Rosa's FloatVsDoubleBenchmark

Percentage Accurate: 69.9% → 99.5%

Time: 1.3min

Alternatives: 27

Speedup: 3.3×

• 47.2% 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: 69.9% 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

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

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 (- t_4 (* 2.0 x2))) (- -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))))))
     (+ 9.0 (* x1 (+ 2.0 (* 6.0 (pow x1 3.0))))))))

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 - (t_4 - (2.0 * x2))) / (-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 = 9.0 + (x1 * (2.0 + (6.0 * pow(x1, 3.0))));
	}
	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(t_4 - Float64(2.0 * x2))) / 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(9.0 + Float64(x1 * Float64(2.0 + Float64(6.0 * (x1 ^ 3.0)))));
	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[(t$95$4 - N[(2.0 * x2), $MachinePrecision]), $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[(9.0 + N[(x1 * N[(2.0 + N[(6.0 * N[Power[x1, 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 99.3%

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

   3. Simplified 99.6%

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

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

   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 13.3%

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

   4. Taylor expanded in x1 around inf 100.0%

      \[\leadsto x1 + \left(\left(6 \cdot {x1}^{4} + x1\right) + \color{blue}{9}\right) \]

   5. Taylor expanded in x1 around 0 100.0%

      \[\leadsto \color{blue}{9 + x1 \cdot \left(2 + 6 \cdot {x1}^{3}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.7%

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

Alternative 2: 99.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot x1\right)\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := \left(t\_1 + 2 \cdot x2\right) - x1\\ t_3 := -1 - x1 \cdot x1\\ t_4 := x1 \cdot x1 + 1\\ t_5 := \frac{t\_2}{t\_3}\\ t_6 := \frac{t\_2}{t\_4}\\ t_7 := \left(x1 \cdot 2\right) \cdot t\_6\\ t_8 := 3 \cdot \frac{x1 - \left(t\_1 - 2 \cdot x2\right)}{t\_3}\\ \mathbf{if}\;x1 + \left(\left(x1 + \left(\left(t\_4 \cdot \left(t\_7 \cdot \left(t\_6 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(t\_6 \cdot 4 - 6\right)\right) + t\_1 \cdot t\_6\right) + t\_0\right)\right) + t\_8\right) \leq \infty:\\ \;\;\;\;x1 + \left(t\_8 - \left(\left(\left(t\_1 \cdot t\_5 - \left(\left(x1 \cdot x1\right) \cdot \left(6 - 4 \cdot \frac{1}{\frac{\mathsf{fma}\left(x1, x1, 1\right)}{\mathsf{fma}\left(3, {x1}^{2}, 2 \cdot x2 - x1\right)}}\right) + t\_7 \cdot \left(3 + t\_5\right)\right) \cdot t\_3\right) - t\_0\right) - x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;9 + x1 \cdot \left(2 + 6 \cdot {x1}^{3}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 x1)))
        (t_1 (* x1 (* x1 3.0)))
        (t_2 (- (+ t_1 (* 2.0 x2)) x1))
        (t_3 (- -1.0 (* x1 x1)))
        (t_4 (+ (* x1 x1) 1.0))
        (t_5 (/ t_2 t_3))
        (t_6 (/ t_2 t_4))
        (t_7 (* (* x1 2.0) t_6))
        (t_8 (* 3.0 (/ (- x1 (- t_1 (* 2.0 x2))) t_3))))
   (if (<=
        (+
         x1
         (+
          (+
           x1
           (+
            (+
             (* t_4 (+ (* t_7 (- t_6 3.0)) (* (* x1 x1) (- (* t_6 4.0) 6.0))))
             (* t_1 t_6))
            t_0))
          t_8))
        INFINITY)
     (+
      x1
      (-
       t_8
       (-
        (-
         (-
          (* t_1 t_5)
          (*
           (+
            (*
             (* x1 x1)
             (-
              6.0
              (*
               4.0
               (/
                1.0
                (/
                 (fma x1 x1 1.0)
                 (fma 3.0 (pow x1 2.0) (- (* 2.0 x2) x1)))))))
            (* t_7 (+ 3.0 t_5)))
           t_3))
         t_0)
        x1)))
     (+ 9.0 (* x1 (+ 2.0 (* 6.0 (pow x1 3.0))))))))

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_3;
	double t_6 = t_2 / t_4;
	double t_7 = (x1 * 2.0) * t_6;
	double t_8 = 3.0 * ((x1 - (t_1 - (2.0 * x2))) / t_3);
	double tmp;
	if ((x1 + ((x1 + (((t_4 * ((t_7 * (t_6 - 3.0)) + ((x1 * x1) * ((t_6 * 4.0) - 6.0)))) + (t_1 * t_6)) + t_0)) + t_8)) <= ((double) INFINITY)) {
		tmp = x1 + (t_8 - ((((t_1 * t_5) - ((((x1 * x1) * (6.0 - (4.0 * (1.0 / (fma(x1, x1, 1.0) / fma(3.0, pow(x1, 2.0), ((2.0 * x2) - x1))))))) + (t_7 * (3.0 + t_5))) * t_3)) - t_0) - x1));
	} else {
		tmp = 9.0 + (x1 * (2.0 + (6.0 * pow(x1, 3.0))));
	}
	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_3)
	t_6 = Float64(t_2 / t_4)
	t_7 = Float64(Float64(x1 * 2.0) * t_6)
	t_8 = Float64(3.0 * Float64(Float64(x1 - Float64(t_1 - Float64(2.0 * x2))) / t_3))
	tmp = 0.0
	if (Float64(x1 + Float64(Float64(x1 + Float64(Float64(Float64(t_4 * Float64(Float64(t_7 * Float64(t_6 - 3.0)) + Float64(Float64(x1 * x1) * Float64(Float64(t_6 * 4.0) - 6.0)))) + Float64(t_1 * t_6)) + t_0)) + t_8)) <= Inf)
		tmp = Float64(x1 + Float64(t_8 - Float64(Float64(Float64(Float64(t_1 * t_5) - Float64(Float64(Float64(Float64(x1 * x1) * Float64(6.0 - Float64(4.0 * Float64(1.0 / Float64(fma(x1, x1, 1.0) / fma(3.0, (x1 ^ 2.0), Float64(Float64(2.0 * x2) - x1))))))) + Float64(t_7 * Float64(3.0 + t_5))) * t_3)) - t_0) - x1)));
	else
		tmp = Float64(9.0 + Float64(x1 * Float64(2.0 + Float64(6.0 * (x1 ^ 3.0)))));
	end
	return tmp
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(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$3), $MachinePrecision]}, Block[{t$95$6 = N[(t$95$2 / t$95$4), $MachinePrecision]}, Block[{t$95$7 = N[(N[(x1 * 2.0), $MachinePrecision] * t$95$6), $MachinePrecision]}, Block[{t$95$8 = N[(3.0 * N[(N[(x1 - N[(t$95$1 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$3), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x1 + N[(N[(x1 + N[(N[(N[(t$95$4 * N[(N[(t$95$7 * N[(t$95$6 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$6 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$1 * t$95$6), $MachinePrecision]), $MachinePrecision] + t$95$0), $MachinePrecision]), $MachinePrecision] + t$95$8), $MachinePrecision]), $MachinePrecision], Infinity], N[(x1 + N[(t$95$8 - N[(N[(N[(N[(t$95$1 * t$95$5), $MachinePrecision] - N[(N[(N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 - N[(4.0 * N[(1.0 / N[(N[(x1 * x1 + 1.0), $MachinePrecision] / N[(3.0 * N[Power[x1, 2.0], $MachinePrecision] + N[(N[(2.0 * x2), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$7 * N[(3.0 + t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * t$95$3), $MachinePrecision]), $MachinePrecision] - t$95$0), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(9.0 + N[(x1 * N[(2.0 + N[(6.0 * N[Power[x1, 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 2 regimes

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

   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. Step-by-step derivation

      1. fma-define 99.3%

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

      2. *-commutative 99.3%

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

      3. fma-define 99.3%

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

      4. clear-num 99.3%

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

      5. inv-pow 99.3%

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

      6. *-commutative 99.3%

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

      7. fma-define 99.3%

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

      8. associate--l+ 99.3%

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

      9. associate-*r* 99.3%

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

      10. fma-define 99.4%

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

      11. pow2 99.4%

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

   4. Applied egg-rr 99.4%

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

      1. unpow-1 99.4%

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

   6. Simplified 99.4%

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

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

   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 13.3%

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

   4. Taylor expanded in x1 around inf 100.0%

      \[\leadsto x1 + \left(\left(6 \cdot {x1}^{4} + x1\right) + \color{blue}{9}\right) \]

   5. Taylor expanded in x1 around 0 100.0%

      \[\leadsto \color{blue}{9 + x1 \cdot \left(2 + 6 \cdot {x1}^{3}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.5%

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

Alternative 3: 99.3% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 x1)))
        (t_1 (* x1 (* x1 3.0)))
        (t_2 (- -1.0 (* x1 x1)))
        (t_3 (+ (* x1 x1) 1.0))
        (t_4 (/ (- (+ t_1 (* 2.0 x2)) x1) t_3))
        (t_5
         (+
          (* (* (* x1 2.0) t_4) (- t_4 3.0))
          (* (* x1 x1) (- (* t_4 4.0) 6.0)))))
   (if (<=
        (+
         x1
         (+
          (+ x1 (+ (+ (* t_3 t_5) (* t_1 t_4)) t_0))
          (* 3.0 (/ (- x1 (- t_1 (* 2.0 x2))) t_2))))
        INFINITY)
     (+
      x1
      (+
       (+ x1 (- t_0 (- (* t_5 t_2) (* 3.0 t_1))))
       (+ (* x2 -6.0) (* x1 -3.0))))
     (+ 9.0 (* x1 (+ 2.0 (* 6.0 (pow x1 3.0))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * x1);
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = -1.0 - (x1 * x1);
	double t_3 = (x1 * x1) + 1.0;
	double t_4 = ((t_1 + (2.0 * x2)) - x1) / t_3;
	double t_5 = (((x1 * 2.0) * t_4) * (t_4 - 3.0)) + ((x1 * x1) * ((t_4 * 4.0) - 6.0));
	double tmp;
	if ((x1 + ((x1 + (((t_3 * t_5) + (t_1 * t_4)) + t_0)) + (3.0 * ((x1 - (t_1 - (2.0 * x2))) / t_2)))) <= ((double) INFINITY)) {
		tmp = x1 + ((x1 + (t_0 - ((t_5 * t_2) - (3.0 * t_1)))) + ((x2 * -6.0) + (x1 * -3.0)));
	} else {
		tmp = 9.0 + (x1 * (2.0 + (6.0 * pow(x1, 3.0))));
	}
	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 = -1.0 - (x1 * x1);
	double t_3 = (x1 * x1) + 1.0;
	double t_4 = ((t_1 + (2.0 * x2)) - x1) / t_3;
	double t_5 = (((x1 * 2.0) * t_4) * (t_4 - 3.0)) + ((x1 * x1) * ((t_4 * 4.0) - 6.0));
	double tmp;
	if ((x1 + ((x1 + (((t_3 * t_5) + (t_1 * t_4)) + t_0)) + (3.0 * ((x1 - (t_1 - (2.0 * x2))) / t_2)))) <= Double.POSITIVE_INFINITY) {
		tmp = x1 + ((x1 + (t_0 - ((t_5 * t_2) - (3.0 * t_1)))) + ((x2 * -6.0) + (x1 * -3.0)));
	} else {
		tmp = 9.0 + (x1 * (2.0 + (6.0 * Math.pow(x1, 3.0))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * x1)
	t_1 = x1 * (x1 * 3.0)
	t_2 = -1.0 - (x1 * x1)
	t_3 = (x1 * x1) + 1.0
	t_4 = ((t_1 + (2.0 * x2)) - x1) / t_3
	t_5 = (((x1 * 2.0) * t_4) * (t_4 - 3.0)) + ((x1 * x1) * ((t_4 * 4.0) - 6.0))
	tmp = 0
	if (x1 + ((x1 + (((t_3 * t_5) + (t_1 * t_4)) + t_0)) + (3.0 * ((x1 - (t_1 - (2.0 * x2))) / t_2)))) <= math.inf:
		tmp = x1 + ((x1 + (t_0 - ((t_5 * t_2) - (3.0 * t_1)))) + ((x2 * -6.0) + (x1 * -3.0)))
	else:
		tmp = 9.0 + (x1 * (2.0 + (6.0 * math.pow(x1, 3.0))))
	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(-1.0 - Float64(x1 * x1))
	t_3 = Float64(Float64(x1 * x1) + 1.0)
	t_4 = Float64(Float64(Float64(t_1 + Float64(2.0 * x2)) - x1) / t_3)
	t_5 = Float64(Float64(Float64(Float64(x1 * 2.0) * t_4) * Float64(t_4 - 3.0)) + Float64(Float64(x1 * x1) * Float64(Float64(t_4 * 4.0) - 6.0)))
	tmp = 0.0
	if (Float64(x1 + Float64(Float64(x1 + Float64(Float64(Float64(t_3 * t_5) + Float64(t_1 * t_4)) + t_0)) + Float64(3.0 * Float64(Float64(x1 - Float64(t_1 - Float64(2.0 * x2))) / t_2)))) <= Inf)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(t_0 - Float64(Float64(t_5 * t_2) - Float64(3.0 * t_1)))) + Float64(Float64(x2 * -6.0) + Float64(x1 * -3.0))));
	else
		tmp = Float64(9.0 + Float64(x1 * Float64(2.0 + Float64(6.0 * (x1 ^ 3.0)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * x1);
	t_1 = x1 * (x1 * 3.0);
	t_2 = -1.0 - (x1 * x1);
	t_3 = (x1 * x1) + 1.0;
	t_4 = ((t_1 + (2.0 * x2)) - x1) / t_3;
	t_5 = (((x1 * 2.0) * t_4) * (t_4 - 3.0)) + ((x1 * x1) * ((t_4 * 4.0) - 6.0));
	tmp = 0.0;
	if ((x1 + ((x1 + (((t_3 * t_5) + (t_1 * t_4)) + t_0)) + (3.0 * ((x1 - (t_1 - (2.0 * x2))) / t_2)))) <= Inf)
		tmp = x1 + ((x1 + (t_0 - ((t_5 * t_2) - (3.0 * t_1)))) + ((x2 * -6.0) + (x1 * -3.0)));
	else
		tmp = 9.0 + (x1 * (2.0 + (6.0 * (x1 ^ 3.0))));
	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[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(t$95$1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$3), $MachinePrecision]}, Block[{t$95$5 = N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$4), $MachinePrecision] * N[(t$95$4 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$4 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x1 + N[(N[(x1 + N[(N[(N[(t$95$3 * t$95$5), $MachinePrecision] + N[(t$95$1 * t$95$4), $MachinePrecision]), $MachinePrecision] + t$95$0), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(N[(x1 - N[(t$95$1 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(x1 + N[(N[(x1 + N[(t$95$0 - N[(N[(t$95$5 * t$95$2), $MachinePrecision] - N[(3.0 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(9.0 + N[(x1 * N[(2.0 + N[(6.0 * N[Power[x1, 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 2 regimes

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

   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 98.1%

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

   4. Taylor expanded in x1 around 0 99.3%

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

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

   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 13.3%

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

   4. Taylor expanded in x1 around inf 100.0%

      \[\leadsto x1 + \left(\left(6 \cdot {x1}^{4} + x1\right) + \color{blue}{9}\right) \]

   5. Taylor expanded in x1 around 0 100.0%

      \[\leadsto \color{blue}{9 + x1 \cdot \left(2 + 6 \cdot {x1}^{3}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.5%

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

Alternative 4: 92.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 3 - 2 \cdot x2\\ t_1 := 2 \cdot x2 - 3\\ t_2 := x1 \cdot \left(x1 \cdot x1\right)\\ t_3 := x1 \cdot \left(x1 \cdot 3\right)\\ t_4 := \left(t\_3 + 2 \cdot x2\right) - x1\\ t_5 := x1 \cdot x1 + 1\\ t_6 := \frac{t\_4}{t\_5}\\ t_7 := 3 \cdot t\_3\\ t_8 := \left(x1 \cdot 2\right) \cdot t\_6\\ t_9 := 4 \cdot \left(x2 \cdot t\_0\right)\\ t_10 := -1 - x1 \cdot x1\\ t_11 := x1 + \left(9 + \left(x1 + \left(t\_2 + \left(t\_7 - t\_5 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \left(\frac{1 + \frac{t\_0}{x1}}{x1} - 3\right)\right) + t\_8 \cdot \left(3 + \frac{t\_4}{t\_10}\right)\right)\right)\right)\right)\right)\\ \mathbf{if}\;x1 \leq -1.15 \cdot 10^{+110}:\\ \;\;\;\;x1 + \left(9 + \left(x1 - x1 \cdot \left(x1 \cdot \left(\left(2 \cdot \left(t\_1 - x2 \cdot -2\right) - \left(x2 \cdot 8 - x1 \cdot \left(3 + \left(t\_9 + 2 \cdot \left(2 \cdot \left(x2 \cdot t\_1\right) + \left(-1 - \left(2 \cdot \left(x2 \cdot \left(3 + x2 \cdot -2\right)\right) + 3 \cdot t\_1\right)\right)\right)\right)\right)\right)\right) - 3\right) + t\_9\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -0.36:\\ \;\;\;\;t\_11\\ \mathbf{elif}\;x1 \leq 0.025:\\ \;\;\;\;x1 + \left(\left(x2 \cdot -6 + x1 \cdot -3\right) + \left(x1 + \left(t\_2 + \left(t\_7 + \left(t\_8 \cdot \left(3 + \left(x1 - 2 \cdot x2\right)\right) - \left(x1 \cdot x1\right) \cdot \left(t\_6 \cdot 4 - 6\right)\right) \cdot t\_10\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.5 \cdot 10^{+97}:\\ \;\;\;\;t\_11\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 + \left(x1 \cdot \left(3 \cdot \left(x2 \cdot -2 - 3\right) - x1 \cdot 3\right) + t\_9\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (- 3.0 (* 2.0 x2)))
        (t_1 (- (* 2.0 x2) 3.0))
        (t_2 (* x1 (* x1 x1)))
        (t_3 (* x1 (* x1 3.0)))
        (t_4 (- (+ t_3 (* 2.0 x2)) x1))
        (t_5 (+ (* x1 x1) 1.0))
        (t_6 (/ t_4 t_5))
        (t_7 (* 3.0 t_3))
        (t_8 (* (* x1 2.0) t_6))
        (t_9 (* 4.0 (* x2 t_0)))
        (t_10 (- -1.0 (* x1 x1)))
        (t_11
         (+
          x1
          (+
           9.0
           (+
            x1
            (+
             t_2
             (-
              t_7
              (*
               t_5
               (+
                (* (* x1 x1) (+ 6.0 (* 4.0 (- (/ (+ 1.0 (/ t_0 x1)) x1) 3.0))))
                (* t_8 (+ 3.0 (/ t_4 t_10))))))))))))
   (if (<= x1 -1.15e+110)
     (+
      x1
      (+
       9.0
       (-
        x1
        (*
         x1
         (+
          (*
           x1
           (-
            (-
             (* 2.0 (- t_1 (* x2 -2.0)))
             (-
              (* x2 8.0)
              (*
               x1
               (+
                3.0
                (+
                 t_9
                 (*
                  2.0
                  (+
                   (* 2.0 (* x2 t_1))
                   (-
                    -1.0
                    (+ (* 2.0 (* x2 (+ 3.0 (* x2 -2.0)))) (* 3.0 t_1))))))))))
            3.0))
          t_9)))))
     (if (<= x1 -0.36)
       t_11
       (if (<= x1 0.025)
         (+
          x1
          (+
           (+ (* x2 -6.0) (* x1 -3.0))
           (+
            x1
            (+
             t_2
             (+
              t_7
              (*
               (-
                (* t_8 (+ 3.0 (- x1 (* 2.0 x2))))
                (* (* x1 x1) (- (* t_6 4.0) 6.0)))
               t_10))))))
         (if (<= x1 1.5e+97)
           t_11
           (+
            x1
            (-
             (* x2 -6.0)
             (*
              x1
              (+
               2.0
               (+
                (* x1 (- (* 3.0 (- (* x2 -2.0) 3.0)) (* x1 3.0)))
                t_9)))))))))))

C

double code(double x1, double x2) {
	double t_0 = 3.0 - (2.0 * x2);
	double t_1 = (2.0 * x2) - 3.0;
	double t_2 = x1 * (x1 * x1);
	double t_3 = x1 * (x1 * 3.0);
	double t_4 = (t_3 + (2.0 * x2)) - x1;
	double t_5 = (x1 * x1) + 1.0;
	double t_6 = t_4 / t_5;
	double t_7 = 3.0 * t_3;
	double t_8 = (x1 * 2.0) * t_6;
	double t_9 = 4.0 * (x2 * t_0);
	double t_10 = -1.0 - (x1 * x1);
	double t_11 = x1 + (9.0 + (x1 + (t_2 + (t_7 - (t_5 * (((x1 * x1) * (6.0 + (4.0 * (((1.0 + (t_0 / x1)) / x1) - 3.0)))) + (t_8 * (3.0 + (t_4 / t_10)))))))));
	double tmp;
	if (x1 <= -1.15e+110) {
		tmp = x1 + (9.0 + (x1 - (x1 * ((x1 * (((2.0 * (t_1 - (x2 * -2.0))) - ((x2 * 8.0) - (x1 * (3.0 + (t_9 + (2.0 * ((2.0 * (x2 * t_1)) + (-1.0 - ((2.0 * (x2 * (3.0 + (x2 * -2.0)))) + (3.0 * t_1)))))))))) - 3.0)) + t_9))));
	} else if (x1 <= -0.36) {
		tmp = t_11;
	} else if (x1 <= 0.025) {
		tmp = x1 + (((x2 * -6.0) + (x1 * -3.0)) + (x1 + (t_2 + (t_7 + (((t_8 * (3.0 + (x1 - (2.0 * x2)))) - ((x1 * x1) * ((t_6 * 4.0) - 6.0))) * t_10)))));
	} else if (x1 <= 1.5e+97) {
		tmp = t_11;
	} else {
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - (x1 * 3.0))) + t_9))));
	}
	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_10
    real(8) :: t_11
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: t_8
    real(8) :: t_9
    real(8) :: tmp
    t_0 = 3.0d0 - (2.0d0 * x2)
    t_1 = (2.0d0 * x2) - 3.0d0
    t_2 = x1 * (x1 * x1)
    t_3 = x1 * (x1 * 3.0d0)
    t_4 = (t_3 + (2.0d0 * x2)) - x1
    t_5 = (x1 * x1) + 1.0d0
    t_6 = t_4 / t_5
    t_7 = 3.0d0 * t_3
    t_8 = (x1 * 2.0d0) * t_6
    t_9 = 4.0d0 * (x2 * t_0)
    t_10 = (-1.0d0) - (x1 * x1)
    t_11 = x1 + (9.0d0 + (x1 + (t_2 + (t_7 - (t_5 * (((x1 * x1) * (6.0d0 + (4.0d0 * (((1.0d0 + (t_0 / x1)) / x1) - 3.0d0)))) + (t_8 * (3.0d0 + (t_4 / t_10)))))))))
    if (x1 <= (-1.15d+110)) then
        tmp = x1 + (9.0d0 + (x1 - (x1 * ((x1 * (((2.0d0 * (t_1 - (x2 * (-2.0d0)))) - ((x2 * 8.0d0) - (x1 * (3.0d0 + (t_9 + (2.0d0 * ((2.0d0 * (x2 * t_1)) + ((-1.0d0) - ((2.0d0 * (x2 * (3.0d0 + (x2 * (-2.0d0))))) + (3.0d0 * t_1)))))))))) - 3.0d0)) + t_9))))
    else if (x1 <= (-0.36d0)) then
        tmp = t_11
    else if (x1 <= 0.025d0) then
        tmp = x1 + (((x2 * (-6.0d0)) + (x1 * (-3.0d0))) + (x1 + (t_2 + (t_7 + (((t_8 * (3.0d0 + (x1 - (2.0d0 * x2)))) - ((x1 * x1) * ((t_6 * 4.0d0) - 6.0d0))) * t_10)))))
    else if (x1 <= 1.5d+97) then
        tmp = t_11
    else
        tmp = x1 + ((x2 * (-6.0d0)) - (x1 * (2.0d0 + ((x1 * ((3.0d0 * ((x2 * (-2.0d0)) - 3.0d0)) - (x1 * 3.0d0))) + t_9))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = 3.0 - (2.0 * x2);
	double t_1 = (2.0 * x2) - 3.0;
	double t_2 = x1 * (x1 * x1);
	double t_3 = x1 * (x1 * 3.0);
	double t_4 = (t_3 + (2.0 * x2)) - x1;
	double t_5 = (x1 * x1) + 1.0;
	double t_6 = t_4 / t_5;
	double t_7 = 3.0 * t_3;
	double t_8 = (x1 * 2.0) * t_6;
	double t_9 = 4.0 * (x2 * t_0);
	double t_10 = -1.0 - (x1 * x1);
	double t_11 = x1 + (9.0 + (x1 + (t_2 + (t_7 - (t_5 * (((x1 * x1) * (6.0 + (4.0 * (((1.0 + (t_0 / x1)) / x1) - 3.0)))) + (t_8 * (3.0 + (t_4 / t_10)))))))));
	double tmp;
	if (x1 <= -1.15e+110) {
		tmp = x1 + (9.0 + (x1 - (x1 * ((x1 * (((2.0 * (t_1 - (x2 * -2.0))) - ((x2 * 8.0) - (x1 * (3.0 + (t_9 + (2.0 * ((2.0 * (x2 * t_1)) + (-1.0 - ((2.0 * (x2 * (3.0 + (x2 * -2.0)))) + (3.0 * t_1)))))))))) - 3.0)) + t_9))));
	} else if (x1 <= -0.36) {
		tmp = t_11;
	} else if (x1 <= 0.025) {
		tmp = x1 + (((x2 * -6.0) + (x1 * -3.0)) + (x1 + (t_2 + (t_7 + (((t_8 * (3.0 + (x1 - (2.0 * x2)))) - ((x1 * x1) * ((t_6 * 4.0) - 6.0))) * t_10)))));
	} else if (x1 <= 1.5e+97) {
		tmp = t_11;
	} else {
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - (x1 * 3.0))) + t_9))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = 3.0 - (2.0 * x2)
	t_1 = (2.0 * x2) - 3.0
	t_2 = x1 * (x1 * x1)
	t_3 = x1 * (x1 * 3.0)
	t_4 = (t_3 + (2.0 * x2)) - x1
	t_5 = (x1 * x1) + 1.0
	t_6 = t_4 / t_5
	t_7 = 3.0 * t_3
	t_8 = (x1 * 2.0) * t_6
	t_9 = 4.0 * (x2 * t_0)
	t_10 = -1.0 - (x1 * x1)
	t_11 = x1 + (9.0 + (x1 + (t_2 + (t_7 - (t_5 * (((x1 * x1) * (6.0 + (4.0 * (((1.0 + (t_0 / x1)) / x1) - 3.0)))) + (t_8 * (3.0 + (t_4 / t_10)))))))))
	tmp = 0
	if x1 <= -1.15e+110:
		tmp = x1 + (9.0 + (x1 - (x1 * ((x1 * (((2.0 * (t_1 - (x2 * -2.0))) - ((x2 * 8.0) - (x1 * (3.0 + (t_9 + (2.0 * ((2.0 * (x2 * t_1)) + (-1.0 - ((2.0 * (x2 * (3.0 + (x2 * -2.0)))) + (3.0 * t_1)))))))))) - 3.0)) + t_9))))
	elif x1 <= -0.36:
		tmp = t_11
	elif x1 <= 0.025:
		tmp = x1 + (((x2 * -6.0) + (x1 * -3.0)) + (x1 + (t_2 + (t_7 + (((t_8 * (3.0 + (x1 - (2.0 * x2)))) - ((x1 * x1) * ((t_6 * 4.0) - 6.0))) * t_10)))))
	elif x1 <= 1.5e+97:
		tmp = t_11
	else:
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - (x1 * 3.0))) + t_9))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(3.0 - Float64(2.0 * x2))
	t_1 = Float64(Float64(2.0 * x2) - 3.0)
	t_2 = Float64(x1 * Float64(x1 * x1))
	t_3 = Float64(x1 * Float64(x1 * 3.0))
	t_4 = Float64(Float64(t_3 + Float64(2.0 * x2)) - x1)
	t_5 = Float64(Float64(x1 * x1) + 1.0)
	t_6 = Float64(t_4 / t_5)
	t_7 = Float64(3.0 * t_3)
	t_8 = Float64(Float64(x1 * 2.0) * t_6)
	t_9 = Float64(4.0 * Float64(x2 * t_0))
	t_10 = Float64(-1.0 - Float64(x1 * x1))
	t_11 = Float64(x1 + Float64(9.0 + Float64(x1 + Float64(t_2 + Float64(t_7 - Float64(t_5 * Float64(Float64(Float64(x1 * x1) * Float64(6.0 + Float64(4.0 * Float64(Float64(Float64(1.0 + Float64(t_0 / x1)) / x1) - 3.0)))) + Float64(t_8 * Float64(3.0 + Float64(t_4 / t_10))))))))))
	tmp = 0.0
	if (x1 <= -1.15e+110)
		tmp = Float64(x1 + Float64(9.0 + Float64(x1 - Float64(x1 * Float64(Float64(x1 * Float64(Float64(Float64(2.0 * Float64(t_1 - Float64(x2 * -2.0))) - Float64(Float64(x2 * 8.0) - Float64(x1 * Float64(3.0 + Float64(t_9 + Float64(2.0 * Float64(Float64(2.0 * Float64(x2 * t_1)) + Float64(-1.0 - Float64(Float64(2.0 * Float64(x2 * Float64(3.0 + Float64(x2 * -2.0)))) + Float64(3.0 * t_1)))))))))) - 3.0)) + t_9)))));
	elseif (x1 <= -0.36)
		tmp = t_11;
	elseif (x1 <= 0.025)
		tmp = Float64(x1 + Float64(Float64(Float64(x2 * -6.0) + Float64(x1 * -3.0)) + Float64(x1 + Float64(t_2 + Float64(t_7 + Float64(Float64(Float64(t_8 * Float64(3.0 + Float64(x1 - Float64(2.0 * x2)))) - Float64(Float64(x1 * x1) * Float64(Float64(t_6 * 4.0) - 6.0))) * t_10))))));
	elseif (x1 <= 1.5e+97)
		tmp = t_11;
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) - Float64(x1 * Float64(2.0 + Float64(Float64(x1 * Float64(Float64(3.0 * Float64(Float64(x2 * -2.0) - 3.0)) - Float64(x1 * 3.0))) + t_9)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = 3.0 - (2.0 * x2);
	t_1 = (2.0 * x2) - 3.0;
	t_2 = x1 * (x1 * x1);
	t_3 = x1 * (x1 * 3.0);
	t_4 = (t_3 + (2.0 * x2)) - x1;
	t_5 = (x1 * x1) + 1.0;
	t_6 = t_4 / t_5;
	t_7 = 3.0 * t_3;
	t_8 = (x1 * 2.0) * t_6;
	t_9 = 4.0 * (x2 * t_0);
	t_10 = -1.0 - (x1 * x1);
	t_11 = x1 + (9.0 + (x1 + (t_2 + (t_7 - (t_5 * (((x1 * x1) * (6.0 + (4.0 * (((1.0 + (t_0 / x1)) / x1) - 3.0)))) + (t_8 * (3.0 + (t_4 / t_10)))))))));
	tmp = 0.0;
	if (x1 <= -1.15e+110)
		tmp = x1 + (9.0 + (x1 - (x1 * ((x1 * (((2.0 * (t_1 - (x2 * -2.0))) - ((x2 * 8.0) - (x1 * (3.0 + (t_9 + (2.0 * ((2.0 * (x2 * t_1)) + (-1.0 - ((2.0 * (x2 * (3.0 + (x2 * -2.0)))) + (3.0 * t_1)))))))))) - 3.0)) + t_9))));
	elseif (x1 <= -0.36)
		tmp = t_11;
	elseif (x1 <= 0.025)
		tmp = x1 + (((x2 * -6.0) + (x1 * -3.0)) + (x1 + (t_2 + (t_7 + (((t_8 * (3.0 + (x1 - (2.0 * x2)))) - ((x1 * x1) * ((t_6 * 4.0) - 6.0))) * t_10)))));
	elseif (x1 <= 1.5e+97)
		tmp = t_11;
	else
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - (x1 * 3.0))) + t_9))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]}, Block[{t$95$2 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(t$95$3 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]}, Block[{t$95$5 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$6 = N[(t$95$4 / t$95$5), $MachinePrecision]}, Block[{t$95$7 = N[(3.0 * t$95$3), $MachinePrecision]}, Block[{t$95$8 = N[(N[(x1 * 2.0), $MachinePrecision] * t$95$6), $MachinePrecision]}, Block[{t$95$9 = N[(4.0 * N[(x2 * t$95$0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$10 = N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$11 = N[(x1 + N[(9.0 + N[(x1 + N[(t$95$2 + N[(t$95$7 - N[(t$95$5 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 + N[(4.0 * N[(N[(N[(1.0 + N[(t$95$0 / x1), $MachinePrecision]), $MachinePrecision] / x1), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$8 * N[(3.0 + N[(t$95$4 / t$95$10), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -1.15e+110], N[(x1 + N[(9.0 + 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[(x2 * 8.0), $MachinePrecision] - N[(x1 * N[(3.0 + N[(t$95$9 + N[(2.0 * N[(N[(2.0 * N[(x2 * t$95$1), $MachinePrecision]), $MachinePrecision] + 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]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision] + t$95$9), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -0.36], t$95$11, If[LessEqual[x1, 0.025], N[(x1 + N[(N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * -3.0), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(t$95$2 + N[(t$95$7 + N[(N[(N[(t$95$8 * N[(3.0 + 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] * t$95$10), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.5e+97], t$95$11, N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] - 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$9), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -1.15e110

