Rosa's FloatVsDoubleBenchmark

Percentage Accurate: 70.5% → 99.7%

Time: 1.1min

Alternatives: 29

Speedup: 2.9×

• 47.6% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    t_0 = (3.0d0 * x1) * x1
    t_1 = (x1 * x1) + 1.0d0
    t_2 = ((t_0 + (2.0d0 * x2)) - x1) / t_1
    code = x1 + (((((((((2.0d0 * x1) * t_2) * (t_2 - 3.0d0)) + ((x1 * x1) * ((4.0d0 * t_2) - 6.0d0))) * t_1) + (t_0 * t_2)) + ((x1 * x1) * x1)) + x1) + (3.0d0 * (((t_0 - (2.0d0 * x2)) - x1) / t_1)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 70.5% 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: 99.7% accurate, 0.1× speedup

Math

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

FPCore

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

C

double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = (fma(x1, (x1 * 3.0), (2.0 * x2)) - x1) / fma(x1, x1, 1.0);
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = (t_2 + (2.0 * x2)) - x1;
	double t_4 = t_3 / t_0;
	double t_5 = t_3 / (-1.0 - (x1 * x1));
	double t_6 = 3.0 * (x1 * x1);
	double tmp;
	if ((x1 + ((x1 + (((t_2 * t_4) - (t_0 * (((x1 * x1) * (6.0 + (4.0 * t_5))) + (((x1 * 2.0) * t_4) * (3.0 + t_5))))) + (x1 * (x1 * x1)))) + (3.0 * (((t_2 - (2.0 * x2)) - x1) / t_0)))) <= ((double) INFINITY)) {
		tmp = x1 + fma(3.0, ((t_6 - fma(2.0, x2, x1)) / fma(x1, x1, 1.0)), (x1 + fma(fma(x1, x1, 1.0), fma(x1, (x1 * fma(t_1, 4.0, -6.0)), ((x1 * (2.0 * t_1)) * (t_1 + -3.0))), fma(t_6, t_1, pow(x1, 3.0)))));
	} else {
		tmp = x1 + (9.0 + (x1 + (pow(x1, 4.0) * (6.0 + ((((9.0 + (4.0 * ((2.0 * x2) - 3.0))) / x1) - 3.0) / x1)))));
	}
	return tmp;
}

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * x1) + 1.0)
	t_1 = Float64(Float64(fma(x1, Float64(x1 * 3.0), Float64(2.0 * x2)) - x1) / fma(x1, x1, 1.0))
	t_2 = Float64(x1 * Float64(x1 * 3.0))
	t_3 = Float64(Float64(t_2 + Float64(2.0 * x2)) - x1)
	t_4 = Float64(t_3 / t_0)
	t_5 = Float64(t_3 / Float64(-1.0 - Float64(x1 * x1)))
	t_6 = Float64(3.0 * Float64(x1 * x1))
	tmp = 0.0
	if (Float64(x1 + Float64(Float64(x1 + Float64(Float64(Float64(t_2 * t_4) - Float64(t_0 * Float64(Float64(Float64(x1 * x1) * Float64(6.0 + Float64(4.0 * t_5))) + Float64(Float64(Float64(x1 * 2.0) * t_4) * Float64(3.0 + t_5))))) + Float64(x1 * Float64(x1 * x1)))) + Float64(3.0 * Float64(Float64(Float64(t_2 - Float64(2.0 * x2)) - x1) / t_0)))) <= Inf)
		tmp = Float64(x1 + fma(3.0, Float64(Float64(t_6 - fma(2.0, x2, x1)) / fma(x1, x1, 1.0)), Float64(x1 + fma(fma(x1, x1, 1.0), fma(x1, Float64(x1 * fma(t_1, 4.0, -6.0)), Float64(Float64(x1 * Float64(2.0 * t_1)) * Float64(t_1 + -3.0))), fma(t_6, t_1, (x1 ^ 3.0))))));
	else
		tmp = Float64(x1 + Float64(9.0 + Float64(x1 + Float64((x1 ^ 4.0) * Float64(6.0 + Float64(Float64(Float64(Float64(9.0 + Float64(4.0 * Float64(Float64(2.0 * x2) - 3.0))) / x1) - 3.0) / x1))))));
	end
	return tmp
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$1 = N[(N[(N[(x1 * N[(x1 * 3.0), $MachinePrecision] + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t$95$2 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$3 / t$95$0), $MachinePrecision]}, Block[{t$95$5 = N[(t$95$3 / N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(3.0 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x1 + N[(N[(x1 + N[(N[(N[(t$95$2 * t$95$4), $MachinePrecision] - N[(t$95$0 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 + N[(4.0 * t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$4), $MachinePrecision] * N[(3.0 + t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(N[(N[(t$95$2 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(x1 + N[(3.0 * N[(N[(t$95$6 - 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$1 * 4.0 + -6.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * N[(2.0 * t$95$1), $MachinePrecision]), $MachinePrecision] * N[(t$95$1 + -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$6 * t$95$1 + N[Power[x1, 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(9.0 + N[(x1 + N[(N[Power[x1, 4.0], $MachinePrecision] * N[(6.0 + N[(N[(N[(N[(9.0 + N[(4.0 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x1), $MachinePrecision] - 3.0), $MachinePrecision] / x1), $MachinePrecision]), $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 #s(literal 2 binary64) x1) (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64)))) (-.f64 (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64))) #s(literal 3 binary64))) (*.f64 (*.f64 x1 x1) (-.f64 (*.f64 #s(literal 4 binary64) (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64)))) #s(literal 6 binary64)))) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64))) (*.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64))))) (*.f64 (*.f64 x1 x1) x1)) x1) (*.f64 #s(literal 3 binary64) (/.f64 (-.f64 (-.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64)))))) < +inf.0

   1. Initial program 99.4%

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

   3. Simplified 99.7%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in x1 around -inf 12.5%

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

   4. Taylor expanded in x1 around inf 100.0%

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

4. Final simplification 99.8%

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

Alternative 2: 99.5% accurate, 0.5× speedup

Math

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

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

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

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 = t_1 / t_2;
	double t_4 = t_1 / (-1.0 - (x1 * x1));
	double t_5 = x1 + ((x1 + (((t_0 * t_3) - (t_2 * (((x1 * x1) * (6.0 + (4.0 * t_4))) + (((x1 * 2.0) * t_3) * (3.0 + t_4))))) + (x1 * (x1 * x1)))) + (3.0 * (((t_0 - (2.0 * x2)) - x1) / t_2)));
	double tmp;
	if (t_5 <= Double.POSITIVE_INFINITY) {
		tmp = t_5;
	} else {
		tmp = x1 + (9.0 + (x1 + (Math.pow(x1, 4.0) * (6.0 + ((((9.0 + (4.0 * ((2.0 * x2) - 3.0))) / x1) - 3.0) / x1)))));
	}
	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 = t_1 / t_2
	t_4 = t_1 / (-1.0 - (x1 * x1))
	t_5 = x1 + ((x1 + (((t_0 * t_3) - (t_2 * (((x1 * x1) * (6.0 + (4.0 * t_4))) + (((x1 * 2.0) * t_3) * (3.0 + t_4))))) + (x1 * (x1 * x1)))) + (3.0 * (((t_0 - (2.0 * x2)) - x1) / t_2)))
	tmp = 0
	if t_5 <= math.inf:
		tmp = t_5
	else:
		tmp = x1 + (9.0 + (x1 + (math.pow(x1, 4.0) * (6.0 + ((((9.0 + (4.0 * ((2.0 * x2) - 3.0))) / x1) - 3.0) / x1)))))
	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(t_1 / t_2)
	t_4 = Float64(t_1 / Float64(-1.0 - Float64(x1 * x1)))
	t_5 = Float64(x1 + Float64(Float64(x1 + Float64(Float64(Float64(t_0 * t_3) - Float64(t_2 * Float64(Float64(Float64(x1 * x1) * Float64(6.0 + Float64(4.0 * t_4))) + Float64(Float64(Float64(x1 * 2.0) * t_3) * Float64(3.0 + t_4))))) + Float64(x1 * Float64(x1 * x1)))) + Float64(3.0 * Float64(Float64(Float64(t_0 - Float64(2.0 * x2)) - x1) / t_2))))
	tmp = 0.0
	if (t_5 <= Inf)
		tmp = t_5;
	else
		tmp = Float64(x1 + Float64(9.0 + Float64(x1 + Float64((x1 ^ 4.0) * Float64(6.0 + Float64(Float64(Float64(Float64(9.0 + Float64(4.0 * Float64(Float64(2.0 * x2) - 3.0))) / x1) - 3.0) / x1))))));
	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 = t_1 / t_2;
	t_4 = t_1 / (-1.0 - (x1 * x1));
	t_5 = x1 + ((x1 + (((t_0 * t_3) - (t_2 * (((x1 * x1) * (6.0 + (4.0 * t_4))) + (((x1 * 2.0) * t_3) * (3.0 + t_4))))) + (x1 * (x1 * x1)))) + (3.0 * (((t_0 - (2.0 * x2)) - x1) / t_2)));
	tmp = 0.0;
	if (t_5 <= Inf)
		tmp = t_5;
	else
		tmp = x1 + (9.0 + (x1 + ((x1 ^ 4.0) * (6.0 + ((((9.0 + (4.0 * ((2.0 * x2) - 3.0))) / x1) - 3.0) / x1)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(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[(t$95$1 / t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$1 / N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(x1 + N[(N[(x1 + N[(N[(N[(t$95$0 * t$95$3), $MachinePrecision] - N[(t$95$2 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 + N[(4.0 * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$3), $MachinePrecision] * N[(3.0 + t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(N[(N[(t$95$0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$5, Infinity], t$95$5, N[(x1 + N[(9.0 + N[(x1 + N[(N[Power[x1, 4.0], $MachinePrecision] * N[(6.0 + N[(N[(N[(N[(9.0 + N[(4.0 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x1), $MachinePrecision] - 3.0), $MachinePrecision] / x1), $MachinePrecision]), $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 #s(literal 2 binary64) x1) (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64)))) (-.f64 (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64))) #s(literal 3 binary64))) (*.f64 (*.f64 x1 x1) (-.f64 (*.f64 #s(literal 4 binary64) (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64)))) #s(literal 6 binary64)))) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64))) (*.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64))))) (*.f64 (*.f64 x1 x1) x1)) x1) (*.f64 #s(literal 3 binary64) (/.f64 (-.f64 (-.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64)))))) < +inf.0

   1. Initial program 99.4%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in x1 around -inf 12.5%

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

   4. Taylor expanded in x1 around inf 100.0%

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

4. Final simplification 99.6%

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

Alternative 3: 99.4% accurate, 0.5× speedup

Math

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

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

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

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 = t_1 / t_2;
	double t_4 = t_1 / (-1.0 - (x1 * x1));
	double t_5 = x1 + ((x1 + (((t_0 * t_3) - (t_2 * (((x1 * x1) * (6.0 + (4.0 * t_4))) + (((x1 * 2.0) * t_3) * (3.0 + t_4))))) + (x1 * (x1 * x1)))) + (3.0 * (((t_0 - (2.0 * x2)) - x1) / t_2)));
	double tmp;
	if (t_5 <= Double.POSITIVE_INFINITY) {
		tmp = t_5;
	} else {
		tmp = x1 + ((x1 + (6.0 * Math.pow(x1, 4.0))) + (3.0 * (x2 * -2.0)));
	}
	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 = t_1 / t_2
	t_4 = t_1 / (-1.0 - (x1 * x1))
	t_5 = x1 + ((x1 + (((t_0 * t_3) - (t_2 * (((x1 * x1) * (6.0 + (4.0 * t_4))) + (((x1 * 2.0) * t_3) * (3.0 + t_4))))) + (x1 * (x1 * x1)))) + (3.0 * (((t_0 - (2.0 * x2)) - x1) / t_2)))
	tmp = 0
	if t_5 <= math.inf:
		tmp = t_5
	else:
		tmp = x1 + ((x1 + (6.0 * math.pow(x1, 4.0))) + (3.0 * (x2 * -2.0)))
	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(t_1 / t_2)
	t_4 = Float64(t_1 / Float64(-1.0 - Float64(x1 * x1)))
	t_5 = Float64(x1 + Float64(Float64(x1 + Float64(Float64(Float64(t_0 * t_3) - Float64(t_2 * Float64(Float64(Float64(x1 * x1) * Float64(6.0 + Float64(4.0 * t_4))) + Float64(Float64(Float64(x1 * 2.0) * t_3) * Float64(3.0 + t_4))))) + Float64(x1 * Float64(x1 * x1)))) + Float64(3.0 * Float64(Float64(Float64(t_0 - Float64(2.0 * x2)) - x1) / t_2))))
	tmp = 0.0
	if (t_5 <= Inf)
		tmp = t_5;
	else
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(6.0 * (x1 ^ 4.0))) + Float64(3.0 * Float64(x2 * -2.0))));
	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 = t_1 / t_2;
	t_4 = t_1 / (-1.0 - (x1 * x1));
	t_5 = x1 + ((x1 + (((t_0 * t_3) - (t_2 * (((x1 * x1) * (6.0 + (4.0 * t_4))) + (((x1 * 2.0) * t_3) * (3.0 + t_4))))) + (x1 * (x1 * x1)))) + (3.0 * (((t_0 - (2.0 * x2)) - x1) / t_2)));
	tmp = 0.0;
	if (t_5 <= Inf)
		tmp = t_5;
	else
		tmp = x1 + ((x1 + (6.0 * (x1 ^ 4.0))) + (3.0 * (x2 * -2.0)));
	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[(t$95$1 / t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$1 / N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(x1 + N[(N[(x1 + N[(N[(N[(t$95$0 * t$95$3), $MachinePrecision] - N[(t$95$2 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 + N[(4.0 * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$3), $MachinePrecision] * N[(3.0 + t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(N[(N[(t$95$0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$5, Infinity], t$95$5, N[(x1 + N[(N[(x1 + N[(6.0 * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 99.4%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in x1 around 0 0.0%

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

      1. *-commutative 0.0%

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

   5. Simplified 0.0%

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

   6. Taylor expanded in x1 around inf 97.5%

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

4. Final simplification 98.8%

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

Alternative 4: 97.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := 3 \cdot \left(x2 \cdot -2\right)\\ t_2 := x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ t_3 := x1 \cdot \left(x1 \cdot x1\right)\\ t_4 := x1 \cdot \left(x1 \cdot 3\right)\\ t_5 := \left(t\_4 + 2 \cdot x2\right) - x1\\ t_6 := \frac{t\_5}{t\_0}\\ t_7 := \left(x1 \cdot 2\right) \cdot t\_6\\ t_8 := \frac{t\_5}{-1 - x1 \cdot x1}\\ t_9 := 2 \cdot x2 - 3\\ t_10 := t\_4 \cdot t\_6\\ \mathbf{if}\;x1 \leq -1 \cdot 10^{+144}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x1 \leq -3.4 \cdot 10^{+106}:\\ \;\;\;\;x1 + \left(t\_1 + \left(x1 + x1 \cdot \left(4 \cdot \left(x2 \cdot t\_9\right) + x1 \cdot \left(x1 \cdot -22\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -0.008:\\ \;\;\;\;x1 + \left(t\_1 + \left(x1 + \left(t\_3 + \left(t\_10 + t\_0 \cdot \left(t\_7 \cdot \left(t\_6 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \left(3 + \frac{-1 + \frac{t\_9}{x1}}{x1}\right) - 6\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 0.00015:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t\_4 - 2 \cdot x2\right) - x1}{t\_0} + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot -3 + 2 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(t\_10 - t\_0 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot t\_8\right) + t\_7 \cdot \left(3 + t\_8\right)\right)\right) + t\_3\right)\right) + t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ (* x1 x1) 1.0))
        (t_1 (* 3.0 (* x2 -2.0)))
        (t_2 (+ x1 (+ x1 (* 3.0 (* x1 (+ (* x1 3.0) -1.0))))))
        (t_3 (* x1 (* x1 x1)))
        (t_4 (* x1 (* x1 3.0)))
        (t_5 (- (+ t_4 (* 2.0 x2)) x1))
        (t_6 (/ t_5 t_0))
        (t_7 (* (* x1 2.0) t_6))
        (t_8 (/ t_5 (- -1.0 (* x1 x1))))
        (t_9 (- (* 2.0 x2) 3.0))
        (t_10 (* t_4 t_6)))
   (if (<= x1 -1e+144)
     t_2
     (if (<= x1 -3.4e+106)
       (+ x1 (+ t_1 (+ x1 (* x1 (+ (* 4.0 (* x2 t_9)) (* x1 (* x1 -22.0)))))))
       (if (<= x1 -0.008)
         (+
          x1
          (+
           t_1
           (+
            x1
            (+
             t_3
             (+
              t_10
              (*
               t_0
               (+
                (* t_7 (- t_6 3.0))
                (*
                 (* x1 x1)
                 (- (* 4.0 (+ 3.0 (/ (+ -1.0 (/ t_9 x1)) x1))) 6.0)))))))))
         (if (<= x1 0.00015)
           (+
            x1
            (+
             (* 3.0 (/ (- (- t_4 (* 2.0 x2)) x1) t_0))
             (+ x1 (* 4.0 (* x2 (+ (* x1 -3.0) (* 2.0 (* x1 x2))))))))
           (if (<= x1 5e+153)
             (+
              x1
              (+
               (+
                x1
                (+
                 (-
                  t_10
                  (*
                   t_0
                   (+ (* (* x1 x1) (+ 6.0 (* 4.0 t_8))) (* t_7 (+ 3.0 t_8)))))
                 t_3))
               t_1))
             t_2)))))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = 3.0 * (x2 * -2.0);
	double t_2 = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	double t_3 = x1 * (x1 * x1);
	double t_4 = x1 * (x1 * 3.0);
	double t_5 = (t_4 + (2.0 * x2)) - x1;
	double t_6 = t_5 / t_0;
	double t_7 = (x1 * 2.0) * t_6;
	double t_8 = t_5 / (-1.0 - (x1 * x1));
	double t_9 = (2.0 * x2) - 3.0;
	double t_10 = t_4 * t_6;
	double tmp;
	if (x1 <= -1e+144) {
		tmp = t_2;
	} else if (x1 <= -3.4e+106) {
		tmp = x1 + (t_1 + (x1 + (x1 * ((4.0 * (x2 * t_9)) + (x1 * (x1 * -22.0))))));
	} else if (x1 <= -0.008) {
		tmp = x1 + (t_1 + (x1 + (t_3 + (t_10 + (t_0 * ((t_7 * (t_6 - 3.0)) + ((x1 * x1) * ((4.0 * (3.0 + ((-1.0 + (t_9 / x1)) / x1))) - 6.0))))))));
	} else if (x1 <= 0.00015) {
		tmp = x1 + ((3.0 * (((t_4 - (2.0 * x2)) - x1) / t_0)) + (x1 + (4.0 * (x2 * ((x1 * -3.0) + (2.0 * (x1 * x2)))))));
	} else if (x1 <= 5e+153) {
		tmp = x1 + ((x1 + ((t_10 - (t_0 * (((x1 * x1) * (6.0 + (4.0 * t_8))) + (t_7 * (3.0 + t_8))))) + t_3)) + t_1);
	} else {
		tmp = 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_10
    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) + 1.0d0
    t_1 = 3.0d0 * (x2 * (-2.0d0))
    t_2 = x1 + (x1 + (3.0d0 * (x1 * ((x1 * 3.0d0) + (-1.0d0)))))
    t_3 = x1 * (x1 * x1)
    t_4 = x1 * (x1 * 3.0d0)
    t_5 = (t_4 + (2.0d0 * x2)) - x1
    t_6 = t_5 / t_0
    t_7 = (x1 * 2.0d0) * t_6
    t_8 = t_5 / ((-1.0d0) - (x1 * x1))
    t_9 = (2.0d0 * x2) - 3.0d0
    t_10 = t_4 * t_6
    if (x1 <= (-1d+144)) then
        tmp = t_2
    else if (x1 <= (-3.4d+106)) then
        tmp = x1 + (t_1 + (x1 + (x1 * ((4.0d0 * (x2 * t_9)) + (x1 * (x1 * (-22.0d0)))))))
    else if (x1 <= (-0.008d0)) then
        tmp = x1 + (t_1 + (x1 + (t_3 + (t_10 + (t_0 * ((t_7 * (t_6 - 3.0d0)) + ((x1 * x1) * ((4.0d0 * (3.0d0 + (((-1.0d0) + (t_9 / x1)) / x1))) - 6.0d0))))))))
    else if (x1 <= 0.00015d0) then
        tmp = x1 + ((3.0d0 * (((t_4 - (2.0d0 * x2)) - x1) / t_0)) + (x1 + (4.0d0 * (x2 * ((x1 * (-3.0d0)) + (2.0d0 * (x1 * x2)))))))
    else if (x1 <= 5d+153) then
        tmp = x1 + ((x1 + ((t_10 - (t_0 * (((x1 * x1) * (6.0d0 + (4.0d0 * t_8))) + (t_7 * (3.0d0 + t_8))))) + t_3)) + t_1)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = 3.0 * (x2 * -2.0);
	double t_2 = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	double t_3 = x1 * (x1 * x1);
	double t_4 = x1 * (x1 * 3.0);
	double t_5 = (t_4 + (2.0 * x2)) - x1;
	double t_6 = t_5 / t_0;
	double t_7 = (x1 * 2.0) * t_6;
	double t_8 = t_5 / (-1.0 - (x1 * x1));
	double t_9 = (2.0 * x2) - 3.0;
	double t_10 = t_4 * t_6;
	double tmp;
	if (x1 <= -1e+144) {
		tmp = t_2;
	} else if (x1 <= -3.4e+106) {
		tmp = x1 + (t_1 + (x1 + (x1 * ((4.0 * (x2 * t_9)) + (x1 * (x1 * -22.0))))));
	} else if (x1 <= -0.008) {
		tmp = x1 + (t_1 + (x1 + (t_3 + (t_10 + (t_0 * ((t_7 * (t_6 - 3.0)) + ((x1 * x1) * ((4.0 * (3.0 + ((-1.0 + (t_9 / x1)) / x1))) - 6.0))))))));
	} else if (x1 <= 0.00015) {
		tmp = x1 + ((3.0 * (((t_4 - (2.0 * x2)) - x1) / t_0)) + (x1 + (4.0 * (x2 * ((x1 * -3.0) + (2.0 * (x1 * x2)))))));
	} else if (x1 <= 5e+153) {
		tmp = x1 + ((x1 + ((t_10 - (t_0 * (((x1 * x1) * (6.0 + (4.0 * t_8))) + (t_7 * (3.0 + t_8))))) + t_3)) + t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x1 * x1) + 1.0
	t_1 = 3.0 * (x2 * -2.0)
	t_2 = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))))
	t_3 = x1 * (x1 * x1)
	t_4 = x1 * (x1 * 3.0)
	t_5 = (t_4 + (2.0 * x2)) - x1
	t_6 = t_5 / t_0
	t_7 = (x1 * 2.0) * t_6
	t_8 = t_5 / (-1.0 - (x1 * x1))
	t_9 = (2.0 * x2) - 3.0
	t_10 = t_4 * t_6
	tmp = 0
	if x1 <= -1e+144:
		tmp = t_2
	elif x1 <= -3.4e+106:
		tmp = x1 + (t_1 + (x1 + (x1 * ((4.0 * (x2 * t_9)) + (x1 * (x1 * -22.0))))))
	elif x1 <= -0.008:
		tmp = x1 + (t_1 + (x1 + (t_3 + (t_10 + (t_0 * ((t_7 * (t_6 - 3.0)) + ((x1 * x1) * ((4.0 * (3.0 + ((-1.0 + (t_9 / x1)) / x1))) - 6.0))))))))
	elif x1 <= 0.00015:
		tmp = x1 + ((3.0 * (((t_4 - (2.0 * x2)) - x1) / t_0)) + (x1 + (4.0 * (x2 * ((x1 * -3.0) + (2.0 * (x1 * x2)))))))
	elif x1 <= 5e+153:
		tmp = x1 + ((x1 + ((t_10 - (t_0 * (((x1 * x1) * (6.0 + (4.0 * t_8))) + (t_7 * (3.0 + t_8))))) + t_3)) + t_1)
	else:
		tmp = t_2
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * x1) + 1.0)
	t_1 = Float64(3.0 * Float64(x2 * -2.0))
	t_2 = Float64(x1 + Float64(x1 + Float64(3.0 * Float64(x1 * Float64(Float64(x1 * 3.0) + -1.0)))))
	t_3 = Float64(x1 * Float64(x1 * x1))
	t_4 = Float64(x1 * Float64(x1 * 3.0))
	t_5 = Float64(Float64(t_4 + Float64(2.0 * x2)) - x1)
	t_6 = Float64(t_5 / t_0)
	t_7 = Float64(Float64(x1 * 2.0) * t_6)
	t_8 = Float64(t_5 / Float64(-1.0 - Float64(x1 * x1)))
	t_9 = Float64(Float64(2.0 * x2) - 3.0)
	t_10 = Float64(t_4 * t_6)
	tmp = 0.0
	if (x1 <= -1e+144)
		tmp = t_2;
	elseif (x1 <= -3.4e+106)
		tmp = Float64(x1 + Float64(t_1 + Float64(x1 + Float64(x1 * Float64(Float64(4.0 * Float64(x2 * t_9)) + Float64(x1 * Float64(x1 * -22.0)))))));
	elseif (x1 <= -0.008)
		tmp = Float64(x1 + Float64(t_1 + Float64(x1 + Float64(t_3 + Float64(t_10 + Float64(t_0 * Float64(Float64(t_7 * Float64(t_6 - 3.0)) + Float64(Float64(x1 * x1) * Float64(Float64(4.0 * Float64(3.0 + Float64(Float64(-1.0 + Float64(t_9 / x1)) / x1))) - 6.0)))))))));
	elseif (x1 <= 0.00015)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_4 - Float64(2.0 * x2)) - x1) / t_0)) + Float64(x1 + Float64(4.0 * Float64(x2 * Float64(Float64(x1 * -3.0) + Float64(2.0 * Float64(x1 * x2))))))));
	elseif (x1 <= 5e+153)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(Float64(t_10 - Float64(t_0 * Float64(Float64(Float64(x1 * x1) * Float64(6.0 + Float64(4.0 * t_8))) + Float64(t_7 * Float64(3.0 + t_8))))) + t_3)) + t_1));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x1 * x1) + 1.0;
	t_1 = 3.0 * (x2 * -2.0);
	t_2 = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	t_3 = x1 * (x1 * x1);
	t_4 = x1 * (x1 * 3.0);
	t_5 = (t_4 + (2.0 * x2)) - x1;
	t_6 = t_5 / t_0;
	t_7 = (x1 * 2.0) * t_6;
	t_8 = t_5 / (-1.0 - (x1 * x1));
	t_9 = (2.0 * x2) - 3.0;
	t_10 = t_4 * t_6;
	tmp = 0.0;
	if (x1 <= -1e+144)
		tmp = t_2;
	elseif (x1 <= -3.4e+106)
		tmp = x1 + (t_1 + (x1 + (x1 * ((4.0 * (x2 * t_9)) + (x1 * (x1 * -22.0))))));
	elseif (x1 <= -0.008)
		tmp = x1 + (t_1 + (x1 + (t_3 + (t_10 + (t_0 * ((t_7 * (t_6 - 3.0)) + ((x1 * x1) * ((4.0 * (3.0 + ((-1.0 + (t_9 / x1)) / x1))) - 6.0))))))));
	elseif (x1 <= 0.00015)
		tmp = x1 + ((3.0 * (((t_4 - (2.0 * x2)) - x1) / t_0)) + (x1 + (4.0 * (x2 * ((x1 * -3.0) + (2.0 * (x1 * x2)))))));
	elseif (x1 <= 5e+153)
		tmp = x1 + ((x1 + ((t_10 - (t_0 * (((x1 * x1) * (6.0 + (4.0 * t_8))) + (t_7 * (3.0 + t_8))))) + t_3)) + t_1);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$1 = N[(3.0 * N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x1 + N[(x1 + N[(3.0 * N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(t$95$4 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]}, Block[{t$95$6 = N[(t$95$5 / t$95$0), $MachinePrecision]}, Block[{t$95$7 = N[(N[(x1 * 2.0), $MachinePrecision] * t$95$6), $MachinePrecision]}, Block[{t$95$8 = N[(t$95$5 / N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$9 = N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]}, Block[{t$95$10 = N[(t$95$4 * t$95$6), $MachinePrecision]}, If[LessEqual[x1, -1e+144], t$95$2, If[LessEqual[x1, -3.4e+106], N[(x1 + N[(t$95$1 + N[(x1 + N[(x1 * N[(N[(4.0 * N[(x2 * t$95$9), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(x1 * -22.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -0.008], N[(x1 + N[(t$95$1 + N[(x1 + N[(t$95$3 + N[(t$95$10 + N[(t$95$0 * N[(N[(t$95$7 * N[(t$95$6 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(4.0 * N[(3.0 + N[(N[(-1.0 + N[(t$95$9 / x1), $MachinePrecision]), $MachinePrecision] / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 0.00015], N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$4 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $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, 5e+153], N[(x1 + N[(N[(x1 + N[(N[(t$95$10 - N[(t$95$0 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 + N[(4.0 * t$95$8), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$7 * N[(3.0 + t$95$8), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$3), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x1 < -1.00000000000000002e144 or 5.00000000000000018e153 < x1

   1. Initial program 0.0%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   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 60.6%

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

   5. Taylor expanded in x2 around 0 98.7%

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

   if -1.00000000000000002e144 < x1 < -3.39999999999999994e106

   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%

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

      1. *-commutative 0.0%

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

   5. Simplified 0.0%

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

   6. Taylor expanded in x1 around 0 75.0%

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

   7. Taylor expanded in x2 around 0 75.0%

      \[\leadsto x1 + \left(\left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \color{blue}{\left(-22 \cdot x1\right)}\right) + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]
   8. Step-by-step derivation

      1. *-commutative 75.0%

         \[\leadsto x1 + \left(\left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \color{blue}{\left(x1 \cdot -22\right)}\right) + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]

   9. Simplified 75.0%

      \[\leadsto x1 + \left(\left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \color{blue}{\left(x1 \cdot -22\right)}\right) + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]

   if -3.39999999999999994e106 < x1 < -0.0080000000000000002

   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 99.3%

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

      1. *-commutative 99.3%

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

   5. Simplified 99.3%

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

   6. Taylor expanded in x1 around -inf 99.4%

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

   if -0.0080000000000000002 < x1 < 1.49999999999999987e-4

   1. Initial program 99.4%

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

   3. Taylor expanded in x1 around 0 89.3%

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

   4. Taylor expanded in x2 around 0 99.4%

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

   if 1.49999999999999987e-4 < x1 < 5.00000000000000018e153

   1. Initial program 96.2%

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

   3. Taylor expanded in x1 around 0 96.2%

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

      1. *-commutative 96.2%

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

   5. Simplified 96.2%

      \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \color{blue}{\left(x2 \cdot -2\right)}\right) \]
3. Recombined 5 regimes into one program.

