 * (3.0 + ((x2 * 8.0) - (2.0 * (((2.0 * x2) - 3.0) - (x2 * -2.0)))))))) - x1))
	elif x1 <= 6.5e+108:
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / ((x1 * x1) + 1.0))) + (x1 + (4.0 * (x2 * ((x1 * -3.0) + (2.0 * (x1 * x2)))))))
	else:
		tmp = x1 + ((x2 * -6.0) + (x1 * (((x2 * -12.0) + (x1 * ((x1 * 3.0) + (3.0 * (3.0 - (x2 * -2.0)))))) - 2.0)))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -3e-25)
		tmp = Float64(x1 - Float64(Float64(x2 * Float64(6.0 - Float64(-3.0 * Float64(x1 / x2)))) + Float64(Float64(x1 * Float64(Float64(4.0 * Float64(x2 * Float64(3.0 - Float64(2.0 * x2)))) - Float64(x1 * Float64(3.0 + Float64(Float64(x2 * 8.0) - Float64(2.0 * Float64(Float64(Float64(2.0 * x2) - 3.0) - Float64(x2 * -2.0)))))))) - x1)));
	elseif (x1 <= 6.5e+108)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(Float64(x1 * Float64(x1 * 3.0)) - Float64(2.0 * x2)) - x1) / Float64(Float64(x1 * x1) + 1.0))) + Float64(x1 + Float64(4.0 * Float64(x2 * Float64(Float64(x1 * -3.0) + Float64(2.0 * Float64(x1 * x2))))))));
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(Float64(x2 * -12.0) + Float64(x1 * Float64(Float64(x1 * 3.0) + Float64(3.0 * Float64(3.0 - Float64(x2 * -2.0)))))) - 2.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -3e-25)
		tmp = x1 - ((x2 * (6.0 - (-3.0 * (x1 / x2)))) + ((x1 * ((4.0 * (x2 * (3.0 - (2.0 * x2)))) - (x1 * (3.0 + ((x2 * 8.0) - (2.0 * (((2.0 * x2) - 3.0) - (x2 * -2.0)))))))) - x1));
	elseif (x1 <= 6.5e+108)
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / ((x1 * x1) + 1.0))) + (x1 + (4.0 * (x2 * ((x1 * -3.0) + (2.0 * (x1 * x2)))))));
	else
		tmp = x1 + ((x2 * -6.0) + (x1 * (((x2 * -12.0) + (x1 * ((x1 * 3.0) + (3.0 * (3.0 - (x2 * -2.0)))))) - 2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -3e-25], N[(x1 - N[(N[(x2 * N[(6.0 - N[(-3.0 * N[(x1 / x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * N[(N[(4.0 * N[(x2 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x1 * N[(3.0 + N[(N[(x2 * 8.0), $MachinePrecision] - N[(2.0 * N[(N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision] - N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 6.5e+108], N[(x1 + N[(N[(3.0 * N[(N[(N[(N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision] - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(4.0 * N[(x2 * N[(N[(x1 * -3.0), $MachinePrecision] + N[(2.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(N[(x2 * -12.0), $MachinePrecision] + N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + N[(3.0 * N[(3.0 - N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -2.9999999999999998e-25

   1. Initial program 41.3%

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

   3. Taylor expanded in x1 around inf 39.1%

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

   4. Taylor expanded in x1 around 0 41.3%

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

      1. neg-mul-1 41.3%

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

      2. unsub-neg 41.3%

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

      3. *-commutative 41.3%

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

   6. Simplified 41.3%

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

   7. Taylor expanded in x1 around 0 40.4%

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

   8. Taylor expanded in x2 around inf 48.9%

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

   if -2.9999999999999998e-25 < x1 < 6.4999999999999996e108

   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 82.6%

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

   4. Taylor expanded in x2 around 0 91.8%

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

   if 6.4999999999999996e108 < x1

   1. Initial program 22.7%

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

   3. Taylor expanded in x1 around 0 9.8%

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

   4. Taylor expanded in x2 around 0 2.8%

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

      1. *-commutative 2.8%

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

      2. associate-*l* 2.8%

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

   6. Simplified 2.8%

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

   7. Taylor expanded in x1 around 0 95.5%

      \[\leadsto x1 + \color{blue}{\left(-6 \cdot x2 + x1 \cdot \left(\left(-12 \cdot x2 + x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)\right) - 2\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -3 \cdot 10^{-25}:\\ \;\;\;\;x1 - \left(x2 \cdot \left(6 - -3 \cdot \frac{x1}{x2}\right) + \left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right) - x1 \cdot \left(3 + \left(x2 \cdot 8 - 2 \cdot \left(\left(2 \cdot x2 - 3\right) - x2 \cdot -2\right)\right)\right)\right) - x1\right)\right)\\ \mathbf{elif}\;x1 \leq 6.5 \cdot 10^{+108}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot -3 + 2 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(\left(x2 \cdot -12 + x1 \cdot \left(x1 \cdot 3 + 3 \cdot \left(3 - x2 \cdot -2\right)\right)\right) - 2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 72.8% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 - 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right)\\ \mathbf{if}\;x1 \leq -3 \cdot 10^{+30}:\\ \;\;\;\;x1 + x2 \cdot \left(\left(\frac{x1 + x1 \cdot -3}{x2} - x1 \cdot 12\right) - 6\right)\\ \mathbf{elif}\;x1 \leq -3 \cdot 10^{-163}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x1 \leq 6.4 \cdot 10^{-259}:\\ \;\;\;\;x1 - \left(x1 \cdot \left(2 + \left(3 \cdot \left(x1 \cdot \left(x2 \cdot -2 - 3\right)\right) - x2 \cdot -12\right)\right) - x2 \cdot -6\right)\\ \mathbf{elif}\;x1 \leq 6.5 \cdot 10^{+108}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;x1 - \left(x1 \cdot \left(2 - \left(x2 \cdot -12 + x1 \cdot \left(x1 \cdot 3 + 3 \cdot \left(3 - x2 \cdot -2\right)\right)\right)\right) - x2 \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0
         (+
          x1
          (- (* x2 -6.0) (* x1 (- 2.0 (* 4.0 (* x2 (- (* 2.0 x2) 3.0)))))))))
   (if (<= x1 -3e+30)
     (+ x1 (* x2 (- (- (/ (+ x1 (* x1 -3.0)) x2) (* x1 12.0)) 6.0)))
     (if (<= x1 -3e-163)
       t_0
       (if (<= x1 6.4e-259)
         (-
          x1
          (-
           (* x1 (+ 2.0 (- (* 3.0 (* x1 (- (* x2 -2.0) 3.0))) (* x2 -12.0))))
           (* x2 -6.0)))
         (if (<= x1 6.5e+108)
           t_0
           (-
            x1
            (-
             (*
              x1
              (-
               2.0
               (+
                (* x2 -12.0)
                (* x1 (+ (* x1 3.0) (* 3.0 (- 3.0 (* x2 -2.0))))))))
             (* x2 -6.0)))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 + ((x2 * -6.0) - (x1 * (2.0 - (4.0 * (x2 * ((2.0 * x2) - 3.0))))));
	double tmp;
	if (x1 <= -3e+30) {
		tmp = x1 + (x2 * ((((x1 + (x1 * -3.0)) / x2) - (x1 * 12.0)) - 6.0));
	} else if (x1 <= -3e-163) {
		tmp = t_0;
	} else if (x1 <= 6.4e-259) {
		tmp = x1 - ((x1 * (2.0 + ((3.0 * (x1 * ((x2 * -2.0) - 3.0))) - (x2 * -12.0)))) - (x2 * -6.0));
	} else if (x1 <= 6.5e+108) {
		tmp = t_0;
	} else {
		tmp = x1 - ((x1 * (2.0 - ((x2 * -12.0) + (x1 * ((x1 * 3.0) + (3.0 * (3.0 - (x2 * -2.0)))))))) - (x2 * -6.0));
	}
	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 + ((x2 * (-6.0d0)) - (x1 * (2.0d0 - (4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0))))))
    if (x1 <= (-3d+30)) then
        tmp = x1 + (x2 * ((((x1 + (x1 * (-3.0d0))) / x2) - (x1 * 12.0d0)) - 6.0d0))
    else if (x1 <= (-3d-163)) then
        tmp = t_0
    else if (x1 <= 6.4d-259) then
        tmp = x1 - ((x1 * (2.0d0 + ((3.0d0 * (x1 * ((x2 * (-2.0d0)) - 3.0d0))) - (x2 * (-12.0d0))))) - (x2 * (-6.0d0)))
    else if (x1 <= 6.5d+108) then
        tmp = t_0
    else
        tmp = x1 - ((x1 * (2.0d0 - ((x2 * (-12.0d0)) + (x1 * ((x1 * 3.0d0) + (3.0d0 * (3.0d0 - (x2 * (-2.0d0))))))))) - (x2 * (-6.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 + ((x2 * -6.0) - (x1 * (2.0 - (4.0 * (x2 * ((2.0 * x2) - 3.0))))));
	double tmp;
	if (x1 <= -3e+30) {
		tmp = x1 + (x2 * ((((x1 + (x1 * -3.0)) / x2) - (x1 * 12.0)) - 6.0));
	} else if (x1 <= -3e-163) {
		tmp = t_0;
	} else if (x1 <= 6.4e-259) {
		tmp = x1 - ((x1 * (2.0 + ((3.0 * (x1 * ((x2 * -2.0) - 3.0))) - (x2 * -12.0)))) - (x2 * -6.0));
	} else if (x1 <= 6.5e+108) {
		tmp = t_0;
	} else {
		tmp = x1 - ((x1 * (2.0 - ((x2 * -12.0) + (x1 * ((x1 * 3.0) + (3.0 * (3.0 - (x2 * -2.0)))))))) - (x2 * -6.0));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 + ((x2 * -6.0) - (x1 * (2.0 - (4.0 * (x2 * ((2.0 * x2) - 3.0))))))
	tmp = 0
	if x1 <= -3e+30:
		tmp = x1 + (x2 * ((((x1 + (x1 * -3.0)) / x2) - (x1 * 12.0)) - 6.0))
	elif x1 <= -3e-163:
		tmp = t_0
	elif x1 <= 6.4e-259:
		tmp = x1 - ((x1 * (2.0 + ((3.0 * (x1 * ((x2 * -2.0) - 3.0))) - (x2 * -12.0)))) - (x2 * -6.0))
	elif x1 <= 6.5e+108:
		tmp = t_0
	else:
		tmp = x1 - ((x1 * (2.0 - ((x2 * -12.0) + (x1 * ((x1 * 3.0) + (3.0 * (3.0 - (x2 * -2.0)))))))) - (x2 * -6.0))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 + Float64(Float64(x2 * -6.0) - Float64(x1 * Float64(2.0 - Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0)))))))
	tmp = 0.0
	if (x1 <= -3e+30)
		tmp = Float64(x1 + Float64(x2 * Float64(Float64(Float64(Float64(x1 + Float64(x1 * -3.0)) / x2) - Float64(x1 * 12.0)) - 6.0)));
	elseif (x1 <= -3e-163)
		tmp = t_0;
	elseif (x1 <= 6.4e-259)
		tmp = Float64(x1 - Float64(Float64(x1 * Float64(2.0 + Float64(Float64(3.0 * Float64(x1 * Float64(Float64(x2 * -2.0) - 3.0))) - Float64(x2 * -12.0)))) - Float64(x2 * -6.0)));
	elseif (x1 <= 6.5e+108)
		tmp = t_0;
	else
		tmp = Float64(x1 - Float64(Float64(x1 * Float64(2.0 - Float64(Float64(x2 * -12.0) + Float64(x1 * Float64(Float64(x1 * 3.0) + Float64(3.0 * Float64(3.0 - Float64(x2 * -2.0)))))))) - Float64(x2 * -6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 + ((x2 * -6.0) - (x1 * (2.0 - (4.0 * (x2 * ((2.0 * x2) - 3.0))))));
	tmp = 0.0;
	if (x1 <= -3e+30)
		tmp = x1 + (x2 * ((((x1 + (x1 * -3.0)) / x2) - (x1 * 12.0)) - 6.0));
	elseif (x1 <= -3e-163)
		tmp = t_0;
	elseif (x1 <= 6.4e-259)
		tmp = x1 - ((x1 * (2.0 + ((3.0 * (x1 * ((x2 * -2.0) - 3.0))) - (x2 * -12.0)))) - (x2 * -6.0));
	elseif (x1 <= 6.5e+108)
		tmp = t_0;
	else
		tmp = x1 - ((x1 * (2.0 - ((x2 * -12.0) + (x1 * ((x1 * 3.0) + (3.0 * (3.0 - (x2 * -2.0)))))))) - (x2 * -6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] - N[(x1 * N[(2.0 - N[(4.0 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -3e+30], N[(x1 + N[(x2 * N[(N[(N[(N[(x1 + N[(x1 * -3.0), $MachinePrecision]), $MachinePrecision] / x2), $MachinePrecision] - N[(x1 * 12.0), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -3e-163], t$95$0, If[LessEqual[x1, 6.4e-259], N[(x1 - N[(N[(x1 * N[(2.0 + N[(N[(3.0 * N[(x1 * N[(N[(x2 * -2.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x2 * -12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 6.5e+108], t$95$0, N[(x1 - N[(N[(x1 * N[(2.0 - N[(N[(x2 * -12.0), $MachinePrecision] + N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + N[(3.0 * N[(3.0 - N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -2.99999999999999978e30