   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 inf 0.0%

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

   5. Taylor expanded in x1 around 0 75.0%

      \[\leadsto x1 + \left(\left(\color{blue}{x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(3 + \left(2 \cdot \left(-2 \cdot x2 + -1 \cdot \left(2 \cdot x2 - 3\right)\right) + \left(8 \cdot x2 + x1 \cdot \left(\left(2 \cdot \left(\left(1 + \left(2 \cdot \left(x2 \cdot \left(3 + -2 \cdot x2\right)\right) + 3 \cdot \left(2 \cdot x2 - 3\right)\right)\right) - 2 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) - 3\right)\right)\right)\right)\right)} + x1\right) + 9\right) \]

   if -1.15e110 < x1 < -0.35999999999999999 or 0.025000000000000001 < x1 < 1.4999999999999999e97

   1. Initial program 94.7%

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

   3. Taylor expanded in x1 around inf 93.1%

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

   4. Taylor expanded in x1 around inf 93.1%

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

   5. Taylor expanded in x1 around -inf 93.6%

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

   if -0.35999999999999999 < x1 < 0.025000000000000001

   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 98.2%

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

   4. Taylor expanded in x1 around 0 99.4%

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

   5. Taylor expanded in x1 around 0 99.1%

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

      1. +-commutative 99.1%

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

      2. mul-1-neg 99.1%

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

      3. sub-neg 99.1%

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

   7. Simplified 99.1%

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

   if 1.4999999999999999e97 < x1

   1. Initial program 19.6%

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

   3. Taylor expanded in x1 around 0 13.4%

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

   4. Taylor expanded in x1 around 0 100.0%

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

4. Final simplification 94.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.15 \cdot 10^{+110}:\\ \;\;\;\;x1 + \left(9 + \left(x1 - x1 \cdot \left(x1 \cdot \left(\left(2 \cdot \left(\left(2 \cdot x2 - 3\right) - x2 \cdot -2\right) - \left(x2 \cdot 8 - x1 \cdot \left(3 + \left(4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right) + 2 \cdot \left(2 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + \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)\right)\right)\right)\right)\right) - 3\right) + 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -0.36:\\ \;\;\;\;x1 + \left(9 + \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(6 + 4 \cdot \left(\frac{1 + \frac{3 - 2 \cdot x2}{x1}}{x1} - 3\right)\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(3 + \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1}\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 0.025:\\ \;\;\;\;x1 + \left(\left(x2 \cdot -6 + x1 \cdot -3\right) + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) + \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 + \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) \cdot \left(-1 - x1 \cdot x1\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.5 \cdot 10^{+97}:\\ \;\;\;\;x1 + \left(9 + \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(6 + 4 \cdot \left(\frac{1 + \frac{3 - 2 \cdot x2}{x1}}{x1} - 3\right)\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(3 + \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1}\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - 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)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 93.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 2 \cdot x2 - 3\\ t_1 := 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\\ t_2 := x1 \cdot \left(x1 \cdot 3\right)\\ t_3 := \frac{\left(t\_2 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\\ \mathbf{if}\;x1 \leq -1.15 \cdot 10^{+110}:\\ \;\;\;\;x1 + \left(9 + \left(x1 - x1 \cdot \left(x1 \cdot \left(\left(2 \cdot \left(t\_0 - x2 \cdot -2\right) - \left(x2 \cdot 8 - x1 \cdot \left(3 + \left(t\_1 + 2 \cdot \left(2 \cdot \left(x2 \cdot t\_0\right) + \left(-1 - \left(2 \cdot \left(x2 \cdot \left(3 + x2 \cdot -2\right)\right) + 3 \cdot t\_0\right)\right)\right)\right)\right)\right)\right) - 3\right) + t\_1\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.5 \cdot 10^{+97}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) - \left(\left(\left(\left(x1 \cdot 2\right) \cdot t\_3\right) \cdot \left(t\_3 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(t\_3 \cdot 4 - 6\right)\right) \cdot \left(-1 - x1 \cdot x1\right) - 3 \cdot t\_2\right)\right)\right) + \left(x2 \cdot -6 + x1 \cdot -3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 + \left(x1 \cdot \left(3 \cdot \left(x2 \cdot -2 - 3\right) - x1 \cdot 3\right) + t\_1\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (- (* 2.0 x2) 3.0))
        (t_1 (* 4.0 (* x2 (- 3.0 (* 2.0 x2)))))
        (t_2 (* x1 (* x1 3.0)))
        (t_3 (/ (- (+ t_2 (* 2.0 x2)) x1) (+ (* x1 x1) 1.0))))
   (if (<= x1 -1.15e+110)
     (+
      x1
      (+
       9.0
       (-
        x1
        (*
         x1
         (+
          (*
           x1
           (-
            (-
             (* 2.0 (- t_0 (* x2 -2.0)))
             (-
              (* x2 8.0)
              (*
               x1
               (+
                3.0
                (+
                 t_1
                 (*
                  2.0
                  (+
                   (* 2.0 (* x2 t_0))
                   (-
                    -1.0
                    (+ (* 2.0 (* x2 (+ 3.0 (* x2 -2.0)))) (* 3.0 t_0))))))))))
            3.0))
          t_1)))))
     (if (<= x1 1.5e+97)
       (+
        x1
        (+
         (+
          x1
          (-
           (* x1 (* x1 x1))
           (-
            (*
             (+
              (* (* (* x1 2.0) t_3) (- t_3 3.0))
              (* (* x1 x1) (- (* t_3 4.0) 6.0)))
             (- -1.0 (* x1 x1)))
            (* 3.0 t_2))))
         (+ (* x2 -6.0) (* x1 -3.0))))
       (+
        x1
        (-
         (* x2 -6.0)
         (*
          x1
          (+
           2.0
           (+ (* x1 (- (* 3.0 (- (* x2 -2.0) 3.0)) (* x1 3.0))) t_1)))))))))

C

double code(double x1, double x2) {
	double t_0 = (2.0 * x2) - 3.0;
	double t_1 = 4.0 * (x2 * (3.0 - (2.0 * x2)));
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = ((t_2 + (2.0 * x2)) - x1) / ((x1 * x1) + 1.0);
	double tmp;
	if (x1 <= -1.15e+110) {
		tmp = x1 + (9.0 + (x1 - (x1 * ((x1 * (((2.0 * (t_0 - (x2 * -2.0))) - ((x2 * 8.0) - (x1 * (3.0 + (t_1 + (2.0 * ((2.0 * (x2 * t_0)) + (-1.0 - ((2.0 * (x2 * (3.0 + (x2 * -2.0)))) + (3.0 * t_0)))))))))) - 3.0)) + t_1))));
	} else if (x1 <= 1.5e+97) {
		tmp = x1 + ((x1 + ((x1 * (x1 * x1)) - ((((((x1 * 2.0) * t_3) * (t_3 - 3.0)) + ((x1 * x1) * ((t_3 * 4.0) - 6.0))) * (-1.0 - (x1 * x1))) - (3.0 * t_2)))) + ((x2 * -6.0) + (x1 * -3.0)));
	} else {
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - (x1 * 3.0))) + 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) :: t_3
    real(8) :: tmp
    t_0 = (2.0d0 * x2) - 3.0d0
    t_1 = 4.0d0 * (x2 * (3.0d0 - (2.0d0 * x2)))
    t_2 = x1 * (x1 * 3.0d0)
    t_3 = ((t_2 + (2.0d0 * x2)) - x1) / ((x1 * x1) + 1.0d0)
    if (x1 <= (-1.15d+110)) then
        tmp = x1 + (9.0d0 + (x1 - (x1 * ((x1 * (((2.0d0 * (t_0 - (x2 * (-2.0d0)))) - ((x2 * 8.0d0) - (x1 * (3.0d0 + (t_1 + (2.0d0 * ((2.0d0 * (x2 * t_0)) + ((-1.0d0) - ((2.0d0 * (x2 * (3.0d0 + (x2 * (-2.0d0))))) + (3.0d0 * t_0)))))))))) - 3.0d0)) + t_1))))
    else if (x1 <= 1.5d+97) then
        tmp = x1 + ((x1 + ((x1 * (x1 * x1)) - ((((((x1 * 2.0d0) * t_3) * (t_3 - 3.0d0)) + ((x1 * x1) * ((t_3 * 4.0d0) - 6.0d0))) * ((-1.0d0) - (x1 * x1))) - (3.0d0 * t_2)))) + ((x2 * (-6.0d0)) + (x1 * (-3.0d0))))
    else
        tmp = x1 + ((x2 * (-6.0d0)) - (x1 * (2.0d0 + ((x1 * ((3.0d0 * ((x2 * (-2.0d0)) - 3.0d0)) - (x1 * 3.0d0))) + t_1))))
    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 * (3.0 - (2.0 * x2)));
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = ((t_2 + (2.0 * x2)) - x1) / ((x1 * x1) + 1.0);
	double tmp;
	if (x1 <= -1.15e+110) {
		tmp = x1 + (9.0 + (x1 - (x1 * ((x1 * (((2.0 * (t_0 - (x2 * -2.0))) - ((x2 * 8.0) - (x1 * (3.0 + (t_1 + (2.0 * ((2.0 * (x2 * t_0)) + (-1.0 - ((2.0 * (x2 * (3.0 + (x2 * -2.0)))) + (3.0 * t_0)))))))))) - 3.0)) + t_1))));
	} else if (x1 <= 1.5e+97) {
		tmp = x1 + ((x1 + ((x1 * (x1 * x1)) - ((((((x1 * 2.0) * t_3) * (t_3 - 3.0)) + ((x1 * x1) * ((t_3 * 4.0) - 6.0))) * (-1.0 - (x1 * x1))) - (3.0 * t_2)))) + ((x2 * -6.0) + (x1 * -3.0)));
	} else {
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - (x1 * 3.0))) + t_1))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (2.0 * x2) - 3.0
	t_1 = 4.0 * (x2 * (3.0 - (2.0 * x2)))
	t_2 = x1 * (x1 * 3.0)
	t_3 = ((t_2 + (2.0 * x2)) - x1) / ((x1 * x1) + 1.0)
	tmp = 0
	if x1 <= -1.15e+110:
		tmp = x1 + (9.0 + (x1 - (x1 * ((x1 * (((2.0 * (t_0 - (x2 * -2.0))) - ((x2 * 8.0) - (x1 * (3.0 + (t_1 + (2.0 * ((2.0 * (x2 * t_0)) + (-1.0 - ((2.0 * (x2 * (3.0 + (x2 * -2.0)))) + (3.0 * t_0)))))))))) - 3.0)) + t_1))))
	elif x1 <= 1.5e+97:
		tmp = x1 + ((x1 + ((x1 * (x1 * x1)) - ((((((x1 * 2.0) * t_3) * (t_3 - 3.0)) + ((x1 * x1) * ((t_3 * 4.0) - 6.0))) * (-1.0 - (x1 * x1))) - (3.0 * t_2)))) + ((x2 * -6.0) + (x1 * -3.0)))
	else:
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - (x1 * 3.0))) + t_1))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(2.0 * x2) - 3.0)
	t_1 = Float64(4.0 * Float64(x2 * Float64(3.0 - Float64(2.0 * x2))))
	t_2 = Float64(x1 * Float64(x1 * 3.0))
	t_3 = Float64(Float64(Float64(t_2 + Float64(2.0 * x2)) - x1) / Float64(Float64(x1 * x1) + 1.0))
	tmp = 0.0
	if (x1 <= -1.15e+110)
		tmp = Float64(x1 + Float64(9.0 + Float64(x1 - Float64(x1 * Float64(Float64(x1 * Float64(Float64(Float64(2.0 * Float64(t_0 - Float64(x2 * -2.0))) - Float64(Float64(x2 * 8.0) - Float64(x1 * Float64(3.0 + Float64(t_1 + Float64(2.0 * Float64(Float64(2.0 * Float64(x2 * t_0)) + Float64(-1.0 - Float64(Float64(2.0 * Float64(x2 * Float64(3.0 + Float64(x2 * -2.0)))) + Float64(3.0 * t_0)))))))))) - 3.0)) + t_1)))));
	elseif (x1 <= 1.5e+97)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) - Float64(Float64(Float64(Float64(Float64(Float64(x1 * 2.0) * t_3) * Float64(t_3 - 3.0)) + Float64(Float64(x1 * x1) * Float64(Float64(t_3 * 4.0) - 6.0))) * Float64(-1.0 - Float64(x1 * x1))) - Float64(3.0 * t_2)))) + Float64(Float64(x2 * -6.0) + Float64(x1 * -3.0))));
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) - Float64(x1 * Float64(2.0 + Float64(Float64(x1 * Float64(Float64(3.0 * Float64(Float64(x2 * -2.0) - 3.0)) - Float64(x1 * 3.0))) + t_1)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (2.0 * x2) - 3.0;
	t_1 = 4.0 * (x2 * (3.0 - (2.0 * x2)));
	t_2 = x1 * (x1 * 3.0);
	t_3 = ((t_2 + (2.0 * x2)) - x1) / ((x1 * x1) + 1.0);
	tmp = 0.0;
	if (x1 <= -1.15e+110)
		tmp = x1 + (9.0 + (x1 - (x1 * ((x1 * (((2.0 * (t_0 - (x2 * -2.0))) - ((x2 * 8.0) - (x1 * (3.0 + (t_1 + (2.0 * ((2.0 * (x2 * t_0)) + (-1.0 - ((2.0 * (x2 * (3.0 + (x2 * -2.0)))) + (3.0 * t_0)))))))))) - 3.0)) + t_1))));
	elseif (x1 <= 1.5e+97)
		tmp = x1 + ((x1 + ((x1 * (x1 * x1)) - ((((((x1 * 2.0) * t_3) * (t_3 - 3.0)) + ((x1 * x1) * ((t_3 * 4.0) - 6.0))) * (-1.0 - (x1 * x1))) - (3.0 * t_2)))) + ((x2 * -6.0) + (x1 * -3.0)));
	else
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - (x1 * 3.0))) + t_1))));
	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 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $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] / N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -1.15e+110], N[(x1 + N[(9.0 + 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[(x2 * 8.0), $MachinePrecision] - N[(x1 * N[(3.0 + N[(t$95$1 + N[(2.0 * N[(N[(2.0 * N[(x2 * t$95$0), $MachinePrecision]), $MachinePrecision] + 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]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.5e+97], N[(x1 + N[(N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$3), $MachinePrecision] * N[(t$95$3 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$3 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(3.0 * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] - 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$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -1.15e110

   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 inf 0.0%

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

   5. Taylor expanded in x1 around 0 75.0%

      \[\leadsto x1 + \left(\left(\color{blue}{x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(3 + \left(2 \cdot \left(-2 \cdot x2 + -1 \cdot \left(2 \cdot x2 - 3\right)\right) + \left(8 \cdot x2 + x1 \cdot \left(\left(2 \cdot \left(\left(1 + \left(2 \cdot \left(x2 \cdot \left(3 + -2 \cdot x2\right)\right) + 3 \cdot \left(2 \cdot x2 - 3\right)\right)\right) - 2 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) - 3\right)\right)\right)\right)\right)} + x1\right) + 9\right) \]

   if -1.15e110 < x1 < 1.4999999999999999e97

   1. Initial program 98.1%

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

   3. Taylor expanded in x1 around inf 96.8%

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

   4. Taylor expanded in x1 around 0 98.1%

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

   if 1.4999999999999999e97 < x1

   1. Initial program 19.6%

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

   3. Taylor expanded in x1 around 0 13.4%

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

   4. Taylor expanded in x1 around 0 100.0%

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

4. Final simplification 95.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.15 \cdot 10^{+110}:\\ \;\;\;\;x1 + \left(9 + \left(x1 - x1 \cdot \left(x1 \cdot \left(\left(2 \cdot \left(\left(2 \cdot x2 - 3\right) - x2 \cdot -2\right) - \left(x2 \cdot 8 - x1 \cdot \left(3 + \left(4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right) + 2 \cdot \left(2 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + \left(-1 - \left(2 \cdot \left(x2 \cdot \left(3 + x2 \cdot -2\right)\right) + 3 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right)\right)\right)\right)\right) - 3\right) + 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.5 \cdot 10^{+97}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) - \left(\left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right)\right) \cdot \left(-1 - x1 \cdot x1\right) - 3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right)\right)\right)\right) + \left(x2 \cdot -6 + x1 \cdot -3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 + \left(x1 \cdot \left(3 \cdot \left(x2 \cdot -2 - 3\right) - x1 \cdot 3\right) + 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 92.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 2 \cdot x2 - 3\\ t_1 := x1 \cdot x1 + 1\\ t_2 := 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\\ t_3 := x1 \cdot \left(x1 \cdot 3\right)\\ t_4 := 3 \cdot t\_3\\ t_5 := \frac{\left(t\_3 + 2 \cdot x2\right) - x1}{t\_1}\\ t_6 := \left(x1 \cdot x1\right) \cdot \left(t\_5 \cdot 4 - 6\right)\\ t_7 := \left(x1 \cdot 2\right) \cdot t\_5\\ t_8 := x1 \cdot \left(x1 \cdot x1\right)\\ t_9 := x1 + \left(9 + \left(x1 - \left(\left(t\_1 \cdot \left(t\_7 \cdot \frac{\left(1 + \frac{3}{x1}\right) - 2 \cdot \frac{x2}{x1}}{x1} - t\_6\right) - t\_4\right) - t\_8\right)\right)\right)\\ \mathbf{if}\;x1 \leq -1.15 \cdot 10^{+110}:\\ \;\;\;\;x1 + \left(9 + \left(x1 - x1 \cdot \left(x1 \cdot \left(\left(2 \cdot \left(t\_0 - x2 \cdot -2\right) - \left(x2 \cdot 8 - x1 \cdot \left(3 + \left(t\_2 + 2 \cdot \left(2 \cdot \left(x2 \cdot t\_0\right) + \left(-1 - \left(2 \cdot \left(x2 \cdot \left(3 + x2 \cdot -2\right)\right) + 3 \cdot t\_0\right)\right)\right)\right)\right)\right)\right) - 3\right) + t\_2\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -1.05:\\ \;\;\;\;t\_9\\ \mathbf{elif}\;x1 \leq 1.38:\\ \;\;\;\;x1 + \left(\left(x2 \cdot -6 + x1 \cdot -3\right) + \left(x1 + \left(t\_8 + \left(t\_4 + \left(t\_7 \cdot \left(3 + \left(x1 - 2 \cdot x2\right)\right) - t\_6\right) \cdot \left(-1 - x1 \cdot x1\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.5 \cdot 10^{+97}:\\ \;\;\;\;t\_9\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 + \left(x1 \cdot \left(3 \cdot \left(x2 \cdot -2 - 3\right) - x1 \cdot 3\right) + t\_2\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (- (* 2.0 x2) 3.0))
        (t_1 (+ (* x1 x1) 1.0))
        (t_2 (* 4.0 (* x2 (- 3.0 (* 2.0 x2)))))
        (t_3 (* x1 (* x1 3.0)))
        (t_4 (* 3.0 t_3))
        (t_5 (/ (- (+ t_3 (* 2.0 x2)) x1) t_1))
        (t_6 (* (* x1 x1) (- (* t_5 4.0) 6.0)))
        (t_7 (* (* x1 2.0) t_5))
        (t_8 (* x1 (* x1 x1)))
        (t_9
         (+
          x1
          (+
           9.0
           (-
            x1
            (-
             (-
              (*
               t_1
               (- (* t_7 (/ (- (+ 1.0 (/ 3.0 x1)) (* 2.0 (/ x2 x1))) x1)) t_6))
              t_4)
             t_8))))))
   (if (<= x1 -1.15e+110)
     (+
      x1
      (+
       9.0
       (-
        x1
        (*
         x1
         (+
          (*
           x1
           (-
            (-
             (* 2.0 (- t_0 (* x2 -2.0)))
             (-
              (* x2 8.0)
              (*
               x1
               (+
                3.0
                (+
                 t_2
                 (*
                  2.0
                  (+
                   (* 2.0 (* x2 t_0))
                   (-
                    -1.0
                    (+ (* 2.0 (* x2 (+ 3.0 (* x2 -2.0)))) (* 3.0 t_0))))))))))
            3.0))
          t_2)))))
     (if (<= x1 -1.05)
       t_9
       (if (<= x1 1.38)
         (+
          x1
          (+
           (+ (* x2 -6.0) (* x1 -3.0))
           (+
            x1
            (+
             t_8
             (+
              t_4
              (*
               (- (* t_7 (+ 3.0 (- x1 (* 2.0 x2)))) t_6)
               (- -1.0 (* x1 x1))))))))
         (if (<= x1 1.5e+97)
           t_9
           (+
            x1
            (-
             (* x2 -6.0)
             (*
              x1
              (+
               2.0
               (+
                (* x1 (- (* 3.0 (- (* x2 -2.0) 3.0)) (* x1 3.0)))
                t_2)))))))))))

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 = 4.0 * (x2 * (3.0 - (2.0 * x2)));
	double t_3 = x1 * (x1 * 3.0);
	double t_4 = 3.0 * t_3;
	double t_5 = ((t_3 + (2.0 * x2)) - x1) / t_1;
	double t_6 = (x1 * x1) * ((t_5 * 4.0) - 6.0);
	double t_7 = (x1 * 2.0) * t_5;
	double t_8 = x1 * (x1 * x1);
	double t_9 = x1 + (9.0 + (x1 - (((t_1 * ((t_7 * (((1.0 + (3.0 / x1)) - (2.0 * (x2 / x1))) / x1)) - t_6)) - t_4) - t_8)));
	double tmp;
	if (x1 <= -1.15e+110) {
		tmp = x1 + (9.0 + (x1 - (x1 * ((x1 * (((2.0 * (t_0 - (x2 * -2.0))) - ((x2 * 8.0) - (x1 * (3.0 + (t_2 + (2.0 * ((2.0 * (x2 * t_0)) + (-1.0 - ((2.0 * (x2 * (3.0 + (x2 * -2.0)))) + (3.0 * t_0)))))))))) - 3.0)) + t_2))));
	} else if (x1 <= -1.05) {
		tmp = t_9;
	} else if (x1 <= 1.38) {
		tmp = x1 + (((x2 * -6.0) + (x1 * -3.0)) + (x1 + (t_8 + (t_4 + (((t_7 * (3.0 + (x1 - (2.0 * x2)))) - t_6) * (-1.0 - (x1 * x1)))))));
	} else if (x1 <= 1.5e+97) {
		tmp = t_9;
	} else {
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - (x1 * 3.0))) + t_2))));
	}
	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) :: t_8
    real(8) :: t_9
    real(8) :: tmp
    t_0 = (2.0d0 * x2) - 3.0d0
    t_1 = (x1 * x1) + 1.0d0
    t_2 = 4.0d0 * (x2 * (3.0d0 - (2.0d0 * x2)))
    t_3 = x1 * (x1 * 3.0d0)
    t_4 = 3.0d0 * t_3
    t_5 = ((t_3 + (2.0d0 * x2)) - x1) / t_1
    t_6 = (x1 * x1) * ((t_5 * 4.0d0) - 6.0d0)
    t_7 = (x1 * 2.0d0) * t_5
    t_8 = x1 * (x1 * x1)
    t_9 = x1 + (9.0d0 + (x1 - (((t_1 * ((t_7 * (((1.0d0 + (3.0d0 / x1)) - (2.0d0 * (x2 / x1))) / x1)) - t_6)) - t_4) - t_8)))
    if (x1 <= (-1.15d+110)) then
        tmp = x1 + (9.0d0 + (x1 - (x1 * ((x1 * (((2.0d0 * (t_0 - (x2 * (-2.0d0)))) - ((x2 * 8.0d0) - (x1 * (3.0d0 + (t_2 + (2.0d0 * ((2.0d0 * (x2 * t_0)) + ((-1.0d0) - ((2.0d0 * (x2 * (3.0d0 + (x2 * (-2.0d0))))) + (3.0d0 * t_0)))))))))) - 3.0d0)) + t_2))))
    else if (x1 <= (-1.05d0)) then
        tmp = t_9
    else if (x1 <= 1.38d0) then
        tmp = x1 + (((x2 * (-6.0d0)) + (x1 * (-3.0d0))) + (x1 + (t_8 + (t_4 + (((t_7 * (3.0d0 + (x1 - (2.0d0 * x2)))) - t_6) * ((-1.0d0) - (x1 * x1)))))))
    else if (x1 <= 1.5d+97) then
        tmp = t_9
    else
        tmp = x1 + ((x2 * (-6.0d0)) - (x1 * (2.0d0 + ((x1 * ((3.0d0 * ((x2 * (-2.0d0)) - 3.0d0)) - (x1 * 3.0d0))) + t_2))))
    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 = 4.0 * (x2 * (3.0 - (2.0 * x2)));
	double t_3 = x1 * (x1 * 3.0);
	double t_4 = 3.0 * t_3;
	double t_5 = ((t_3 + (2.0 * x2)) - x1) / t_1;
	double t_6 = (x1 * x1) * ((t_5 * 4.0) - 6.0);
	double t_7 = (x1 * 2.0) * t_5;
	double t_8 = x1 * (x1 * x1);
	double t_9 = x1 + (9.0 + (x1 - (((t_1 * ((t_7 * (((1.0 + (3.0 / x1)) - (2.0 * (x2 / x1))) / x1)) - t_6)) - t_4) - t_8)));
	double tmp;
	if (x1 <= -1.15e+110) {
		tmp = x1 + (9.0 + (x1 - (x1 * ((x1 * (((2.0 * (t_0 - (x2 * -2.0))) - ((x2 * 8.0) - (x1 * (3.0 + (t_2 + (2.0 * ((2.0 * (x2 * t_0)) + (-1.0 - ((2.0 * (x2 * (3.0 + (x2 * -2.0)))) + (3.0 * t_0)))))))))) - 3.0)) + t_2))));
	} else if (x1 <= -1.05) {
		tmp = t_9;
	} else if (x1 <= 1.38) {
		tmp = x1 + (((x2 * -6.0) + (x1 * -3.0)) + (x1 + (t_8 + (t_4 + (((t_7 * (3.0 + (x1 - (2.0 * x2)))) - t_6) * (-1.0 - (x1 * x1)))))));
	} else if (x1 <= 1.5e+97) {
		tmp = t_9;
	} else {
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - (x1 * 3.0))) + t_2))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (2.0 * x2) - 3.0
	t_1 = (x1 * x1) + 1.0
	t_2 = 4.0 * (x2 * (3.0 - (2.0 * x2)))
	t_3 = x1 * (x1 * 3.0)
	t_4 = 3.0 * t_3
	t_5 = ((t_3 + (2.0 * x2)) - x1) / t_1
	t_6 = (x1 * x1) * ((t_5 * 4.0) - 6.0)
	t_7 = (x1 * 2.0) * t_5
	t_8 = x1 * (x1 * x1)
	t_9 = x1 + (9.0 + (x1 - (((t_1 * ((t_7 * (((1.0 + (3.0 / x1)) - (2.0 * (x2 / x1))) / x1)) - t_6)) - t_4) - t_8)))
	tmp = 0
	if x1 <= -1.15e+110:
		tmp = x1 + (9.0 + (x1 - (x1 * ((x1 * (((2.0 * (t_0 - (x2 * -2.0))) - ((x2 * 8.0) - (x1 * (3.0 + (t_2 + (2.0 * ((2.0 * (x2 * t_0)) + (-1.0 - ((2.0 * (x2 * (3.0 + (x2 * -2.0)))) + (3.0 * t_0)))))))))) - 3.0)) + t_2))))
	elif x1 <= -1.05:
		tmp = t_9
	elif x1 <= 1.38:
		tmp = x1 + (((x2 * -6.0) + (x1 * -3.0)) + (x1 + (t_8 + (t_4 + (((t_7 * (3.0 + (x1 - (2.0 * x2)))) - t_6) * (-1.0 - (x1 * x1)))))))
	elif x1 <= 1.5e+97:
		tmp = t_9
	else:
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - (x1 * 3.0))) + t_2))))
	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(4.0 * Float64(x2 * Float64(3.0 - Float64(2.0 * x2))))
	t_3 = Float64(x1 * Float64(x1 * 3.0))
	t_4 = Float64(3.0 * t_3)
	t_5 = Float64(Float64(Float64(t_3 + Float64(2.0 * x2)) - x1) / t_1)
	t_6 = Float64(Float64(x1 * x1) * Float64(Float64(t_5 * 4.0) - 6.0))
	t_7 = Float64(Float64(x1 * 2.0) * t_5)
	t_8 = Float64(x1 * Float64(x1 * x1))
	t_9 = Float64(x1 + Float64(9.0 + Float64(x1 - Float64(Float64(Float64(t_1 * Float64(Float64(t_7 * Float64(Float64(Float64(1.0 + Float64(3.0 / x1)) - Float64(2.0 * Float64(x2 / x1))) / x1)) - t_6)) - t_4) - t_8))))
	tmp = 0.0
	if (x1 <= -1.15e+110)
		tmp = Float64(x1 + Float64(9.0 + Float64(x1 - Float64(x1 * Float64(Float64(x1 * Float64(Float64(Float64(2.0 * Float64(t_0 - Float64(x2 * -2.0))) - Float64(Float64(x2 * 8.0) - Float64(x1 * Float64(3.0 + Float64(t_2 + Float64(2.0 * Float64(Float64(2.0 * Float64(x2 * t_0)) + Float64(-1.0 - Float64(Float64(2.0 * Float64(x2 * Float64(3.0 + Float64(x2 * -2.0)))) + Float64(3.0 * t_0)))))))))) - 3.0)) + t_2)))));
	elseif (x1 <= -1.05)
		tmp = t_9;
	elseif (x1 <= 1.38)
		tmp = Float64(x1 + Float64(Float64(Float64(x2 * -6.0) + Float64(x1 * -3.0)) + Float64(x1 + Float64(t_8 + Float64(t_4 + Float64(Float64(Float64(t_7 * Float64(3.0 + Float64(x1 - Float64(2.0 * x2)))) - t_6) * Float64(-1.0 - Float64(x1 * x1))))))));
	elseif (x1 <= 1.5e+97)
		tmp = t_9;
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) - Float64(x1 * Float64(2.0 + Float64(Float64(x1 * Float64(Float64(3.0 * Float64(Float64(x2 * -2.0) - 3.0)) - Float64(x1 * 3.0))) + t_2)))));
	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 = 4.0 * (x2 * (3.0 - (2.0 * x2)));
	t_3 = x1 * (x1 * 3.0);
	t_4 = 3.0 * t_3;
	t_5 = ((t_3 + (2.0 * x2)) - x1) / t_1;
	t_6 = (x1 * x1) * ((t_5 * 4.0) - 6.0);
	t_7 = (x1 * 2.0) * t_5;
	t_8 = x1 * (x1 * x1);
	t_9 = x1 + (9.0 + (x1 - (((t_1 * ((t_7 * (((1.0 + (3.0 / x1)) - (2.0 * (x2 / x1))) / x1)) - t_6)) - t_4) - t_8)));
	tmp = 0.0;
	if (x1 <= -1.15e+110)
		tmp = x1 + (9.0 + (x1 - (x1 * ((x1 * (((2.0 * (t_0 - (x2 * -2.0))) - ((x2 * 8.0) - (x1 * (3.0 + (t_2 + (2.0 * ((2.0 * (x2 * t_0)) + (-1.0 - ((2.0 * (x2 * (3.0 + (x2 * -2.0)))) + (3.0 * t_0)))))))))) - 3.0)) + t_2))));
	elseif (x1 <= -1.05)
		tmp = t_9;
	elseif (x1 <= 1.38)
		tmp = x1 + (((x2 * -6.0) + (x1 * -3.0)) + (x1 + (t_8 + (t_4 + (((t_7 * (3.0 + (x1 - (2.0 * x2)))) - t_6) * (-1.0 - (x1 * x1)))))));
	elseif (x1 <= 1.5e+97)
		tmp = t_9;
	else
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - (x1 * 3.0))) + t_2))));
	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[(4.0 * N[(x2 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(3.0 * t$95$3), $MachinePrecision]}, Block[{t$95$5 = N[(N[(N[(t$95$3 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$6 = N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$5 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(N[(x1 * 2.0), $MachinePrecision] * t$95$5), $MachinePrecision]}, Block[{t$95$8 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$9 = N[(x1 + N[(9.0 + N[(x1 - N[(N[(N[(t$95$1 * N[(N[(t$95$7 * N[(N[(N[(1.0 + N[(3.0 / x1), $MachinePrecision]), $MachinePrecision] - N[(2.0 * N[(x2 / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x1), $MachinePrecision]), $MachinePrecision] - t$95$6), $MachinePrecision]), $MachinePrecision] - t$95$4), $MachinePrecision] - t$95$8), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -1.15e+110], N[(x1 + N[(9.0 + 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[(x2 * 8.0), $MachinePrecision] - N[(x1 * N[(3.0 + N[(t$95$2 + N[(2.0 * N[(N[(2.0 * N[(x2 * t$95$0), $MachinePrecision]), $MachinePrecision] + 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]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -1.05], t$95$9, If[LessEqual[x1, 1.38], N[(x1 + N[(N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * -3.0), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(t$95$8 + N[(t$95$4 + N[(N[(N[(t$95$7 * N[(3.0 + N[(x1 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$6), $MachinePrecision] * N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.5e+97], t$95$9, N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] - 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$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -1.15e110

