Rosa's FloatVsDoubleBenchmark

Percentage Accurate: 70.7% → 99.7%

Time: 1.5min

Alternatives: 25

Speedup: 3.4×

• 46.5% 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: 70.7% 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

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

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ (* x1 x1) 1.0))
        (t_1 (* x1 (* x1 3.0)))
        (t_2 (* 3.0 (* x1 x1)))
        (t_3 (- -1.0 (* x1 x1)))
        (t_4 (- x1 (+ t_1 (* 2.0 x2))))
        (t_5 (/ t_4 t_0))
        (t_6 (/ t_4 t_3))
        (t_7 (fma x1 (* x1 3.0) (* 2.0 x2)))
        (t_8 (/ (- t_7 x1) (fma x1 x1 1.0)))
        (t_9 (/ (- x1 t_7) (fma x1 x1 1.0))))
   (if (<=
        (+
         x1
         (-
          (* 3.0 (/ (- x1 (- t_1 (* 2.0 x2))) t_3))
          (-
           (-
            (+
             (* t_1 t_5)
             (*
              t_0
              (-
               (* (* t_6 (* x1 2.0)) (+ 3.0 t_5))
               (* (* x1 x1) (- (* t_6 4.0) 6.0)))))
            (* x1 (* x1 x1)))
           x1)))
        INFINITY)
     (+
      x1
      (fma
       3.0
       (/ (- t_2 (fma 2.0 x2 x1)) (fma x1 x1 1.0))
       (+
        x1
        (fma
         (fma x1 x1 1.0)
         (fma x1 (* x1 (fma t_8 4.0 -6.0)) (* (* x1 (* 2.0 t_9)) (- t_9 -3.0)))
         (fma t_2 t_8 (pow x1 3.0))))))
     (+
      x1
      (+
       (+ x1 (* (pow x1 4.0) (- 6.0 (/ (- 3.0 (/ (* x2 8.0) x1)) x1))))
       9.0)))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = 3.0 * (x1 * x1);
	double t_3 = -1.0 - (x1 * x1);
	double t_4 = x1 - (t_1 + (2.0 * x2));
	double t_5 = t_4 / t_0;
	double t_6 = t_4 / t_3;
	double t_7 = fma(x1, (x1 * 3.0), (2.0 * x2));
	double t_8 = (t_7 - x1) / fma(x1, x1, 1.0);
	double t_9 = (x1 - t_7) / fma(x1, x1, 1.0);
	double tmp;
	if ((x1 + ((3.0 * ((x1 - (t_1 - (2.0 * x2))) / t_3)) - ((((t_1 * t_5) + (t_0 * (((t_6 * (x1 * 2.0)) * (3.0 + t_5)) - ((x1 * x1) * ((t_6 * 4.0) - 6.0))))) - (x1 * (x1 * x1))) - x1))) <= ((double) INFINITY)) {
		tmp = x1 + fma(3.0, ((t_2 - fma(2.0, x2, x1)) / fma(x1, x1, 1.0)), (x1 + fma(fma(x1, x1, 1.0), fma(x1, (x1 * fma(t_8, 4.0, -6.0)), ((x1 * (2.0 * t_9)) * (t_9 - -3.0))), fma(t_2, t_8, pow(x1, 3.0)))));
	} else {
		tmp = x1 + ((x1 + (pow(x1, 4.0) * (6.0 - ((3.0 - ((x2 * 8.0) / x1)) / x1)))) + 9.0);
	}
	return tmp;
}

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * x1) + 1.0)
	t_1 = Float64(x1 * Float64(x1 * 3.0))
	t_2 = Float64(3.0 * Float64(x1 * x1))
	t_3 = Float64(-1.0 - Float64(x1 * x1))
	t_4 = Float64(x1 - Float64(t_1 + Float64(2.0 * x2)))
	t_5 = Float64(t_4 / t_0)
	t_6 = Float64(t_4 / t_3)
	t_7 = fma(x1, Float64(x1 * 3.0), Float64(2.0 * x2))
	t_8 = Float64(Float64(t_7 - x1) / fma(x1, x1, 1.0))
	t_9 = Float64(Float64(x1 - t_7) / fma(x1, x1, 1.0))
	tmp = 0.0
	if (Float64(x1 + Float64(Float64(3.0 * Float64(Float64(x1 - Float64(t_1 - Float64(2.0 * x2))) / t_3)) - Float64(Float64(Float64(Float64(t_1 * t_5) + Float64(t_0 * Float64(Float64(Float64(t_6 * Float64(x1 * 2.0)) * Float64(3.0 + t_5)) - Float64(Float64(x1 * x1) * Float64(Float64(t_6 * 4.0) - 6.0))))) - Float64(x1 * Float64(x1 * x1))) - x1))) <= Inf)
		tmp = Float64(x1 + fma(3.0, Float64(Float64(t_2 - fma(2.0, x2, x1)) / fma(x1, x1, 1.0)), Float64(x1 + fma(fma(x1, x1, 1.0), fma(x1, Float64(x1 * fma(t_8, 4.0, -6.0)), Float64(Float64(x1 * Float64(2.0 * t_9)) * Float64(t_9 - -3.0))), fma(t_2, t_8, (x1 ^ 3.0))))));
	else
		tmp = Float64(x1 + Float64(Float64(x1 + Float64((x1 ^ 4.0) * Float64(6.0 - Float64(Float64(3.0 - Float64(Float64(x2 * 8.0) / x1)) / x1)))) + 9.0));
	end
	return tmp
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(3.0 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(x1 - N[(t$95$1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(t$95$4 / t$95$0), $MachinePrecision]}, Block[{t$95$6 = N[(t$95$4 / t$95$3), $MachinePrecision]}, Block[{t$95$7 = N[(x1 * N[(x1 * 3.0), $MachinePrecision] + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$8 = N[(N[(t$95$7 - x1), $MachinePrecision] / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$9 = N[(N[(x1 - t$95$7), $MachinePrecision] / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x1 + N[(N[(3.0 * N[(N[(x1 - N[(t$95$1 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$3), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(N[(t$95$1 * t$95$5), $MachinePrecision] + N[(t$95$0 * N[(N[(N[(t$95$6 * N[(x1 * 2.0), $MachinePrecision]), $MachinePrecision] * N[(3.0 + t$95$5), $MachinePrecision]), $MachinePrecision] - N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$6 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(x1 + N[(3.0 * N[(N[(t$95$2 - 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$8 * 4.0 + -6.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * N[(2.0 * t$95$9), $MachinePrecision]), $MachinePrecision] * N[(t$95$9 - -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$2 * t$95$8 + N[Power[x1, 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x1 + N[(N[Power[x1, 4.0], $MachinePrecision] * N[(6.0 - N[(N[(3.0 - N[(N[(x2 * 8.0), $MachinePrecision] / x1), $MachinePrecision]), $MachinePrecision] / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 9.0), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 99.4%

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

   3. Simplified 99.6%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in x1 around -inf 21.3%

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

   4. Taylor expanded in x1 around inf 100.0%

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

   5. Taylor expanded in x2 around inf 100.0%

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

      1. *-commutative 100.0%

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

   7. Simplified 100.0%

      \[\leadsto x1 + \left(\left({x1}^{4} \cdot \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{\color{blue}{x2 \cdot 8}}{x1}}{x1}\right) + x1\right) + 9\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.7%

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

Alternative 2: 99.5% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

public static double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = x1 - (t_1 + (2.0 * x2));
	double t_3 = t_2 / t_0;
	double t_4 = -1.0 - (x1 * x1);
	double t_5 = t_2 / t_4;
	double t_6 = x1 + ((3.0 * ((x1 - (t_1 - (2.0 * x2))) / t_4)) - ((((t_1 * t_3) + (t_0 * (((t_5 * (x1 * 2.0)) * (3.0 + t_3)) - ((x1 * x1) * ((t_5 * 4.0) - 6.0))))) - (x1 * (x1 * x1))) - x1));
	double tmp;
	if (t_6 <= Double.POSITIVE_INFINITY) {
		tmp = t_6;
	} else {
		tmp = x1 + ((x1 + (Math.pow(x1, 4.0) * (6.0 - ((3.0 - ((x2 * 8.0) / x1)) / x1)))) + 9.0);
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x1 * x1) + 1.0
	t_1 = x1 * (x1 * 3.0)
	t_2 = x1 - (t_1 + (2.0 * x2))
	t_3 = t_2 / t_0
	t_4 = -1.0 - (x1 * x1)
	t_5 = t_2 / t_4
	t_6 = x1 + ((3.0 * ((x1 - (t_1 - (2.0 * x2))) / t_4)) - ((((t_1 * t_3) + (t_0 * (((t_5 * (x1 * 2.0)) * (3.0 + t_3)) - ((x1 * x1) * ((t_5 * 4.0) - 6.0))))) - (x1 * (x1 * x1))) - x1))
	tmp = 0
	if t_6 <= math.inf:
		tmp = t_6
	else:
		tmp = x1 + ((x1 + (math.pow(x1, 4.0) * (6.0 - ((3.0 - ((x2 * 8.0) / x1)) / x1)))) + 9.0)
	return tmp

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 99.4%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in x1 around -inf 21.3%

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

   4. Taylor expanded in x1 around inf 100.0%

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

   5. Taylor expanded in x2 around inf 100.0%

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

      1. *-commutative 100.0%

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

   7. Simplified 100.0%

      \[\leadsto x1 + \left(\left({x1}^{4} \cdot \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{\color{blue}{x2 \cdot 8}}{x1}}{x1}\right) + x1\right) + 9\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.6%

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

Alternative 3: 98.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -1 - x1 \cdot x1\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := x1 - \left(t\_1 + 2 \cdot x2\right)\\ t_3 := \frac{t\_2}{t\_0}\\ \mathbf{if}\;x1 \leq -9 \cdot 10^{+65} \lor \neg \left(x1 \leq 2.65 \cdot 10^{+44}\right):\\ \;\;\;\;x1 + \left(\left(x1 + {x1}^{4} \cdot \left(6 - \frac{3 - \frac{x2 \cdot 8}{x1}}{x1}\right)\right) + 9\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{x1 - \left(t\_1 - 2 \cdot x2\right)}{t\_0} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(\left(t\_3 \cdot \left(x1 \cdot 2\right)\right) \cdot \left(3 + \frac{t\_2}{x1 \cdot x1 + 1}\right) - \left(x1 \cdot x1\right) \cdot \left(t\_3 \cdot 4 - 6\right)\right) \cdot t\_0 + 3 \cdot t\_1\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (- -1.0 (* x1 x1)))
        (t_1 (* x1 (* x1 3.0)))
        (t_2 (- x1 (+ t_1 (* 2.0 x2))))
        (t_3 (/ t_2 t_0)))
   (if (or (<= x1 -9e+65) (not (<= x1 2.65e+44)))
     (+
      x1
      (+ (+ x1 (* (pow x1 4.0) (- 6.0 (/ (- 3.0 (/ (* x2 8.0) x1)) x1)))) 9.0))
     (+
      x1
      (+
       (* 3.0 (/ (- x1 (- t_1 (* 2.0 x2))) t_0))
       (+
        x1
        (+
         (* x1 (* x1 x1))
         (+
          (*
           (-
            (* (* t_3 (* x1 2.0)) (+ 3.0 (/ t_2 (+ (* x1 x1) 1.0))))
            (* (* x1 x1) (- (* t_3 4.0) 6.0)))
           t_0)
          (* 3.0 t_1)))))))))