4. Final simplification 98.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1 \cdot 10^{+144}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -3.4 \cdot 10^{+106}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2\right) + \left(x1 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(x1 \cdot -22\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -0.008:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2\right) + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \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(4 \cdot \left(3 + \frac{-1 + \frac{2 \cdot x2 - 3}{x1}}{x1}\right) - 6\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 0.00015:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot -3 + 2 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(\left(x1 + \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}{x1 \cdot x1 + 1} - \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1}\right) + \left(\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) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 3 \cdot \left(x2 \cdot -2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 97.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := 3 \cdot \left(x2 \cdot -2\right)\\ t_2 := x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ t_3 := x1 \cdot \left(x1 \cdot x1\right)\\ t_4 := x1 \cdot \left(x1 \cdot 3\right)\\ t_5 := \left(t\_4 + 2 \cdot x2\right) - x1\\ t_6 := \frac{t\_5}{t\_0}\\ t_7 := \left(x1 \cdot 2\right) \cdot t\_6\\ t_8 := \frac{t\_5}{-1 - x1 \cdot x1}\\ t_9 := 2 \cdot x2 - 3\\ t_10 := t\_4 \cdot t\_6\\ \mathbf{if}\;x1 \leq -1 \cdot 10^{+144}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x1 \leq -3.4 \cdot 10^{+106}:\\ \;\;\;\;x1 + \left(t\_1 + \left(x1 + x1 \cdot \left(4 \cdot \left(x2 \cdot t\_9\right) + x1 \cdot \left(x1 \cdot -22\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -0.0042:\\ \;\;\;\;x1 + \left(t\_1 + \left(x1 + \left(t\_3 + \left(t\_10 + t\_0 \cdot \left(t\_7 \cdot \left(t\_6 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \left(3 + \frac{-1 + \frac{t\_9}{x1}}{x1}\right) - 6\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 0.00085:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t\_4 - 2 \cdot x2\right) - x1}{t\_0} + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot -3 + 2 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(t\_10 - t\_0 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot t\_8\right) + t\_7 \cdot \left(3 + t\_8\right)\right)\right) + t\_3\right)\right) + 9\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ (* x1 x1) 1.0))
        (t_1 (* 3.0 (* x2 -2.0)))
        (t_2 (+ x1 (+ x1 (* 3.0 (* x1 (+ (* x1 3.0) -1.0))))))
        (t_3 (* x1 (* x1 x1)))
        (t_4 (* x1 (* x1 3.0)))
        (t_5 (- (+ t_4 (* 2.0 x2)) x1))
        (t_6 (/ t_5 t_0))
        (t_7 (* (* x1 2.0) t_6))
        (t_8 (/ t_5 (- -1.0 (* x1 x1))))
        (t_9 (- (* 2.0 x2) 3.0))
        (t_10 (* t_4 t_6)))
   (if (<= x1 -1e+144)
     t_2
     (if (<= x1 -3.4e+106)
       (+ x1 (+ t_1 (+ x1 (* x1 (+ (* 4.0 (* x2 t_9)) (* x1 (* x1 -22.0)))))))
       (if (<= x1 -0.0042)
         (+
          x1
          (+
           t_1
           (+
            x1
            (+
             t_3
             (+
              t_10
              (*
               t_0
               (+
                (* t_7 (- t_6 3.0))
                (*
                 (* x1 x1)
                 (- (* 4.0 (+ 3.0 (/ (+ -1.0 (/ t_9 x1)) x1))) 6.0)))))))))
         (if (<= x1 0.00085)
           (+
            x1
            (+
             (* 3.0 (/ (- (- t_4 (* 2.0 x2)) x1) t_0))
             (+ x1 (* 4.0 (* x2 (+ (* x1 -3.0) (* 2.0 (* x1 x2))))))))
           (if (<= x1 2e+153)
             (+
              x1
              (+
               (+
                x1
                (+
                 (-
                  t_10
                  (*
                   t_0
                   (+ (* (* x1 x1) (+ 6.0 (* 4.0 t_8))) (* t_7 (+ 3.0 t_8)))))
                 t_3))
               9.0))
             t_2)))))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = 3.0 * (x2 * -2.0);
	double t_2 = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	double t_3 = x1 * (x1 * x1);
	double t_4 = x1 * (x1 * 3.0);
	double t_5 = (t_4 + (2.0 * x2)) - x1;
	double t_6 = t_5 / t_0;
	double t_7 = (x1 * 2.0) * t_6;
	double t_8 = t_5 / (-1.0 - (x1 * x1));
	double t_9 = (2.0 * x2) - 3.0;
	double t_10 = t_4 * t_6;
	double tmp;
	if (x1 <= -1e+144) {
		tmp = t_2;
	} else if (x1 <= -3.4e+106) {
		tmp = x1 + (t_1 + (x1 + (x1 * ((4.0 * (x2 * t_9)) + (x1 * (x1 * -22.0))))));
	} else if (x1 <= -0.0042) {
		tmp = x1 + (t_1 + (x1 + (t_3 + (t_10 + (t_0 * ((t_7 * (t_6 - 3.0)) + ((x1 * x1) * ((4.0 * (3.0 + ((-1.0 + (t_9 / x1)) / x1))) - 6.0))))))));
	} else if (x1 <= 0.00085) {
		tmp = x1 + ((3.0 * (((t_4 - (2.0 * x2)) - x1) / t_0)) + (x1 + (4.0 * (x2 * ((x1 * -3.0) + (2.0 * (x1 * x2)))))));
	} else if (x1 <= 2e+153) {
		tmp = x1 + ((x1 + ((t_10 - (t_0 * (((x1 * x1) * (6.0 + (4.0 * t_8))) + (t_7 * (3.0 + t_8))))) + t_3)) + 9.0);
	} else {
		tmp = 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_10
    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) + 1.0d0
    t_1 = 3.0d0 * (x2 * (-2.0d0))
    t_2 = x1 + (x1 + (3.0d0 * (x1 * ((x1 * 3.0d0) + (-1.0d0)))))
    t_3 = x1 * (x1 * x1)
    t_4 = x1 * (x1 * 3.0d0)
    t_5 = (t_4 + (2.0d0 * x2)) - x1
    t_6 = t_5 / t_0
    t_7 = (x1 * 2.0d0) * t_6
    t_8 = t_5 / ((-1.0d0) - (x1 * x1))
    t_9 = (2.0d0 * x2) - 3.0d0
    t_10 = t_4 * t_6
    if (x1 <= (-1d+144)) then
        tmp = t_2
    else if (x1 <= (-3.4d+106)) then
        tmp = x1 + (t_1 + (x1 + (x1 * ((4.0d0 * (x2 * t_9)) + (x1 * (x1 * (-22.0d0)))))))
    else if (x1 <= (-0.0042d0)) then
        tmp = x1 + (t_1 + (x1 + (t_3 + (t_10 + (t_0 * ((t_7 * (t_6 - 3.0d0)) + ((x1 * x1) * ((4.0d0 * (3.0d0 + (((-1.0d0) + (t_9 / x1)) / x1))) - 6.0d0))))))))
    else if (x1 <= 0.00085d0) then
        tmp = x1 + ((3.0d0 * (((t_4 - (2.0d0 * x2)) - x1) / t_0)) + (x1 + (4.0d0 * (x2 * ((x1 * (-3.0d0)) + (2.0d0 * (x1 * x2)))))))
    else if (x1 <= 2d+153) then
        tmp = x1 + ((x1 + ((t_10 - (t_0 * (((x1 * x1) * (6.0d0 + (4.0d0 * t_8))) + (t_7 * (3.0d0 + t_8))))) + t_3)) + 9.0d0)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = 3.0 * (x2 * -2.0);
	double t_2 = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	double t_3 = x1 * (x1 * x1);
	double t_4 = x1 * (x1 * 3.0);
	double t_5 = (t_4 + (2.0 * x2)) - x1;
	double t_6 = t_5 / t_0;
	double t_7 = (x1 * 2.0) * t_6;
	double t_8 = t_5 / (-1.0 - (x1 * x1));
	double t_9 = (2.0 * x2) - 3.0;
	double t_10 = t_4 * t_6;
	double tmp;
	if (x1 <= -1e+144) {
		tmp = t_2;
	} else if (x1 <= -3.4e+106) {
		tmp = x1 + (t_1 + (x1 + (x1 * ((4.0 * (x2 * t_9)) + (x1 * (x1 * -22.0))))));
	} else if (x1 <= -0.0042) {
		tmp = x1 + (t_1 + (x1 + (t_3 + (t_10 + (t_0 * ((t_7 * (t_6 - 3.0)) + ((x1 * x1) * ((4.0 * (3.0 + ((-1.0 + (t_9 / x1)) / x1))) - 6.0))))))));
	} else if (x1 <= 0.00085) {
		tmp = x1 + ((3.0 * (((t_4 - (2.0 * x2)) - x1) / t_0)) + (x1 + (4.0 * (x2 * ((x1 * -3.0) + (2.0 * (x1 * x2)))))));
	} else if (x1 <= 2e+153) {
		tmp = x1 + ((x1 + ((t_10 - (t_0 * (((x1 * x1) * (6.0 + (4.0 * t_8))) + (t_7 * (3.0 + t_8))))) + t_3)) + 9.0);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x1 * x1) + 1.0
	t_1 = 3.0 * (x2 * -2.0)
	t_2 = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))))
	t_3 = x1 * (x1 * x1)
	t_4 = x1 * (x1 * 3.0)
	t_5 = (t_4 + (2.0 * x2)) - x1
	t_6 = t_5 / t_0
	t_7 = (x1 * 2.0) * t_6
	t_8 = t_5 / (-1.0 - (x1 * x1))
	t_9 = (2.0 * x2) - 3.0
	t_10 = t_4 * t_6
	tmp = 0
	if x1 <= -1e+144:
		tmp = t_2
	elif x1 <= -3.4e+106:
		tmp = x1 + (t_1 + (x1 + (x1 * ((4.0 * (x2 * t_9)) + (x1 * (x1 * -22.0))))))
	elif x1 <= -0.0042:
		tmp = x1 + (t_1 + (x1 + (t_3 + (t_10 + (t_0 * ((t_7 * (t_6 - 3.0)) + ((x1 * x1) * ((4.0 * (3.0 + ((-1.0 + (t_9 / x1)) / x1))) - 6.0))))))))
	elif x1 <= 0.00085:
		tmp = x1 + ((3.0 * (((t_4 - (2.0 * x2)) - x1) / t_0)) + (x1 + (4.0 * (x2 * ((x1 * -3.0) + (2.0 * (x1 * x2)))))))
	elif x1 <= 2e+153:
		tmp = x1 + ((x1 + ((t_10 - (t_0 * (((x1 * x1) * (6.0 + (4.0 * t_8))) + (t_7 * (3.0 + t_8))))) + t_3)) + 9.0)
	else:
		tmp = t_2
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * x1) + 1.0)
	t_1 = Float64(3.0 * Float64(x2 * -2.0))
	t_2 = Float64(x1 + Float64(x1 + Float64(3.0 * Float64(x1 * Float64(Float64(x1 * 3.0) + -1.0)))))
	t_3 = Float64(x1 * Float64(x1 * x1))
	t_4 = Float64(x1 * Float64(x1 * 3.0))
	t_5 = Float64(Float64(t_4 + Float64(2.0 * x2)) - x1)
	t_6 = Float64(t_5 / t_0)
	t_7 = Float64(Float64(x1 * 2.0) * t_6)
	t_8 = Float64(t_5 / Float64(-1.0 - Float64(x1 * x1)))
	t_9 = Float64(Float64(2.0 * x2) - 3.0)
	t_10 = Float64(t_4 * t_6)
	tmp = 0.0
	if (x1 <= -1e+144)
		tmp = t_2;
	elseif (x1 <= -3.4e+106)
		tmp = Float64(x1 + Float64(t_1 + Float64(x1 + Float64(x1 * Float64(Float64(4.0 * Float64(x2 * t_9)) + Float64(x1 * Float64(x1 * -22.0)))))));
	elseif (x1 <= -0.0042)
		tmp = Float64(x1 + Float64(t_1 + Float64(x1 + Float64(t_3 + Float64(t_10 + Float64(t_0 * Float64(Float64(t_7 * Float64(t_6 - 3.0)) + Float64(Float64(x1 * x1) * Float64(Float64(4.0 * Float64(3.0 + Float64(Float64(-1.0 + Float64(t_9 / x1)) / x1))) - 6.0)))))))));
	elseif (x1 <= 0.00085)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_4 - Float64(2.0 * x2)) - x1) / t_0)) + Float64(x1 + Float64(4.0 * Float64(x2 * Float64(Float64(x1 * -3.0) + Float64(2.0 * Float64(x1 * x2))))))));
	elseif (x1 <= 2e+153)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(Float64(t_10 - Float64(t_0 * Float64(Float64(Float64(x1 * x1) * Float64(6.0 + Float64(4.0 * t_8))) + Float64(t_7 * Float64(3.0 + t_8))))) + t_3)) + 9.0));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x1 * x1) + 1.0;
	t_1 = 3.0 * (x2 * -2.0);
	t_2 = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	t_3 = x1 * (x1 * x1);
	t_4 = x1 * (x1 * 3.0);
	t_5 = (t_4 + (2.0 * x2)) - x1;
	t_6 = t_5 / t_0;
	t_7 = (x1 * 2.0) * t_6;
	t_8 = t_5 / (-1.0 - (x1 * x1));
	t_9 = (2.0 * x2) - 3.0;
	t_10 = t_4 * t_6;
	tmp = 0.0;
	if (x1 <= -1e+144)
		tmp = t_2;
	elseif (x1 <= -3.4e+106)
		tmp = x1 + (t_1 + (x1 + (x1 * ((4.0 * (x2 * t_9)) + (x1 * (x1 * -22.0))))));
	elseif (x1 <= -0.0042)
		tmp = x1 + (t_1 + (x1 + (t_3 + (t_10 + (t_0 * ((t_7 * (t_6 - 3.0)) + ((x1 * x1) * ((4.0 * (3.0 + ((-1.0 + (t_9 / x1)) / x1))) - 6.0))))))));
	elseif (x1 <= 0.00085)
		tmp = x1 + ((3.0 * (((t_4 - (2.0 * x2)) - x1) / t_0)) + (x1 + (4.0 * (x2 * ((x1 * -3.0) + (2.0 * (x1 * x2)))))));
	elseif (x1 <= 2e+153)
		tmp = x1 + ((x1 + ((t_10 - (t_0 * (((x1 * x1) * (6.0 + (4.0 * t_8))) + (t_7 * (3.0 + t_8))))) + t_3)) + 9.0);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$1 = N[(3.0 * N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x1 + N[(x1 + N[(3.0 * N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(t$95$4 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]}, Block[{t$95$6 = N[(t$95$5 / t$95$0), $MachinePrecision]}, Block[{t$95$7 = N[(N[(x1 * 2.0), $MachinePrecision] * t$95$6), $MachinePrecision]}, Block[{t$95$8 = N[(t$95$5 / N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$9 = N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]}, Block[{t$95$10 = N[(t$95$4 * t$95$6), $MachinePrecision]}, If[LessEqual[x1, -1e+144], t$95$2, If[LessEqual[x1, -3.4e+106], N[(x1 + N[(t$95$1 + N[(x1 + N[(x1 * N[(N[(4.0 * N[(x2 * t$95$9), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(x1 * -22.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -0.0042], N[(x1 + N[(t$95$1 + N[(x1 + N[(t$95$3 + N[(t$95$10 + N[(t$95$0 * N[(N[(t$95$7 * N[(t$95$6 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(4.0 * N[(3.0 + N[(N[(-1.0 + N[(t$95$9 / x1), $MachinePrecision]), $MachinePrecision] / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 0.00085], N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$4 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $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, 2e+153], N[(x1 + N[(N[(x1 + N[(N[(t$95$10 - N[(t$95$0 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 + N[(4.0 * t$95$8), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$7 * N[(3.0 + t$95$8), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$3), $MachinePrecision]), $MachinePrecision] + 9.0), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x1 < -1.00000000000000002e144 or 2e153 < x1

   1. Initial program 0.0%

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

   3. Taylor expanded in x1 around 0 0.0%

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

   4. Taylor expanded in x1 around 0 60.6%

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

   5. Taylor expanded in x2 around 0 98.7%

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

   if -1.00000000000000002e144 < x1 < -3.39999999999999994e106

   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%

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

      1. *-commutative 0.0%

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

   5. Simplified 0.0%

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

   6. Taylor expanded in x1 around 0 75.0%

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

   7. Taylor expanded in x2 around 0 75.0%

      \[\leadsto x1 + \left(\left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \color{blue}{\left(-22 \cdot x1\right)}\right) + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]
   8. Step-by-step derivation

      1. *-commutative 75.0%

         \[\leadsto x1 + \left(\left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \color{blue}{\left(x1 \cdot -22\right)}\right) + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]

   9. Simplified 75.0%

      \[\leadsto x1 + \left(\left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \color{blue}{\left(x1 \cdot -22\right)}\right) + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]

   if -3.39999999999999994e106 < x1 < -0.00419999999999999974

   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 99.3%

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

      1. *-commutative 99.3%

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

   5. Simplified 99.3%

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

   6. Taylor expanded in x1 around -inf 99.4%

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

   if -0.00419999999999999974 < x1 < 8.49999999999999953e-4

   1. Initial program 99.4%

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

   3. Taylor expanded in x1 around 0 89.3%

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

   4. Taylor expanded in x2 around 0 99.4%

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

   if 8.49999999999999953e-4 < x1 < 2e153

   1. Initial program 96.2%

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

   3. Taylor expanded in x1 around inf 96.2%

      \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \color{blue}{3}\right) \]
3. Recombined 5 regimes into one program.

4. Final simplification 98.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1 \cdot 10^{+144}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -3.4 \cdot 10^{+106}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2\right) + \left(x1 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(x1 \cdot -22\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -0.0042:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2\right) + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \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(4 \cdot \left(3 + \frac{-1 + \frac{2 \cdot x2 - 3}{x1}}{x1}\right) - 6\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 0.00085:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot -3 + 2 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(\left(x1 + \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}{x1 \cdot x1 + 1} - \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1}\right) + \left(\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) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 9\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 97.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := 3 \cdot \left(x2 \cdot -2\right)\\ t_2 := x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ t_3 := x1 \cdot \left(x1 \cdot x1\right)\\ t_4 := x1 \cdot \left(x1 \cdot 3\right)\\ t_5 := \left(t\_4 + 2 \cdot x2\right) - x1\\ t_6 := \frac{t\_5}{-1 - x1 \cdot x1}\\ t_7 := \frac{t\_5}{t\_0}\\ t_8 := \left(x1 \cdot 2\right) \cdot t\_7\\ t_9 := t\_4 \cdot t\_7\\ \mathbf{if}\;x1 \leq -1 \cdot 10^{+144}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x1 \leq -3.4 \cdot 10^{+106}:\\ \;\;\;\;x1 + \left(t\_1 + \left(x1 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(x1 \cdot -22\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -0.65:\\ \;\;\;\;x1 + \left(t\_1 + \left(x1 + \left(t\_3 + \left(t\_9 + t\_0 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(t\_7 \cdot 4 - 6\right) + t\_8 \cdot \frac{2 \cdot \frac{x2}{x1} + \left(-1 - \frac{3}{x1}\right)}{x1}\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 0.0034:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t\_4 - 2 \cdot x2\right) - x1}{t\_0} + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot -3 + 2 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(t\_9 - t\_0 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot t\_6\right) + t\_8 \cdot \left(3 + t\_6\right)\right)\right) + t\_3\right)\right) + 9\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ (* x1 x1) 1.0))
        (t_1 (* 3.0 (* x2 -2.0)))
        (t_2 (+ x1 (+ x1 (* 3.0 (* x1 (+ (* x1 3.0) -1.0))))))
        (t_3 (* x1 (* x1 x1)))
        (t_4 (* x1 (* x1 3.0)))
        (t_5 (- (+ t_4 (* 2.0 x2)) x1))
        (t_6 (/ t_5 (- -1.0 (* x1 x1))))
        (t_7 (/ t_5 t_0))
        (t_8 (* (* x1 2.0) t_7))
        (t_9 (* t_4 t_7)))
   (if (<= x1 -1e+144)
     t_2
     (if (<= x1 -3.4e+106)
       (+
        x1
        (+
         t_1
         (+
          x1
          (* x1 (+ (* 4.0 (* x2 (- (* 2.0 x2) 3.0))) (* x1 (* x1 -22.0)))))))
       (if (<= x1 -0.65)
         (+
          x1
          (+
           t_1
           (+
            x1
            (+
             t_3
             (+
              t_9
              (*
               t_0
               (+
                (* (* x1 x1) (- (* t_7 4.0) 6.0))
                (* t_8 (/ (+ (* 2.0 (/ x2 x1)) (- -1.0 (/ 3.0 x1))) x1)))))))))
         (if (<= x1 0.0034)
           (+
            x1
            (+
             (* 3.0 (/ (- (- t_4 (* 2.0 x2)) x1) t_0))
             (+ x1 (* 4.0 (* x2 (+ (* x1 -3.0) (* 2.0 (* x1 x2))))))))
           (if (<= x1 2e+153)
             (+
              x1
              (+
               (+
                x1
                (+
                 (-
                  t_9
                  (*
                   t_0
                   (+ (* (* x1 x1) (+ 6.0 (* 4.0 t_6))) (* t_8 (+ 3.0 t_6)))))
                 t_3))
               9.0))
             t_2)))))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = 3.0 * (x2 * -2.0);
	double t_2 = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	double t_3 = x1 * (x1 * x1);
	double t_4 = x1 * (x1 * 3.0);
	double t_5 = (t_4 + (2.0 * x2)) - x1;
	double t_6 = t_5 / (-1.0 - (x1 * x1));
	double t_7 = t_5 / t_0;
	double t_8 = (x1 * 2.0) * t_7;
	double t_9 = t_4 * t_7;
	double tmp;
	if (x1 <= -1e+144) {
		tmp = t_2;
	} else if (x1 <= -3.4e+106) {
		tmp = x1 + (t_1 + (x1 + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) + (x1 * (x1 * -22.0))))));
	} else if (x1 <= -0.65) {
		tmp = x1 + (t_1 + (x1 + (t_3 + (t_9 + (t_0 * (((x1 * x1) * ((t_7 * 4.0) - 6.0)) + (t_8 * (((2.0 * (x2 / x1)) + (-1.0 - (3.0 / x1))) / x1))))))));
	} else if (x1 <= 0.0034) {
		tmp = x1 + ((3.0 * (((t_4 - (2.0 * x2)) - x1) / t_0)) + (x1 + (4.0 * (x2 * ((x1 * -3.0) + (2.0 * (x1 * x2)))))));
	} else if (x1 <= 2e+153) {
		tmp = x1 + ((x1 + ((t_9 - (t_0 * (((x1 * x1) * (6.0 + (4.0 * t_6))) + (t_8 * (3.0 + t_6))))) + t_3)) + 9.0);
	} else {
		tmp = 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 = (x1 * x1) + 1.0d0
    t_1 = 3.0d0 * (x2 * (-2.0d0))
    t_2 = x1 + (x1 + (3.0d0 * (x1 * ((x1 * 3.0d0) + (-1.0d0)))))
    t_3 = x1 * (x1 * x1)
    t_4 = x1 * (x1 * 3.0d0)
    t_5 = (t_4 + (2.0d0 * x2)) - x1
    t_6 = t_5 / ((-1.0d0) - (x1 * x1))
    t_7 = t_5 / t_0
    t_8 = (x1 * 2.0d0) * t_7
    t_9 = t_4 * t_7
    if (x1 <= (-1d+144)) then
        tmp = t_2
    else if (x1 <= (-3.4d+106)) then
        tmp = x1 + (t_1 + (x1 + (x1 * ((4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0))) + (x1 * (x1 * (-22.0d0)))))))
    else if (x1 <= (-0.65d0)) then
        tmp = x1 + (t_1 + (x1 + (t_3 + (t_9 + (t_0 * (((x1 * x1) * ((t_7 * 4.0d0) - 6.0d0)) + (t_8 * (((2.0d0 * (x2 / x1)) + ((-1.0d0) - (3.0d0 / x1))) / x1))))))))
    else if (x1 <= 0.0034d0) then
        tmp = x1 + ((3.0d0 * (((t_4 - (2.0d0 * x2)) - x1) / t_0)) + (x1 + (4.0d0 * (x2 * ((x1 * (-3.0d0)) + (2.0d0 * (x1 * x2)))))))
    else if (x1 <= 2d+153) then
        tmp = x1 + ((x1 + ((t_9 - (t_0 * (((x1 * x1) * (6.0d0 + (4.0d0 * t_6))) + (t_8 * (3.0d0 + t_6))))) + t_3)) + 9.0d0)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = 3.0 * (x2 * -2.0);
	double t_2 = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	double t_3 = x1 * (x1 * x1);
	double t_4 = x1 * (x1 * 3.0);
	double t_5 = (t_4 + (2.0 * x2)) - x1;
	double t_6 = t_5 / (-1.0 - (x1 * x1));
	double t_7 = t_5 / t_0;
	double t_8 = (x1 * 2.0) * t_7;
	double t_9 = t_4 * t_7;
	double tmp;
	if (x1 <= -1e+144) {
		tmp = t_2;
	} else if (x1 <= -3.4e+106) {
		tmp = x1 + (t_1 + (x1 + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) + (x1 * (x1 * -22.0))))));
	} else if (x1 <= -0.65) {
		tmp = x1 + (t_1 + (x1 + (t_3 + (t_9 + (t_0 * (((x1 * x1) * ((t_7 * 4.0) - 6.0)) + (t_8 * (((2.0 * (x2 / x1)) + (-1.0 - (3.0 / x1))) / x1))))))));
	} else if (x1 <= 0.0034) {
		tmp = x1 + ((3.0 * (((t_4 - (2.0 * x2)) - x1) / t_0)) + (x1 + (4.0 * (x2 * ((x1 * -3.0) + (2.0 * (x1 * x2)))))));
	} else if (x1 <= 2e+153) {
		tmp = x1 + ((x1 + ((t_9 - (t_0 * (((x1 * x1) * (6.0 + (4.0 * t_6))) + (t_8 * (3.0 + t_6))))) + t_3)) + 9.0);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x1 * x1) + 1.0
	t_1 = 3.0 * (x2 * -2.0)
	t_2 = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))))
	t_3 = x1 * (x1 * x1)
	t_4 = x1 * (x1 * 3.0)
	t_5 = (t_4 + (2.0 * x2)) - x1
	t_6 = t_5 / (-1.0 - (x1 * x1))
	t_7 = t_5 / t_0
	t_8 = (x1 * 2.0) * t_7
	t_9 = t_4 * t_7
	tmp = 0
	if x1 <= -1e+144:
		tmp = t_2
	elif x1 <= -3.4e+106:
		tmp = x1 + (t_1 + (x1 + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) + (x1 * (x1 * -22.0))))))
	elif x1 <= -0.65:
		tmp = x1 + (t_1 + (x1 + (t_3 + (t_9 + (t_0 * (((x1 * x1) * ((t_7 * 4.0) - 6.0)) + (t_8 * (((2.0 * (x2 / x1)) + (-1.0 - (3.0 / x1))) / x1))))))))
	elif x1 <= 0.0034:
		tmp = x1 + ((3.0 * (((t_4 - (2.0 * x2)) - x1) / t_0)) + (x1 + (4.0 * (x2 * ((x1 * -3.0) + (2.0 * (x1 * x2)))))))
	elif x1 <= 2e+153:
		tmp = x1 + ((x1 + ((t_9 - (t_0 * (((x1 * x1) * (6.0 + (4.0 * t_6))) + (t_8 * (3.0 + t_6))))) + t_3)) + 9.0)
	else:
		tmp = t_2
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * x1) + 1.0)
	t_1 = Float64(3.0 * Float64(x2 * -2.0))
	t_2 = Float64(x1 + Float64(x1 + Float64(3.0 * Float64(x1 * Float64(Float64(x1 * 3.0) + -1.0)))))
	t_3 = Float64(x1 * Float64(x1 * x1))
	t_4 = Float64(x1 * Float64(x1 * 3.0))
	t_5 = Float64(Float64(t_4 + Float64(2.0 * x2)) - x1)
	t_6 = Float64(t_5 / Float64(-1.0 - Float64(x1 * x1)))
	t_7 = Float64(t_5 / t_0)
	t_8 = Float64(Float64(x1 * 2.0) * t_7)
	t_9 = Float64(t_4 * t_7)
	tmp = 0.0
	if (x1 <= -1e+144)
		tmp = t_2;
	elseif (x1 <= -3.4e+106)
		tmp = Float64(x1 + Float64(t_1 + Float64(x1 + Float64(x1 * Float64(Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0))) + Float64(x1 * Float64(x1 * -22.0)))))));
	elseif (x1 <= -0.65)
		tmp = Float64(x1 + Float64(t_1 + Float64(x1 + Float64(t_3 + Float64(t_9 + Float64(t_0 * Float64(Float64(Float64(x1 * x1) * Float64(Float64(t_7 * 4.0) - 6.0)) + Float64(t_8 * Float64(Float64(Float64(2.0 * Float64(x2 / x1)) + Float64(-1.0 - Float64(3.0 / x1))) / x1)))))))));
	elseif (x1 <= 0.0034)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_4 - Float64(2.0 * x2)) - x1) / t_0)) + Float64(x1 + Float64(4.0 * Float64(x2 * Float64(Float64(x1 * -3.0) + Float64(2.0 * Float64(x1 * x2))))))));
	elseif (x1 <= 2e+153)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(Float64(t_9 - Float64(t_0 * Float64(Float64(Float64(x1 * x1) * Float64(6.0 + Float64(4.0 * t_6))) + Float64(t_8 * Float64(3.0 + t_6))))) + t_3)) + 9.0));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x1 * x1) + 1.0;
	t_1 = 3.0 * (x2 * -2.0);
	t_2 = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	t_3 = x1 * (x1 * x1);
	t_4 = x1 * (x1 * 3.0);
	t_5 = (t_4 + (2.0 * x2)) - x1;
	t_6 = t_5 / (-1.0 - (x1 * x1));
	t_7 = t_5 / t_0;
	t_8 = (x1 * 2.0) * t_7;
	t_9 = t_4 * t_7;
	tmp = 0.0;
	if (x1 <= -1e+144)
		tmp = t_2;
	elseif (x1 <= -3.4e+106)
		tmp = x1 + (t_1 + (x1 + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) + (x1 * (x1 * -22.0))))));
	elseif (x1 <= -0.65)
		tmp = x1 + (t_1 + (x1 + (t_3 + (t_9 + (t_0 * (((x1 * x1) * ((t_7 * 4.0) - 6.0)) + (t_8 * (((2.0 * (x2 / x1)) + (-1.0 - (3.0 / x1))) / x1))))))));
	elseif (x1 <= 0.0034)
		tmp = x1 + ((3.0 * (((t_4 - (2.0 * x2)) - x1) / t_0)) + (x1 + (4.0 * (x2 * ((x1 * -3.0) + (2.0 * (x1 * x2)))))));
	elseif (x1 <= 2e+153)
		tmp = x1 + ((x1 + ((t_9 - (t_0 * (((x1 * x1) * (6.0 + (4.0 * t_6))) + (t_8 * (3.0 + t_6))))) + t_3)) + 9.0);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$1 = N[(3.0 * N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x1 + N[(x1 + N[(3.0 * N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(t$95$4 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]}, Block[{t$95$6 = N[(t$95$5 / N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(t$95$5 / t$95$0), $MachinePrecision]}, Block[{t$95$8 = N[(N[(x1 * 2.0), $MachinePrecision] * t$95$7), $MachinePrecision]}, Block[{t$95$9 = N[(t$95$4 * t$95$7), $MachinePrecision]}, If[LessEqual[x1, -1e+144], t$95$2, If[LessEqual[x1, -3.4e+106], N[(x1 + N[(t$95$1 + N[(x1 + N[(x1 * N[(N[(4.0 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(x1 * -22.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -0.65], N[(x1 + N[(t$95$1 + N[(x1 + N[(t$95$3 + N[(t$95$9 + N[(t$95$0 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$7 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] + N[(t$95$8 * N[(N[(N[(2.0 * N[(x2 / x1), $MachinePrecision]), $MachinePrecision] + N[(-1.0 - N[(3.0 / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 0.0034], N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$4 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $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, 2e+153], N[(x1 + N[(N[(x1 + N[(N[(t$95$9 - N[(t$95$0 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 + N[(4.0 * t$95$6), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$8 * N[(3.0 + t$95$6), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$3), $MachinePrecision]), $MachinePrecision] + 9.0), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x1 < -1.00000000000000002e144 or 2e153 < x1

   1. Initial program 0.0%

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

   3. Taylor expanded in x1 around 0 0.0%

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

   4. Taylor expanded in x1 around 0 60.6%

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

   5. Taylor expanded in x2 around 0 98.7%

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

   if -1.00000000000000002e144 < x1 < -3.39999999999999994e106

   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%

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

      1. *-commutative 0.0%

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

   5. Simplified 0.0%

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

   6. Taylor expanded in x1 around 0 75.0%

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

   7. Taylor expanded in x2 around 0 75.0%

      \[\leadsto x1 + \left(\left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \color{blue}{\left(-22 \cdot x1\right)}\right) + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]
   8. Step-by-step derivation

      1. *-commutative 75.0%

         \[\leadsto x1 + \left(\left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \color{blue}{\left(x1 \cdot -22\right)}\right) + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]

   9. Simplified 75.0%

      \[\leadsto x1 + \left(\left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \color{blue}{\left(x1 \cdot -22\right)}\right) + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]

   if -3.39999999999999994e106 < x1 < -0.650000000000000022

   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 99.3%

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

      1. *-commutative 99.3%

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

   5. Simplified 99.3%

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

   6. Taylor expanded in x1 around inf 99.3%

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

      1. associate-*r/ 99.3%

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

      2. metadata-eval 99.3%

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

   8. Simplified 99.3%

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

   if -0.650000000000000022 < x1 < 0.00339999999999999981

   1. Initial program 99.4%

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

   3. Taylor expanded in x1 around 0 89.3%

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

   4. Taylor expanded in x2 around 0 99.4%

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

   if 0.00339999999999999981 < x1 < 2e153

   1. Initial program 96.2%

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

   3. Taylor expanded in x1 around inf 96.2%

      \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \color{blue}{3}\right) \]
3. Recombined 5 regimes into one program.