   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 inf 0.0%

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

   5. Taylor expanded in x1 around 0 75.0%

      \[\leadsto x1 + \left(\left(\color{blue}{x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(3 + \left(2 \cdot \left(-2 \cdot x2 + -1 \cdot \left(2 \cdot x2 - 3\right)\right) + \left(8 \cdot x2 + x1 \cdot \left(\left(2 \cdot \left(\left(1 + \left(2 \cdot \left(x2 \cdot \left(3 + -2 \cdot x2\right)\right) + 3 \cdot \left(2 \cdot x2 - 3\right)\right)\right) - 2 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) - 3\right)\right)\right)\right)\right)} + x1\right) + 9\right) \]

   if -1.15e110 < x1 < -1.05000000000000004 or 1.3799999999999999 < x1 < 1.4999999999999999e97

   1. Initial program 94.7%

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

   3. Taylor expanded in x1 around inf 93.1%

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

   4. Taylor expanded in x1 around inf 93.1%

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

   5. Taylor expanded in x1 around inf 91.7%

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

      1. associate-*r/ 91.7%

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

      2. metadata-eval 91.7%

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

   7. Simplified 91.7%

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

   if -1.05000000000000004 < x1 < 1.3799999999999999

   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 98.2%

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

   4. Taylor expanded in x1 around 0 99.4%

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

   5. Taylor expanded in x1 around 0 99.1%

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

      1. +-commutative 99.1%

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

      2. mul-1-neg 99.1%

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

      3. sub-neg 99.1%

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

   7. Simplified 99.1%

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

   if 1.4999999999999999e97 < x1

   1. Initial program 19.6%

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

   3. Taylor expanded in x1 around 0 13.4%

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

   4. Taylor expanded in x1 around 0 100.0%

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

4. Final simplification 94.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.15 \cdot 10^{+110}:\\ \;\;\;\;x1 + \left(9 + \left(x1 - x1 \cdot \left(x1 \cdot \left(\left(2 \cdot \left(\left(2 \cdot x2 - 3\right) - x2 \cdot -2\right) - \left(x2 \cdot 8 - x1 \cdot \left(3 + \left(4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right) + 2 \cdot \left(2 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + \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)\right)\right)\right)\right)\right) - 3\right) + 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -1.05:\\ \;\;\;\;x1 + \left(9 + \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 \frac{\left(1 + \frac{3}{x1}\right) - 2 \cdot \frac{x2}{x1}}{x1} - \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) - x1 \cdot \left(x1 \cdot x1\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.38:\\ \;\;\;\;x1 + \left(\left(x2 \cdot -6 + x1 \cdot -3\right) + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) + \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 + \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) \cdot \left(-1 - x1 \cdot x1\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.5 \cdot 10^{+97}:\\ \;\;\;\;x1 + \left(9 + \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 \frac{\left(1 + \frac{3}{x1}\right) - 2 \cdot \frac{x2}{x1}}{x1} - \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) - x1 \cdot \left(x1 \cdot x1\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - 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)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 91.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 3 - 2 \cdot x2\\ t_1 := 2 \cdot x2 - 3\\ t_2 := x1 \cdot \left(x1 \cdot x1\right)\\ t_3 := x1 \cdot \left(x1 \cdot 3\right)\\ t_4 := 3 \cdot t\_3\\ t_5 := \left(t\_3 + 2 \cdot x2\right) - x1\\ t_6 := x1 \cdot x1 + 1\\ t_7 := \left(\left(x1 \cdot 2\right) \cdot \frac{t\_5}{t\_6}\right) \cdot \left(3 + \frac{t\_5}{-1 - x1 \cdot x1}\right)\\ t_8 := 4 \cdot \left(x2 \cdot t\_0\right)\\ \mathbf{if}\;x1 \leq -1.15 \cdot 10^{+110}:\\ \;\;\;\;x1 + \left(9 + \left(x1 - x1 \cdot \left(x1 \cdot \left(\left(2 \cdot \left(t\_1 - x2 \cdot -2\right) - \left(x2 \cdot 8 - x1 \cdot \left(3 + \left(t\_8 + 2 \cdot \left(2 \cdot \left(x2 \cdot t\_1\right) + \left(-1 - \left(2 \cdot \left(x2 \cdot \left(3 + x2 \cdot -2\right)\right) + 3 \cdot t\_1\right)\right)\right)\right)\right)\right)\right) - 3\right) + t\_8\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -12:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(t\_2 + \left(t\_4 - t\_6 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \left(\frac{1 + \frac{t\_0}{x1}}{x1} - 3\right)\right) + t\_7\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 8.6 \cdot 10^{+93}:\\ \;\;\;\;x1 - \left(3 \cdot \frac{x1 - \left(t\_3 - 2 \cdot x2\right)}{t\_6} - \left(x1 - \left(\left(t\_6 \cdot \left(t\_7 - \left(x1 \cdot x1\right) \cdot 6\right) - t\_4\right) - t\_2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 + \left(x1 \cdot \left(3 \cdot \left(x2 \cdot -2 - 3\right) - x1 \cdot 3\right) + t\_8\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (- 3.0 (* 2.0 x2)))
        (t_1 (- (* 2.0 x2) 3.0))
        (t_2 (* x1 (* x1 x1)))
        (t_3 (* x1 (* x1 3.0)))
        (t_4 (* 3.0 t_3))
        (t_5 (- (+ t_3 (* 2.0 x2)) x1))
        (t_6 (+ (* x1 x1) 1.0))
        (t_7 (* (* (* x1 2.0) (/ t_5 t_6)) (+ 3.0 (/ t_5 (- -1.0 (* x1 x1))))))
        (t_8 (* 4.0 (* x2 t_0))))
   (if (<= x1 -1.15e+110)
     (+
      x1
      (+
       9.0
       (-
        x1
        (*
         x1
         (+
          (*
           x1
           (-
            (-
             (* 2.0 (- t_1 (* x2 -2.0)))
             (-
              (* x2 8.0)
              (*
               x1
               (+
                3.0
                (+
                 t_8
                 (*
                  2.0
                  (+
                   (* 2.0 (* x2 t_1))
                   (-
                    -1.0
                    (+ (* 2.0 (* x2 (+ 3.0 (* x2 -2.0)))) (* 3.0 t_1))))))))))
            3.0))
          t_8)))))
     (if (<= x1 -12.0)
       (+
        x1
        (+
         9.0
         (+
          x1
          (+
           t_2
           (-
            t_4
            (*
             t_6
             (+
              (* (* x1 x1) (+ 6.0 (* 4.0 (- (/ (+ 1.0 (/ t_0 x1)) x1) 3.0))))
              t_7)))))))
       (if (<= x1 8.6e+93)
         (-
          x1
          (-
           (* 3.0 (/ (- x1 (- t_3 (* 2.0 x2))) t_6))
           (- x1 (- (- (* t_6 (- t_7 (* (* x1 x1) 6.0))) t_4) t_2))))
         (+
          x1
          (-
           (* x2 -6.0)
           (*
            x1
            (+
             2.0
             (+ (* x1 (- (* 3.0 (- (* x2 -2.0) 3.0)) (* x1 3.0))) t_8))))))))))

C

double code(double x1, double x2) {
	double t_0 = 3.0 - (2.0 * x2);
	double t_1 = (2.0 * x2) - 3.0;
	double t_2 = x1 * (x1 * x1);
	double t_3 = x1 * (x1 * 3.0);
	double t_4 = 3.0 * t_3;
	double t_5 = (t_3 + (2.0 * x2)) - x1;
	double t_6 = (x1 * x1) + 1.0;
	double t_7 = ((x1 * 2.0) * (t_5 / t_6)) * (3.0 + (t_5 / (-1.0 - (x1 * x1))));
	double t_8 = 4.0 * (x2 * t_0);
	double tmp;
	if (x1 <= -1.15e+110) {
		tmp = x1 + (9.0 + (x1 - (x1 * ((x1 * (((2.0 * (t_1 - (x2 * -2.0))) - ((x2 * 8.0) - (x1 * (3.0 + (t_8 + (2.0 * ((2.0 * (x2 * t_1)) + (-1.0 - ((2.0 * (x2 * (3.0 + (x2 * -2.0)))) + (3.0 * t_1)))))))))) - 3.0)) + t_8))));
	} else if (x1 <= -12.0) {
		tmp = x1 + (9.0 + (x1 + (t_2 + (t_4 - (t_6 * (((x1 * x1) * (6.0 + (4.0 * (((1.0 + (t_0 / x1)) / x1) - 3.0)))) + t_7))))));
	} else if (x1 <= 8.6e+93) {
		tmp = x1 - ((3.0 * ((x1 - (t_3 - (2.0 * x2))) / t_6)) - (x1 - (((t_6 * (t_7 - ((x1 * x1) * 6.0))) - t_4) - t_2)));
	} else {
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - (x1 * 3.0))) + t_8))));
	}
	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) :: t_8
    real(8) :: tmp
    t_0 = 3.0d0 - (2.0d0 * x2)
    t_1 = (2.0d0 * x2) - 3.0d0
    t_2 = x1 * (x1 * x1)
    t_3 = x1 * (x1 * 3.0d0)
    t_4 = 3.0d0 * t_3
    t_5 = (t_3 + (2.0d0 * x2)) - x1
    t_6 = (x1 * x1) + 1.0d0
    t_7 = ((x1 * 2.0d0) * (t_5 / t_6)) * (3.0d0 + (t_5 / ((-1.0d0) - (x1 * x1))))
    t_8 = 4.0d0 * (x2 * t_0)
    if (x1 <= (-1.15d+110)) then
        tmp = x1 + (9.0d0 + (x1 - (x1 * ((x1 * (((2.0d0 * (t_1 - (x2 * (-2.0d0)))) - ((x2 * 8.0d0) - (x1 * (3.0d0 + (t_8 + (2.0d0 * ((2.0d0 * (x2 * t_1)) + ((-1.0d0) - ((2.0d0 * (x2 * (3.0d0 + (x2 * (-2.0d0))))) + (3.0d0 * t_1)))))))))) - 3.0d0)) + t_8))))
    else if (x1 <= (-12.0d0)) then
        tmp = x1 + (9.0d0 + (x1 + (t_2 + (t_4 - (t_6 * (((x1 * x1) * (6.0d0 + (4.0d0 * (((1.0d0 + (t_0 / x1)) / x1) - 3.0d0)))) + t_7))))))
    else if (x1 <= 8.6d+93) then
        tmp = x1 - ((3.0d0 * ((x1 - (t_3 - (2.0d0 * x2))) / t_6)) - (x1 - (((t_6 * (t_7 - ((x1 * x1) * 6.0d0))) - t_4) - t_2)))
    else
        tmp = x1 + ((x2 * (-6.0d0)) - (x1 * (2.0d0 + ((x1 * ((3.0d0 * ((x2 * (-2.0d0)) - 3.0d0)) - (x1 * 3.0d0))) + t_8))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = 3.0 - (2.0 * x2);
	double t_1 = (2.0 * x2) - 3.0;
	double t_2 = x1 * (x1 * x1);
	double t_3 = x1 * (x1 * 3.0);
	double t_4 = 3.0 * t_3;
	double t_5 = (t_3 + (2.0 * x2)) - x1;
	double t_6 = (x1 * x1) + 1.0;
	double t_7 = ((x1 * 2.0) * (t_5 / t_6)) * (3.0 + (t_5 / (-1.0 - (x1 * x1))));
	double t_8 = 4.0 * (x2 * t_0);
	double tmp;
	if (x1 <= -1.15e+110) {
		tmp = x1 + (9.0 + (x1 - (x1 * ((x1 * (((2.0 * (t_1 - (x2 * -2.0))) - ((x2 * 8.0) - (x1 * (3.0 + (t_8 + (2.0 * ((2.0 * (x2 * t_1)) + (-1.0 - ((2.0 * (x2 * (3.0 + (x2 * -2.0)))) + (3.0 * t_1)))))))))) - 3.0)) + t_8))));
	} else if (x1 <= -12.0) {
		tmp = x1 + (9.0 + (x1 + (t_2 + (t_4 - (t_6 * (((x1 * x1) * (6.0 + (4.0 * (((1.0 + (t_0 / x1)) / x1) - 3.0)))) + t_7))))));
	} else if (x1 <= 8.6e+93) {
		tmp = x1 - ((3.0 * ((x1 - (t_3 - (2.0 * x2))) / t_6)) - (x1 - (((t_6 * (t_7 - ((x1 * x1) * 6.0))) - t_4) - t_2)));
	} else {
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - (x1 * 3.0))) + t_8))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = 3.0 - (2.0 * x2)
	t_1 = (2.0 * x2) - 3.0
	t_2 = x1 * (x1 * x1)
	t_3 = x1 * (x1 * 3.0)
	t_4 = 3.0 * t_3
	t_5 = (t_3 + (2.0 * x2)) - x1
	t_6 = (x1 * x1) + 1.0
	t_7 = ((x1 * 2.0) * (t_5 / t_6)) * (3.0 + (t_5 / (-1.0 - (x1 * x1))))
	t_8 = 4.0 * (x2 * t_0)
	tmp = 0
	if x1 <= -1.15e+110:
		tmp = x1 + (9.0 + (x1 - (x1 * ((x1 * (((2.0 * (t_1 - (x2 * -2.0))) - ((x2 * 8.0) - (x1 * (3.0 + (t_8 + (2.0 * ((2.0 * (x2 * t_1)) + (-1.0 - ((2.0 * (x2 * (3.0 + (x2 * -2.0)))) + (3.0 * t_1)))))))))) - 3.0)) + t_8))))
	elif x1 <= -12.0:
		tmp = x1 + (9.0 + (x1 + (t_2 + (t_4 - (t_6 * (((x1 * x1) * (6.0 + (4.0 * (((1.0 + (t_0 / x1)) / x1) - 3.0)))) + t_7))))))
	elif x1 <= 8.6e+93:
		tmp = x1 - ((3.0 * ((x1 - (t_3 - (2.0 * x2))) / t_6)) - (x1 - (((t_6 * (t_7 - ((x1 * x1) * 6.0))) - t_4) - t_2)))
	else:
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - (x1 * 3.0))) + t_8))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(3.0 - Float64(2.0 * x2))
	t_1 = Float64(Float64(2.0 * x2) - 3.0)
	t_2 = Float64(x1 * Float64(x1 * x1))
	t_3 = Float64(x1 * Float64(x1 * 3.0))
	t_4 = Float64(3.0 * t_3)
	t_5 = Float64(Float64(t_3 + Float64(2.0 * x2)) - x1)
	t_6 = Float64(Float64(x1 * x1) + 1.0)
	t_7 = Float64(Float64(Float64(x1 * 2.0) * Float64(t_5 / t_6)) * Float64(3.0 + Float64(t_5 / Float64(-1.0 - Float64(x1 * x1)))))
	t_8 = Float64(4.0 * Float64(x2 * t_0))
	tmp = 0.0
	if (x1 <= -1.15e+110)
		tmp = Float64(x1 + Float64(9.0 + Float64(x1 - Float64(x1 * Float64(Float64(x1 * Float64(Float64(Float64(2.0 * Float64(t_1 - Float64(x2 * -2.0))) - Float64(Float64(x2 * 8.0) - Float64(x1 * Float64(3.0 + Float64(t_8 + Float64(2.0 * Float64(Float64(2.0 * Float64(x2 * t_1)) + Float64(-1.0 - Float64(Float64(2.0 * Float64(x2 * Float64(3.0 + Float64(x2 * -2.0)))) + Float64(3.0 * t_1)))))))))) - 3.0)) + t_8)))));
	elseif (x1 <= -12.0)
		tmp = Float64(x1 + Float64(9.0 + Float64(x1 + Float64(t_2 + Float64(t_4 - Float64(t_6 * Float64(Float64(Float64(x1 * x1) * Float64(6.0 + Float64(4.0 * Float64(Float64(Float64(1.0 + Float64(t_0 / x1)) / x1) - 3.0)))) + t_7)))))));
	elseif (x1 <= 8.6e+93)
		tmp = Float64(x1 - Float64(Float64(3.0 * Float64(Float64(x1 - Float64(t_3 - Float64(2.0 * x2))) / t_6)) - Float64(x1 - Float64(Float64(Float64(t_6 * Float64(t_7 - Float64(Float64(x1 * x1) * 6.0))) - t_4) - t_2))));
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) - Float64(x1 * Float64(2.0 + Float64(Float64(x1 * Float64(Float64(3.0 * Float64(Float64(x2 * -2.0) - 3.0)) - Float64(x1 * 3.0))) + t_8)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = 3.0 - (2.0 * x2);
	t_1 = (2.0 * x2) - 3.0;
	t_2 = x1 * (x1 * x1);
	t_3 = x1 * (x1 * 3.0);
	t_4 = 3.0 * t_3;
	t_5 = (t_3 + (2.0 * x2)) - x1;
	t_6 = (x1 * x1) + 1.0;
	t_7 = ((x1 * 2.0) * (t_5 / t_6)) * (3.0 + (t_5 / (-1.0 - (x1 * x1))));
	t_8 = 4.0 * (x2 * t_0);
	tmp = 0.0;
	if (x1 <= -1.15e+110)
		tmp = x1 + (9.0 + (x1 - (x1 * ((x1 * (((2.0 * (t_1 - (x2 * -2.0))) - ((x2 * 8.0) - (x1 * (3.0 + (t_8 + (2.0 * ((2.0 * (x2 * t_1)) + (-1.0 - ((2.0 * (x2 * (3.0 + (x2 * -2.0)))) + (3.0 * t_1)))))))))) - 3.0)) + t_8))));
	elseif (x1 <= -12.0)
		tmp = x1 + (9.0 + (x1 + (t_2 + (t_4 - (t_6 * (((x1 * x1) * (6.0 + (4.0 * (((1.0 + (t_0 / x1)) / x1) - 3.0)))) + t_7))))));
	elseif (x1 <= 8.6e+93)
		tmp = x1 - ((3.0 * ((x1 - (t_3 - (2.0 * x2))) / t_6)) - (x1 - (((t_6 * (t_7 - ((x1 * x1) * 6.0))) - t_4) - t_2)));
	else
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - (x1 * 3.0))) + t_8))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]}, Block[{t$95$2 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(3.0 * t$95$3), $MachinePrecision]}, Block[{t$95$5 = N[(N[(t$95$3 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]}, Block[{t$95$6 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$7 = N[(N[(N[(x1 * 2.0), $MachinePrecision] * N[(t$95$5 / t$95$6), $MachinePrecision]), $MachinePrecision] * N[(3.0 + N[(t$95$5 / N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$8 = N[(4.0 * N[(x2 * t$95$0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -1.15e+110], N[(x1 + N[(9.0 + 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[(x2 * 8.0), $MachinePrecision] - N[(x1 * N[(3.0 + N[(t$95$8 + N[(2.0 * N[(N[(2.0 * N[(x2 * t$95$1), $MachinePrecision]), $MachinePrecision] + 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]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision] + t$95$8), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -12.0], N[(x1 + N[(9.0 + N[(x1 + N[(t$95$2 + N[(t$95$4 - N[(t$95$6 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 + N[(4.0 * N[(N[(N[(1.0 + N[(t$95$0 / x1), $MachinePrecision]), $MachinePrecision] / x1), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$7), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 8.6e+93], N[(x1 - N[(N[(3.0 * N[(N[(x1 - N[(t$95$3 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$6), $MachinePrecision]), $MachinePrecision] - N[(x1 - N[(N[(N[(t$95$6 * N[(t$95$7 - N[(N[(x1 * x1), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$4), $MachinePrecision] - t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] - 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$8), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -1.15e110

   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 inf 0.0%

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

   5. Taylor expanded in x1 around 0 75.0%

      \[\leadsto x1 + \left(\left(\color{blue}{x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(3 + \left(2 \cdot \left(-2 \cdot x2 + -1 \cdot \left(2 \cdot x2 - 3\right)\right) + \left(8 \cdot x2 + x1 \cdot \left(\left(2 \cdot \left(\left(1 + \left(2 \cdot \left(x2 \cdot \left(3 + -2 \cdot x2\right)\right) + 3 \cdot \left(2 \cdot x2 - 3\right)\right)\right) - 2 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) - 3\right)\right)\right)\right)\right)} + x1\right) + 9\right) \]

   if -1.15e110 < x1 < -12

   1. Initial program 90.3%

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

   3. Taylor expanded in x1 around inf 90.2%

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

   4. Taylor expanded in x1 around inf 90.2%

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

   5. Taylor expanded in x1 around -inf 90.6%

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

   if -12 < x1 < 8.6e93

   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 97.8%

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

   4. Taylor expanded in x1 around inf 97.3%

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

   if 8.6e93 < x1

   1. Initial program 21.3%

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

   3. Taylor expanded in x1 around 0 13.1%

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

   4. Taylor expanded in x1 around 0 97.9%

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

4. Final simplification 93.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.15 \cdot 10^{+110}:\\ \;\;\;\;x1 + \left(9 + \left(x1 - x1 \cdot \left(x1 \cdot \left(\left(2 \cdot \left(\left(2 \cdot x2 - 3\right) - x2 \cdot -2\right) - \left(x2 \cdot 8 - x1 \cdot \left(3 + \left(4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right) + 2 \cdot \left(2 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + \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)\right)\right)\right)\right)\right) - 3\right) + 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -12:\\ \;\;\;\;x1 + \left(9 + \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(6 + 4 \cdot \left(\frac{1 + \frac{3 - 2 \cdot x2}{x1}}{x1} - 3\right)\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(3 + \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1}\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 8.6 \cdot 10^{+93}:\\ \;\;\;\;x1 - \left(3 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right)}{x1 \cdot x1 + 1} - \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(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 6\right) - 3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right)\right) - x1 \cdot \left(x1 \cdot x1\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - 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)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 91.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 2 \cdot x2 - 3\\ t_1 := -1 - x1 \cdot x1\\ t_2 := x1 \cdot \left(x1 \cdot x1\right)\\ t_3 := x1 \cdot \left(x1 \cdot 3\right)\\ t_4 := \left(t\_3 + 2 \cdot x2\right) - x1\\ t_5 := 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\\ t_6 := x1 \cdot x1 + 1\\ t_7 := \frac{t\_4}{t\_6}\\ t_8 := \left(x1 \cdot 2\right) \cdot t\_7\\ t_9 := 3 \cdot t\_3\\ \mathbf{if}\;x1 \leq -1.15 \cdot 10^{+110}:\\ \;\;\;\;x1 + \left(9 + \left(x1 - x1 \cdot \left(x1 \cdot \left(\left(2 \cdot \left(t\_0 - x2 \cdot -2\right) - \left(x2 \cdot 8 - x1 \cdot \left(3 + \left(t\_5 + 2 \cdot \left(2 \cdot \left(x2 \cdot t\_0\right) + \left(-1 - \left(2 \cdot \left(x2 \cdot \left(3 + x2 \cdot -2\right)\right) + 3 \cdot t\_0\right)\right)\right)\right)\right)\right)\right) - 3\right) + t\_5\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -5.6 \cdot 10^{-12}:\\ \;\;\;\;x1 - \left(\left(\left(\left(\left(t\_8 \cdot \left(t\_7 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(t\_7 \cdot 4 - 6\right)\right) \cdot t\_1 - t\_9\right) - t\_2\right) - x1\right) - x1 \cdot -3\right)\\ \mathbf{elif}\;x1 \leq 8.6 \cdot 10^{+93}:\\ \;\;\;\;x1 - \left(3 \cdot \frac{x1 - \left(t\_3 - 2 \cdot x2\right)}{t\_6} - \left(x1 - \left(\left(t\_6 \cdot \left(t\_8 \cdot \left(3 + \frac{t\_4}{t\_1}\right) - \left(x1 \cdot x1\right) \cdot 6\right) - t\_9\right) - t\_2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 + \left(x1 \cdot \left(3 \cdot \left(x2 \cdot -2 - 3\right) - x1 \cdot 3\right) + t\_5\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (- (* 2.0 x2) 3.0))
        (t_1 (- -1.0 (* x1 x1)))
        (t_2 (* x1 (* x1 x1)))
        (t_3 (* x1 (* x1 3.0)))
        (t_4 (- (+ t_3 (* 2.0 x2)) x1))
        (t_5 (* 4.0 (* x2 (- 3.0 (* 2.0 x2)))))
        (t_6 (+ (* x1 x1) 1.0))
        (t_7 (/ t_4 t_6))
        (t_8 (* (* x1 2.0) t_7))
        (t_9 (* 3.0 t_3)))
   (if (<= x1 -1.15e+110)
     (+
      x1
      (+
       9.0
       (-
        x1
        (*
         x1
         (+
          (*
           x1
           (-
            (-
             (* 2.0 (- t_0 (* x2 -2.0)))
             (-
              (* x2 8.0)
              (*
               x1
               (+
                3.0
                (+
                 t_5
                 (*
                  2.0
                  (+
                   (* 2.0 (* x2 t_0))
                   (-
                    -1.0
                    (+ (* 2.0 (* x2 (+ 3.0 (* x2 -2.0)))) (* 3.0 t_0))))))))))
            3.0))
          t_5)))))
     (if (<= x1 -5.6e-12)
       (-
        x1
        (-
         (-
          (-
           (-
            (* (+ (* t_8 (- t_7 3.0)) (* (* x1 x1) (- (* t_7 4.0) 6.0))) t_1)
            t_9)
           t_2)
          x1)
         (* x1 -3.0)))
       (if (<= x1 8.6e+93)
         (-
          x1
          (-
           (* 3.0 (/ (- x1 (- t_3 (* 2.0 x2))) t_6))
           (-
            x1
            (-
             (- (* t_6 (- (* t_8 (+ 3.0 (/ t_4 t_1))) (* (* x1 x1) 6.0))) t_9)
             t_2))))
         (+
          x1
          (-
           (* x2 -6.0)
           (*
            x1
            (+
             2.0
             (+ (* x1 (- (* 3.0 (- (* x2 -2.0) 3.0)) (* x1 3.0))) t_5))))))))))