   1. Initial program 31.7%

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

   3. Taylor expanded in x1 around 0 3.4%

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

   4. Taylor expanded in x2 around 0 5.4%

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

      1. *-commutative 5.4%

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

      2. associate-*l* 5.4%

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

   6. Simplified 5.4%

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

   7. Taylor expanded in x1 around 0 13.0%

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

      1. neg-mul-1 31.7%

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

      2. unsub-neg 31.7%

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

      3. *-commutative 31.7%

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

   9. Simplified 13.0%

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

   10. Taylor expanded in x2 around -inf 41.5%

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

   if -2.99999999999999978e30 < x1 < -3.0000000000000002e-163 or 6.39999999999999975e-259 < x1 < 6.4999999999999996e108

   1. Initial program 99.3%

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

   3. Taylor expanded in x1 around 0 81.0%

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

   4. Taylor expanded in x1 around 0 80.4%

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

   if -3.0000000000000002e-163 < x1 < 6.39999999999999975e-259

   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 79.5%

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

   4. Taylor expanded in x2 around 0 98.0%

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

      1. *-commutative 98.0%

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

      2. associate-*l* 98.0%

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

   6. Simplified 98.0%

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

   7. Taylor expanded in x1 around 0 98.2%

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

   if 6.4999999999999996e108 < x1

   1. Initial program 22.7%

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

   3. Taylor expanded in x1 around 0 9.8%

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

   4. Taylor expanded in x2 around 0 2.8%

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

      1. *-commutative 2.8%

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

      2. associate-*l* 2.8%

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

   6. Simplified 2.8%

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

   7. Taylor expanded in x1 around 0 95.5%

      \[\leadsto x1 + \color{blue}{\left(-6 \cdot x2 + x1 \cdot \left(\left(-12 \cdot x2 + x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)\right) - 2\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 75.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -3 \cdot 10^{+30}:\\ \;\;\;\;x1 + x2 \cdot \left(\left(\frac{x1 + x1 \cdot -3}{x2} - x1 \cdot 12\right) - 6\right)\\ \mathbf{elif}\;x1 \leq -3 \cdot 10^{-163}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 - 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 6.4 \cdot 10^{-259}:\\ \;\;\;\;x1 - \left(x1 \cdot \left(2 + \left(3 \cdot \left(x1 \cdot \left(x2 \cdot -2 - 3\right)\right) - x2 \cdot -12\right)\right) - x2 \cdot -6\right)\\ \mathbf{elif}\;x1 \leq 6.5 \cdot 10^{+108}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 - 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 - \left(x1 \cdot \left(2 - \left(x2 \cdot -12 + x1 \cdot \left(x1 \cdot 3 + 3 \cdot \left(3 - x2 \cdot -2\right)\right)\right)\right) - x2 \cdot -6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 72.9% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 3 \cdot \left(x1 \cdot \left(x2 \cdot -2 - 3\right)\right)\\ \mathbf{if}\;x1 \leq -3 \cdot 10^{+30}:\\ \;\;\;\;x1 + x2 \cdot \left(\left(\frac{x1 + x1 \cdot -3}{x2} - x1 \cdot 12\right) - 6\right)\\ \mathbf{elif}\;x1 \leq -3 \cdot 10^{-163}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 + \left(4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right) + t\_0\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 3.1 \cdot 10^{-259}:\\ \;\;\;\;x1 - \left(x1 \cdot \left(2 + \left(t\_0 - x2 \cdot -12\right)\right) - x2 \cdot -6\right)\\ \mathbf{elif}\;x1 \leq 6.5 \cdot 10^{+108}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 - 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 - \left(x1 \cdot \left(2 - \left(x2 \cdot -12 + x1 \cdot \left(x1 \cdot 3 + 3 \cdot \left(3 - x2 \cdot -2\right)\right)\right)\right) - x2 \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* 3.0 (* x1 (- (* x2 -2.0) 3.0)))))
   (if (<= x1 -3e+30)
     (+ x1 (* x2 (- (- (/ (+ x1 (* x1 -3.0)) x2) (* x1 12.0)) 6.0)))
     (if (<= x1 -3e-163)
       (+
        x1
        (-
         (* x2 -6.0)
         (* x1 (+ 2.0 (+ (* 4.0 (* x2 (- 3.0 (* 2.0 x2)))) t_0)))))
       (if (<= x1 3.1e-259)
         (- x1 (- (* x1 (+ 2.0 (- t_0 (* x2 -12.0)))) (* x2 -6.0)))
         (if (<= x1 6.5e+108)
           (+
            x1
            (- (* x2 -6.0) (* x1 (- 2.0 (* 4.0 (* x2 (- (* 2.0 x2) 3.0)))))))
           (-
            x1
            (-
             (*
              x1
              (-
               2.0
               (+
                (* x2 -12.0)
                (* x1 (+ (* x1 3.0) (* 3.0 (- 3.0 (* x2 -2.0))))))))
             (* x2 -6.0)))))))))

C

double code(double x1, double x2) {
	double t_0 = 3.0 * (x1 * ((x2 * -2.0) - 3.0));
	double tmp;
	if (x1 <= -3e+30) {
		tmp = x1 + (x2 * ((((x1 + (x1 * -3.0)) / x2) - (x1 * 12.0)) - 6.0));
	} else if (x1 <= -3e-163) {
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((4.0 * (x2 * (3.0 - (2.0 * x2)))) + t_0))));
	} else if (x1 <= 3.1e-259) {
		tmp = x1 - ((x1 * (2.0 + (t_0 - (x2 * -12.0)))) - (x2 * -6.0));
	} else if (x1 <= 6.5e+108) {
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 - (4.0 * (x2 * ((2.0 * x2) - 3.0))))));
	} else {
		tmp = x1 - ((x1 * (2.0 - ((x2 * -12.0) + (x1 * ((x1 * 3.0) + (3.0 * (3.0 - (x2 * -2.0)))))))) - (x2 * -6.0));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 3.0d0 * (x1 * ((x2 * (-2.0d0)) - 3.0d0))
    if (x1 <= (-3d+30)) then
        tmp = x1 + (x2 * ((((x1 + (x1 * (-3.0d0))) / x2) - (x1 * 12.0d0)) - 6.0d0))
    else if (x1 <= (-3d-163)) then
        tmp = x1 + ((x2 * (-6.0d0)) - (x1 * (2.0d0 + ((4.0d0 * (x2 * (3.0d0 - (2.0d0 * x2)))) + t_0))))
    else if (x1 <= 3.1d-259) then
        tmp = x1 - ((x1 * (2.0d0 + (t_0 - (x2 * (-12.0d0))))) - (x2 * (-6.0d0)))
    else if (x1 <= 6.5d+108) then
        tmp = x1 + ((x2 * (-6.0d0)) - (x1 * (2.0d0 - (4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0))))))
    else
        tmp = x1 - ((x1 * (2.0d0 - ((x2 * (-12.0d0)) + (x1 * ((x1 * 3.0d0) + (3.0d0 * (3.0d0 - (x2 * (-2.0d0))))))))) - (x2 * (-6.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = 3.0 * (x1 * ((x2 * -2.0) - 3.0));
	double tmp;
	if (x1 <= -3e+30) {
		tmp = x1 + (x2 * ((((x1 + (x1 * -3.0)) / x2) - (x1 * 12.0)) - 6.0));
	} else if (x1 <= -3e-163) {
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((4.0 * (x2 * (3.0 - (2.0 * x2)))) + t_0))));
	} else if (x1 <= 3.1e-259) {
		tmp = x1 - ((x1 * (2.0 + (t_0 - (x2 * -12.0)))) - (x2 * -6.0));
	} else if (x1 <= 6.5e+108) {
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 - (4.0 * (x2 * ((2.0 * x2) - 3.0))))));
	} else {
		tmp = x1 - ((x1 * (2.0 - ((x2 * -12.0) + (x1 * ((x1 * 3.0) + (3.0 * (3.0 - (x2 * -2.0)))))))) - (x2 * -6.0));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = 3.0 * (x1 * ((x2 * -2.0) - 3.0))
	tmp = 0
	if x1 <= -3e+30:
		tmp = x1 + (x2 * ((((x1 + (x1 * -3.0)) / x2) - (x1 * 12.0)) - 6.0))
	elif x1 <= -3e-163:
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((4.0 * (x2 * (3.0 - (2.0 * x2)))) + t_0))))
	elif x1 <= 3.1e-259:
		tmp = x1 - ((x1 * (2.0 + (t_0 - (x2 * -12.0)))) - (x2 * -6.0))
	elif x1 <= 6.5e+108:
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 - (4.0 * (x2 * ((2.0 * x2) - 3.0))))))
	else:
		tmp = x1 - ((x1 * (2.0 - ((x2 * -12.0) + (x1 * ((x1 * 3.0) + (3.0 * (3.0 - (x2 * -2.0)))))))) - (x2 * -6.0))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(3.0 * Float64(x1 * Float64(Float64(x2 * -2.0) - 3.0)))
	tmp = 0.0
	if (x1 <= -3e+30)
		tmp = Float64(x1 + Float64(x2 * Float64(Float64(Float64(Float64(x1 + Float64(x1 * -3.0)) / x2) - Float64(x1 * 12.0)) - 6.0)));
	elseif (x1 <= -3e-163)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) - Float64(x1 * Float64(2.0 + Float64(Float64(4.0 * Float64(x2 * Float64(3.0 - Float64(2.0 * x2)))) + t_0)))));
	elseif (x1 <= 3.1e-259)
		tmp = Float64(x1 - Float64(Float64(x1 * Float64(2.0 + Float64(t_0 - Float64(x2 * -12.0)))) - Float64(x2 * -6.0)));
	elseif (x1 <= 6.5e+108)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) - Float64(x1 * Float64(2.0 - Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0)))))));
	else
		tmp = Float64(x1 - Float64(Float64(x1 * Float64(2.0 - Float64(Float64(x2 * -12.0) + Float64(x1 * Float64(Float64(x1 * 3.0) + Float64(3.0 * Float64(3.0 - Float64(x2 * -2.0)))))))) - Float64(x2 * -6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = 3.0 * (x1 * ((x2 * -2.0) - 3.0));
	tmp = 0.0;
	if (x1 <= -3e+30)
		tmp = x1 + (x2 * ((((x1 + (x1 * -3.0)) / x2) - (x1 * 12.0)) - 6.0));
	elseif (x1 <= -3e-163)
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((4.0 * (x2 * (3.0 - (2.0 * x2)))) + t_0))));
	elseif (x1 <= 3.1e-259)
		tmp = x1 - ((x1 * (2.0 + (t_0 - (x2 * -12.0)))) - (x2 * -6.0));
	elseif (x1 <= 6.5e+108)
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 - (4.0 * (x2 * ((2.0 * x2) - 3.0))))));
	else
		tmp = x1 - ((x1 * (2.0 - ((x2 * -12.0) + (x1 * ((x1 * 3.0) + (3.0 * (3.0 - (x2 * -2.0)))))))) - (x2 * -6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(3.0 * N[(x1 * N[(N[(x2 * -2.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -3e+30], N[(x1 + N[(x2 * N[(N[(N[(N[(x1 + N[(x1 * -3.0), $MachinePrecision]), $MachinePrecision] / x2), $MachinePrecision] - N[(x1 * 12.0), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -3e-163], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] - N[(x1 * N[(2.0 + N[(N[(4.0 * N[(x2 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 3.1e-259], N[(x1 - N[(N[(x1 * N[(2.0 + N[(t$95$0 - N[(x2 * -12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 6.5e+108], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] - N[(x1 * N[(2.0 - N[(4.0 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 - N[(N[(x1 * N[(2.0 - N[(N[(x2 * -12.0), $MachinePrecision] + N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + N[(3.0 * N[(3.0 - N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if x1 < -2.99999999999999978e30