4. Final simplification 98.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1 \cdot 10^{+144}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -3.4 \cdot 10^{+106}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2\right) + \left(x1 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(x1 \cdot -22\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -0.65:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2\right) + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right) + \left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \frac{2 \cdot \frac{x2}{x1} + \left(-1 - \frac{3}{x1}\right)}{x1}\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 0.0034:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot -3 + 2 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(\left(x1 + \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}{x1 \cdot x1 + 1} - \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1}\right) + \left(\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) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 9\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 96.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := 3 \cdot \left(x2 \cdot -2\right)\\ t_2 := -1 - x1 \cdot x1\\ t_3 := x1 \cdot \left(x1 \cdot 3\right)\\ t_4 := \left(t\_3 + 2 \cdot x2\right) - x1\\ t_5 := \frac{t\_4}{t\_0}\\ t_6 := x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ t_7 := x1 + \left(t\_1 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(t\_3 \cdot t\_5 - t\_0 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t\_5\right) \cdot \frac{\left(1 + \frac{3}{x1}\right) - 2 \cdot \frac{x2}{x1}}{x1} + \left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{t\_4}{t\_2}\right)\right)\right)\right)\right)\right)\\ \mathbf{if}\;x1 \leq -1 \cdot 10^{+144}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;x1 \leq -3.4 \cdot 10^{+106}:\\ \;\;\;\;x1 + \left(t\_1 + \left(x1 + x1 \cdot \left(x1 \cdot \left(x1 \cdot -22\right) - 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -1.4:\\ \;\;\;\;t\_7\\ \mathbf{elif}\;x1 \leq 0.042:\\ \;\;\;\;x1 + \left(3 \cdot \frac{x1 - \left(t\_3 - 2 \cdot x2\right)}{t\_2} + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot -3 + 2 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{+153}:\\ \;\;\;\;t\_7\\ \mathbf{else}:\\ \;\;\;\;t\_6\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ (* x1 x1) 1.0))
        (t_1 (* 3.0 (* x2 -2.0)))
        (t_2 (- -1.0 (* x1 x1)))
        (t_3 (* x1 (* x1 3.0)))
        (t_4 (- (+ t_3 (* 2.0 x2)) x1))
        (t_5 (/ t_4 t_0))
        (t_6 (+ x1 (+ x1 (* 3.0 (* x1 (+ (* x1 3.0) -1.0))))))
        (t_7
         (+
          x1
          (+
           t_1
           (+
            x1
            (+
             (* x1 (* x1 x1))
             (-
              (* t_3 t_5)
              (*
               t_0
               (+
                (*
                 (* (* x1 2.0) t_5)
                 (/ (- (+ 1.0 (/ 3.0 x1)) (* 2.0 (/ x2 x1))) x1))
                (* (* x1 x1) (+ 6.0 (* 4.0 (/ t_4 t_2)))))))))))))
   (if (<= x1 -1e+144)
     t_6
     (if (<= x1 -3.4e+106)
       (+
        x1
        (+
         t_1
         (+
          x1
          (* x1 (- (* x1 (* x1 -22.0)) (* 4.0 (* x2 (- 3.0 (* 2.0 x2)))))))))
       (if (<= x1 -1.4)
         t_7
         (if (<= x1 0.042)
           (+
            x1
            (+
             (* 3.0 (/ (- x1 (- t_3 (* 2.0 x2))) t_2))
             (+ x1 (* 4.0 (* x2 (+ (* x1 -3.0) (* 2.0 (* x1 x2))))))))
           (if (<= x1 2e+153) t_7 t_6)))))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = 3.0 * (x2 * -2.0);
	double t_2 = -1.0 - (x1 * x1);
	double t_3 = x1 * (x1 * 3.0);
	double t_4 = (t_3 + (2.0 * x2)) - x1;
	double t_5 = t_4 / t_0;
	double t_6 = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	double t_7 = x1 + (t_1 + (x1 + ((x1 * (x1 * x1)) + ((t_3 * t_5) - (t_0 * ((((x1 * 2.0) * t_5) * (((1.0 + (3.0 / x1)) - (2.0 * (x2 / x1))) / x1)) + ((x1 * x1) * (6.0 + (4.0 * (t_4 / t_2))))))))));
	double tmp;
	if (x1 <= -1e+144) {
		tmp = t_6;
	} else if (x1 <= -3.4e+106) {
		tmp = x1 + (t_1 + (x1 + (x1 * ((x1 * (x1 * -22.0)) - (4.0 * (x2 * (3.0 - (2.0 * x2))))))));
	} else if (x1 <= -1.4) {
		tmp = t_7;
	} else if (x1 <= 0.042) {
		tmp = x1 + ((3.0 * ((x1 - (t_3 - (2.0 * x2))) / t_2)) + (x1 + (4.0 * (x2 * ((x1 * -3.0) + (2.0 * (x1 * x2)))))));
	} else if (x1 <= 2e+153) {
		tmp = t_7;
	} else {
		tmp = t_6;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: tmp
    t_0 = (x1 * x1) + 1.0d0
    t_1 = 3.0d0 * (x2 * (-2.0d0))
    t_2 = (-1.0d0) - (x1 * x1)
    t_3 = x1 * (x1 * 3.0d0)
    t_4 = (t_3 + (2.0d0 * x2)) - x1
    t_5 = t_4 / t_0
    t_6 = x1 + (x1 + (3.0d0 * (x1 * ((x1 * 3.0d0) + (-1.0d0)))))
    t_7 = x1 + (t_1 + (x1 + ((x1 * (x1 * x1)) + ((t_3 * t_5) - (t_0 * ((((x1 * 2.0d0) * t_5) * (((1.0d0 + (3.0d0 / x1)) - (2.0d0 * (x2 / x1))) / x1)) + ((x1 * x1) * (6.0d0 + (4.0d0 * (t_4 / t_2))))))))))
    if (x1 <= (-1d+144)) then
        tmp = t_6
    else if (x1 <= (-3.4d+106)) then
        tmp = x1 + (t_1 + (x1 + (x1 * ((x1 * (x1 * (-22.0d0))) - (4.0d0 * (x2 * (3.0d0 - (2.0d0 * x2))))))))
    else if (x1 <= (-1.4d0)) then
        tmp = t_7
    else if (x1 <= 0.042d0) then
        tmp = x1 + ((3.0d0 * ((x1 - (t_3 - (2.0d0 * x2))) / t_2)) + (x1 + (4.0d0 * (x2 * ((x1 * (-3.0d0)) + (2.0d0 * (x1 * x2)))))))
    else if (x1 <= 2d+153) then
        tmp = t_7
    else
        tmp = t_6
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = 3.0 * (x2 * -2.0);
	double t_2 = -1.0 - (x1 * x1);
	double t_3 = x1 * (x1 * 3.0);
	double t_4 = (t_3 + (2.0 * x2)) - x1;
	double t_5 = t_4 / t_0;
	double t_6 = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	double t_7 = x1 + (t_1 + (x1 + ((x1 * (x1 * x1)) + ((t_3 * t_5) - (t_0 * ((((x1 * 2.0) * t_5) * (((1.0 + (3.0 / x1)) - (2.0 * (x2 / x1))) / x1)) + ((x1 * x1) * (6.0 + (4.0 * (t_4 / t_2))))))))));
	double tmp;
	if (x1 <= -1e+144) {
		tmp = t_6;
	} else if (x1 <= -3.4e+106) {
		tmp = x1 + (t_1 + (x1 + (x1 * ((x1 * (x1 * -22.0)) - (4.0 * (x2 * (3.0 - (2.0 * x2))))))));
	} else if (x1 <= -1.4) {
		tmp = t_7;
	} else if (x1 <= 0.042) {
		tmp = x1 + ((3.0 * ((x1 - (t_3 - (2.0 * x2))) / t_2)) + (x1 + (4.0 * (x2 * ((x1 * -3.0) + (2.0 * (x1 * x2)))))));
	} else if (x1 <= 2e+153) {
		tmp = t_7;
	} else {
		tmp = t_6;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x1 * x1) + 1.0
	t_1 = 3.0 * (x2 * -2.0)
	t_2 = -1.0 - (x1 * x1)
	t_3 = x1 * (x1 * 3.0)
	t_4 = (t_3 + (2.0 * x2)) - x1
	t_5 = t_4 / t_0
	t_6 = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))))
	t_7 = x1 + (t_1 + (x1 + ((x1 * (x1 * x1)) + ((t_3 * t_5) - (t_0 * ((((x1 * 2.0) * t_5) * (((1.0 + (3.0 / x1)) - (2.0 * (x2 / x1))) / x1)) + ((x1 * x1) * (6.0 + (4.0 * (t_4 / t_2))))))))))
	tmp = 0
	if x1 <= -1e+144:
		tmp = t_6
	elif x1 <= -3.4e+106:
		tmp = x1 + (t_1 + (x1 + (x1 * ((x1 * (x1 * -22.0)) - (4.0 * (x2 * (3.0 - (2.0 * x2))))))))
	elif x1 <= -1.4:
		tmp = t_7
	elif x1 <= 0.042:
		tmp = x1 + ((3.0 * ((x1 - (t_3 - (2.0 * x2))) / t_2)) + (x1 + (4.0 * (x2 * ((x1 * -3.0) + (2.0 * (x1 * x2)))))))
	elif x1 <= 2e+153:
		tmp = t_7
	else:
		tmp = t_6
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * x1) + 1.0)
	t_1 = Float64(3.0 * Float64(x2 * -2.0))
	t_2 = Float64(-1.0 - 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(t_4 / t_0)
	t_6 = Float64(x1 + Float64(x1 + Float64(3.0 * Float64(x1 * Float64(Float64(x1 * 3.0) + -1.0)))))
	t_7 = Float64(x1 + Float64(t_1 + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(t_3 * t_5) - Float64(t_0 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_5) * Float64(Float64(Float64(1.0 + Float64(3.0 / x1)) - Float64(2.0 * Float64(x2 / x1))) / x1)) + Float64(Float64(x1 * x1) * Float64(6.0 + Float64(4.0 * Float64(t_4 / t_2)))))))))))
	tmp = 0.0
	if (x1 <= -1e+144)
		tmp = t_6;
	elseif (x1 <= -3.4e+106)
		tmp = Float64(x1 + Float64(t_1 + Float64(x1 + Float64(x1 * Float64(Float64(x1 * Float64(x1 * -22.0)) - Float64(4.0 * Float64(x2 * Float64(3.0 - Float64(2.0 * x2)))))))));
	elseif (x1 <= -1.4)
		tmp = t_7;
	elseif (x1 <= 0.042)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(x1 - Float64(t_3 - 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 <= 2e+153)
		tmp = t_7;
	else
		tmp = t_6;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x1 * x1) + 1.0;
	t_1 = 3.0 * (x2 * -2.0);
	t_2 = -1.0 - (x1 * x1);
	t_3 = x1 * (x1 * 3.0);
	t_4 = (t_3 + (2.0 * x2)) - x1;
	t_5 = t_4 / t_0;
	t_6 = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	t_7 = x1 + (t_1 + (x1 + ((x1 * (x1 * x1)) + ((t_3 * t_5) - (t_0 * ((((x1 * 2.0) * t_5) * (((1.0 + (3.0 / x1)) - (2.0 * (x2 / x1))) / x1)) + ((x1 * x1) * (6.0 + (4.0 * (t_4 / t_2))))))))));
	tmp = 0.0;
	if (x1 <= -1e+144)
		tmp = t_6;
	elseif (x1 <= -3.4e+106)
		tmp = x1 + (t_1 + (x1 + (x1 * ((x1 * (x1 * -22.0)) - (4.0 * (x2 * (3.0 - (2.0 * x2))))))));
	elseif (x1 <= -1.4)
		tmp = t_7;
	elseif (x1 <= 0.042)
		tmp = x1 + ((3.0 * ((x1 - (t_3 - (2.0 * x2))) / t_2)) + (x1 + (4.0 * (x2 * ((x1 * -3.0) + (2.0 * (x1 * x2)))))));
	elseif (x1 <= 2e+153)
		tmp = t_7;
	else
		tmp = t_6;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$1 = N[(3.0 * N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-1.0 - 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[(t$95$4 / t$95$0), $MachinePrecision]}, Block[{t$95$6 = N[(x1 + N[(x1 + N[(3.0 * N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(x1 + N[(t$95$1 + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$3 * t$95$5), $MachinePrecision] - N[(t$95$0 * N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$5), $MachinePrecision] * N[(N[(N[(1.0 + N[(3.0 / x1), $MachinePrecision]), $MachinePrecision] - N[(2.0 * N[(x2 / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x1), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 + N[(4.0 * N[(t$95$4 / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -1e+144], t$95$6, If[LessEqual[x1, -3.4e+106], N[(x1 + N[(t$95$1 + N[(x1 + N[(x1 * N[(N[(x1 * N[(x1 * -22.0), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(x2 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -1.4], t$95$7, If[LessEqual[x1, 0.042], N[(x1 + N[(N[(3.0 * N[(N[(x1 - N[(t$95$3 - 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, 2e+153], t$95$7, t$95$6]]]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -1.00000000000000002e144 or 2e153 < x1

   1. Initial program 0.0%

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

   3. Taylor expanded in x1 around 0 0.0%

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

   4. Taylor expanded in x1 around 0 60.6%

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

   5. Taylor expanded in x2 around 0 98.7%

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

   if -1.00000000000000002e144 < x1 < -3.39999999999999994e106

   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%

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

      1. *-commutative 0.0%

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

   5. Simplified 0.0%

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

   6. Taylor expanded in x1 around 0 75.0%

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

   7. Taylor expanded in x2 around 0 75.0%

      \[\leadsto x1 + \left(\left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \color{blue}{\left(-22 \cdot x1\right)}\right) + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]
   8. Step-by-step derivation

      1. *-commutative 75.0%

         \[\leadsto x1 + \left(\left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \color{blue}{\left(x1 \cdot -22\right)}\right) + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]

   9. Simplified 75.0%

      \[\leadsto x1 + \left(\left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \color{blue}{\left(x1 \cdot -22\right)}\right) + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]

   if -3.39999999999999994e106 < x1 < -1.3999999999999999 or 0.0420000000000000026 < x1 < 2e153

   1. Initial program 97.2%

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

   3. Taylor expanded in x1 around 0 97.2%

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

      1. *-commutative 97.2%

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

   5. Simplified 97.2%

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

   6. Taylor expanded in x1 around inf 97.1%

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

      1. associate-*r/ 97.1%

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

      2. metadata-eval 97.1%

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

   8. Simplified 97.1%

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

   if -1.3999999999999999 < x1 < 0.0420000000000000026

   1. Initial program 99.4%

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

   3. Taylor expanded in x1 around 0 89.3%

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

   4. Taylor expanded in x2 around 0 99.4%

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

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1 \cdot 10^{+144}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -3.4 \cdot 10^{+106}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2\right) + \left(x1 + x1 \cdot \left(x1 \cdot \left(x1 \cdot -22\right) - 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -1.4:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2\right) + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - \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(6 + 4 \cdot \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 0.042:\\ \;\;\;\;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 2 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2\right) + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - \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(6 + 4 \cdot \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(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 95.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := 3 \cdot \left(x2 \cdot -2\right)\\ t_2 := x1 + \left(\left(x1 + 6 \cdot {x1}^{4}\right) + t\_1\right)\\ t_3 := x1 \cdot \left(x1 \cdot 3\right)\\ t_4 := \frac{\left(t\_3 + 2 \cdot x2\right) - x1}{t\_0}\\ \mathbf{if}\;x1 \leq -3.4 \cdot 10^{+106}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x1 \leq -0.01:\\ \;\;\;\;x1 + \left(t\_1 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(t\_3 \cdot t\_4 + t\_0 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t\_4\right) \cdot \left(t\_4 - 3\right) - \left(x1 \cdot x1\right) \cdot \left(6 - 4 \cdot \left(3 + \frac{-1 + \frac{2 \cdot x2 - 3}{x1}}{x1}\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 8.5 \cdot 10^{+21}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{x1 - \left(t\_3 - 2 \cdot x2\right)}{-1 - x1 \cdot x1} + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot -3 + 2 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ (* x1 x1) 1.0))
        (t_1 (* 3.0 (* x2 -2.0)))
        (t_2 (+ x1 (+ (+ x1 (* 6.0 (pow x1 4.0))) t_1)))
        (t_3 (* x1 (* x1 3.0)))
        (t_4 (/ (- (+ t_3 (* 2.0 x2)) x1) t_0)))
   (if (<= x1 -3.4e+106)
     t_2
     (if (<= x1 -0.01)
       (+
        x1
        (+
         t_1
         (+
          x1
          (+
           (* x1 (* x1 x1))
           (+
            (* t_3 t_4)
            (*
             t_0
             (-
              (* (* (* x1 2.0) t_4) (- t_4 3.0))
              (*
               (* x1 x1)
               (-
                6.0
                (*
                 4.0
                 (+ 3.0 (/ (+ -1.0 (/ (- (* 2.0 x2) 3.0) x1)) x1))))))))))))
       (if (<= x1 8.5e+21)
         (+
          x1
          (+
           (* 3.0 (/ (- x1 (- t_3 (* 2.0 x2))) (- -1.0 (* x1 x1))))
           (+ x1 (* 4.0 (* x2 (+ (* x1 -3.0) (* 2.0 (* x1 x2))))))))
         t_2)))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = 3.0 * (x2 * -2.0);
	double t_2 = x1 + ((x1 + (6.0 * pow(x1, 4.0))) + t_1);
	double t_3 = x1 * (x1 * 3.0);
	double t_4 = ((t_3 + (2.0 * x2)) - x1) / t_0;
	double tmp;
	if (x1 <= -3.4e+106) {
		tmp = t_2;
	} else if (x1 <= -0.01) {
		tmp = x1 + (t_1 + (x1 + ((x1 * (x1 * x1)) + ((t_3 * t_4) + (t_0 * ((((x1 * 2.0) * t_4) * (t_4 - 3.0)) - ((x1 * x1) * (6.0 - (4.0 * (3.0 + ((-1.0 + (((2.0 * x2) - 3.0) / x1)) / x1)))))))))));
	} else if (x1 <= 8.5e+21) {
		tmp = x1 + ((3.0 * ((x1 - (t_3 - (2.0 * x2))) / (-1.0 - (x1 * x1)))) + (x1 + (4.0 * (x2 * ((x1 * -3.0) + (2.0 * (x1 * x2)))))));
	} else {
		tmp = 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) :: tmp
    t_0 = (x1 * x1) + 1.0d0
    t_1 = 3.0d0 * (x2 * (-2.0d0))
    t_2 = x1 + ((x1 + (6.0d0 * (x1 ** 4.0d0))) + t_1)
    t_3 = x1 * (x1 * 3.0d0)
    t_4 = ((t_3 + (2.0d0 * x2)) - x1) / t_0
    if (x1 <= (-3.4d+106)) then
        tmp = t_2
    else if (x1 <= (-0.01d0)) then
        tmp = x1 + (t_1 + (x1 + ((x1 * (x1 * x1)) + ((t_3 * t_4) + (t_0 * ((((x1 * 2.0d0) * t_4) * (t_4 - 3.0d0)) - ((x1 * x1) * (6.0d0 - (4.0d0 * (3.0d0 + (((-1.0d0) + (((2.0d0 * x2) - 3.0d0) / x1)) / x1)))))))))))
    else if (x1 <= 8.5d+21) then
        tmp = x1 + ((3.0d0 * ((x1 - (t_3 - (2.0d0 * x2))) / ((-1.0d0) - (x1 * x1)))) + (x1 + (4.0d0 * (x2 * ((x1 * (-3.0d0)) + (2.0d0 * (x1 * x2)))))))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = 3.0 * (x2 * -2.0);
	double t_2 = x1 + ((x1 + (6.0 * Math.pow(x1, 4.0))) + t_1);
	double t_3 = x1 * (x1 * 3.0);
	double t_4 = ((t_3 + (2.0 * x2)) - x1) / t_0;
	double tmp;
	if (x1 <= -3.4e+106) {
		tmp = t_2;
	} else if (x1 <= -0.01) {
		tmp = x1 + (t_1 + (x1 + ((x1 * (x1 * x1)) + ((t_3 * t_4) + (t_0 * ((((x1 * 2.0) * t_4) * (t_4 - 3.0)) - ((x1 * x1) * (6.0 - (4.0 * (3.0 + ((-1.0 + (((2.0 * x2) - 3.0) / x1)) / x1)))))))))));
	} else if (x1 <= 8.5e+21) {
		tmp = x1 + ((3.0 * ((x1 - (t_3 - (2.0 * x2))) / (-1.0 - (x1 * x1)))) + (x1 + (4.0 * (x2 * ((x1 * -3.0) + (2.0 * (x1 * x2)))))));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x1 * x1) + 1.0
	t_1 = 3.0 * (x2 * -2.0)
	t_2 = x1 + ((x1 + (6.0 * math.pow(x1, 4.0))) + t_1)
	t_3 = x1 * (x1 * 3.0)
	t_4 = ((t_3 + (2.0 * x2)) - x1) / t_0
	tmp = 0
	if x1 <= -3.4e+106:
		tmp = t_2
	elif x1 <= -0.01:
		tmp = x1 + (t_1 + (x1 + ((x1 * (x1 * x1)) + ((t_3 * t_4) + (t_0 * ((((x1 * 2.0) * t_4) * (t_4 - 3.0)) - ((x1 * x1) * (6.0 - (4.0 * (3.0 + ((-1.0 + (((2.0 * x2) - 3.0) / x1)) / x1)))))))))))
	elif x1 <= 8.5e+21:
		tmp = x1 + ((3.0 * ((x1 - (t_3 - (2.0 * x2))) / (-1.0 - (x1 * x1)))) + (x1 + (4.0 * (x2 * ((x1 * -3.0) + (2.0 * (x1 * x2)))))))
	else:
		tmp = t_2
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * x1) + 1.0)
	t_1 = Float64(3.0 * Float64(x2 * -2.0))
	t_2 = Float64(x1 + Float64(Float64(x1 + Float64(6.0 * (x1 ^ 4.0))) + t_1))
	t_3 = Float64(x1 * Float64(x1 * 3.0))
	t_4 = Float64(Float64(Float64(t_3 + Float64(2.0 * x2)) - x1) / t_0)
	tmp = 0.0
	if (x1 <= -3.4e+106)
		tmp = t_2;
	elseif (x1 <= -0.01)
		tmp = Float64(x1 + Float64(t_1 + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(t_3 * t_4) + Float64(t_0 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_4) * Float64(t_4 - 3.0)) - Float64(Float64(x1 * x1) * Float64(6.0 - Float64(4.0 * Float64(3.0 + Float64(Float64(-1.0 + Float64(Float64(Float64(2.0 * x2) - 3.0) / x1)) / x1))))))))))));
	elseif (x1 <= 8.5e+21)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(x1 - Float64(t_3 - 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 = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x1 * x1) + 1.0;
	t_1 = 3.0 * (x2 * -2.0);
	t_2 = x1 + ((x1 + (6.0 * (x1 ^ 4.0))) + t_1);
	t_3 = x1 * (x1 * 3.0);
	t_4 = ((t_3 + (2.0 * x2)) - x1) / t_0;
	tmp = 0.0;
	if (x1 <= -3.4e+106)
		tmp = t_2;
	elseif (x1 <= -0.01)
		tmp = x1 + (t_1 + (x1 + ((x1 * (x1 * x1)) + ((t_3 * t_4) + (t_0 * ((((x1 * 2.0) * t_4) * (t_4 - 3.0)) - ((x1 * x1) * (6.0 - (4.0 * (3.0 + ((-1.0 + (((2.0 * x2) - 3.0) / x1)) / x1)))))))))));
	elseif (x1 <= 8.5e+21)
		tmp = x1 + ((3.0 * ((x1 - (t_3 - (2.0 * x2))) / (-1.0 - (x1 * x1)))) + (x1 + (4.0 * (x2 * ((x1 * -3.0) + (2.0 * (x1 * x2)))))));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$1 = N[(3.0 * N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x1 + N[(N[(x1 + N[(6.0 * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(t$95$3 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]}, If[LessEqual[x1, -3.4e+106], t$95$2, If[LessEqual[x1, -0.01], N[(x1 + N[(t$95$1 + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$3 * t$95$4), $MachinePrecision] + N[(t$95$0 * 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[(6.0 - N[(4.0 * N[(3.0 + N[(N[(-1.0 + N[(N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision] / x1), $MachinePrecision]), $MachinePrecision] / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 8.5e+21], N[(x1 + N[(N[(3.0 * N[(N[(x1 - N[(t$95$3 - 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], t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -3.39999999999999994e106 or 8.5e21 < x1