C

double code(double x1, double x2) {
	double t_0 = -1.0 - (x1 * x1);
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = x1 - (t_1 + (2.0 * x2));
	double t_3 = t_2 / t_0;
	double tmp;
	if ((x1 <= -9e+65) || !(x1 <= 2.65e+44)) {
		tmp = x1 + ((x1 + (pow(x1, 4.0) * (6.0 - ((3.0 - ((x2 * 8.0) / x1)) / x1)))) + 9.0);
	} else {
		tmp = x1 + ((3.0 * ((x1 - (t_1 - (2.0 * x2))) / t_0)) + (x1 + ((x1 * (x1 * x1)) + (((((t_3 * (x1 * 2.0)) * (3.0 + (t_2 / ((x1 * x1) + 1.0)))) - ((x1 * x1) * ((t_3 * 4.0) - 6.0))) * t_0) + (3.0 * t_1)))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_0 = (-1.0d0) - (x1 * x1)
    t_1 = x1 * (x1 * 3.0d0)
    t_2 = x1 - (t_1 + (2.0d0 * x2))
    t_3 = t_2 / t_0
    if ((x1 <= (-9d+65)) .or. (.not. (x1 <= 2.65d+44))) then
        tmp = x1 + ((x1 + ((x1 ** 4.0d0) * (6.0d0 - ((3.0d0 - ((x2 * 8.0d0) / x1)) / x1)))) + 9.0d0)
    else
        tmp = x1 + ((3.0d0 * ((x1 - (t_1 - (2.0d0 * x2))) / t_0)) + (x1 + ((x1 * (x1 * x1)) + (((((t_3 * (x1 * 2.0d0)) * (3.0d0 + (t_2 / ((x1 * x1) + 1.0d0)))) - ((x1 * x1) * ((t_3 * 4.0d0) - 6.0d0))) * t_0) + (3.0d0 * t_1)))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = -1.0 - (x1 * x1);
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = x1 - (t_1 + (2.0 * x2));
	double t_3 = t_2 / t_0;
	double tmp;
	if ((x1 <= -9e+65) || !(x1 <= 2.65e+44)) {
		tmp = x1 + ((x1 + (Math.pow(x1, 4.0) * (6.0 - ((3.0 - ((x2 * 8.0) / x1)) / x1)))) + 9.0);
	} else {
		tmp = x1 + ((3.0 * ((x1 - (t_1 - (2.0 * x2))) / t_0)) + (x1 + ((x1 * (x1 * x1)) + (((((t_3 * (x1 * 2.0)) * (3.0 + (t_2 / ((x1 * x1) + 1.0)))) - ((x1 * x1) * ((t_3 * 4.0) - 6.0))) * t_0) + (3.0 * t_1)))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = -1.0 - (x1 * x1)
	t_1 = x1 * (x1 * 3.0)
	t_2 = x1 - (t_1 + (2.0 * x2))
	t_3 = t_2 / t_0
	tmp = 0
	if (x1 <= -9e+65) or not (x1 <= 2.65e+44):
		tmp = x1 + ((x1 + (math.pow(x1, 4.0) * (6.0 - ((3.0 - ((x2 * 8.0) / x1)) / x1)))) + 9.0)
	else:
		tmp = x1 + ((3.0 * ((x1 - (t_1 - (2.0 * x2))) / t_0)) + (x1 + ((x1 * (x1 * x1)) + (((((t_3 * (x1 * 2.0)) * (3.0 + (t_2 / ((x1 * x1) + 1.0)))) - ((x1 * x1) * ((t_3 * 4.0) - 6.0))) * t_0) + (3.0 * t_1)))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(-1.0 - Float64(x1 * x1))
	t_1 = Float64(x1 * Float64(x1 * 3.0))
	t_2 = Float64(x1 - Float64(t_1 + Float64(2.0 * x2)))
	t_3 = Float64(t_2 / t_0)
	tmp = 0.0
	if ((x1 <= -9e+65) || !(x1 <= 2.65e+44))
		tmp = Float64(x1 + Float64(Float64(x1 + Float64((x1 ^ 4.0) * Float64(6.0 - Float64(Float64(3.0 - Float64(Float64(x2 * 8.0) / x1)) / x1)))) + 9.0));
	else
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(x1 - Float64(t_1 - Float64(2.0 * x2))) / t_0)) + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(Float64(Float64(Float64(t_3 * Float64(x1 * 2.0)) * Float64(3.0 + Float64(t_2 / Float64(Float64(x1 * x1) + 1.0)))) - Float64(Float64(x1 * x1) * Float64(Float64(t_3 * 4.0) - 6.0))) * t_0) + Float64(3.0 * t_1))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = -1.0 - (x1 * x1);
	t_1 = x1 * (x1 * 3.0);
	t_2 = x1 - (t_1 + (2.0 * x2));
	t_3 = t_2 / t_0;
	tmp = 0.0;
	if ((x1 <= -9e+65) || ~((x1 <= 2.65e+44)))
		tmp = x1 + ((x1 + ((x1 ^ 4.0) * (6.0 - ((3.0 - ((x2 * 8.0) / x1)) / x1)))) + 9.0);
	else
		tmp = x1 + ((3.0 * ((x1 - (t_1 - (2.0 * x2))) / t_0)) + (x1 + ((x1 * (x1 * x1)) + (((((t_3 * (x1 * 2.0)) * (3.0 + (t_2 / ((x1 * x1) + 1.0)))) - ((x1 * x1) * ((t_3 * 4.0) - 6.0))) * t_0) + (3.0 * t_1)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x1 - N[(t$95$1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 / t$95$0), $MachinePrecision]}, If[Or[LessEqual[x1, -9e+65], N[Not[LessEqual[x1, 2.65e+44]], $MachinePrecision]], N[(x1 + N[(N[(x1 + N[(N[Power[x1, 4.0], $MachinePrecision] * N[(6.0 - N[(N[(3.0 - N[(N[(x2 * 8.0), $MachinePrecision] / x1), $MachinePrecision]), $MachinePrecision] / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 9.0), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(3.0 * N[(N[(x1 - N[(t$95$1 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(N[(N[(t$95$3 * N[(x1 * 2.0), $MachinePrecision]), $MachinePrecision] * N[(3.0 + N[(t$95$2 / N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$3 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * t$95$0), $MachinePrecision] + N[(3.0 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 2 regimes

2. if x1 < -9e65 or 2.65e44 < x1

   1. Initial program 26.4%

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

   3. Taylor expanded in x1 around -inf 42.1%

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

   4. Taylor expanded in x1 around inf 100.0%

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

   5. Taylor expanded in x2 around inf 100.0%

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

      1. *-commutative 100.0%

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

   7. Simplified 100.0%

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

   if -9e65 < x1 < 2.65e44

   1. Initial program 99.4%

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

   3. Taylor expanded in x1 around inf 99.2%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -9 \cdot 10^{+65} \lor \neg \left(x1 \leq 2.65 \cdot 10^{+44}\right):\\ \;\;\;\;x1 + \left(\left(x1 + {x1}^{4} \cdot \left(6 - \frac{3 - \frac{x2 \cdot 8}{x1}}{x1}\right)\right) + 9\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right)}{-1 - x1 \cdot x1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(\left(\frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{-1 - x1 \cdot x1} \cdot \left(x1 \cdot 2\right)\right) \cdot \left(3 + \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right) - \left(x1 \cdot x1\right) \cdot \left(\frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{-1 - x1 \cdot x1} \cdot 4 - 6\right)\right) \cdot \left(-1 - x1 \cdot x1\right) + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right)\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 97.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -1 - x1 \cdot x1\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := x1 - \left(t\_1 + 2 \cdot x2\right)\\ t_3 := \frac{t\_2}{t\_0}\\ \mathbf{if}\;x1 \leq -2 \cdot 10^{+103} \lor \neg \left(x1 \leq 2.15 \cdot 10^{+49}\right):\\ \;\;\;\;x1 + \left(9 + \left(x1 + 6 \cdot {x1}^{4}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{x1 - \left(t\_1 - 2 \cdot x2\right)}{t\_0} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(\left(t\_3 \cdot \left(x1 \cdot 2\right)\right) \cdot \left(3 + \frac{t\_2}{x1 \cdot x1 + 1}\right) - \left(x1 \cdot x1\right) \cdot \left(t\_3 \cdot 4 - 6\right)\right) \cdot t\_0 + 3 \cdot t\_1\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (- -1.0 (* x1 x1)))
        (t_1 (* x1 (* x1 3.0)))
        (t_2 (- x1 (+ t_1 (* 2.0 x2))))
        (t_3 (/ t_2 t_0)))
   (if (or (<= x1 -2e+103) (not (<= x1 2.15e+49)))
     (+ x1 (+ 9.0 (+ x1 (* 6.0 (pow x1 4.0)))))
     (+
      x1
      (+
       (* 3.0 (/ (- x1 (- t_1 (* 2.0 x2))) t_0))
       (+
        x1
        (+
         (* x1 (* x1 x1))
         (+
          (*
           (-
            (* (* t_3 (* x1 2.0)) (+ 3.0 (/ t_2 (+ (* x1 x1) 1.0))))
            (* (* x1 x1) (- (* t_3 4.0) 6.0)))
           t_0)
          (* 3.0 t_1)))))))))

C

double code(double x1, double x2) {
	double t_0 = -1.0 - (x1 * x1);
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = x1 - (t_1 + (2.0 * x2));
	double t_3 = t_2 / t_0;
	double tmp;
	if ((x1 <= -2e+103) || !(x1 <= 2.15e+49)) {
		tmp = x1 + (9.0 + (x1 + (6.0 * pow(x1, 4.0))));
	} else {
		tmp = x1 + ((3.0 * ((x1 - (t_1 - (2.0 * x2))) / t_0)) + (x1 + ((x1 * (x1 * x1)) + (((((t_3 * (x1 * 2.0)) * (3.0 + (t_2 / ((x1 * x1) + 1.0)))) - ((x1 * x1) * ((t_3 * 4.0) - 6.0))) * t_0) + (3.0 * t_1)))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_0 = (-1.0d0) - (x1 * x1)
    t_1 = x1 * (x1 * 3.0d0)
    t_2 = x1 - (t_1 + (2.0d0 * x2))
    t_3 = t_2 / t_0
    if ((x1 <= (-2d+103)) .or. (.not. (x1 <= 2.15d+49))) then
        tmp = x1 + (9.0d0 + (x1 + (6.0d0 * (x1 ** 4.0d0))))
    else
        tmp = x1 + ((3.0d0 * ((x1 - (t_1 - (2.0d0 * x2))) / t_0)) + (x1 + ((x1 * (x1 * x1)) + (((((t_3 * (x1 * 2.0d0)) * (3.0d0 + (t_2 / ((x1 * x1) + 1.0d0)))) - ((x1 * x1) * ((t_3 * 4.0d0) - 6.0d0))) * t_0) + (3.0d0 * t_1)))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = -1.0 - (x1 * x1);
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = x1 - (t_1 + (2.0 * x2));
	double t_3 = t_2 / t_0;
	double tmp;
	if ((x1 <= -2e+103) || !(x1 <= 2.15e+49)) {
		tmp = x1 + (9.0 + (x1 + (6.0 * Math.pow(x1, 4.0))));
	} else {
		tmp = x1 + ((3.0 * ((x1 - (t_1 - (2.0 * x2))) / t_0)) + (x1 + ((x1 * (x1 * x1)) + (((((t_3 * (x1 * 2.0)) * (3.0 + (t_2 / ((x1 * x1) + 1.0)))) - ((x1 * x1) * ((t_3 * 4.0) - 6.0))) * t_0) + (3.0 * t_1)))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = -1.0 - (x1 * x1)
	t_1 = x1 * (x1 * 3.0)
	t_2 = x1 - (t_1 + (2.0 * x2))
	t_3 = t_2 / t_0
	tmp = 0
	if (x1 <= -2e+103) or not (x1 <= 2.15e+49):
		tmp = x1 + (9.0 + (x1 + (6.0 * math.pow(x1, 4.0))))
	else:
		tmp = x1 + ((3.0 * ((x1 - (t_1 - (2.0 * x2))) / t_0)) + (x1 + ((x1 * (x1 * x1)) + (((((t_3 * (x1 * 2.0)) * (3.0 + (t_2 / ((x1 * x1) + 1.0)))) - ((x1 * x1) * ((t_3 * 4.0) - 6.0))) * t_0) + (3.0 * t_1)))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(-1.0 - Float64(x1 * x1))
	t_1 = Float64(x1 * Float64(x1 * 3.0))
	t_2 = Float64(x1 - Float64(t_1 + Float64(2.0 * x2)))
	t_3 = Float64(t_2 / t_0)
	tmp = 0.0
	if ((x1 <= -2e+103) || !(x1 <= 2.15e+49))
		tmp = Float64(x1 + Float64(9.0 + Float64(x1 + Float64(6.0 * (x1 ^ 4.0)))));
	else
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(x1 - Float64(t_1 - Float64(2.0 * x2))) / t_0)) + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(Float64(Float64(Float64(t_3 * Float64(x1 * 2.0)) * Float64(3.0 + Float64(t_2 / Float64(Float64(x1 * x1) + 1.0)))) - Float64(Float64(x1 * x1) * Float64(Float64(t_3 * 4.0) - 6.0))) * t_0) + Float64(3.0 * t_1))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = -1.0 - (x1 * x1);
	t_1 = x1 * (x1 * 3.0);
	t_2 = x1 - (t_1 + (2.0 * x2));
	t_3 = t_2 / t_0;
	tmp = 0.0;
	if ((x1 <= -2e+103) || ~((x1 <= 2.15e+49)))
		tmp = x1 + (9.0 + (x1 + (6.0 * (x1 ^ 4.0))));
	else
		tmp = x1 + ((3.0 * ((x1 - (t_1 - (2.0 * x2))) / t_0)) + (x1 + ((x1 * (x1 * x1)) + (((((t_3 * (x1 * 2.0)) * (3.0 + (t_2 / ((x1 * x1) + 1.0)))) - ((x1 * x1) * ((t_3 * 4.0) - 6.0))) * t_0) + (3.0 * t_1)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x1 - N[(t$95$1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 / t$95$0), $MachinePrecision]}, If[Or[LessEqual[x1, -2e+103], N[Not[LessEqual[x1, 2.15e+49]], $MachinePrecision]], N[(x1 + N[(9.0 + N[(x1 + N[(6.0 * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(3.0 * N[(N[(x1 - N[(t$95$1 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(N[(N[(t$95$3 * N[(x1 * 2.0), $MachinePrecision]), $MachinePrecision] * N[(3.0 + N[(t$95$2 / N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$3 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * t$95$0), $MachinePrecision] + N[(3.0 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 2 regimes