   1. Initial program 31.7%

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

   3. Taylor expanded in x1 around 0 3.4%

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

   4. Taylor expanded in x2 around 0 5.4%

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

      1. *-commutative 5.4%

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

      2. associate-*l* 5.4%

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

   6. Simplified 5.4%

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

   7. Taylor expanded in x1 around 0 13.0%

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

      1. neg-mul-1 31.7%

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

      2. unsub-neg 31.7%

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

      3. *-commutative 31.7%

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

   9. Simplified 13.0%

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

   10. Taylor expanded in x2 around -inf 41.5%

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

   if -2.99999999999999978e30 < x1 < -3.0000000000000002e-163

   1. Initial program 99.1%

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

   3. Taylor expanded in x1 around 0 77.1%

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

   4. Taylor expanded in x1 around 0 77.8%

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

   if -3.0000000000000002e-163 < x1 < 3.0999999999999998e-259

   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 79.5%

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

   4. Taylor expanded in x2 around 0 98.0%

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

      1. *-commutative 98.0%

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

      2. associate-*l* 98.0%

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

   6. Simplified 98.0%

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

   7. Taylor expanded in x1 around 0 98.2%

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

   if 3.0999999999999998e-259 < x1 < 6.4999999999999996e108

   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 82.8%

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

   4. Taylor expanded in x1 around 0 82.6%

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

   if 6.4999999999999996e108 < x1

   1. Initial program 22.7%

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

   3. Taylor expanded in x1 around 0 9.8%

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

   4. Taylor expanded in x2 around 0 2.8%

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

      1. *-commutative 2.8%

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

      2. associate-*l* 2.8%

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

   6. Simplified 2.8%

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

   7. Taylor expanded in x1 around 0 95.5%

      \[\leadsto x1 + \color{blue}{\left(-6 \cdot x2 + x1 \cdot \left(\left(-12 \cdot x2 + x1 \cdot \left(3 \cdot x1 + 3 \cdot \left(3 - -2 \cdot x2\right)\right)\right) - 2\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -3 \cdot 10^{+30}:\\ \;\;\;\;x1 + x2 \cdot \left(\left(\frac{x1 + x1 \cdot -3}{x2} - x1 \cdot 12\right) - 6\right)\\ \mathbf{elif}\;x1 \leq -3 \cdot 10^{-163}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 + \left(4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right) + 3 \cdot \left(x1 \cdot \left(x2 \cdot -2 - 3\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 3.1 \cdot 10^{-259}:\\ \;\;\;\;x1 - \left(x1 \cdot \left(2 + \left(3 \cdot \left(x1 \cdot \left(x2 \cdot -2 - 3\right)\right) - x2 \cdot -12\right)\right) - x2 \cdot -6\right)\\ \mathbf{elif}\;x1 \leq 6.5 \cdot 10^{+108}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 - 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 - \left(x1 \cdot \left(2 - \left(x2 \cdot -12 + x1 \cdot \left(x1 \cdot 3 + 3 \cdot \left(3 - x2 \cdot -2\right)\right)\right)\right) - x2 \cdot -6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 73.4% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\\ \mathbf{if}\;x1 \leq -2.7 \cdot 10^{+161}:\\ \;\;\;\;x1 - \left(3 \cdot \left(x1 - x2 \cdot -2\right) + \left(x1 \cdot \left(t\_0 - x1 \cdot 9\right) - x1\right)\right)\\ \mathbf{elif}\;x1 \leq -8.8 \cdot 10^{+29}:\\ \;\;\;\;x1 + x2 \cdot \left(\left(\frac{x1 + x1 \cdot -3}{x2} - x1 \cdot 12\right) - 6\right)\\ \mathbf{else}:\\ \;\;\;\;x1 - \left(x1 \cdot \left(2 + \left(x1 \cdot \left(3 \cdot \left(x2 \cdot -2 - 3\right) - x1 \cdot 3\right) + t\_0\right)\right) - x2 \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* 4.0 (* x2 (- 3.0 (* 2.0 x2))))))
   (if (<= x1 -2.7e+161)
     (- x1 (+ (* 3.0 (- x1 (* x2 -2.0))) (- (* x1 (- t_0 (* x1 9.0))) x1)))
     (if (<= x1 -8.8e+29)
       (+ x1 (* x2 (- (- (/ (+ x1 (* x1 -3.0)) x2) (* x1 12.0)) 6.0)))
       (-
        x1
        (-
         (*
          x1
          (+ 2.0 (+ (* x1 (- (* 3.0 (- (* x2 -2.0) 3.0)) (* x1 3.0))) t_0)))
         (* x2 -6.0)))))))

C

double code(double x1, double x2) {
	double t_0 = 4.0 * (x2 * (3.0 - (2.0 * x2)));
	double tmp;
	if (x1 <= -2.7e+161) {
		tmp = x1 - ((3.0 * (x1 - (x2 * -2.0))) + ((x1 * (t_0 - (x1 * 9.0))) - x1));
	} else if (x1 <= -8.8e+29) {
		tmp = x1 + (x2 * ((((x1 + (x1 * -3.0)) / x2) - (x1 * 12.0)) - 6.0));
	} else {
		tmp = x1 - ((x1 * (2.0 + ((x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - (x1 * 3.0))) + t_0))) - (x2 * -6.0));
	}
	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 = 4.0d0 * (x2 * (3.0d0 - (2.0d0 * x2)))
    if (x1 <= (-2.7d+161)) then
        tmp = x1 - ((3.0d0 * (x1 - (x2 * (-2.0d0)))) + ((x1 * (t_0 - (x1 * 9.0d0))) - x1))
    else if (x1 <= (-8.8d+29)) then
        tmp = x1 + (x2 * ((((x1 + (x1 * (-3.0d0))) / x2) - (x1 * 12.0d0)) - 6.0d0))
    else
        tmp = x1 - ((x1 * (2.0d0 + ((x1 * ((3.0d0 * ((x2 * (-2.0d0)) - 3.0d0)) - (x1 * 3.0d0))) + t_0))) - (x2 * (-6.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = 4.0 * (x2 * (3.0 - (2.0 * x2)));
	double tmp;
	if (x1 <= -2.7e+161) {
		tmp = x1 - ((3.0 * (x1 - (x2 * -2.0))) + ((x1 * (t_0 - (x1 * 9.0))) - x1));
	} else if (x1 <= -8.8e+29) {
		tmp = x1 + (x2 * ((((x1 + (x1 * -3.0)) / x2) - (x1 * 12.0)) - 6.0));
	} else {
		tmp = x1 - ((x1 * (2.0 + ((x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - (x1 * 3.0))) + t_0))) - (x2 * -6.0));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = 4.0 * (x2 * (3.0 - (2.0 * x2)))
	tmp = 0
	if x1 <= -2.7e+161:
		tmp = x1 - ((3.0 * (x1 - (x2 * -2.0))) + ((x1 * (t_0 - (x1 * 9.0))) - x1))
	elif x1 <= -8.8e+29:
		tmp = x1 + (x2 * ((((x1 + (x1 * -3.0)) / x2) - (x1 * 12.0)) - 6.0))
	else:
		tmp = x1 - ((x1 * (2.0 + ((x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - (x1 * 3.0))) + t_0))) - (x2 * -6.0))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(4.0 * Float64(x2 * Float64(3.0 - Float64(2.0 * x2))))
	tmp = 0.0
	if (x1 <= -2.7e+161)
		tmp = Float64(x1 - Float64(Float64(3.0 * Float64(x1 - Float64(x2 * -2.0))) + Float64(Float64(x1 * Float64(t_0 - Float64(x1 * 9.0))) - x1)));
	elseif (x1 <= -8.8e+29)
		tmp = Float64(x1 + Float64(x2 * Float64(Float64(Float64(Float64(x1 + Float64(x1 * -3.0)) / x2) - Float64(x1 * 12.0)) - 6.0)));
	else
		tmp = Float64(x1 - Float64(Float64(x1 * Float64(2.0 + Float64(Float64(x1 * Float64(Float64(3.0 * Float64(Float64(x2 * -2.0) - 3.0)) - Float64(x1 * 3.0))) + t_0))) - Float64(x2 * -6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = 4.0 * (x2 * (3.0 - (2.0 * x2)));
	tmp = 0.0;
	if (x1 <= -2.7e+161)
		tmp = x1 - ((3.0 * (x1 - (x2 * -2.0))) + ((x1 * (t_0 - (x1 * 9.0))) - x1));
	elseif (x1 <= -8.8e+29)
		tmp = x1 + (x2 * ((((x1 + (x1 * -3.0)) / x2) - (x1 * 12.0)) - 6.0));
	else
		tmp = x1 - ((x1 * (2.0 + ((x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - (x1 * 3.0))) + t_0))) - (x2 * -6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(4.0 * N[(x2 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -2.7e+161], N[(x1 - N[(N[(3.0 * N[(x1 - N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * N[(t$95$0 - N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -8.8e+29], N[(x1 + N[(x2 * N[(N[(N[(N[(x1 + N[(x1 * -3.0), $MachinePrecision]), $MachinePrecision] / x2), $MachinePrecision] - N[(x1 * 12.0), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 - N[(N[(x1 * N[(2.0 + N[(N[(x1 * N[(N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision] - N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -2.6999999999999998e161

   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 0.0%

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

   4. Taylor expanded in x1 around 0 0.0%

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

      1. neg-mul-1 0.0%

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

      2. unsub-neg 0.0%

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

      3. *-commutative 0.0%

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

   6. Simplified 0.0%

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

   7. Taylor expanded in x1 around 0 70.4%

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

   8. Taylor expanded in x2 around 0 70.4%

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

   if -2.6999999999999998e161 < x1 < -8.8000000000000005e29

   1. Initial program 54.7%

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

   3. Taylor expanded in x1 around 0 5.6%

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

   4. Taylor expanded in x2 around 0 8.9%

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

      1. *-commutative 8.9%

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

      2. associate-*l* 8.9%

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

   6. Simplified 8.9%

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

   7. Taylor expanded in x1 around 0 11.5%

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

      1. neg-mul-1 54.7%

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

      2. unsub-neg 54.7%

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

      3. *-commutative 54.7%

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

   9. Simplified 11.5%

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

   10. Taylor expanded in x2 around -inf 33.0%

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

   if -8.8000000000000005e29 < x1

   1. Initial program 81.5%

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

   3. Taylor expanded in x1 around 0 64.5%

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

   4. Taylor expanded in x1 around 0 83.8%

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

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -2.7 \cdot 10^{+161}:\\ \;\;\;\;x1 - \left(3 \cdot \left(x1 - x2 \cdot -2\right) + \left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right) - x1 \cdot 9\right) - x1\right)\right)\\ \mathbf{elif}\;x1 \leq -8.8 \cdot 10^{+29}:\\ \;\;\;\;x1 + x2 \cdot \left(\left(\frac{x1 + x1 \cdot -3}{x2} - x1 \cdot 12\right) - 6\right)\\ \mathbf{else}:\\ \;\;\;\;x1 - \left(x1 \cdot \left(2 + \left(x1 \cdot \left(3 \cdot \left(x2 \cdot -2 - 3\right) - x1 \cdot 3\right) + 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right) - x2 \cdot -6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 58.6% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\\ t_1 := x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 - t\_0\right)\right)\\ \mathbf{if}\;x1 \leq -3 \cdot 10^{+30}:\\ \;\;\;\;x1 \cdot \left(-1 + x2 \cdot -12\right)\\ \mathbf{elif}\;x1 \leq -1.36 \cdot 10^{-161}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x1 \leq 3.8 \cdot 10^{-260}:\\ \;\;\;\;x2 \cdot -6 - x1\\ \mathbf{elif}\;x1 \leq 9 \cdot 10^{+154}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x1 \leq 3.7 \cdot 10^{+257}:\\ \;\;\;\;x2 \cdot \left(\frac{x1}{x2} - 6\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot \left(1 + t\_0\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* 4.0 (* x2 (- (* 2.0 x2) 3.0))))
        (t_1 (+ x1 (- (* x2 -6.0) (* x1 (- 2.0 t_0))))))
   (if (<= x1 -3e+30)
     (* x1 (+ -1.0 (* x2 -12.0)))
     (if (<= x1 -1.36e-161)
       t_1
       (if (<= x1 3.8e-260)
         (- (* x2 -6.0) x1)
         (if (<= x1 9e+154)
           t_1
           (if (<= x1 3.7e+257)
             (* x2 (- (/ x1 x2) 6.0))
             (+ x1 (* x1 (+ 1.0 t_0))))))))))