   1. Initial program 25.1%

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

   3. Taylor expanded in x1 around 0 25.1%

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

      1. *-commutative 25.1%

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

   5. Simplified 25.1%

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

   6. Taylor expanded in x1 around inf 95.4%

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

   if -3.39999999999999994e106 < x1 < -0.0100000000000000002

   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 99.3%

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

      1. *-commutative 99.3%

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

   5. Simplified 99.3%

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

   6. Taylor expanded in x1 around -inf 99.4%

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

   if -0.0100000000000000002 < x1 < 8.5e21

   1. Initial program 99.4%

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

   3. Taylor expanded in x1 around 0 88.9%

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

   4. Taylor expanded in x2 around 0 98.7%

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

4. Final simplification 97.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -3.4 \cdot 10^{+106}:\\ \;\;\;\;x1 + \left(\left(x1 + 6 \cdot {x1}^{4}\right) + 3 \cdot \left(x2 \cdot -2\right)\right)\\ \mathbf{elif}\;x1 \leq -0.01:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2\right) + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) - \left(x1 \cdot x1\right) \cdot \left(6 - 4 \cdot \left(3 + \frac{-1 + \frac{2 \cdot x2 - 3}{x1}}{x1}\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 8.5 \cdot 10^{+21}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right)}{-1 - x1 \cdot x1} + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot -3 + 2 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 + 6 \cdot {x1}^{4}\right) + 3 \cdot \left(x2 \cdot -2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 95.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := -1 - x1 \cdot x1\\ t_2 := x1 \cdot \left(x1 \cdot 3\right)\\ t_3 := \left(t\_2 + 2 \cdot x2\right) - x1\\ t_4 := \frac{t\_3}{t\_0}\\ \mathbf{if}\;x1 \leq -3.4 \cdot 10^{+106} \lor \neg \left(x1 \leq 1.3 \cdot 10^{+58}\right):\\ \;\;\;\;x1 + \left(\left(x1 + 6 \cdot {x1}^{4}\right) + 3 \cdot \left(x2 \cdot -2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t\_2 - 2 \cdot x2\right) - x1}{t\_0} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(t\_2 \cdot t\_4 + \left(\left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{t\_3}{t\_1}\right) + \left(t\_4 - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(x1 - 2 \cdot x2\right)\right)\right) \cdot t\_1\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ (* x1 x1) 1.0))
        (t_1 (- -1.0 (* x1 x1)))
        (t_2 (* x1 (* x1 3.0)))
        (t_3 (- (+ t_2 (* 2.0 x2)) x1))
        (t_4 (/ t_3 t_0)))
   (if (or (<= x1 -3.4e+106) (not (<= x1 1.3e+58)))
     (+ x1 (+ (+ x1 (* 6.0 (pow x1 4.0))) (* 3.0 (* x2 -2.0))))
     (+
      x1
      (+
       (* 3.0 (/ (- (- t_2 (* 2.0 x2)) x1) t_0))
       (+
        x1
        (+
         (* x1 (* x1 x1))
         (+
          (* t_2 t_4)
          (*
           (+
            (* (* x1 x1) (+ 6.0 (* 4.0 (/ t_3 t_1))))
            (* (- t_4 3.0) (* (* x1 2.0) (- x1 (* 2.0 x2)))))
           t_1)))))))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = -1.0 - (x1 * x1);
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = (t_2 + (2.0 * x2)) - x1;
	double t_4 = t_3 / t_0;
	double tmp;
	if ((x1 <= -3.4e+106) || !(x1 <= 1.3e+58)) {
		tmp = x1 + ((x1 + (6.0 * pow(x1, 4.0))) + (3.0 * (x2 * -2.0)));
	} else {
		tmp = x1 + ((3.0 * (((t_2 - (2.0 * x2)) - x1) / t_0)) + (x1 + ((x1 * (x1 * x1)) + ((t_2 * t_4) + ((((x1 * x1) * (6.0 + (4.0 * (t_3 / t_1)))) + ((t_4 - 3.0) * ((x1 * 2.0) * (x1 - (2.0 * x2))))) * 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) :: t_4
    real(8) :: tmp
    t_0 = (x1 * x1) + 1.0d0
    t_1 = (-1.0d0) - (x1 * x1)
    t_2 = x1 * (x1 * 3.0d0)
    t_3 = (t_2 + (2.0d0 * x2)) - x1
    t_4 = t_3 / t_0
    if ((x1 <= (-3.4d+106)) .or. (.not. (x1 <= 1.3d+58))) then
        tmp = x1 + ((x1 + (6.0d0 * (x1 ** 4.0d0))) + (3.0d0 * (x2 * (-2.0d0))))
    else
        tmp = x1 + ((3.0d0 * (((t_2 - (2.0d0 * x2)) - x1) / t_0)) + (x1 + ((x1 * (x1 * x1)) + ((t_2 * t_4) + ((((x1 * x1) * (6.0d0 + (4.0d0 * (t_3 / t_1)))) + ((t_4 - 3.0d0) * ((x1 * 2.0d0) * (x1 - (2.0d0 * x2))))) * t_1)))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = -1.0 - (x1 * x1);
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = (t_2 + (2.0 * x2)) - x1;
	double t_4 = t_3 / t_0;
	double tmp;
	if ((x1 <= -3.4e+106) || !(x1 <= 1.3e+58)) {
		tmp = x1 + ((x1 + (6.0 * Math.pow(x1, 4.0))) + (3.0 * (x2 * -2.0)));
	} else {
		tmp = x1 + ((3.0 * (((t_2 - (2.0 * x2)) - x1) / t_0)) + (x1 + ((x1 * (x1 * x1)) + ((t_2 * t_4) + ((((x1 * x1) * (6.0 + (4.0 * (t_3 / t_1)))) + ((t_4 - 3.0) * ((x1 * 2.0) * (x1 - (2.0 * x2))))) * t_1)))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x1 * x1) + 1.0
	t_1 = -1.0 - (x1 * x1)
	t_2 = x1 * (x1 * 3.0)
	t_3 = (t_2 + (2.0 * x2)) - x1
	t_4 = t_3 / t_0
	tmp = 0
	if (x1 <= -3.4e+106) or not (x1 <= 1.3e+58):
		tmp = x1 + ((x1 + (6.0 * math.pow(x1, 4.0))) + (3.0 * (x2 * -2.0)))
	else:
		tmp = x1 + ((3.0 * (((t_2 - (2.0 * x2)) - x1) / t_0)) + (x1 + ((x1 * (x1 * x1)) + ((t_2 * t_4) + ((((x1 * x1) * (6.0 + (4.0 * (t_3 / t_1)))) + ((t_4 - 3.0) * ((x1 * 2.0) * (x1 - (2.0 * x2))))) * t_1)))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * x1) + 1.0)
	t_1 = Float64(-1.0 - Float64(x1 * x1))
	t_2 = Float64(x1 * Float64(x1 * 3.0))
	t_3 = Float64(Float64(t_2 + Float64(2.0 * x2)) - x1)
	t_4 = Float64(t_3 / t_0)
	tmp = 0.0
	if ((x1 <= -3.4e+106) || !(x1 <= 1.3e+58))
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(6.0 * (x1 ^ 4.0))) + Float64(3.0 * Float64(x2 * -2.0))));
	else
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_2 - Float64(2.0 * x2)) - x1) / t_0)) + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(t_2 * t_4) + Float64(Float64(Float64(Float64(x1 * x1) * Float64(6.0 + Float64(4.0 * Float64(t_3 / t_1)))) + Float64(Float64(t_4 - 3.0) * Float64(Float64(x1 * 2.0) * Float64(x1 - Float64(2.0 * x2))))) * t_1))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x1 * x1) + 1.0;
	t_1 = -1.0 - (x1 * x1);
	t_2 = x1 * (x1 * 3.0);
	t_3 = (t_2 + (2.0 * x2)) - x1;
	t_4 = t_3 / t_0;
	tmp = 0.0;
	if ((x1 <= -3.4e+106) || ~((x1 <= 1.3e+58)))
		tmp = x1 + ((x1 + (6.0 * (x1 ^ 4.0))) + (3.0 * (x2 * -2.0)));
	else
		tmp = x1 + ((3.0 * (((t_2 - (2.0 * x2)) - x1) / t_0)) + (x1 + ((x1 * (x1 * x1)) + ((t_2 * t_4) + ((((x1 * x1) * (6.0 + (4.0 * (t_3 / t_1)))) + ((t_4 - 3.0) * ((x1 * 2.0) * (x1 - (2.0 * x2))))) * t_1)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$1 = N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t$95$2 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$3 / t$95$0), $MachinePrecision]}, If[Or[LessEqual[x1, -3.4e+106], N[Not[LessEqual[x1, 1.3e+58]], $MachinePrecision]], N[(x1 + N[(N[(x1 + N[(6.0 * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$2 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$2 * t$95$4), $MachinePrecision] + N[(N[(N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 + N[(4.0 * N[(t$95$3 / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$4 - 3.0), $MachinePrecision] * N[(N[(x1 * 2.0), $MachinePrecision] * N[(x1 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 2 regimes

2. if x1 < -3.39999999999999994e106 or 1.29999999999999994e58 < x1

   1. Initial program 19.1%

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

   3. Taylor expanded in x1 around 0 19.1%

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

      1. *-commutative 19.1%

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

   5. Simplified 19.1%

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

   6. Taylor expanded in x1 around inf 98.0%

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

   if -3.39999999999999994e106 < x1 < 1.29999999999999994e58

   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 95.3%

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

      1. +-commutative 95.3%

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

      2. mul-1-neg 95.3%

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

      3. sub-neg 95.3%

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

   5. Simplified 95.3%

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

4. Final simplification 96.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -3.4 \cdot 10^{+106} \lor \neg \left(x1 \leq 1.3 \cdot 10^{+58}\right):\\ \;\;\;\;x1 + \left(\left(x1 + 6 \cdot {x1}^{4}\right) + 3 \cdot \left(x2 \cdot -2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(\left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1}\right) + \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(x1 - 2 \cdot x2\right)\right)\right) \cdot \left(-1 - x1 \cdot x1\right)\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 94.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 3 \cdot \left(x2 \cdot -2\right)\\ t_1 := -1 - x1 \cdot x1\\ t_2 := x1 \cdot \left(x1 \cdot 3\right)\\ t_3 := \left(t\_2 + 2 \cdot x2\right) - x1\\ t_4 := \frac{t\_3}{x1 \cdot x1 + 1}\\ t_5 := x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ t_6 := x1 + \left(t\_0 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(t\_2 \cdot t\_4 - \left(\left(x1 \cdot x1\right) \cdot 6 - \left(t\_4 - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \frac{t\_3}{t\_1}\right)\right) \cdot t\_1\right)\right)\right)\right)\\ \mathbf{if}\;x1 \leq -1 \cdot 10^{+144}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;x1 \leq -7.3 \cdot 10^{+84}:\\ \;\;\;\;x1 + \left(t\_0 + \left(x1 + x1 \cdot \left(x1 \cdot \left(x1 \cdot -22\right) - 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -0.00072:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;x1 \leq 0.00086:\\ \;\;\;\;x1 + \left(3 \cdot \frac{x1 - \left(t\_2 - 2 \cdot x2\right)}{t\_1} + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot -3 + 2 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{+153}:\\ \;\;\;\;t\_6\\ \mathbf{else}:\\ \;\;\;\;t\_5\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* 3.0 (* x2 -2.0)))
        (t_1 (- -1.0 (* x1 x1)))
        (t_2 (* x1 (* x1 3.0)))
        (t_3 (- (+ t_2 (* 2.0 x2)) x1))
        (t_4 (/ t_3 (+ (* x1 x1) 1.0)))
        (t_5 (+ x1 (+ x1 (* 3.0 (* x1 (+ (* x1 3.0) -1.0))))))
        (t_6
         (+
          x1
          (+
           t_0
           (+
            x1
            (+
             (* x1 (* x1 x1))
             (-
              (* t_2 t_4)
              (*
               (- (* (* x1 x1) 6.0) (* (- t_4 3.0) (* (* x1 2.0) (/ t_3 t_1))))
               t_1))))))))
   (if (<= x1 -1e+144)
     t_5
     (if (<= x1 -7.3e+84)
       (+
        x1
        (+
         t_0
         (+
          x1
          (* x1 (- (* x1 (* x1 -22.0)) (* 4.0 (* x2 (- 3.0 (* 2.0 x2)))))))))
       (if (<= x1 -0.00072)
         t_6
         (if (<= x1 0.00086)
           (+
            x1
            (+
             (* 3.0 (/ (- x1 (- t_2 (* 2.0 x2))) t_1))
             (+ x1 (* 4.0 (* x2 (+ (* x1 -3.0) (* 2.0 (* x1 x2))))))))
           (if (<= x1 2e+153) t_6 t_5)))))))

C

double code(double x1, double x2) {
	double t_0 = 3.0 * (x2 * -2.0);
	double t_1 = -1.0 - (x1 * x1);
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = (t_2 + (2.0 * x2)) - x1;
	double t_4 = t_3 / ((x1 * x1) + 1.0);
	double t_5 = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	double t_6 = x1 + (t_0 + (x1 + ((x1 * (x1 * x1)) + ((t_2 * t_4) - ((((x1 * x1) * 6.0) - ((t_4 - 3.0) * ((x1 * 2.0) * (t_3 / t_1)))) * t_1)))));
	double tmp;
	if (x1 <= -1e+144) {
		tmp = t_5;
	} else if (x1 <= -7.3e+84) {
		tmp = x1 + (t_0 + (x1 + (x1 * ((x1 * (x1 * -22.0)) - (4.0 * (x2 * (3.0 - (2.0 * x2))))))));
	} else if (x1 <= -0.00072) {
		tmp = t_6;
	} else if (x1 <= 0.00086) {
		tmp = x1 + ((3.0 * ((x1 - (t_2 - (2.0 * x2))) / t_1)) + (x1 + (4.0 * (x2 * ((x1 * -3.0) + (2.0 * (x1 * x2)))))));
	} else if (x1 <= 2e+153) {
		tmp = t_6;
	} else {
		tmp = 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) :: tmp
    t_0 = 3.0d0 * (x2 * (-2.0d0))
    t_1 = (-1.0d0) - (x1 * x1)
    t_2 = x1 * (x1 * 3.0d0)
    t_3 = (t_2 + (2.0d0 * x2)) - x1
    t_4 = t_3 / ((x1 * x1) + 1.0d0)
    t_5 = x1 + (x1 + (3.0d0 * (x1 * ((x1 * 3.0d0) + (-1.0d0)))))
    t_6 = x1 + (t_0 + (x1 + ((x1 * (x1 * x1)) + ((t_2 * t_4) - ((((x1 * x1) * 6.0d0) - ((t_4 - 3.0d0) * ((x1 * 2.0d0) * (t_3 / t_1)))) * t_1)))))
    if (x1 <= (-1d+144)) then
        tmp = t_5
    else if (x1 <= (-7.3d+84)) then
        tmp = x1 + (t_0 + (x1 + (x1 * ((x1 * (x1 * (-22.0d0))) - (4.0d0 * (x2 * (3.0d0 - (2.0d0 * x2))))))))
    else if (x1 <= (-0.00072d0)) then
        tmp = t_6
    else if (x1 <= 0.00086d0) then
        tmp = x1 + ((3.0d0 * ((x1 - (t_2 - (2.0d0 * x2))) / t_1)) + (x1 + (4.0d0 * (x2 * ((x1 * (-3.0d0)) + (2.0d0 * (x1 * x2)))))))
    else if (x1 <= 2d+153) then
        tmp = t_6
    else
        tmp = t_5
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = 3.0 * (x2 * -2.0);
	double t_1 = -1.0 - (x1 * x1);
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = (t_2 + (2.0 * x2)) - x1;
	double t_4 = t_3 / ((x1 * x1) + 1.0);
	double t_5 = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	double t_6 = x1 + (t_0 + (x1 + ((x1 * (x1 * x1)) + ((t_2 * t_4) - ((((x1 * x1) * 6.0) - ((t_4 - 3.0) * ((x1 * 2.0) * (t_3 / t_1)))) * t_1)))));
	double tmp;
	if (x1 <= -1e+144) {
		tmp = t_5;
	} else if (x1 <= -7.3e+84) {
		tmp = x1 + (t_0 + (x1 + (x1 * ((x1 * (x1 * -22.0)) - (4.0 * (x2 * (3.0 - (2.0 * x2))))))));
	} else if (x1 <= -0.00072) {
		tmp = t_6;
	} else if (x1 <= 0.00086) {
		tmp = x1 + ((3.0 * ((x1 - (t_2 - (2.0 * x2))) / t_1)) + (x1 + (4.0 * (x2 * ((x1 * -3.0) + (2.0 * (x1 * x2)))))));
	} else if (x1 <= 2e+153) {
		tmp = t_6;
	} else {
		tmp = t_5;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = 3.0 * (x2 * -2.0)
	t_1 = -1.0 - (x1 * x1)
	t_2 = x1 * (x1 * 3.0)
	t_3 = (t_2 + (2.0 * x2)) - x1
	t_4 = t_3 / ((x1 * x1) + 1.0)
	t_5 = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))))
	t_6 = x1 + (t_0 + (x1 + ((x1 * (x1 * x1)) + ((t_2 * t_4) - ((((x1 * x1) * 6.0) - ((t_4 - 3.0) * ((x1 * 2.0) * (t_3 / t_1)))) * t_1)))))
	tmp = 0
	if x1 <= -1e+144:
		tmp = t_5
	elif x1 <= -7.3e+84:
		tmp = x1 + (t_0 + (x1 + (x1 * ((x1 * (x1 * -22.0)) - (4.0 * (x2 * (3.0 - (2.0 * x2))))))))
	elif x1 <= -0.00072:
		tmp = t_6
	elif x1 <= 0.00086:
		tmp = x1 + ((3.0 * ((x1 - (t_2 - (2.0 * x2))) / t_1)) + (x1 + (4.0 * (x2 * ((x1 * -3.0) + (2.0 * (x1 * x2)))))))
	elif x1 <= 2e+153:
		tmp = t_6
	else:
		tmp = t_5
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(3.0 * Float64(x2 * -2.0))
	t_1 = Float64(-1.0 - Float64(x1 * x1))
	t_2 = Float64(x1 * Float64(x1 * 3.0))
	t_3 = Float64(Float64(t_2 + Float64(2.0 * x2)) - x1)
	t_4 = Float64(t_3 / Float64(Float64(x1 * x1) + 1.0))
	t_5 = Float64(x1 + Float64(x1 + Float64(3.0 * Float64(x1 * Float64(Float64(x1 * 3.0) + -1.0)))))
	t_6 = Float64(x1 + Float64(t_0 + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(t_2 * t_4) - Float64(Float64(Float64(Float64(x1 * x1) * 6.0) - Float64(Float64(t_4 - 3.0) * Float64(Float64(x1 * 2.0) * Float64(t_3 / t_1)))) * t_1))))))
	tmp = 0.0
	if (x1 <= -1e+144)
		tmp = t_5;
	elseif (x1 <= -7.3e+84)
		tmp = Float64(x1 + Float64(t_0 + Float64(x1 + Float64(x1 * Float64(Float64(x1 * Float64(x1 * -22.0)) - Float64(4.0 * Float64(x2 * Float64(3.0 - Float64(2.0 * x2)))))))));
	elseif (x1 <= -0.00072)
		tmp = t_6;
	elseif (x1 <= 0.00086)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(x1 - Float64(t_2 - Float64(2.0 * x2))) / t_1)) + Float64(x1 + Float64(4.0 * Float64(x2 * Float64(Float64(x1 * -3.0) + Float64(2.0 * Float64(x1 * x2))))))));
	elseif (x1 <= 2e+153)
		tmp = t_6;
	else
		tmp = t_5;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = 3.0 * (x2 * -2.0);
	t_1 = -1.0 - (x1 * x1);
	t_2 = x1 * (x1 * 3.0);
	t_3 = (t_2 + (2.0 * x2)) - x1;
	t_4 = t_3 / ((x1 * x1) + 1.0);
	t_5 = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	t_6 = x1 + (t_0 + (x1 + ((x1 * (x1 * x1)) + ((t_2 * t_4) - ((((x1 * x1) * 6.0) - ((t_4 - 3.0) * ((x1 * 2.0) * (t_3 / t_1)))) * t_1)))));
	tmp = 0.0;
	if (x1 <= -1e+144)
		tmp = t_5;
	elseif (x1 <= -7.3e+84)
		tmp = x1 + (t_0 + (x1 + (x1 * ((x1 * (x1 * -22.0)) - (4.0 * (x2 * (3.0 - (2.0 * x2))))))));
	elseif (x1 <= -0.00072)
		tmp = t_6;
	elseif (x1 <= 0.00086)
		tmp = x1 + ((3.0 * ((x1 - (t_2 - (2.0 * x2))) / t_1)) + (x1 + (4.0 * (x2 * ((x1 * -3.0) + (2.0 * (x1 * x2)))))));
	elseif (x1 <= 2e+153)
		tmp = t_6;
	else
		tmp = t_5;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(3.0 * N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t$95$2 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$3 / N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(x1 + N[(x1 + N[(3.0 * N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(x1 + N[(t$95$0 + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$2 * t$95$4), $MachinePrecision] - N[(N[(N[(N[(x1 * x1), $MachinePrecision] * 6.0), $MachinePrecision] - N[(N[(t$95$4 - 3.0), $MachinePrecision] * N[(N[(x1 * 2.0), $MachinePrecision] * N[(t$95$3 / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -1e+144], t$95$5, If[LessEqual[x1, -7.3e+84], N[(x1 + N[(t$95$0 + N[(x1 + N[(x1 * N[(N[(x1 * N[(x1 * -22.0), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(x2 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -0.00072], t$95$6, If[LessEqual[x1, 0.00086], N[(x1 + N[(N[(3.0 * N[(N[(x1 - N[(t$95$2 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(4.0 * N[(x2 * N[(N[(x1 * -3.0), $MachinePrecision] + N[(2.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 2e+153], t$95$6, t$95$5]]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -1.00000000000000002e144 or 2e153 < x1

   1. Initial program 0.0%

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

   3. Taylor expanded in x1 around 0 0.0%

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

   4. Taylor expanded in x1 around 0 60.6%

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

   5. Taylor expanded in x2 around 0 98.7%

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

   if -1.00000000000000002e144 < x1 < -7.3e84

   1. Initial program 27.3%

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

   3. Taylor expanded in x1 around 0 27.3%

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

      1. *-commutative 27.3%

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

   5. Simplified 27.3%

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

   6. Taylor expanded in x1 around 0 55.4%

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

   7. Taylor expanded in x2 around 0 73.6%

      \[\leadsto x1 + \left(\left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \color{blue}{\left(-22 \cdot x1\right)}\right) + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]
   8. Step-by-step derivation

      1. *-commutative 73.6%

         \[\leadsto x1 + \left(\left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \color{blue}{\left(x1 \cdot -22\right)}\right) + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]

   9. Simplified 73.6%

      \[\leadsto x1 + \left(\left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \color{blue}{\left(x1 \cdot -22\right)}\right) + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]

   if -7.3e84 < x1 < -7.20000000000000045e-4 or 8.59999999999999979e-4 < x1 < 2e153

   1. Initial program 97.0%

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

   3. Taylor expanded in x1 around 0 97.0%

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

      1. *-commutative 97.0%

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

   5. Simplified 97.0%

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

      1. associate-*r* 97.0%

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

      2. add-cbrt-cube 72.8%

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

      3. pow1/3 71.3%

         \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\color{blue}{{\left(\left(\left(3 \cdot \left(x1 \cdot x1\right)\right) \cdot \left(3 \cdot \left(x1 \cdot x1\right)\right)\right) \cdot \left(3 \cdot \left(x1 \cdot x1\right)\right)\right)}^{0.3333333333333333}} + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]

      4. pow3 71.3%

         \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left({\color{blue}{\left({\left(3 \cdot \left(x1 \cdot x1\right)\right)}^{3}\right)}}^{0.3333333333333333} + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]

      5. *-commutative 71.3%

         \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left({\left({\color{blue}{\left(\left(x1 \cdot x1\right) \cdot 3\right)}}^{3}\right)}^{0.3333333333333333} + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]

      6. unpow-prod-down 71.3%

         \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left({\color{blue}{\left({\left(x1 \cdot x1\right)}^{3} \cdot {3}^{3}\right)}}^{0.3333333333333333} + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]

      7. pow2 71.3%

         \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left({\left({\color{blue}{\left({x1}^{2}\right)}}^{3} \cdot {3}^{3}\right)}^{0.3333333333333333} + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]

      8. pow-pow 71.3%

         \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left({\left(\color{blue}{{x1}^{\left(2 \cdot 3\right)}} \cdot {3}^{3}\right)}^{0.3333333333333333} + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]

      9. metadata-eval 71.3%

         \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left({\left({x1}^{\color{blue}{6}} \cdot {3}^{3}\right)}^{0.3333333333333333} + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]

      10. metadata-eval 71.3%

          \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left({\left({x1}^{6} \cdot \color{blue}{27}\right)}^{0.3333333333333333} + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]

   7. Applied egg-rr 71.3%

      \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\color{blue}{{\left({x1}^{6} \cdot 27\right)}^{0.3333333333333333}} + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]
   8. Step-by-step derivation

      1. unpow1/3 72.9%

         \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\color{blue}{\sqrt[3]{{x1}^{6} \cdot 27}} + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]

   9. Simplified 72.9%

      \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\color{blue}{\sqrt[3]{{x1}^{6} \cdot 27}} + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]

   10. Taylor expanded in x1 around inf 91.2%

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

   if -7.20000000000000045e-4 < x1 < 8.59999999999999979e-4

   1. Initial program 99.4%

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

   3. Taylor expanded in x1 around 0 89.3%

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

   4. Taylor expanded in x2 around 0 99.4%

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

4. Final simplification 96.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1 \cdot 10^{+144}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -7.3 \cdot 10^{+84}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2\right) + \left(x1 + x1 \cdot \left(x1 \cdot \left(x1 \cdot -22\right) - 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -0.00072:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2\right) + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - \left(\left(x1 \cdot x1\right) \cdot 6 - \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \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)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 0.00086:\\ \;\;\;\;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 2 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2\right) + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - \left(\left(x1 \cdot x1\right) \cdot 6 - \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \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)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 94.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 3 \cdot \left(x2 \cdot -2\right)\\ t_1 := x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ t_2 := x1 \cdot \left(x1 \cdot 3\right)\\ t_3 := \left(t\_2 + 2 \cdot x2\right) - x1\\ t_4 := x1 \cdot \left(x1 \cdot x1\right)\\ t_5 := x1 \cdot x1 + 1\\ t_6 := \frac{t\_3}{t\_5}\\ \mathbf{if}\;x1 \leq -1 \cdot 10^{+144}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x1 \leq -3.4 \cdot 10^{+106}:\\ \;\;\;\;x1 + \left(t\_0 + \left(x1 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(x1 \cdot -22\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -0.6:\\ \;\;\;\;x1 + \left(t\_0 + \left(x1 + \left(t\_4 + \left(t\_5 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(t\_6 \cdot 4 - 6\right) + \left(\left(x1 \cdot 2\right) \cdot t\_6\right) \cdot \frac{2 \cdot \frac{x2}{x1} + \left(-1 - \frac{3}{x1}\right)}{x1}\right) + t\_2 \cdot \left(2 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 2.75 \cdot 10^{+16}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t\_2 - 2 \cdot x2\right) - x1}{t\_5} + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot -3 + 2 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(t\_0 + \left(x1 + \left(t\_4 + \left(t\_2 \cdot t\_6 + t\_5 \cdot \left(-6 - \left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{t\_3}{-1 - x1 \cdot x1}\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* 3.0 (* x2 -2.0)))
        (t_1 (+ x1 (+ x1 (* 3.0 (* x1 (+ (* x1 3.0) -1.0))))))
        (t_2 (* x1 (* x1 3.0)))
        (t_3 (- (+ t_2 (* 2.0 x2)) x1))
        (t_4 (* x1 (* x1 x1)))
        (t_5 (+ (* x1 x1) 1.0))
        (t_6 (/ t_3 t_5)))
   (if (<= x1 -1e+144)
     t_1
     (if (<= x1 -3.4e+106)
       (+
        x1
        (+
         t_0
         (+
          x1
          (* x1 (+ (* 4.0 (* x2 (- (* 2.0 x2) 3.0))) (* x1 (* x1 -22.0)))))))
       (if (<= x1 -0.6)
         (+
          x1
          (+
           t_0
           (+
            x1
            (+
             t_4
             (+
              (*
               t_5
               (+
                (* (* x1 x1) (- (* t_6 4.0) 6.0))
                (*
                 (* (* x1 2.0) t_6)
                 (/ (+ (* 2.0 (/ x2 x1)) (- -1.0 (/ 3.0 x1))) x1))))
              (* t_2 (* 2.0 x2)))))))
         (if (<= x1 2.75e+16)
           (+
            x1
            (+
             (* 3.0 (/ (- (- t_2 (* 2.0 x2)) x1) t_5))
             (+ x1 (* 4.0 (* x2 (+ (* x1 -3.0) (* 2.0 (* x1 x2))))))))
           (if (<= x1 2e+153)
             (+
              x1
              (+
               t_0
               (+
                x1
                (+
                 t_4
                 (+
                  (* t_2 t_6)
                  (*
                   t_5
                   (-
                    -6.0
                    (*
                     (* x1 x1)
                     (+ 6.0 (* 4.0 (/ t_3 (- -1.0 (* x1 x1)))))))))))))
             t_1)))))))