2. if x1 < -2e103 or 2.15e49 < x1

   1. Initial program 19.5%

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

   3. Taylor expanded in x1 around -inf 36.9%

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

   4. Taylor expanded in x1 around inf 100.0%

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

   5. Taylor expanded in x1 around inf 98.9%

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

   if -2e103 < x1 < 2.15e49

   1. Initial program 98.8%

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

   3. Taylor expanded in x1 around inf 98.6%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -2 \cdot 10^{+103} \lor \neg \left(x1 \leq 2.15 \cdot 10^{+49}\right):\\ \;\;\;\;x1 + \left(9 + \left(x1 + 6 \cdot {x1}^{4}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right)}{-1 - x1 \cdot x1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(\left(\frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{-1 - x1 \cdot x1} \cdot \left(x1 \cdot 2\right)\right) \cdot \left(3 + \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right) - \left(x1 \cdot x1\right) \cdot \left(\frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{-1 - x1 \cdot x1} \cdot 4 - 6\right)\right) \cdot \left(-1 - x1 \cdot x1\right) + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right)\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 97.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := x1 - \left(t\_0 + 2 \cdot x2\right)\\ t_2 := -1 - x1 \cdot x1\\ \mathbf{if}\;x1 \leq -2 \cdot 10^{+103} \lor \neg \left(x1 \leq 1.6 \cdot 10^{+75}\right):\\ \;\;\;\;x1 + \left(9 + \left(x1 + 6 \cdot {x1}^{4}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 - \left(3 \cdot \frac{\left(t\_0 - 2 \cdot x2\right) - x1}{t\_2} - \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot t\_0 + \left(\left(\frac{t\_1}{t\_2} \cdot \left(x1 \cdot 2\right)\right) \cdot \left(3 + \frac{t\_1}{x1 \cdot x1 + 1}\right) - \left(x1 \cdot x1\right) \cdot 6\right) \cdot t\_2\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (- x1 (+ t_0 (* 2.0 x2))))
        (t_2 (- -1.0 (* x1 x1))))
   (if (or (<= x1 -2e+103) (not (<= x1 1.6e+75)))
     (+ x1 (+ 9.0 (+ x1 (* 6.0 (pow x1 4.0)))))
     (-
      x1
      (-
       (* 3.0 (/ (- (- t_0 (* 2.0 x2)) x1) t_2))
       (+
        x1
        (+
         (* x1 (* x1 x1))
         (+
          (* 3.0 t_0)
          (*
           (-
            (* (* (/ t_1 t_2) (* x1 2.0)) (+ 3.0 (/ t_1 (+ (* x1 x1) 1.0))))
            (* (* x1 x1) 6.0))
           t_2)))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = x1 - (t_0 + (2.0 * x2));
	double t_2 = -1.0 - (x1 * x1);
	double tmp;
	if ((x1 <= -2e+103) || !(x1 <= 1.6e+75)) {
		tmp = x1 + (9.0 + (x1 + (6.0 * pow(x1, 4.0))));
	} else {
		tmp = x1 - ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_2)) - (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_0) + (((((t_1 / t_2) * (x1 * 2.0)) * (3.0 + (t_1 / ((x1 * x1) + 1.0)))) - ((x1 * x1) * 6.0)) * t_2)))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = x1 * (x1 * 3.0d0)
    t_1 = x1 - (t_0 + (2.0d0 * x2))
    t_2 = (-1.0d0) - (x1 * x1)
    if ((x1 <= (-2d+103)) .or. (.not. (x1 <= 1.6d+75))) then
        tmp = x1 + (9.0d0 + (x1 + (6.0d0 * (x1 ** 4.0d0))))
    else
        tmp = x1 - ((3.0d0 * (((t_0 - (2.0d0 * x2)) - x1) / t_2)) - (x1 + ((x1 * (x1 * x1)) + ((3.0d0 * t_0) + (((((t_1 / t_2) * (x1 * 2.0d0)) * (3.0d0 + (t_1 / ((x1 * x1) + 1.0d0)))) - ((x1 * x1) * 6.0d0)) * t_2)))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = x1 - (t_0 + (2.0 * x2));
	double t_2 = -1.0 - (x1 * x1);
	double tmp;
	if ((x1 <= -2e+103) || !(x1 <= 1.6e+75)) {
		tmp = x1 + (9.0 + (x1 + (6.0 * Math.pow(x1, 4.0))));
	} else {
		tmp = x1 - ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_2)) - (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_0) + (((((t_1 / t_2) * (x1 * 2.0)) * (3.0 + (t_1 / ((x1 * x1) + 1.0)))) - ((x1 * x1) * 6.0)) * t_2)))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = x1 - (t_0 + (2.0 * x2))
	t_2 = -1.0 - (x1 * x1)
	tmp = 0
	if (x1 <= -2e+103) or not (x1 <= 1.6e+75):
		tmp = x1 + (9.0 + (x1 + (6.0 * math.pow(x1, 4.0))))
	else:
		tmp = x1 - ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_2)) - (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_0) + (((((t_1 / t_2) * (x1 * 2.0)) * (3.0 + (t_1 / ((x1 * x1) + 1.0)))) - ((x1 * x1) * 6.0)) * t_2)))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(x1 - Float64(t_0 + Float64(2.0 * x2)))
	t_2 = Float64(-1.0 - Float64(x1 * x1))
	tmp = 0.0
	if ((x1 <= -2e+103) || !(x1 <= 1.6e+75))
		tmp = Float64(x1 + Float64(9.0 + Float64(x1 + Float64(6.0 * (x1 ^ 4.0)))));
	else
		tmp = Float64(x1 - Float64(Float64(3.0 * Float64(Float64(Float64(t_0 - Float64(2.0 * x2)) - x1) / t_2)) - Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(3.0 * t_0) + Float64(Float64(Float64(Float64(Float64(t_1 / t_2) * Float64(x1 * 2.0)) * Float64(3.0 + Float64(t_1 / Float64(Float64(x1 * x1) + 1.0)))) - Float64(Float64(x1 * x1) * 6.0)) * t_2))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * 3.0);
	t_1 = x1 - (t_0 + (2.0 * x2));
	t_2 = -1.0 - (x1 * x1);
	tmp = 0.0;
	if ((x1 <= -2e+103) || ~((x1 <= 1.6e+75)))
		tmp = x1 + (9.0 + (x1 + (6.0 * (x1 ^ 4.0))));
	else
		tmp = x1 - ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_2)) - (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_0) + (((((t_1 / t_2) * (x1 * 2.0)) * (3.0 + (t_1 / ((x1 * x1) + 1.0)))) - ((x1 * x1) * 6.0)) * t_2)))));
	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[(x1 - N[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[x1, -2e+103], N[Not[LessEqual[x1, 1.6e+75]], $MachinePrecision]], N[(x1 + N[(9.0 + N[(x1 + N[(6.0 * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 - N[(N[(3.0 * N[(N[(N[(t$95$0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision] - N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(3.0 * t$95$0), $MachinePrecision] + N[(N[(N[(N[(N[(t$95$1 / t$95$2), $MachinePrecision] * N[(x1 * 2.0), $MachinePrecision]), $MachinePrecision] * N[(3.0 + N[(t$95$1 / N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x1 * x1), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision] * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 2 regimes

2. if x1 < -2e103 or 1.59999999999999992e75 < x1

   1. Initial program 16.8%

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

   3. Taylor expanded in x1 around -inf 34.8%

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

   4. Taylor expanded in x1 around inf 100.0%

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

   5. Taylor expanded in x1 around inf 98.9%

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

   if -2e103 < x1 < 1.59999999999999992e75

   1. Initial program 98.8%

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

   3. Taylor expanded in x1 around inf 98.6%

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

   4. Taylor expanded in x1 around inf 97.1%

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

4. Final simplification 97.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -2 \cdot 10^{+103} \lor \neg \left(x1 \leq 1.6 \cdot 10^{+75}\right):\\ \;\;\;\;x1 + \left(9 + \left(x1 + 6 \cdot {x1}^{4}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 - \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1} - \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) + \left(\left(\frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{-1 - x1 \cdot x1} \cdot \left(x1 \cdot 2\right)\right) \cdot \left(3 + \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right) - \left(x1 \cdot x1\right) \cdot 6\right) \cdot \left(-1 - x1 \cdot x1\right)\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 97.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := x1 - \left(t\_0 + 2 \cdot x2\right)\\ t_2 := \frac{t\_1}{x1 \cdot x1 + 1}\\ t_3 := -1 - x1 \cdot x1\\ \mathbf{if}\;x1 \leq -1 \cdot 10^{+98} \lor \neg \left(x1 \leq 1.6 \cdot 10^{+75}\right):\\ \;\;\;\;x1 + \left(9 + \left(x1 + 6 \cdot {x1}^{4}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{x1 - \left(t\_0 - 2 \cdot x2\right)}{t\_3} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) - \left(t\_0 \cdot t\_2 - \left(\left(\frac{t\_1}{t\_3} \cdot \left(x1 \cdot 2\right)\right) \cdot \left(3 + t\_2\right) - \left(x1 \cdot x1\right) \cdot 6\right) \cdot t\_3\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (- x1 (+ t_0 (* 2.0 x2))))
        (t_2 (/ t_1 (+ (* x1 x1) 1.0)))
        (t_3 (- -1.0 (* x1 x1))))
   (if (or (<= x1 -1e+98) (not (<= x1 1.6e+75)))
     (+ x1 (+ 9.0 (+ x1 (* 6.0 (pow x1 4.0)))))
     (+
      x1
      (+
       (* 3.0 (/ (- x1 (- t_0 (* 2.0 x2))) t_3))
       (+
        x1
        (-
         (* x1 (* x1 x1))
         (-
          (* t_0 t_2)
          (*
           (- (* (* (/ t_1 t_3) (* x1 2.0)) (+ 3.0 t_2)) (* (* x1 x1) 6.0))
           t_3)))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = x1 - (t_0 + (2.0 * x2));
	double t_2 = t_1 / ((x1 * x1) + 1.0);
	double t_3 = -1.0 - (x1 * x1);
	double tmp;
	if ((x1 <= -1e+98) || !(x1 <= 1.6e+75)) {
		tmp = x1 + (9.0 + (x1 + (6.0 * pow(x1, 4.0))));
	} else {
		tmp = x1 + ((3.0 * ((x1 - (t_0 - (2.0 * x2))) / t_3)) + (x1 + ((x1 * (x1 * x1)) - ((t_0 * t_2) - (((((t_1 / t_3) * (x1 * 2.0)) * (3.0 + t_2)) - ((x1 * x1) * 6.0)) * t_3)))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_0 = x1 * (x1 * 3.0d0)
    t_1 = x1 - (t_0 + (2.0d0 * x2))
    t_2 = t_1 / ((x1 * x1) + 1.0d0)
    t_3 = (-1.0d0) - (x1 * x1)
    if ((x1 <= (-1d+98)) .or. (.not. (x1 <= 1.6d+75))) then
        tmp = x1 + (9.0d0 + (x1 + (6.0d0 * (x1 ** 4.0d0))))
    else
        tmp = x1 + ((3.0d0 * ((x1 - (t_0 - (2.0d0 * x2))) / t_3)) + (x1 + ((x1 * (x1 * x1)) - ((t_0 * t_2) - (((((t_1 / t_3) * (x1 * 2.0d0)) * (3.0d0 + t_2)) - ((x1 * x1) * 6.0d0)) * t_3)))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = x1 - (t_0 + (2.0 * x2));
	double t_2 = t_1 / ((x1 * x1) + 1.0);
	double t_3 = -1.0 - (x1 * x1);
	double tmp;
	if ((x1 <= -1e+98) || !(x1 <= 1.6e+75)) {
		tmp = x1 + (9.0 + (x1 + (6.0 * Math.pow(x1, 4.0))));
	} else {
		tmp = x1 + ((3.0 * ((x1 - (t_0 - (2.0 * x2))) / t_3)) + (x1 + ((x1 * (x1 * x1)) - ((t_0 * t_2) - (((((t_1 / t_3) * (x1 * 2.0)) * (3.0 + t_2)) - ((x1 * x1) * 6.0)) * t_3)))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = x1 - (t_0 + (2.0 * x2))
	t_2 = t_1 / ((x1 * x1) + 1.0)
	t_3 = -1.0 - (x1 * x1)
	tmp = 0
	if (x1 <= -1e+98) or not (x1 <= 1.6e+75):
		tmp = x1 + (9.0 + (x1 + (6.0 * math.pow(x1, 4.0))))
	else:
		tmp = x1 + ((3.0 * ((x1 - (t_0 - (2.0 * x2))) / t_3)) + (x1 + ((x1 * (x1 * x1)) - ((t_0 * t_2) - (((((t_1 / t_3) * (x1 * 2.0)) * (3.0 + t_2)) - ((x1 * x1) * 6.0)) * t_3)))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(x1 - Float64(t_0 + Float64(2.0 * x2)))
	t_2 = Float64(t_1 / Float64(Float64(x1 * x1) + 1.0))
	t_3 = Float64(-1.0 - Float64(x1 * x1))
	tmp = 0.0
	if ((x1 <= -1e+98) || !(x1 <= 1.6e+75))
		tmp = Float64(x1 + Float64(9.0 + Float64(x1 + Float64(6.0 * (x1 ^ 4.0)))));
	else
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(x1 - Float64(t_0 - Float64(2.0 * x2))) / t_3)) + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) - Float64(Float64(t_0 * t_2) - Float64(Float64(Float64(Float64(Float64(t_1 / t_3) * Float64(x1 * 2.0)) * Float64(3.0 + t_2)) - Float64(Float64(x1 * x1) * 6.0)) * t_3))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * 3.0);
	t_1 = x1 - (t_0 + (2.0 * x2));
	t_2 = t_1 / ((x1 * x1) + 1.0);
	t_3 = -1.0 - (x1 * x1);
	tmp = 0.0;
	if ((x1 <= -1e+98) || ~((x1 <= 1.6e+75)))
		tmp = x1 + (9.0 + (x1 + (6.0 * (x1 ^ 4.0))));
	else
		tmp = x1 + ((3.0 * ((x1 - (t_0 - (2.0 * x2))) / t_3)) + (x1 + ((x1 * (x1 * x1)) - ((t_0 * t_2) - (((((t_1 / t_3) * (x1 * 2.0)) * (3.0 + t_2)) - ((x1 * x1) * 6.0)) * t_3)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 - N[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 / N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[x1, -1e+98], N[Not[LessEqual[x1, 1.6e+75]], $MachinePrecision]], N[(x1 + N[(9.0 + N[(x1 + N[(6.0 * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(3.0 * N[(N[(x1 - N[(t$95$0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$3), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] - N[(N[(t$95$0 * t$95$2), $MachinePrecision] - N[(N[(N[(N[(N[(t$95$1 / t$95$3), $MachinePrecision] * N[(x1 * 2.0), $MachinePrecision]), $MachinePrecision] * N[(3.0 + t$95$2), $MachinePrecision]), $MachinePrecision] - N[(N[(x1 * x1), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision] * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 2 regimes