C

double code(double x1, double x2) {
	double t_0 = 4.0 * (x2 * ((2.0 * x2) - 3.0));
	double t_1 = x1 + ((x2 * -6.0) - (x1 * (2.0 - t_0)));
	double tmp;
	if (x1 <= -3e+30) {
		tmp = x1 * (-1.0 + (x2 * -12.0));
	} else if (x1 <= -1.36e-161) {
		tmp = t_1;
	} else if (x1 <= 3.8e-260) {
		tmp = (x2 * -6.0) - x1;
	} else if (x1 <= 9e+154) {
		tmp = t_1;
	} else if (x1 <= 3.7e+257) {
		tmp = x2 * ((x1 / x2) - 6.0);
	} else {
		tmp = x1 + (x1 * (1.0 + t_0));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = 4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0))
    t_1 = x1 + ((x2 * (-6.0d0)) - (x1 * (2.0d0 - t_0)))
    if (x1 <= (-3d+30)) then
        tmp = x1 * ((-1.0d0) + (x2 * (-12.0d0)))
    else if (x1 <= (-1.36d-161)) then
        tmp = t_1
    else if (x1 <= 3.8d-260) then
        tmp = (x2 * (-6.0d0)) - x1
    else if (x1 <= 9d+154) then
        tmp = t_1
    else if (x1 <= 3.7d+257) then
        tmp = x2 * ((x1 / x2) - 6.0d0)
    else
        tmp = x1 + (x1 * (1.0d0 + t_0))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = 4.0 * (x2 * ((2.0 * x2) - 3.0));
	double t_1 = x1 + ((x2 * -6.0) - (x1 * (2.0 - t_0)));
	double tmp;
	if (x1 <= -3e+30) {
		tmp = x1 * (-1.0 + (x2 * -12.0));
	} else if (x1 <= -1.36e-161) {
		tmp = t_1;
	} else if (x1 <= 3.8e-260) {
		tmp = (x2 * -6.0) - x1;
	} else if (x1 <= 9e+154) {
		tmp = t_1;
	} else if (x1 <= 3.7e+257) {
		tmp = x2 * ((x1 / x2) - 6.0);
	} else {
		tmp = x1 + (x1 * (1.0 + t_0));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = 4.0 * (x2 * ((2.0 * x2) - 3.0))
	t_1 = x1 + ((x2 * -6.0) - (x1 * (2.0 - t_0)))
	tmp = 0
	if x1 <= -3e+30:
		tmp = x1 * (-1.0 + (x2 * -12.0))
	elif x1 <= -1.36e-161:
		tmp = t_1
	elif x1 <= 3.8e-260:
		tmp = (x2 * -6.0) - x1
	elif x1 <= 9e+154:
		tmp = t_1
	elif x1 <= 3.7e+257:
		tmp = x2 * ((x1 / x2) - 6.0)
	else:
		tmp = x1 + (x1 * (1.0 + t_0))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0)))
	t_1 = Float64(x1 + Float64(Float64(x2 * -6.0) - Float64(x1 * Float64(2.0 - t_0))))
	tmp = 0.0
	if (x1 <= -3e+30)
		tmp = Float64(x1 * Float64(-1.0 + Float64(x2 * -12.0)));
	elseif (x1 <= -1.36e-161)
		tmp = t_1;
	elseif (x1 <= 3.8e-260)
		tmp = Float64(Float64(x2 * -6.0) - x1);
	elseif (x1 <= 9e+154)
		tmp = t_1;
	elseif (x1 <= 3.7e+257)
		tmp = Float64(x2 * Float64(Float64(x1 / x2) - 6.0));
	else
		tmp = Float64(x1 + Float64(x1 * Float64(1.0 + t_0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = 4.0 * (x2 * ((2.0 * x2) - 3.0));
	t_1 = x1 + ((x2 * -6.0) - (x1 * (2.0 - t_0)));
	tmp = 0.0;
	if (x1 <= -3e+30)
		tmp = x1 * (-1.0 + (x2 * -12.0));
	elseif (x1 <= -1.36e-161)
		tmp = t_1;
	elseif (x1 <= 3.8e-260)
		tmp = (x2 * -6.0) - x1;
	elseif (x1 <= 9e+154)
		tmp = t_1;
	elseif (x1 <= 3.7e+257)
		tmp = x2 * ((x1 / x2) - 6.0);
	else
		tmp = x1 + (x1 * (1.0 + t_0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(4.0 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] - N[(x1 * N[(2.0 - t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -3e+30], N[(x1 * N[(-1.0 + N[(x2 * -12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -1.36e-161], t$95$1, If[LessEqual[x1, 3.8e-260], N[(N[(x2 * -6.0), $MachinePrecision] - x1), $MachinePrecision], If[LessEqual[x1, 9e+154], t$95$1, If[LessEqual[x1, 3.7e+257], N[(x2 * N[(N[(x1 / x2), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(x1 * N[(1.0 + t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x1 < -2.99999999999999978e30

   1. Initial program 31.7%

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

   3. Taylor expanded in x1 around 0 3.4%

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

   4. Taylor expanded in x2 around 0 5.4%

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

      1. *-commutative 5.4%

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

      2. associate-*l* 5.4%

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

   6. Simplified 5.4%

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

   7. Taylor expanded in x1 around 0 13.0%

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

      1. neg-mul-1 31.7%

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

      2. unsub-neg 31.7%

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

      3. *-commutative 31.7%

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

   9. Simplified 13.0%

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

   10. Taylor expanded in x1 around inf 13.0%

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

   if -2.99999999999999978e30 < x1 < -1.36e-161 or 3.8000000000000003e-260 < x1 < 9.00000000000000018e154

   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 77.7%

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

   4. Taylor expanded in x1 around 0 77.0%

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

   if -1.36e-161 < x1 < 3.8000000000000003e-260

   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 inf 99.5%

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

   4. Taylor expanded in x1 around 0 99.5%

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

      1. neg-mul-1 99.5%

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

      2. unsub-neg 99.5%

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

      3. *-commutative 99.5%

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

   6. Simplified 99.5%

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

   7. Taylor expanded in x1 around inf 98.0%

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

   8. Taylor expanded in x1 around 0 98.2%

      \[\leadsto \color{blue}{-6 \cdot x2 + -1 \cdot x1} \]

   if 9.00000000000000018e154 < x1 < 3.69999999999999991e257

   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 0 0.0%

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

   4. Taylor expanded in x1 around 0 5.7%

      \[\leadsto x1 + \color{blue}{-6 \cdot x2} \]
   5. Step-by-step derivation

      1. *-commutative 5.7%

         \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]

   6. Simplified 5.7%

      \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]

   7. Taylor expanded in x2 around inf 58.5%

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

   if 3.69999999999999991e257 < x1

   1. Initial program 0.0%

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

   3. Taylor expanded in x1 around 0 0.0%

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

   4. Taylor expanded in x1 around inf 100.0%

      \[\leadsto x1 + \color{blue}{x1 \cdot \left(1 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 62.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -3 \cdot 10^{+30}:\\ \;\;\;\;x1 \cdot \left(-1 + x2 \cdot -12\right)\\ \mathbf{elif}\;x1 \leq -1.36 \cdot 10^{-161}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 - 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 3.8 \cdot 10^{-260}:\\ \;\;\;\;x2 \cdot -6 - x1\\ \mathbf{elif}\;x1 \leq 9 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 - 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 3.7 \cdot 10^{+257}:\\ \;\;\;\;x2 \cdot \left(\frac{x1}{x2} - 6\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot \left(1 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 64.4% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 + x2 \cdot \left(\left(\frac{x1 + x1 \cdot -3}{x2} - x1 \cdot 12\right) - 6\right)\\ t_1 := 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\\ t_2 := x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 - t\_1\right)\right)\\ \mathbf{if}\;x1 \leq -3 \cdot 10^{+30}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x1 \leq -1.5 \cdot 10^{-203}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x1 \leq 6.4 \cdot 10^{-259}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x1 \leq 1.32 \cdot 10^{+155}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x1 \leq 4.4 \cdot 10^{+256}:\\ \;\;\;\;x2 \cdot \left(\frac{x1}{x2} - 6\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot \left(1 + t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ x1 (* x2 (- (- (/ (+ x1 (* x1 -3.0)) x2) (* x1 12.0)) 6.0))))
        (t_1 (* 4.0 (* x2 (- (* 2.0 x2) 3.0))))
        (t_2 (+ x1 (- (* x2 -6.0) (* x1 (- 2.0 t_1))))))
   (if (<= x1 -3e+30)
     t_0
     (if (<= x1 -1.5e-203)
       t_2
       (if (<= x1 6.4e-259)
         t_0
         (if (<= x1 1.32e+155)
           t_2
           (if (<= x1 4.4e+256)
             (* x2 (- (/ x1 x2) 6.0))
             (+ x1 (* x1 (+ 1.0 t_1))))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 + (x2 * ((((x1 + (x1 * -3.0)) / x2) - (x1 * 12.0)) - 6.0));
	double t_1 = 4.0 * (x2 * ((2.0 * x2) - 3.0));
	double t_2 = x1 + ((x2 * -6.0) - (x1 * (2.0 - t_1)));
	double tmp;
	if (x1 <= -3e+30) {
		tmp = t_0;
	} else if (x1 <= -1.5e-203) {
		tmp = t_2;
	} else if (x1 <= 6.4e-259) {
		tmp = t_0;
	} else if (x1 <= 1.32e+155) {
		tmp = t_2;
	} else if (x1 <= 4.4e+256) {
		tmp = x2 * ((x1 / x2) - 6.0);
	} else {
		tmp = x1 + (x1 * (1.0 + t_1));
	}
	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 + (x2 * ((((x1 + (x1 * (-3.0d0))) / x2) - (x1 * 12.0d0)) - 6.0d0))
    t_1 = 4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0))
    t_2 = x1 + ((x2 * (-6.0d0)) - (x1 * (2.0d0 - t_1)))
    if (x1 <= (-3d+30)) then
        tmp = t_0
    else if (x1 <= (-1.5d-203)) then
        tmp = t_2
    else if (x1 <= 6.4d-259) then
        tmp = t_0
    else if (x1 <= 1.32d+155) then
        tmp = t_2
    else if (x1 <= 4.4d+256) then
        tmp = x2 * ((x1 / x2) - 6.0d0)
    else
        tmp = x1 + (x1 * (1.0d0 + t_1))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 + (x2 * ((((x1 + (x1 * -3.0)) / x2) - (x1 * 12.0)) - 6.0));
	double t_1 = 4.0 * (x2 * ((2.0 * x2) - 3.0));
	double t_2 = x1 + ((x2 * -6.0) - (x1 * (2.0 - t_1)));
	double tmp;
	if (x1 <= -3e+30) {
		tmp = t_0;
	} else if (x1 <= -1.5e-203) {
		tmp = t_2;
	} else if (x1 <= 6.4e-259) {
		tmp = t_0;
	} else if (x1 <= 1.32e+155) {
		tmp = t_2;
	} else if (x1 <= 4.4e+256) {
		tmp = x2 * ((x1 / x2) - 6.0);
	} else {
		tmp = x1 + (x1 * (1.0 + t_1));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 + (x2 * ((((x1 + (x1 * -3.0)) / x2) - (x1 * 12.0)) - 6.0))
	t_1 = 4.0 * (x2 * ((2.0 * x2) - 3.0))
	t_2 = x1 + ((x2 * -6.0) - (x1 * (2.0 - t_1)))
	tmp = 0
	if x1 <= -3e+30:
		tmp = t_0
	elif x1 <= -1.5e-203:
		tmp = t_2
	elif x1 <= 6.4e-259:
		tmp = t_0
	elif x1 <= 1.32e+155:
		tmp = t_2
	elif x1 <= 4.4e+256:
		tmp = x2 * ((x1 / x2) - 6.0)
	else:
		tmp = x1 + (x1 * (1.0 + t_1))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 + Float64(x2 * Float64(Float64(Float64(Float64(x1 + Float64(x1 * -3.0)) / x2) - Float64(x1 * 12.0)) - 6.0)))
	t_1 = Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0)))
	t_2 = Float64(x1 + Float64(Float64(x2 * -6.0) - Float64(x1 * Float64(2.0 - t_1))))
	tmp = 0.0
	if (x1 <= -3e+30)
		tmp = t_0;
	elseif (x1 <= -1.5e-203)
		tmp = t_2;
	elseif (x1 <= 6.4e-259)
		tmp = t_0;
	elseif (x1 <= 1.32e+155)
		tmp = t_2;
	elseif (x1 <= 4.4e+256)
		tmp = Float64(x2 * Float64(Float64(x1 / x2) - 6.0));
	else
		tmp = Float64(x1 + Float64(x1 * Float64(1.0 + t_1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 + (x2 * ((((x1 + (x1 * -3.0)) / x2) - (x1 * 12.0)) - 6.0));
	t_1 = 4.0 * (x2 * ((2.0 * x2) - 3.0));
	t_2 = x1 + ((x2 * -6.0) - (x1 * (2.0 - t_1)));
	tmp = 0.0;
	if (x1 <= -3e+30)
		tmp = t_0;
	elseif (x1 <= -1.5e-203)
		tmp = t_2;
	elseif (x1 <= 6.4e-259)
		tmp = t_0;
	elseif (x1 <= 1.32e+155)
		tmp = t_2;
	elseif (x1 <= 4.4e+256)
		tmp = x2 * ((x1 / x2) - 6.0);
	else
		tmp = x1 + (x1 * (1.0 + t_1));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 + N[(x2 * N[(N[(N[(N[(x1 + N[(x1 * -3.0), $MachinePrecision]), $MachinePrecision] / x2), $MachinePrecision] - N[(x1 * 12.0), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(4.0 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] - N[(x1 * N[(2.0 - t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -3e+30], t$95$0, If[LessEqual[x1, -1.5e-203], t$95$2, If[LessEqual[x1, 6.4e-259], t$95$0, If[LessEqual[x1, 1.32e+155], t$95$2, If[LessEqual[x1, 4.4e+256], N[(x2 * N[(N[(x1 / x2), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(x1 * N[(1.0 + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -2.99999999999999978e30 or -1.5000000000000001e-203 < x1 < 6.39999999999999975e-259