C

double code(double x1, double x2) {
	double t_0 = 3.0 * (x2 * -2.0);
	double t_1 = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = (t_2 + (2.0 * x2)) - x1;
	double t_4 = x1 * (x1 * x1);
	double t_5 = (x1 * x1) + 1.0;
	double t_6 = t_3 / t_5;
	double tmp;
	if (x1 <= -1e+144) {
		tmp = t_1;
	} else if (x1 <= -3.4e+106) {
		tmp = x1 + (t_0 + (x1 + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) + (x1 * (x1 * -22.0))))));
	} else if (x1 <= -0.6) {
		tmp = x1 + (t_0 + (x1 + (t_4 + ((t_5 * (((x1 * x1) * ((t_6 * 4.0) - 6.0)) + (((x1 * 2.0) * t_6) * (((2.0 * (x2 / x1)) + (-1.0 - (3.0 / x1))) / x1)))) + (t_2 * (2.0 * x2))))));
	} else if (x1 <= 2.75e+16) {
		tmp = x1 + ((3.0 * (((t_2 - (2.0 * x2)) - x1) / t_5)) + (x1 + (4.0 * (x2 * ((x1 * -3.0) + (2.0 * (x1 * x2)))))));
	} else if (x1 <= 2e+153) {
		tmp = x1 + (t_0 + (x1 + (t_4 + ((t_2 * t_6) + (t_5 * (-6.0 - ((x1 * x1) * (6.0 + (4.0 * (t_3 / (-1.0 - (x1 * x1))))))))))));
	} 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) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: tmp
    t_0 = 3.0d0 * (x2 * (-2.0d0))
    t_1 = x1 + (x1 + (3.0d0 * (x1 * ((x1 * 3.0d0) + (-1.0d0)))))
    t_2 = x1 * (x1 * 3.0d0)
    t_3 = (t_2 + (2.0d0 * x2)) - x1
    t_4 = x1 * (x1 * x1)
    t_5 = (x1 * x1) + 1.0d0
    t_6 = t_3 / t_5
    if (x1 <= (-1d+144)) then
        tmp = t_1
    else if (x1 <= (-3.4d+106)) then
        tmp = x1 + (t_0 + (x1 + (x1 * ((4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0))) + (x1 * (x1 * (-22.0d0)))))))
    else if (x1 <= (-0.6d0)) then
        tmp = x1 + (t_0 + (x1 + (t_4 + ((t_5 * (((x1 * x1) * ((t_6 * 4.0d0) - 6.0d0)) + (((x1 * 2.0d0) * t_6) * (((2.0d0 * (x2 / x1)) + ((-1.0d0) - (3.0d0 / x1))) / x1)))) + (t_2 * (2.0d0 * x2))))))
    else if (x1 <= 2.75d+16) then
        tmp = x1 + ((3.0d0 * (((t_2 - (2.0d0 * x2)) - x1) / t_5)) + (x1 + (4.0d0 * (x2 * ((x1 * (-3.0d0)) + (2.0d0 * (x1 * x2)))))))
    else if (x1 <= 2d+153) then
        tmp = x1 + (t_0 + (x1 + (t_4 + ((t_2 * t_6) + (t_5 * ((-6.0d0) - ((x1 * x1) * (6.0d0 + (4.0d0 * (t_3 / ((-1.0d0) - (x1 * x1))))))))))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = 3.0 * (x2 * -2.0);
	double t_1 = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = (t_2 + (2.0 * x2)) - x1;
	double t_4 = x1 * (x1 * x1);
	double t_5 = (x1 * x1) + 1.0;
	double t_6 = t_3 / t_5;
	double tmp;
	if (x1 <= -1e+144) {
		tmp = t_1;
	} else if (x1 <= -3.4e+106) {
		tmp = x1 + (t_0 + (x1 + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) + (x1 * (x1 * -22.0))))));
	} else if (x1 <= -0.6) {
		tmp = x1 + (t_0 + (x1 + (t_4 + ((t_5 * (((x1 * x1) * ((t_6 * 4.0) - 6.0)) + (((x1 * 2.0) * t_6) * (((2.0 * (x2 / x1)) + (-1.0 - (3.0 / x1))) / x1)))) + (t_2 * (2.0 * x2))))));
	} else if (x1 <= 2.75e+16) {
		tmp = x1 + ((3.0 * (((t_2 - (2.0 * x2)) - x1) / t_5)) + (x1 + (4.0 * (x2 * ((x1 * -3.0) + (2.0 * (x1 * x2)))))));
	} else if (x1 <= 2e+153) {
		tmp = x1 + (t_0 + (x1 + (t_4 + ((t_2 * t_6) + (t_5 * (-6.0 - ((x1 * x1) * (6.0 + (4.0 * (t_3 / (-1.0 - (x1 * x1))))))))))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = 3.0 * (x2 * -2.0)
	t_1 = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))))
	t_2 = x1 * (x1 * 3.0)
	t_3 = (t_2 + (2.0 * x2)) - x1
	t_4 = x1 * (x1 * x1)
	t_5 = (x1 * x1) + 1.0
	t_6 = t_3 / t_5
	tmp = 0
	if x1 <= -1e+144:
		tmp = t_1
	elif x1 <= -3.4e+106:
		tmp = x1 + (t_0 + (x1 + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) + (x1 * (x1 * -22.0))))))
	elif x1 <= -0.6:
		tmp = x1 + (t_0 + (x1 + (t_4 + ((t_5 * (((x1 * x1) * ((t_6 * 4.0) - 6.0)) + (((x1 * 2.0) * t_6) * (((2.0 * (x2 / x1)) + (-1.0 - (3.0 / x1))) / x1)))) + (t_2 * (2.0 * x2))))))
	elif x1 <= 2.75e+16:
		tmp = x1 + ((3.0 * (((t_2 - (2.0 * x2)) - x1) / t_5)) + (x1 + (4.0 * (x2 * ((x1 * -3.0) + (2.0 * (x1 * x2)))))))
	elif x1 <= 2e+153:
		tmp = x1 + (t_0 + (x1 + (t_4 + ((t_2 * t_6) + (t_5 * (-6.0 - ((x1 * x1) * (6.0 + (4.0 * (t_3 / (-1.0 - (x1 * x1))))))))))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(3.0 * Float64(x2 * -2.0))
	t_1 = Float64(x1 + Float64(x1 + Float64(3.0 * Float64(x1 * Float64(Float64(x1 * 3.0) + -1.0)))))
	t_2 = Float64(x1 * Float64(x1 * 3.0))
	t_3 = Float64(Float64(t_2 + Float64(2.0 * x2)) - x1)
	t_4 = Float64(x1 * Float64(x1 * x1))
	t_5 = Float64(Float64(x1 * x1) + 1.0)
	t_6 = Float64(t_3 / t_5)
	tmp = 0.0
	if (x1 <= -1e+144)
		tmp = t_1;
	elseif (x1 <= -3.4e+106)
		tmp = Float64(x1 + Float64(t_0 + Float64(x1 + Float64(x1 * Float64(Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0))) + Float64(x1 * Float64(x1 * -22.0)))))));
	elseif (x1 <= -0.6)
		tmp = Float64(x1 + Float64(t_0 + Float64(x1 + Float64(t_4 + Float64(Float64(t_5 * Float64(Float64(Float64(x1 * x1) * Float64(Float64(t_6 * 4.0) - 6.0)) + Float64(Float64(Float64(x1 * 2.0) * t_6) * Float64(Float64(Float64(2.0 * Float64(x2 / x1)) + Float64(-1.0 - Float64(3.0 / x1))) / x1)))) + Float64(t_2 * Float64(2.0 * x2)))))));
	elseif (x1 <= 2.75e+16)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_2 - Float64(2.0 * x2)) - x1) / t_5)) + Float64(x1 + Float64(4.0 * Float64(x2 * Float64(Float64(x1 * -3.0) + Float64(2.0 * Float64(x1 * x2))))))));
	elseif (x1 <= 2e+153)
		tmp = Float64(x1 + Float64(t_0 + Float64(x1 + Float64(t_4 + Float64(Float64(t_2 * t_6) + Float64(t_5 * Float64(-6.0 - Float64(Float64(x1 * x1) * Float64(6.0 + Float64(4.0 * Float64(t_3 / Float64(-1.0 - Float64(x1 * x1)))))))))))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = 3.0 * (x2 * -2.0);
	t_1 = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	t_2 = x1 * (x1 * 3.0);
	t_3 = (t_2 + (2.0 * x2)) - x1;
	t_4 = x1 * (x1 * x1);
	t_5 = (x1 * x1) + 1.0;
	t_6 = t_3 / t_5;
	tmp = 0.0;
	if (x1 <= -1e+144)
		tmp = t_1;
	elseif (x1 <= -3.4e+106)
		tmp = x1 + (t_0 + (x1 + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) + (x1 * (x1 * -22.0))))));
	elseif (x1 <= -0.6)
		tmp = x1 + (t_0 + (x1 + (t_4 + ((t_5 * (((x1 * x1) * ((t_6 * 4.0) - 6.0)) + (((x1 * 2.0) * t_6) * (((2.0 * (x2 / x1)) + (-1.0 - (3.0 / x1))) / x1)))) + (t_2 * (2.0 * x2))))));
	elseif (x1 <= 2.75e+16)
		tmp = x1 + ((3.0 * (((t_2 - (2.0 * x2)) - x1) / t_5)) + (x1 + (4.0 * (x2 * ((x1 * -3.0) + (2.0 * (x1 * x2)))))));
	elseif (x1 <= 2e+153)
		tmp = x1 + (t_0 + (x1 + (t_4 + ((t_2 * t_6) + (t_5 * (-6.0 - ((x1 * x1) * (6.0 + (4.0 * (t_3 / (-1.0 - (x1 * x1))))))))))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(3.0 * N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 + N[(x1 + N[(3.0 * N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t$95$2 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]}, Block[{t$95$4 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$6 = N[(t$95$3 / t$95$5), $MachinePrecision]}, If[LessEqual[x1, -1e+144], t$95$1, If[LessEqual[x1, -3.4e+106], N[(x1 + N[(t$95$0 + N[(x1 + N[(x1 * N[(N[(4.0 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(x1 * -22.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -0.6], N[(x1 + N[(t$95$0 + N[(x1 + N[(t$95$4 + N[(N[(t$95$5 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$6 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$6), $MachinePrecision] * N[(N[(N[(2.0 * N[(x2 / x1), $MachinePrecision]), $MachinePrecision] + N[(-1.0 - N[(3.0 / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$2 * N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 2.75e+16], N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$2 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$5), $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, 2e+153], N[(x1 + N[(t$95$0 + N[(x1 + N[(t$95$4 + N[(N[(t$95$2 * t$95$6), $MachinePrecision] + N[(t$95$5 * N[(-6.0 - N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 + N[(4.0 * N[(t$95$3 / N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x1 < -1.00000000000000002e144 or 2e153 < x1

   1. Initial program 0.0%

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

   3. Taylor expanded in x1 around 0 0.0%

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

   4. Taylor expanded in x1 around 0 60.6%

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

   5. Taylor expanded in x2 around 0 98.7%

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

   if -1.00000000000000002e144 < x1 < -3.39999999999999994e106

   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%

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

      1. *-commutative 0.0%

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

   5. Simplified 0.0%

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

   6. Taylor expanded in x1 around 0 75.0%

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

   7. Taylor expanded in x2 around 0 75.0%

      \[\leadsto x1 + \left(\left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \color{blue}{\left(-22 \cdot x1\right)}\right) + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]
   8. Step-by-step derivation

      1. *-commutative 75.0%

         \[\leadsto x1 + \left(\left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \color{blue}{\left(x1 \cdot -22\right)}\right) + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]

   9. Simplified 75.0%

      \[\leadsto x1 + \left(\left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \color{blue}{\left(x1 \cdot -22\right)}\right) + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]

   if -3.39999999999999994e106 < x1 < -0.599999999999999978

   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 99.3%

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

      1. *-commutative 99.3%

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

   5. Simplified 99.3%

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

   6. Taylor expanded in x1 around inf 99.3%

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

      1. associate-*r/ 99.3%

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

      2. metadata-eval 99.3%

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

   8. Simplified 99.3%

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

   9. Taylor expanded in x1 around 0 83.4%

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

   if -0.599999999999999978 < x1 < 2.75e16

   1. Initial program 99.4%

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

   3. Taylor expanded in x1 around 0 88.9%

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

   4. Taylor expanded in x2 around 0 98.7%

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

   if 2.75e16 < x1 < 2e153

   1. Initial program 95.9%

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

   3. Taylor expanded in x1 around 0 95.9%

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

      1. *-commutative 95.9%

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

   5. Simplified 95.9%

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

   6. Taylor expanded in x1 around inf 95.9%

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

      1. associate-*r/ 95.9%

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

      2. metadata-eval 95.9%

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

   8. Simplified 95.9%

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

   9. Taylor expanded in x1 around inf 90.1%

      \[\leadsto x1 + \left(\left(\left(\left(\left(\color{blue}{-6} + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]
3. Recombined 5 regimes into one program.

4. Final simplification 96.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1 \cdot 10^{+144}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -3.4 \cdot 10^{+106}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2\right) + \left(x1 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(x1 \cdot -22\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -0.6:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2\right) + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right) + \left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \frac{2 \cdot \frac{x2}{x1} + \left(-1 - \frac{3}{x1}\right)}{x1}\right) + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(2 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 2.75 \cdot 10^{+16}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot -3 + 2 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2\right) + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 \cdot x1 + 1\right) \cdot \left(-6 - \left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1}\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 93.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := 3 \cdot \left(x2 \cdot -2\right)\\ t_2 := x1 \cdot \left(x1 \cdot 3\right)\\ t_3 := \left(t\_2 + 2 \cdot x2\right) - x1\\ t_4 := x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ t_5 := x1 + \left(t\_1 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(t\_2 \cdot \frac{t\_3}{t\_0} + t\_0 \cdot \left(-6 - \left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{t\_3}{-1 - x1 \cdot x1}\right)\right)\right)\right)\right)\right)\\ \mathbf{if}\;x1 \leq -1 \cdot 10^{+144}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;x1 \leq -3.4 \cdot 10^{+106}:\\ \;\;\;\;x1 + \left(t\_1 + \left(x1 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(x1 \cdot -22\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -5.1 \cdot 10^{+14}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;x1 \leq 520000000:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t\_2 - 2 \cdot x2\right) - x1}{t\_0} + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot -3 + 2 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{+153}:\\ \;\;\;\;t\_5\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ (* x1 x1) 1.0))
        (t_1 (* 3.0 (* x2 -2.0)))
        (t_2 (* x1 (* x1 3.0)))
        (t_3 (- (+ t_2 (* 2.0 x2)) x1))
        (t_4 (+ x1 (+ x1 (* 3.0 (* x1 (+ (* x1 3.0) -1.0))))))
        (t_5
         (+
          x1
          (+
           t_1
           (+
            x1
            (+
             (* x1 (* x1 x1))
             (+
              (* t_2 (/ t_3 t_0))
              (*
               t_0
               (-
                -6.0
                (*
                 (* x1 x1)
                 (+ 6.0 (* 4.0 (/ t_3 (- -1.0 (* x1 x1)))))))))))))))
   (if (<= x1 -1e+144)
     t_4
     (if (<= x1 -3.4e+106)
       (+
        x1
        (+
         t_1
         (+
          x1
          (* x1 (+ (* 4.0 (* x2 (- (* 2.0 x2) 3.0))) (* x1 (* x1 -22.0)))))))
       (if (<= x1 -5.1e+14)
         t_5
         (if (<= x1 520000000.0)
           (+
            x1
            (+
             (* 3.0 (/ (- (- t_2 (* 2.0 x2)) x1) t_0))
             (+ x1 (* 4.0 (* x2 (+ (* x1 -3.0) (* 2.0 (* x1 x2))))))))
           (if (<= x1 2e+153) t_5 t_4)))))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = 3.0 * (x2 * -2.0);
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = (t_2 + (2.0 * x2)) - x1;
	double t_4 = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	double t_5 = x1 + (t_1 + (x1 + ((x1 * (x1 * x1)) + ((t_2 * (t_3 / t_0)) + (t_0 * (-6.0 - ((x1 * x1) * (6.0 + (4.0 * (t_3 / (-1.0 - (x1 * x1))))))))))));
	double tmp;
	if (x1 <= -1e+144) {
		tmp = t_4;
	} else if (x1 <= -3.4e+106) {
		tmp = x1 + (t_1 + (x1 + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) + (x1 * (x1 * -22.0))))));
	} else if (x1 <= -5.1e+14) {
		tmp = t_5;
	} else if (x1 <= 520000000.0) {
		tmp = x1 + ((3.0 * (((t_2 - (2.0 * x2)) - x1) / t_0)) + (x1 + (4.0 * (x2 * ((x1 * -3.0) + (2.0 * (x1 * x2)))))));
	} else if (x1 <= 2e+153) {
		tmp = t_5;
	} else {
		tmp = t_4;
	}
	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) + 1.0d0
    t_1 = 3.0d0 * (x2 * (-2.0d0))
    t_2 = x1 * (x1 * 3.0d0)
    t_3 = (t_2 + (2.0d0 * x2)) - x1
    t_4 = x1 + (x1 + (3.0d0 * (x1 * ((x1 * 3.0d0) + (-1.0d0)))))
    t_5 = x1 + (t_1 + (x1 + ((x1 * (x1 * x1)) + ((t_2 * (t_3 / t_0)) + (t_0 * ((-6.0d0) - ((x1 * x1) * (6.0d0 + (4.0d0 * (t_3 / ((-1.0d0) - (x1 * x1))))))))))))
    if (x1 <= (-1d+144)) then
        tmp = t_4
    else if (x1 <= (-3.4d+106)) then
        tmp = x1 + (t_1 + (x1 + (x1 * ((4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0))) + (x1 * (x1 * (-22.0d0)))))))
    else if (x1 <= (-5.1d+14)) then
        tmp = t_5
    else if (x1 <= 520000000.0d0) then
        tmp = x1 + ((3.0d0 * (((t_2 - (2.0d0 * x2)) - x1) / t_0)) + (x1 + (4.0d0 * (x2 * ((x1 * (-3.0d0)) + (2.0d0 * (x1 * x2)))))))
    else if (x1 <= 2d+153) then
        tmp = t_5
    else
        tmp = t_4
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = 3.0 * (x2 * -2.0);
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = (t_2 + (2.0 * x2)) - x1;
	double t_4 = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	double t_5 = x1 + (t_1 + (x1 + ((x1 * (x1 * x1)) + ((t_2 * (t_3 / t_0)) + (t_0 * (-6.0 - ((x1 * x1) * (6.0 + (4.0 * (t_3 / (-1.0 - (x1 * x1))))))))))));
	double tmp;
	if (x1 <= -1e+144) {
		tmp = t_4;
	} else if (x1 <= -3.4e+106) {
		tmp = x1 + (t_1 + (x1 + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) + (x1 * (x1 * -22.0))))));
	} else if (x1 <= -5.1e+14) {
		tmp = t_5;
	} else if (x1 <= 520000000.0) {
		tmp = x1 + ((3.0 * (((t_2 - (2.0 * x2)) - x1) / t_0)) + (x1 + (4.0 * (x2 * ((x1 * -3.0) + (2.0 * (x1 * x2)))))));
	} else if (x1 <= 2e+153) {
		tmp = t_5;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x1 * x1) + 1.0
	t_1 = 3.0 * (x2 * -2.0)
	t_2 = x1 * (x1 * 3.0)
	t_3 = (t_2 + (2.0 * x2)) - x1
	t_4 = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))))
	t_5 = x1 + (t_1 + (x1 + ((x1 * (x1 * x1)) + ((t_2 * (t_3 / t_0)) + (t_0 * (-6.0 - ((x1 * x1) * (6.0 + (4.0 * (t_3 / (-1.0 - (x1 * x1))))))))))))
	tmp = 0
	if x1 <= -1e+144:
		tmp = t_4
	elif x1 <= -3.4e+106:
		tmp = x1 + (t_1 + (x1 + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) + (x1 * (x1 * -22.0))))))
	elif x1 <= -5.1e+14:
		tmp = t_5
	elif x1 <= 520000000.0:
		tmp = x1 + ((3.0 * (((t_2 - (2.0 * x2)) - x1) / t_0)) + (x1 + (4.0 * (x2 * ((x1 * -3.0) + (2.0 * (x1 * x2)))))))
	elif x1 <= 2e+153:
		tmp = t_5
	else:
		tmp = t_4
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * x1) + 1.0)
	t_1 = Float64(3.0 * Float64(x2 * -2.0))
	t_2 = Float64(x1 * Float64(x1 * 3.0))
	t_3 = Float64(Float64(t_2 + Float64(2.0 * x2)) - x1)
	t_4 = Float64(x1 + Float64(x1 + Float64(3.0 * Float64(x1 * Float64(Float64(x1 * 3.0) + -1.0)))))
	t_5 = Float64(x1 + Float64(t_1 + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(t_2 * Float64(t_3 / t_0)) + Float64(t_0 * Float64(-6.0 - Float64(Float64(x1 * x1) * Float64(6.0 + Float64(4.0 * Float64(t_3 / Float64(-1.0 - Float64(x1 * x1)))))))))))))
	tmp = 0.0
	if (x1 <= -1e+144)
		tmp = t_4;
	elseif (x1 <= -3.4e+106)
		tmp = Float64(x1 + Float64(t_1 + Float64(x1 + Float64(x1 * Float64(Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0))) + Float64(x1 * Float64(x1 * -22.0)))))));
	elseif (x1 <= -5.1e+14)
		tmp = t_5;
	elseif (x1 <= 520000000.0)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_2 - Float64(2.0 * x2)) - x1) / t_0)) + Float64(x1 + Float64(4.0 * Float64(x2 * Float64(Float64(x1 * -3.0) + Float64(2.0 * Float64(x1 * x2))))))));
	elseif (x1 <= 2e+153)
		tmp = t_5;
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x1 * x1) + 1.0;
	t_1 = 3.0 * (x2 * -2.0);
	t_2 = x1 * (x1 * 3.0);
	t_3 = (t_2 + (2.0 * x2)) - x1;
	t_4 = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	t_5 = x1 + (t_1 + (x1 + ((x1 * (x1 * x1)) + ((t_2 * (t_3 / t_0)) + (t_0 * (-6.0 - ((x1 * x1) * (6.0 + (4.0 * (t_3 / (-1.0 - (x1 * x1))))))))))));
	tmp = 0.0;
	if (x1 <= -1e+144)
		tmp = t_4;
	elseif (x1 <= -3.4e+106)
		tmp = x1 + (t_1 + (x1 + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) + (x1 * (x1 * -22.0))))));
	elseif (x1 <= -5.1e+14)
		tmp = t_5;
	elseif (x1 <= 520000000.0)
		tmp = x1 + ((3.0 * (((t_2 - (2.0 * x2)) - x1) / t_0)) + (x1 + (4.0 * (x2 * ((x1 * -3.0) + (2.0 * (x1 * x2)))))));
	elseif (x1 <= 2e+153)
		tmp = t_5;
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$1 = N[(3.0 * N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t$95$2 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]}, Block[{t$95$4 = N[(x1 + N[(x1 + N[(3.0 * N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(x1 + N[(t$95$1 + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$2 * N[(t$95$3 / t$95$0), $MachinePrecision]), $MachinePrecision] + N[(t$95$0 * N[(-6.0 - N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 + N[(4.0 * N[(t$95$3 / N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -1e+144], t$95$4, If[LessEqual[x1, -3.4e+106], N[(x1 + N[(t$95$1 + N[(x1 + N[(x1 * N[(N[(4.0 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(x1 * -22.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -5.1e+14], t$95$5, If[LessEqual[x1, 520000000.0], N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$2 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $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, 2e+153], t$95$5, t$95$4]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -1.00000000000000002e144 or 2e153 < x1

   1. Initial program 0.0%

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

   3. Taylor expanded in x1 around 0 0.0%

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

   4. Taylor expanded in x1 around 0 60.6%

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

   5. Taylor expanded in x2 around 0 98.7%

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

   if -1.00000000000000002e144 < x1 < -3.39999999999999994e106

   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%

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

      1. *-commutative 0.0%

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

   5. Simplified 0.0%

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

   6. Taylor expanded in x1 around 0 75.0%

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

   7. Taylor expanded in x2 around 0 75.0%

      \[\leadsto x1 + \left(\left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \color{blue}{\left(-22 \cdot x1\right)}\right) + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]
   8. Step-by-step derivation

      1. *-commutative 75.0%

         \[\leadsto x1 + \left(\left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \color{blue}{\left(x1 \cdot -22\right)}\right) + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]

   9. Simplified 75.0%

      \[\leadsto x1 + \left(\left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \color{blue}{\left(x1 \cdot -22\right)}\right) + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]

   if -3.39999999999999994e106 < x1 < -5.1e14 or 5.2e8 < x1 < 2e153

   1. Initial program 96.9%

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

   3. Taylor expanded in x1 around 0 96.9%

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

      1. *-commutative 96.9%

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

   5. Simplified 96.9%

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

   6. Taylor expanded in x1 around inf 97.0%

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

      1. associate-*r/ 97.0%

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

      2. metadata-eval 97.0%

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

   8. Simplified 97.0%

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

   9. Taylor expanded in x1 around inf 85.6%

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

   if -5.1e14 < x1 < 5.2e8

   1. Initial program 99.4%

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

   3. Taylor expanded in x1 around 0 88.3%

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

   4. Taylor expanded in x2 around 0 98.1%

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

4. Final simplification 95.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1 \cdot 10^{+144}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -3.4 \cdot 10^{+106}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2\right) + \left(x1 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(x1 \cdot -22\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -5.1 \cdot 10^{+14}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2\right) + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 \cdot x1 + 1\right) \cdot \left(-6 - \left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1}\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 520000000:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot -3 + 2 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2\right) + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 \cdot x1 + 1\right) \cdot \left(-6 - \left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1}\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 77.1% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 3 \cdot \left(x2 \cdot -2\right)\\ t_1 := x2 \cdot \left(2 \cdot x2 - 3\right)\\ \mathbf{if}\;x1 \leq -1 \cdot 10^{+144}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -5.1 \cdot 10^{+14}:\\ \;\;\;\;x1 + \left(t\_0 + \left(x1 + x1 \cdot \left(4 \cdot t\_1 + x1 \cdot \left(x1 \cdot -22\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -6.5 \cdot 10^{-285}:\\ \;\;\;\;x1 + \left(\left(x1 + 4 \cdot \left(x1 \cdot t\_1\right)\right) + 3 \cdot \left(x2 \cdot -2 - x1\right)\right)\\ \mathbf{elif}\;x1 \leq 2.3 \cdot 10^{-239}:\\ \;\;\;\;x1 + \left(t\_0 + \left(x1 - x2 \cdot \left(x1 \cdot \left(12 - x1 \cdot 6\right) - \left(x1 \cdot x2\right) \cdot 8\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 2.45 \cdot 10^{+144}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(\left(3 \cdot \left(x1 \cdot \left(3 - x2 \cdot -2\right)\right) - 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right) - 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 - 2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* 3.0 (* x2 -2.0))) (t_1 (* x2 (- (* 2.0 x2) 3.0))))
   (if (<= x1 -1e+144)
     (+ x1 (+ x1 (* 3.0 (* x1 (+ (* x1 3.0) -1.0)))))
     (if (<= x1 -5.1e+14)
       (+ x1 (+ t_0 (+ x1 (* x1 (+ (* 4.0 t_1) (* x1 (* x1 -22.0)))))))
       (if (<= x1 -6.5e-285)
         (+ x1 (+ (+ x1 (* 4.0 (* x1 t_1))) (* 3.0 (- (* x2 -2.0) x1))))
         (if (<= x1 2.3e-239)
           (+
            x1
            (+
             t_0
             (- x1 (* x2 (- (* x1 (- 12.0 (* x1 6.0))) (* (* x1 x2) 8.0))))))
           (if (<= x1 2.45e+144)
             (+
              x1
              (+
               (* x2 -6.0)
               (*
                x1
                (-
                 (-
                  (* 3.0 (* x1 (- 3.0 (* x2 -2.0))))
                  (* 4.0 (* x2 (- 3.0 (* 2.0 x2)))))
                 2.0))))
             (+ x1 (+ (* x2 -6.0) (* x1 (- (* x1 9.0) 2.0)))))))))))

C

double code(double x1, double x2) {
	double t_0 = 3.0 * (x2 * -2.0);
	double t_1 = x2 * ((2.0 * x2) - 3.0);
	double tmp;
	if (x1 <= -1e+144) {
		tmp = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	} else if (x1 <= -5.1e+14) {
		tmp = x1 + (t_0 + (x1 + (x1 * ((4.0 * t_1) + (x1 * (x1 * -22.0))))));
	} else if (x1 <= -6.5e-285) {
		tmp = x1 + ((x1 + (4.0 * (x1 * t_1))) + (3.0 * ((x2 * -2.0) - x1)));
	} else if (x1 <= 2.3e-239) {
		tmp = x1 + (t_0 + (x1 - (x2 * ((x1 * (12.0 - (x1 * 6.0))) - ((x1 * x2) * 8.0)))));
	} else if (x1 <= 2.45e+144) {
		tmp = x1 + ((x2 * -6.0) + (x1 * (((3.0 * (x1 * (3.0 - (x2 * -2.0)))) - (4.0 * (x2 * (3.0 - (2.0 * x2))))) - 2.0)));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) - 2.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = 3.0d0 * (x2 * (-2.0d0))
    t_1 = x2 * ((2.0d0 * x2) - 3.0d0)
    if (x1 <= (-1d+144)) then
        tmp = x1 + (x1 + (3.0d0 * (x1 * ((x1 * 3.0d0) + (-1.0d0)))))
    else if (x1 <= (-5.1d+14)) then
        tmp = x1 + (t_0 + (x1 + (x1 * ((4.0d0 * t_1) + (x1 * (x1 * (-22.0d0)))))))
    else if (x1 <= (-6.5d-285)) then
        tmp = x1 + ((x1 + (4.0d0 * (x1 * t_1))) + (3.0d0 * ((x2 * (-2.0d0)) - x1)))
    else if (x1 <= 2.3d-239) then
        tmp = x1 + (t_0 + (x1 - (x2 * ((x1 * (12.0d0 - (x1 * 6.0d0))) - ((x1 * x2) * 8.0d0)))))
    else if (x1 <= 2.45d+144) then
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * (((3.0d0 * (x1 * (3.0d0 - (x2 * (-2.0d0))))) - (4.0d0 * (x2 * (3.0d0 - (2.0d0 * x2))))) - 2.0d0)))
    else
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * ((x1 * 9.0d0) - 2.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = 3.0 * (x2 * -2.0);
	double t_1 = x2 * ((2.0 * x2) - 3.0);
	double tmp;
	if (x1 <= -1e+144) {
		tmp = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	} else if (x1 <= -5.1e+14) {
		tmp = x1 + (t_0 + (x1 + (x1 * ((4.0 * t_1) + (x1 * (x1 * -22.0))))));
	} else if (x1 <= -6.5e-285) {
		tmp = x1 + ((x1 + (4.0 * (x1 * t_1))) + (3.0 * ((x2 * -2.0) - x1)));
	} else if (x1 <= 2.3e-239) {
		tmp = x1 + (t_0 + (x1 - (x2 * ((x1 * (12.0 - (x1 * 6.0))) - ((x1 * x2) * 8.0)))));
	} else if (x1 <= 2.45e+144) {
		tmp = x1 + ((x2 * -6.0) + (x1 * (((3.0 * (x1 * (3.0 - (x2 * -2.0)))) - (4.0 * (x2 * (3.0 - (2.0 * x2))))) - 2.0)));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) - 2.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = 3.0 * (x2 * -2.0)
	t_1 = x2 * ((2.0 * x2) - 3.0)
	tmp = 0
	if x1 <= -1e+144:
		tmp = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))))
	elif x1 <= -5.1e+14:
		tmp = x1 + (t_0 + (x1 + (x1 * ((4.0 * t_1) + (x1 * (x1 * -22.0))))))
	elif x1 <= -6.5e-285:
		tmp = x1 + ((x1 + (4.0 * (x1 * t_1))) + (3.0 * ((x2 * -2.0) - x1)))
	elif x1 <= 2.3e-239:
		tmp = x1 + (t_0 + (x1 - (x2 * ((x1 * (12.0 - (x1 * 6.0))) - ((x1 * x2) * 8.0)))))
	elif x1 <= 2.45e+144:
		tmp = x1 + ((x2 * -6.0) + (x1 * (((3.0 * (x1 * (3.0 - (x2 * -2.0)))) - (4.0 * (x2 * (3.0 - (2.0 * x2))))) - 2.0)))
	else:
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) - 2.0)))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(3.0 * Float64(x2 * -2.0))
	t_1 = Float64(x2 * Float64(Float64(2.0 * x2) - 3.0))
	tmp = 0.0
	if (x1 <= -1e+144)
		tmp = Float64(x1 + Float64(x1 + Float64(3.0 * Float64(x1 * Float64(Float64(x1 * 3.0) + -1.0)))));
	elseif (x1 <= -5.1e+14)
		tmp = Float64(x1 + Float64(t_0 + Float64(x1 + Float64(x1 * Float64(Float64(4.0 * t_1) + Float64(x1 * Float64(x1 * -22.0)))))));
	elseif (x1 <= -6.5e-285)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(4.0 * Float64(x1 * t_1))) + Float64(3.0 * Float64(Float64(x2 * -2.0) - x1))));
	elseif (x1 <= 2.3e-239)
		tmp = Float64(x1 + Float64(t_0 + Float64(x1 - Float64(x2 * Float64(Float64(x1 * Float64(12.0 - Float64(x1 * 6.0))) - Float64(Float64(x1 * x2) * 8.0))))));
	elseif (x1 <= 2.45e+144)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(Float64(3.0 * Float64(x1 * Float64(3.0 - Float64(x2 * -2.0)))) - Float64(4.0 * Float64(x2 * Float64(3.0 - Float64(2.0 * x2))))) - 2.0))));
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(x1 * 9.0) - 2.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = 3.0 * (x2 * -2.0);
	t_1 = x2 * ((2.0 * x2) - 3.0);
	tmp = 0.0;
	if (x1 <= -1e+144)
		tmp = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	elseif (x1 <= -5.1e+14)
		tmp = x1 + (t_0 + (x1 + (x1 * ((4.0 * t_1) + (x1 * (x1 * -22.0))))));
	elseif (x1 <= -6.5e-285)
		tmp = x1 + ((x1 + (4.0 * (x1 * t_1))) + (3.0 * ((x2 * -2.0) - x1)));
	elseif (x1 <= 2.3e-239)
		tmp = x1 + (t_0 + (x1 - (x2 * ((x1 * (12.0 - (x1 * 6.0))) - ((x1 * x2) * 8.0)))));
	elseif (x1 <= 2.45e+144)
		tmp = x1 + ((x2 * -6.0) + (x1 * (((3.0 * (x1 * (3.0 - (x2 * -2.0)))) - (4.0 * (x2 * (3.0 - (2.0 * x2))))) - 2.0)));
	else
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) - 2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(3.0 * N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -1e+144], N[(x1 + N[(x1 + N[(3.0 * N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -5.1e+14], N[(x1 + N[(t$95$0 + N[(x1 + N[(x1 * N[(N[(4.0 * t$95$1), $MachinePrecision] + N[(x1 * N[(x1 * -22.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -6.5e-285], N[(x1 + N[(N[(x1 + N[(4.0 * N[(x1 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 2.3e-239], N[(x1 + N[(t$95$0 + N[(x1 - N[(x2 * N[(N[(x1 * N[(12.0 - N[(x1 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x1 * x2), $MachinePrecision] * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 2.45e+144], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(N[(3.0 * N[(x1 * N[(3.0 - N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(x2 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if x1 < -1.00000000000000002e144

   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 43.9%

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

   5. Taylor expanded in x2 around 0 97.8%

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

   if -1.00000000000000002e144 < x1 < -5.1e14

   1. Initial program 61.4%

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

   3. Taylor expanded in x1 around 0 61.4%

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

      1. *-commutative 61.4%

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

   5. Simplified 61.4%

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

   6. Taylor expanded in x1 around 0 30.9%

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

   7. Taylor expanded in x2 around 0 50.8%

      \[\leadsto x1 + \left(\left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \color{blue}{\left(-22 \cdot x1\right)}\right) + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]
   8. Step-by-step derivation