C

double code(double x1, double x2) {
	double t_0 = (2.0 * x2) - 3.0;
	double t_1 = -1.0 - (x1 * x1);
	double t_2 = x1 * (x1 * x1);
	double t_3 = x1 * (x1 * 3.0);
	double t_4 = (t_3 + (2.0 * x2)) - x1;
	double t_5 = 4.0 * (x2 * (3.0 - (2.0 * x2)));
	double t_6 = (x1 * x1) + 1.0;
	double t_7 = t_4 / t_6;
	double t_8 = (x1 * 2.0) * t_7;
	double t_9 = 3.0 * t_3;
	double tmp;
	if (x1 <= -1.15e+110) {
		tmp = x1 + (9.0 + (x1 - (x1 * ((x1 * (((2.0 * (t_0 - (x2 * -2.0))) - ((x2 * 8.0) - (x1 * (3.0 + (t_5 + (2.0 * ((2.0 * (x2 * t_0)) + (-1.0 - ((2.0 * (x2 * (3.0 + (x2 * -2.0)))) + (3.0 * t_0)))))))))) - 3.0)) + t_5))));
	} else if (x1 <= -5.6e-12) {
		tmp = x1 - (((((((t_8 * (t_7 - 3.0)) + ((x1 * x1) * ((t_7 * 4.0) - 6.0))) * t_1) - t_9) - t_2) - x1) - (x1 * -3.0));
	} else if (x1 <= 8.6e+93) {
		tmp = x1 - ((3.0 * ((x1 - (t_3 - (2.0 * x2))) / t_6)) - (x1 - (((t_6 * ((t_8 * (3.0 + (t_4 / t_1))) - ((x1 * x1) * 6.0))) - t_9) - t_2)));
	} else {
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - (x1 * 3.0))) + t_5))));
	}
	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) :: t_8
    real(8) :: t_9
    real(8) :: tmp
    t_0 = (2.0d0 * x2) - 3.0d0
    t_1 = (-1.0d0) - (x1 * x1)
    t_2 = x1 * (x1 * x1)
    t_3 = x1 * (x1 * 3.0d0)
    t_4 = (t_3 + (2.0d0 * x2)) - x1
    t_5 = 4.0d0 * (x2 * (3.0d0 - (2.0d0 * x2)))
    t_6 = (x1 * x1) + 1.0d0
    t_7 = t_4 / t_6
    t_8 = (x1 * 2.0d0) * t_7
    t_9 = 3.0d0 * t_3
    if (x1 <= (-1.15d+110)) then
        tmp = x1 + (9.0d0 + (x1 - (x1 * ((x1 * (((2.0d0 * (t_0 - (x2 * (-2.0d0)))) - ((x2 * 8.0d0) - (x1 * (3.0d0 + (t_5 + (2.0d0 * ((2.0d0 * (x2 * t_0)) + ((-1.0d0) - ((2.0d0 * (x2 * (3.0d0 + (x2 * (-2.0d0))))) + (3.0d0 * t_0)))))))))) - 3.0d0)) + t_5))))
    else if (x1 <= (-5.6d-12)) then
        tmp = x1 - (((((((t_8 * (t_7 - 3.0d0)) + ((x1 * x1) * ((t_7 * 4.0d0) - 6.0d0))) * t_1) - t_9) - t_2) - x1) - (x1 * (-3.0d0)))
    else if (x1 <= 8.6d+93) then
        tmp = x1 - ((3.0d0 * ((x1 - (t_3 - (2.0d0 * x2))) / t_6)) - (x1 - (((t_6 * ((t_8 * (3.0d0 + (t_4 / t_1))) - ((x1 * x1) * 6.0d0))) - t_9) - t_2)))
    else
        tmp = x1 + ((x2 * (-6.0d0)) - (x1 * (2.0d0 + ((x1 * ((3.0d0 * ((x2 * (-2.0d0)) - 3.0d0)) - (x1 * 3.0d0))) + t_5))))
    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 = -1.0 - (x1 * x1);
	double t_2 = x1 * (x1 * x1);
	double t_3 = x1 * (x1 * 3.0);
	double t_4 = (t_3 + (2.0 * x2)) - x1;
	double t_5 = 4.0 * (x2 * (3.0 - (2.0 * x2)));
	double t_6 = (x1 * x1) + 1.0;
	double t_7 = t_4 / t_6;
	double t_8 = (x1 * 2.0) * t_7;
	double t_9 = 3.0 * t_3;
	double tmp;
	if (x1 <= -1.15e+110) {
		tmp = x1 + (9.0 + (x1 - (x1 * ((x1 * (((2.0 * (t_0 - (x2 * -2.0))) - ((x2 * 8.0) - (x1 * (3.0 + (t_5 + (2.0 * ((2.0 * (x2 * t_0)) + (-1.0 - ((2.0 * (x2 * (3.0 + (x2 * -2.0)))) + (3.0 * t_0)))))))))) - 3.0)) + t_5))));
	} else if (x1 <= -5.6e-12) {
		tmp = x1 - (((((((t_8 * (t_7 - 3.0)) + ((x1 * x1) * ((t_7 * 4.0) - 6.0))) * t_1) - t_9) - t_2) - x1) - (x1 * -3.0));
	} else if (x1 <= 8.6e+93) {
		tmp = x1 - ((3.0 * ((x1 - (t_3 - (2.0 * x2))) / t_6)) - (x1 - (((t_6 * ((t_8 * (3.0 + (t_4 / t_1))) - ((x1 * x1) * 6.0))) - t_9) - t_2)));
	} else {
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - (x1 * 3.0))) + t_5))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (2.0 * x2) - 3.0
	t_1 = -1.0 - (x1 * x1)
	t_2 = x1 * (x1 * x1)
	t_3 = x1 * (x1 * 3.0)
	t_4 = (t_3 + (2.0 * x2)) - x1
	t_5 = 4.0 * (x2 * (3.0 - (2.0 * x2)))
	t_6 = (x1 * x1) + 1.0
	t_7 = t_4 / t_6
	t_8 = (x1 * 2.0) * t_7
	t_9 = 3.0 * t_3
	tmp = 0
	if x1 <= -1.15e+110:
		tmp = x1 + (9.0 + (x1 - (x1 * ((x1 * (((2.0 * (t_0 - (x2 * -2.0))) - ((x2 * 8.0) - (x1 * (3.0 + (t_5 + (2.0 * ((2.0 * (x2 * t_0)) + (-1.0 - ((2.0 * (x2 * (3.0 + (x2 * -2.0)))) + (3.0 * t_0)))))))))) - 3.0)) + t_5))))
	elif x1 <= -5.6e-12:
		tmp = x1 - (((((((t_8 * (t_7 - 3.0)) + ((x1 * x1) * ((t_7 * 4.0) - 6.0))) * t_1) - t_9) - t_2) - x1) - (x1 * -3.0))
	elif x1 <= 8.6e+93:
		tmp = x1 - ((3.0 * ((x1 - (t_3 - (2.0 * x2))) / t_6)) - (x1 - (((t_6 * ((t_8 * (3.0 + (t_4 / t_1))) - ((x1 * x1) * 6.0))) - t_9) - t_2)))
	else:
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - (x1 * 3.0))) + t_5))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(2.0 * x2) - 3.0)
	t_1 = Float64(-1.0 - Float64(x1 * x1))
	t_2 = Float64(x1 * Float64(x1 * x1))
	t_3 = Float64(x1 * Float64(x1 * 3.0))
	t_4 = Float64(Float64(t_3 + Float64(2.0 * x2)) - x1)
	t_5 = Float64(4.0 * Float64(x2 * Float64(3.0 - Float64(2.0 * x2))))
	t_6 = Float64(Float64(x1 * x1) + 1.0)
	t_7 = Float64(t_4 / t_6)
	t_8 = Float64(Float64(x1 * 2.0) * t_7)
	t_9 = Float64(3.0 * t_3)
	tmp = 0.0
	if (x1 <= -1.15e+110)
		tmp = Float64(x1 + Float64(9.0 + Float64(x1 - Float64(x1 * Float64(Float64(x1 * Float64(Float64(Float64(2.0 * Float64(t_0 - Float64(x2 * -2.0))) - Float64(Float64(x2 * 8.0) - Float64(x1 * Float64(3.0 + Float64(t_5 + Float64(2.0 * Float64(Float64(2.0 * Float64(x2 * t_0)) + Float64(-1.0 - Float64(Float64(2.0 * Float64(x2 * Float64(3.0 + Float64(x2 * -2.0)))) + Float64(3.0 * t_0)))))))))) - 3.0)) + t_5)))));
	elseif (x1 <= -5.6e-12)
		tmp = Float64(x1 - Float64(Float64(Float64(Float64(Float64(Float64(Float64(t_8 * Float64(t_7 - 3.0)) + Float64(Float64(x1 * x1) * Float64(Float64(t_7 * 4.0) - 6.0))) * t_1) - t_9) - t_2) - x1) - Float64(x1 * -3.0)));
	elseif (x1 <= 8.6e+93)
		tmp = Float64(x1 - Float64(Float64(3.0 * Float64(Float64(x1 - Float64(t_3 - Float64(2.0 * x2))) / t_6)) - Float64(x1 - Float64(Float64(Float64(t_6 * Float64(Float64(t_8 * Float64(3.0 + Float64(t_4 / t_1))) - Float64(Float64(x1 * x1) * 6.0))) - t_9) - t_2))));
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) - Float64(x1 * Float64(2.0 + Float64(Float64(x1 * Float64(Float64(3.0 * Float64(Float64(x2 * -2.0) - 3.0)) - Float64(x1 * 3.0))) + t_5)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (2.0 * x2) - 3.0;
	t_1 = -1.0 - (x1 * x1);
	t_2 = x1 * (x1 * x1);
	t_3 = x1 * (x1 * 3.0);
	t_4 = (t_3 + (2.0 * x2)) - x1;
	t_5 = 4.0 * (x2 * (3.0 - (2.0 * x2)));
	t_6 = (x1 * x1) + 1.0;
	t_7 = t_4 / t_6;
	t_8 = (x1 * 2.0) * t_7;
	t_9 = 3.0 * t_3;
	tmp = 0.0;
	if (x1 <= -1.15e+110)
		tmp = x1 + (9.0 + (x1 - (x1 * ((x1 * (((2.0 * (t_0 - (x2 * -2.0))) - ((x2 * 8.0) - (x1 * (3.0 + (t_5 + (2.0 * ((2.0 * (x2 * t_0)) + (-1.0 - ((2.0 * (x2 * (3.0 + (x2 * -2.0)))) + (3.0 * t_0)))))))))) - 3.0)) + t_5))));
	elseif (x1 <= -5.6e-12)
		tmp = x1 - (((((((t_8 * (t_7 - 3.0)) + ((x1 * x1) * ((t_7 * 4.0) - 6.0))) * t_1) - t_9) - t_2) - x1) - (x1 * -3.0));
	elseif (x1 <= 8.6e+93)
		tmp = x1 - ((3.0 * ((x1 - (t_3 - (2.0 * x2))) / t_6)) - (x1 - (((t_6 * ((t_8 * (3.0 + (t_4 / t_1))) - ((x1 * x1) * 6.0))) - t_9) - t_2)));
	else
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - (x1 * 3.0))) + t_5))));
	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[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(t$95$3 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]}, Block[{t$95$5 = N[(4.0 * N[(x2 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$7 = N[(t$95$4 / t$95$6), $MachinePrecision]}, Block[{t$95$8 = N[(N[(x1 * 2.0), $MachinePrecision] * t$95$7), $MachinePrecision]}, Block[{t$95$9 = N[(3.0 * t$95$3), $MachinePrecision]}, If[LessEqual[x1, -1.15e+110], N[(x1 + N[(9.0 + 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[(x2 * 8.0), $MachinePrecision] - N[(x1 * N[(3.0 + N[(t$95$5 + N[(2.0 * N[(N[(2.0 * N[(x2 * t$95$0), $MachinePrecision]), $MachinePrecision] + 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]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision] + t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -5.6e-12], N[(x1 - N[(N[(N[(N[(N[(N[(N[(t$95$8 * N[(t$95$7 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$7 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * t$95$1), $MachinePrecision] - t$95$9), $MachinePrecision] - t$95$2), $MachinePrecision] - x1), $MachinePrecision] - N[(x1 * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 8.6e+93], N[(x1 - N[(N[(3.0 * N[(N[(x1 - N[(t$95$3 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$6), $MachinePrecision]), $MachinePrecision] - N[(x1 - N[(N[(N[(t$95$6 * N[(N[(t$95$8 * N[(3.0 + N[(t$95$4 / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x1 * x1), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$9), $MachinePrecision] - t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] - 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$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -1.15e110

   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 inf 0.0%

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

   5. Taylor expanded in x1 around 0 75.0%

      \[\leadsto x1 + \left(\left(\color{blue}{x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(3 + \left(2 \cdot \left(-2 \cdot x2 + -1 \cdot \left(2 \cdot x2 - 3\right)\right) + \left(8 \cdot x2 + x1 \cdot \left(\left(2 \cdot \left(\left(1 + \left(2 \cdot \left(x2 \cdot \left(3 + -2 \cdot x2\right)\right) + 3 \cdot \left(2 \cdot x2 - 3\right)\right)\right) - 2 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) - 3\right)\right)\right)\right)\right)} + x1\right) + 9\right) \]

   if -1.15e110 < x1 < -5.6000000000000004e-12

   1. Initial program 91.0%

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

   3. Taylor expanded in x1 around inf 88.1%

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

   4. Taylor expanded in x1 around 0 90.9%

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

   5. Taylor expanded in x2 around 0 90.9%

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

      1. *-commutative 90.9%

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

   7. Simplified 90.9%

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

   if -5.6000000000000004e-12 < x1 < 8.6e93

   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 98.3%

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

   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 8.6e93 < x1

   1. Initial program 21.3%

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

   3. Taylor expanded in x1 around 0 13.1%

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

   4. Taylor expanded in x1 around 0 97.9%

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

4. Final simplification 93.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.15 \cdot 10^{+110}:\\ \;\;\;\;x1 + \left(9 + \left(x1 - x1 \cdot \left(x1 \cdot \left(\left(2 \cdot \left(\left(2 \cdot x2 - 3\right) - x2 \cdot -2\right) - \left(x2 \cdot 8 - x1 \cdot \left(3 + \left(4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right) + 2 \cdot \left(2 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + \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)\right)\right)\right)\right)\right) - 3\right) + 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -5.6 \cdot 10^{-12}:\\ \;\;\;\;x1 - \left(\left(\left(\left(\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) \cdot \left(-1 - x1 \cdot x1\right) - 3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right)\right) - x1 \cdot \left(x1 \cdot x1\right)\right) - x1\right) - x1 \cdot -3\right)\\ \mathbf{elif}\;x1 \leq 8.6 \cdot 10^{+93}:\\ \;\;\;\;x1 - \left(3 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right)}{x1 \cdot x1 + 1} - \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(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 6\right) - 3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right)\right) - x1 \cdot \left(x1 \cdot x1\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - 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)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 90.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := 2 \cdot x2 - 3\\ t_2 := -1 - x1 \cdot x1\\ t_3 := 3 \cdot t\_0\\ t_4 := x1 \cdot \left(x1 \cdot x1\right)\\ t_5 := \left(t\_0 + 2 \cdot x2\right) - x1\\ t_6 := x1 \cdot x1 + 1\\ t_7 := 3 + \frac{t\_5}{t\_2}\\ t_8 := 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\\ t_9 := \frac{t\_5}{t\_6}\\ t_10 := \left(x1 \cdot 2\right) \cdot t\_9\\ t_11 := t\_9 \cdot 4\\ \mathbf{if}\;x1 \leq -1.15 \cdot 10^{+110}:\\ \;\;\;\;x1 + \left(9 + \left(x1 - x1 \cdot \left(x1 \cdot \left(\left(2 \cdot \left(t\_1 - x2 \cdot -2\right) - \left(x2 \cdot 8 - x1 \cdot \left(3 + \left(t\_8 + 2 \cdot \left(2 \cdot \left(x2 \cdot t\_1\right) + \left(-1 - \left(2 \cdot \left(x2 \cdot \left(3 + x2 \cdot -2\right)\right) + 3 \cdot t\_1\right)\right)\right)\right)\right)\right)\right) - 3\right) + t\_8\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -21:\\ \;\;\;\;x1 + \left(9 + \left(x1 - \left(\left(t\_6 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 - t\_11\right) + \left(\left(x1 \cdot 2\right) \cdot 3\right) \cdot t\_7\right) - t\_3\right) - t\_4\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 0.051:\\ \;\;\;\;x1 + \left(\left(x2 \cdot -6 + x1 \cdot -3\right) + \left(x1 + \left(t\_4 + \left(t\_3 + \left(t\_10 \cdot \left(3 + \left(x1 - 2 \cdot x2\right)\right) - \left(x1 \cdot x1\right) \cdot \left(t\_11 - 6\right)\right) \cdot t\_2\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 8.6 \cdot 10^{+93}:\\ \;\;\;\;x1 + \left(9 + \left(x1 - \left(\left(t\_6 \cdot \left(t\_10 \cdot t\_7 - \left(x1 \cdot x1\right) \cdot 6\right) - t\_3\right) - t\_4\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 + \left(x1 \cdot \left(3 \cdot \left(x2 \cdot -2 - 3\right) - x1 \cdot 3\right) + t\_8\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (- (* 2.0 x2) 3.0))
        (t_2 (- -1.0 (* x1 x1)))
        (t_3 (* 3.0 t_0))
        (t_4 (* x1 (* x1 x1)))
        (t_5 (- (+ t_0 (* 2.0 x2)) x1))
        (t_6 (+ (* x1 x1) 1.0))
        (t_7 (+ 3.0 (/ t_5 t_2)))
        (t_8 (* 4.0 (* x2 (- 3.0 (* 2.0 x2)))))
        (t_9 (/ t_5 t_6))
        (t_10 (* (* x1 2.0) t_9))
        (t_11 (* t_9 4.0)))
   (if (<= x1 -1.15e+110)
     (+
      x1
      (+
       9.0
       (-
        x1
        (*
         x1
         (+
          (*
           x1
           (-
            (-
             (* 2.0 (- t_1 (* x2 -2.0)))
             (-
              (* x2 8.0)
              (*
               x1
               (+
                3.0
                (+
                 t_8
                 (*
                  2.0
                  (+
                   (* 2.0 (* x2 t_1))
                   (-
                    -1.0
                    (+ (* 2.0 (* x2 (+ 3.0 (* x2 -2.0)))) (* 3.0 t_1))))))))))
            3.0))
          t_8)))))
     (if (<= x1 -21.0)
       (+
        x1
        (+
         9.0
         (-
          x1
          (-
           (-
            (* t_6 (+ (* (* x1 x1) (- 6.0 t_11)) (* (* (* x1 2.0) 3.0) t_7)))
            t_3)
           t_4))))
       (if (<= x1 0.051)
         (+
          x1
          (+
           (+ (* x2 -6.0) (* x1 -3.0))
           (+
            x1
            (+
             t_4
             (+
              t_3
              (*
               (-
                (* t_10 (+ 3.0 (- x1 (* 2.0 x2))))
                (* (* x1 x1) (- t_11 6.0)))
               t_2))))))
         (if (<= x1 8.6e+93)
           (+
            x1
            (+
             9.0
             (-
              x1
              (- (- (* t_6 (- (* t_10 t_7) (* (* x1 x1) 6.0))) t_3) t_4))))
           (+
            x1
            (-
             (* x2 -6.0)
             (*
              x1
              (+
               2.0
               (+
                (* x1 (- (* 3.0 (- (* x2 -2.0) 3.0)) (* x1 3.0)))
                t_8)))))))))))

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 = -1.0 - (x1 * x1);
	double t_3 = 3.0 * t_0;
	double t_4 = x1 * (x1 * x1);
	double t_5 = (t_0 + (2.0 * x2)) - x1;
	double t_6 = (x1 * x1) + 1.0;
	double t_7 = 3.0 + (t_5 / t_2);
	double t_8 = 4.0 * (x2 * (3.0 - (2.0 * x2)));
	double t_9 = t_5 / t_6;
	double t_10 = (x1 * 2.0) * t_9;
	double t_11 = t_9 * 4.0;
	double tmp;
	if (x1 <= -1.15e+110) {
		tmp = x1 + (9.0 + (x1 - (x1 * ((x1 * (((2.0 * (t_1 - (x2 * -2.0))) - ((x2 * 8.0) - (x1 * (3.0 + (t_8 + (2.0 * ((2.0 * (x2 * t_1)) + (-1.0 - ((2.0 * (x2 * (3.0 + (x2 * -2.0)))) + (3.0 * t_1)))))))))) - 3.0)) + t_8))));
	} else if (x1 <= -21.0) {
		tmp = x1 + (9.0 + (x1 - (((t_6 * (((x1 * x1) * (6.0 - t_11)) + (((x1 * 2.0) * 3.0) * t_7))) - t_3) - t_4)));
	} else if (x1 <= 0.051) {
		tmp = x1 + (((x2 * -6.0) + (x1 * -3.0)) + (x1 + (t_4 + (t_3 + (((t_10 * (3.0 + (x1 - (2.0 * x2)))) - ((x1 * x1) * (t_11 - 6.0))) * t_2)))));
	} else if (x1 <= 8.6e+93) {
		tmp = x1 + (9.0 + (x1 - (((t_6 * ((t_10 * t_7) - ((x1 * x1) * 6.0))) - t_3) - t_4)));
	} else {
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - (x1 * 3.0))) + t_8))));
	}
	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_10
    real(8) :: t_11
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: t_8
    real(8) :: t_9
    real(8) :: tmp
    t_0 = x1 * (x1 * 3.0d0)
    t_1 = (2.0d0 * x2) - 3.0d0
    t_2 = (-1.0d0) - (x1 * x1)
    t_3 = 3.0d0 * t_0
    t_4 = x1 * (x1 * x1)
    t_5 = (t_0 + (2.0d0 * x2)) - x1
    t_6 = (x1 * x1) + 1.0d0
    t_7 = 3.0d0 + (t_5 / t_2)
    t_8 = 4.0d0 * (x2 * (3.0d0 - (2.0d0 * x2)))
    t_9 = t_5 / t_6
    t_10 = (x1 * 2.0d0) * t_9
    t_11 = t_9 * 4.0d0
    if (x1 <= (-1.15d+110)) then
        tmp = x1 + (9.0d0 + (x1 - (x1 * ((x1 * (((2.0d0 * (t_1 - (x2 * (-2.0d0)))) - ((x2 * 8.0d0) - (x1 * (3.0d0 + (t_8 + (2.0d0 * ((2.0d0 * (x2 * t_1)) + ((-1.0d0) - ((2.0d0 * (x2 * (3.0d0 + (x2 * (-2.0d0))))) + (3.0d0 * t_1)))))))))) - 3.0d0)) + t_8))))
    else if (x1 <= (-21.0d0)) then
        tmp = x1 + (9.0d0 + (x1 - (((t_6 * (((x1 * x1) * (6.0d0 - t_11)) + (((x1 * 2.0d0) * 3.0d0) * t_7))) - t_3) - t_4)))
    else if (x1 <= 0.051d0) then
        tmp = x1 + (((x2 * (-6.0d0)) + (x1 * (-3.0d0))) + (x1 + (t_4 + (t_3 + (((t_10 * (3.0d0 + (x1 - (2.0d0 * x2)))) - ((x1 * x1) * (t_11 - 6.0d0))) * t_2)))))
    else if (x1 <= 8.6d+93) then
        tmp = x1 + (9.0d0 + (x1 - (((t_6 * ((t_10 * t_7) - ((x1 * x1) * 6.0d0))) - t_3) - t_4)))
    else
        tmp = x1 + ((x2 * (-6.0d0)) - (x1 * (2.0d0 + ((x1 * ((3.0d0 * ((x2 * (-2.0d0)) - 3.0d0)) - (x1 * 3.0d0))) + t_8))))
    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 = -1.0 - (x1 * x1);
	double t_3 = 3.0 * t_0;
	double t_4 = x1 * (x1 * x1);
	double t_5 = (t_0 + (2.0 * x2)) - x1;
	double t_6 = (x1 * x1) + 1.0;
	double t_7 = 3.0 + (t_5 / t_2);
	double t_8 = 4.0 * (x2 * (3.0 - (2.0 * x2)));
	double t_9 = t_5 / t_6;
	double t_10 = (x1 * 2.0) * t_9;
	double t_11 = t_9 * 4.0;
	double tmp;
	if (x1 <= -1.15e+110) {
		tmp = x1 + (9.0 + (x1 - (x1 * ((x1 * (((2.0 * (t_1 - (x2 * -2.0))) - ((x2 * 8.0) - (x1 * (3.0 + (t_8 + (2.0 * ((2.0 * (x2 * t_1)) + (-1.0 - ((2.0 * (x2 * (3.0 + (x2 * -2.0)))) + (3.0 * t_1)))))))))) - 3.0)) + t_8))));
	} else if (x1 <= -21.0) {
		tmp = x1 + (9.0 + (x1 - (((t_6 * (((x1 * x1) * (6.0 - t_11)) + (((x1 * 2.0) * 3.0) * t_7))) - t_3) - t_4)));
	} else if (x1 <= 0.051) {
		tmp = x1 + (((x2 * -6.0) + (x1 * -3.0)) + (x1 + (t_4 + (t_3 + (((t_10 * (3.0 + (x1 - (2.0 * x2)))) - ((x1 * x1) * (t_11 - 6.0))) * t_2)))));
	} else if (x1 <= 8.6e+93) {
		tmp = x1 + (9.0 + (x1 - (((t_6 * ((t_10 * t_7) - ((x1 * x1) * 6.0))) - t_3) - t_4)));
	} else {
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - (x1 * 3.0))) + t_8))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = (2.0 * x2) - 3.0
	t_2 = -1.0 - (x1 * x1)
	t_3 = 3.0 * t_0
	t_4 = x1 * (x1 * x1)
	t_5 = (t_0 + (2.0 * x2)) - x1
	t_6 = (x1 * x1) + 1.0
	t_7 = 3.0 + (t_5 / t_2)
	t_8 = 4.0 * (x2 * (3.0 - (2.0 * x2)))
	t_9 = t_5 / t_6
	t_10 = (x1 * 2.0) * t_9
	t_11 = t_9 * 4.0
	tmp = 0
	if x1 <= -1.15e+110:
		tmp = x1 + (9.0 + (x1 - (x1 * ((x1 * (((2.0 * (t_1 - (x2 * -2.0))) - ((x2 * 8.0) - (x1 * (3.0 + (t_8 + (2.0 * ((2.0 * (x2 * t_1)) + (-1.0 - ((2.0 * (x2 * (3.0 + (x2 * -2.0)))) + (3.0 * t_1)))))))))) - 3.0)) + t_8))))
	elif x1 <= -21.0:
		tmp = x1 + (9.0 + (x1 - (((t_6 * (((x1 * x1) * (6.0 - t_11)) + (((x1 * 2.0) * 3.0) * t_7))) - t_3) - t_4)))
	elif x1 <= 0.051:
		tmp = x1 + (((x2 * -6.0) + (x1 * -3.0)) + (x1 + (t_4 + (t_3 + (((t_10 * (3.0 + (x1 - (2.0 * x2)))) - ((x1 * x1) * (t_11 - 6.0))) * t_2)))))
	elif x1 <= 8.6e+93:
		tmp = x1 + (9.0 + (x1 - (((t_6 * ((t_10 * t_7) - ((x1 * x1) * 6.0))) - t_3) - t_4)))
	else:
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - (x1 * 3.0))) + t_8))))
	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(-1.0 - Float64(x1 * x1))
	t_3 = Float64(3.0 * t_0)
	t_4 = Float64(x1 * Float64(x1 * x1))
	t_5 = Float64(Float64(t_0 + Float64(2.0 * x2)) - x1)
	t_6 = Float64(Float64(x1 * x1) + 1.0)
	t_7 = Float64(3.0 + Float64(t_5 / t_2))
	t_8 = Float64(4.0 * Float64(x2 * Float64(3.0 - Float64(2.0 * x2))))
	t_9 = Float64(t_5 / t_6)
	t_10 = Float64(Float64(x1 * 2.0) * t_9)
	t_11 = Float64(t_9 * 4.0)
	tmp = 0.0
	if (x1 <= -1.15e+110)
		tmp = Float64(x1 + Float64(9.0 + Float64(x1 - Float64(x1 * Float64(Float64(x1 * Float64(Float64(Float64(2.0 * Float64(t_1 - Float64(x2 * -2.0))) - Float64(Float64(x2 * 8.0) - Float64(x1 * Float64(3.0 + Float64(t_8 + Float64(2.0 * Float64(Float64(2.0 * Float64(x2 * t_1)) + Float64(-1.0 - Float64(Float64(2.0 * Float64(x2 * Float64(3.0 + Float64(x2 * -2.0)))) + Float64(3.0 * t_1)))))))))) - 3.0)) + t_8)))));
	elseif (x1 <= -21.0)
		tmp = Float64(x1 + Float64(9.0 + Float64(x1 - Float64(Float64(Float64(t_6 * Float64(Float64(Float64(x1 * x1) * Float64(6.0 - t_11)) + Float64(Float64(Float64(x1 * 2.0) * 3.0) * t_7))) - t_3) - t_4))));
	elseif (x1 <= 0.051)
		tmp = Float64(x1 + Float64(Float64(Float64(x2 * -6.0) + Float64(x1 * -3.0)) + Float64(x1 + Float64(t_4 + Float64(t_3 + Float64(Float64(Float64(t_10 * Float64(3.0 + Float64(x1 - Float64(2.0 * x2)))) - Float64(Float64(x1 * x1) * Float64(t_11 - 6.0))) * t_2))))));
	elseif (x1 <= 8.6e+93)
		tmp = Float64(x1 + Float64(9.0 + Float64(x1 - Float64(Float64(Float64(t_6 * Float64(Float64(t_10 * t_7) - Float64(Float64(x1 * x1) * 6.0))) - t_3) - t_4))));
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) - Float64(x1 * Float64(2.0 + Float64(Float64(x1 * Float64(Float64(3.0 * Float64(Float64(x2 * -2.0) - 3.0)) - Float64(x1 * 3.0))) + t_8)))));
	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 = -1.0 - (x1 * x1);
	t_3 = 3.0 * t_0;
	t_4 = x1 * (x1 * x1);
	t_5 = (t_0 + (2.0 * x2)) - x1;
	t_6 = (x1 * x1) + 1.0;
	t_7 = 3.0 + (t_5 / t_2);
	t_8 = 4.0 * (x2 * (3.0 - (2.0 * x2)));
	t_9 = t_5 / t_6;
	t_10 = (x1 * 2.0) * t_9;
	t_11 = t_9 * 4.0;
	tmp = 0.0;
	if (x1 <= -1.15e+110)
		tmp = x1 + (9.0 + (x1 - (x1 * ((x1 * (((2.0 * (t_1 - (x2 * -2.0))) - ((x2 * 8.0) - (x1 * (3.0 + (t_8 + (2.0 * ((2.0 * (x2 * t_1)) + (-1.0 - ((2.0 * (x2 * (3.0 + (x2 * -2.0)))) + (3.0 * t_1)))))))))) - 3.0)) + t_8))));
	elseif (x1 <= -21.0)
		tmp = x1 + (9.0 + (x1 - (((t_6 * (((x1 * x1) * (6.0 - t_11)) + (((x1 * 2.0) * 3.0) * t_7))) - t_3) - t_4)));
	elseif (x1 <= 0.051)
		tmp = x1 + (((x2 * -6.0) + (x1 * -3.0)) + (x1 + (t_4 + (t_3 + (((t_10 * (3.0 + (x1 - (2.0 * x2)))) - ((x1 * x1) * (t_11 - 6.0))) * t_2)))));
	elseif (x1 <= 8.6e+93)
		tmp = x1 + (9.0 + (x1 - (((t_6 * ((t_10 * t_7) - ((x1 * x1) * 6.0))) - t_3) - t_4)));
	else
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - (x1 * 3.0))) + t_8))));
	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[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(3.0 * t$95$0), $MachinePrecision]}, Block[{t$95$4 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]}, Block[{t$95$6 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$7 = N[(3.0 + N[(t$95$5 / t$95$2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$8 = N[(4.0 * N[(x2 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$9 = N[(t$95$5 / t$95$6), $MachinePrecision]}, Block[{t$95$10 = N[(N[(x1 * 2.0), $MachinePrecision] * t$95$9), $MachinePrecision]}, Block[{t$95$11 = N[(t$95$9 * 4.0), $MachinePrecision]}, If[LessEqual[x1, -1.15e+110], N[(x1 + N[(9.0 + 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[(x2 * 8.0), $MachinePrecision] - N[(x1 * N[(3.0 + N[(t$95$8 + N[(2.0 * N[(N[(2.0 * N[(x2 * t$95$1), $MachinePrecision]), $MachinePrecision] + 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]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision] + t$95$8), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -21.0], N[(x1 + N[(9.0 + N[(x1 - N[(N[(N[(t$95$6 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 - t$95$11), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(x1 * 2.0), $MachinePrecision] * 3.0), $MachinePrecision] * t$95$7), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$3), $MachinePrecision] - t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 0.051], N[(x1 + N[(N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * -3.0), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(t$95$4 + N[(t$95$3 + N[(N[(N[(t$95$10 * N[(3.0 + N[(x1 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x1 * x1), $MachinePrecision] * N[(t$95$11 - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 8.6e+93], N[(x1 + N[(9.0 + N[(x1 - N[(N[(N[(t$95$6 * N[(N[(t$95$10 * t$95$7), $MachinePrecision] - N[(N[(x1 * x1), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$3), $MachinePrecision] - t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] - 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$8), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x1 < -1.15e110