   1. Initial program 54.3%

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

   3. Taylor expanded in x1 around 0 27.5%

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

   4. Taylor expanded in x2 around 0 36.2%

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

      1. *-commutative 36.2%

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

      2. associate-*l* 36.2%

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

   6. Simplified 36.2%

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

   7. Taylor expanded in x1 around 0 41.3%

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

      1. neg-mul-1 54.3%

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

      2. unsub-neg 54.3%

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

      3. *-commutative 54.3%

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

   9. Simplified 41.3%

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

   10. Taylor expanded in x2 around -inf 60.3%

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

   if -2.99999999999999978e30 < x1 < -1.5000000000000001e-203 or 6.39999999999999975e-259 < x1 < 1.32e155

   1. Initial program 99.3%

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

   3. Taylor expanded in x1 around 0 78.8%

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

   4. Taylor expanded in x1 around 0 78.1%

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

   if 1.32e155 < x1 < 4.3999999999999999e256

   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 0 0.0%

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

   4. Taylor expanded in x1 around 0 5.7%

      \[\leadsto x1 + \color{blue}{-6 \cdot x2} \]
   5. Step-by-step derivation

      1. *-commutative 5.7%

         \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]

   6. Simplified 5.7%

      \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]

   7. Taylor expanded in x2 around inf 58.5%

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

   if 4.3999999999999999e256 < x1

   1. Initial program 0.0%

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

   3. Taylor expanded in x1 around 0 0.0%

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

   4. Taylor expanded in x1 around inf 100.0%

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

4. Final simplification 70.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -3 \cdot 10^{+30}:\\ \;\;\;\;x1 + x2 \cdot \left(\left(\frac{x1 + x1 \cdot -3}{x2} - x1 \cdot 12\right) - 6\right)\\ \mathbf{elif}\;x1 \leq -1.5 \cdot 10^{-203}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 - 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 6.4 \cdot 10^{-259}:\\ \;\;\;\;x1 + x2 \cdot \left(\left(\frac{x1 + x1 \cdot -3}{x2} - x1 \cdot 12\right) - 6\right)\\ \mathbf{elif}\;x1 \leq 1.32 \cdot 10^{+155}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 - 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 4.4 \cdot 10^{+256}:\\ \;\;\;\;x2 \cdot \left(\frac{x1}{x2} - 6\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot \left(1 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 71.9% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -2.7 \cdot 10^{+161} \lor \neg \left(x1 \leq -3 \cdot 10^{+30}\right):\\ \;\;\;\;x1 - \left(3 \cdot \left(x1 - x2 \cdot -2\right) + \left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right) - x1 \cdot 9\right) - x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x2 \cdot \left(\left(\frac{x1 + x1 \cdot -3}{x2} - x1 \cdot 12\right) - 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x1 -2.7e+161) (not (<= x1 -3e+30)))
   (-
    x1
    (+
     (* 3.0 (- x1 (* x2 -2.0)))
     (- (* x1 (- (* 4.0 (* x2 (- 3.0 (* 2.0 x2)))) (* x1 9.0))) x1)))
   (+ x1 (* x2 (- (- (/ (+ x1 (* x1 -3.0)) x2) (* x1 12.0)) 6.0)))))

C

double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -2.7e+161) || !(x1 <= -3e+30)) {
		tmp = x1 - ((3.0 * (x1 - (x2 * -2.0))) + ((x1 * ((4.0 * (x2 * (3.0 - (2.0 * x2)))) - (x1 * 9.0))) - x1));
	} else {
		tmp = x1 + (x2 * ((((x1 + (x1 * -3.0)) / x2) - (x1 * 12.0)) - 6.0));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if ((x1 <= (-2.7d+161)) .or. (.not. (x1 <= (-3d+30)))) then
        tmp = x1 - ((3.0d0 * (x1 - (x2 * (-2.0d0)))) + ((x1 * ((4.0d0 * (x2 * (3.0d0 - (2.0d0 * x2)))) - (x1 * 9.0d0))) - x1))
    else
        tmp = x1 + (x2 * ((((x1 + (x1 * (-3.0d0))) / x2) - (x1 * 12.0d0)) - 6.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -2.7e+161) || !(x1 <= -3e+30)) {
		tmp = x1 - ((3.0 * (x1 - (x2 * -2.0))) + ((x1 * ((4.0 * (x2 * (3.0 - (2.0 * x2)))) - (x1 * 9.0))) - x1));
	} else {
		tmp = x1 + (x2 * ((((x1 + (x1 * -3.0)) / x2) - (x1 * 12.0)) - 6.0));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x1 <= -2.7e+161) or not (x1 <= -3e+30):
		tmp = x1 - ((3.0 * (x1 - (x2 * -2.0))) + ((x1 * ((4.0 * (x2 * (3.0 - (2.0 * x2)))) - (x1 * 9.0))) - x1))
	else:
		tmp = x1 + (x2 * ((((x1 + (x1 * -3.0)) / x2) - (x1 * 12.0)) - 6.0))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x1 <= -2.7e+161) || !(x1 <= -3e+30))
		tmp = Float64(x1 - Float64(Float64(3.0 * Float64(x1 - Float64(x2 * -2.0))) + Float64(Float64(x1 * Float64(Float64(4.0 * Float64(x2 * Float64(3.0 - Float64(2.0 * x2)))) - Float64(x1 * 9.0))) - x1)));
	else
		tmp = Float64(x1 + Float64(x2 * Float64(Float64(Float64(Float64(x1 + Float64(x1 * -3.0)) / x2) - Float64(x1 * 12.0)) - 6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x1 <= -2.7e+161) || ~((x1 <= -3e+30)))
		tmp = x1 - ((3.0 * (x1 - (x2 * -2.0))) + ((x1 * ((4.0 * (x2 * (3.0 - (2.0 * x2)))) - (x1 * 9.0))) - x1));
	else
		tmp = x1 + (x2 * ((((x1 + (x1 * -3.0)) / x2) - (x1 * 12.0)) - 6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x1, -2.7e+161], N[Not[LessEqual[x1, -3e+30]], $MachinePrecision]], N[(x1 - N[(N[(3.0 * N[(x1 - N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * N[(N[(4.0 * N[(x2 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(x2 * N[(N[(N[(N[(x1 + N[(x1 * -3.0), $MachinePrecision]), $MachinePrecision] / x2), $MachinePrecision] - N[(x1 * 12.0), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x1 < -2.6999999999999998e161 or -2.99999999999999978e30 < x1

   1. Initial program 71.5%

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

   3. Taylor expanded in x1 around inf 70.7%

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

   4. Taylor expanded in x1 around 0 71.5%

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

      1. neg-mul-1 71.5%

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

      2. unsub-neg 71.5%

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

      3. *-commutative 71.5%

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

   6. Simplified 71.5%

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

   7. Taylor expanded in x1 around 0 80.9%

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

   8. Taylor expanded in x2 around 0 81.2%

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

   if -2.6999999999999998e161 < x1 < -2.99999999999999978e30

   1. Initial program 53.6%

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

   3. Taylor expanded in x1 around 0 5.7%

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

   4. Taylor expanded in x2 around 0 9.1%

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

      1. *-commutative 9.1%

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

      2. associate-*l* 9.1%

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

   6. Simplified 9.1%

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

   7. Taylor expanded in x1 around 0 11.6%

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

      1. neg-mul-1 53.6%

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

      2. unsub-neg 53.6%

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

      3. *-commutative 53.6%

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

   9. Simplified 11.6%

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

   10. Taylor expanded in x2 around -inf 33.7%

       \[\leadsto x1 + \color{blue}{-1 \cdot \left(x2 \cdot \left(6 + \left(-1 \cdot \frac{x1 + -3 \cdot x1}{x2} + 12 \cdot x1\right)\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 74.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -2.7 \cdot 10^{+161} \lor \neg \left(x1 \leq -3 \cdot 10^{+30}\right):\\ \;\;\;\;x1 - \left(3 \cdot \left(x1 - x2 \cdot -2\right) + \left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right) - x1 \cdot 9\right) - x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x2 \cdot \left(\left(\frac{x1 + x1 \cdot -3}{x2} - x1 \cdot 12\right) - 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 69.7% accurate, 3.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\\ \mathbf{if}\;x2 \leq -1.5:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 - t\_0\right)\right)\\ \mathbf{elif}\;x2 \leq 2.45 \cdot 10^{+218}:\\ \;\;\;\;x1 - \left(x1 \cdot \left(2 + \left(3 \cdot \left(x1 \cdot \left(x2 \cdot -2 - 3\right)\right) - x2 \cdot -12\right)\right) - x2 \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot \left(1 + t\_0\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* 4.0 (* x2 (- (* 2.0 x2) 3.0)))))
   (if (<= x2 -1.5)
     (+ x1 (- (* x2 -6.0) (* x1 (- 2.0 t_0))))
     (if (<= x2 2.45e+218)
       (-
        x1
        (-
         (* x1 (+ 2.0 (- (* 3.0 (* x1 (- (* x2 -2.0) 3.0))) (* x2 -12.0))))
         (* x2 -6.0)))
       (+ x1 (* x1 (+ 1.0 t_0)))))))