      1. *-commutative 50.8%

         \[\leadsto x1 + \left(\left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \color{blue}{\left(x1 \cdot -22\right)}\right) + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]

   9. Simplified 50.8%

      \[\leadsto x1 + \left(\left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \color{blue}{\left(x1 \cdot -22\right)}\right) + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]

   if -5.1e14 < x1 < -6.5e-285

   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 93.7%

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

   4. Taylor expanded in x1 around 0 93.7%

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

      1. mul-1-neg 93.7%

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

      2. unsub-neg 93.7%

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

      3. *-commutative 93.7%

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

   6. Simplified 93.7%

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

   if -6.5e-285 < x1 < 2.2999999999999999e-239

   1. Initial program 99.8%

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

   3. Taylor expanded in x1 around 0 98.7%

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

      1. *-commutative 98.7%

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

   5. Simplified 98.7%

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

   6. Taylor expanded in x1 around 0 50.5%

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

   7. Taylor expanded in x2 around 0 98.7%

      \[\leadsto x1 + \left(\left(\color{blue}{x2 \cdot \left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(6 \cdot x1 - 12\right)\right)} + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]

   if 2.2999999999999999e-239 < x1 < 2.45e144

   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 0 69.0%

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

   4. Taylor expanded in x1 around 0 69.0%

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

   5. Taylor expanded in x1 around 0 70.6%

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

   if 2.45e144 < x1

   1. Initial program 3.2%

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

   3. Taylor expanded in x1 around 0 0.2%

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

   4. Taylor expanded in x1 around 0 80.6%

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

   5. Taylor expanded in x1 around 0 80.6%

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

   6. Taylor expanded in x2 around 0 97.1%

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

      1. *-commutative 97.1%

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

   8. Simplified 97.1%

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

4. Final simplification 84.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1 \cdot 10^{+144}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -5.1 \cdot 10^{+14}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2\right) + \left(x1 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(x1 \cdot -22\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -6.5 \cdot 10^{-285}:\\ \;\;\;\;x1 + \left(\left(x1 + 4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right) + 3 \cdot \left(x2 \cdot -2 - x1\right)\right)\\ \mathbf{elif}\;x1 \leq 2.3 \cdot 10^{-239}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2\right) + \left(x1 - x2 \cdot \left(x1 \cdot \left(12 - x1 \cdot 6\right) - \left(x1 \cdot x2\right) \cdot 8\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 2.45 \cdot 10^{+144}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(\left(3 \cdot \left(x1 \cdot \left(3 - x2 \cdot -2\right)\right) - 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right) - 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 - 2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 82.5% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x2 \cdot \left(3 - 2 \cdot x2\right)\\ \mathbf{if}\;x1 \leq -1 \cdot 10^{+144}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -3.8 \cdot 10^{-12}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2\right) + \left(x1 + x1 \cdot \left(x1 \cdot \left(x1 \cdot -22\right) - 4 \cdot t\_0\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 10^{-113}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right)}{-1 - x1 \cdot x1} + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot -3 + 2 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 - 4 \cdot \left(x1 \cdot t\_0\right)\right) + 3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(-1 - x1 \cdot \left(x2 \cdot -2 - \left(x1 + 3\right)\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x2 (- 3.0 (* 2.0 x2)))))
   (if (<= x1 -1e+144)
     (+ x1 (+ x1 (* 3.0 (* x1 (+ (* x1 3.0) -1.0)))))
     (if (<= x1 -3.8e-12)
       (+
        x1
        (+
         (* 3.0 (* x2 -2.0))
         (+ x1 (* x1 (- (* x1 (* x1 -22.0)) (* 4.0 t_0))))))
       (if (<= x1 1e-113)
         (+
          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
          (+
           (- x1 (* 4.0 (* x1 t_0)))
           (*
            3.0
            (+
             (* x2 -2.0)
             (* x1 (- -1.0 (* x1 (- (* x2 -2.0) (+ x1 3.0))))))))))))))

C

double code(double x1, double x2) {
	double t_0 = x2 * (3.0 - (2.0 * x2));
	double tmp;
	if (x1 <= -1e+144) {
		tmp = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	} else if (x1 <= -3.8e-12) {
		tmp = x1 + ((3.0 * (x2 * -2.0)) + (x1 + (x1 * ((x1 * (x1 * -22.0)) - (4.0 * t_0)))));
	} else if (x1 <= 1e-113) {
		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 + ((x1 - (4.0 * (x1 * t_0))) + (3.0 * ((x2 * -2.0) + (x1 * (-1.0 - (x1 * ((x2 * -2.0) - (x1 + 3.0))))))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x2 * (3.0d0 - (2.0d0 * x2))
    if (x1 <= (-1d+144)) then
        tmp = x1 + (x1 + (3.0d0 * (x1 * ((x1 * 3.0d0) + (-1.0d0)))))
    else if (x1 <= (-3.8d-12)) then
        tmp = x1 + ((3.0d0 * (x2 * (-2.0d0))) + (x1 + (x1 * ((x1 * (x1 * (-22.0d0))) - (4.0d0 * t_0)))))
    else if (x1 <= 1d-113) 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 + ((x1 - (4.0d0 * (x1 * t_0))) + (3.0d0 * ((x2 * (-2.0d0)) + (x1 * ((-1.0d0) - (x1 * ((x2 * (-2.0d0)) - (x1 + 3.0d0))))))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x2 * (3.0 - (2.0 * x2));
	double tmp;
	if (x1 <= -1e+144) {
		tmp = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	} else if (x1 <= -3.8e-12) {
		tmp = x1 + ((3.0 * (x2 * -2.0)) + (x1 + (x1 * ((x1 * (x1 * -22.0)) - (4.0 * t_0)))));
	} else if (x1 <= 1e-113) {
		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 + ((x1 - (4.0 * (x1 * t_0))) + (3.0 * ((x2 * -2.0) + (x1 * (-1.0 - (x1 * ((x2 * -2.0) - (x1 + 3.0))))))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x2 * (3.0 - (2.0 * x2))
	tmp = 0
	if x1 <= -1e+144:
		tmp = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))))
	elif x1 <= -3.8e-12:
		tmp = x1 + ((3.0 * (x2 * -2.0)) + (x1 + (x1 * ((x1 * (x1 * -22.0)) - (4.0 * t_0)))))
	elif x1 <= 1e-113:
		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 + ((x1 - (4.0 * (x1 * t_0))) + (3.0 * ((x2 * -2.0) + (x1 * (-1.0 - (x1 * ((x2 * -2.0) - (x1 + 3.0))))))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x2 * Float64(3.0 - Float64(2.0 * x2)))
	tmp = 0.0
	if (x1 <= -1e+144)
		tmp = Float64(x1 + Float64(x1 + Float64(3.0 * Float64(x1 * Float64(Float64(x1 * 3.0) + -1.0)))));
	elseif (x1 <= -3.8e-12)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(x2 * -2.0)) + Float64(x1 + Float64(x1 * Float64(Float64(x1 * Float64(x1 * -22.0)) - Float64(4.0 * t_0))))));
	elseif (x1 <= 1e-113)
		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(x1 - Float64(4.0 * Float64(x1 * t_0))) + Float64(3.0 * Float64(Float64(x2 * -2.0) + Float64(x1 * Float64(-1.0 - Float64(x1 * Float64(Float64(x2 * -2.0) - Float64(x1 + 3.0)))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x2 * (3.0 - (2.0 * x2));
	tmp = 0.0;
	if (x1 <= -1e+144)
		tmp = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	elseif (x1 <= -3.8e-12)
		tmp = x1 + ((3.0 * (x2 * -2.0)) + (x1 + (x1 * ((x1 * (x1 * -22.0)) - (4.0 * t_0)))));
	elseif (x1 <= 1e-113)
		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 + ((x1 - (4.0 * (x1 * t_0))) + (3.0 * ((x2 * -2.0) + (x1 * (-1.0 - (x1 * ((x2 * -2.0) - (x1 + 3.0))))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x2 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -1e+144], N[(x1 + N[(x1 + N[(3.0 * N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -3.8e-12], N[(x1 + N[(N[(3.0 * N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(x1 * N[(N[(x1 * N[(x1 * -22.0), $MachinePrecision]), $MachinePrecision] - N[(4.0 * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1e-113], 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[(x1 - N[(4.0 * N[(x1 * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] + N[(x1 * N[(-1.0 - N[(x1 * N[(N[(x2 * -2.0), $MachinePrecision] - N[(x1 + 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -1.00000000000000002e144

   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 43.9%

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

   5. Taylor expanded in x2 around 0 97.8%

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

   if -1.00000000000000002e144 < x1 < -3.79999999999999996e-12

   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 68.8%

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

      1. *-commutative 68.8%

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

   5. Simplified 68.8%

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

   6. Taylor expanded in x1 around 0 28.8%

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

   7. Taylor expanded in x2 around 0 56.8%

      \[\leadsto x1 + \left(\left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \color{blue}{\left(-22 \cdot x1\right)}\right) + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]
   8. Step-by-step derivation

      1. *-commutative 56.8%

         \[\leadsto x1 + \left(\left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \color{blue}{\left(x1 \cdot -22\right)}\right) + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]

   9. Simplified 56.8%

      \[\leadsto x1 + \left(\left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \color{blue}{\left(x1 \cdot -22\right)}\right) + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]

   if -3.79999999999999996e-12 < x1 < 9.99999999999999979e-114

   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 86.5%

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

   4. Taylor expanded in x2 around 0 99.5%

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

   if 9.99999999999999979e-114 < x1

   1. Initial program 63.5%

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

   3. Taylor expanded in x1 around 0 38.5%

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

   4. Taylor expanded in x1 around 0 76.9%

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

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1 \cdot 10^{+144}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -3.8 \cdot 10^{-12}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2\right) + \left(x1 + x1 \cdot \left(x1 \cdot \left(x1 \cdot -22\right) - 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 10^{-113}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right)}{-1 - x1 \cdot x1} + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot -3 + 2 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 - 4 \cdot \left(x1 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right) + 3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(-1 - x1 \cdot \left(x2 \cdot -2 - \left(x1 + 3\right)\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 77.0% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 + \left(x2 \cdot -6 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x2 \cdot \left(x1 \cdot 6 + 9 \cdot \frac{x1}{x2}\right)\right) - 2\right)\right)\\ \mathbf{if}\;x1 \leq -4 \cdot 10^{+142}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -4.1 \cdot 10^{-285}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x1 \leq 3.6 \cdot 10^{-240}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2\right) + \left(x1 - x2 \cdot \left(x1 \cdot \left(12 - x1 \cdot 6\right) - \left(x1 \cdot x2\right) \cdot 8\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 2.45 \cdot 10^{+144}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 - 2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0
         (+
          x1
          (+
           (* x2 -6.0)
           (*
            x1
            (-
             (+
              (* 4.0 (* x2 (- (* 2.0 x2) 3.0)))
              (* x2 (+ (* x1 6.0) (* 9.0 (/ x1 x2)))))
             2.0))))))
   (if (<= x1 -4e+142)
     (+ x1 (+ x1 (* 3.0 (* x1 (+ (* x1 3.0) -1.0)))))
     (if (<= x1 -4.1e-285)
       t_0
       (if (<= x1 3.6e-240)
         (+
          x1
          (+
           (* 3.0 (* x2 -2.0))
           (- x1 (* x2 (- (* x1 (- 12.0 (* x1 6.0))) (* (* x1 x2) 8.0))))))
         (if (<= x1 2.45e+144)
           t_0
           (+ x1 (+ (* x2 -6.0) (* x1 (- (* x1 9.0) 2.0))))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 + ((x2 * -6.0) + (x1 * (((4.0 * (x2 * ((2.0 * x2) - 3.0))) + (x2 * ((x1 * 6.0) + (9.0 * (x1 / x2))))) - 2.0)));
	double tmp;
	if (x1 <= -4e+142) {
		tmp = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	} else if (x1 <= -4.1e-285) {
		tmp = t_0;
	} else if (x1 <= 3.6e-240) {
		tmp = x1 + ((3.0 * (x2 * -2.0)) + (x1 - (x2 * ((x1 * (12.0 - (x1 * 6.0))) - ((x1 * x2) * 8.0)))));
	} else if (x1 <= 2.45e+144) {
		tmp = t_0;
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) - 2.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x1 + ((x2 * (-6.0d0)) + (x1 * (((4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0))) + (x2 * ((x1 * 6.0d0) + (9.0d0 * (x1 / x2))))) - 2.0d0)))
    if (x1 <= (-4d+142)) then
        tmp = x1 + (x1 + (3.0d0 * (x1 * ((x1 * 3.0d0) + (-1.0d0)))))
    else if (x1 <= (-4.1d-285)) then
        tmp = t_0
    else if (x1 <= 3.6d-240) then
        tmp = x1 + ((3.0d0 * (x2 * (-2.0d0))) + (x1 - (x2 * ((x1 * (12.0d0 - (x1 * 6.0d0))) - ((x1 * x2) * 8.0d0)))))
    else if (x1 <= 2.45d+144) then
        tmp = t_0
    else
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * ((x1 * 9.0d0) - 2.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 + ((x2 * -6.0) + (x1 * (((4.0 * (x2 * ((2.0 * x2) - 3.0))) + (x2 * ((x1 * 6.0) + (9.0 * (x1 / x2))))) - 2.0)));
	double tmp;
	if (x1 <= -4e+142) {
		tmp = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	} else if (x1 <= -4.1e-285) {
		tmp = t_0;
	} else if (x1 <= 3.6e-240) {
		tmp = x1 + ((3.0 * (x2 * -2.0)) + (x1 - (x2 * ((x1 * (12.0 - (x1 * 6.0))) - ((x1 * x2) * 8.0)))));
	} else if (x1 <= 2.45e+144) {
		tmp = t_0;
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) - 2.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 + ((x2 * -6.0) + (x1 * (((4.0 * (x2 * ((2.0 * x2) - 3.0))) + (x2 * ((x1 * 6.0) + (9.0 * (x1 / x2))))) - 2.0)))
	tmp = 0
	if x1 <= -4e+142:
		tmp = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))))
	elif x1 <= -4.1e-285:
		tmp = t_0
	elif x1 <= 3.6e-240:
		tmp = x1 + ((3.0 * (x2 * -2.0)) + (x1 - (x2 * ((x1 * (12.0 - (x1 * 6.0))) - ((x1 * x2) * 8.0)))))
	elif x1 <= 2.45e+144:
		tmp = t_0
	else:
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) - 2.0)))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0))) + Float64(x2 * Float64(Float64(x1 * 6.0) + Float64(9.0 * Float64(x1 / x2))))) - 2.0))))
	tmp = 0.0
	if (x1 <= -4e+142)
		tmp = Float64(x1 + Float64(x1 + Float64(3.0 * Float64(x1 * Float64(Float64(x1 * 3.0) + -1.0)))));
	elseif (x1 <= -4.1e-285)
		tmp = t_0;
	elseif (x1 <= 3.6e-240)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(x2 * -2.0)) + Float64(x1 - Float64(x2 * Float64(Float64(x1 * Float64(12.0 - Float64(x1 * 6.0))) - Float64(Float64(x1 * x2) * 8.0))))));
	elseif (x1 <= 2.45e+144)
		tmp = t_0;
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(x1 * 9.0) - 2.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 + ((x2 * -6.0) + (x1 * (((4.0 * (x2 * ((2.0 * x2) - 3.0))) + (x2 * ((x1 * 6.0) + (9.0 * (x1 / x2))))) - 2.0)));
	tmp = 0.0;
	if (x1 <= -4e+142)
		tmp = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	elseif (x1 <= -4.1e-285)
		tmp = t_0;
	elseif (x1 <= 3.6e-240)
		tmp = x1 + ((3.0 * (x2 * -2.0)) + (x1 - (x2 * ((x1 * (12.0 - (x1 * 6.0))) - ((x1 * x2) * 8.0)))));
	elseif (x1 <= 2.45e+144)
		tmp = t_0;
	else
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) - 2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(N[(4.0 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x2 * N[(N[(x1 * 6.0), $MachinePrecision] + N[(9.0 * N[(x1 / x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -4e+142], N[(x1 + N[(x1 + N[(3.0 * N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -4.1e-285], t$95$0, If[LessEqual[x1, 3.6e-240], N[(x1 + N[(N[(3.0 * N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision] + N[(x1 - N[(x2 * N[(N[(x1 * N[(12.0 - N[(x1 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x1 * x2), $MachinePrecision] * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 2.45e+144], t$95$0, N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -4.0000000000000002e142

   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 42.9%

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

   5. Taylor expanded in x2 around 0 95.7%

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

   if -4.0000000000000002e142 < x1 < -4.1e-285 or 3.5999999999999999e-240 < x1 < 2.45e144

   1. Initial program 94.6%

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

   3. Taylor expanded in x1 around 0 73.2%

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

   4. Taylor expanded in x1 around 0 73.5%

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

   5. Taylor expanded in x1 around 0 75.1%

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

   6. Taylor expanded in x2 around inf 76.2%

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

   if -4.1e-285 < x1 < 3.5999999999999999e-240

   1. Initial program 99.8%

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

   3. Taylor expanded in x1 around 0 98.7%

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

      1. *-commutative 98.7%

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

   5. Simplified 98.7%

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

   6. Taylor expanded in x1 around 0 50.5%

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

   7. Taylor expanded in x2 around 0 98.7%

      \[\leadsto x1 + \left(\left(\color{blue}{x2 \cdot \left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(6 \cdot x1 - 12\right)\right)} + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]

   if 2.45e144 < x1

   1. Initial program 3.2%

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

   3. Taylor expanded in x1 around 0 0.2%

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

   4. Taylor expanded in x1 around 0 80.6%

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

   5. Taylor expanded in x1 around 0 80.6%

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

   6. Taylor expanded in x2 around 0 97.1%

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

      1. *-commutative 97.1%

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

   8. Simplified 97.1%

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

4. Final simplification 83.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4 \cdot 10^{+142}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -4.1 \cdot 10^{-285}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x2 \cdot \left(x1 \cdot 6 + 9 \cdot \frac{x1}{x2}\right)\right) - 2\right)\right)\\ \mathbf{elif}\;x1 \leq 3.6 \cdot 10^{-240}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2\right) + \left(x1 - x2 \cdot \left(x1 \cdot \left(12 - x1 \cdot 6\right) - \left(x1 \cdot x2\right) \cdot 8\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 2.45 \cdot 10^{+144}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x2 \cdot \left(x1 \cdot 6 + 9 \cdot \frac{x1}{x2}\right)\right) - 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 - 2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 74.3% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 3 \cdot \left(x2 \cdot -2\right)\\ t_1 := x2 \cdot \left(2 \cdot x2 - 3\right)\\ \mathbf{if}\;x1 \leq -1 \cdot 10^{+144}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -5.1 \cdot 10^{+14}:\\ \;\;\;\;x1 + \left(t\_0 + \left(x1 + x1 \cdot \left(4 \cdot t\_1 + x1 \cdot \left(x1 \cdot -22\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -6.5 \cdot 10^{-285}:\\ \;\;\;\;x1 + \left(\left(x1 + 4 \cdot \left(x1 \cdot t\_1\right)\right) + 3 \cdot \left(x2 \cdot -2 - x1\right)\right)\\ \mathbf{elif}\;x1 \leq 2.8 \cdot 10^{-239}:\\ \;\;\;\;x1 + \left(t\_0 + \left(x1 - x2 \cdot \left(x1 \cdot \left(12 - x1 \cdot 6\right) - \left(x1 \cdot x2\right) \cdot 8\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot \left(3 \cdot \left(3 - x2 \cdot -2\right) + 4 \cdot \frac{t\_1}{x1}\right) - 2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* 3.0 (* x2 -2.0))) (t_1 (* x2 (- (* 2.0 x2) 3.0))))
   (if (<= x1 -1e+144)
     (+ x1 (+ x1 (* 3.0 (* x1 (+ (* x1 3.0) -1.0)))))
     (if (<= x1 -5.1e+14)
       (+ x1 (+ t_0 (+ x1 (* x1 (+ (* 4.0 t_1) (* x1 (* x1 -22.0)))))))
       (if (<= x1 -6.5e-285)
         (+ x1 (+ (+ x1 (* 4.0 (* x1 t_1))) (* 3.0 (- (* x2 -2.0) x1))))
         (if (<= x1 2.8e-239)
           (+
            x1
            (+
             t_0
             (- x1 (* x2 (- (* x1 (- 12.0 (* x1 6.0))) (* (* x1 x2) 8.0))))))
           (+
            x1
            (+
             (* x2 -6.0)
             (*
              x1
              (-
               (* x1 (+ (* 3.0 (- 3.0 (* x2 -2.0))) (* 4.0 (/ t_1 x1))))
               2.0))))))))))

C

double code(double x1, double x2) {
	double t_0 = 3.0 * (x2 * -2.0);
	double t_1 = x2 * ((2.0 * x2) - 3.0);
	double tmp;
	if (x1 <= -1e+144) {
		tmp = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	} else if (x1 <= -5.1e+14) {
		tmp = x1 + (t_0 + (x1 + (x1 * ((4.0 * t_1) + (x1 * (x1 * -22.0))))));
	} else if (x1 <= -6.5e-285) {
		tmp = x1 + ((x1 + (4.0 * (x1 * t_1))) + (3.0 * ((x2 * -2.0) - x1)));
	} else if (x1 <= 2.8e-239) {
		tmp = x1 + (t_0 + (x1 - (x2 * ((x1 * (12.0 - (x1 * 6.0))) - ((x1 * x2) * 8.0)))));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * ((3.0 * (3.0 - (x2 * -2.0))) + (4.0 * (t_1 / x1)))) - 2.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = 3.0d0 * (x2 * (-2.0d0))
    t_1 = x2 * ((2.0d0 * x2) - 3.0d0)
    if (x1 <= (-1d+144)) then
        tmp = x1 + (x1 + (3.0d0 * (x1 * ((x1 * 3.0d0) + (-1.0d0)))))
    else if (x1 <= (-5.1d+14)) then
        tmp = x1 + (t_0 + (x1 + (x1 * ((4.0d0 * t_1) + (x1 * (x1 * (-22.0d0)))))))
    else if (x1 <= (-6.5d-285)) then
        tmp = x1 + ((x1 + (4.0d0 * (x1 * t_1))) + (3.0d0 * ((x2 * (-2.0d0)) - x1)))
    else if (x1 <= 2.8d-239) then
        tmp = x1 + (t_0 + (x1 - (x2 * ((x1 * (12.0d0 - (x1 * 6.0d0))) - ((x1 * x2) * 8.0d0)))))
    else
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * ((x1 * ((3.0d0 * (3.0d0 - (x2 * (-2.0d0)))) + (4.0d0 * (t_1 / x1)))) - 2.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = 3.0 * (x2 * -2.0);
	double t_1 = x2 * ((2.0 * x2) - 3.0);
	double tmp;
	if (x1 <= -1e+144) {
		tmp = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	} else if (x1 <= -5.1e+14) {
		tmp = x1 + (t_0 + (x1 + (x1 * ((4.0 * t_1) + (x1 * (x1 * -22.0))))));
	} else if (x1 <= -6.5e-285) {
		tmp = x1 + ((x1 + (4.0 * (x1 * t_1))) + (3.0 * ((x2 * -2.0) - x1)));
	} else if (x1 <= 2.8e-239) {
		tmp = x1 + (t_0 + (x1 - (x2 * ((x1 * (12.0 - (x1 * 6.0))) - ((x1 * x2) * 8.0)))));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * ((3.0 * (3.0 - (x2 * -2.0))) + (4.0 * (t_1 / x1)))) - 2.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = 3.0 * (x2 * -2.0)
	t_1 = x2 * ((2.0 * x2) - 3.0)
	tmp = 0
	if x1 <= -1e+144:
		tmp = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))))
	elif x1 <= -5.1e+14:
		tmp = x1 + (t_0 + (x1 + (x1 * ((4.0 * t_1) + (x1 * (x1 * -22.0))))))
	elif x1 <= -6.5e-285:
		tmp = x1 + ((x1 + (4.0 * (x1 * t_1))) + (3.0 * ((x2 * -2.0) - x1)))
	elif x1 <= 2.8e-239:
		tmp = x1 + (t_0 + (x1 - (x2 * ((x1 * (12.0 - (x1 * 6.0))) - ((x1 * x2) * 8.0)))))
	else:
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * ((3.0 * (3.0 - (x2 * -2.0))) + (4.0 * (t_1 / x1)))) - 2.0)))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(3.0 * Float64(x2 * -2.0))
	t_1 = Float64(x2 * Float64(Float64(2.0 * x2) - 3.0))
	tmp = 0.0
	if (x1 <= -1e+144)
		tmp = Float64(x1 + Float64(x1 + Float64(3.0 * Float64(x1 * Float64(Float64(x1 * 3.0) + -1.0)))));
	elseif (x1 <= -5.1e+14)
		tmp = Float64(x1 + Float64(t_0 + Float64(x1 + Float64(x1 * Float64(Float64(4.0 * t_1) + Float64(x1 * Float64(x1 * -22.0)))))));
	elseif (x1 <= -6.5e-285)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(4.0 * Float64(x1 * t_1))) + Float64(3.0 * Float64(Float64(x2 * -2.0) - x1))));
	elseif (x1 <= 2.8e-239)
		tmp = Float64(x1 + Float64(t_0 + Float64(x1 - Float64(x2 * Float64(Float64(x1 * Float64(12.0 - Float64(x1 * 6.0))) - Float64(Float64(x1 * x2) * 8.0))))));
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(x1 * Float64(Float64(3.0 * Float64(3.0 - Float64(x2 * -2.0))) + Float64(4.0 * Float64(t_1 / x1)))) - 2.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = 3.0 * (x2 * -2.0);
	t_1 = x2 * ((2.0 * x2) - 3.0);
	tmp = 0.0;
	if (x1 <= -1e+144)
		tmp = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	elseif (x1 <= -5.1e+14)
		tmp = x1 + (t_0 + (x1 + (x1 * ((4.0 * t_1) + (x1 * (x1 * -22.0))))));
	elseif (x1 <= -6.5e-285)
		tmp = x1 + ((x1 + (4.0 * (x1 * t_1))) + (3.0 * ((x2 * -2.0) - x1)));
	elseif (x1 <= 2.8e-239)
		tmp = x1 + (t_0 + (x1 - (x2 * ((x1 * (12.0 - (x1 * 6.0))) - ((x1 * x2) * 8.0)))));
	else
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * ((3.0 * (3.0 - (x2 * -2.0))) + (4.0 * (t_1 / x1)))) - 2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(3.0 * N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -1e+144], N[(x1 + N[(x1 + N[(3.0 * N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -5.1e+14], N[(x1 + N[(t$95$0 + N[(x1 + N[(x1 * N[(N[(4.0 * t$95$1), $MachinePrecision] + N[(x1 * N[(x1 * -22.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -6.5e-285], N[(x1 + N[(N[(x1 + N[(4.0 * N[(x1 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 2.8e-239], N[(x1 + N[(t$95$0 + N[(x1 - N[(x2 * N[(N[(x1 * N[(12.0 - N[(x1 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x1 * x2), $MachinePrecision] * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(x1 * N[(N[(3.0 * N[(3.0 - N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(4.0 * N[(t$95$1 / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x1 < -1.00000000000000002e144

   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 43.9%

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

   5. Taylor expanded in x2 around 0 97.8%

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

   if -1.00000000000000002e144 < x1 < -5.1e14

   1. Initial program 61.4%

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

   3. Taylor expanded in x1 around 0 61.4%

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

      1. *-commutative 61.4%

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

   5. Simplified 61.4%

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

   6. Taylor expanded in x1 around 0 30.9%

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

   7. Taylor expanded in x2 around 0 50.8%

      \[\leadsto x1 + \left(\left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \color{blue}{\left(-22 \cdot x1\right)}\right) + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]
   8. Step-by-step derivation

      1. *-commutative 50.8%

         \[\leadsto x1 + \left(\left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \color{blue}{\left(x1 \cdot -22\right)}\right) + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]

   9. Simplified 50.8%

      \[\leadsto x1 + \left(\left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \color{blue}{\left(x1 \cdot -22\right)}\right) + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]

   if -5.1e14 < x1 < -6.5e-285

   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 93.7%

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

   4. Taylor expanded in x1 around 0 93.7%

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

      1. mul-1-neg 93.7%

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

      2. unsub-neg 93.7%

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

      3. *-commutative 93.7%

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

   6. Simplified 93.7%

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

   if -6.5e-285 < x1 < 2.80000000000000013e-239

   1. Initial program 99.8%

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

   3. Taylor expanded in x1 around 0 98.7%

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

      1. *-commutative 98.7%

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

   5. Simplified 98.7%

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

   6. Taylor expanded in x1 around 0 50.5%

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

   7. Taylor expanded in x2 around 0 98.7%

      \[\leadsto x1 + \left(\left(\color{blue}{x2 \cdot \left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(6 \cdot x1 - 12\right)\right)} + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]

   if 2.80000000000000013e-239 < x1

   1. Initial program 71.6%

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

   3. Taylor expanded in x1 around 0 49.8%

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

   4. Taylor expanded in x1 around 0 72.3%

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

   5. Taylor expanded in x1 around 0 73.4%

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

   6. Taylor expanded in x1 around inf 75.2%

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

4. Final simplification 83.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1 \cdot 10^{+144}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -5.1 \cdot 10^{+14}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2\right) + \left(x1 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(x1 \cdot -22\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -6.5 \cdot 10^{-285}:\\ \;\;\;\;x1 + \left(\left(x1 + 4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right) + 3 \cdot \left(x2 \cdot -2 - x1\right)\right)\\ \mathbf{elif}\;x1 \leq 2.8 \cdot 10^{-239}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2\right) + \left(x1 - x2 \cdot \left(x1 \cdot \left(12 - x1 \cdot 6\right) - \left(x1 \cdot x2\right) \cdot 8\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot \left(3 \cdot \left(3 - x2 \cdot -2\right) + 4 \cdot \frac{x2 \cdot \left(2 \cdot x2 - 3\right)}{x1}\right) - 2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 77.4% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x2 \cdot \left(2 \cdot x2 - 3\right)\\ \mathbf{if}\;x1 \leq -4 \cdot 10^{+142}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -6.2 \cdot 10^{-285}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(\left(4 \cdot t\_0 + x2 \cdot \left(x1 \cdot 6 + 9 \cdot \frac{x1}{x2}\right)\right) - 2\right)\right)\\ \mathbf{elif}\;x1 \leq 2.8 \cdot 10^{-239}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2\right) + \left(x1 - x2 \cdot \left(x1 \cdot \left(12 - x1 \cdot 6\right) - \left(x1 \cdot x2\right) \cdot 8\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 + 4 \cdot \left(x1 \cdot t\_0\right)\right) + 3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(-1 + x1 \cdot \left(\left(x1 + 3\right) - x2 \cdot -2\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x2 (- (* 2.0 x2) 3.0))))
   (if (<= x1 -4e+142)
     (+ x1 (+ x1 (* 3.0 (* x1 (+ (* x1 3.0) -1.0)))))
     (if (<= x1 -6.2e-285)
       (+
        x1
        (+
         (* x2 -6.0)
         (*
          x1
          (- (+ (* 4.0 t_0) (* x2 (+ (* x1 6.0) (* 9.0 (/ x1 x2))))) 2.0))))
       (if (<= x1 2.8e-239)
         (+
          x1
          (+
           (* 3.0 (* x2 -2.0))
           (- x1 (* x2 (- (* x1 (- 12.0 (* x1 6.0))) (* (* x1 x2) 8.0))))))
         (+
          x1
          (+
           (+ x1 (* 4.0 (* x1 t_0)))
           (*
            3.0
            (+
             (* x2 -2.0)
             (* x1 (+ -1.0 (* x1 (- (+ x1 3.0) (* x2 -2.0))))))))))))))