2. if x1 < -9.99999999999999998e97 or 1.59999999999999992e75 < x1

   1. Initial program 16.8%

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

   3. Taylor expanded in x1 around -inf 34.8%

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

   4. Taylor expanded in x1 around inf 100.0%

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

   5. Taylor expanded in x1 around inf 98.9%

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

   if -9.99999999999999998e97 < x1 < 1.59999999999999992e75

   1. Initial program 98.8%

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

   3. Taylor expanded in x1 around inf 97.1%

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

4. Final simplification 97.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1 \cdot 10^{+98} \lor \neg \left(x1 \leq 1.6 \cdot 10^{+75}\right):\\ \;\;\;\;x1 + \left(9 + \left(x1 + 6 \cdot {x1}^{4}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right)}{-1 - x1 \cdot x1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) - \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1} - \left(\left(\frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{-1 - x1 \cdot x1} \cdot \left(x1 \cdot 2\right)\right) \cdot \left(3 + \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right) - \left(x1 \cdot x1\right) \cdot 6\right) \cdot \left(-1 - x1 \cdot x1\right)\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 96.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := x1 - \left(t\_0 + 2 \cdot x2\right)\\ t_2 := -1 - x1 \cdot x1\\ t_3 := x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot t\_0 + \left(\left(\frac{t\_1}{t\_2} \cdot \left(x1 \cdot 2\right)\right) \cdot \left(3 + \frac{t\_1}{x1 \cdot x1 + 1}\right) - \left(x1 \cdot x1\right) \cdot 6\right) \cdot t\_2\right)\right)\\ \mathbf{if}\;x1 \leq -4.5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 - 2\right)\right)\\ \mathbf{elif}\;x1 \leq -5.2 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{x1 - \left(t\_0 - 2 \cdot x2\right)}{t\_2} + \left(x1 + x1 \cdot \left(2 + x1 \cdot \left(\left(x1 \cdot -4 + \left(x2 \cdot 6 + x2 \cdot 8\right)\right) - 6\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -7.2 \cdot 10^{+38}:\\ \;\;\;\;x1 + \left(t\_3 + 3 \cdot \left(x2 \cdot -2\right)\right)\\ \mathbf{elif}\;x1 \leq 3.9 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(t\_3 + 3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(-1 + x1 \cdot \left(3 - x2 \cdot -2\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(-1 + x1 \cdot \left(x1 + 3\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (- x1 (+ t_0 (* 2.0 x2))))
        (t_2 (- -1.0 (* x1 x1)))
        (t_3
         (+
          x1
          (+
           (* x1 (* x1 x1))
           (+
            (* 3.0 t_0)
            (*
             (-
              (* (* (/ t_1 t_2) (* x1 2.0)) (+ 3.0 (/ t_1 (+ (* x1 x1) 1.0))))
              (* (* x1 x1) 6.0))
             t_2))))))
   (if (<= x1 -4.5e+153)
     (+ x1 (+ (* x2 -6.0) (* x1 (- (* x1 9.0) 2.0))))
     (if (<= x1 -5.2e+102)
       (+
        x1
        (+
         (* 3.0 (/ (- x1 (- t_0 (* 2.0 x2))) t_2))
         (+
          x1
          (*
           x1
           (+ 2.0 (* x1 (- (+ (* x1 -4.0) (+ (* x2 6.0) (* x2 8.0))) 6.0)))))))
       (if (<= x1 -7.2e+38)
         (+ x1 (+ t_3 (* 3.0 (* x2 -2.0))))
         (if (<= x1 3.9e+102)
           (+
            x1
            (+
             t_3
             (*
              3.0
              (+ (* x2 -2.0) (* x1 (+ -1.0 (* x1 (- 3.0 (* x2 -2.0)))))))))
           (+ x1 (+ x1 (* 3.0 (* x1 (+ -1.0 (* x1 (+ x1 3.0)))))))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = x1 - (t_0 + (2.0 * x2));
	double t_2 = -1.0 - (x1 * x1);
	double t_3 = x1 + ((x1 * (x1 * x1)) + ((3.0 * t_0) + (((((t_1 / t_2) * (x1 * 2.0)) * (3.0 + (t_1 / ((x1 * x1) + 1.0)))) - ((x1 * x1) * 6.0)) * t_2)));
	double tmp;
	if (x1 <= -4.5e+153) {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) - 2.0)));
	} else if (x1 <= -5.2e+102) {
		tmp = x1 + ((3.0 * ((x1 - (t_0 - (2.0 * x2))) / t_2)) + (x1 + (x1 * (2.0 + (x1 * (((x1 * -4.0) + ((x2 * 6.0) + (x2 * 8.0))) - 6.0))))));
	} else if (x1 <= -7.2e+38) {
		tmp = x1 + (t_3 + (3.0 * (x2 * -2.0)));
	} else if (x1 <= 3.9e+102) {
		tmp = x1 + (t_3 + (3.0 * ((x2 * -2.0) + (x1 * (-1.0 + (x1 * (3.0 - (x2 * -2.0))))))));
	} else {
		tmp = x1 + (x1 + (3.0 * (x1 * (-1.0 + (x1 * (x1 + 3.0))))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_0 = x1 * (x1 * 3.0d0)
    t_1 = x1 - (t_0 + (2.0d0 * x2))
    t_2 = (-1.0d0) - (x1 * x1)
    t_3 = x1 + ((x1 * (x1 * x1)) + ((3.0d0 * t_0) + (((((t_1 / t_2) * (x1 * 2.0d0)) * (3.0d0 + (t_1 / ((x1 * x1) + 1.0d0)))) - ((x1 * x1) * 6.0d0)) * t_2)))
    if (x1 <= (-4.5d+153)) then
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * ((x1 * 9.0d0) - 2.0d0)))
    else if (x1 <= (-5.2d+102)) then
        tmp = x1 + ((3.0d0 * ((x1 - (t_0 - (2.0d0 * x2))) / t_2)) + (x1 + (x1 * (2.0d0 + (x1 * (((x1 * (-4.0d0)) + ((x2 * 6.0d0) + (x2 * 8.0d0))) - 6.0d0))))))
    else if (x1 <= (-7.2d+38)) then
        tmp = x1 + (t_3 + (3.0d0 * (x2 * (-2.0d0))))
    else if (x1 <= 3.9d+102) then
        tmp = x1 + (t_3 + (3.0d0 * ((x2 * (-2.0d0)) + (x1 * ((-1.0d0) + (x1 * (3.0d0 - (x2 * (-2.0d0)))))))))
    else
        tmp = x1 + (x1 + (3.0d0 * (x1 * ((-1.0d0) + (x1 * (x1 + 3.0d0))))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = x1 - (t_0 + (2.0 * x2));
	double t_2 = -1.0 - (x1 * x1);
	double t_3 = x1 + ((x1 * (x1 * x1)) + ((3.0 * t_0) + (((((t_1 / t_2) * (x1 * 2.0)) * (3.0 + (t_1 / ((x1 * x1) + 1.0)))) - ((x1 * x1) * 6.0)) * t_2)));
	double tmp;
	if (x1 <= -4.5e+153) {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) - 2.0)));
	} else if (x1 <= -5.2e+102) {
		tmp = x1 + ((3.0 * ((x1 - (t_0 - (2.0 * x2))) / t_2)) + (x1 + (x1 * (2.0 + (x1 * (((x1 * -4.0) + ((x2 * 6.0) + (x2 * 8.0))) - 6.0))))));
	} else if (x1 <= -7.2e+38) {
		tmp = x1 + (t_3 + (3.0 * (x2 * -2.0)));
	} else if (x1 <= 3.9e+102) {
		tmp = x1 + (t_3 + (3.0 * ((x2 * -2.0) + (x1 * (-1.0 + (x1 * (3.0 - (x2 * -2.0))))))));
	} else {
		tmp = x1 + (x1 + (3.0 * (x1 * (-1.0 + (x1 * (x1 + 3.0))))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = x1 - (t_0 + (2.0 * x2))
	t_2 = -1.0 - (x1 * x1)
	t_3 = x1 + ((x1 * (x1 * x1)) + ((3.0 * t_0) + (((((t_1 / t_2) * (x1 * 2.0)) * (3.0 + (t_1 / ((x1 * x1) + 1.0)))) - ((x1 * x1) * 6.0)) * t_2)))
	tmp = 0
	if x1 <= -4.5e+153:
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) - 2.0)))
	elif x1 <= -5.2e+102:
		tmp = x1 + ((3.0 * ((x1 - (t_0 - (2.0 * x2))) / t_2)) + (x1 + (x1 * (2.0 + (x1 * (((x1 * -4.0) + ((x2 * 6.0) + (x2 * 8.0))) - 6.0))))))
	elif x1 <= -7.2e+38:
		tmp = x1 + (t_3 + (3.0 * (x2 * -2.0)))
	elif x1 <= 3.9e+102:
		tmp = x1 + (t_3 + (3.0 * ((x2 * -2.0) + (x1 * (-1.0 + (x1 * (3.0 - (x2 * -2.0))))))))
	else:
		tmp = x1 + (x1 + (3.0 * (x1 * (-1.0 + (x1 * (x1 + 3.0))))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(x1 - Float64(t_0 + Float64(2.0 * x2)))
	t_2 = Float64(-1.0 - Float64(x1 * x1))
	t_3 = Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(3.0 * t_0) + Float64(Float64(Float64(Float64(Float64(t_1 / t_2) * Float64(x1 * 2.0)) * Float64(3.0 + Float64(t_1 / Float64(Float64(x1 * x1) + 1.0)))) - Float64(Float64(x1 * x1) * 6.0)) * t_2))))
	tmp = 0.0
	if (x1 <= -4.5e+153)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(x1 * 9.0) - 2.0))));
	elseif (x1 <= -5.2e+102)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(x1 - Float64(t_0 - Float64(2.0 * x2))) / t_2)) + Float64(x1 + Float64(x1 * Float64(2.0 + Float64(x1 * Float64(Float64(Float64(x1 * -4.0) + Float64(Float64(x2 * 6.0) + Float64(x2 * 8.0))) - 6.0)))))));
	elseif (x1 <= -7.2e+38)
		tmp = Float64(x1 + Float64(t_3 + Float64(3.0 * Float64(x2 * -2.0))));
	elseif (x1 <= 3.9e+102)
		tmp = Float64(x1 + Float64(t_3 + Float64(3.0 * Float64(Float64(x2 * -2.0) + Float64(x1 * Float64(-1.0 + Float64(x1 * Float64(3.0 - Float64(x2 * -2.0)))))))));
	else
		tmp = Float64(x1 + Float64(x1 + Float64(3.0 * Float64(x1 * Float64(-1.0 + Float64(x1 * Float64(x1 + 3.0)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * 3.0);
	t_1 = x1 - (t_0 + (2.0 * x2));
	t_2 = -1.0 - (x1 * x1);
	t_3 = x1 + ((x1 * (x1 * x1)) + ((3.0 * t_0) + (((((t_1 / t_2) * (x1 * 2.0)) * (3.0 + (t_1 / ((x1 * x1) + 1.0)))) - ((x1 * x1) * 6.0)) * t_2)));
	tmp = 0.0;
	if (x1 <= -4.5e+153)
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) - 2.0)));
	elseif (x1 <= -5.2e+102)
		tmp = x1 + ((3.0 * ((x1 - (t_0 - (2.0 * x2))) / t_2)) + (x1 + (x1 * (2.0 + (x1 * (((x1 * -4.0) + ((x2 * 6.0) + (x2 * 8.0))) - 6.0))))));
	elseif (x1 <= -7.2e+38)
		tmp = x1 + (t_3 + (3.0 * (x2 * -2.0)));
	elseif (x1 <= 3.9e+102)
		tmp = x1 + (t_3 + (3.0 * ((x2 * -2.0) + (x1 * (-1.0 + (x1 * (3.0 - (x2 * -2.0))))))));
	else
		tmp = x1 + (x1 + (3.0 * (x1 * (-1.0 + (x1 * (x1 + 3.0))))));
	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[(x1 - N[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(3.0 * t$95$0), $MachinePrecision] + N[(N[(N[(N[(N[(t$95$1 / t$95$2), $MachinePrecision] * N[(x1 * 2.0), $MachinePrecision]), $MachinePrecision] * N[(3.0 + N[(t$95$1 / N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x1 * x1), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision] * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -4.5e+153], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -5.2e+102], N[(x1 + N[(N[(3.0 * N[(N[(x1 - N[(t$95$0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(x1 * N[(2.0 + N[(x1 * N[(N[(N[(x1 * -4.0), $MachinePrecision] + N[(N[(x2 * 6.0), $MachinePrecision] + N[(x2 * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -7.2e+38], N[(x1 + N[(t$95$3 + N[(3.0 * N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 3.9e+102], N[(x1 + N[(t$95$3 + N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] + N[(x1 * N[(-1.0 + N[(x1 * N[(3.0 - N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(x1 + N[(3.0 * N[(x1 * N[(-1.0 + N[(x1 * N[(x1 + 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x1 < -4.5000000000000001e153