C

double code(double x1, double x2) {
	double t_0 = 4.0 * (x2 * ((2.0 * x2) - 3.0));
	double tmp;
	if (x2 <= -1.5) {
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 - t_0)));
	} else if (x2 <= 2.45e+218) {
		tmp = x1 - ((x1 * (2.0 + ((3.0 * (x1 * ((x2 * -2.0) - 3.0))) - (x2 * -12.0)))) - (x2 * -6.0));
	} else {
		tmp = x1 + (x1 * (1.0 + t_0));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0))
    if (x2 <= (-1.5d0)) then
        tmp = x1 + ((x2 * (-6.0d0)) - (x1 * (2.0d0 - t_0)))
    else if (x2 <= 2.45d+218) then
        tmp = x1 - ((x1 * (2.0d0 + ((3.0d0 * (x1 * ((x2 * (-2.0d0)) - 3.0d0))) - (x2 * (-12.0d0))))) - (x2 * (-6.0d0)))
    else
        tmp = x1 + (x1 * (1.0d0 + t_0))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = 4.0 * (x2 * ((2.0 * x2) - 3.0));
	double tmp;
	if (x2 <= -1.5) {
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 - t_0)));
	} else if (x2 <= 2.45e+218) {
		tmp = x1 - ((x1 * (2.0 + ((3.0 * (x1 * ((x2 * -2.0) - 3.0))) - (x2 * -12.0)))) - (x2 * -6.0));
	} else {
		tmp = x1 + (x1 * (1.0 + t_0));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = 4.0 * (x2 * ((2.0 * x2) - 3.0))
	tmp = 0
	if x2 <= -1.5:
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 - t_0)))
	elif x2 <= 2.45e+218:
		tmp = x1 - ((x1 * (2.0 + ((3.0 * (x1 * ((x2 * -2.0) - 3.0))) - (x2 * -12.0)))) - (x2 * -6.0))
	else:
		tmp = x1 + (x1 * (1.0 + t_0))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0)))
	tmp = 0.0
	if (x2 <= -1.5)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) - Float64(x1 * Float64(2.0 - t_0))));
	elseif (x2 <= 2.45e+218)
		tmp = Float64(x1 - Float64(Float64(x1 * Float64(2.0 + Float64(Float64(3.0 * Float64(x1 * Float64(Float64(x2 * -2.0) - 3.0))) - Float64(x2 * -12.0)))) - Float64(x2 * -6.0)));
	else
		tmp = Float64(x1 + Float64(x1 * Float64(1.0 + t_0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = 4.0 * (x2 * ((2.0 * x2) - 3.0));
	tmp = 0.0;
	if (x2 <= -1.5)
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 - t_0)));
	elseif (x2 <= 2.45e+218)
		tmp = x1 - ((x1 * (2.0 + ((3.0 * (x1 * ((x2 * -2.0) - 3.0))) - (x2 * -12.0)))) - (x2 * -6.0));
	else
		tmp = x1 + (x1 * (1.0 + t_0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(4.0 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x2, -1.5], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] - N[(x1 * N[(2.0 - t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x2, 2.45e+218], N[(x1 - N[(N[(x1 * N[(2.0 + N[(N[(3.0 * N[(x1 * N[(N[(x2 * -2.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x2 * -12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(x1 * N[(1.0 + t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x2 < -1.5

   1. Initial program 64.2%

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

   3. Taylor expanded in x1 around 0 42.7%

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

   4. Taylor expanded in x1 around 0 57.4%

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

   if -1.5 < x2 < 2.4499999999999999e218

   1. Initial program 67.9%

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

   3. Taylor expanded in x1 around 0 47.0%

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

   4. Taylor expanded in x2 around 0 44.9%

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

      1. *-commutative 44.9%

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

      2. associate-*l* 44.9%

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

   6. Simplified 44.9%

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

   7. Taylor expanded in x1 around 0 71.7%

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

   if 2.4499999999999999e218 < x2

   1. Initial program 100.0%

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

   3. Taylor expanded in x1 around 0 93.3%

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

   4. Taylor expanded in x1 around inf 93.3%

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

4. Final simplification 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq -1.5:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 - 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right)\\ \mathbf{elif}\;x2 \leq 2.45 \cdot 10^{+218}:\\ \;\;\;\;x1 - \left(x1 \cdot \left(2 + \left(3 \cdot \left(x1 \cdot \left(x2 \cdot -2 - 3\right)\right) - x2 \cdot -12\right)\right) - x2 \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot \left(1 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 51.1% accurate, 4.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq 9 \cdot 10^{-33}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + x2 \cdot -12\right)\\ \mathbf{elif}\;x1 \leq 1.3 \cdot 10^{+163} \lor \neg \left(x1 \leq 4.7 \cdot 10^{+254}\right):\\ \;\;\;\;x1 + x1 \cdot \left(1 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot \left(\frac{x1}{x2} - 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 9e-33)
   (+ (* x2 -6.0) (* x1 (+ -1.0 (* x2 -12.0))))
   (if (or (<= x1 1.3e+163) (not (<= x1 4.7e+254)))
     (+ x1 (* x1 (+ 1.0 (* 4.0 (* x2 (- (* 2.0 x2) 3.0))))))
     (* x2 (- (/ x1 x2) 6.0)))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= 9e-33) {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x2 * -12.0)));
	} else if ((x1 <= 1.3e+163) || !(x1 <= 4.7e+254)) {
		tmp = x1 + (x1 * (1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0)))));
	} else {
		tmp = x2 * ((x1 / x2) - 6.0);
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x1 <= 9d-33) then
        tmp = (x2 * (-6.0d0)) + (x1 * ((-1.0d0) + (x2 * (-12.0d0))))
    else if ((x1 <= 1.3d+163) .or. (.not. (x1 <= 4.7d+254))) then
        tmp = x1 + (x1 * (1.0d0 + (4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0)))))
    else
        tmp = x2 * ((x1 / x2) - 6.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= 9e-33) {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x2 * -12.0)));
	} else if ((x1 <= 1.3e+163) || !(x1 <= 4.7e+254)) {
		tmp = x1 + (x1 * (1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0)))));
	} else {
		tmp = x2 * ((x1 / x2) - 6.0);
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= 9e-33:
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x2 * -12.0)))
	elif (x1 <= 1.3e+163) or not (x1 <= 4.7e+254):
		tmp = x1 + (x1 * (1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0)))))
	else:
		tmp = x2 * ((x1 / x2) - 6.0)
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= 9e-33)
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(-1.0 + Float64(x2 * -12.0))));
	elseif ((x1 <= 1.3e+163) || !(x1 <= 4.7e+254))
		tmp = Float64(x1 + Float64(x1 * Float64(1.0 + Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0))))));
	else
		tmp = Float64(x2 * Float64(Float64(x1 / x2) - 6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= 9e-33)
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x2 * -12.0)));
	elseif ((x1 <= 1.3e+163) || ~((x1 <= 4.7e+254)))
		tmp = x1 + (x1 * (1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0)))));
	else
		tmp = x2 * ((x1 / x2) - 6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, 9e-33], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(-1.0 + N[(x2 * -12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x1, 1.3e+163], N[Not[LessEqual[x1, 4.7e+254]], $MachinePrecision]], N[(x1 + N[(x1 * N[(1.0 + N[(4.0 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x2 * N[(N[(x1 / x2), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x1 < 8.99999999999999982e-33

   1. Initial program 76.1%

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

   3. Taylor expanded in x1 around 0 57.4%

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

   4. Taylor expanded in x2 around 0 51.2%

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

      1. *-commutative 51.2%

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

      2. associate-*l* 51.2%

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

   6. Simplified 51.2%

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

   7. Taylor expanded in x1 around 0 53.4%

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

      1. neg-mul-1 76.1%

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

      2. unsub-neg 76.1%

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

      3. *-commutative 76.1%

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

   9. Simplified 53.4%

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

   10. Taylor expanded in x1 around 0 53.6%

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

   if 8.99999999999999982e-33 < x1 < 1.3000000000000001e163 or 4.7000000000000001e254 < x1

   1. Initial program 71.2%

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

   3. Taylor expanded in x1 around 0 33.2%

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

   4. Taylor expanded in x1 around inf 52.9%

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

   if 1.3000000000000001e163 < x1 < 4.7000000000000001e254

   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 0 0.0%

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

   4. Taylor expanded in x1 around 0 5.9%

      \[\leadsto x1 + \color{blue}{-6 \cdot x2} \]
   5. Step-by-step derivation

      1. *-commutative 5.9%

         \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]

   6. Simplified 5.9%

      \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]

   7. Taylor expanded in x2 around inf 65.8%

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

4. Final simplification 54.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq 9 \cdot 10^{-33}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + x2 \cdot -12\right)\\ \mathbf{elif}\;x1 \leq 1.3 \cdot 10^{+163} \lor \neg \left(x1 \leq 4.7 \cdot 10^{+254}\right):\\ \;\;\;\;x1 + x1 \cdot \left(1 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot \left(\frac{x1}{x2} - 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 39.7% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(-1 + x2 \cdot -12\right)\\ \mathbf{if}\;x1 \leq -2.8 \cdot 10^{-54}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x1 \leq 2.35 \cdot 10^{-110}:\\ \;\;\;\;x2 \cdot -6\\ \mathbf{elif}\;x1 \leq 2.15 \cdot 10^{+36}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot \left(\frac{x1}{x2} - 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (+ -1.0 (* x2 -12.0)))))
   (if (<= x1 -2.8e-54)
     t_0
     (if (<= x1 2.35e-110)
       (* x2 -6.0)
       (if (<= x1 2.15e+36) t_0 (* x2 (- (/ x1 x2) 6.0)))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (-1.0 + (x2 * -12.0));
	double tmp;
	if (x1 <= -2.8e-54) {
		tmp = t_0;
	} else if (x1 <= 2.35e-110) {
		tmp = x2 * -6.0;
	} else if (x1 <= 2.15e+36) {
		tmp = t_0;
	} else {
		tmp = x2 * ((x1 / x2) - 6.0);
	}
	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 * ((-1.0d0) + (x2 * (-12.0d0)))
    if (x1 <= (-2.8d-54)) then
        tmp = t_0
    else if (x1 <= 2.35d-110) then
        tmp = x2 * (-6.0d0)
    else if (x1 <= 2.15d+36) then
        tmp = t_0
    else
        tmp = x2 * ((x1 / x2) - 6.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (-1.0 + (x2 * -12.0));
	double tmp;
	if (x1 <= -2.8e-54) {
		tmp = t_0;
	} else if (x1 <= 2.35e-110) {
		tmp = x2 * -6.0;
	} else if (x1 <= 2.15e+36) {
		tmp = t_0;
	} else {
		tmp = x2 * ((x1 / x2) - 6.0);
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (-1.0 + (x2 * -12.0))
	tmp = 0
	if x1 <= -2.8e-54:
		tmp = t_0
	elif x1 <= 2.35e-110:
		tmp = x2 * -6.0
	elif x1 <= 2.15e+36:
		tmp = t_0
	else:
		tmp = x2 * ((x1 / x2) - 6.0)
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(-1.0 + Float64(x2 * -12.0)))
	tmp = 0.0
	if (x1 <= -2.8e-54)
		tmp = t_0;
	elseif (x1 <= 2.35e-110)
		tmp = Float64(x2 * -6.0);
	elseif (x1 <= 2.15e+36)
		tmp = t_0;
	else
		tmp = Float64(x2 * Float64(Float64(x1 / x2) - 6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (-1.0 + (x2 * -12.0));
	tmp = 0.0;
	if (x1 <= -2.8e-54)
		tmp = t_0;
	elseif (x1 <= 2.35e-110)
		tmp = x2 * -6.0;
	elseif (x1 <= 2.15e+36)
		tmp = t_0;
	else
		tmp = x2 * ((x1 / x2) - 6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(-1.0 + N[(x2 * -12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -2.8e-54], t$95$0, If[LessEqual[x1, 2.35e-110], N[(x2 * -6.0), $MachinePrecision], If[LessEqual[x1, 2.15e+36], t$95$0, N[(x2 * N[(N[(x1 / x2), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -2.8000000000000002e-54 or 2.34999999999999996e-110 < x1 < 2.15000000000000002e36