   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 inf 0.0%

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

   5. Taylor expanded in x1 around 0 75.0%

      \[\leadsto x1 + \left(\left(\color{blue}{x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(3 + \left(2 \cdot \left(-2 \cdot x2 + -1 \cdot \left(2 \cdot x2 - 3\right)\right) + \left(8 \cdot x2 + x1 \cdot \left(\left(2 \cdot \left(\left(1 + \left(2 \cdot \left(x2 \cdot \left(3 + -2 \cdot x2\right)\right) + 3 \cdot \left(2 \cdot x2 - 3\right)\right)\right) - 2 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) - 3\right)\right)\right)\right)\right)} + x1\right) + 9\right) \]

   if -1.15e110 < x1 < -21

   1. Initial program 90.3%

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

   3. Taylor expanded in x1 around inf 90.2%

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

   4. Taylor expanded in x1 around inf 90.2%

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

   5. Taylor expanded in x1 around inf 79.3%

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

   if -21 < x1 < 0.0509999999999999967

   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 98.2%

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

   4. Taylor expanded in x1 around 0 99.3%

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

   5. Taylor expanded in x1 around 0 98.4%

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

      1. +-commutative 98.4%

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

      2. mul-1-neg 98.4%

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

      3. sub-neg 98.4%

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

   7. Simplified 98.4%

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

   if 0.0509999999999999967 < x1 < 8.6e93

   1. Initial program 98.9%

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

   3. Taylor expanded in x1 around inf 95.5%

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

   4. Taylor expanded in x1 around inf 95.5%

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

   5. Taylor expanded in x1 around inf 92.0%

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

   if 8.6e93 < x1

   1. Initial program 21.3%

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

   3. Taylor expanded in x1 around 0 13.1%

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

   4. Taylor expanded in x1 around 0 97.9%

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

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.15 \cdot 10^{+110}:\\ \;\;\;\;x1 + \left(9 + \left(x1 - x1 \cdot \left(x1 \cdot \left(\left(2 \cdot \left(\left(2 \cdot x2 - 3\right) - x2 \cdot -2\right) - \left(x2 \cdot 8 - x1 \cdot \left(3 + \left(4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right) + 2 \cdot \left(2 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + \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)\right)\right)\right)\right)\right) - 3\right) + 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -21:\\ \;\;\;\;x1 + \left(9 + \left(x1 - \left(\left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 - \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4\right) + \left(\left(x1 \cdot 2\right) \cdot 3\right) \cdot \left(3 + \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1}\right)\right) - 3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right)\right) - x1 \cdot \left(x1 \cdot x1\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 0.051:\\ \;\;\;\;x1 + \left(\left(x2 \cdot -6 + x1 \cdot -3\right) + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) + \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 + \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) \cdot \left(-1 - x1 \cdot x1\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 8.6 \cdot 10^{+93}:\\ \;\;\;\;x1 + \left(9 + \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(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 6\right) - 3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right)\right) - x1 \cdot \left(x1 \cdot x1\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - 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)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 90.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := 2 \cdot x2 - 3\\ t_2 := -1 - x1 \cdot x1\\ t_3 := 3 \cdot t\_0\\ t_4 := x1 \cdot \left(x1 \cdot x1\right)\\ t_5 := \left(t\_0 + 2 \cdot x2\right) - x1\\ t_6 := x1 \cdot x1 + 1\\ t_7 := 3 + \frac{t\_5}{t\_2}\\ t_8 := 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\\ t_9 := \frac{t\_5}{t\_6}\\ t_10 := t\_9 \cdot 4\\ t_11 := \left(x1 \cdot 2\right) \cdot t\_9\\ \mathbf{if}\;x1 \leq -1.15 \cdot 10^{+110}:\\ \;\;\;\;x1 + \left(9 + \left(x1 - x1 \cdot \left(x1 \cdot \left(\left(2 \cdot \left(t\_1 - x2 \cdot -2\right) - \left(x2 \cdot 8 - x1 \cdot \left(3 + \left(t\_8 + 2 \cdot \left(2 \cdot \left(x2 \cdot t\_1\right) + \left(-1 - \left(2 \cdot \left(x2 \cdot \left(3 + x2 \cdot -2\right)\right) + 3 \cdot t\_1\right)\right)\right)\right)\right)\right)\right) - 3\right) + t\_8\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -9500:\\ \;\;\;\;x1 + \left(9 + \left(x1 - \left(\left(t\_6 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 - t\_10\right) + \left(\left(x1 \cdot 2\right) \cdot 3\right) \cdot t\_7\right) - t\_3\right) - t\_4\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 0.0068:\\ \;\;\;\;x1 + \left(\left(x2 \cdot -6 + x1 \cdot -3\right) + \left(x1 + \left(t\_4 + \left(t\_3 - \left(\left(x1 \cdot x1\right) \cdot \left(t\_10 - 6\right) + t\_11 \cdot t\_1\right) \cdot t\_2\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 8.6 \cdot 10^{+93}:\\ \;\;\;\;x1 + \left(9 + \left(x1 - \left(\left(t\_6 \cdot \left(t\_11 \cdot t\_7 - \left(x1 \cdot x1\right) \cdot 6\right) - t\_3\right) - t\_4\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 + \left(x1 \cdot \left(3 \cdot \left(x2 \cdot -2 - 3\right) - x1 \cdot 3\right) + t\_8\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (- (* 2.0 x2) 3.0))
        (t_2 (- -1.0 (* x1 x1)))
        (t_3 (* 3.0 t_0))
        (t_4 (* x1 (* x1 x1)))
        (t_5 (- (+ t_0 (* 2.0 x2)) x1))
        (t_6 (+ (* x1 x1) 1.0))
        (t_7 (+ 3.0 (/ t_5 t_2)))
        (t_8 (* 4.0 (* x2 (- 3.0 (* 2.0 x2)))))
        (t_9 (/ t_5 t_6))
        (t_10 (* t_9 4.0))
        (t_11 (* (* x1 2.0) t_9)))
   (if (<= x1 -1.15e+110)
     (+
      x1
      (+
       9.0
       (-
        x1
        (*
         x1
         (+
          (*
           x1
           (-
            (-
             (* 2.0 (- t_1 (* x2 -2.0)))
             (-
              (* x2 8.0)
              (*
               x1
               (+
                3.0
                (+
                 t_8
                 (*
                  2.0
                  (+
                   (* 2.0 (* x2 t_1))
                   (-
                    -1.0
                    (+ (* 2.0 (* x2 (+ 3.0 (* x2 -2.0)))) (* 3.0 t_1))))))))))
            3.0))
          t_8)))))
     (if (<= x1 -9500.0)
       (+
        x1
        (+
         9.0
         (-
          x1
          (-
           (-
            (* t_6 (+ (* (* x1 x1) (- 6.0 t_10)) (* (* (* x1 2.0) 3.0) t_7)))
            t_3)
           t_4))))
       (if (<= x1 0.0068)
         (+
          x1
          (+
           (+ (* x2 -6.0) (* x1 -3.0))
           (+
            x1
            (+
             t_4
             (- t_3 (* (+ (* (* x1 x1) (- t_10 6.0)) (* t_11 t_1)) t_2))))))
         (if (<= x1 8.6e+93)
           (+
            x1
            (+
             9.0
             (-
              x1
              (- (- (* t_6 (- (* t_11 t_7) (* (* x1 x1) 6.0))) t_3) t_4))))
           (+
            x1
            (-
             (* x2 -6.0)
             (*
              x1
              (+
               2.0
               (+
                (* x1 (- (* 3.0 (- (* x2 -2.0) 3.0)) (* x1 3.0)))
                t_8)))))))))))

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 = -1.0 - (x1 * x1);
	double t_3 = 3.0 * t_0;
	double t_4 = x1 * (x1 * x1);
	double t_5 = (t_0 + (2.0 * x2)) - x1;
	double t_6 = (x1 * x1) + 1.0;
	double t_7 = 3.0 + (t_5 / t_2);
	double t_8 = 4.0 * (x2 * (3.0 - (2.0 * x2)));
	double t_9 = t_5 / t_6;
	double t_10 = t_9 * 4.0;
	double t_11 = (x1 * 2.0) * t_9;
	double tmp;
	if (x1 <= -1.15e+110) {
		tmp = x1 + (9.0 + (x1 - (x1 * ((x1 * (((2.0 * (t_1 - (x2 * -2.0))) - ((x2 * 8.0) - (x1 * (3.0 + (t_8 + (2.0 * ((2.0 * (x2 * t_1)) + (-1.0 - ((2.0 * (x2 * (3.0 + (x2 * -2.0)))) + (3.0 * t_1)))))))))) - 3.0)) + t_8))));
	} else if (x1 <= -9500.0) {
		tmp = x1 + (9.0 + (x1 - (((t_6 * (((x1 * x1) * (6.0 - t_10)) + (((x1 * 2.0) * 3.0) * t_7))) - t_3) - t_4)));
	} else if (x1 <= 0.0068) {
		tmp = x1 + (((x2 * -6.0) + (x1 * -3.0)) + (x1 + (t_4 + (t_3 - ((((x1 * x1) * (t_10 - 6.0)) + (t_11 * t_1)) * t_2)))));
	} else if (x1 <= 8.6e+93) {
		tmp = x1 + (9.0 + (x1 - (((t_6 * ((t_11 * t_7) - ((x1 * x1) * 6.0))) - t_3) - t_4)));
	} else {
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - (x1 * 3.0))) + t_8))));
	}
	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_10
    real(8) :: t_11
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: t_8
    real(8) :: t_9
    real(8) :: tmp
    t_0 = x1 * (x1 * 3.0d0)
    t_1 = (2.0d0 * x2) - 3.0d0
    t_2 = (-1.0d0) - (x1 * x1)
    t_3 = 3.0d0 * t_0
    t_4 = x1 * (x1 * x1)
    t_5 = (t_0 + (2.0d0 * x2)) - x1
    t_6 = (x1 * x1) + 1.0d0
    t_7 = 3.0d0 + (t_5 / t_2)
    t_8 = 4.0d0 * (x2 * (3.0d0 - (2.0d0 * x2)))
    t_9 = t_5 / t_6
    t_10 = t_9 * 4.0d0
    t_11 = (x1 * 2.0d0) * t_9
    if (x1 <= (-1.15d+110)) then
        tmp = x1 + (9.0d0 + (x1 - (x1 * ((x1 * (((2.0d0 * (t_1 - (x2 * (-2.0d0)))) - ((x2 * 8.0d0) - (x1 * (3.0d0 + (t_8 + (2.0d0 * ((2.0d0 * (x2 * t_1)) + ((-1.0d0) - ((2.0d0 * (x2 * (3.0d0 + (x2 * (-2.0d0))))) + (3.0d0 * t_1)))))))))) - 3.0d0)) + t_8))))
    else if (x1 <= (-9500.0d0)) then
        tmp = x1 + (9.0d0 + (x1 - (((t_6 * (((x1 * x1) * (6.0d0 - t_10)) + (((x1 * 2.0d0) * 3.0d0) * t_7))) - t_3) - t_4)))
    else if (x1 <= 0.0068d0) then
        tmp = x1 + (((x2 * (-6.0d0)) + (x1 * (-3.0d0))) + (x1 + (t_4 + (t_3 - ((((x1 * x1) * (t_10 - 6.0d0)) + (t_11 * t_1)) * t_2)))))
    else if (x1 <= 8.6d+93) then
        tmp = x1 + (9.0d0 + (x1 - (((t_6 * ((t_11 * t_7) - ((x1 * x1) * 6.0d0))) - t_3) - t_4)))
    else
        tmp = x1 + ((x2 * (-6.0d0)) - (x1 * (2.0d0 + ((x1 * ((3.0d0 * ((x2 * (-2.0d0)) - 3.0d0)) - (x1 * 3.0d0))) + t_8))))
    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 = -1.0 - (x1 * x1);
	double t_3 = 3.0 * t_0;
	double t_4 = x1 * (x1 * x1);
	double t_5 = (t_0 + (2.0 * x2)) - x1;
	double t_6 = (x1 * x1) + 1.0;
	double t_7 = 3.0 + (t_5 / t_2);
	double t_8 = 4.0 * (x2 * (3.0 - (2.0 * x2)));
	double t_9 = t_5 / t_6;
	double t_10 = t_9 * 4.0;
	double t_11 = (x1 * 2.0) * t_9;
	double tmp;
	if (x1 <= -1.15e+110) {
		tmp = x1 + (9.0 + (x1 - (x1 * ((x1 * (((2.0 * (t_1 - (x2 * -2.0))) - ((x2 * 8.0) - (x1 * (3.0 + (t_8 + (2.0 * ((2.0 * (x2 * t_1)) + (-1.0 - ((2.0 * (x2 * (3.0 + (x2 * -2.0)))) + (3.0 * t_1)))))))))) - 3.0)) + t_8))));
	} else if (x1 <= -9500.0) {
		tmp = x1 + (9.0 + (x1 - (((t_6 * (((x1 * x1) * (6.0 - t_10)) + (((x1 * 2.0) * 3.0) * t_7))) - t_3) - t_4)));
	} else if (x1 <= 0.0068) {
		tmp = x1 + (((x2 * -6.0) + (x1 * -3.0)) + (x1 + (t_4 + (t_3 - ((((x1 * x1) * (t_10 - 6.0)) + (t_11 * t_1)) * t_2)))));
	} else if (x1 <= 8.6e+93) {
		tmp = x1 + (9.0 + (x1 - (((t_6 * ((t_11 * t_7) - ((x1 * x1) * 6.0))) - t_3) - t_4)));
	} else {
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - (x1 * 3.0))) + t_8))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = (2.0 * x2) - 3.0
	t_2 = -1.0 - (x1 * x1)
	t_3 = 3.0 * t_0
	t_4 = x1 * (x1 * x1)
	t_5 = (t_0 + (2.0 * x2)) - x1
	t_6 = (x1 * x1) + 1.0
	t_7 = 3.0 + (t_5 / t_2)
	t_8 = 4.0 * (x2 * (3.0 - (2.0 * x2)))
	t_9 = t_5 / t_6
	t_10 = t_9 * 4.0
	t_11 = (x1 * 2.0) * t_9
	tmp = 0
	if x1 <= -1.15e+110:
		tmp = x1 + (9.0 + (x1 - (x1 * ((x1 * (((2.0 * (t_1 - (x2 * -2.0))) - ((x2 * 8.0) - (x1 * (3.0 + (t_8 + (2.0 * ((2.0 * (x2 * t_1)) + (-1.0 - ((2.0 * (x2 * (3.0 + (x2 * -2.0)))) + (3.0 * t_1)))))))))) - 3.0)) + t_8))))
	elif x1 <= -9500.0:
		tmp = x1 + (9.0 + (x1 - (((t_6 * (((x1 * x1) * (6.0 - t_10)) + (((x1 * 2.0) * 3.0) * t_7))) - t_3) - t_4)))
	elif x1 <= 0.0068:
		tmp = x1 + (((x2 * -6.0) + (x1 * -3.0)) + (x1 + (t_4 + (t_3 - ((((x1 * x1) * (t_10 - 6.0)) + (t_11 * t_1)) * t_2)))))
	elif x1 <= 8.6e+93:
		tmp = x1 + (9.0 + (x1 - (((t_6 * ((t_11 * t_7) - ((x1 * x1) * 6.0))) - t_3) - t_4)))
	else:
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - (x1 * 3.0))) + t_8))))
	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(-1.0 - Float64(x1 * x1))
	t_3 = Float64(3.0 * t_0)
	t_4 = Float64(x1 * Float64(x1 * x1))
	t_5 = Float64(Float64(t_0 + Float64(2.0 * x2)) - x1)
	t_6 = Float64(Float64(x1 * x1) + 1.0)
	t_7 = Float64(3.0 + Float64(t_5 / t_2))
	t_8 = Float64(4.0 * Float64(x2 * Float64(3.0 - Float64(2.0 * x2))))
	t_9 = Float64(t_5 / t_6)
	t_10 = Float64(t_9 * 4.0)
	t_11 = Float64(Float64(x1 * 2.0) * t_9)
	tmp = 0.0
	if (x1 <= -1.15e+110)
		tmp = Float64(x1 + Float64(9.0 + Float64(x1 - Float64(x1 * Float64(Float64(x1 * Float64(Float64(Float64(2.0 * Float64(t_1 - Float64(x2 * -2.0))) - Float64(Float64(x2 * 8.0) - Float64(x1 * Float64(3.0 + Float64(t_8 + Float64(2.0 * Float64(Float64(2.0 * Float64(x2 * t_1)) + Float64(-1.0 - Float64(Float64(2.0 * Float64(x2 * Float64(3.0 + Float64(x2 * -2.0)))) + Float64(3.0 * t_1)))))))))) - 3.0)) + t_8)))));
	elseif (x1 <= -9500.0)
		tmp = Float64(x1 + Float64(9.0 + Float64(x1 - Float64(Float64(Float64(t_6 * Float64(Float64(Float64(x1 * x1) * Float64(6.0 - t_10)) + Float64(Float64(Float64(x1 * 2.0) * 3.0) * t_7))) - t_3) - t_4))));
	elseif (x1 <= 0.0068)
		tmp = Float64(x1 + Float64(Float64(Float64(x2 * -6.0) + Float64(x1 * -3.0)) + Float64(x1 + Float64(t_4 + Float64(t_3 - Float64(Float64(Float64(Float64(x1 * x1) * Float64(t_10 - 6.0)) + Float64(t_11 * t_1)) * t_2))))));
	elseif (x1 <= 8.6e+93)
		tmp = Float64(x1 + Float64(9.0 + Float64(x1 - Float64(Float64(Float64(t_6 * Float64(Float64(t_11 * t_7) - Float64(Float64(x1 * x1) * 6.0))) - t_3) - t_4))));
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) - Float64(x1 * Float64(2.0 + Float64(Float64(x1 * Float64(Float64(3.0 * Float64(Float64(x2 * -2.0) - 3.0)) - Float64(x1 * 3.0))) + t_8)))));
	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 = -1.0 - (x1 * x1);
	t_3 = 3.0 * t_0;
	t_4 = x1 * (x1 * x1);
	t_5 = (t_0 + (2.0 * x2)) - x1;
	t_6 = (x1 * x1) + 1.0;
	t_7 = 3.0 + (t_5 / t_2);
	t_8 = 4.0 * (x2 * (3.0 - (2.0 * x2)));
	t_9 = t_5 / t_6;
	t_10 = t_9 * 4.0;
	t_11 = (x1 * 2.0) * t_9;
	tmp = 0.0;
	if (x1 <= -1.15e+110)
		tmp = x1 + (9.0 + (x1 - (x1 * ((x1 * (((2.0 * (t_1 - (x2 * -2.0))) - ((x2 * 8.0) - (x1 * (3.0 + (t_8 + (2.0 * ((2.0 * (x2 * t_1)) + (-1.0 - ((2.0 * (x2 * (3.0 + (x2 * -2.0)))) + (3.0 * t_1)))))))))) - 3.0)) + t_8))));
	elseif (x1 <= -9500.0)
		tmp = x1 + (9.0 + (x1 - (((t_6 * (((x1 * x1) * (6.0 - t_10)) + (((x1 * 2.0) * 3.0) * t_7))) - t_3) - t_4)));
	elseif (x1 <= 0.0068)
		tmp = x1 + (((x2 * -6.0) + (x1 * -3.0)) + (x1 + (t_4 + (t_3 - ((((x1 * x1) * (t_10 - 6.0)) + (t_11 * t_1)) * t_2)))));
	elseif (x1 <= 8.6e+93)
		tmp = x1 + (9.0 + (x1 - (((t_6 * ((t_11 * t_7) - ((x1 * x1) * 6.0))) - t_3) - t_4)));
	else
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - (x1 * 3.0))) + t_8))));
	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[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(3.0 * t$95$0), $MachinePrecision]}, Block[{t$95$4 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]}, Block[{t$95$6 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$7 = N[(3.0 + N[(t$95$5 / t$95$2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$8 = N[(4.0 * N[(x2 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$9 = N[(t$95$5 / t$95$6), $MachinePrecision]}, Block[{t$95$10 = N[(t$95$9 * 4.0), $MachinePrecision]}, Block[{t$95$11 = N[(N[(x1 * 2.0), $MachinePrecision] * t$95$9), $MachinePrecision]}, If[LessEqual[x1, -1.15e+110], N[(x1 + N[(9.0 + 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[(x2 * 8.0), $MachinePrecision] - N[(x1 * N[(3.0 + N[(t$95$8 + N[(2.0 * N[(N[(2.0 * N[(x2 * t$95$1), $MachinePrecision]), $MachinePrecision] + 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]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision] + t$95$8), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -9500.0], N[(x1 + N[(9.0 + N[(x1 - N[(N[(N[(t$95$6 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 - t$95$10), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(x1 * 2.0), $MachinePrecision] * 3.0), $MachinePrecision] * t$95$7), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$3), $MachinePrecision] - t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 0.0068], N[(x1 + N[(N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * -3.0), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(t$95$4 + N[(t$95$3 - N[(N[(N[(N[(x1 * x1), $MachinePrecision] * N[(t$95$10 - 6.0), $MachinePrecision]), $MachinePrecision] + N[(t$95$11 * t$95$1), $MachinePrecision]), $MachinePrecision] * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 8.6e+93], N[(x1 + N[(9.0 + N[(x1 - N[(N[(N[(t$95$6 * N[(N[(t$95$11 * t$95$7), $MachinePrecision] - N[(N[(x1 * x1), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$3), $MachinePrecision] - t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] - 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$8), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x1 < -1.15e110

   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 inf 0.0%

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

   5. Taylor expanded in x1 around 0 75.0%

      \[\leadsto x1 + \left(\left(\color{blue}{x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(3 + \left(2 \cdot \left(-2 \cdot x2 + -1 \cdot \left(2 \cdot x2 - 3\right)\right) + \left(8 \cdot x2 + x1 \cdot \left(\left(2 \cdot \left(\left(1 + \left(2 \cdot \left(x2 \cdot \left(3 + -2 \cdot x2\right)\right) + 3 \cdot \left(2 \cdot x2 - 3\right)\right)\right) - 2 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) - 3\right)\right)\right)\right)\right)} + x1\right) + 9\right) \]

   if -1.15e110 < x1 < -9500

   1. Initial program 90.3%

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

   3. Taylor expanded in x1 around inf 90.2%

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

   4. Taylor expanded in x1 around inf 90.2%

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

   5. Taylor expanded in x1 around inf 79.3%

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

   if -9500 < x1 < 0.00679999999999999962

   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 98.2%

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

   4. Taylor expanded in x1 around 0 99.3%

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

   5. Taylor expanded in x1 around 0 98.3%

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

   if 0.00679999999999999962 < x1 < 8.6e93

   1. Initial program 98.9%

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

   3. Taylor expanded in x1 around inf 95.5%

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

   4. Taylor expanded in x1 around inf 95.5%

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

   5. Taylor expanded in x1 around inf 92.0%

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

   if 8.6e93 < x1

   1. Initial program 21.3%

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

   3. Taylor expanded in x1 around 0 13.1%

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

   4. Taylor expanded in x1 around 0 97.9%

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

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.15 \cdot 10^{+110}:\\ \;\;\;\;x1 + \left(9 + \left(x1 - x1 \cdot \left(x1 \cdot \left(\left(2 \cdot \left(\left(2 \cdot x2 - 3\right) - x2 \cdot -2\right) - \left(x2 \cdot 8 - x1 \cdot \left(3 + \left(4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right) + 2 \cdot \left(2 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + \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)\right)\right)\right)\right)\right) - 3\right) + 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -9500:\\ \;\;\;\;x1 + \left(9 + \left(x1 - \left(\left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 - \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4\right) + \left(\left(x1 \cdot 2\right) \cdot 3\right) \cdot \left(3 + \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1}\right)\right) - 3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right)\right) - x1 \cdot \left(x1 \cdot x1\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 0.0068:\\ \;\;\;\;x1 + \left(\left(x2 \cdot -6 + x1 \cdot -3\right) + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) - \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) \cdot \left(-1 - x1 \cdot x1\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 8.6 \cdot 10^{+93}:\\ \;\;\;\;x1 + \left(9 + \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(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 6\right) - 3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right)\right) - x1 \cdot \left(x1 \cdot x1\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - 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)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 86.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := \left(t\_0 + 2 \cdot x2\right) - x1\\ t_2 := x1 \cdot x1 + 1\\ t_3 := -1 - x1 \cdot x1\\ t_4 := x1 + \left(9 + \left(x1 - \left(\left(t\_2 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 - \frac{t\_1}{t\_2} \cdot 4\right) + \left(\left(x1 \cdot 2\right) \cdot 3\right) \cdot \left(3 + \frac{t\_1}{t\_3}\right)\right) - 3 \cdot t\_0\right) - x1 \cdot \left(x1 \cdot x1\right)\right)\right)\right)\\ t_5 := 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\\ \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(9 + \left(x1 - x1 \cdot \left(x1 \cdot \left(\left(2 \cdot \left(\left(2 \cdot x2 - 3\right) - x2 \cdot -2\right) - x2 \cdot 8\right) - 3\right) + t\_5\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -4800:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;x1 \leq 27:\\ \;\;\;\;x1 + \left(3 \cdot \frac{x1 - \left(t\_0 - 2 \cdot x2\right)}{t\_3} + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot -3 + 2 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.5 \cdot 10^{+97}:\\ \;\;\;\;t\_4\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 + \left(x1 \cdot \left(3 \cdot \left(x2 \cdot -2 - 3\right) - x1 \cdot 3\right) + t\_5\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (- (+ t_0 (* 2.0 x2)) x1))
        (t_2 (+ (* x1 x1) 1.0))
        (t_3 (- -1.0 (* x1 x1)))
        (t_4
         (+
          x1
          (+
           9.0
           (-
            x1
            (-
             (-
              (*
               t_2
               (+
                (* (* x1 x1) (- 6.0 (* (/ t_1 t_2) 4.0)))
                (* (* (* x1 2.0) 3.0) (+ 3.0 (/ t_1 t_3)))))
              (* 3.0 t_0))
             (* x1 (* x1 x1)))))))
        (t_5 (* 4.0 (* x2 (- 3.0 (* 2.0 x2))))))
   (if (<= x1 -5.6e+102)
     (+
      x1
      (+
       9.0
       (-
        x1
        (*
         x1
         (+
          (*
           x1
           (- (- (* 2.0 (- (- (* 2.0 x2) 3.0) (* x2 -2.0))) (* x2 8.0)) 3.0))
          t_5)))))
     (if (<= x1 -4800.0)
       t_4
       (if (<= x1 27.0)
         (+
          x1
          (+
           (* 3.0 (/ (- x1 (- t_0 (* 2.0 x2))) t_3))
           (+ x1 (* 4.0 (* x2 (+ (* x1 -3.0) (* 2.0 (* x1 x2))))))))
         (if (<= x1 1.5e+97)
           t_4
           (+
            x1
            (-
             (* x2 -6.0)
             (*
              x1
              (+
               2.0
               (+
                (* x1 (- (* 3.0 (- (* x2 -2.0) 3.0)) (* x1 3.0)))
                t_5)))))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = (t_0 + (2.0 * x2)) - x1;
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = -1.0 - (x1 * x1);
	double t_4 = x1 + (9.0 + (x1 - (((t_2 * (((x1 * x1) * (6.0 - ((t_1 / t_2) * 4.0))) + (((x1 * 2.0) * 3.0) * (3.0 + (t_1 / t_3))))) - (3.0 * t_0)) - (x1 * (x1 * x1)))));
	double t_5 = 4.0 * (x2 * (3.0 - (2.0 * x2)));
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = x1 + (9.0 + (x1 - (x1 * ((x1 * (((2.0 * (((2.0 * x2) - 3.0) - (x2 * -2.0))) - (x2 * 8.0)) - 3.0)) + t_5))));
	} else if (x1 <= -4800.0) {
		tmp = t_4;
	} else if (x1 <= 27.0) {
		tmp = x1 + ((3.0 * ((x1 - (t_0 - (2.0 * x2))) / t_3)) + (x1 + (4.0 * (x2 * ((x1 * -3.0) + (2.0 * (x1 * x2)))))));
	} else if (x1 <= 1.5e+97) {
		tmp = t_4;
	} else {
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - (x1 * 3.0))) + t_5))));
	}
	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) :: tmp
    t_0 = x1 * (x1 * 3.0d0)
    t_1 = (t_0 + (2.0d0 * x2)) - x1
    t_2 = (x1 * x1) + 1.0d0
    t_3 = (-1.0d0) - (x1 * x1)
    t_4 = x1 + (9.0d0 + (x1 - (((t_2 * (((x1 * x1) * (6.0d0 - ((t_1 / t_2) * 4.0d0))) + (((x1 * 2.0d0) * 3.0d0) * (3.0d0 + (t_1 / t_3))))) - (3.0d0 * t_0)) - (x1 * (x1 * x1)))))
    t_5 = 4.0d0 * (x2 * (3.0d0 - (2.0d0 * x2)))
    if (x1 <= (-5.6d+102)) then
        tmp = x1 + (9.0d0 + (x1 - (x1 * ((x1 * (((2.0d0 * (((2.0d0 * x2) - 3.0d0) - (x2 * (-2.0d0)))) - (x2 * 8.0d0)) - 3.0d0)) + t_5))))
    else if (x1 <= (-4800.0d0)) then
        tmp = t_4
    else if (x1 <= 27.0d0) then
        tmp = x1 + ((3.0d0 * ((x1 - (t_0 - (2.0d0 * x2))) / t_3)) + (x1 + (4.0d0 * (x2 * ((x1 * (-3.0d0)) + (2.0d0 * (x1 * x2)))))))
    else if (x1 <= 1.5d+97) then
        tmp = t_4
    else
        tmp = x1 + ((x2 * (-6.0d0)) - (x1 * (2.0d0 + ((x1 * ((3.0d0 * ((x2 * (-2.0d0)) - 3.0d0)) - (x1 * 3.0d0))) + t_5))))
    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 = (t_0 + (2.0 * x2)) - x1;
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = -1.0 - (x1 * x1);
	double t_4 = x1 + (9.0 + (x1 - (((t_2 * (((x1 * x1) * (6.0 - ((t_1 / t_2) * 4.0))) + (((x1 * 2.0) * 3.0) * (3.0 + (t_1 / t_3))))) - (3.0 * t_0)) - (x1 * (x1 * x1)))));
	double t_5 = 4.0 * (x2 * (3.0 - (2.0 * x2)));
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = x1 + (9.0 + (x1 - (x1 * ((x1 * (((2.0 * (((2.0 * x2) - 3.0) - (x2 * -2.0))) - (x2 * 8.0)) - 3.0)) + t_5))));
	} else if (x1 <= -4800.0) {
		tmp = t_4;
	} else if (x1 <= 27.0) {
		tmp = x1 + ((3.0 * ((x1 - (t_0 - (2.0 * x2))) / t_3)) + (x1 + (4.0 * (x2 * ((x1 * -3.0) + (2.0 * (x1 * x2)))))));
	} else if (x1 <= 1.5e+97) {
		tmp = t_4;
	} else {
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - (x1 * 3.0))) + t_5))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = (t_0 + (2.0 * x2)) - x1
	t_2 = (x1 * x1) + 1.0
	t_3 = -1.0 - (x1 * x1)
	t_4 = x1 + (9.0 + (x1 - (((t_2 * (((x1 * x1) * (6.0 - ((t_1 / t_2) * 4.0))) + (((x1 * 2.0) * 3.0) * (3.0 + (t_1 / t_3))))) - (3.0 * t_0)) - (x1 * (x1 * x1)))))
	t_5 = 4.0 * (x2 * (3.0 - (2.0 * x2)))
	tmp = 0
	if x1 <= -5.6e+102:
		tmp = x1 + (9.0 + (x1 - (x1 * ((x1 * (((2.0 * (((2.0 * x2) - 3.0) - (x2 * -2.0))) - (x2 * 8.0)) - 3.0)) + t_5))))
	elif x1 <= -4800.0:
		tmp = t_4
	elif x1 <= 27.0:
		tmp = x1 + ((3.0 * ((x1 - (t_0 - (2.0 * x2))) / t_3)) + (x1 + (4.0 * (x2 * ((x1 * -3.0) + (2.0 * (x1 * x2)))))))
	elif x1 <= 1.5e+97:
		tmp = t_4
	else:
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - (x1 * 3.0))) + t_5))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(Float64(t_0 + Float64(2.0 * x2)) - x1)
	t_2 = Float64(Float64(x1 * x1) + 1.0)
	t_3 = Float64(-1.0 - Float64(x1 * x1))
	t_4 = Float64(x1 + Float64(9.0 + Float64(x1 - Float64(Float64(Float64(t_2 * Float64(Float64(Float64(x1 * x1) * Float64(6.0 - Float64(Float64(t_1 / t_2) * 4.0))) + Float64(Float64(Float64(x1 * 2.0) * 3.0) * Float64(3.0 + Float64(t_1 / t_3))))) - Float64(3.0 * t_0)) - Float64(x1 * Float64(x1 * x1))))))
	t_5 = Float64(4.0 * Float64(x2 * Float64(3.0 - Float64(2.0 * x2))))
	tmp = 0.0
	if (x1 <= -5.6e+102)
		tmp = Float64(x1 + Float64(9.0 + Float64(x1 - Float64(x1 * Float64(Float64(x1 * Float64(Float64(Float64(2.0 * Float64(Float64(Float64(2.0 * x2) - 3.0) - Float64(x2 * -2.0))) - Float64(x2 * 8.0)) - 3.0)) + t_5)))));
	elseif (x1 <= -4800.0)
		tmp = t_4;
	elseif (x1 <= 27.0)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(x1 - Float64(t_0 - Float64(2.0 * x2))) / t_3)) + Float64(x1 + Float64(4.0 * Float64(x2 * Float64(Float64(x1 * -3.0) + Float64(2.0 * Float64(x1 * x2))))))));
	elseif (x1 <= 1.5e+97)
		tmp = t_4;
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) - Float64(x1 * Float64(2.0 + Float64(Float64(x1 * Float64(Float64(3.0 * Float64(Float64(x2 * -2.0) - 3.0)) - Float64(x1 * 3.0))) + t_5)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * 3.0);
	t_1 = (t_0 + (2.0 * x2)) - x1;
	t_2 = (x1 * x1) + 1.0;
	t_3 = -1.0 - (x1 * x1);
	t_4 = x1 + (9.0 + (x1 - (((t_2 * (((x1 * x1) * (6.0 - ((t_1 / t_2) * 4.0))) + (((x1 * 2.0) * 3.0) * (3.0 + (t_1 / t_3))))) - (3.0 * t_0)) - (x1 * (x1 * x1)))));
	t_5 = 4.0 * (x2 * (3.0 - (2.0 * x2)));
	tmp = 0.0;
	if (x1 <= -5.6e+102)
		tmp = x1 + (9.0 + (x1 - (x1 * ((x1 * (((2.0 * (((2.0 * x2) - 3.0) - (x2 * -2.0))) - (x2 * 8.0)) - 3.0)) + t_5))));
	elseif (x1 <= -4800.0)
		tmp = t_4;
	elseif (x1 <= 27.0)
		tmp = x1 + ((3.0 * ((x1 - (t_0 - (2.0 * x2))) / t_3)) + (x1 + (4.0 * (x2 * ((x1 * -3.0) + (2.0 * (x1 * x2)))))));
	elseif (x1 <= 1.5e+97)
		tmp = t_4;
	else
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - (x1 * 3.0))) + t_5))));
	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[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$3 = N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(x1 + N[(9.0 + N[(x1 - N[(N[(N[(t$95$2 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 - N[(N[(t$95$1 / t$95$2), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(x1 * 2.0), $MachinePrecision] * 3.0), $MachinePrecision] * N[(3.0 + N[(t$95$1 / t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(3.0 * t$95$0), $MachinePrecision]), $MachinePrecision] - N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(4.0 * N[(x2 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -5.6e+102], N[(x1 + N[(9.0 + N[(x1 - N[(x1 * N[(N[(x1 * N[(N[(N[(2.0 * N[(N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision] - N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x2 * 8.0), $MachinePrecision]), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision] + t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -4800.0], t$95$4, If[LessEqual[x1, 27.0], N[(x1 + N[(N[(3.0 * N[(N[(x1 - N[(t$95$0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$3), $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, 1.5e+97], t$95$4, N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] - 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$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -5.60000000000000037e102