   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 0.0%

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

   5. Taylor expanded in x1 around 0 67.6%

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

   6. Taylor expanded in x2 around 0 100.0%

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

      1. *-commutative 100.0%

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

   8. Simplified 100.0%

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

   if -4.5000000000000001e153 < x1 < -5.20000000000000013e102

   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%

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

      1. +-commutative 0.0%

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

      2. mul-1-neg 0.0%

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

      3. sub-neg 0.0%

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

   5. Simplified 0.0%

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

   6. Taylor expanded in x1 around inf 0.0%

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

      1. *-commutative 0.0%

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

   8. Simplified 0.0%

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

   9. Taylor expanded in x1 around 0 93.3%

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

   if -5.20000000000000013e102 < x1 < -7.19999999999999938e38

   1. Initial program 92.5%

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

   3. Taylor expanded in x1 around inf 92.5%

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

   4. Taylor expanded in x1 around inf 85.4%

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

   5. Taylor expanded in x1 around 0 85.4%

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

      1. *-commutative 85.4%

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

   7. Simplified 85.4%

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

   if -7.19999999999999938e38 < x1 < 3.8999999999999998e102

   1. Initial program 99.3%

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

   3. Taylor expanded in x1 around inf 99.2%

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

   4. Taylor expanded in x1 around inf 98.2%

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

   5. Taylor expanded in x1 around 0 97.0%

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

   if 3.8999999999999998e102 < x1

   1. Initial program 26.5%

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

   3. Taylor expanded in x1 around 0 15.3%

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

   4. Taylor expanded in x1 around 0 79.4%

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

   5. Taylor expanded in x2 around 0 97.1%

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

4. Final simplification 96.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4.5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 - 2\right)\right)\\ \mathbf{elif}\;x1 \leq -5.2 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right)}{-1 - x1 \cdot x1} + \left(x1 + x1 \cdot \left(2 + x1 \cdot \left(\left(x1 \cdot -4 + \left(x2 \cdot 6 + x2 \cdot 8\right)\right) - 6\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -7.2 \cdot 10^{+38}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) + \left(\left(\frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{-1 - x1 \cdot x1} \cdot \left(x1 \cdot 2\right)\right) \cdot \left(3 + \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right) - \left(x1 \cdot x1\right) \cdot 6\right) \cdot \left(-1 - x1 \cdot x1\right)\right)\right)\right) + 3 \cdot \left(x2 \cdot -2\right)\right)\\ \mathbf{elif}\;x1 \leq 3.9 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) + \left(\left(\frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{-1 - x1 \cdot x1} \cdot \left(x1 \cdot 2\right)\right) \cdot \left(3 + \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right) - \left(x1 \cdot x1\right) \cdot 6\right) \cdot \left(-1 - x1 \cdot x1\right)\right)\right)\right) + 3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(-1 + x1 \cdot \left(3 - x2 \cdot -2\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(-1 + x1 \cdot \left(x1 + 3\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 95.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 - 2\right)\right)\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := t\_1 - 2 \cdot x2\\ t_3 := -1 - x1 \cdot x1\\ t_4 := x1 - \left(t\_1 + 2 \cdot x2\right)\\ \mathbf{if}\;x1 \leq -4.5 \cdot 10^{+153}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x1 \leq -3.6 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{x1 - t\_2}{t\_3} + \left(x1 + x1 \cdot \left(2 + x1 \cdot \left(\left(x1 \cdot -4 + \left(x2 \cdot 6 + x2 \cdot 8\right)\right) - 6\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 4.2 \cdot 10^{+144}:\\ \;\;\;\;x1 - \left(3 \cdot \frac{t\_2 - x1}{t\_3} - \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot t\_1 + \left(\left(\frac{t\_4}{t\_3} \cdot \left(x1 \cdot 2\right)\right) \cdot \left(3 + \frac{t\_4}{x1 \cdot x1 + 1}\right) - \left(x1 \cdot x1\right) \cdot 6\right) \cdot t\_3\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ x1 (+ (* x2 -6.0) (* x1 (- (* x1 9.0) 2.0)))))
        (t_1 (* x1 (* x1 3.0)))
        (t_2 (- t_1 (* 2.0 x2)))
        (t_3 (- -1.0 (* x1 x1)))
        (t_4 (- x1 (+ t_1 (* 2.0 x2)))))
   (if (<= x1 -4.5e+153)
     t_0
     (if (<= x1 -3.6e+102)
       (+
        x1
        (+
         (* 3.0 (/ (- x1 t_2) t_3))
         (+
          x1
          (*
           x1
           (+ 2.0 (* x1 (- (+ (* x1 -4.0) (+ (* x2 6.0) (* x2 8.0))) 6.0)))))))
       (if (<= x1 4.2e+144)
         (-
          x1
          (-
           (* 3.0 (/ (- t_2 x1) t_3))
           (+
            x1
            (+
             (* x1 (* x1 x1))
             (+
              (* 3.0 t_1)
              (*
               (-
                (*
                 (* (/ t_4 t_3) (* x1 2.0))
                 (+ 3.0 (/ t_4 (+ (* x1 x1) 1.0))))
                (* (* x1 x1) 6.0))
               t_3))))))
         t_0)))))

C

double code(double x1, double x2) {
	double t_0 = x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) - 2.0)));
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = t_1 - (2.0 * x2);
	double t_3 = -1.0 - (x1 * x1);
	double t_4 = x1 - (t_1 + (2.0 * x2));
	double tmp;
	if (x1 <= -4.5e+153) {
		tmp = t_0;
	} else if (x1 <= -3.6e+102) {
		tmp = x1 + ((3.0 * ((x1 - t_2) / t_3)) + (x1 + (x1 * (2.0 + (x1 * (((x1 * -4.0) + ((x2 * 6.0) + (x2 * 8.0))) - 6.0))))));
	} else if (x1 <= 4.2e+144) {
		tmp = x1 - ((3.0 * ((t_2 - x1) / t_3)) - (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_1) + (((((t_4 / t_3) * (x1 * 2.0)) * (3.0 + (t_4 / ((x1 * x1) + 1.0)))) - ((x1 * x1) * 6.0)) * t_3)))));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_0 = x1 + ((x2 * (-6.0d0)) + (x1 * ((x1 * 9.0d0) - 2.0d0)))
    t_1 = x1 * (x1 * 3.0d0)
    t_2 = t_1 - (2.0d0 * x2)
    t_3 = (-1.0d0) - (x1 * x1)
    t_4 = x1 - (t_1 + (2.0d0 * x2))
    if (x1 <= (-4.5d+153)) then
        tmp = t_0
    else if (x1 <= (-3.6d+102)) then
        tmp = x1 + ((3.0d0 * ((x1 - t_2) / t_3)) + (x1 + (x1 * (2.0d0 + (x1 * (((x1 * (-4.0d0)) + ((x2 * 6.0d0) + (x2 * 8.0d0))) - 6.0d0))))))
    else if (x1 <= 4.2d+144) then
        tmp = x1 - ((3.0d0 * ((t_2 - x1) / t_3)) - (x1 + ((x1 * (x1 * x1)) + ((3.0d0 * t_1) + (((((t_4 / t_3) * (x1 * 2.0d0)) * (3.0d0 + (t_4 / ((x1 * x1) + 1.0d0)))) - ((x1 * x1) * 6.0d0)) * t_3)))))
    else
        tmp = t_0
    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) - 2.0)));
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = t_1 - (2.0 * x2);
	double t_3 = -1.0 - (x1 * x1);
	double t_4 = x1 - (t_1 + (2.0 * x2));
	double tmp;
	if (x1 <= -4.5e+153) {
		tmp = t_0;
	} else if (x1 <= -3.6e+102) {
		tmp = x1 + ((3.0 * ((x1 - t_2) / t_3)) + (x1 + (x1 * (2.0 + (x1 * (((x1 * -4.0) + ((x2 * 6.0) + (x2 * 8.0))) - 6.0))))));
	} else if (x1 <= 4.2e+144) {
		tmp = x1 - ((3.0 * ((t_2 - x1) / t_3)) - (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_1) + (((((t_4 / t_3) * (x1 * 2.0)) * (3.0 + (t_4 / ((x1 * x1) + 1.0)))) - ((x1 * x1) * 6.0)) * t_3)))));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) - 2.0)))
	t_1 = x1 * (x1 * 3.0)
	t_2 = t_1 - (2.0 * x2)
	t_3 = -1.0 - (x1 * x1)
	t_4 = x1 - (t_1 + (2.0 * x2))
	tmp = 0
	if x1 <= -4.5e+153:
		tmp = t_0
	elif x1 <= -3.6e+102:
		tmp = x1 + ((3.0 * ((x1 - t_2) / t_3)) + (x1 + (x1 * (2.0 + (x1 * (((x1 * -4.0) + ((x2 * 6.0) + (x2 * 8.0))) - 6.0))))))
	elif x1 <= 4.2e+144:
		tmp = x1 - ((3.0 * ((t_2 - x1) / t_3)) - (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_1) + (((((t_4 / t_3) * (x1 * 2.0)) * (3.0 + (t_4 / ((x1 * x1) + 1.0)))) - ((x1 * x1) * 6.0)) * t_3)))))
	else:
		tmp = t_0
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(x1 * 9.0) - 2.0))))
	t_1 = Float64(x1 * Float64(x1 * 3.0))
	t_2 = Float64(t_1 - Float64(2.0 * x2))
	t_3 = Float64(-1.0 - Float64(x1 * x1))
	t_4 = Float64(x1 - Float64(t_1 + Float64(2.0 * x2)))
	tmp = 0.0
	if (x1 <= -4.5e+153)
		tmp = t_0;
	elseif (x1 <= -3.6e+102)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(x1 - t_2) / t_3)) + Float64(x1 + Float64(x1 * Float64(2.0 + Float64(x1 * Float64(Float64(Float64(x1 * -4.0) + Float64(Float64(x2 * 6.0) + Float64(x2 * 8.0))) - 6.0)))))));
	elseif (x1 <= 4.2e+144)
		tmp = Float64(x1 - Float64(Float64(3.0 * Float64(Float64(t_2 - x1) / t_3)) - Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(3.0 * t_1) + Float64(Float64(Float64(Float64(Float64(t_4 / t_3) * Float64(x1 * 2.0)) * Float64(3.0 + Float64(t_4 / Float64(Float64(x1 * x1) + 1.0)))) - Float64(Float64(x1 * x1) * 6.0)) * t_3))))));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) - 2.0)));
	t_1 = x1 * (x1 * 3.0);
	t_2 = t_1 - (2.0 * x2);
	t_3 = -1.0 - (x1 * x1);
	t_4 = x1 - (t_1 + (2.0 * x2));
	tmp = 0.0;
	if (x1 <= -4.5e+153)
		tmp = t_0;
	elseif (x1 <= -3.6e+102)
		tmp = x1 + ((3.0 * ((x1 - t_2) / t_3)) + (x1 + (x1 * (2.0 + (x1 * (((x1 * -4.0) + ((x2 * 6.0) + (x2 * 8.0))) - 6.0))))));
	elseif (x1 <= 4.2e+144)
		tmp = x1 - ((3.0 * ((t_2 - x1) / t_3)) - (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_1) + (((((t_4 / t_3) * (x1 * 2.0)) * (3.0 + (t_4 / ((x1 * x1) + 1.0)))) - ((x1 * x1) * 6.0)) * t_3)))));
	else
		tmp = t_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 * 9.0), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(x1 - N[(t$95$1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -4.5e+153], t$95$0, If[LessEqual[x1, -3.6e+102], N[(x1 + N[(N[(3.0 * N[(N[(x1 - t$95$2), $MachinePrecision] / t$95$3), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(x1 * N[(2.0 + N[(x1 * N[(N[(N[(x1 * -4.0), $MachinePrecision] + N[(N[(x2 * 6.0), $MachinePrecision] + N[(x2 * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 4.2e+144], N[(x1 - N[(N[(3.0 * N[(N[(t$95$2 - x1), $MachinePrecision] / t$95$3), $MachinePrecision]), $MachinePrecision] - N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(3.0 * t$95$1), $MachinePrecision] + N[(N[(N[(N[(N[(t$95$4 / t$95$3), $MachinePrecision] * N[(x1 * 2.0), $MachinePrecision]), $MachinePrecision] * N[(3.0 + N[(t$95$4 / N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x1 * x1), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision] * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -4.5000000000000001e153 or 4.19999999999999993e144 < 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 32.2%