C

double code(double x1, double x2) {
	double t_0 = x2 * ((2.0 * x2) - 3.0);
	double tmp;
	if (x1 <= -4e+142) {
		tmp = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	} else if (x1 <= -6.2e-285) {
		tmp = x1 + ((x2 * -6.0) + (x1 * (((4.0 * t_0) + (x2 * ((x1 * 6.0) + (9.0 * (x1 / x2))))) - 2.0)));
	} else if (x1 <= 2.8e-239) {
		tmp = x1 + ((3.0 * (x2 * -2.0)) + (x1 - (x2 * ((x1 * (12.0 - (x1 * 6.0))) - ((x1 * x2) * 8.0)))));
	} else {
		tmp = x1 + ((x1 + (4.0 * (x1 * t_0))) + (3.0 * ((x2 * -2.0) + (x1 * (-1.0 + (x1 * ((x1 + 3.0) - (x2 * -2.0))))))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x2 * ((2.0d0 * x2) - 3.0d0)
    if (x1 <= (-4d+142)) then
        tmp = x1 + (x1 + (3.0d0 * (x1 * ((x1 * 3.0d0) + (-1.0d0)))))
    else if (x1 <= (-6.2d-285)) then
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * (((4.0d0 * t_0) + (x2 * ((x1 * 6.0d0) + (9.0d0 * (x1 / x2))))) - 2.0d0)))
    else if (x1 <= 2.8d-239) then
        tmp = x1 + ((3.0d0 * (x2 * (-2.0d0))) + (x1 - (x2 * ((x1 * (12.0d0 - (x1 * 6.0d0))) - ((x1 * x2) * 8.0d0)))))
    else
        tmp = x1 + ((x1 + (4.0d0 * (x1 * t_0))) + (3.0d0 * ((x2 * (-2.0d0)) + (x1 * ((-1.0d0) + (x1 * ((x1 + 3.0d0) - (x2 * (-2.0d0)))))))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x2 * ((2.0 * x2) - 3.0);
	double tmp;
	if (x1 <= -4e+142) {
		tmp = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	} else if (x1 <= -6.2e-285) {
		tmp = x1 + ((x2 * -6.0) + (x1 * (((4.0 * t_0) + (x2 * ((x1 * 6.0) + (9.0 * (x1 / x2))))) - 2.0)));
	} else if (x1 <= 2.8e-239) {
		tmp = x1 + ((3.0 * (x2 * -2.0)) + (x1 - (x2 * ((x1 * (12.0 - (x1 * 6.0))) - ((x1 * x2) * 8.0)))));
	} else {
		tmp = x1 + ((x1 + (4.0 * (x1 * t_0))) + (3.0 * ((x2 * -2.0) + (x1 * (-1.0 + (x1 * ((x1 + 3.0) - (x2 * -2.0))))))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x2 * ((2.0 * x2) - 3.0)
	tmp = 0
	if x1 <= -4e+142:
		tmp = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))))
	elif x1 <= -6.2e-285:
		tmp = x1 + ((x2 * -6.0) + (x1 * (((4.0 * t_0) + (x2 * ((x1 * 6.0) + (9.0 * (x1 / x2))))) - 2.0)))
	elif x1 <= 2.8e-239:
		tmp = x1 + ((3.0 * (x2 * -2.0)) + (x1 - (x2 * ((x1 * (12.0 - (x1 * 6.0))) - ((x1 * x2) * 8.0)))))
	else:
		tmp = x1 + ((x1 + (4.0 * (x1 * t_0))) + (3.0 * ((x2 * -2.0) + (x1 * (-1.0 + (x1 * ((x1 + 3.0) - (x2 * -2.0))))))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x2 * Float64(Float64(2.0 * x2) - 3.0))
	tmp = 0.0
	if (x1 <= -4e+142)
		tmp = Float64(x1 + Float64(x1 + Float64(3.0 * Float64(x1 * Float64(Float64(x1 * 3.0) + -1.0)))));
	elseif (x1 <= -6.2e-285)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(Float64(4.0 * t_0) + Float64(x2 * Float64(Float64(x1 * 6.0) + Float64(9.0 * Float64(x1 / x2))))) - 2.0))));
	elseif (x1 <= 2.8e-239)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(x2 * -2.0)) + Float64(x1 - Float64(x2 * Float64(Float64(x1 * Float64(12.0 - Float64(x1 * 6.0))) - Float64(Float64(x1 * x2) * 8.0))))));
	else
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(4.0 * Float64(x1 * t_0))) + Float64(3.0 * Float64(Float64(x2 * -2.0) + Float64(x1 * Float64(-1.0 + Float64(x1 * Float64(Float64(x1 + 3.0) - Float64(x2 * -2.0)))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x2 * ((2.0 * x2) - 3.0);
	tmp = 0.0;
	if (x1 <= -4e+142)
		tmp = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	elseif (x1 <= -6.2e-285)
		tmp = x1 + ((x2 * -6.0) + (x1 * (((4.0 * t_0) + (x2 * ((x1 * 6.0) + (9.0 * (x1 / x2))))) - 2.0)));
	elseif (x1 <= 2.8e-239)
		tmp = x1 + ((3.0 * (x2 * -2.0)) + (x1 - (x2 * ((x1 * (12.0 - (x1 * 6.0))) - ((x1 * x2) * 8.0)))));
	else
		tmp = x1 + ((x1 + (4.0 * (x1 * t_0))) + (3.0 * ((x2 * -2.0) + (x1 * (-1.0 + (x1 * ((x1 + 3.0) - (x2 * -2.0))))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -4e+142], N[(x1 + N[(x1 + N[(3.0 * N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -6.2e-285], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(N[(4.0 * t$95$0), $MachinePrecision] + N[(x2 * N[(N[(x1 * 6.0), $MachinePrecision] + N[(9.0 * N[(x1 / x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 2.8e-239], N[(x1 + N[(N[(3.0 * N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision] + N[(x1 - N[(x2 * N[(N[(x1 * N[(12.0 - N[(x1 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x1 * x2), $MachinePrecision] * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x1 + N[(4.0 * N[(x1 * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] + N[(x1 * N[(-1.0 + N[(x1 * N[(N[(x1 + 3.0), $MachinePrecision] - N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -4.0000000000000002e142

   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 42.9%

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

   5. Taylor expanded in x2 around 0 95.7%

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

   if -4.0000000000000002e142 < x1 < -6.2000000000000002e-285

   1. Initial program 91.3%

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

   3. Taylor expanded in x1 around 0 77.1%

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

   4. Taylor expanded in x1 around 0 77.7%

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

   5. Taylor expanded in x1 around 0 79.3%

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

   6. Taylor expanded in x2 around inf 80.4%

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

   if -6.2000000000000002e-285 < x1 < 2.80000000000000013e-239

   1. Initial program 99.8%

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

   3. Taylor expanded in x1 around 0 98.7%

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

      1. *-commutative 98.7%

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

   5. Simplified 98.7%

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

   6. Taylor expanded in x1 around 0 50.5%

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

   7. Taylor expanded in x2 around 0 98.7%

      \[\leadsto x1 + \left(\left(\color{blue}{x2 \cdot \left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(6 \cdot x1 - 12\right)\right)} + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]

   if 2.80000000000000013e-239 < x1

   1. Initial program 71.6%

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

   3. Taylor expanded in x1 around 0 49.8%

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

   4. Taylor expanded in x1 around 0 79.5%

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

4. Final simplification 83.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4 \cdot 10^{+142}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -6.2 \cdot 10^{-285}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x2 \cdot \left(x1 \cdot 6 + 9 \cdot \frac{x1}{x2}\right)\right) - 2\right)\right)\\ \mathbf{elif}\;x1 \leq 2.8 \cdot 10^{-239}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2\right) + \left(x1 - x2 \cdot \left(x1 \cdot \left(12 - x1 \cdot 6\right) - \left(x1 \cdot x2\right) \cdot 8\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 + 4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right) + 3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(-1 + x1 \cdot \left(\left(x1 + 3\right) - x2 \cdot -2\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 77.0% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 3 \cdot \left(x2 \cdot -2\right)\\ t_1 := x2 \cdot \left(2 \cdot x2 - 3\right)\\ t_2 := 4 \cdot t\_1\\ \mathbf{if}\;x1 \leq -1 \cdot 10^{+144}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -5.1 \cdot 10^{+14}:\\ \;\;\;\;x1 + \left(t\_0 + \left(x1 + x1 \cdot \left(t\_2 + x1 \cdot \left(x1 \cdot -22\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -6.4 \cdot 10^{-285}:\\ \;\;\;\;x1 + \left(\left(x1 + 4 \cdot \left(x1 \cdot t\_1\right)\right) + 3 \cdot \left(x2 \cdot -2 - x1\right)\right)\\ \mathbf{elif}\;x1 \leq 1.85 \cdot 10^{-239}:\\ \;\;\;\;x1 + \left(t\_0 + \left(x1 - x2 \cdot \left(x1 \cdot \left(12 - x1 \cdot 6\right) - \left(x1 \cdot x2\right) \cdot 8\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 2.45 \cdot 10^{+144}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(t\_2 - 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 - 2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* 3.0 (* x2 -2.0)))
        (t_1 (* x2 (- (* 2.0 x2) 3.0)))
        (t_2 (* 4.0 t_1)))
   (if (<= x1 -1e+144)
     (+ x1 (+ x1 (* 3.0 (* x1 (+ (* x1 3.0) -1.0)))))
     (if (<= x1 -5.1e+14)
       (+ x1 (+ t_0 (+ x1 (* x1 (+ t_2 (* x1 (* x1 -22.0)))))))
       (if (<= x1 -6.4e-285)
         (+ x1 (+ (+ x1 (* 4.0 (* x1 t_1))) (* 3.0 (- (* x2 -2.0) x1))))
         (if (<= x1 1.85e-239)
           (+
            x1
            (+
             t_0
             (- x1 (* x2 (- (* x1 (- 12.0 (* x1 6.0))) (* (* x1 x2) 8.0))))))
           (if (<= x1 2.45e+144)
             (+ x1 (+ (* x2 -6.0) (* x1 (- t_2 2.0))))
             (+ x1 (+ (* x2 -6.0) (* x1 (- (* x1 9.0) 2.0)))))))))))

C

double code(double x1, double x2) {
	double t_0 = 3.0 * (x2 * -2.0);
	double t_1 = x2 * ((2.0 * x2) - 3.0);
	double t_2 = 4.0 * t_1;
	double tmp;
	if (x1 <= -1e+144) {
		tmp = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	} else if (x1 <= -5.1e+14) {
		tmp = x1 + (t_0 + (x1 + (x1 * (t_2 + (x1 * (x1 * -22.0))))));
	} else if (x1 <= -6.4e-285) {
		tmp = x1 + ((x1 + (4.0 * (x1 * t_1))) + (3.0 * ((x2 * -2.0) - x1)));
	} else if (x1 <= 1.85e-239) {
		tmp = x1 + (t_0 + (x1 - (x2 * ((x1 * (12.0 - (x1 * 6.0))) - ((x1 * x2) * 8.0)))));
	} else if (x1 <= 2.45e+144) {
		tmp = x1 + ((x2 * -6.0) + (x1 * (t_2 - 2.0)));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) - 2.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = 3.0d0 * (x2 * (-2.0d0))
    t_1 = x2 * ((2.0d0 * x2) - 3.0d0)
    t_2 = 4.0d0 * t_1
    if (x1 <= (-1d+144)) then
        tmp = x1 + (x1 + (3.0d0 * (x1 * ((x1 * 3.0d0) + (-1.0d0)))))
    else if (x1 <= (-5.1d+14)) then
        tmp = x1 + (t_0 + (x1 + (x1 * (t_2 + (x1 * (x1 * (-22.0d0)))))))
    else if (x1 <= (-6.4d-285)) then
        tmp = x1 + ((x1 + (4.0d0 * (x1 * t_1))) + (3.0d0 * ((x2 * (-2.0d0)) - x1)))
    else if (x1 <= 1.85d-239) then
        tmp = x1 + (t_0 + (x1 - (x2 * ((x1 * (12.0d0 - (x1 * 6.0d0))) - ((x1 * x2) * 8.0d0)))))
    else if (x1 <= 2.45d+144) then
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * (t_2 - 2.0d0)))
    else
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * ((x1 * 9.0d0) - 2.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = 3.0 * (x2 * -2.0);
	double t_1 = x2 * ((2.0 * x2) - 3.0);
	double t_2 = 4.0 * t_1;
	double tmp;
	if (x1 <= -1e+144) {
		tmp = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	} else if (x1 <= -5.1e+14) {
		tmp = x1 + (t_0 + (x1 + (x1 * (t_2 + (x1 * (x1 * -22.0))))));
	} else if (x1 <= -6.4e-285) {
		tmp = x1 + ((x1 + (4.0 * (x1 * t_1))) + (3.0 * ((x2 * -2.0) - x1)));
	} else if (x1 <= 1.85e-239) {
		tmp = x1 + (t_0 + (x1 - (x2 * ((x1 * (12.0 - (x1 * 6.0))) - ((x1 * x2) * 8.0)))));
	} else if (x1 <= 2.45e+144) {
		tmp = x1 + ((x2 * -6.0) + (x1 * (t_2 - 2.0)));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) - 2.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = 3.0 * (x2 * -2.0)
	t_1 = x2 * ((2.0 * x2) - 3.0)
	t_2 = 4.0 * t_1
	tmp = 0
	if x1 <= -1e+144:
		tmp = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))))
	elif x1 <= -5.1e+14:
		tmp = x1 + (t_0 + (x1 + (x1 * (t_2 + (x1 * (x1 * -22.0))))))
	elif x1 <= -6.4e-285:
		tmp = x1 + ((x1 + (4.0 * (x1 * t_1))) + (3.0 * ((x2 * -2.0) - x1)))
	elif x1 <= 1.85e-239:
		tmp = x1 + (t_0 + (x1 - (x2 * ((x1 * (12.0 - (x1 * 6.0))) - ((x1 * x2) * 8.0)))))
	elif x1 <= 2.45e+144:
		tmp = x1 + ((x2 * -6.0) + (x1 * (t_2 - 2.0)))
	else:
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) - 2.0)))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(3.0 * Float64(x2 * -2.0))
	t_1 = Float64(x2 * Float64(Float64(2.0 * x2) - 3.0))
	t_2 = Float64(4.0 * t_1)
	tmp = 0.0
	if (x1 <= -1e+144)
		tmp = Float64(x1 + Float64(x1 + Float64(3.0 * Float64(x1 * Float64(Float64(x1 * 3.0) + -1.0)))));
	elseif (x1 <= -5.1e+14)
		tmp = Float64(x1 + Float64(t_0 + Float64(x1 + Float64(x1 * Float64(t_2 + Float64(x1 * Float64(x1 * -22.0)))))));
	elseif (x1 <= -6.4e-285)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(4.0 * Float64(x1 * t_1))) + Float64(3.0 * Float64(Float64(x2 * -2.0) - x1))));
	elseif (x1 <= 1.85e-239)
		tmp = Float64(x1 + Float64(t_0 + Float64(x1 - Float64(x2 * Float64(Float64(x1 * Float64(12.0 - Float64(x1 * 6.0))) - Float64(Float64(x1 * x2) * 8.0))))));
	elseif (x1 <= 2.45e+144)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(t_2 - 2.0))));
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(x1 * 9.0) - 2.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = 3.0 * (x2 * -2.0);
	t_1 = x2 * ((2.0 * x2) - 3.0);
	t_2 = 4.0 * t_1;
	tmp = 0.0;
	if (x1 <= -1e+144)
		tmp = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	elseif (x1 <= -5.1e+14)
		tmp = x1 + (t_0 + (x1 + (x1 * (t_2 + (x1 * (x1 * -22.0))))));
	elseif (x1 <= -6.4e-285)
		tmp = x1 + ((x1 + (4.0 * (x1 * t_1))) + (3.0 * ((x2 * -2.0) - x1)));
	elseif (x1 <= 1.85e-239)
		tmp = x1 + (t_0 + (x1 - (x2 * ((x1 * (12.0 - (x1 * 6.0))) - ((x1 * x2) * 8.0)))));
	elseif (x1 <= 2.45e+144)
		tmp = x1 + ((x2 * -6.0) + (x1 * (t_2 - 2.0)));
	else
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) - 2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(3.0 * N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(4.0 * t$95$1), $MachinePrecision]}, If[LessEqual[x1, -1e+144], N[(x1 + N[(x1 + N[(3.0 * N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -5.1e+14], N[(x1 + N[(t$95$0 + N[(x1 + N[(x1 * N[(t$95$2 + N[(x1 * N[(x1 * -22.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -6.4e-285], N[(x1 + N[(N[(x1 + N[(4.0 * N[(x1 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.85e-239], N[(x1 + N[(t$95$0 + N[(x1 - N[(x2 * N[(N[(x1 * N[(12.0 - N[(x1 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x1 * x2), $MachinePrecision] * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 2.45e+144], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(t$95$2 - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if x1 < -1.00000000000000002e144

   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 43.9%

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

   5. Taylor expanded in x2 around 0 97.8%

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

   if -1.00000000000000002e144 < x1 < -5.1e14

   1. Initial program 61.4%

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

   3. Taylor expanded in x1 around 0 61.4%

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

      1. *-commutative 61.4%

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

   5. Simplified 61.4%

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

   6. Taylor expanded in x1 around 0 30.9%

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

   7. Taylor expanded in x2 around 0 50.8%

      \[\leadsto x1 + \left(\left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \color{blue}{\left(-22 \cdot x1\right)}\right) + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]
   8. Step-by-step derivation

      1. *-commutative 50.8%

         \[\leadsto x1 + \left(\left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \color{blue}{\left(x1 \cdot -22\right)}\right) + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]

   9. Simplified 50.8%

      \[\leadsto x1 + \left(\left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \color{blue}{\left(x1 \cdot -22\right)}\right) + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]

   if -5.1e14 < x1 < -6.40000000000000032e-285

   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 93.7%

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

   4. Taylor expanded in x1 around 0 93.7%

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

      1. mul-1-neg 93.7%

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

      2. unsub-neg 93.7%

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

      3. *-commutative 93.7%

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

   6. Simplified 93.7%

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

   if -6.40000000000000032e-285 < x1 < 1.85000000000000008e-239

   1. Initial program 99.8%

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

   3. Taylor expanded in x1 around 0 98.7%

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

      1. *-commutative 98.7%

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

   5. Simplified 98.7%

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

   6. Taylor expanded in x1 around 0 50.5%

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

   7. Taylor expanded in x2 around 0 98.7%

      \[\leadsto x1 + \left(\left(\color{blue}{x2 \cdot \left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(6 \cdot x1 - 12\right)\right)} + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]

   if 1.85000000000000008e-239 < x1 < 2.45e144

   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 0 69.0%

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

   4. Taylor expanded in x1 around 0 69.0%

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

   5. Taylor expanded in x1 around 0 67.9%

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

   if 2.45e144 < x1

   1. Initial program 3.2%

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

   3. Taylor expanded in x1 around 0 0.2%

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

   4. Taylor expanded in x1 around 0 80.6%

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

   5. Taylor expanded in x1 around 0 80.6%

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

   6. Taylor expanded in x2 around 0 97.1%

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

      1. *-commutative 97.1%

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

   8. Simplified 97.1%

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

4. Final simplification 83.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1 \cdot 10^{+144}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -5.1 \cdot 10^{+14}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2\right) + \left(x1 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(x1 \cdot -22\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -6.4 \cdot 10^{-285}:\\ \;\;\;\;x1 + \left(\left(x1 + 4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right) + 3 \cdot \left(x2 \cdot -2 - x1\right)\right)\\ \mathbf{elif}\;x1 \leq 1.85 \cdot 10^{-239}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2\right) + \left(x1 - x2 \cdot \left(x1 \cdot \left(12 - x1 \cdot 6\right) - \left(x1 \cdot x2\right) \cdot 8\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 2.45 \cdot 10^{+144}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 - 2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 75.7% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x2 \cdot \left(2 \cdot x2 - 3\right)\\ \mathbf{if}\;x1 \leq -4.4 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -2.4 \cdot 10^{+64}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot \left(9 + x2 \cdot 6\right) - 2\right)\right)\\ \mathbf{elif}\;x1 \leq -6.5 \cdot 10^{-285}:\\ \;\;\;\;x1 + \left(\left(x1 + 4 \cdot \left(x1 \cdot t\_0\right)\right) + 3 \cdot \left(x2 \cdot -2 - x1\right)\right)\\ \mathbf{elif}\;x1 \leq 2.6 \cdot 10^{-239}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2\right) + \left(x1 - x2 \cdot \left(x1 \cdot \left(12 - x1 \cdot 6\right) - \left(x1 \cdot x2\right) \cdot 8\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 2.45 \cdot 10^{+144}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(4 \cdot t\_0 - 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 - 2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x2 (- (* 2.0 x2) 3.0))))
   (if (<= x1 -4.4e+153)
     (+ x1 (+ x1 (* 3.0 (* x1 (+ (* x1 3.0) -1.0)))))
     (if (<= x1 -2.4e+64)
       (+ x1 (+ (* x2 -6.0) (* x1 (- (* x1 (+ 9.0 (* x2 6.0))) 2.0))))
       (if (<= x1 -6.5e-285)
         (+ x1 (+ (+ x1 (* 4.0 (* x1 t_0))) (* 3.0 (- (* x2 -2.0) x1))))
         (if (<= x1 2.6e-239)
           (+
            x1
            (+
             (* 3.0 (* x2 -2.0))
             (- x1 (* x2 (- (* x1 (- 12.0 (* x1 6.0))) (* (* x1 x2) 8.0))))))
           (if (<= x1 2.45e+144)
             (+ x1 (+ (* x2 -6.0) (* x1 (- (* 4.0 t_0) 2.0))))
             (+ x1 (+ (* x2 -6.0) (* x1 (- (* x1 9.0) 2.0)))))))))))

C

double code(double x1, double x2) {
	double t_0 = x2 * ((2.0 * x2) - 3.0);
	double tmp;
	if (x1 <= -4.4e+153) {
		tmp = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	} else if (x1 <= -2.4e+64) {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * (9.0 + (x2 * 6.0))) - 2.0)));
	} else if (x1 <= -6.5e-285) {
		tmp = x1 + ((x1 + (4.0 * (x1 * t_0))) + (3.0 * ((x2 * -2.0) - x1)));
	} else if (x1 <= 2.6e-239) {
		tmp = x1 + ((3.0 * (x2 * -2.0)) + (x1 - (x2 * ((x1 * (12.0 - (x1 * 6.0))) - ((x1 * x2) * 8.0)))));
	} else if (x1 <= 2.45e+144) {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((4.0 * t_0) - 2.0)));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) - 2.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x2 * ((2.0d0 * x2) - 3.0d0)
    if (x1 <= (-4.4d+153)) then
        tmp = x1 + (x1 + (3.0d0 * (x1 * ((x1 * 3.0d0) + (-1.0d0)))))
    else if (x1 <= (-2.4d+64)) then
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * ((x1 * (9.0d0 + (x2 * 6.0d0))) - 2.0d0)))
    else if (x1 <= (-6.5d-285)) then
        tmp = x1 + ((x1 + (4.0d0 * (x1 * t_0))) + (3.0d0 * ((x2 * (-2.0d0)) - x1)))
    else if (x1 <= 2.6d-239) then
        tmp = x1 + ((3.0d0 * (x2 * (-2.0d0))) + (x1 - (x2 * ((x1 * (12.0d0 - (x1 * 6.0d0))) - ((x1 * x2) * 8.0d0)))))
    else if (x1 <= 2.45d+144) then
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * ((4.0d0 * t_0) - 2.0d0)))
    else
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * ((x1 * 9.0d0) - 2.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x2 * ((2.0 * x2) - 3.0);
	double tmp;
	if (x1 <= -4.4e+153) {
		tmp = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	} else if (x1 <= -2.4e+64) {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * (9.0 + (x2 * 6.0))) - 2.0)));
	} else if (x1 <= -6.5e-285) {
		tmp = x1 + ((x1 + (4.0 * (x1 * t_0))) + (3.0 * ((x2 * -2.0) - x1)));
	} else if (x1 <= 2.6e-239) {
		tmp = x1 + ((3.0 * (x2 * -2.0)) + (x1 - (x2 * ((x1 * (12.0 - (x1 * 6.0))) - ((x1 * x2) * 8.0)))));
	} else if (x1 <= 2.45e+144) {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((4.0 * t_0) - 2.0)));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) - 2.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x2 * ((2.0 * x2) - 3.0)
	tmp = 0
	if x1 <= -4.4e+153:
		tmp = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))))
	elif x1 <= -2.4e+64:
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * (9.0 + (x2 * 6.0))) - 2.0)))
	elif x1 <= -6.5e-285:
		tmp = x1 + ((x1 + (4.0 * (x1 * t_0))) + (3.0 * ((x2 * -2.0) - x1)))
	elif x1 <= 2.6e-239:
		tmp = x1 + ((3.0 * (x2 * -2.0)) + (x1 - (x2 * ((x1 * (12.0 - (x1 * 6.0))) - ((x1 * x2) * 8.0)))))
	elif x1 <= 2.45e+144:
		tmp = x1 + ((x2 * -6.0) + (x1 * ((4.0 * t_0) - 2.0)))
	else:
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) - 2.0)))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x2 * Float64(Float64(2.0 * x2) - 3.0))
	tmp = 0.0
	if (x1 <= -4.4e+153)
		tmp = Float64(x1 + Float64(x1 + Float64(3.0 * Float64(x1 * Float64(Float64(x1 * 3.0) + -1.0)))));
	elseif (x1 <= -2.4e+64)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(x1 * Float64(9.0 + Float64(x2 * 6.0))) - 2.0))));
	elseif (x1 <= -6.5e-285)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(4.0 * Float64(x1 * t_0))) + Float64(3.0 * Float64(Float64(x2 * -2.0) - x1))));
	elseif (x1 <= 2.6e-239)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(x2 * -2.0)) + Float64(x1 - Float64(x2 * Float64(Float64(x1 * Float64(12.0 - Float64(x1 * 6.0))) - Float64(Float64(x1 * x2) * 8.0))))));
	elseif (x1 <= 2.45e+144)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(4.0 * t_0) - 2.0))));
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(x1 * 9.0) - 2.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x2 * ((2.0 * x2) - 3.0);
	tmp = 0.0;
	if (x1 <= -4.4e+153)
		tmp = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	elseif (x1 <= -2.4e+64)
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * (9.0 + (x2 * 6.0))) - 2.0)));
	elseif (x1 <= -6.5e-285)
		tmp = x1 + ((x1 + (4.0 * (x1 * t_0))) + (3.0 * ((x2 * -2.0) - x1)));
	elseif (x1 <= 2.6e-239)
		tmp = x1 + ((3.0 * (x2 * -2.0)) + (x1 - (x2 * ((x1 * (12.0 - (x1 * 6.0))) - ((x1 * x2) * 8.0)))));
	elseif (x1 <= 2.45e+144)
		tmp = x1 + ((x2 * -6.0) + (x1 * ((4.0 * t_0) - 2.0)));
	else
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) - 2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -4.4e+153], N[(x1 + N[(x1 + N[(3.0 * N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -2.4e+64], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(x1 * N[(9.0 + N[(x2 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -6.5e-285], N[(x1 + N[(N[(x1 + N[(4.0 * N[(x1 * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 2.6e-239], N[(x1 + N[(N[(3.0 * N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision] + N[(x1 - N[(x2 * N[(N[(x1 * N[(12.0 - N[(x1 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x1 * x2), $MachinePrecision] * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 2.45e+144], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(4.0 * t$95$0), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 6 regimes