   1. Initial program 2.6%

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

   3. Taylor expanded in x1 around inf 2.6%

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

   4. Taylor expanded in x1 around inf 2.6%

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

   5. Taylor expanded in x1 around 0 47.9%

      \[\leadsto x1 + \left(\left(\color{blue}{x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(3 + \left(2 \cdot \left(-2 \cdot x2 + -1 \cdot \left(2 \cdot x2 - 3\right)\right) + 8 \cdot x2\right)\right)\right)} + x1\right) + 9\right) \]

   if -5.60000000000000037e102 < x1 < -4800 or 27 < x1 < 1.4999999999999999e97

   1. Initial program 98.9%

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

   3. Taylor expanded in x1 around inf 97.1%

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

   4. Taylor expanded in x1 around inf 97.1%

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

   5. Taylor expanded in x1 around inf 84.6%

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

   if -4800 < x1 < 27

   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 87.8%

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

   4. Taylor expanded in x2 around 0 98.2%

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

   if 1.4999999999999999e97 < x1

   1. Initial program 19.6%

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

   3. Taylor expanded in x1 around 0 13.4%

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

   4. Taylor expanded in x1 around 0 100.0%

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

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(9 + \left(x1 - x1 \cdot \left(x1 \cdot \left(\left(2 \cdot \left(\left(2 \cdot x2 - 3\right) - x2 \cdot -2\right) - x2 \cdot 8\right) - 3\right) + 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -4800:\\ \;\;\;\;x1 + \left(9 + \left(x1 - \left(\left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 - \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4\right) + \left(\left(x1 \cdot 2\right) \cdot 3\right) \cdot \left(3 + \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1}\right)\right) - 3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right)\right) - x1 \cdot \left(x1 \cdot x1\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 27:\\ \;\;\;\;x1 + \left(3 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right)}{-1 - x1 \cdot x1} + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot -3 + 2 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.5 \cdot 10^{+97}:\\ \;\;\;\;x1 + \left(9 + \left(x1 - \left(\left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 - \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4\right) + \left(\left(x1 \cdot 2\right) \cdot 3\right) \cdot \left(3 + \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1}\right)\right) - 3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right)\right) - x1 \cdot \left(x1 \cdot x1\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 + \left(x1 \cdot \left(3 \cdot \left(x2 \cdot -2 - 3\right) - x1 \cdot 3\right) + 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 86.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := \left(t\_0 + 2 \cdot x2\right) - x1\\ t_2 := -1 - x1 \cdot x1\\ t_3 := 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\\ t_4 := 3 \cdot t\_0\\ t_5 := x1 \cdot \left(x1 \cdot x1\right)\\ t_6 := x1 \cdot x1 + 1\\ t_7 := \frac{t\_1}{t\_6}\\ t_8 := 3 + \frac{t\_1}{t\_2}\\ \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(9 + \left(x1 - x1 \cdot \left(x1 \cdot \left(\left(2 \cdot \left(\left(2 \cdot x2 - 3\right) - x2 \cdot -2\right) - x2 \cdot 8\right) - 3\right) + t\_3\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -75:\\ \;\;\;\;x1 + \left(9 + \left(x1 - \left(\left(t\_6 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 - t\_7 \cdot 4\right) + \left(\left(x1 \cdot 2\right) \cdot 3\right) \cdot t\_8\right) - t\_4\right) - t\_5\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 0.0185:\\ \;\;\;\;x1 + \left(3 \cdot \frac{x1 - \left(t\_0 - 2 \cdot x2\right)}{t\_2} + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot -3 + 2 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 8.6 \cdot 10^{+93}:\\ \;\;\;\;x1 + \left(9 + \left(x1 - \left(\left(t\_6 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t\_7\right) \cdot t\_8 - \left(x1 \cdot x1\right) \cdot 6\right) - t\_4\right) - t\_5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 + \left(x1 \cdot \left(3 \cdot \left(x2 \cdot -2 - 3\right) - x1 \cdot 3\right) + t\_3\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (- (+ t_0 (* 2.0 x2)) x1))
        (t_2 (- -1.0 (* x1 x1)))
        (t_3 (* 4.0 (* x2 (- 3.0 (* 2.0 x2)))))
        (t_4 (* 3.0 t_0))
        (t_5 (* x1 (* x1 x1)))
        (t_6 (+ (* x1 x1) 1.0))
        (t_7 (/ t_1 t_6))
        (t_8 (+ 3.0 (/ t_1 t_2))))
   (if (<= x1 -5.6e+102)
     (+
      x1
      (+
       9.0
       (-
        x1
        (*
         x1
         (+
          (*
           x1
           (- (- (* 2.0 (- (- (* 2.0 x2) 3.0) (* x2 -2.0))) (* x2 8.0)) 3.0))
          t_3)))))
     (if (<= x1 -75.0)
       (+
        x1
        (+
         9.0
         (-
          x1
          (-
           (-
            (*
             t_6
             (+ (* (* x1 x1) (- 6.0 (* t_7 4.0))) (* (* (* x1 2.0) 3.0) t_8)))
            t_4)
           t_5))))
       (if (<= x1 0.0185)
         (+
          x1
          (+
           (* 3.0 (/ (- x1 (- t_0 (* 2.0 x2))) t_2))
           (+ x1 (* 4.0 (* x2 (+ (* x1 -3.0) (* 2.0 (* x1 x2))))))))
         (if (<= x1 8.6e+93)
           (+
            x1
            (+
             9.0
             (-
              x1
              (-
               (- (* t_6 (- (* (* (* x1 2.0) t_7) t_8) (* (* x1 x1) 6.0))) t_4)
               t_5))))
           (+
            x1
            (-
             (* x2 -6.0)
             (*
              x1
              (+
               2.0
               (+
                (* x1 (- (* 3.0 (- (* x2 -2.0) 3.0)) (* x1 3.0)))
                t_3)))))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = (t_0 + (2.0 * x2)) - x1;
	double t_2 = -1.0 - (x1 * x1);
	double t_3 = 4.0 * (x2 * (3.0 - (2.0 * x2)));
	double t_4 = 3.0 * t_0;
	double t_5 = x1 * (x1 * x1);
	double t_6 = (x1 * x1) + 1.0;
	double t_7 = t_1 / t_6;
	double t_8 = 3.0 + (t_1 / t_2);
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = x1 + (9.0 + (x1 - (x1 * ((x1 * (((2.0 * (((2.0 * x2) - 3.0) - (x2 * -2.0))) - (x2 * 8.0)) - 3.0)) + t_3))));
	} else if (x1 <= -75.0) {
		tmp = x1 + (9.0 + (x1 - (((t_6 * (((x1 * x1) * (6.0 - (t_7 * 4.0))) + (((x1 * 2.0) * 3.0) * t_8))) - t_4) - t_5)));
	} else if (x1 <= 0.0185) {
		tmp = x1 + ((3.0 * ((x1 - (t_0 - (2.0 * x2))) / t_2)) + (x1 + (4.0 * (x2 * ((x1 * -3.0) + (2.0 * (x1 * x2)))))));
	} else if (x1 <= 8.6e+93) {
		tmp = x1 + (9.0 + (x1 - (((t_6 * ((((x1 * 2.0) * t_7) * t_8) - ((x1 * x1) * 6.0))) - t_4) - t_5)));
	} else {
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - (x1 * 3.0))) + t_3))));
	}
	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) :: t_8
    real(8) :: tmp
    t_0 = x1 * (x1 * 3.0d0)
    t_1 = (t_0 + (2.0d0 * x2)) - x1
    t_2 = (-1.0d0) - (x1 * x1)
    t_3 = 4.0d0 * (x2 * (3.0d0 - (2.0d0 * x2)))
    t_4 = 3.0d0 * t_0
    t_5 = x1 * (x1 * x1)
    t_6 = (x1 * x1) + 1.0d0
    t_7 = t_1 / t_6
    t_8 = 3.0d0 + (t_1 / t_2)
    if (x1 <= (-5.6d+102)) then
        tmp = x1 + (9.0d0 + (x1 - (x1 * ((x1 * (((2.0d0 * (((2.0d0 * x2) - 3.0d0) - (x2 * (-2.0d0)))) - (x2 * 8.0d0)) - 3.0d0)) + t_3))))
    else if (x1 <= (-75.0d0)) then
        tmp = x1 + (9.0d0 + (x1 - (((t_6 * (((x1 * x1) * (6.0d0 - (t_7 * 4.0d0))) + (((x1 * 2.0d0) * 3.0d0) * t_8))) - t_4) - t_5)))
    else if (x1 <= 0.0185d0) then
        tmp = x1 + ((3.0d0 * ((x1 - (t_0 - (2.0d0 * x2))) / t_2)) + (x1 + (4.0d0 * (x2 * ((x1 * (-3.0d0)) + (2.0d0 * (x1 * x2)))))))
    else if (x1 <= 8.6d+93) then
        tmp = x1 + (9.0d0 + (x1 - (((t_6 * ((((x1 * 2.0d0) * t_7) * t_8) - ((x1 * x1) * 6.0d0))) - t_4) - t_5)))
    else
        tmp = x1 + ((x2 * (-6.0d0)) - (x1 * (2.0d0 + ((x1 * ((3.0d0 * ((x2 * (-2.0d0)) - 3.0d0)) - (x1 * 3.0d0))) + t_3))))
    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 = (t_0 + (2.0 * x2)) - x1;
	double t_2 = -1.0 - (x1 * x1);
	double t_3 = 4.0 * (x2 * (3.0 - (2.0 * x2)));
	double t_4 = 3.0 * t_0;
	double t_5 = x1 * (x1 * x1);
	double t_6 = (x1 * x1) + 1.0;
	double t_7 = t_1 / t_6;
	double t_8 = 3.0 + (t_1 / t_2);
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = x1 + (9.0 + (x1 - (x1 * ((x1 * (((2.0 * (((2.0 * x2) - 3.0) - (x2 * -2.0))) - (x2 * 8.0)) - 3.0)) + t_3))));
	} else if (x1 <= -75.0) {
		tmp = x1 + (9.0 + (x1 - (((t_6 * (((x1 * x1) * (6.0 - (t_7 * 4.0))) + (((x1 * 2.0) * 3.0) * t_8))) - t_4) - t_5)));
	} else if (x1 <= 0.0185) {
		tmp = x1 + ((3.0 * ((x1 - (t_0 - (2.0 * x2))) / t_2)) + (x1 + (4.0 * (x2 * ((x1 * -3.0) + (2.0 * (x1 * x2)))))));
	} else if (x1 <= 8.6e+93) {
		tmp = x1 + (9.0 + (x1 - (((t_6 * ((((x1 * 2.0) * t_7) * t_8) - ((x1 * x1) * 6.0))) - t_4) - t_5)));
	} else {
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - (x1 * 3.0))) + t_3))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = (t_0 + (2.0 * x2)) - x1
	t_2 = -1.0 - (x1 * x1)
	t_3 = 4.0 * (x2 * (3.0 - (2.0 * x2)))
	t_4 = 3.0 * t_0
	t_5 = x1 * (x1 * x1)
	t_6 = (x1 * x1) + 1.0
	t_7 = t_1 / t_6
	t_8 = 3.0 + (t_1 / t_2)
	tmp = 0
	if x1 <= -5.6e+102:
		tmp = x1 + (9.0 + (x1 - (x1 * ((x1 * (((2.0 * (((2.0 * x2) - 3.0) - (x2 * -2.0))) - (x2 * 8.0)) - 3.0)) + t_3))))
	elif x1 <= -75.0:
		tmp = x1 + (9.0 + (x1 - (((t_6 * (((x1 * x1) * (6.0 - (t_7 * 4.0))) + (((x1 * 2.0) * 3.0) * t_8))) - t_4) - t_5)))
	elif x1 <= 0.0185:
		tmp = x1 + ((3.0 * ((x1 - (t_0 - (2.0 * x2))) / t_2)) + (x1 + (4.0 * (x2 * ((x1 * -3.0) + (2.0 * (x1 * x2)))))))
	elif x1 <= 8.6e+93:
		tmp = x1 + (9.0 + (x1 - (((t_6 * ((((x1 * 2.0) * t_7) * t_8) - ((x1 * x1) * 6.0))) - t_4) - t_5)))
	else:
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - (x1 * 3.0))) + t_3))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(Float64(t_0 + Float64(2.0 * x2)) - x1)
	t_2 = Float64(-1.0 - Float64(x1 * x1))
	t_3 = Float64(4.0 * Float64(x2 * Float64(3.0 - Float64(2.0 * x2))))
	t_4 = Float64(3.0 * t_0)
	t_5 = Float64(x1 * Float64(x1 * x1))
	t_6 = Float64(Float64(x1 * x1) + 1.0)
	t_7 = Float64(t_1 / t_6)
	t_8 = Float64(3.0 + Float64(t_1 / t_2))
	tmp = 0.0
	if (x1 <= -5.6e+102)
		tmp = Float64(x1 + Float64(9.0 + Float64(x1 - Float64(x1 * Float64(Float64(x1 * Float64(Float64(Float64(2.0 * Float64(Float64(Float64(2.0 * x2) - 3.0) - Float64(x2 * -2.0))) - Float64(x2 * 8.0)) - 3.0)) + t_3)))));
	elseif (x1 <= -75.0)
		tmp = Float64(x1 + Float64(9.0 + Float64(x1 - Float64(Float64(Float64(t_6 * Float64(Float64(Float64(x1 * x1) * Float64(6.0 - Float64(t_7 * 4.0))) + Float64(Float64(Float64(x1 * 2.0) * 3.0) * t_8))) - t_4) - t_5))));
	elseif (x1 <= 0.0185)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(x1 - Float64(t_0 - Float64(2.0 * x2))) / t_2)) + Float64(x1 + Float64(4.0 * Float64(x2 * Float64(Float64(x1 * -3.0) + Float64(2.0 * Float64(x1 * x2))))))));
	elseif (x1 <= 8.6e+93)
		tmp = Float64(x1 + Float64(9.0 + Float64(x1 - Float64(Float64(Float64(t_6 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_7) * t_8) - Float64(Float64(x1 * x1) * 6.0))) - t_4) - t_5))));
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) - Float64(x1 * Float64(2.0 + Float64(Float64(x1 * Float64(Float64(3.0 * Float64(Float64(x2 * -2.0) - 3.0)) - Float64(x1 * 3.0))) + t_3)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * 3.0);
	t_1 = (t_0 + (2.0 * x2)) - x1;
	t_2 = -1.0 - (x1 * x1);
	t_3 = 4.0 * (x2 * (3.0 - (2.0 * x2)));
	t_4 = 3.0 * t_0;
	t_5 = x1 * (x1 * x1);
	t_6 = (x1 * x1) + 1.0;
	t_7 = t_1 / t_6;
	t_8 = 3.0 + (t_1 / t_2);
	tmp = 0.0;
	if (x1 <= -5.6e+102)
		tmp = x1 + (9.0 + (x1 - (x1 * ((x1 * (((2.0 * (((2.0 * x2) - 3.0) - (x2 * -2.0))) - (x2 * 8.0)) - 3.0)) + t_3))));
	elseif (x1 <= -75.0)
		tmp = x1 + (9.0 + (x1 - (((t_6 * (((x1 * x1) * (6.0 - (t_7 * 4.0))) + (((x1 * 2.0) * 3.0) * t_8))) - t_4) - t_5)));
	elseif (x1 <= 0.0185)
		tmp = x1 + ((3.0 * ((x1 - (t_0 - (2.0 * x2))) / t_2)) + (x1 + (4.0 * (x2 * ((x1 * -3.0) + (2.0 * (x1 * x2)))))));
	elseif (x1 <= 8.6e+93)
		tmp = x1 + (9.0 + (x1 - (((t_6 * ((((x1 * 2.0) * t_7) * t_8) - ((x1 * x1) * 6.0))) - t_4) - t_5)));
	else
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - (x1 * 3.0))) + t_3))));
	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[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]}, Block[{t$95$2 = N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(4.0 * N[(x2 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(3.0 * t$95$0), $MachinePrecision]}, Block[{t$95$5 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$7 = N[(t$95$1 / t$95$6), $MachinePrecision]}, Block[{t$95$8 = N[(3.0 + N[(t$95$1 / t$95$2), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -5.6e+102], N[(x1 + N[(9.0 + N[(x1 - N[(x1 * N[(N[(x1 * N[(N[(N[(2.0 * N[(N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision] - N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x2 * 8.0), $MachinePrecision]), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision] + t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -75.0], N[(x1 + N[(9.0 + N[(x1 - N[(N[(N[(t$95$6 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 - N[(t$95$7 * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(x1 * 2.0), $MachinePrecision] * 3.0), $MachinePrecision] * t$95$8), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$4), $MachinePrecision] - t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 0.0185], N[(x1 + N[(N[(3.0 * N[(N[(x1 - N[(t$95$0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $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, 8.6e+93], N[(x1 + N[(9.0 + N[(x1 - N[(N[(N[(t$95$6 * N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$7), $MachinePrecision] * t$95$8), $MachinePrecision] - N[(N[(x1 * x1), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$4), $MachinePrecision] - t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] - 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$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x1 < -5.60000000000000037e102

   1. Initial program 2.6%

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

   3. Taylor expanded in x1 around inf 2.6%

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

   4. Taylor expanded in x1 around inf 2.6%

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

   5. Taylor expanded in x1 around 0 47.9%

      \[\leadsto x1 + \left(\left(\color{blue}{x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(3 + \left(2 \cdot \left(-2 \cdot x2 + -1 \cdot \left(2 \cdot x2 - 3\right)\right) + 8 \cdot x2\right)\right)\right)} + x1\right) + 9\right) \]

   if -5.60000000000000037e102 < x1 < -75

   1. Initial program 98.8%

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

   3. Taylor expanded in x1 around inf 98.8%

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

   4. Taylor expanded in x1 around inf 98.8%

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

   5. Taylor expanded in x1 around inf 86.2%

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

   if -75 < x1 < 0.0184999999999999991

   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 87.8%

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

   4. Taylor expanded in x2 around 0 98.2%

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

   if 0.0184999999999999991 < x1 < 8.6e93

   1. Initial program 98.9%

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

   3. Taylor expanded in x1 around inf 95.5%

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

   4. Taylor expanded in x1 around inf 95.5%

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

   5. Taylor expanded in x1 around inf 92.0%

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

   if 8.6e93 < x1

   1. Initial program 21.3%

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

   3. Taylor expanded in x1 around 0 13.1%

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

   4. Taylor expanded in x1 around 0 97.9%

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

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(9 + \left(x1 - x1 \cdot \left(x1 \cdot \left(\left(2 \cdot \left(\left(2 \cdot x2 - 3\right) - x2 \cdot -2\right) - x2 \cdot 8\right) - 3\right) + 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -75:\\ \;\;\;\;x1 + \left(9 + \left(x1 - \left(\left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 - \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4\right) + \left(\left(x1 \cdot 2\right) \cdot 3\right) \cdot \left(3 + \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1}\right)\right) - 3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right)\right) - x1 \cdot \left(x1 \cdot x1\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 0.0185:\\ \;\;\;\;x1 + \left(3 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right)}{-1 - x1 \cdot x1} + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot -3 + 2 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 8.6 \cdot 10^{+93}:\\ \;\;\;\;x1 + \left(9 + \left(x1 - \left(\left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(3 + \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1}\right) - \left(x1 \cdot x1\right) \cdot 6\right) - 3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right)\right) - x1 \cdot \left(x1 \cdot x1\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 + \left(x1 \cdot \left(3 \cdot \left(x2 \cdot -2 - 3\right) - x1 \cdot 3\right) + 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 90.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := 2 \cdot x2 - 3\\ t_2 := -1 - x1 \cdot x1\\ t_3 := 3 \cdot t\_0\\ t_4 := x1 \cdot \left(x1 \cdot x1\right)\\ t_5 := \left(t\_0 + 2 \cdot x2\right) - x1\\ t_6 := x1 \cdot x1 + 1\\ t_7 := 3 + \frac{t\_5}{t\_2}\\ t_8 := 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\\ t_9 := \frac{t\_5}{t\_6}\\ \mathbf{if}\;x1 \leq -1.15 \cdot 10^{+110}:\\ \;\;\;\;x1 + \left(9 + \left(x1 - x1 \cdot \left(x1 \cdot \left(\left(2 \cdot \left(t\_1 - x2 \cdot -2\right) - \left(x2 \cdot 8 - x1 \cdot \left(3 + \left(t\_8 + 2 \cdot \left(2 \cdot \left(x2 \cdot t\_1\right) + \left(-1 - \left(2 \cdot \left(x2 \cdot \left(3 + x2 \cdot -2\right)\right) + 3 \cdot t\_1\right)\right)\right)\right)\right)\right)\right) - 3\right) + t\_8\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -2300:\\ \;\;\;\;x1 + \left(9 + \left(x1 - \left(\left(t\_6 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 - t\_9 \cdot 4\right) + \left(\left(x1 \cdot 2\right) \cdot 3\right) \cdot t\_7\right) - t\_3\right) - t\_4\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 0.006:\\ \;\;\;\;x1 + \left(3 \cdot \frac{x1 - \left(t\_0 - 2 \cdot x2\right)}{t\_2} + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot -3 + 2 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 8.6 \cdot 10^{+93}:\\ \;\;\;\;x1 + \left(9 + \left(x1 - \left(\left(t\_6 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t\_9\right) \cdot t\_7 - \left(x1 \cdot x1\right) \cdot 6\right) - t\_3\right) - t\_4\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 + \left(x1 \cdot \left(3 \cdot \left(x2 \cdot -2 - 3\right) - x1 \cdot 3\right) + t\_8\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (- (* 2.0 x2) 3.0))
        (t_2 (- -1.0 (* x1 x1)))
        (t_3 (* 3.0 t_0))
        (t_4 (* x1 (* x1 x1)))
        (t_5 (- (+ t_0 (* 2.0 x2)) x1))
        (t_6 (+ (* x1 x1) 1.0))
        (t_7 (+ 3.0 (/ t_5 t_2)))
        (t_8 (* 4.0 (* x2 (- 3.0 (* 2.0 x2)))))
        (t_9 (/ t_5 t_6)))
   (if (<= x1 -1.15e+110)
     (+
      x1
      (+
       9.0
       (-
        x1
        (*
         x1
         (+
          (*
           x1
           (-
            (-
             (* 2.0 (- t_1 (* x2 -2.0)))
             (-
              (* x2 8.0)
              (*
               x1
               (+
                3.0
                (+
                 t_8
                 (*
                  2.0
                  (+
                   (* 2.0 (* x2 t_1))
                   (-
                    -1.0
                    (+ (* 2.0 (* x2 (+ 3.0 (* x2 -2.0)))) (* 3.0 t_1))))))))))
            3.0))
          t_8)))))
     (if (<= x1 -2300.0)
       (+
        x1
        (+
         9.0
         (-
          x1
          (-
           (-
            (*
             t_6
             (+ (* (* x1 x1) (- 6.0 (* t_9 4.0))) (* (* (* x1 2.0) 3.0) t_7)))
            t_3)
           t_4))))
       (if (<= x1 0.006)
         (+
          x1
          (+
           (* 3.0 (/ (- x1 (- t_0 (* 2.0 x2))) t_2))
           (+ x1 (* 4.0 (* x2 (+ (* x1 -3.0) (* 2.0 (* x1 x2))))))))
         (if (<= x1 8.6e+93)
           (+
            x1
            (+
             9.0
             (-
              x1
              (-
               (- (* t_6 (- (* (* (* x1 2.0) t_9) t_7) (* (* x1 x1) 6.0))) t_3)
               t_4))))
           (+
            x1
            (-
             (* x2 -6.0)
             (*
              x1
              (+
               2.0
               (+
                (* x1 (- (* 3.0 (- (* x2 -2.0) 3.0)) (* x1 3.0)))
                t_8)))))))))))