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

   5. Taylor expanded in x1 around 0 66.1%

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

   6. Taylor expanded in x2 around 0 98.3%

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

      1. *-commutative 98.3%

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

   8. Simplified 98.3%

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

   if -4.5000000000000001e153 < x1 < -3.6000000000000002e102

   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%

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

      1. +-commutative 0.0%

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

      2. mul-1-neg 0.0%

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

      3. sub-neg 0.0%

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

   5. Simplified 0.0%

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

   6. Taylor expanded in x1 around inf 0.0%

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

      1. *-commutative 0.0%

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

   8. Simplified 0.0%

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

   9. Taylor expanded in x1 around 0 93.3%

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

   if -3.6000000000000002e102 < x1 < 4.19999999999999993e144

   1. Initial program 98.9%

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

   3. Taylor expanded in x1 around inf 98.7%

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

   4. Taylor expanded in x1 around inf 97.3%

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

4. Final simplification 97.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4.5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 - 2\right)\right)\\ \mathbf{elif}\;x1 \leq -3.6 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right)}{-1 - x1 \cdot x1} + \left(x1 + x1 \cdot \left(2 + x1 \cdot \left(\left(x1 \cdot -4 + \left(x2 \cdot 6 + x2 \cdot 8\right)\right) - 6\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 4.2 \cdot 10^{+144}:\\ \;\;\;\;x1 - \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1} - \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) + \left(\left(\frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{-1 - x1 \cdot x1} \cdot \left(x1 \cdot 2\right)\right) \cdot \left(3 + \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right) - \left(x1 \cdot x1\right) \cdot 6\right) \cdot \left(-1 - x1 \cdot x1\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 - 2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 95.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := x1 \cdot \left(x1 \cdot 9 - 2\right)\\ t_2 := x1 + \left(x2 \cdot -6 + t\_1\right)\\ t_3 := x1 - \left(t\_0 + 2 \cdot x2\right)\\ t_4 := -1 - x1 \cdot x1\\ t_5 := x1 + \left(\left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot t\_0 + \left(\left(\frac{t\_3}{t\_4} \cdot \left(x1 \cdot 2\right)\right) \cdot \left(3 + \frac{t\_3}{x1 \cdot x1 + 1}\right) - \left(x1 \cdot x1\right) \cdot 6\right) \cdot t\_4\right)\right)\right) + 3 \cdot \left(x2 \cdot -2\right)\right)\\ \mathbf{if}\;x1 \leq -4.5 \cdot 10^{+153}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x1 \leq -3.9 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{x1 - \left(t\_0 - 2 \cdot x2\right)}{t\_4} + \left(x1 + x1 \cdot \left(2 + x1 \cdot \left(\left(x1 \cdot -4 + \left(x2 \cdot 6 + x2 \cdot 8\right)\right) - 6\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -0.0051:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;x1 \leq 2.9 \cdot 10^{-23}:\\ \;\;\;\;x1 + \left(t\_1 - x2 \cdot \left(6 + \left(x1 \cdot \left(12 - x1 \cdot 6\right) - 8 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 4.2 \cdot 10^{+144}:\\ \;\;\;\;t\_5\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (* x1 (- (* x1 9.0) 2.0)))
        (t_2 (+ x1 (+ (* x2 -6.0) t_1)))
        (t_3 (- x1 (+ t_0 (* 2.0 x2))))
        (t_4 (- -1.0 (* x1 x1)))
        (t_5
         (+
          x1
          (+
           (+
            x1
            (+
             (* x1 (* x1 x1))
             (+
              (* 3.0 t_0)
              (*
               (-
                (*
                 (* (/ t_3 t_4) (* x1 2.0))
                 (+ 3.0 (/ t_3 (+ (* x1 x1) 1.0))))
                (* (* x1 x1) 6.0))
               t_4))))
           (* 3.0 (* x2 -2.0))))))
   (if (<= x1 -4.5e+153)
     t_2
     (if (<= x1 -3.9e+102)
       (+
        x1
        (+
         (* 3.0 (/ (- x1 (- t_0 (* 2.0 x2))) t_4))
         (+
          x1
          (*
           x1
           (+ 2.0 (* x1 (- (+ (* x1 -4.0) (+ (* x2 6.0) (* x2 8.0))) 6.0)))))))
       (if (<= x1 -0.0051)
         t_5
         (if (<= x1 2.9e-23)
           (+
            x1
            (-
             t_1
             (* x2 (+ 6.0 (- (* x1 (- 12.0 (* x1 6.0))) (* 8.0 (* x1 x2)))))))
           (if (<= x1 4.2e+144) t_5 t_2)))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = x1 * ((x1 * 9.0) - 2.0);
	double t_2 = x1 + ((x2 * -6.0) + t_1);
	double t_3 = x1 - (t_0 + (2.0 * x2));
	double t_4 = -1.0 - (x1 * x1);
	double t_5 = x1 + ((x1 + ((x1 * (x1 * x1)) + ((3.0 * t_0) + (((((t_3 / t_4) * (x1 * 2.0)) * (3.0 + (t_3 / ((x1 * x1) + 1.0)))) - ((x1 * x1) * 6.0)) * t_4)))) + (3.0 * (x2 * -2.0)));
	double tmp;
	if (x1 <= -4.5e+153) {
		tmp = t_2;
	} else if (x1 <= -3.9e+102) {
		tmp = x1 + ((3.0 * ((x1 - (t_0 - (2.0 * x2))) / t_4)) + (x1 + (x1 * (2.0 + (x1 * (((x1 * -4.0) + ((x2 * 6.0) + (x2 * 8.0))) - 6.0))))));
	} else if (x1 <= -0.0051) {
		tmp = t_5;
	} else if (x1 <= 2.9e-23) {
		tmp = x1 + (t_1 - (x2 * (6.0 + ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))));
	} else if (x1 <= 4.2e+144) {
		tmp = t_5;
	} 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) :: tmp
    t_0 = x1 * (x1 * 3.0d0)
    t_1 = x1 * ((x1 * 9.0d0) - 2.0d0)
    t_2 = x1 + ((x2 * (-6.0d0)) + t_1)
    t_3 = x1 - (t_0 + (2.0d0 * x2))
    t_4 = (-1.0d0) - (x1 * x1)
    t_5 = x1 + ((x1 + ((x1 * (x1 * x1)) + ((3.0d0 * t_0) + (((((t_3 / t_4) * (x1 * 2.0d0)) * (3.0d0 + (t_3 / ((x1 * x1) + 1.0d0)))) - ((x1 * x1) * 6.0d0)) * t_4)))) + (3.0d0 * (x2 * (-2.0d0))))
    if (x1 <= (-4.5d+153)) then
        tmp = t_2
    else if (x1 <= (-3.9d+102)) then
        tmp = x1 + ((3.0d0 * ((x1 - (t_0 - (2.0d0 * x2))) / t_4)) + (x1 + (x1 * (2.0d0 + (x1 * (((x1 * (-4.0d0)) + ((x2 * 6.0d0) + (x2 * 8.0d0))) - 6.0d0))))))
    else if (x1 <= (-0.0051d0)) then
        tmp = t_5
    else if (x1 <= 2.9d-23) then
        tmp = x1 + (t_1 - (x2 * (6.0d0 + ((x1 * (12.0d0 - (x1 * 6.0d0))) - (8.0d0 * (x1 * x2))))))
    else if (x1 <= 4.2d+144) then
        tmp = t_5
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = x1 * ((x1 * 9.0) - 2.0);
	double t_2 = x1 + ((x2 * -6.0) + t_1);
	double t_3 = x1 - (t_0 + (2.0 * x2));
	double t_4 = -1.0 - (x1 * x1);
	double t_5 = x1 + ((x1 + ((x1 * (x1 * x1)) + ((3.0 * t_0) + (((((t_3 / t_4) * (x1 * 2.0)) * (3.0 + (t_3 / ((x1 * x1) + 1.0)))) - ((x1 * x1) * 6.0)) * t_4)))) + (3.0 * (x2 * -2.0)));
	double tmp;
	if (x1 <= -4.5e+153) {
		tmp = t_2;
	} else if (x1 <= -3.9e+102) {
		tmp = x1 + ((3.0 * ((x1 - (t_0 - (2.0 * x2))) / t_4)) + (x1 + (x1 * (2.0 + (x1 * (((x1 * -4.0) + ((x2 * 6.0) + (x2 * 8.0))) - 6.0))))));
	} else if (x1 <= -0.0051) {
		tmp = t_5;
	} else if (x1 <= 2.9e-23) {
		tmp = x1 + (t_1 - (x2 * (6.0 + ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))));
	} else if (x1 <= 4.2e+144) {
		tmp = t_5;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = x1 * ((x1 * 9.0) - 2.0)
	t_2 = x1 + ((x2 * -6.0) + t_1)
	t_3 = x1 - (t_0 + (2.0 * x2))
	t_4 = -1.0 - (x1 * x1)
	t_5 = x1 + ((x1 + ((x1 * (x1 * x1)) + ((3.0 * t_0) + (((((t_3 / t_4) * (x1 * 2.0)) * (3.0 + (t_3 / ((x1 * x1) + 1.0)))) - ((x1 * x1) * 6.0)) * t_4)))) + (3.0 * (x2 * -2.0)))
	tmp = 0
	if x1 <= -4.5e+153:
		tmp = t_2
	elif x1 <= -3.9e+102:
		tmp = x1 + ((3.0 * ((x1 - (t_0 - (2.0 * x2))) / t_4)) + (x1 + (x1 * (2.0 + (x1 * (((x1 * -4.0) + ((x2 * 6.0) + (x2 * 8.0))) - 6.0))))))
	elif x1 <= -0.0051:
		tmp = t_5
	elif x1 <= 2.9e-23:
		tmp = x1 + (t_1 - (x2 * (6.0 + ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))))
	elif x1 <= 4.2e+144:
		tmp = t_5
	else:
		tmp = t_2
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(x1 * Float64(Float64(x1 * 9.0) - 2.0))
	t_2 = Float64(x1 + Float64(Float64(x2 * -6.0) + t_1))
	t_3 = Float64(x1 - Float64(t_0 + Float64(2.0 * x2)))
	t_4 = Float64(-1.0 - Float64(x1 * x1))
	t_5 = Float64(x1 + Float64(Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(3.0 * t_0) + Float64(Float64(Float64(Float64(Float64(t_3 / t_4) * Float64(x1 * 2.0)) * Float64(3.0 + Float64(t_3 / Float64(Float64(x1 * x1) + 1.0)))) - Float64(Float64(x1 * x1) * 6.0)) * t_4)))) + Float64(3.0 * Float64(x2 * -2.0))))
	tmp = 0.0
	if (x1 <= -4.5e+153)
		tmp = t_2;
	elseif (x1 <= -3.9e+102)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(x1 - Float64(t_0 - Float64(2.0 * x2))) / t_4)) + Float64(x1 + Float64(x1 * Float64(2.0 + Float64(x1 * Float64(Float64(Float64(x1 * -4.0) + Float64(Float64(x2 * 6.0) + Float64(x2 * 8.0))) - 6.0)))))));
	elseif (x1 <= -0.0051)
		tmp = t_5;
	elseif (x1 <= 2.9e-23)
		tmp = Float64(x1 + Float64(t_1 - Float64(x2 * Float64(6.0 + Float64(Float64(x1 * Float64(12.0 - Float64(x1 * 6.0))) - Float64(8.0 * Float64(x1 * x2)))))));
	elseif (x1 <= 4.2e+144)
		tmp = t_5;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * 3.0);
	t_1 = x1 * ((x1 * 9.0) - 2.0);
	t_2 = x1 + ((x2 * -6.0) + t_1);
	t_3 = x1 - (t_0 + (2.0 * x2));
	t_4 = -1.0 - (x1 * x1);
	t_5 = x1 + ((x1 + ((x1 * (x1 * x1)) + ((3.0 * t_0) + (((((t_3 / t_4) * (x1 * 2.0)) * (3.0 + (t_3 / ((x1 * x1) + 1.0)))) - ((x1 * x1) * 6.0)) * t_4)))) + (3.0 * (x2 * -2.0)));
	tmp = 0.0;
	if (x1 <= -4.5e+153)
		tmp = t_2;
	elseif (x1 <= -3.9e+102)
		tmp = x1 + ((3.0 * ((x1 - (t_0 - (2.0 * x2))) / t_4)) + (x1 + (x1 * (2.0 + (x1 * (((x1 * -4.0) + ((x2 * 6.0) + (x2 * 8.0))) - 6.0))))));
	elseif (x1 <= -0.0051)
		tmp = t_5;
	elseif (x1 <= 2.9e-23)
		tmp = x1 + (t_1 - (x2 * (6.0 + ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))));
	elseif (x1 <= 4.2e+144)
		tmp = t_5;
	else
		tmp = t_2;
	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[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x1 - N[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(x1 + N[(N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(3.0 * t$95$0), $MachinePrecision] + N[(N[(N[(N[(N[(t$95$3 / t$95$4), $MachinePrecision] * N[(x1 * 2.0), $MachinePrecision]), $MachinePrecision] * N[(3.0 + N[(t$95$3 / N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x1 * x1), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision] * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -4.5e+153], t$95$2, If[LessEqual[x1, -3.9e+102], N[(x1 + N[(N[(3.0 * N[(N[(x1 - N[(t$95$0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$4), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(x1 * N[(2.0 + N[(x1 * N[(N[(N[(x1 * -4.0), $MachinePrecision] + N[(N[(x2 * 6.0), $MachinePrecision] + N[(x2 * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -0.0051], t$95$5, If[LessEqual[x1, 2.9e-23], N[(x1 + N[(t$95$1 - N[(x2 * N[(6.0 + N[(N[(x1 * N[(12.0 - N[(x1 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 4.2e+144], t$95$5, t$95$2]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -4.5000000000000001e153 or 4.19999999999999993e144 < 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 32.2%