2. if x1 < -4.3999999999999999e153

   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 45.0%

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

   5. Taylor expanded in x2 around 0 100.0%

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

   if -4.3999999999999999e153 < x1 < -2.39999999999999999e64

   1. Initial program 30.6%

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

   3. Taylor expanded in x1 around 0 15.6%

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

   4. Taylor expanded in x1 around 0 25.7%

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

   5. Taylor expanded in x1 around 0 33.4%

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

   6. Taylor expanded in x1 around inf 56.5%

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

      1. associate-*r* 56.5%

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

      2. *-commutative 56.5%

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

      3. associate-*r* 56.5%

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

      4. cancel-sign-sub-inv 56.5%

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

      5. metadata-eval 56.5%

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

      6. distribute-lft-in 56.5%

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

      7. metadata-eval 56.5%

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

      8. metadata-eval 56.5%

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

      9. distribute-lft-neg-in 56.5%

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

      10. distribute-rgt-neg-in 56.5%

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

      11. associate-*r* 56.5%

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

      12. metadata-eval 56.5%

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

      13. distribute-lft-neg-in 56.5%

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

      14. metadata-eval 56.5%

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

      15. *-commutative 56.5%

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

   8. Simplified 56.5%

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

   if -2.39999999999999999e64 < x1 < -6.5e-285

   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 85.6%

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

   4. Taylor expanded in x1 around 0 85.7%

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

      1. mul-1-neg 85.7%

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

      2. unsub-neg 85.7%

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

      3. *-commutative 85.7%

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

   6. Simplified 85.7%

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

   if -6.5e-285 < x1 < 2.60000000000000003e-239

   1. Initial program 99.8%

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

   3. Taylor expanded in x1 around 0 98.7%

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

      1. *-commutative 98.7%

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

   5. Simplified 98.7%

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

   6. Taylor expanded in x1 around 0 50.5%

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

   7. Taylor expanded in x2 around 0 98.7%

      \[\leadsto x1 + \left(\left(\color{blue}{x2 \cdot \left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(6 \cdot x1 - 12\right)\right)} + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]

   if 2.60000000000000003e-239 < x1 < 2.45e144

   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 0 69.0%

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

   4. Taylor expanded in x1 around 0 69.0%

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

   5. Taylor expanded in x1 around 0 67.9%

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

   if 2.45e144 < x1

   1. Initial program 3.2%

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

   3. Taylor expanded in x1 around 0 0.2%

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

   4. Taylor expanded in x1 around 0 80.6%

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

   5. Taylor expanded in x1 around 0 80.6%

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

   6. Taylor expanded in x2 around 0 97.1%

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

      1. *-commutative 97.1%

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

   8. Simplified 97.1%

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

4. Final simplification 83.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4.4 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -2.4 \cdot 10^{+64}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot \left(9 + x2 \cdot 6\right) - 2\right)\right)\\ \mathbf{elif}\;x1 \leq -6.5 \cdot 10^{-285}:\\ \;\;\;\;x1 + \left(\left(x1 + 4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right) + 3 \cdot \left(x2 \cdot -2 - x1\right)\right)\\ \mathbf{elif}\;x1 \leq 2.6 \cdot 10^{-239}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2\right) + \left(x1 - x2 \cdot \left(x1 \cdot \left(12 - x1 \cdot 6\right) - \left(x1 \cdot x2\right) \cdot 8\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 2.45 \cdot 10^{+144}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 - 2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 76.1% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot \left(9 + x2 \cdot 6\right) - 2\right)\right)\\ t_1 := x2 \cdot \left(3 - 2 \cdot x2\right)\\ \mathbf{if}\;x1 \leq -4.4 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -5.2 \cdot 10^{+64}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x1 \leq -1.16 \cdot 10^{-191}:\\ \;\;\;\;x1 + \left(\left(x1 - 4 \cdot \left(x1 \cdot t\_1\right)\right) + 3 \cdot \left(x2 \cdot -2 - x1\right)\right)\\ \mathbf{elif}\;x1 \leq 3.6 \cdot 10^{-251}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x1 \leq 2.45 \cdot 10^{+144}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 + 4 \cdot t\_1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 - x1 \cdot 9\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ x1 (+ (* x2 -6.0) (* x1 (- (* x1 (+ 9.0 (* x2 6.0))) 2.0)))))
        (t_1 (* x2 (- 3.0 (* 2.0 x2)))))
   (if (<= x1 -4.4e+153)
     (+ x1 (+ x1 (* 3.0 (* x1 (+ (* x1 3.0) -1.0)))))
     (if (<= x1 -5.2e+64)
       t_0
       (if (<= x1 -1.16e-191)
         (+ x1 (+ (- x1 (* 4.0 (* x1 t_1))) (* 3.0 (- (* x2 -2.0) x1))))
         (if (<= x1 3.6e-251)
           t_0
           (if (<= x1 2.45e+144)
             (+ x1 (- (* x2 -6.0) (* x1 (+ 2.0 (* 4.0 t_1)))))
             (+ x1 (- (* x2 -6.0) (* x1 (- 2.0 (* x1 9.0))))))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 + ((x2 * -6.0) + (x1 * ((x1 * (9.0 + (x2 * 6.0))) - 2.0)));
	double t_1 = x2 * (3.0 - (2.0 * x2));
	double tmp;
	if (x1 <= -4.4e+153) {
		tmp = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	} else if (x1 <= -5.2e+64) {
		tmp = t_0;
	} else if (x1 <= -1.16e-191) {
		tmp = x1 + ((x1 - (4.0 * (x1 * t_1))) + (3.0 * ((x2 * -2.0) - x1)));
	} else if (x1 <= 3.6e-251) {
		tmp = t_0;
	} else if (x1 <= 2.45e+144) {
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + (4.0 * t_1))));
	} else {
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 - (x1 * 9.0))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x1 + ((x2 * (-6.0d0)) + (x1 * ((x1 * (9.0d0 + (x2 * 6.0d0))) - 2.0d0)))
    t_1 = x2 * (3.0d0 - (2.0d0 * x2))
    if (x1 <= (-4.4d+153)) then
        tmp = x1 + (x1 + (3.0d0 * (x1 * ((x1 * 3.0d0) + (-1.0d0)))))
    else if (x1 <= (-5.2d+64)) then
        tmp = t_0
    else if (x1 <= (-1.16d-191)) then
        tmp = x1 + ((x1 - (4.0d0 * (x1 * t_1))) + (3.0d0 * ((x2 * (-2.0d0)) - x1)))
    else if (x1 <= 3.6d-251) then
        tmp = t_0
    else if (x1 <= 2.45d+144) then
        tmp = x1 + ((x2 * (-6.0d0)) - (x1 * (2.0d0 + (4.0d0 * t_1))))
    else
        tmp = x1 + ((x2 * (-6.0d0)) - (x1 * (2.0d0 - (x1 * 9.0d0))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 + ((x2 * -6.0) + (x1 * ((x1 * (9.0 + (x2 * 6.0))) - 2.0)));
	double t_1 = x2 * (3.0 - (2.0 * x2));
	double tmp;
	if (x1 <= -4.4e+153) {
		tmp = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	} else if (x1 <= -5.2e+64) {
		tmp = t_0;
	} else if (x1 <= -1.16e-191) {
		tmp = x1 + ((x1 - (4.0 * (x1 * t_1))) + (3.0 * ((x2 * -2.0) - x1)));
	} else if (x1 <= 3.6e-251) {
		tmp = t_0;
	} else if (x1 <= 2.45e+144) {
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + (4.0 * t_1))));
	} else {
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 - (x1 * 9.0))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 + ((x2 * -6.0) + (x1 * ((x1 * (9.0 + (x2 * 6.0))) - 2.0)))
	t_1 = x2 * (3.0 - (2.0 * x2))
	tmp = 0
	if x1 <= -4.4e+153:
		tmp = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))))
	elif x1 <= -5.2e+64:
		tmp = t_0
	elif x1 <= -1.16e-191:
		tmp = x1 + ((x1 - (4.0 * (x1 * t_1))) + (3.0 * ((x2 * -2.0) - x1)))
	elif x1 <= 3.6e-251:
		tmp = t_0
	elif x1 <= 2.45e+144:
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + (4.0 * t_1))))
	else:
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 - (x1 * 9.0))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(x1 * Float64(9.0 + Float64(x2 * 6.0))) - 2.0))))
	t_1 = Float64(x2 * Float64(3.0 - Float64(2.0 * x2)))
	tmp = 0.0
	if (x1 <= -4.4e+153)
		tmp = Float64(x1 + Float64(x1 + Float64(3.0 * Float64(x1 * Float64(Float64(x1 * 3.0) + -1.0)))));
	elseif (x1 <= -5.2e+64)
		tmp = t_0;
	elseif (x1 <= -1.16e-191)
		tmp = Float64(x1 + Float64(Float64(x1 - Float64(4.0 * Float64(x1 * t_1))) + Float64(3.0 * Float64(Float64(x2 * -2.0) - x1))));
	elseif (x1 <= 3.6e-251)
		tmp = t_0;
	elseif (x1 <= 2.45e+144)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) - Float64(x1 * Float64(2.0 + Float64(4.0 * t_1)))));
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) - Float64(x1 * Float64(2.0 - Float64(x1 * 9.0)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 + ((x2 * -6.0) + (x1 * ((x1 * (9.0 + (x2 * 6.0))) - 2.0)));
	t_1 = x2 * (3.0 - (2.0 * x2));
	tmp = 0.0;
	if (x1 <= -4.4e+153)
		tmp = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	elseif (x1 <= -5.2e+64)
		tmp = t_0;
	elseif (x1 <= -1.16e-191)
		tmp = x1 + ((x1 - (4.0 * (x1 * t_1))) + (3.0 * ((x2 * -2.0) - x1)));
	elseif (x1 <= 3.6e-251)
		tmp = t_0;
	elseif (x1 <= 2.45e+144)
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + (4.0 * t_1))));
	else
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 - (x1 * 9.0))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(x1 * N[(9.0 + N[(x2 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x2 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -4.4e+153], N[(x1 + N[(x1 + N[(3.0 * N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -5.2e+64], t$95$0, If[LessEqual[x1, -1.16e-191], N[(x1 + N[(N[(x1 - N[(4.0 * N[(x1 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 3.6e-251], t$95$0, If[LessEqual[x1, 2.45e+144], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] - N[(x1 * N[(2.0 + N[(4.0 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] - N[(x1 * N[(2.0 - N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x1 < -4.3999999999999999e153

   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 45.0%

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

   5. Taylor expanded in x2 around 0 100.0%

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

   if -4.3999999999999999e153 < x1 < -5.19999999999999994e64 or -1.16000000000000007e-191 < x1 < 3.6000000000000001e-251

   1. Initial program 80.1%

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

   3. Taylor expanded in x1 around 0 58.9%

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

   4. Taylor expanded in x1 around 0 61.7%

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

   5. Taylor expanded in x1 around 0 64.1%

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

   6. Taylor expanded in x1 around inf 85.6%

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

      1. associate-*r* 85.6%

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

      2. *-commutative 85.6%

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

      3. associate-*r* 85.6%

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

      4. cancel-sign-sub-inv 85.6%

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

      5. metadata-eval 85.6%

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

      6. distribute-lft-in 85.6%

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

      7. metadata-eval 85.6%

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

      8. metadata-eval 85.6%

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

      9. distribute-lft-neg-in 85.6%

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

      10. distribute-rgt-neg-in 85.6%

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

      11. associate-*r* 85.6%

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

      12. metadata-eval 85.6%

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

      13. distribute-lft-neg-in 85.6%

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

      14. metadata-eval 85.6%

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

      15. *-commutative 85.6%

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

   8. Simplified 85.6%

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

   if -5.19999999999999994e64 < x1 < -1.16000000000000007e-191

   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 82.7%

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

   4. Taylor expanded in x1 around 0 83.0%

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

      1. mul-1-neg 83.0%

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

      2. unsub-neg 83.0%

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

      3. *-commutative 83.0%

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

   6. Simplified 83.0%

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

   if 3.6000000000000001e-251 < x1 < 2.45e144

   1. Initial program 98.2%

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

   3. Taylor expanded in x1 around 0 68.6%

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

   4. Taylor expanded in x1 around 0 68.7%

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

   5. Taylor expanded in x1 around 0 67.6%

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

   if 2.45e144 < x1

   1. Initial program 3.2%

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

   3. Taylor expanded in x1 around 0 0.2%

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

   4. Taylor expanded in x1 around 0 80.6%

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

   5. Taylor expanded in x1 around 0 80.6%

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

   6. Taylor expanded in x2 around 0 97.1%

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

      1. *-commutative 97.1%

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

   8. Simplified 97.1%

      \[\leadsto x1 + \left(-6 \cdot x2 + x1 \cdot \left(\color{blue}{x1 \cdot 9} - 2\right)\right) \]
3. Recombined 5 regimes into one program.

4. Final simplification 82.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4.4 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -5.2 \cdot 10^{+64}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot \left(9 + x2 \cdot 6\right) - 2\right)\right)\\ \mathbf{elif}\;x1 \leq -1.16 \cdot 10^{-191}:\\ \;\;\;\;x1 + \left(\left(x1 - 4 \cdot \left(x1 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right) + 3 \cdot \left(x2 \cdot -2 - x1\right)\right)\\ \mathbf{elif}\;x1 \leq 3.6 \cdot 10^{-251}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot \left(9 + x2 \cdot 6\right) - 2\right)\right)\\ \mathbf{elif}\;x1 \leq 2.45 \cdot 10^{+144}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 + 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 - x1 \cdot 9\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 76.1% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot \left(9 + x2 \cdot 6\right) - 2\right)\right)\\ t_1 := x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 + 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right)\\ \mathbf{if}\;x1 \leq -1 \cdot 10^{+155}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -1.2 \cdot 10^{+63}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x1 \leq -6.5 \cdot 10^{-192}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x1 \leq 8.5 \cdot 10^{-259}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x1 \leq 2.45 \cdot 10^{+144}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 - x1 \cdot 9\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ x1 (+ (* x2 -6.0) (* x1 (- (* x1 (+ 9.0 (* x2 6.0))) 2.0)))))
        (t_1
         (+
          x1
          (- (* x2 -6.0) (* x1 (+ 2.0 (* 4.0 (* x2 (- 3.0 (* 2.0 x2))))))))))
   (if (<= x1 -1e+155)
     (+ x1 (+ x1 (* 3.0 (* x1 (+ (* x1 3.0) -1.0)))))
     (if (<= x1 -1.2e+63)
       t_0
       (if (<= x1 -6.5e-192)
         t_1
         (if (<= x1 8.5e-259)
           t_0
           (if (<= x1 2.45e+144)
             t_1
             (+ x1 (- (* x2 -6.0) (* x1 (- 2.0 (* x1 9.0))))))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 + ((x2 * -6.0) + (x1 * ((x1 * (9.0 + (x2 * 6.0))) - 2.0)));
	double t_1 = x1 + ((x2 * -6.0) - (x1 * (2.0 + (4.0 * (x2 * (3.0 - (2.0 * x2)))))));
	double tmp;
	if (x1 <= -1e+155) {
		tmp = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	} else if (x1 <= -1.2e+63) {
		tmp = t_0;
	} else if (x1 <= -6.5e-192) {
		tmp = t_1;
	} else if (x1 <= 8.5e-259) {
		tmp = t_0;
	} else if (x1 <= 2.45e+144) {
		tmp = t_1;
	} else {
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 - (x1 * 9.0))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x1 + ((x2 * (-6.0d0)) + (x1 * ((x1 * (9.0d0 + (x2 * 6.0d0))) - 2.0d0)))
    t_1 = x1 + ((x2 * (-6.0d0)) - (x1 * (2.0d0 + (4.0d0 * (x2 * (3.0d0 - (2.0d0 * x2)))))))
    if (x1 <= (-1d+155)) then
        tmp = x1 + (x1 + (3.0d0 * (x1 * ((x1 * 3.0d0) + (-1.0d0)))))
    else if (x1 <= (-1.2d+63)) then
        tmp = t_0
    else if (x1 <= (-6.5d-192)) then
        tmp = t_1
    else if (x1 <= 8.5d-259) then
        tmp = t_0
    else if (x1 <= 2.45d+144) then
        tmp = t_1
    else
        tmp = x1 + ((x2 * (-6.0d0)) - (x1 * (2.0d0 - (x1 * 9.0d0))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 + ((x2 * -6.0) + (x1 * ((x1 * (9.0 + (x2 * 6.0))) - 2.0)));
	double t_1 = x1 + ((x2 * -6.0) - (x1 * (2.0 + (4.0 * (x2 * (3.0 - (2.0 * x2)))))));
	double tmp;
	if (x1 <= -1e+155) {
		tmp = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	} else if (x1 <= -1.2e+63) {
		tmp = t_0;
	} else if (x1 <= -6.5e-192) {
		tmp = t_1;
	} else if (x1 <= 8.5e-259) {
		tmp = t_0;
	} else if (x1 <= 2.45e+144) {
		tmp = t_1;
	} else {
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 - (x1 * 9.0))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 + ((x2 * -6.0) + (x1 * ((x1 * (9.0 + (x2 * 6.0))) - 2.0)))
	t_1 = x1 + ((x2 * -6.0) - (x1 * (2.0 + (4.0 * (x2 * (3.0 - (2.0 * x2)))))))
	tmp = 0
	if x1 <= -1e+155:
		tmp = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))))
	elif x1 <= -1.2e+63:
		tmp = t_0
	elif x1 <= -6.5e-192:
		tmp = t_1
	elif x1 <= 8.5e-259:
		tmp = t_0
	elif x1 <= 2.45e+144:
		tmp = t_1
	else:
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 - (x1 * 9.0))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(x1 * Float64(9.0 + Float64(x2 * 6.0))) - 2.0))))
	t_1 = Float64(x1 + Float64(Float64(x2 * -6.0) - Float64(x1 * Float64(2.0 + Float64(4.0 * Float64(x2 * Float64(3.0 - Float64(2.0 * x2))))))))
	tmp = 0.0
	if (x1 <= -1e+155)
		tmp = Float64(x1 + Float64(x1 + Float64(3.0 * Float64(x1 * Float64(Float64(x1 * 3.0) + -1.0)))));
	elseif (x1 <= -1.2e+63)
		tmp = t_0;
	elseif (x1 <= -6.5e-192)
		tmp = t_1;
	elseif (x1 <= 8.5e-259)
		tmp = t_0;
	elseif (x1 <= 2.45e+144)
		tmp = t_1;
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) - Float64(x1 * Float64(2.0 - Float64(x1 * 9.0)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 + ((x2 * -6.0) + (x1 * ((x1 * (9.0 + (x2 * 6.0))) - 2.0)));
	t_1 = x1 + ((x2 * -6.0) - (x1 * (2.0 + (4.0 * (x2 * (3.0 - (2.0 * x2)))))));
	tmp = 0.0;
	if (x1 <= -1e+155)
		tmp = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	elseif (x1 <= -1.2e+63)
		tmp = t_0;
	elseif (x1 <= -6.5e-192)
		tmp = t_1;
	elseif (x1 <= 8.5e-259)
		tmp = t_0;
	elseif (x1 <= 2.45e+144)
		tmp = t_1;
	else
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 - (x1 * 9.0))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(x1 * N[(9.0 + N[(x2 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] - N[(x1 * N[(2.0 + N[(4.0 * N[(x2 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -1e+155], N[(x1 + N[(x1 + N[(3.0 * N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -1.2e+63], t$95$0, If[LessEqual[x1, -6.5e-192], t$95$1, If[LessEqual[x1, 8.5e-259], t$95$0, If[LessEqual[x1, 2.45e+144], t$95$1, N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] - N[(x1 * N[(2.0 - N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -1.00000000000000001e155

   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 45.0%

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

   5. Taylor expanded in x2 around 0 100.0%

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

   if -1.00000000000000001e155 < x1 < -1.2e63 or -6.49999999999999966e-192 < x1 < 8.4999999999999994e-259

   1. Initial program 80.1%

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

   3. Taylor expanded in x1 around 0 58.9%

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

   4. Taylor expanded in x1 around 0 61.7%

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

   5. Taylor expanded in x1 around 0 64.1%

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

   6. Taylor expanded in x1 around inf 85.6%

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

      1. associate-*r* 85.6%

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

      2. *-commutative 85.6%

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

      3. associate-*r* 85.6%

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

      4. cancel-sign-sub-inv 85.6%

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

      5. metadata-eval 85.6%

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

      6. distribute-lft-in 85.6%

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

      7. metadata-eval 85.6%

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

      8. metadata-eval 85.6%

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

      9. distribute-lft-neg-in 85.6%

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

      10. distribute-rgt-neg-in 85.6%

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

      11. associate-*r* 85.6%

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

      12. metadata-eval 85.6%

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

      13. distribute-lft-neg-in 85.6%

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

      14. metadata-eval 85.6%

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

      15. *-commutative 85.6%

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

   8. Simplified 85.6%

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

   if -1.2e63 < x1 < -6.49999999999999966e-192 or 8.4999999999999994e-259 < x1 < 2.45e144

   1. Initial program 98.6%

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

   3. Taylor expanded in x1 around 0 74.4%

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

   4. Taylor expanded in x1 around 0 73.9%

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

   5. Taylor expanded in x1 around 0 73.4%

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

   if 2.45e144 < x1

   1. Initial program 3.2%

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

   3. Taylor expanded in x1 around 0 0.2%

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

   4. Taylor expanded in x1 around 0 80.6%

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

   5. Taylor expanded in x1 around 0 80.6%

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

   6. Taylor expanded in x2 around 0 97.1%

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

      1. *-commutative 97.1%

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

   8. Simplified 97.1%

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

4. Final simplification 82.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1 \cdot 10^{+155}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -1.2 \cdot 10^{+63}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot \left(9 + x2 \cdot 6\right) - 2\right)\right)\\ \mathbf{elif}\;x1 \leq -6.5 \cdot 10^{-192}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 + 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 8.5 \cdot 10^{-259}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot \left(9 + x2 \cdot 6\right) - 2\right)\right)\\ \mathbf{elif}\;x1 \leq 2.45 \cdot 10^{+144}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 + 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 - x1 \cdot 9\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 66.3% accurate, 4.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -4.4 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 2.45 \cdot 10^{+144}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot \left(9 + x2 \cdot 6\right) - 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 - x1 \cdot 9\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -4.4e+153)
   (+ x1 (+ x1 (* 3.0 (* x1 (+ (* x1 3.0) -1.0)))))
   (if (<= x1 2.45e+144)
     (+ x1 (+ (* x2 -6.0) (* x1 (- (* x1 (+ 9.0 (* x2 6.0))) 2.0))))
     (+ x1 (- (* x2 -6.0) (* x1 (- 2.0 (* x1 9.0))))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -4.4e+153) {
		tmp = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	} else if (x1 <= 2.45e+144) {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * (9.0 + (x2 * 6.0))) - 2.0)));
	} else {
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 - (x1 * 9.0))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x1 <= (-4.4d+153)) then
        tmp = x1 + (x1 + (3.0d0 * (x1 * ((x1 * 3.0d0) + (-1.0d0)))))
    else if (x1 <= 2.45d+144) then
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * ((x1 * (9.0d0 + (x2 * 6.0d0))) - 2.0d0)))
    else
        tmp = x1 + ((x2 * (-6.0d0)) - (x1 * (2.0d0 - (x1 * 9.0d0))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= -4.4e+153) {
		tmp = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	} else if (x1 <= 2.45e+144) {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * (9.0 + (x2 * 6.0))) - 2.0)));
	} else {
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 - (x1 * 9.0))));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -4.4e+153:
		tmp = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))))
	elif x1 <= 2.45e+144:
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * (9.0 + (x2 * 6.0))) - 2.0)))
	else:
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 - (x1 * 9.0))))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -4.4e+153)
		tmp = Float64(x1 + Float64(x1 + Float64(3.0 * Float64(x1 * Float64(Float64(x1 * 3.0) + -1.0)))));
	elseif (x1 <= 2.45e+144)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(x1 * Float64(9.0 + Float64(x2 * 6.0))) - 2.0))));
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) - Float64(x1 * Float64(2.0 - Float64(x1 * 9.0)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -4.4e+153)
		tmp = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	elseif (x1 <= 2.45e+144)
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * (9.0 + (x2 * 6.0))) - 2.0)));
	else
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 - (x1 * 9.0))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -4.4e+153], N[(x1 + N[(x1 + N[(3.0 * N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 2.45e+144], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(x1 * N[(9.0 + N[(x2 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] - N[(x1 * N[(2.0 - N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -4.3999999999999999e153

   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 45.0%

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

   5. Taylor expanded in x2 around 0 100.0%

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

   if -4.3999999999999999e153 < x1 < 2.45e144

   1. Initial program 94.0%

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

   3. Taylor expanded in x1 around 0 70.5%

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

   4. Taylor expanded in x1 around 0 70.8%

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

   5. Taylor expanded in x1 around 0 72.3%

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

   6. Taylor expanded in x1 around inf 62.2%

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

      1. associate-*r* 62.2%

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

      2. *-commutative 62.2%

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

      3. associate-*r* 62.2%

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

      4. cancel-sign-sub-inv 62.2%

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

      5. metadata-eval 62.2%

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

      6. distribute-lft-in 62.2%

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

      7. metadata-eval 62.2%

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

      8. metadata-eval 62.2%

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

      9. distribute-lft-neg-in 62.2%

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

      10. distribute-rgt-neg-in 62.2%

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

      11. associate-*r* 62.2%

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

      12. metadata-eval 62.2%

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

      13. distribute-lft-neg-in 62.2%

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

      14. metadata-eval 62.2%

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

      15. *-commutative 62.2%

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

   8. Simplified 62.2%

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

   if 2.45e144 < x1

   1. Initial program 3.2%

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

   3. Taylor expanded in x1 around 0 0.2%

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

   4. Taylor expanded in x1 around 0 80.6%

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

   5. Taylor expanded in x1 around 0 80.6%

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

   6. Taylor expanded in x2 around 0 97.1%

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

      1. *-commutative 97.1%

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

   8. Simplified 97.1%

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

4. Final simplification 72.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4.4 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 2.45 \cdot 10^{+144}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot \left(9 + x2 \cdot 6\right) - 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 - x1 \cdot 9\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 62.8% accurate, 5.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -9 \cdot 10^{+60} \lor \neg \left(x1 \leq 1.25 \cdot 10^{-23}\right):\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot -2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x1 -9e+60) (not (<= x1 1.25e-23)))
   (+ x1 (+ x1 (* 3.0 (* x1 (+ (* x1 3.0) -1.0)))))
   (+ x1 (+ (* x2 -6.0) (* x1 -2.0)))))

C

double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -9e+60) || !(x1 <= 1.25e-23)) {
		tmp = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	} else {
		tmp = x1 + ((x2 * -6.0) + (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 ((x1 <= (-9d+60)) .or. (.not. (x1 <= 1.25d-23))) then
        tmp = x1 + (x1 + (3.0d0 * (x1 * ((x1 * 3.0d0) + (-1.0d0)))))
    else
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * (-2.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -9e+60) || !(x1 <= 1.25e-23)) {
		tmp = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * -2.0));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x1 <= -9e+60) or not (x1 <= 1.25e-23):
		tmp = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))))
	else:
		tmp = x1 + ((x2 * -6.0) + (x1 * -2.0))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x1 <= -9e+60) || !(x1 <= 1.25e-23))
		tmp = Float64(x1 + Float64(x1 + Float64(3.0 * Float64(x1 * Float64(Float64(x1 * 3.0) + -1.0)))));
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * -2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x1 <= -9e+60) || ~((x1 <= 1.25e-23)))
		tmp = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	else
		tmp = x1 + ((x2 * -6.0) + (x1 * -2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x1, -9e+60], N[Not[LessEqual[x1, 1.25e-23]], $MachinePrecision]], N[(x1 + N[(x1 + N[(3.0 * N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x1 < -9.00000000000000026e60 or 1.2500000000000001e-23 < x1

   1. Initial program 31.4%

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

   3. Taylor expanded in x1 around 0 11.4%

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

   4. Taylor expanded in x1 around 0 49.2%

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

   5. Taylor expanded in x2 around 0 63.6%

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

   if -9.00000000000000026e60 < x1 < 1.2500000000000001e-23

   1. Initial program 99.4%

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

   3. Taylor expanded in x1 around 0 84.3%

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

   4. Taylor expanded in x1 around 0 83.8%

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

   5. Taylor expanded in x2 around 0 70.3%

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

   6. Taylor expanded in x1 around 0 69.8%

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

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -9 \cdot 10^{+60} \lor \neg \left(x1 \leq 1.25 \cdot 10^{-23}\right):\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot -2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 44.3% accurate, 9.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq 1.35:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot -2\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot \left(\frac{x1}{x2} - 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 1.35) (+ x1 (+ (* x2 -6.0) (* x1 -2.0))) (* x2 (- (/ x1 x2) 6.0))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= 1.35) {
		tmp = x1 + ((x2 * -6.0) + (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 <= 1.35d0) then
        tmp = x1 + ((x2 * (-6.0d0)) + (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 <= 1.35) {
		tmp = x1 + ((x2 * -6.0) + (x1 * -2.0));
	} else {
		tmp = x2 * ((x1 / x2) - 6.0);
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= 1.35:
		tmp = x1 + ((x2 * -6.0) + (x1 * -2.0))
	else:
		tmp = x2 * ((x1 / x2) - 6.0)
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= 1.35)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + 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 <= 1.35)
		tmp = x1 + ((x2 * -6.0) + (x1 * -2.0));
	else
		tmp = x2 * ((x1 / x2) - 6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, 1.35], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x2 * N[(N[(x1 / x2), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x1 < 1.3500000000000001

   1. Initial program 74.5%

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

   3. Taylor expanded in x1 around 0 62.9%

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

   4. Taylor expanded in x1 around 0 72.3%

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

   5. Taylor expanded in x2 around 0 70.0%

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

   6. Taylor expanded in x1 around 0 51.7%

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

   if 1.3500000000000001 < x1

   1. Initial program 48.0%

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

   3. Taylor expanded in x1 around 0 12.2%

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

   4. Taylor expanded in x1 around 0 53.8%

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

   5. Taylor expanded in x1 around 0 5.1%

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

   6. Taylor expanded in x2 around inf 20.7%

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

4. Final simplification 44.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq 1.35:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot -2\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot \left(\frac{x1}{x2} - 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 63.0% accurate, 9.8× speedup

Math

\[\begin{array}{l} \\ x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 - x1 \cdot 9\right)\right) \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (+ x1 (- (* x2 -6.0) (* x1 (- 2.0 (* x1 9.0))))))

C

double code(double x1, double x2) {
	return x1 + ((x2 * -6.0) - (x1 * (2.0 - (x1 * 9.0))));
}

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 - (x1 * 9.0d0))))
end function

Java

public static double code(double x1, double x2) {
	return x1 + ((x2 * -6.0) - (x1 * (2.0 - (x1 * 9.0))));
}

Python

def code(x1, x2):
	return x1 + ((x2 * -6.0) - (x1 * (2.0 - (x1 * 9.0))))

Julia

function code(x1, x2)
	return Float64(x1 + Float64(Float64(x2 * -6.0) - Float64(x1 * Float64(2.0 - Float64(x1 * 9.0)))))
end

MATLAB

function tmp = code(x1, x2)
	tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 - (x1 * 9.0))));
end

Wolfram

code[x1_, x2_] := N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] - N[(x1 * N[(2.0 - N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 68.3%

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

3. Taylor expanded in x1 around 0 51.0%

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

4. Taylor expanded in x1 around 0 68.0%

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

5. Taylor expanded in x1 around 0 71.4%

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

6. Taylor expanded in x2 around 0 66.6%

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

   1. *-commutative 66.6%

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

8. Simplified 66.6%

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

9. Final simplification 66.6%

   \[\leadsto x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 - x1 \cdot 9\right)\right) \]
10. Add Preprocessing

Alternative 26: 31.8% accurate, 18.1× speedup

Math

\[\begin{array}{l} \\ x2 \cdot \left(\frac{x1}{x2} - 6\right) \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x1_, x2_] := N[(x2 * N[(N[(x1 / x2), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 68.3%

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

3. Taylor expanded in x1 around 0 51.0%

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

4. Taylor expanded in x1 around 0 68.0%

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

5. Taylor expanded in x1 around 0 27.1%

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

6. Taylor expanded in x2 around inf 30.8%

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

Alternative 27: 26.4% accurate, 25.4× speedup

Math

\[\begin{array}{l} \\ x1 + x2 \cdot -6 \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 68.3%

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

3. Taylor expanded in x1 around 0 51.0%

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

4. Taylor expanded in x1 around 0 68.0%

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

5. Taylor expanded in x1 around 0 27.1%

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

6. Final simplification 27.1%

   \[\leadsto x1 + x2 \cdot -6 \]
7. Add Preprocessing

Alternative 28: 26.2% accurate, 42.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 68.3%

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

3. Taylor expanded in x1 around 0 51.0%

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

4. Taylor expanded in x1 around 0 68.0%

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

5. Taylor expanded in x1 around 0 27.1%

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

6. Taylor expanded in x1 around 0 26.9%

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

   1. *-commutative 26.9%

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

8. Simplified 26.9%

   \[\leadsto \color{blue}{x2 \cdot -6} \]
9. Add Preprocessing

Alternative 29: 3.3% accurate, 127.0× speedup

Math

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

FPCore

(FPCore (x1 x2) :precision binary64 x1)

C

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

Fortran

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

Java

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

Python

def code(x1, x2):
	return x1

Julia

function code(x1, x2)
	return x1
end

MATLAB

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

Wolfram

code[x1_, x2_] := x1

Derivation

1. Initial program 68.3%

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

3. Taylor expanded in x1 around 0 51.0%

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

4. Taylor expanded in x1 around 0 68.0%

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

5. Taylor expanded in x1 around 0 27.1%

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

6. Taylor expanded in x1 around inf 3.1%

   \[\leadsto \color{blue}{x1} \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024103 
(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))))))