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 = -1.0 - (x1 * x1);
	double t_3 = 3.0 * t_0;
	double t_4 = x1 * (x1 * x1);
	double t_5 = (t_0 + (2.0 * x2)) - x1;
	double t_6 = (x1 * x1) + 1.0;
	double t_7 = 3.0 + (t_5 / t_2);
	double t_8 = 4.0 * (x2 * (3.0 - (2.0 * x2)));
	double t_9 = t_5 / t_6;
	double tmp;
	if (x1 <= -1.15e+110) {
		tmp = x1 + (9.0 + (x1 - (x1 * ((x1 * (((2.0 * (t_1 - (x2 * -2.0))) - ((x2 * 8.0) - (x1 * (3.0 + (t_8 + (2.0 * ((2.0 * (x2 * t_1)) + (-1.0 - ((2.0 * (x2 * (3.0 + (x2 * -2.0)))) + (3.0 * t_1)))))))))) - 3.0)) + t_8))));
	} else if (x1 <= -2300.0) {
		tmp = x1 + (9.0 + (x1 - (((t_6 * (((x1 * x1) * (6.0 - (t_9 * 4.0))) + (((x1 * 2.0) * 3.0) * t_7))) - t_3) - t_4)));
	} else if (x1 <= 0.006) {
		tmp = x1 + ((3.0 * ((x1 - (t_0 - (2.0 * x2))) / t_2)) + (x1 + (4.0 * (x2 * ((x1 * -3.0) + (2.0 * (x1 * x2)))))));
	} else if (x1 <= 8.6e+93) {
		tmp = x1 + (9.0 + (x1 - (((t_6 * ((((x1 * 2.0) * t_9) * t_7) - ((x1 * x1) * 6.0))) - t_3) - t_4)));
	} else {
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - (x1 * 3.0))) + t_8))));
	}
	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) :: t_8
    real(8) :: t_9
    real(8) :: tmp
    t_0 = x1 * (x1 * 3.0d0)
    t_1 = (2.0d0 * x2) - 3.0d0
    t_2 = (-1.0d0) - (x1 * x1)
    t_3 = 3.0d0 * t_0
    t_4 = x1 * (x1 * x1)
    t_5 = (t_0 + (2.0d0 * x2)) - x1
    t_6 = (x1 * x1) + 1.0d0
    t_7 = 3.0d0 + (t_5 / t_2)
    t_8 = 4.0d0 * (x2 * (3.0d0 - (2.0d0 * x2)))
    t_9 = t_5 / t_6
    if (x1 <= (-1.15d+110)) then
        tmp = x1 + (9.0d0 + (x1 - (x1 * ((x1 * (((2.0d0 * (t_1 - (x2 * (-2.0d0)))) - ((x2 * 8.0d0) - (x1 * (3.0d0 + (t_8 + (2.0d0 * ((2.0d0 * (x2 * t_1)) + ((-1.0d0) - ((2.0d0 * (x2 * (3.0d0 + (x2 * (-2.0d0))))) + (3.0d0 * t_1)))))))))) - 3.0d0)) + t_8))))
    else if (x1 <= (-2300.0d0)) then
        tmp = x1 + (9.0d0 + (x1 - (((t_6 * (((x1 * x1) * (6.0d0 - (t_9 * 4.0d0))) + (((x1 * 2.0d0) * 3.0d0) * t_7))) - t_3) - t_4)))
    else if (x1 <= 0.006d0) then
        tmp = x1 + ((3.0d0 * ((x1 - (t_0 - (2.0d0 * x2))) / t_2)) + (x1 + (4.0d0 * (x2 * ((x1 * (-3.0d0)) + (2.0d0 * (x1 * x2)))))))
    else if (x1 <= 8.6d+93) then
        tmp = x1 + (9.0d0 + (x1 - (((t_6 * ((((x1 * 2.0d0) * t_9) * t_7) - ((x1 * x1) * 6.0d0))) - t_3) - t_4)))
    else
        tmp = x1 + ((x2 * (-6.0d0)) - (x1 * (2.0d0 + ((x1 * ((3.0d0 * ((x2 * (-2.0d0)) - 3.0d0)) - (x1 * 3.0d0))) + t_8))))
    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 = -1.0 - (x1 * x1);
	double t_3 = 3.0 * t_0;
	double t_4 = x1 * (x1 * x1);
	double t_5 = (t_0 + (2.0 * x2)) - x1;
	double t_6 = (x1 * x1) + 1.0;
	double t_7 = 3.0 + (t_5 / t_2);
	double t_8 = 4.0 * (x2 * (3.0 - (2.0 * x2)));
	double t_9 = t_5 / t_6;
	double tmp;
	if (x1 <= -1.15e+110) {
		tmp = x1 + (9.0 + (x1 - (x1 * ((x1 * (((2.0 * (t_1 - (x2 * -2.0))) - ((x2 * 8.0) - (x1 * (3.0 + (t_8 + (2.0 * ((2.0 * (x2 * t_1)) + (-1.0 - ((2.0 * (x2 * (3.0 + (x2 * -2.0)))) + (3.0 * t_1)))))))))) - 3.0)) + t_8))));
	} else if (x1 <= -2300.0) {
		tmp = x1 + (9.0 + (x1 - (((t_6 * (((x1 * x1) * (6.0 - (t_9 * 4.0))) + (((x1 * 2.0) * 3.0) * t_7))) - t_3) - t_4)));
	} else if (x1 <= 0.006) {
		tmp = x1 + ((3.0 * ((x1 - (t_0 - (2.0 * x2))) / t_2)) + (x1 + (4.0 * (x2 * ((x1 * -3.0) + (2.0 * (x1 * x2)))))));
	} else if (x1 <= 8.6e+93) {
		tmp = x1 + (9.0 + (x1 - (((t_6 * ((((x1 * 2.0) * t_9) * t_7) - ((x1 * x1) * 6.0))) - t_3) - t_4)));
	} else {
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - (x1 * 3.0))) + t_8))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = (2.0 * x2) - 3.0
	t_2 = -1.0 - (x1 * x1)
	t_3 = 3.0 * t_0
	t_4 = x1 * (x1 * x1)
	t_5 = (t_0 + (2.0 * x2)) - x1
	t_6 = (x1 * x1) + 1.0
	t_7 = 3.0 + (t_5 / t_2)
	t_8 = 4.0 * (x2 * (3.0 - (2.0 * x2)))
	t_9 = t_5 / t_6
	tmp = 0
	if x1 <= -1.15e+110:
		tmp = x1 + (9.0 + (x1 - (x1 * ((x1 * (((2.0 * (t_1 - (x2 * -2.0))) - ((x2 * 8.0) - (x1 * (3.0 + (t_8 + (2.0 * ((2.0 * (x2 * t_1)) + (-1.0 - ((2.0 * (x2 * (3.0 + (x2 * -2.0)))) + (3.0 * t_1)))))))))) - 3.0)) + t_8))))
	elif x1 <= -2300.0:
		tmp = x1 + (9.0 + (x1 - (((t_6 * (((x1 * x1) * (6.0 - (t_9 * 4.0))) + (((x1 * 2.0) * 3.0) * t_7))) - t_3) - t_4)))
	elif x1 <= 0.006:
		tmp = x1 + ((3.0 * ((x1 - (t_0 - (2.0 * x2))) / t_2)) + (x1 + (4.0 * (x2 * ((x1 * -3.0) + (2.0 * (x1 * x2)))))))
	elif x1 <= 8.6e+93:
		tmp = x1 + (9.0 + (x1 - (((t_6 * ((((x1 * 2.0) * t_9) * t_7) - ((x1 * x1) * 6.0))) - t_3) - t_4)))
	else:
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - (x1 * 3.0))) + t_8))))
	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(-1.0 - Float64(x1 * x1))
	t_3 = Float64(3.0 * t_0)
	t_4 = Float64(x1 * Float64(x1 * x1))
	t_5 = Float64(Float64(t_0 + Float64(2.0 * x2)) - x1)
	t_6 = Float64(Float64(x1 * x1) + 1.0)
	t_7 = Float64(3.0 + Float64(t_5 / t_2))
	t_8 = Float64(4.0 * Float64(x2 * Float64(3.0 - Float64(2.0 * x2))))
	t_9 = Float64(t_5 / t_6)
	tmp = 0.0
	if (x1 <= -1.15e+110)
		tmp = Float64(x1 + Float64(9.0 + Float64(x1 - Float64(x1 * Float64(Float64(x1 * Float64(Float64(Float64(2.0 * Float64(t_1 - Float64(x2 * -2.0))) - Float64(Float64(x2 * 8.0) - Float64(x1 * Float64(3.0 + Float64(t_8 + Float64(2.0 * Float64(Float64(2.0 * Float64(x2 * t_1)) + Float64(-1.0 - Float64(Float64(2.0 * Float64(x2 * Float64(3.0 + Float64(x2 * -2.0)))) + Float64(3.0 * t_1)))))))))) - 3.0)) + t_8)))));
	elseif (x1 <= -2300.0)
		tmp = Float64(x1 + Float64(9.0 + Float64(x1 - Float64(Float64(Float64(t_6 * Float64(Float64(Float64(x1 * x1) * Float64(6.0 - Float64(t_9 * 4.0))) + Float64(Float64(Float64(x1 * 2.0) * 3.0) * t_7))) - t_3) - t_4))));
	elseif (x1 <= 0.006)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(x1 - Float64(t_0 - Float64(2.0 * x2))) / t_2)) + Float64(x1 + Float64(4.0 * Float64(x2 * Float64(Float64(x1 * -3.0) + Float64(2.0 * Float64(x1 * x2))))))));
	elseif (x1 <= 8.6e+93)
		tmp = Float64(x1 + Float64(9.0 + Float64(x1 - Float64(Float64(Float64(t_6 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_9) * t_7) - Float64(Float64(x1 * x1) * 6.0))) - t_3) - t_4))));
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) - Float64(x1 * Float64(2.0 + Float64(Float64(x1 * Float64(Float64(3.0 * Float64(Float64(x2 * -2.0) - 3.0)) - Float64(x1 * 3.0))) + t_8)))));
	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 = -1.0 - (x1 * x1);
	t_3 = 3.0 * t_0;
	t_4 = x1 * (x1 * x1);
	t_5 = (t_0 + (2.0 * x2)) - x1;
	t_6 = (x1 * x1) + 1.0;
	t_7 = 3.0 + (t_5 / t_2);
	t_8 = 4.0 * (x2 * (3.0 - (2.0 * x2)));
	t_9 = t_5 / t_6;
	tmp = 0.0;
	if (x1 <= -1.15e+110)
		tmp = x1 + (9.0 + (x1 - (x1 * ((x1 * (((2.0 * (t_1 - (x2 * -2.0))) - ((x2 * 8.0) - (x1 * (3.0 + (t_8 + (2.0 * ((2.0 * (x2 * t_1)) + (-1.0 - ((2.0 * (x2 * (3.0 + (x2 * -2.0)))) + (3.0 * t_1)))))))))) - 3.0)) + t_8))));
	elseif (x1 <= -2300.0)
		tmp = x1 + (9.0 + (x1 - (((t_6 * (((x1 * x1) * (6.0 - (t_9 * 4.0))) + (((x1 * 2.0) * 3.0) * t_7))) - t_3) - t_4)));
	elseif (x1 <= 0.006)
		tmp = x1 + ((3.0 * ((x1 - (t_0 - (2.0 * x2))) / t_2)) + (x1 + (4.0 * (x2 * ((x1 * -3.0) + (2.0 * (x1 * x2)))))));
	elseif (x1 <= 8.6e+93)
		tmp = x1 + (9.0 + (x1 - (((t_6 * ((((x1 * 2.0) * t_9) * t_7) - ((x1 * x1) * 6.0))) - t_3) - t_4)));
	else
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - (x1 * 3.0))) + t_8))));
	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[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(3.0 * t$95$0), $MachinePrecision]}, Block[{t$95$4 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]}, Block[{t$95$6 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$7 = N[(3.0 + N[(t$95$5 / t$95$2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$8 = N[(4.0 * N[(x2 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$9 = N[(t$95$5 / t$95$6), $MachinePrecision]}, If[LessEqual[x1, -1.15e+110], N[(x1 + N[(9.0 + 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[(x2 * 8.0), $MachinePrecision] - N[(x1 * N[(3.0 + N[(t$95$8 + N[(2.0 * N[(N[(2.0 * N[(x2 * t$95$1), $MachinePrecision]), $MachinePrecision] + 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]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision] + t$95$8), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -2300.0], N[(x1 + N[(9.0 + N[(x1 - N[(N[(N[(t$95$6 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 - N[(t$95$9 * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(x1 * 2.0), $MachinePrecision] * 3.0), $MachinePrecision] * t$95$7), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$3), $MachinePrecision] - t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 0.006], N[(x1 + N[(N[(3.0 * N[(N[(x1 - N[(t$95$0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $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, 8.6e+93], N[(x1 + N[(9.0 + N[(x1 - N[(N[(N[(t$95$6 * N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$9), $MachinePrecision] * t$95$7), $MachinePrecision] - N[(N[(x1 * x1), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$3), $MachinePrecision] - t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] - 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$8), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x1 < -1.15e110

   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 inf 0.0%

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

   5. Taylor expanded in x1 around 0 75.0%

      \[\leadsto x1 + \left(\left(\color{blue}{x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(3 + \left(2 \cdot \left(-2 \cdot x2 + -1 \cdot \left(2 \cdot x2 - 3\right)\right) + \left(8 \cdot x2 + x1 \cdot \left(\left(2 \cdot \left(\left(1 + \left(2 \cdot \left(x2 \cdot \left(3 + -2 \cdot x2\right)\right) + 3 \cdot \left(2 \cdot x2 - 3\right)\right)\right) - 2 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) - 3\right)\right)\right)\right)\right)} + x1\right) + 9\right) \]

   if -1.15e110 < x1 < -2300

   1. Initial program 90.3%

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

   3. Taylor expanded in x1 around inf 90.2%

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

   4. Taylor expanded in x1 around inf 90.2%

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

   5. Taylor expanded in x1 around inf 79.3%

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

   if -2300 < x1 < 0.0060000000000000001

   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 87.8%

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

   4. Taylor expanded in x2 around 0 98.2%

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

   if 0.0060000000000000001 < x1 < 8.6e93

   1. Initial program 98.9%

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

   3. Taylor expanded in x1 around inf 95.5%

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

   4. Taylor expanded in x1 around inf 95.5%

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

   5. Taylor expanded in x1 around inf 92.0%

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

   if 8.6e93 < x1

   1. Initial program 21.3%

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

   3. Taylor expanded in x1 around 0 13.1%

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

   4. Taylor expanded in x1 around 0 97.9%

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

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.15 \cdot 10^{+110}:\\ \;\;\;\;x1 + \left(9 + \left(x1 - x1 \cdot \left(x1 \cdot \left(\left(2 \cdot \left(\left(2 \cdot x2 - 3\right) - x2 \cdot -2\right) - \left(x2 \cdot 8 - x1 \cdot \left(3 + \left(4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right) + 2 \cdot \left(2 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + \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)\right)\right)\right)\right)\right) - 3\right) + 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -2300:\\ \;\;\;\;x1 + \left(9 + \left(x1 - \left(\left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 - \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4\right) + \left(\left(x1 \cdot 2\right) \cdot 3\right) \cdot \left(3 + \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1}\right)\right) - 3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right)\right) - x1 \cdot \left(x1 \cdot x1\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 0.006:\\ \;\;\;\;x1 + \left(3 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\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{elif}\;x1 \leq 8.6 \cdot 10^{+93}:\\ \;\;\;\;x1 + \left(9 + \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(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 6\right) - 3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right)\right) - x1 \cdot \left(x1 \cdot x1\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - 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)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 77.9% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 2 \cdot x2 - 3\\ t_1 := 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\\ \mathbf{if}\;x1 \leq -4.6 \cdot 10^{+155}:\\ \;\;\;\;x1 + \left(9 + \left(x1 - x1 \cdot \left(x1 \cdot \left(\left(2 \cdot \left(t\_0 - x2 \cdot -2\right) - x2 \cdot 8\right) - 3\right) + t\_1\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -12:\\ \;\;\;\;x1 + \left(\left(x1 + 4 \cdot \left(x1 \cdot \left(x2 \cdot t\_0\right)\right)\right) + x2 \cdot \left(-3 \cdot \frac{x1}{x2} - 6\right)\right)\\ \mathbf{elif}\;x1 \leq 3.1 \cdot 10^{-154}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right)}{-1 - x1 \cdot x1} + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot -3 + 2 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 + \left(x1 \cdot \left(3 \cdot \left(x2 \cdot -2 - 3\right) - x1 \cdot 3\right) + t\_1\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (- (* 2.0 x2) 3.0)) (t_1 (* 4.0 (* x2 (- 3.0 (* 2.0 x2))))))
   (if (<= x1 -4.6e+155)
     (+
      x1
      (+
       9.0
       (-
        x1
        (*
         x1
         (+ (* x1 (- (- (* 2.0 (- t_0 (* x2 -2.0))) (* x2 8.0)) 3.0)) t_1)))))
     (if (<= x1 -12.0)
       (+
        x1
        (+ (+ x1 (* 4.0 (* x1 (* x2 t_0)))) (* x2 (- (* -3.0 (/ x1 x2)) 6.0))))
       (if (<= x1 3.1e-154)
         (+
          x1
          (+
           (*
            3.0
            (/ (- x1 (- (* x1 (* x1 3.0)) (* 2.0 x2))) (- -1.0 (* x1 x1))))
           (+ x1 (* 4.0 (* x2 (+ (* x1 -3.0) (* 2.0 (* x1 x2))))))))
         (+
          x1
          (-
           (* x2 -6.0)
           (*
            x1
            (+
             2.0
             (+ (* x1 (- (* 3.0 (- (* x2 -2.0) 3.0)) (* x1 3.0))) t_1))))))))))

C

double code(double x1, double x2) {
	double t_0 = (2.0 * x2) - 3.0;
	double t_1 = 4.0 * (x2 * (3.0 - (2.0 * x2)));
	double tmp;
	if (x1 <= -4.6e+155) {
		tmp = x1 + (9.0 + (x1 - (x1 * ((x1 * (((2.0 * (t_0 - (x2 * -2.0))) - (x2 * 8.0)) - 3.0)) + t_1))));
	} else if (x1 <= -12.0) {
		tmp = x1 + ((x1 + (4.0 * (x1 * (x2 * t_0)))) + (x2 * ((-3.0 * (x1 / x2)) - 6.0)));
	} else if (x1 <= 3.1e-154) {
		tmp = x1 + ((3.0 * ((x1 - ((x1 * (x1 * 3.0)) - (2.0 * x2))) / (-1.0 - (x1 * x1)))) + (x1 + (4.0 * (x2 * ((x1 * -3.0) + (2.0 * (x1 * x2)))))));
	} else {
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - (x1 * 3.0))) + 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) :: tmp
    t_0 = (2.0d0 * x2) - 3.0d0
    t_1 = 4.0d0 * (x2 * (3.0d0 - (2.0d0 * x2)))
    if (x1 <= (-4.6d+155)) then
        tmp = x1 + (9.0d0 + (x1 - (x1 * ((x1 * (((2.0d0 * (t_0 - (x2 * (-2.0d0)))) - (x2 * 8.0d0)) - 3.0d0)) + t_1))))
    else if (x1 <= (-12.0d0)) then
        tmp = x1 + ((x1 + (4.0d0 * (x1 * (x2 * t_0)))) + (x2 * (((-3.0d0) * (x1 / x2)) - 6.0d0)))
    else if (x1 <= 3.1d-154) then
        tmp = x1 + ((3.0d0 * ((x1 - ((x1 * (x1 * 3.0d0)) - (2.0d0 * x2))) / ((-1.0d0) - (x1 * x1)))) + (x1 + (4.0d0 * (x2 * ((x1 * (-3.0d0)) + (2.0d0 * (x1 * x2)))))))
    else
        tmp = x1 + ((x2 * (-6.0d0)) - (x1 * (2.0d0 + ((x1 * ((3.0d0 * ((x2 * (-2.0d0)) - 3.0d0)) - (x1 * 3.0d0))) + t_1))))
    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 * (3.0 - (2.0 * x2)));
	double tmp;
	if (x1 <= -4.6e+155) {
		tmp = x1 + (9.0 + (x1 - (x1 * ((x1 * (((2.0 * (t_0 - (x2 * -2.0))) - (x2 * 8.0)) - 3.0)) + t_1))));
	} else if (x1 <= -12.0) {
		tmp = x1 + ((x1 + (4.0 * (x1 * (x2 * t_0)))) + (x2 * ((-3.0 * (x1 / x2)) - 6.0)));
	} else if (x1 <= 3.1e-154) {
		tmp = x1 + ((3.0 * ((x1 - ((x1 * (x1 * 3.0)) - (2.0 * x2))) / (-1.0 - (x1 * x1)))) + (x1 + (4.0 * (x2 * ((x1 * -3.0) + (2.0 * (x1 * x2)))))));
	} else {
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - (x1 * 3.0))) + t_1))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (2.0 * x2) - 3.0
	t_1 = 4.0 * (x2 * (3.0 - (2.0 * x2)))
	tmp = 0
	if x1 <= -4.6e+155:
		tmp = x1 + (9.0 + (x1 - (x1 * ((x1 * (((2.0 * (t_0 - (x2 * -2.0))) - (x2 * 8.0)) - 3.0)) + t_1))))
	elif x1 <= -12.0:
		tmp = x1 + ((x1 + (4.0 * (x1 * (x2 * t_0)))) + (x2 * ((-3.0 * (x1 / x2)) - 6.0)))
	elif x1 <= 3.1e-154:
		tmp = x1 + ((3.0 * ((x1 - ((x1 * (x1 * 3.0)) - (2.0 * x2))) / (-1.0 - (x1 * x1)))) + (x1 + (4.0 * (x2 * ((x1 * -3.0) + (2.0 * (x1 * x2)))))))
	else:
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - (x1 * 3.0))) + t_1))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(2.0 * x2) - 3.0)
	t_1 = Float64(4.0 * Float64(x2 * Float64(3.0 - Float64(2.0 * x2))))
	tmp = 0.0
	if (x1 <= -4.6e+155)
		tmp = Float64(x1 + Float64(9.0 + Float64(x1 - Float64(x1 * Float64(Float64(x1 * Float64(Float64(Float64(2.0 * Float64(t_0 - Float64(x2 * -2.0))) - Float64(x2 * 8.0)) - 3.0)) + t_1)))));
	elseif (x1 <= -12.0)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(4.0 * Float64(x1 * Float64(x2 * t_0)))) + Float64(x2 * Float64(Float64(-3.0 * Float64(x1 / x2)) - 6.0))));
	elseif (x1 <= 3.1e-154)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(x1 - Float64(Float64(x1 * Float64(x1 * 3.0)) - Float64(2.0 * x2))) / 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(x2 * -6.0) - Float64(x1 * Float64(2.0 + Float64(Float64(x1 * Float64(Float64(3.0 * Float64(Float64(x2 * -2.0) - 3.0)) - Float64(x1 * 3.0))) + t_1)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (2.0 * x2) - 3.0;
	t_1 = 4.0 * (x2 * (3.0 - (2.0 * x2)));
	tmp = 0.0;
	if (x1 <= -4.6e+155)
		tmp = x1 + (9.0 + (x1 - (x1 * ((x1 * (((2.0 * (t_0 - (x2 * -2.0))) - (x2 * 8.0)) - 3.0)) + t_1))));
	elseif (x1 <= -12.0)
		tmp = x1 + ((x1 + (4.0 * (x1 * (x2 * t_0)))) + (x2 * ((-3.0 * (x1 / x2)) - 6.0)));
	elseif (x1 <= 3.1e-154)
		tmp = x1 + ((3.0 * ((x1 - ((x1 * (x1 * 3.0)) - (2.0 * x2))) / (-1.0 - (x1 * x1)))) + (x1 + (4.0 * (x2 * ((x1 * -3.0) + (2.0 * (x1 * x2)))))));
	else
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - (x1 * 3.0))) + t_1))));
	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 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -4.6e+155], N[(x1 + N[(9.0 + N[(x1 - N[(x1 * N[(N[(x1 * N[(N[(N[(2.0 * N[(t$95$0 - N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x2 * 8.0), $MachinePrecision]), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -12.0], N[(x1 + N[(N[(x1 + N[(4.0 * N[(x1 * N[(x2 * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x2 * N[(N[(-3.0 * N[(x1 / x2), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 3.1e-154], N[(x1 + N[(N[(3.0 * N[(N[(x1 - N[(N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision] - N[(2.0 * x2), $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[(x2 * -6.0), $MachinePrecision] - 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$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -4.59999999999999996e155

   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 inf 0.0%

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

   5. Taylor expanded in x1 around 0 63.0%

      \[\leadsto x1 + \left(\left(\color{blue}{x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(3 + \left(2 \cdot \left(-2 \cdot x2 + -1 \cdot \left(2 \cdot x2 - 3\right)\right) + 8 \cdot x2\right)\right)\right)} + x1\right) + 9\right) \]

   if -4.59999999999999996e155 < x1 < -12

   1. Initial program 64.9%

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

   3. Taylor expanded in x1 around 0 10.7%

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

   4. Taylor expanded in x1 around 0 13.2%

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

   5. Taylor expanded in x2 around inf 28.3%

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

   if -12 < x1 < 3.09999999999999982e-154

   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 85.3%

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

   4. Taylor expanded in x2 around 0 98.1%

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

   if 3.09999999999999982e-154 < x1

   1. Initial program 59.6%

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

   3. Taylor expanded in x1 around 0 35.8%

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

   4. Taylor expanded in x1 around 0 79.2%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4.6 \cdot 10^{+155}:\\ \;\;\;\;x1 + \left(9 + \left(x1 - x1 \cdot \left(x1 \cdot \left(\left(2 \cdot \left(\left(2 \cdot x2 - 3\right) - x2 \cdot -2\right) - x2 \cdot 8\right) - 3\right) + 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -12:\\ \;\;\;\;x1 + \left(\left(x1 + 4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right) + x2 \cdot \left(-3 \cdot \frac{x1}{x2} - 6\right)\right)\\ \mathbf{elif}\;x1 \leq 3.1 \cdot 10^{-154}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right)}{-1 - x1 \cdot x1} + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot -3 + 2 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 + \left(x1 \cdot \left(3 \cdot \left(x2 \cdot -2 - 3\right) - x1 \cdot 3\right) + 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 76.5% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x2 \cdot -2 - 3\\ t_1 := 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\\ \mathbf{if}\;x1 \leq -4.8 \cdot 10^{-30}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 + \left(3 \cdot \left(x1 \cdot t\_0\right) + t\_1\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 3.1 \cdot 10^{-154}:\\ \;\;\;\;x1 + \left(x1 + \left(x1 \cdot -3 - x2 \cdot \left(6 - \left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 + \left(x1 \cdot \left(3 \cdot t\_0 - x1 \cdot 3\right) + t\_1\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (- (* x2 -2.0) 3.0)) (t_1 (* 4.0 (* x2 (- 3.0 (* 2.0 x2))))))
   (if (<= x1 -4.8e-30)
     (+ x1 (- (* x2 -6.0) (* x1 (+ 2.0 (+ (* 3.0 (* x1 t_0)) t_1)))))
     (if (<= x1 3.1e-154)
       (+
        x1
        (+
         x1
         (- (* x1 -3.0) (* x2 (- 6.0 (+ (* x1 -12.0) (* 8.0 (* x1 x2))))))))
       (+
        x1
        (-
         (* x2 -6.0)
         (* x1 (+ 2.0 (+ (* x1 (- (* 3.0 t_0) (* x1 3.0))) t_1)))))))))

C

double code(double x1, double x2) {
	double t_0 = (x2 * -2.0) - 3.0;
	double t_1 = 4.0 * (x2 * (3.0 - (2.0 * x2)));
	double tmp;
	if (x1 <= -4.8e-30) {
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((3.0 * (x1 * t_0)) + t_1))));
	} else if (x1 <= 3.1e-154) {
		tmp = x1 + (x1 + ((x1 * -3.0) - (x2 * (6.0 - ((x1 * -12.0) + (8.0 * (x1 * x2)))))));
	} else {
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((x1 * ((3.0 * t_0) - (x1 * 3.0))) + 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) :: tmp
    t_0 = (x2 * (-2.0d0)) - 3.0d0
    t_1 = 4.0d0 * (x2 * (3.0d0 - (2.0d0 * x2)))
    if (x1 <= (-4.8d-30)) then
        tmp = x1 + ((x2 * (-6.0d0)) - (x1 * (2.0d0 + ((3.0d0 * (x1 * t_0)) + t_1))))
    else if (x1 <= 3.1d-154) then
        tmp = x1 + (x1 + ((x1 * (-3.0d0)) - (x2 * (6.0d0 - ((x1 * (-12.0d0)) + (8.0d0 * (x1 * x2)))))))
    else
        tmp = x1 + ((x2 * (-6.0d0)) - (x1 * (2.0d0 + ((x1 * ((3.0d0 * t_0) - (x1 * 3.0d0))) + t_1))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (x2 * -2.0) - 3.0;
	double t_1 = 4.0 * (x2 * (3.0 - (2.0 * x2)));
	double tmp;
	if (x1 <= -4.8e-30) {
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((3.0 * (x1 * t_0)) + t_1))));
	} else if (x1 <= 3.1e-154) {
		tmp = x1 + (x1 + ((x1 * -3.0) - (x2 * (6.0 - ((x1 * -12.0) + (8.0 * (x1 * x2)))))));
	} else {
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((x1 * ((3.0 * t_0) - (x1 * 3.0))) + t_1))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x2 * -2.0) - 3.0
	t_1 = 4.0 * (x2 * (3.0 - (2.0 * x2)))
	tmp = 0
	if x1 <= -4.8e-30:
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((3.0 * (x1 * t_0)) + t_1))))
	elif x1 <= 3.1e-154:
		tmp = x1 + (x1 + ((x1 * -3.0) - (x2 * (6.0 - ((x1 * -12.0) + (8.0 * (x1 * x2)))))))
	else:
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((x1 * ((3.0 * t_0) - (x1 * 3.0))) + t_1))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x2 * -2.0) - 3.0)
	t_1 = Float64(4.0 * Float64(x2 * Float64(3.0 - Float64(2.0 * x2))))
	tmp = 0.0
	if (x1 <= -4.8e-30)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) - Float64(x1 * Float64(2.0 + Float64(Float64(3.0 * Float64(x1 * t_0)) + t_1)))));
	elseif (x1 <= 3.1e-154)
		tmp = Float64(x1 + Float64(x1 + Float64(Float64(x1 * -3.0) - Float64(x2 * Float64(6.0 - Float64(Float64(x1 * -12.0) + Float64(8.0 * Float64(x1 * x2))))))));
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) - Float64(x1 * Float64(2.0 + Float64(Float64(x1 * Float64(Float64(3.0 * t_0) - Float64(x1 * 3.0))) + t_1)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x2 * -2.0) - 3.0;
	t_1 = 4.0 * (x2 * (3.0 - (2.0 * x2)));
	tmp = 0.0;
	if (x1 <= -4.8e-30)
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((3.0 * (x1 * t_0)) + t_1))));
	elseif (x1 <= 3.1e-154)
		tmp = x1 + (x1 + ((x1 * -3.0) - (x2 * (6.0 - ((x1 * -12.0) + (8.0 * (x1 * x2)))))));
	else
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((x1 * ((3.0 * t_0) - (x1 * 3.0))) + t_1))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x2 * -2.0), $MachinePrecision] - 3.0), $MachinePrecision]}, Block[{t$95$1 = N[(4.0 * N[(x2 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -4.8e-30], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] - N[(x1 * N[(2.0 + N[(N[(3.0 * N[(x1 * t$95$0), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 3.1e-154], N[(x1 + N[(x1 + N[(N[(x1 * -3.0), $MachinePrecision] - N[(x2 * N[(6.0 - N[(N[(x1 * -12.0), $MachinePrecision] + N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] - N[(x1 * N[(2.0 + N[(N[(x1 * N[(N[(3.0 * t$95$0), $MachinePrecision] - N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -4.7999999999999997e-30

   1. Initial program 43.6%

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

   3. Taylor expanded in x1 around 0 16.1%

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

   4. Taylor expanded in x1 around 0 41.5%

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

   if -4.7999999999999997e-30 < x1 < 3.09999999999999982e-154

   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 85.5%

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

   4. Taylor expanded in x1 around 0 85.5%

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

   5. Taylor expanded in x2 around 0 99.5%

      \[\leadsto x1 + \color{blue}{\left(x1 + \left(-3 \cdot x1 + x2 \cdot \left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right)\right)\right)} \]

   if 3.09999999999999982e-154 < x1

   1. Initial program 59.6%

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

   3. Taylor expanded in x1 around 0 35.8%

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

   4. Taylor expanded in x1 around 0 79.2%

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

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4.8 \cdot 10^{-30}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 + \left(3 \cdot \left(x1 \cdot \left(x2 \cdot -2 - 3\right)\right) + 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 3.1 \cdot 10^{-154}:\\ \;\;\;\;x1 + \left(x1 + \left(x1 \cdot -3 - x2 \cdot \left(6 - \left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 + \left(x1 \cdot \left(3 \cdot \left(x2 \cdot -2 - 3\right) - x1 \cdot 3\right) + 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 76.2% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x2 \leq -9 \cdot 10^{+32}:\\ \;\;\;\;x1 + \left(\left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot -3 + 2 \cdot \left(x1 \cdot x2\right)\right)\right)\right) + 3 \cdot \left(x2 \cdot -2\right)\right)\\ \mathbf{elif}\;x2 \leq 4.7 \cdot 10^{+147}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 + \left(3 \cdot \left(x1 \cdot \left(x2 \cdot -2 - 3\right)\right) + 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + \left(x1 \cdot -3 - x2 \cdot \left(6 - \left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x2 -9e+32)
   (+
    x1
    (+
     (+ x1 (* 4.0 (* x2 (+ (* x1 -3.0) (* 2.0 (* x1 x2))))))
     (* 3.0 (* x2 -2.0))))
   (if (<= x2 4.7e+147)
     (+
      x1
      (-
       (* x2 -6.0)
       (*
        x1
        (+
         2.0
         (+
          (* 3.0 (* x1 (- (* x2 -2.0) 3.0)))
          (* 4.0 (* x2 (- 3.0 (* 2.0 x2)))))))))
     (+
      x1
      (+
       x1
       (- (* x1 -3.0) (* x2 (- 6.0 (+ (* x1 -12.0) (* 8.0 (* x1 x2)))))))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x2 <= -9e+32) {
		tmp = x1 + ((x1 + (4.0 * (x2 * ((x1 * -3.0) + (2.0 * (x1 * x2)))))) + (3.0 * (x2 * -2.0)));
	} else if (x2 <= 4.7e+147) {
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((3.0 * (x1 * ((x2 * -2.0) - 3.0))) + (4.0 * (x2 * (3.0 - (2.0 * x2))))))));
	} else {
		tmp = x1 + (x1 + ((x1 * -3.0) - (x2 * (6.0 - ((x1 * -12.0) + (8.0 * (x1 * x2)))))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x2 <= (-9d+32)) then
        tmp = x1 + ((x1 + (4.0d0 * (x2 * ((x1 * (-3.0d0)) + (2.0d0 * (x1 * x2)))))) + (3.0d0 * (x2 * (-2.0d0))))
    else if (x2 <= 4.7d+147) then
        tmp = x1 + ((x2 * (-6.0d0)) - (x1 * (2.0d0 + ((3.0d0 * (x1 * ((x2 * (-2.0d0)) - 3.0d0))) + (4.0d0 * (x2 * (3.0d0 - (2.0d0 * x2))))))))
    else
        tmp = x1 + (x1 + ((x1 * (-3.0d0)) - (x2 * (6.0d0 - ((x1 * (-12.0d0)) + (8.0d0 * (x1 * x2)))))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x2 <= -9e+32) {
		tmp = x1 + ((x1 + (4.0 * (x2 * ((x1 * -3.0) + (2.0 * (x1 * x2)))))) + (3.0 * (x2 * -2.0)));
	} else if (x2 <= 4.7e+147) {
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((3.0 * (x1 * ((x2 * -2.0) - 3.0))) + (4.0 * (x2 * (3.0 - (2.0 * x2))))))));
	} else {
		tmp = x1 + (x1 + ((x1 * -3.0) - (x2 * (6.0 - ((x1 * -12.0) + (8.0 * (x1 * x2)))))));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x2 <= -9e+32:
		tmp = x1 + ((x1 + (4.0 * (x2 * ((x1 * -3.0) + (2.0 * (x1 * x2)))))) + (3.0 * (x2 * -2.0)))
	elif x2 <= 4.7e+147:
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((3.0 * (x1 * ((x2 * -2.0) - 3.0))) + (4.0 * (x2 * (3.0 - (2.0 * x2))))))))
	else:
		tmp = x1 + (x1 + ((x1 * -3.0) - (x2 * (6.0 - ((x1 * -12.0) + (8.0 * (x1 * x2)))))))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x2 <= -9e+32)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(4.0 * Float64(x2 * Float64(Float64(x1 * -3.0) + Float64(2.0 * Float64(x1 * x2)))))) + Float64(3.0 * Float64(x2 * -2.0))));
	elseif (x2 <= 4.7e+147)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) - Float64(x1 * Float64(2.0 + Float64(Float64(3.0 * Float64(x1 * Float64(Float64(x2 * -2.0) - 3.0))) + Float64(4.0 * Float64(x2 * Float64(3.0 - Float64(2.0 * x2)))))))));
	else
		tmp = Float64(x1 + Float64(x1 + Float64(Float64(x1 * -3.0) - Float64(x2 * Float64(6.0 - Float64(Float64(x1 * -12.0) + Float64(8.0 * Float64(x1 * x2))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x2 <= -9e+32)
		tmp = x1 + ((x1 + (4.0 * (x2 * ((x1 * -3.0) + (2.0 * (x1 * x2)))))) + (3.0 * (x2 * -2.0)));
	elseif (x2 <= 4.7e+147)
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((3.0 * (x1 * ((x2 * -2.0) - 3.0))) + (4.0 * (x2 * (3.0 - (2.0 * x2))))))));
	else
		tmp = x1 + (x1 + ((x1 * -3.0) - (x2 * (6.0 - ((x1 * -12.0) + (8.0 * (x1 * x2)))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x2, -9e+32], N[(x1 + N[(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] + N[(3.0 * N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x2, 4.7e+147], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] - N[(x1 * N[(2.0 + N[(N[(3.0 * N[(x1 * N[(N[(x2 * -2.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(4.0 * N[(x2 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(x1 + N[(N[(x1 * -3.0), $MachinePrecision] - N[(x2 * N[(6.0 - N[(N[(x1 * -12.0), $MachinePrecision] + N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x2 < -9.0000000000000007e32