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

   5. Taylor expanded in x1 around 0 66.1%

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

   6. Taylor expanded in x2 around 0 98.3%

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

      1. *-commutative 98.3%

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

   8. Simplified 98.3%

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

   if -4.5000000000000001e153 < x1 < -3.8999999999999998e102

   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%

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

      1. +-commutative 0.0%

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

      2. mul-1-neg 0.0%

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

      3. sub-neg 0.0%

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

   5. Simplified 0.0%

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

   6. Taylor expanded in x1 around inf 0.0%

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

      1. *-commutative 0.0%

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

   8. Simplified 0.0%

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

   9. Taylor expanded in x1 around 0 93.3%

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

   if -3.8999999999999998e102 < x1 < -0.0051000000000000004 or 2.9000000000000002e-23 < x1 < 4.19999999999999993e144

   1. Initial program 97.8%

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

   3. Taylor expanded in x1 around inf 97.8%

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

   4. Taylor expanded in x1 around inf 93.9%

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

   5. Taylor expanded in x1 around 0 93.9%

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

      1. *-commutative 93.9%

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

   7. Simplified 93.9%

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

   if -0.0051000000000000004 < x1 < 2.9000000000000002e-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 87.3%

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

   4. Taylor expanded in x1 around 0 87.3%

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

   5. Taylor expanded in x1 around 0 87.6%

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

   6. Taylor expanded in x2 around 0 99.7%

      \[\leadsto x1 + \color{blue}{\left(x1 \cdot \left(9 \cdot x1 - 2\right) + x2 \cdot \left(\left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(6 \cdot x1 - 12\right)\right) - 6\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 97.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4.5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 - 2\right)\right)\\ \mathbf{elif}\;x1 \leq -3.9 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right)}{-1 - x1 \cdot x1} + \left(x1 + x1 \cdot \left(2 + x1 \cdot \left(\left(x1 \cdot -4 + \left(x2 \cdot 6 + x2 \cdot 8\right)\right) - 6\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -0.0051:\\ \;\;\;\;x1 + \left(\left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) + \left(\left(\frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{-1 - x1 \cdot x1} \cdot \left(x1 \cdot 2\right)\right) \cdot \left(3 + \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right) - \left(x1 \cdot x1\right) \cdot 6\right) \cdot \left(-1 - x1 \cdot x1\right)\right)\right)\right) + 3 \cdot \left(x2 \cdot -2\right)\right)\\ \mathbf{elif}\;x1 \leq 2.9 \cdot 10^{-23}:\\ \;\;\;\;x1 + \left(x1 \cdot \left(x1 \cdot 9 - 2\right) - x2 \cdot \left(6 + \left(x1 \cdot \left(12 - x1 \cdot 6\right) - 8 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 4.2 \cdot 10^{+144}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) + \left(\left(\frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{-1 - x1 \cdot x1} \cdot \left(x1 \cdot 2\right)\right) \cdot \left(3 + \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right) - \left(x1 \cdot x1\right) \cdot 6\right) \cdot \left(-1 - x1 \cdot x1\right)\right)\right)\right) + 3 \cdot \left(x2 \cdot -2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 - 2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 95.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := \left(x1 \cdot x1\right) \cdot 6\\ t_2 := x1 \cdot \left(x1 \cdot x1\right)\\ t_3 := x1 \cdot \left(x1 \cdot 3\right)\\ t_4 := 3 \cdot t\_3\\ t_5 := x1 - \left(t\_3 + 2 \cdot x2\right)\\ t_6 := -1 - x1 \cdot x1\\ t_7 := 3 \cdot \frac{x1 - \left(t\_3 - 2 \cdot x2\right)}{t\_6}\\ t_8 := \frac{t\_5}{t\_6}\\ \mathbf{if}\;x1 \leq -2 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 - 2\right)\right)\\ \mathbf{elif}\;x1 \leq -5 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(t\_7 + \left(x1 + x1 \cdot \left(2 + x1 \cdot \left(\left(x1 \cdot -4 + \left(x2 \cdot 6 + x2 \cdot 8\right)\right) - 6\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -0.00018:\\ \;\;\;\;x1 + \left(\left(x1 + \left(t\_2 + \left(t\_4 + \left(\left(t\_8 \cdot \left(x1 \cdot 2\right)\right) \cdot \left(3 + \frac{t\_5}{t\_0}\right) - t\_1\right) \cdot t\_6\right)\right)\right) + 3 \cdot \left(x2 \cdot -2\right)\right)\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{+97}:\\ \;\;\;\;x1 + \left(t\_7 + \left(x1 + \left(t\_2 + \left(t\_4 + t\_0 \cdot \left(t\_1 + \left(t\_8 - 3\right) \cdot \left(\left(2 \cdot x2 - x1\right) \cdot \left(x1 \cdot 2\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(-1 + x1 \cdot \left(x1 + 3\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ (* x1 x1) 1.0))
        (t_1 (* (* x1 x1) 6.0))
        (t_2 (* x1 (* x1 x1)))
        (t_3 (* x1 (* x1 3.0)))
        (t_4 (* 3.0 t_3))
        (t_5 (- x1 (+ t_3 (* 2.0 x2))))
        (t_6 (- -1.0 (* x1 x1)))
        (t_7 (* 3.0 (/ (- x1 (- t_3 (* 2.0 x2))) t_6)))
        (t_8 (/ t_5 t_6)))
   (if (<= x1 -2e+154)
     (+ x1 (+ (* x2 -6.0) (* x1 (- (* x1 9.0) 2.0))))
     (if (<= x1 -5e+102)
       (+
        x1
        (+
         t_7
         (+
          x1
          (*
           x1
           (+ 2.0 (* x1 (- (+ (* x1 -4.0) (+ (* x2 6.0) (* x2 8.0))) 6.0)))))))
       (if (<= x1 -0.00018)
         (+
          x1
          (+
           (+
            x1
            (+
             t_2
             (+
              t_4
              (* (- (* (* t_8 (* x1 2.0)) (+ 3.0 (/ t_5 t_0))) t_1) t_6))))
           (* 3.0 (* x2 -2.0))))
         (if (<= x1 2e+97)
           (+
            x1
            (+
             t_7
             (+
              x1
              (+
               t_2
               (+
                t_4
                (*
                 t_0
                 (+ t_1 (* (- t_8 3.0) (* (- (* 2.0 x2) x1) (* x1 2.0))))))))))
           (+ x1 (+ x1 (* 3.0 (* x1 (+ -1.0 (* x1 (+ x1 3.0)))))))))))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = (x1 * x1) * 6.0;
	double t_2 = x1 * (x1 * x1);
	double t_3 = x1 * (x1 * 3.0);
	double t_4 = 3.0 * t_3;
	double t_5 = x1 - (t_3 + (2.0 * x2));
	double t_6 = -1.0 - (x1 * x1);
	double t_7 = 3.0 * ((x1 - (t_3 - (2.0 * x2))) / t_6);
	double t_8 = t_5 / t_6;
	double tmp;
	if (x1 <= -2e+154) {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) - 2.0)));
	} else if (x1 <= -5e+102) {
		tmp = x1 + (t_7 + (x1 + (x1 * (2.0 + (x1 * (((x1 * -4.0) + ((x2 * 6.0) + (x2 * 8.0))) - 6.0))))));
	} else if (x1 <= -0.00018) {
		tmp = x1 + ((x1 + (t_2 + (t_4 + ((((t_8 * (x1 * 2.0)) * (3.0 + (t_5 / t_0))) - t_1) * t_6)))) + (3.0 * (x2 * -2.0)));
	} else if (x1 <= 2e+97) {
		tmp = x1 + (t_7 + (x1 + (t_2 + (t_4 + (t_0 * (t_1 + ((t_8 - 3.0) * (((2.0 * x2) - x1) * (x1 * 2.0)))))))));
	} else {
		tmp = x1 + (x1 + (3.0 * (x1 * (-1.0 + (x1 * (x1 + 3.0))))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: t_8
    real(8) :: tmp
    t_0 = (x1 * x1) + 1.0d0
    t_1 = (x1 * x1) * 6.0d0
    t_2 = x1 * (x1 * x1)
    t_3 = x1 * (x1 * 3.0d0)
    t_4 = 3.0d0 * t_3
    t_5 = x1 - (t_3 + (2.0d0 * x2))
    t_6 = (-1.0d0) - (x1 * x1)
    t_7 = 3.0d0 * ((x1 - (t_3 - (2.0d0 * x2))) / t_6)
    t_8 = t_5 / t_6
    if (x1 <= (-2d+154)) then
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * ((x1 * 9.0d0) - 2.0d0)))
    else if (x1 <= (-5d+102)) then
        tmp = x1 + (t_7 + (x1 + (x1 * (2.0d0 + (x1 * (((x1 * (-4.0d0)) + ((x2 * 6.0d0) + (x2 * 8.0d0))) - 6.0d0))))))
    else if (x1 <= (-0.00018d0)) then
        tmp = x1 + ((x1 + (t_2 + (t_4 + ((((t_8 * (x1 * 2.0d0)) * (3.0d0 + (t_5 / t_0))) - t_1) * t_6)))) + (3.0d0 * (x2 * (-2.0d0))))
    else if (x1 <= 2d+97) then
        tmp = x1 + (t_7 + (x1 + (t_2 + (t_4 + (t_0 * (t_1 + ((t_8 - 3.0d0) * (((2.0d0 * x2) - x1) * (x1 * 2.0d0)))))))))
    else
        tmp = x1 + (x1 + (3.0d0 * (x1 * ((-1.0d0) + (x1 * (x1 + 3.0d0))))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = (x1 * x1) * 6.0;
	double t_2 = x1 * (x1 * x1);
	double t_3 = x1 * (x1 * 3.0);
	double t_4 = 3.0 * t_3;
	double t_5 = x1 - (t_3 + (2.0 * x2));
	double t_6 = -1.0 - (x1 * x1);
	double t_7 = 3.0 * ((x1 - (t_3 - (2.0 * x2))) / t_6);
	double t_8 = t_5 / t_6;
	double tmp;
	if (x1 <= -2e+154) {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) - 2.0)));
	} else if (x1 <= -5e+102) {
		tmp = x1 + (t_7 + (x1 + (x1 * (2.0 + (x1 * (((x1 * -4.0) + ((x2 * 6.0) + (x2 * 8.0))) - 6.0))))));
	} else if (x1 <= -0.00018) {
		tmp = x1 + ((x1 + (t_2 + (t_4 + ((((t_8 * (x1 * 2.0)) * (3.0 + (t_5 / t_0))) - t_1) * t_6)))) + (3.0 * (x2 * -2.0)));
	} else if (x1 <= 2e+97) {
		tmp = x1 + (t_7 + (x1 + (t_2 + (t_4 + (t_0 * (t_1 + ((t_8 - 3.0) * (((2.0 * x2) - x1) * (x1 * 2.0)))))))));
	} else {
		tmp = x1 + (x1 + (3.0 * (x1 * (-1.0 + (x1 * (x1 + 3.0))))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x1 * x1) + 1.0
	t_1 = (x1 * x1) * 6.0
	t_2 = x1 * (x1 * x1)
	t_3 = x1 * (x1 * 3.0)
	t_4 = 3.0 * t_3
	t_5 = x1 - (t_3 + (2.0 * x2))
	t_6 = -1.0 - (x1 * x1)
	t_7 = 3.0 * ((x1 - (t_3 - (2.0 * x2))) / t_6)
	t_8 = t_5 / t_6
	tmp = 0
	if x1 <= -2e+154:
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) - 2.0)))
	elif x1 <= -5e+102:
		tmp = x1 + (t_7 + (x1 + (x1 * (2.0 + (x1 * (((x1 * -4.0) + ((x2 * 6.0) + (x2 * 8.0))) - 6.0))))))