   1. Initial program 58.7%

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

   3. Taylor expanded in x1 around 0 33.2%

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

   4. Taylor expanded in x2 around 0 19.9%

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

      1. *-commutative 19.9%

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

      2. associate-*l* 19.9%

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

   6. Simplified 19.9%

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

   7. Taylor expanded in x1 around 0 23.7%

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

      1. neg-mul-1 58.7%

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

      2. unsub-neg 58.7%

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

      3. *-commutative 58.7%

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

   9. Simplified 23.7%

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

   10. Taylor expanded in x1 around inf 20.3%

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

   if -2.8000000000000002e-54 < x1 < 2.34999999999999996e-110

   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 87.2%

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

   4. Taylor expanded in x1 around 0 65.5%

      \[\leadsto x1 + \color{blue}{-6 \cdot x2} \]
   5. Step-by-step derivation

      1. *-commutative 65.5%

         \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]

   6. Simplified 65.5%

      \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]

   7. Taylor expanded in x1 around 0 65.9%

      \[\leadsto \color{blue}{-6 \cdot x2} \]
   8. Step-by-step derivation

      1. *-commutative 65.9%

         \[\leadsto \color{blue}{x2 \cdot -6} \]

   9. Simplified 65.9%

      \[\leadsto \color{blue}{x2 \cdot -6} \]

   if 2.15000000000000002e36 < x1

   1. Initial program 34.6%

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

   3. Taylor expanded in x1 around 0 10.8%

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

   4. Taylor expanded in x1 around 0 5.7%

      \[\leadsto x1 + \color{blue}{-6 \cdot x2} \]
   5. Step-by-step derivation

      1. *-commutative 5.7%

         \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]

   6. Simplified 5.7%

      \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]

   7. Taylor expanded in x2 around inf 36.6%

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

4. Final simplification 40.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -2.8 \cdot 10^{-54}:\\ \;\;\;\;x1 \cdot \left(-1 + x2 \cdot -12\right)\\ \mathbf{elif}\;x1 \leq 2.35 \cdot 10^{-110}:\\ \;\;\;\;x2 \cdot -6\\ \mathbf{elif}\;x1 \leq 2.15 \cdot 10^{+36}:\\ \;\;\;\;x1 \cdot \left(-1 + x2 \cdot -12\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot \left(\frac{x1}{x2} - 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 35.8% accurate, 7.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -2.8 \cdot 10^{-54} \lor \neg \left(x1 \leq 1.5 \cdot 10^{-117}\right):\\ \;\;\;\;x1 \cdot \left(-1 + x2 \cdot -12\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x1 -2.8e-54) (not (<= x1 1.5e-117)))
   (* x1 (+ -1.0 (* x2 -12.0)))
   (* x2 -6.0)))

C

double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -2.8e-54) || !(x1 <= 1.5e-117)) {
		tmp = x1 * (-1.0 + (x2 * -12.0));
	} else {
		tmp = x2 * -6.0;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if ((x1 <= (-2.8d-54)) .or. (.not. (x1 <= 1.5d-117))) then
        tmp = x1 * ((-1.0d0) + (x2 * (-12.0d0)))
    else
        tmp = x2 * (-6.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -2.8e-54) || !(x1 <= 1.5e-117)) {
		tmp = x1 * (-1.0 + (x2 * -12.0));
	} else {
		tmp = x2 * -6.0;
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x1 <= -2.8e-54) or not (x1 <= 1.5e-117):
		tmp = x1 * (-1.0 + (x2 * -12.0))
	else:
		tmp = x2 * -6.0
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x1 <= -2.8e-54) || !(x1 <= 1.5e-117))
		tmp = Float64(x1 * Float64(-1.0 + Float64(x2 * -12.0)));
	else
		tmp = Float64(x2 * -6.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x1 <= -2.8e-54) || ~((x1 <= 1.5e-117)))
		tmp = x1 * (-1.0 + (x2 * -12.0));
	else
		tmp = x2 * -6.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x1, -2.8e-54], N[Not[LessEqual[x1, 1.5e-117]], $MachinePrecision]], N[(x1 * N[(-1.0 + N[(x2 * -12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x2 * -6.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x1 < -2.8000000000000002e-54 or 1.49999999999999996e-117 < x1

   1. Initial program 50.9%

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

   3. Taylor expanded in x1 around 0 26.0%

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

   4. Taylor expanded in x2 around 0 15.1%

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

      1. *-commutative 15.1%

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

      2. associate-*l* 15.1%

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

   6. Simplified 15.1%

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

   7. Taylor expanded in x1 around 0 21.4%

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

      1. neg-mul-1 51.0%

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

      2. unsub-neg 51.0%

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

      3. *-commutative 51.0%

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

   9. Simplified 21.4%

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

   10. Taylor expanded in x1 around inf 19.2%

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

   if -2.8000000000000002e-54 < x1 < 1.49999999999999996e-117

   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 87.2%

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

   4. Taylor expanded in x1 around 0 65.5%

      \[\leadsto x1 + \color{blue}{-6 \cdot x2} \]
   5. Step-by-step derivation

      1. *-commutative 65.5%

         \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]

   6. Simplified 65.5%

      \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]

   7. Taylor expanded in x1 around 0 65.9%

      \[\leadsto \color{blue}{-6 \cdot x2} \]
   8. Step-by-step derivation

      1. *-commutative 65.9%

         \[\leadsto \color{blue}{x2 \cdot -6} \]

   9. Simplified 65.9%

      \[\leadsto \color{blue}{x2 \cdot -6} \]
3. Recombined 2 regimes into one program.

4. Final simplification 36.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -2.8 \cdot 10^{-54} \lor \neg \left(x1 \leq 1.5 \cdot 10^{-117}\right):\\ \;\;\;\;x1 \cdot \left(-1 + x2 \cdot -12\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 47.6% accurate, 7.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -1.05 \cdot 10^{+30}:\\ \;\;\;\;x1 \cdot \left(-1 + x2 \cdot -12\right)\\ \mathbf{elif}\;x1 \leq 3.1 \cdot 10^{-32}:\\ \;\;\;\;x2 \cdot -6 - x1\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot \left(\frac{x1}{x2} - 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -1.05e+30)
   (* x1 (+ -1.0 (* x2 -12.0)))
   (if (<= x1 3.1e-32) (- (* x2 -6.0) x1) (* x2 (- (/ x1 x2) 6.0)))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -1.05e+30) {
		tmp = x1 * (-1.0 + (x2 * -12.0));
	} else if (x1 <= 3.1e-32) {
		tmp = (x2 * -6.0) - x1;
	} else {
		tmp = x2 * ((x1 / x2) - 6.0);
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x1 <= (-1.05d+30)) then
        tmp = x1 * ((-1.0d0) + (x2 * (-12.0d0)))
    else if (x1 <= 3.1d-32) then
        tmp = (x2 * (-6.0d0)) - x1
    else
        tmp = x2 * ((x1 / x2) - 6.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= -1.05e+30) {
		tmp = x1 * (-1.0 + (x2 * -12.0));
	} else if (x1 <= 3.1e-32) {
		tmp = (x2 * -6.0) - x1;
	} else {
		tmp = x2 * ((x1 / x2) - 6.0);
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -1.05e+30:
		tmp = x1 * (-1.0 + (x2 * -12.0))
	elif x1 <= 3.1e-32:
		tmp = (x2 * -6.0) - x1
	else:
		tmp = x2 * ((x1 / x2) - 6.0)
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -1.05e+30)
		tmp = Float64(x1 * Float64(-1.0 + Float64(x2 * -12.0)));
	elseif (x1 <= 3.1e-32)
		tmp = Float64(Float64(x2 * -6.0) - x1);
	else
		tmp = Float64(x2 * Float64(Float64(x1 / x2) - 6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -1.05e+30)
		tmp = x1 * (-1.0 + (x2 * -12.0));
	elseif (x1 <= 3.1e-32)
		tmp = (x2 * -6.0) - x1;
	else
		tmp = x2 * ((x1 / x2) - 6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -1.05e+30], N[(x1 * N[(-1.0 + N[(x2 * -12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 3.1e-32], N[(N[(x2 * -6.0), $MachinePrecision] - x1), $MachinePrecision], N[(x2 * N[(N[(x1 / x2), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -1.05e30

   1. Initial program 31.7%

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

   3. Taylor expanded in x1 around 0 3.4%

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

   4. Taylor expanded in x2 around 0 5.4%

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

      1. *-commutative 5.4%

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

      2. associate-*l* 5.4%

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

   6. Simplified 5.4%

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

   7. Taylor expanded in x1 around 0 13.0%

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

      1. neg-mul-1 31.7%

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

      2. unsub-neg 31.7%

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

      3. *-commutative 31.7%

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

   9. Simplified 13.0%

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

   10. Taylor expanded in x1 around inf 13.0%

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

   if -1.05e30 < x1 < 3.10000000000000011e-32

   1. Initial program 99.3%

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

   3. Taylor expanded in x1 around inf 98.0%

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

   4. Taylor expanded in x1 around 0 99.4%

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

      1. neg-mul-1 99.4%

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

      2. unsub-neg 99.4%

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

      3. *-commutative 99.4%

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

   6. Simplified 99.4%

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

   7. Taylor expanded in x1 around inf 76.5%

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

   8. Taylor expanded in x1 around 0 75.1%

      \[\leadsto \color{blue}{-6 \cdot x2 + -1 \cdot x1} \]

   if 3.10000000000000011e-32 < x1

   1. Initial program 46.7%

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

   3. Taylor expanded in x1 around 0 21.8%

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

   4. Taylor expanded in x1 around 0 6.2%

      \[\leadsto x1 + \color{blue}{-6 \cdot x2} \]
   5. Step-by-step derivation

      1. *-commutative 6.2%

         \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]

   6. Simplified 6.2%

      \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]

   7. Taylor expanded in x2 around inf 31.4%

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

4. Final simplification 48.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.05 \cdot 10^{+30}:\\ \;\;\;\;x1 \cdot \left(-1 + x2 \cdot -12\right)\\ \mathbf{elif}\;x1 \leq 3.1 \cdot 10^{-32}:\\ \;\;\;\;x2 \cdot -6 - x1\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot \left(\frac{x1}{x2} - 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 48.4% accurate, 7.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq 2.3 \cdot 10^{+36}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + x2 \cdot -12\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot \left(\frac{x1}{x2} - 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 2.3e+36)
   (+ (* x2 -6.0) (* x1 (+ -1.0 (* x2 -12.0))))
   (* x2 (- (/ x1 x2) 6.0))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= 2.3e+36) {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x2 * -12.0)));
	} else {
		tmp = x2 * ((x1 / x2) - 6.0);
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x1 <= 2.3d+36) then
        tmp = (x2 * (-6.0d0)) + (x1 * ((-1.0d0) + (x2 * (-12.0d0))))
    else
        tmp = x2 * ((x1 / x2) - 6.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= 2.3e+36) {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x2 * -12.0)));
	} else {
		tmp = x2 * ((x1 / x2) - 6.0);
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= 2.3e+36:
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x2 * -12.0)))
	else:
		tmp = x2 * ((x1 / x2) - 6.0)
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= 2.3e+36)
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(-1.0 + Float64(x2 * -12.0))));
	else
		tmp = Float64(x2 * Float64(Float64(x1 / x2) - 6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= 2.3e+36)
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x2 * -12.0)));
	else
		tmp = x2 * ((x1 / x2) - 6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, 2.3e+36], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(-1.0 + N[(x2 * -12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x2 * N[(N[(x1 / x2), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x1 < 2.29999999999999996e36