   1. Initial program 75.1%

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

   3. Taylor expanded in x1 around 0 47.4%

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

   4. Taylor expanded in x2 around 0 57.3%

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

   5. Taylor expanded in x1 around 0 66.3%

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

      1. *-commutative 66.3%

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

   7. Simplified 66.3%

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

   if -9.0000000000000007e32 < x2 < 4.7000000000000003e147

   1. Initial program 69.2%

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

   3. Taylor expanded in x1 around 0 51.3%

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

   4. Taylor expanded in x1 around 0 77.1%

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

   if 4.7000000000000003e147 < x2

   1. Initial program 66.5%

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

   3. Taylor expanded in x1 around 0 40.2%

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

   4. Taylor expanded in x1 around 0 61.4%

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

   5. Taylor expanded in x2 around 0 84.8%

      \[\leadsto x1 + \color{blue}{\left(x1 + \left(-3 \cdot x1 + x2 \cdot \left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right)\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 75.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq -9 \cdot 10^{+32}:\\ \;\;\;\;x1 + \left(\left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot -3 + 2 \cdot \left(x1 \cdot x2\right)\right)\right)\right) + 3 \cdot \left(x2 \cdot -2\right)\right)\\ \mathbf{elif}\;x2 \leq 4.7 \cdot 10^{+147}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 + \left(3 \cdot \left(x1 \cdot \left(x2 \cdot -2 - 3\right)\right) + 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + \left(x1 \cdot -3 - x2 \cdot \left(6 - \left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 66.2% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -1 \cdot 10^{+64}:\\ \;\;\;\;x1 + \left(\left(x1 + 4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right) + x2 \cdot \left(-3 \cdot \frac{x1}{x2} - 6\right)\right)\\ \mathbf{elif}\;x1 \leq 2.05 \cdot 10^{+269} \lor \neg \left(x1 \leq 1.05 \cdot 10^{+288}\right):\\ \;\;\;\;x1 + \left(x1 + \left(x1 \cdot -3 - x2 \cdot \left(6 - \left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot \left(\frac{x1}{x2} - 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -1e+64)
   (+
    x1
    (+
     (+ x1 (* 4.0 (* x1 (* x2 (- (* 2.0 x2) 3.0)))))
     (* x2 (- (* -3.0 (/ x1 x2)) 6.0))))
   (if (or (<= x1 2.05e+269) (not (<= x1 1.05e+288)))
     (+
      x1
      (+ x1 (- (* x1 -3.0) (* x2 (- 6.0 (+ (* x1 -12.0) (* 8.0 (* x1 x2))))))))
     (* x2 (- (/ x1 x2) 6.0)))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -1e+64) {
		tmp = x1 + ((x1 + (4.0 * (x1 * (x2 * ((2.0 * x2) - 3.0))))) + (x2 * ((-3.0 * (x1 / x2)) - 6.0)));
	} else if ((x1 <= 2.05e+269) || !(x1 <= 1.05e+288)) {
		tmp = x1 + (x1 + ((x1 * -3.0) - (x2 * (6.0 - ((x1 * -12.0) + (8.0 * (x1 * x2)))))));
	} 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 <= (-1d+64)) then
        tmp = x1 + ((x1 + (4.0d0 * (x1 * (x2 * ((2.0d0 * x2) - 3.0d0))))) + (x2 * (((-3.0d0) * (x1 / x2)) - 6.0d0)))
    else if ((x1 <= 2.05d+269) .or. (.not. (x1 <= 1.05d+288))) then
        tmp = x1 + (x1 + ((x1 * (-3.0d0)) - (x2 * (6.0d0 - ((x1 * (-12.0d0)) + (8.0d0 * (x1 * x2)))))))
    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 <= -1e+64) {
		tmp = x1 + ((x1 + (4.0 * (x1 * (x2 * ((2.0 * x2) - 3.0))))) + (x2 * ((-3.0 * (x1 / x2)) - 6.0)));
	} else if ((x1 <= 2.05e+269) || !(x1 <= 1.05e+288)) {
		tmp = x1 + (x1 + ((x1 * -3.0) - (x2 * (6.0 - ((x1 * -12.0) + (8.0 * (x1 * x2)))))));
	} else {
		tmp = x2 * ((x1 / x2) - 6.0);
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -1e+64:
		tmp = x1 + ((x1 + (4.0 * (x1 * (x2 * ((2.0 * x2) - 3.0))))) + (x2 * ((-3.0 * (x1 / x2)) - 6.0)))
	elif (x1 <= 2.05e+269) or not (x1 <= 1.05e+288):
		tmp = x1 + (x1 + ((x1 * -3.0) - (x2 * (6.0 - ((x1 * -12.0) + (8.0 * (x1 * x2)))))))
	else:
		tmp = x2 * ((x1 / x2) - 6.0)
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -1e+64)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(4.0 * Float64(x1 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0))))) + Float64(x2 * Float64(Float64(-3.0 * Float64(x1 / x2)) - 6.0))));
	elseif ((x1 <= 2.05e+269) || !(x1 <= 1.05e+288))
		tmp = Float64(x1 + Float64(x1 + Float64(Float64(x1 * -3.0) - Float64(x2 * Float64(6.0 - Float64(Float64(x1 * -12.0) + Float64(8.0 * Float64(x1 * x2))))))));
	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 <= -1e+64)
		tmp = x1 + ((x1 + (4.0 * (x1 * (x2 * ((2.0 * x2) - 3.0))))) + (x2 * ((-3.0 * (x1 / x2)) - 6.0)));
	elseif ((x1 <= 2.05e+269) || ~((x1 <= 1.05e+288)))
		tmp = x1 + (x1 + ((x1 * -3.0) - (x2 * (6.0 - ((x1 * -12.0) + (8.0 * (x1 * x2)))))));
	else
		tmp = x2 * ((x1 / x2) - 6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -1e+64], N[(x1 + N[(N[(x1 + N[(4.0 * N[(x1 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x2 * N[(N[(-3.0 * N[(x1 / x2), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x1, 2.05e+269], N[Not[LessEqual[x1, 1.05e+288]], $MachinePrecision]], N[(x1 + N[(x1 + N[(N[(x1 * -3.0), $MachinePrecision] - N[(x2 * N[(6.0 - N[(N[(x1 * -12.0), $MachinePrecision] + N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $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 < -1.00000000000000002e64

   1. Initial program 11.6%

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

   3. Taylor expanded in x1 around 0 4.8%

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

   4. Taylor expanded in x1 around 0 7.5%

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

   5. Taylor expanded in x2 around inf 35.9%

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

   if -1.00000000000000002e64 < x1 < 2.05000000000000004e269 or 1.04999999999999999e288 < x1

   1. Initial program 84.0%

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

   3. Taylor expanded in x1 around 0 59.3%

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

   4. Taylor expanded in x1 around 0 65.6%

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

   5. Taylor expanded in x2 around 0 72.5%

      \[\leadsto x1 + \color{blue}{\left(x1 + \left(-3 \cdot x1 + x2 \cdot \left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right)\right)\right)} \]

   if 2.05000000000000004e269 < x1 < 1.04999999999999999e288

   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 7.9%

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

      1. *-commutative 7.9%

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

   6. Simplified 7.9%

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

   7. Taylor expanded in x2 around inf 81.6%

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

4. Final simplification 66.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1 \cdot 10^{+64}:\\ \;\;\;\;x1 + \left(\left(x1 + 4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right) + x2 \cdot \left(-3 \cdot \frac{x1}{x2} - 6\right)\right)\\ \mathbf{elif}\;x1 \leq 2.05 \cdot 10^{+269} \lor \neg \left(x1 \leq 1.05 \cdot 10^{+288}\right):\\ \;\;\;\;x1 + \left(x1 + \left(x1 \cdot -3 - x2 \cdot \left(6 - \left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot \left(\frac{x1}{x2} - 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 44.5% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x2 \cdot \left(\frac{x1}{x2} - 6\right)\\ t_1 := x1 + x1 \cdot \left(1 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ \mathbf{if}\;x2 \leq -6.8 \cdot 10^{+154}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x2 \leq -1.25 \cdot 10^{-132}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x2 \leq 9 \cdot 10^{-166}:\\ \;\;\;\;x1 + x1 \cdot -2\\ \mathbf{elif}\;x2 \leq 8 \cdot 10^{+128}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x2 (- (/ x1 x2) 6.0)))
        (t_1 (+ x1 (* x1 (+ 1.0 (* 4.0 (* x2 (- (* 2.0 x2) 3.0))))))))
   (if (<= x2 -6.8e+154)
     t_1
     (if (<= x2 -1.25e-132)
       t_0
       (if (<= x2 9e-166) (+ x1 (* x1 -2.0)) (if (<= x2 8e+128) t_0 t_1))))))

C

double code(double x1, double x2) {
	double t_0 = x2 * ((x1 / x2) - 6.0);
	double t_1 = x1 + (x1 * (1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0)))));
	double tmp;
	if (x2 <= -6.8e+154) {
		tmp = t_1;
	} else if (x2 <= -1.25e-132) {
		tmp = t_0;
	} else if (x2 <= 9e-166) {
		tmp = x1 + (x1 * -2.0);
	} else if (x2 <= 8e+128) {
		tmp = t_0;
	} else {
		tmp = 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) :: tmp
    t_0 = x2 * ((x1 / x2) - 6.0d0)
    t_1 = x1 + (x1 * (1.0d0 + (4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0)))))
    if (x2 <= (-6.8d+154)) then
        tmp = t_1
    else if (x2 <= (-1.25d-132)) then
        tmp = t_0
    else if (x2 <= 9d-166) then
        tmp = x1 + (x1 * (-2.0d0))
    else if (x2 <= 8d+128) then
        tmp = t_0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x2 * ((x1 / x2) - 6.0);
	double t_1 = x1 + (x1 * (1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0)))));
	double tmp;
	if (x2 <= -6.8e+154) {
		tmp = t_1;
	} else if (x2 <= -1.25e-132) {
		tmp = t_0;
	} else if (x2 <= 9e-166) {
		tmp = x1 + (x1 * -2.0);
	} else if (x2 <= 8e+128) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x2 * ((x1 / x2) - 6.0)
	t_1 = x1 + (x1 * (1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0)))))
	tmp = 0
	if x2 <= -6.8e+154:
		tmp = t_1
	elif x2 <= -1.25e-132:
		tmp = t_0
	elif x2 <= 9e-166:
		tmp = x1 + (x1 * -2.0)
	elif x2 <= 8e+128:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x2 * Float64(Float64(x1 / x2) - 6.0))
	t_1 = Float64(x1 + Float64(x1 * Float64(1.0 + Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0))))))
	tmp = 0.0
	if (x2 <= -6.8e+154)
		tmp = t_1;
	elseif (x2 <= -1.25e-132)
		tmp = t_0;
	elseif (x2 <= 9e-166)
		tmp = Float64(x1 + Float64(x1 * -2.0));
	elseif (x2 <= 8e+128)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x2 * ((x1 / x2) - 6.0);
	t_1 = x1 + (x1 * (1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0)))));
	tmp = 0.0;
	if (x2 <= -6.8e+154)
		tmp = t_1;
	elseif (x2 <= -1.25e-132)
		tmp = t_0;
	elseif (x2 <= 9e-166)
		tmp = x1 + (x1 * -2.0);
	elseif (x2 <= 8e+128)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x2 * N[(N[(x1 / x2), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = 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]}, If[LessEqual[x2, -6.8e+154], t$95$1, If[LessEqual[x2, -1.25e-132], t$95$0, If[LessEqual[x2, 9e-166], N[(x1 + N[(x1 * -2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x2, 8e+128], t$95$0, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if x2 < -6.79999999999999948e154 or 8.0000000000000006e128 < x2

   1. Initial program 69.7%

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

   3. Taylor expanded in x1 around 0 50.1%

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

   4. Taylor expanded in x1 around inf 63.8%

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

   if -6.79999999999999948e154 < x2 < -1.25e-132 or 8.99999999999999961e-166 < x2 < 8.0000000000000006e128

   1. Initial program 72.1%

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

   3. Taylor expanded in x1 around 0 46.8%

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

   4. Taylor expanded in x1 around 0 41.0%

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

      1. *-commutative 41.0%

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

   6. Simplified 41.0%

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

   7. Taylor expanded in x2 around inf 44.6%

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

   if -1.25e-132 < x2 < 8.99999999999999961e-166

   1. Initial program 66.8%

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

   3. Taylor expanded in x1 around 0 52.2%

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

   4. Taylor expanded in x1 around 0 52.8%

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

   5. Taylor expanded in x2 around 0 47.3%

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

      1. distribute-rgt1-in 47.9%

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

      2. metadata-eval 47.9%

         \[\leadsto x1 + \color{blue}{-2} \cdot x1 \]

      3. *-commutative 47.9%

         \[\leadsto x1 + \color{blue}{x1 \cdot -2} \]

   7. Simplified 47.9%

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

4. Final simplification 50.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq -6.8 \cdot 10^{+154}:\\ \;\;\;\;x1 + x1 \cdot \left(1 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ \mathbf{elif}\;x2 \leq -1.25 \cdot 10^{-132}:\\ \;\;\;\;x2 \cdot \left(\frac{x1}{x2} - 6\right)\\ \mathbf{elif}\;x2 \leq 9 \cdot 10^{-166}:\\ \;\;\;\;x1 + x1 \cdot -2\\ \mathbf{elif}\;x2 \leq 8 \cdot 10^{+128}:\\ \;\;\;\;x2 \cdot \left(\frac{x1}{x2} - 6\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot \left(1 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 50.4% accurate, 5.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x2 \leq -4.1 \cdot 10^{+155} \lor \neg \left(x2 \leq 7 \cdot 10^{+128}\right):\\ \;\;\;\;x1 + x1 \cdot \left(1 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + \left(x1 \cdot -3 + x2 \cdot \left(x1 \cdot -12 - 6\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x2 -4.1e+155) (not (<= x2 7e+128)))
   (+ x1 (* x1 (+ 1.0 (* 4.0 (* x2 (- (* 2.0 x2) 3.0))))))
   (+ x1 (+ x1 (+ (* x1 -3.0) (* x2 (- (* x1 -12.0) 6.0)))))))

C

double code(double x1, double x2) {
	double tmp;
	if ((x2 <= -4.1e+155) || !(x2 <= 7e+128)) {
		tmp = x1 + (x1 * (1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0)))));
	} else {
		tmp = x1 + (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 ((x2 <= (-4.1d+155)) .or. (.not. (x2 <= 7d+128))) then
        tmp = x1 + (x1 * (1.0d0 + (4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0)))))
    else
        tmp = x1 + (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 ((x2 <= -4.1e+155) || !(x2 <= 7e+128)) {
		tmp = x1 + (x1 * (1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0)))));
	} else {
		tmp = x1 + (x1 + ((x1 * -3.0) + (x2 * ((x1 * -12.0) - 6.0))));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x2 <= -4.1e+155) or not (x2 <= 7e+128):
		tmp = x1 + (x1 * (1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0)))))
	else:
		tmp = x1 + (x1 + ((x1 * -3.0) + (x2 * ((x1 * -12.0) - 6.0))))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x2 <= -4.1e+155) || !(x2 <= 7e+128))
		tmp = Float64(x1 + Float64(x1 * Float64(1.0 + Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0))))));
	else
		tmp = Float64(x1 + Float64(x1 + Float64(Float64(x1 * -3.0) + Float64(x2 * Float64(Float64(x1 * -12.0) - 6.0)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x2 <= -4.1e+155) || ~((x2 <= 7e+128)))
		tmp = x1 + (x1 * (1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0)))));
	else
		tmp = x1 + (x1 + ((x1 * -3.0) + (x2 * ((x1 * -12.0) - 6.0))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x2, -4.1e+155], N[Not[LessEqual[x2, 7e+128]], $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[(x1 + N[(x1 + N[(N[(x1 * -3.0), $MachinePrecision] + N[(x2 * N[(N[(x1 * -12.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x2 < -4.0999999999999998e155 or 6.99999999999999937e128 < x2

   1. Initial program 69.7%

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

   3. Taylor expanded in x1 around 0 50.1%

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

   4. Taylor expanded in x1 around inf 63.8%

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

   if -4.0999999999999998e155 < x2 < 6.99999999999999937e128

   1. Initial program 70.4%

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

   3. Taylor expanded in x1 around 0 48.6%

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

   4. Taylor expanded in x1 around 0 49.8%

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

   5. Taylor expanded in x2 around 0 50.3%

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

4. Final simplification 54.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq -4.1 \cdot 10^{+155} \lor \neg \left(x2 \leq 7 \cdot 10^{+128}\right):\\ \;\;\;\;x1 + x1 \cdot \left(1 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + \left(x1 \cdot -3 + x2 \cdot \left(x1 \cdot -12 - 6\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 60.7% accurate, 6.0× speedup

Math

\[\begin{array}{l} \\ x1 + \left(x1 + \left(x1 \cdot -3 - x2 \cdot \left(6 - \left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\right) \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (+
  x1
  (+ x1 (- (* x1 -3.0) (* x2 (- 6.0 (+ (* x1 -12.0) (* 8.0 (* x1 x2)))))))))

C

double code(double x1, double x2) {
	return x1 + (x1 + ((x1 * -3.0) - (x2 * (6.0 - ((x1 * -12.0) + (8.0 * (x1 * x2)))))));
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    code = x1 + (x1 + ((x1 * (-3.0d0)) - (x2 * (6.0d0 - ((x1 * (-12.0d0)) + (8.0d0 * (x1 * x2)))))))
end function

Java

public static double code(double x1, double x2) {
	return x1 + (x1 + ((x1 * -3.0) - (x2 * (6.0 - ((x1 * -12.0) + (8.0 * (x1 * x2)))))));
}

Python

def code(x1, x2):
	return x1 + (x1 + ((x1 * -3.0) - (x2 * (6.0 - ((x1 * -12.0) + (8.0 * (x1 * x2)))))))

Julia

function code(x1, x2)
	return Float64(x1 + Float64(x1 + Float64(Float64(x1 * -3.0) - Float64(x2 * Float64(6.0 - Float64(Float64(x1 * -12.0) + Float64(8.0 * Float64(x1 * x2))))))))
end

MATLAB

function tmp = code(x1, x2)
	tmp = x1 + (x1 + ((x1 * -3.0) - (x2 * (6.0 - ((x1 * -12.0) + (8.0 * (x1 * x2)))))));
end

Wolfram

code[x1_, x2_] := N[(x1 + N[(x1 + N[(N[(x1 * -3.0), $MachinePrecision] - N[(x2 * N[(6.0 - N[(N[(x1 * -12.0), $MachinePrecision] + N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 70.2%

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

3. Taylor expanded in x1 around 0 49.0%

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

4. Taylor expanded in x1 around 0 54.6%

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

5. Taylor expanded in x2 around 0 60.2%

   \[\leadsto x1 + \color{blue}{\left(x1 + \left(-3 \cdot x1 + x2 \cdot \left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right)\right)\right)} \]

6. Final simplification 60.2%

   \[\leadsto x1 + \left(x1 + \left(x1 \cdot -3 - x2 \cdot \left(6 - \left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\right) \]
7. Add Preprocessing

Alternative 21: 55.1% accurate, 6.7× speedup

Math

\[\begin{array}{l} \\ x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 - 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right) \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x1_, x2_] := 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]

Derivation

1. Initial program 70.2%

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

3. Taylor expanded in x1 around 0 49.0%

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

4. Taylor expanded in x1 around 0 54.8%

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

5. Final simplification 54.8%

   \[\leadsto x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 - 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right) \]
6. Add Preprocessing

Alternative 22: 31.8% accurate, 8.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x2 \leq -2 \cdot 10^{-132} \lor \neg \left(x2 \leq 2.8 \cdot 10^{-130}\right):\\ \;\;\;\;x2 \cdot -6\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x2 -2e-132) (not (<= x2 2.8e-130)))
   (* x2 -6.0)
   (+ x1 (* x1 -2.0))))

C

double code(double x1, double x2) {
	double tmp;
	if ((x2 <= -2e-132) || !(x2 <= 2.8e-130)) {
		tmp = x2 * -6.0;
	} else {
		tmp = x1 + (x1 * -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 ((x2 <= (-2d-132)) .or. (.not. (x2 <= 2.8d-130))) then
        tmp = x2 * (-6.0d0)
    else
        tmp = x1 + (x1 * (-2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x2 <= -2e-132) || !(x2 <= 2.8e-130)) {
		tmp = x2 * -6.0;
	} else {
		tmp = x1 + (x1 * -2.0);
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x2 <= -2e-132) or not (x2 <= 2.8e-130):
		tmp = x2 * -6.0
	else:
		tmp = x1 + (x1 * -2.0)
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x2 <= -2e-132) || !(x2 <= 2.8e-130))
		tmp = Float64(x2 * -6.0);
	else
		tmp = Float64(x1 + Float64(x1 * -2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x2 <= -2e-132) || ~((x2 <= 2.8e-130)))
		tmp = x2 * -6.0;
	else
		tmp = x1 + (x1 * -2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x2, -2e-132], N[Not[LessEqual[x2, 2.8e-130]], $MachinePrecision]], N[(x2 * -6.0), $MachinePrecision], N[(x1 + N[(x1 * -2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x2 < -2e-132 or 2.80000000000000016e-130 < x2

   1. Initial program 72.1%

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

   3. Taylor expanded in x1 around 0 48.9%

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

   4. Taylor expanded in x1 around 0 33.1%

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

      1. *-commutative 33.1%

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

   6. Simplified 33.1%

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

   7. Taylor expanded in x1 around 0 32.7%

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

      1. *-commutative 32.7%

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

   9. Simplified 32.7%

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

   if -2e-132 < x2 < 2.80000000000000016e-130

   1. Initial program 65.3%

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

   3. Taylor expanded in x1 around 0 49.3%

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

   4. Taylor expanded in x1 around 0 49.7%

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

   5. Taylor expanded in x2 around 0 42.4%

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

      1. distribute-rgt1-in 43.0%

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

      2. metadata-eval 43.0%

         \[\leadsto x1 + \color{blue}{-2} \cdot x1 \]

      3. *-commutative 43.0%

         \[\leadsto x1 + \color{blue}{x1 \cdot -2} \]

   7. Simplified 43.0%

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

4. Final simplification 35.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq -2 \cdot 10^{-132} \lor \neg \left(x2 \leq 2.8 \cdot 10^{-130}\right):\\ \;\;\;\;x2 \cdot -6\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot -2\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 32.1% accurate, 8.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x2 \leq -2.9 \cdot 10^{-133}:\\ \;\;\;\;x2 \cdot -6\\ \mathbf{elif}\;x2 \leq 2 \cdot 10^{-165}:\\ \;\;\;\;x1 + x1 \cdot -2\\ \mathbf{else}:\\ \;\;\;\;x1 + x2 \cdot -6\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x2 -2.9e-133)
   (* x2 -6.0)
   (if (<= x2 2e-165) (+ x1 (* x1 -2.0)) (+ x1 (* x2 -6.0)))))

C

double code(double x1, double x2) {
	double tmp;
	if (x2 <= -2.9e-133) {
		tmp = x2 * -6.0;
	} else if (x2 <= 2e-165) {
		tmp = x1 + (x1 * -2.0);
	} 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 <= (-2.9d-133)) then
        tmp = x2 * (-6.0d0)
    else if (x2 <= 2d-165) then
        tmp = x1 + (x1 * (-2.0d0))
    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 <= -2.9e-133) {
		tmp = x2 * -6.0;
	} else if (x2 <= 2e-165) {
		tmp = x1 + (x1 * -2.0);
	} else {
		tmp = x1 + (x2 * -6.0);
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x2 <= -2.9e-133:
		tmp = x2 * -6.0
	elif x2 <= 2e-165:
		tmp = x1 + (x1 * -2.0)
	else:
		tmp = x1 + (x2 * -6.0)
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x2 <= -2.9e-133)
		tmp = Float64(x2 * -6.0);
	elseif (x2 <= 2e-165)
		tmp = Float64(x1 + Float64(x1 * -2.0));
	else
		tmp = Float64(x1 + Float64(x2 * -6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x2 <= -2.9e-133)
		tmp = x2 * -6.0;
	elseif (x2 <= 2e-165)
		tmp = x1 + (x1 * -2.0);
	else
		tmp = x1 + (x2 * -6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x2, -2.9e-133], N[(x2 * -6.0), $MachinePrecision], If[LessEqual[x2, 2e-165], N[(x1 + N[(x1 * -2.0), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x2 < -2.8999999999999998e-133

   1. Initial program 74.3%

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

   3. Taylor expanded in x1 around 0 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 27.9%

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

      1. *-commutative 27.9%

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

   6. Simplified 27.9%

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

   7. Taylor expanded in x1 around 0 28.1%

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

      1. *-commutative 28.1%

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

   9. Simplified 28.1%

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

   if -2.8999999999999998e-133 < x2 < 2e-165

   1. Initial program 66.8%

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

   3. Taylor expanded in x1 around 0 52.2%

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

   4. Taylor expanded in x1 around 0 52.8%

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

   5. Taylor expanded in x2 around 0 47.3%

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

      1. distribute-rgt1-in 47.9%

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

      2. metadata-eval 47.9%

         \[\leadsto x1 + \color{blue}{-2} \cdot x1 \]

      3. *-commutative 47.9%

         \[\leadsto x1 + \color{blue}{x1 \cdot -2} \]

   7. Simplified 47.9%

      \[\leadsto x1 + \color{blue}{x1 \cdot -2} \]

   if 2e-165 < x2

   1. Initial program 68.8%

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

   3. Taylor expanded in x1 around 0 47.7%

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

   4. Taylor expanded in x1 around 0 35.8%

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

      1. *-commutative 35.8%

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

   6. Simplified 35.8%

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

4. Final simplification 36.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq -2.9 \cdot 10^{-133}:\\ \;\;\;\;x2 \cdot -6\\ \mathbf{elif}\;x2 \leq 2 \cdot 10^{-165}:\\ \;\;\;\;x1 + x1 \cdot -2\\ \mathbf{else}:\\ \;\;\;\;x1 + x2 \cdot -6\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 34.6% accurate, 10.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -7.5 \cdot 10^{-110}:\\ \;\;\;\;x1 + x1 \cdot -2\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot \left(\frac{x1}{x2} - 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -7.5e-110) (+ x1 (* x1 -2.0)) (* x2 (- (/ x1 x2) 6.0))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -7.5e-110) {
		tmp = x1 + (x1 * -2.0);
	} 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 <= (-7.5d-110)) then
        tmp = x1 + (x1 * (-2.0d0))
    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 <= -7.5e-110) {
		tmp = x1 + (x1 * -2.0);
	} else {
		tmp = x2 * ((x1 / x2) - 6.0);
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -7.5e-110:
		tmp = x1 + (x1 * -2.0)
	else:
		tmp = x2 * ((x1 / x2) - 6.0)
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -7.5e-110)
		tmp = Float64(x1 + Float64(x1 * -2.0));
	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 <= -7.5e-110)
		tmp = x1 + (x1 * -2.0);
	else
		tmp = x2 * ((x1 / x2) - 6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -7.5e-110], N[(x1 + N[(x1 * -2.0), $MachinePrecision]), $MachinePrecision], N[(x2 * N[(N[(x1 / x2), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x1 < -7.50000000000000053e-110

   1. Initial program 58.6%

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

   3. Taylor expanded in x1 around 0 35.6%

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

   4. Taylor expanded in x1 around 0 37.2%

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

   5. Taylor expanded in x2 around 0 20.0%

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

      1. distribute-rgt1-in 20.2%

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

      2. metadata-eval 20.2%

         \[\leadsto x1 + \color{blue}{-2} \cdot x1 \]

      3. *-commutative 20.2%

         \[\leadsto x1 + \color{blue}{x1 \cdot -2} \]

   7. Simplified 20.2%

      \[\leadsto x1 + \color{blue}{x1 \cdot -2} \]

   if -7.50000000000000053e-110 < x1

   1. Initial program 76.8%

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

   3. Taylor expanded in x1 around 0 56.7%

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

   4. Taylor expanded in x1 around 0 38.7%

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

      1. *-commutative 38.7%

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

   6. Simplified 38.7%

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

   7. Taylor expanded in x2 around inf 47.3%

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

4. Final simplification 37.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -7.5 \cdot 10^{-110}:\\ \;\;\;\;x1 + x1 \cdot -2\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot \left(\frac{x1}{x2} - 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 26.1% accurate, 42.3× speedup

Math

\[\begin{array}{l} \\ x2 \cdot -6 \end{array} \]

FPCore

(FPCore (x1 x2) :precision binary64 (* x2 -6.0))

C

double code(double x1, double x2) {
	return x2 * -6.0;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    code = x2 * (-6.0d0)
end function

Java

public static double code(double x1, double x2) {
	return x2 * -6.0;
}

Python

def code(x1, x2):
	return x2 * -6.0

Julia

function code(x1, x2)
	return Float64(x2 * -6.0)
end

MATLAB

function tmp = code(x1, x2)
	tmp = x2 * -6.0;
end

Wolfram

code[x1_, x2_] := N[(x2 * -6.0), $MachinePrecision]

Derivation

1. Initial program 70.2%

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

3. Taylor expanded in x1 around 0 49.0%

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

4. Taylor expanded in x1 around 0 26.3%

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

   1. *-commutative 26.3%

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

6. Simplified 26.3%

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

7. Taylor expanded in x1 around 0 26.0%

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

   1. *-commutative 26.0%

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

9. Simplified 26.0%

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

10. Final simplification 26.0%

    \[\leadsto x2 \cdot -6 \]
11. Add Preprocessing

Alternative 26: 3.5% accurate, 127.0× speedup

Math

\[\begin{array}{l} \\ 9 \end{array} \]

FPCore

(FPCore (x1 x2) :precision binary64 9.0)

C

double code(double x1, double x2) {
	return 9.0;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    code = 9.0d0
end function

Java

public static double code(double x1, double x2) {
	return 9.0;
}

Python

def code(x1, x2):
	return 9.0

Julia

function code(x1, x2)
	return 9.0
end

MATLAB

function tmp = code(x1, x2)
	tmp = 9.0;
end

Wolfram

code[x1_, x2_] := 9.0

Derivation

1. Initial program 70.2%

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

3. Taylor expanded in x1 around inf 56.6%

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

4. Taylor expanded in x1 around inf 45.9%

   \[\leadsto x1 + \left(\left(6 \cdot {x1}^{4} + x1\right) + \color{blue}{9}\right) \]

5. Taylor expanded in x1 around 0 3.3%

   \[\leadsto \color{blue}{9} \]

6. Final simplification 3.3%

   \[\leadsto 9 \]
7. Add Preprocessing

Alternative 27: 3.3% accurate, 127.0× speedup

Math

\[\begin{array}{l} \\ x1 \end{array} \]

FPCore

(FPCore (x1 x2) :precision binary64 x1)

C

double code(double x1, double x2) {
	return x1;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    code = x1
end function

Java

public static double code(double x1, double x2) {
	return x1;
}

Python

def code(x1, x2):
	return x1

Julia

function code(x1, x2)
	return x1
end

MATLAB

function tmp = code(x1, x2)
	tmp = x1;
end

Wolfram

code[x1_, x2_] := x1

Derivation

1. Initial program 70.2%

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

3. Taylor expanded in x1 around 0 49.0%

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

4. Taylor expanded in x1 around 0 26.3%

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

   1. *-commutative 26.3%

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

6. Simplified 26.3%

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

7. Taylor expanded in x1 around inf 3.4%

   \[\leadsto \color{blue}{x1} \]

8. Final simplification 3.4%

   \[\leadsto x1 \]
9. Add Preprocessing

Reproduce

herbie shell --seed 2024050 
(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))))))