   1. Initial program 77.4%

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

   3. Taylor expanded in x1 around 0 58.1%

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

   4. Taylor expanded in x2 around 0 49.1%

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

      1. *-commutative 49.1%

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

      2. associate-*l* 49.1%

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

   6. Simplified 49.1%

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

   7. Taylor expanded in x1 around 0 51.1%

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

      1. neg-mul-1 77.5%

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

      2. unsub-neg 77.5%

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

      3. *-commutative 77.5%

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

   9. Simplified 51.1%

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

   10. Taylor expanded in x1 around 0 51.3%

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

   if 2.29999999999999996e36 < x1

   1. Initial program 34.6%

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

   3. Taylor expanded in x1 around 0 10.8%

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

   4. Taylor expanded in x1 around 0 5.7%

      \[\leadsto x1 + \color{blue}{-6 \cdot x2} \]
   5. Step-by-step derivation

      1. *-commutative 5.7%

         \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]

   6. Simplified 5.7%

      \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]

   7. Taylor expanded in x2 around inf 36.6%

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

4. Final simplification 48.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq 2.3 \cdot 10^{+36}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + x2 \cdot -12\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot \left(\frac{x1}{x2} - 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 31.8% accurate, 8.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x2 \leq -4.8 \cdot 10^{-230}:\\ \;\;\;\;x2 \cdot -6\\ \mathbf{elif}\;x2 \leq 9.6 \cdot 10^{-170}:\\ \;\;\;\;-x1\\ \mathbf{else}:\\ \;\;\;\;x1 + x2 \cdot -6\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x2 -4.8e-230)
   (* x2 -6.0)
   (if (<= x2 9.6e-170) (- x1) (+ x1 (* x2 -6.0)))))

C

double code(double x1, double x2) {
	double tmp;
	if (x2 <= -4.8e-230) {
		tmp = x2 * -6.0;
	} else if (x2 <= 9.6e-170) {
		tmp = -x1;
	} else {
		tmp = x1 + (x2 * -6.0);
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x2 <= (-4.8d-230)) then
        tmp = x2 * (-6.0d0)
    else if (x2 <= 9.6d-170) then
        tmp = -x1
    else
        tmp = x1 + (x2 * (-6.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x2 <= -4.8e-230) {
		tmp = x2 * -6.0;
	} else if (x2 <= 9.6e-170) {
		tmp = -x1;
	} else {
		tmp = x1 + (x2 * -6.0);
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x2 <= -4.8e-230:
		tmp = x2 * -6.0
	elif x2 <= 9.6e-170:
		tmp = -x1
	else:
		tmp = x1 + (x2 * -6.0)
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x2 <= -4.8e-230)
		tmp = Float64(x2 * -6.0);
	elseif (x2 <= 9.6e-170)
		tmp = Float64(-x1);
	else
		tmp = Float64(x1 + Float64(x2 * -6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x2 <= -4.8e-230)
		tmp = x2 * -6.0;
	elseif (x2 <= 9.6e-170)
		tmp = -x1;
	else
		tmp = x1 + (x2 * -6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x2, -4.8e-230], N[(x2 * -6.0), $MachinePrecision], If[LessEqual[x2, 9.6e-170], (-x1), N[(x1 + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x2 < -4.8000000000000004e-230

   1. Initial program 66.6%

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

   3. Taylor expanded in x1 around 0 45.6%

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

   4. Taylor expanded in x1 around 0 31.4%

      \[\leadsto x1 + \color{blue}{-6 \cdot x2} \]
   5. Step-by-step derivation

      1. *-commutative 31.4%

         \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]

   6. Simplified 31.4%

      \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]

   7. Taylor expanded in x1 around 0 31.7%

      \[\leadsto \color{blue}{-6 \cdot x2} \]
   8. Step-by-step derivation

      1. *-commutative 31.7%

         \[\leadsto \color{blue}{x2 \cdot -6} \]

   9. Simplified 31.7%

      \[\leadsto \color{blue}{x2 \cdot -6} \]

   if -4.8000000000000004e-230 < x2 < 9.5999999999999998e-170

   1. Initial program 65.5%

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

   3. Taylor expanded in x1 around 0 45.3%

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

   4. Taylor expanded in x2 around 0 45.3%

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

      1. *-commutative 45.3%

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

      2. associate-*l* 45.3%

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

   6. Simplified 45.3%

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

   7. Taylor expanded in x1 around 0 46.4%

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

      1. neg-mul-1 65.5%

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

      2. unsub-neg 65.5%

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

      3. *-commutative 65.5%

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

   9. Simplified 46.4%

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

   10. Taylor expanded in x2 around 0 38.2%

       \[\leadsto \color{blue}{-3 \cdot x1 + 2 \cdot x1} \]
   11. Step-by-step derivation

       1. distribute-rgt-out 38.6%

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

       2. metadata-eval 38.6%

          \[\leadsto x1 \cdot \color{blue}{-1} \]

       3. *-commutative 38.6%

          \[\leadsto \color{blue}{-1 \cdot x1} \]

       4. mul-1-neg 38.6%

          \[\leadsto \color{blue}{-x1} \]

   12. Simplified 38.6%

       \[\leadsto \color{blue}{-x1} \]

   if 9.5999999999999998e-170 < x2

   1. Initial program 73.7%

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

   3. Taylor expanded in x1 around 0 54.5%

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

   4. Taylor expanded in x1 around 0 30.7%

      \[\leadsto x1 + \color{blue}{-6 \cdot x2} \]
   5. Step-by-step derivation

      1. *-commutative 30.7%

         \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]

   6. Simplified 30.7%

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

4. Final simplification 32.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq -4.8 \cdot 10^{-230}:\\ \;\;\;\;x2 \cdot -6\\ \mathbf{elif}\;x2 \leq 9.6 \cdot 10^{-170}:\\ \;\;\;\;-x1\\ \mathbf{else}:\\ \;\;\;\;x1 + x2 \cdot -6\\ \end{array} \]
5. Add Preprocessing

Alternative 27: 31.6% accurate, 9.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x2 \leq -1.55 \cdot 10^{-229} \lor \neg \left(x2 \leq 2.5 \cdot 10^{-164}\right):\\ \;\;\;\;x2 \cdot -6\\ \mathbf{else}:\\ \;\;\;\;-x1\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x2 -1.55e-229) (not (<= x2 2.5e-164))) (* x2 -6.0) (- x1)))

C

double code(double x1, double x2) {
	double tmp;
	if ((x2 <= -1.55e-229) || !(x2 <= 2.5e-164)) {
		tmp = x2 * -6.0;
	} else {
		tmp = -x1;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if ((x2 <= (-1.55d-229)) .or. (.not. (x2 <= 2.5d-164))) then
        tmp = x2 * (-6.0d0)
    else
        tmp = -x1
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x2 <= -1.55e-229) || !(x2 <= 2.5e-164)) {
		tmp = x2 * -6.0;
	} else {
		tmp = -x1;
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x2 <= -1.55e-229) or not (x2 <= 2.5e-164):
		tmp = x2 * -6.0
	else:
		tmp = -x1
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x2 <= -1.55e-229) || !(x2 <= 2.5e-164))
		tmp = Float64(x2 * -6.0);
	else
		tmp = Float64(-x1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x2 <= -1.55e-229) || ~((x2 <= 2.5e-164)))
		tmp = x2 * -6.0;
	else
		tmp = -x1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x2, -1.55e-229], N[Not[LessEqual[x2, 2.5e-164]], $MachinePrecision]], N[(x2 * -6.0), $MachinePrecision], (-x1)]

Derivation

1. Split input into 2 regimes

2. if x2 < -1.55e-229 or 2.49999999999999981e-164 < x2

   1. Initial program 70.3%

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

   3. Taylor expanded in x1 around 0 49.9%

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

   4. Taylor expanded in x1 around 0 31.4%

      \[\leadsto x1 + \color{blue}{-6 \cdot x2} \]
   5. Step-by-step derivation

      1. *-commutative 31.4%

         \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]

   6. Simplified 31.4%

      \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]

   7. Taylor expanded in x1 around 0 31.3%

      \[\leadsto \color{blue}{-6 \cdot x2} \]
   8. Step-by-step derivation

      1. *-commutative 31.3%

         \[\leadsto \color{blue}{x2 \cdot -6} \]

   9. Simplified 31.3%

      \[\leadsto \color{blue}{x2 \cdot -6} \]

   if -1.55e-229 < x2 < 2.49999999999999981e-164

   1. Initial program 63.2%

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

   3. Taylor expanded in x1 around 0 43.7%

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

   4. Taylor expanded in x2 around 0 43.7%

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

      1. *-commutative 43.7%

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

      2. associate-*l* 43.7%

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

   6. Simplified 43.7%

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

   7. Taylor expanded in x1 around 0 44.9%

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

      1. neg-mul-1 63.2%

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

      2. unsub-neg 63.2%

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

      3. *-commutative 63.2%

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

   9. Simplified 44.9%

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

   10. Taylor expanded in x2 around 0 37.0%

       \[\leadsto \color{blue}{-3 \cdot x1 + 2 \cdot x1} \]
   11. Step-by-step derivation

       1. distribute-rgt-out 37.3%

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

       2. metadata-eval 37.3%

          \[\leadsto x1 \cdot \color{blue}{-1} \]

       3. *-commutative 37.3%

          \[\leadsto \color{blue}{-1 \cdot x1} \]

       4. mul-1-neg 37.3%

          \[\leadsto \color{blue}{-x1} \]

   12. Simplified 37.3%

       \[\leadsto \color{blue}{-x1} \]
3. Recombined 2 regimes into one program.

4. Final simplification 32.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq -1.55 \cdot 10^{-229} \lor \neg \left(x2 \leq 2.5 \cdot 10^{-164}\right):\\ \;\;\;\;x2 \cdot -6\\ \mathbf{else}:\\ \;\;\;\;-x1\\ \end{array} \]
5. Add Preprocessing

Alternative 28: 14.5% accurate, 63.5× 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 Float64(-x1)
end

MATLAB

function tmp = code(x1, x2)
	tmp = -x1;
end

Wolfram

code[x1_, x2_] := (-x1)

Derivation

1. Initial program 68.7%

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

3. Taylor expanded in x1 around 0 48.5%

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

4. Taylor expanded in x2 around 0 40.1%

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

   1. *-commutative 40.1%

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

   2. associate-*l* 40.1%

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

6. Simplified 40.1%

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

7. Taylor expanded in x1 around 0 44.1%

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

   1. neg-mul-1 68.7%

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

   2. unsub-neg 68.7%

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

   3. *-commutative 68.7%

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

9. Simplified 44.1%

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

10. Taylor expanded in x2 around 0 13.2%

    \[\leadsto \color{blue}{-3 \cdot x1 + 2 \cdot x1} \]
11. Step-by-step derivation

    1. distribute-rgt-out 13.3%

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

    2. metadata-eval 13.3%

       \[\leadsto x1 \cdot \color{blue}{-1} \]

    3. *-commutative 13.3%

       \[\leadsto \color{blue}{-1 \cdot x1} \]

    4. mul-1-neg 13.3%

       \[\leadsto \color{blue}{-x1} \]

12. Simplified 13.3%

    \[\leadsto \color{blue}{-x1} \]

13. Final simplification 13.3%

    \[\leadsto -x1 \]
14. Add Preprocessing

Alternative 29: 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 68.7%

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

3. Taylor expanded in x1 around 0 48.5%

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

4. Taylor expanded in x1 around 0 26.7%

   \[\leadsto x1 + \color{blue}{-6 \cdot x2} \]
5. Step-by-step derivation

   1. *-commutative 26.7%

      \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]

6. Simplified 26.7%

   \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]

7. Taylor expanded in x1 around inf 3.2%

   \[\leadsto \color{blue}{x1} \]

8. Final simplification 3.2%

   \[\leadsto x1 \]
9. Add Preprocessing

Reproduce

herbie shell --seed 2024066 
(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))))))