	elif x1 <= -0.00018:
		tmp = x1 + ((x1 + (t_2 + (t_4 + ((((t_8 * (x1 * 2.0)) * (3.0 + (t_5 / t_0))) - t_1) * t_6)))) + (3.0 * (x2 * -2.0)))
	elif x1 <= 2e+97:
		tmp = x1 + (t_7 + (x1 + (t_2 + (t_4 + (t_0 * (t_1 + ((t_8 - 3.0) * (((2.0 * x2) - x1) * (x1 * 2.0)))))))))
	else:
		tmp = x1 + (x1 + (3.0 * (x1 * (-1.0 + (x1 * (x1 + 3.0))))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * x1) + 1.0)
	t_1 = Float64(Float64(x1 * x1) * 6.0)
	t_2 = Float64(x1 * Float64(x1 * x1))
	t_3 = Float64(x1 * Float64(x1 * 3.0))
	t_4 = Float64(3.0 * t_3)
	t_5 = Float64(x1 - Float64(t_3 + Float64(2.0 * x2)))
	t_6 = Float64(-1.0 - Float64(x1 * x1))
	t_7 = Float64(3.0 * Float64(Float64(x1 - Float64(t_3 - Float64(2.0 * x2))) / t_6))
	t_8 = Float64(t_5 / t_6)
	tmp = 0.0
	if (x1 <= -2e+154)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(x1 * 9.0) - 2.0))));
	elseif (x1 <= -5e+102)
		tmp = Float64(x1 + Float64(t_7 + Float64(x1 + Float64(x1 * Float64(2.0 + Float64(x1 * Float64(Float64(Float64(x1 * -4.0) + Float64(Float64(x2 * 6.0) + Float64(x2 * 8.0))) - 6.0)))))));
	elseif (x1 <= -0.00018)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(t_2 + Float64(t_4 + Float64(Float64(Float64(Float64(t_8 * Float64(x1 * 2.0)) * Float64(3.0 + Float64(t_5 / t_0))) - t_1) * t_6)))) + Float64(3.0 * Float64(x2 * -2.0))));
	elseif (x1 <= 2e+97)
		tmp = Float64(x1 + Float64(t_7 + Float64(x1 + Float64(t_2 + Float64(t_4 + Float64(t_0 * Float64(t_1 + Float64(Float64(t_8 - 3.0) * Float64(Float64(Float64(2.0 * x2) - x1) * Float64(x1 * 2.0))))))))));
	else
		tmp = Float64(x1 + Float64(x1 + Float64(3.0 * Float64(x1 * Float64(-1.0 + Float64(x1 * Float64(x1 + 3.0)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x1 * x1) + 1.0;
	t_1 = (x1 * x1) * 6.0;
	t_2 = x1 * (x1 * x1);
	t_3 = x1 * (x1 * 3.0);
	t_4 = 3.0 * t_3;
	t_5 = x1 - (t_3 + (2.0 * x2));
	t_6 = -1.0 - (x1 * x1);
	t_7 = 3.0 * ((x1 - (t_3 - (2.0 * x2))) / t_6);
	t_8 = t_5 / t_6;
	tmp = 0.0;
	if (x1 <= -2e+154)
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) - 2.0)));
	elseif (x1 <= -5e+102)
		tmp = x1 + (t_7 + (x1 + (x1 * (2.0 + (x1 * (((x1 * -4.0) + ((x2 * 6.0) + (x2 * 8.0))) - 6.0))))));
	elseif (x1 <= -0.00018)
		tmp = x1 + ((x1 + (t_2 + (t_4 + ((((t_8 * (x1 * 2.0)) * (3.0 + (t_5 / t_0))) - t_1) * t_6)))) + (3.0 * (x2 * -2.0)));
	elseif (x1 <= 2e+97)
		tmp = x1 + (t_7 + (x1 + (t_2 + (t_4 + (t_0 * (t_1 + ((t_8 - 3.0) * (((2.0 * x2) - x1) * (x1 * 2.0)))))))));
	else
		tmp = x1 + (x1 + (3.0 * (x1 * (-1.0 + (x1 * (x1 + 3.0))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x1 * x1), $MachinePrecision] * 6.0), $MachinePrecision]}, Block[{t$95$2 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(3.0 * t$95$3), $MachinePrecision]}, Block[{t$95$5 = N[(x1 - N[(t$95$3 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(3.0 * N[(N[(x1 - N[(t$95$3 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$6), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$8 = N[(t$95$5 / t$95$6), $MachinePrecision]}, If[LessEqual[x1, -2e+154], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -5e+102], N[(x1 + N[(t$95$7 + N[(x1 + N[(x1 * N[(2.0 + N[(x1 * N[(N[(N[(x1 * -4.0), $MachinePrecision] + N[(N[(x2 * 6.0), $MachinePrecision] + N[(x2 * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -0.00018], N[(x1 + N[(N[(x1 + N[(t$95$2 + N[(t$95$4 + N[(N[(N[(N[(t$95$8 * N[(x1 * 2.0), $MachinePrecision]), $MachinePrecision] * N[(3.0 + N[(t$95$5 / t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision] * t$95$6), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 2e+97], N[(x1 + N[(t$95$7 + N[(x1 + N[(t$95$2 + N[(t$95$4 + N[(t$95$0 * N[(t$95$1 + N[(N[(t$95$8 - 3.0), $MachinePrecision] * N[(N[(N[(2.0 * x2), $MachinePrecision] - x1), $MachinePrecision] * N[(x1 * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(x1 + N[(3.0 * N[(x1 * N[(-1.0 + N[(x1 * N[(x1 + 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x1 < -2.00000000000000007e154

   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 0.0%

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

   5. Taylor expanded in x1 around 0 67.6%

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

   6. Taylor expanded in x2 around 0 100.0%

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

      1. *-commutative 100.0%

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

   8. Simplified 100.0%

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

   if -2.00000000000000007e154 < x1 < -5e102

   1. Initial program 0.0%

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

   3. Taylor expanded in x1 around 0 0.0%

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

      1. +-commutative 0.0%

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

      2. mul-1-neg 0.0%

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

      3. sub-neg 0.0%

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

   5. Simplified 0.0%

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

   6. Taylor expanded in x1 around inf 0.0%

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

      1. *-commutative 0.0%

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

   8. Simplified 0.0%

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

   9. Taylor expanded in x1 around 0 93.3%

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

   if -5e102 < x1 < -1.80000000000000011e-4

   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 inf 95.9%

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

   4. Taylor expanded in x1 around inf 87.0%

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

   5. Taylor expanded in x1 around 0 87.0%

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

      1. *-commutative 87.0%

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

   7. Simplified 87.0%

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

   if -1.80000000000000011e-4 < x1 < 2.0000000000000001e97

   1. Initial program 99.4%

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

   3. Taylor expanded in x1 around inf 99.2%

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

   4. Taylor expanded in x1 around inf 99.2%

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

   5. Taylor expanded in x1 around 0 97.3%

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

      1. +-commutative 97.4%

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

      2. mul-1-neg 97.4%

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

      3. sub-neg 97.4%

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

   7. Simplified 97.3%

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

   if 2.0000000000000001e97 < x1

   1. Initial program 26.5%

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

   3. Taylor expanded in x1 around 0 15.3%

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

   4. Taylor expanded in x1 around 0 79.4%

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

   5. Taylor expanded in x2 around 0 97.1%

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

4. Final simplification 96.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -2 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 - 2\right)\right)\\ \mathbf{elif}\;x1 \leq -5 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right)}{-1 - x1 \cdot x1} + \left(x1 + x1 \cdot \left(2 + x1 \cdot \left(\left(x1 \cdot -4 + \left(x2 \cdot 6 + x2 \cdot 8\right)\right) - 6\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -0.00018:\\ \;\;\;\;x1 + \left(\left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) + \left(\left(\frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{-1 - x1 \cdot x1} \cdot \left(x1 \cdot 2\right)\right) \cdot \left(3 + \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right) - \left(x1 \cdot x1\right) \cdot 6\right) \cdot \left(-1 - x1 \cdot x1\right)\right)\right)\right) + 3 \cdot \left(x2 \cdot -2\right)\right)\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{+97}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right)}{-1 - x1 \cdot x1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot 6 + \left(\frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{-1 - x1 \cdot x1} - 3\right) \cdot \left(\left(2 \cdot x2 - x1\right) \cdot \left(x1 \cdot 2\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(-1 + x1 \cdot \left(x1 + 3\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 93.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := x1 \cdot \left(x1 \cdot 9 - 2\right)\\ t_2 := x1 + \left(x2 \cdot -6 + t\_1\right)\\ t_3 := -1 - x1 \cdot x1\\ t_4 := 3 \cdot \frac{x1 - \left(t\_0 - 2 \cdot x2\right)}{t\_3}\\ t_5 := x1 + \left(t\_4 - \left(\left(\left(\left(\left(x1 \cdot x1\right) \cdot \left(\frac{x1 - \left(t\_0 + 2 \cdot x2\right)}{t\_3} \cdot 4 - 6\right) + x1 \cdot 2\right) \cdot t\_3 - 3 \cdot t\_0\right) - x1 \cdot \left(x1 \cdot x1\right)\right) - x1\right)\right)\\ \mathbf{if}\;x1 \leq -4.5 \cdot 10^{+153}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(t\_4 + \left(x1 + x1 \cdot \left(2 + x1 \cdot \left(\left(x1 \cdot -4 + \left(x2 \cdot 6 + x2 \cdot 8\right)\right) - 6\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -6.8 \cdot 10^{+30}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;x1 \leq 23000000000000:\\ \;\;\;\;x1 + \left(t\_1 - x2 \cdot \left(6 + \left(x1 \cdot \left(12 - x1 \cdot 6\right) - 8 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 4.2 \cdot 10^{+144}:\\ \;\;\;\;t\_5\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (* x1 (- (* x1 9.0) 2.0)))
        (t_2 (+ x1 (+ (* x2 -6.0) t_1)))
        (t_3 (- -1.0 (* x1 x1)))
        (t_4 (* 3.0 (/ (- x1 (- t_0 (* 2.0 x2))) t_3)))
        (t_5
         (+
          x1
          (-
           t_4
           (-
            (-
             (-
              (*
               (+
                (* (* x1 x1) (- (* (/ (- x1 (+ t_0 (* 2.0 x2))) t_3) 4.0) 6.0))
                (* x1 2.0))
               t_3)
              (* 3.0 t_0))
             (* x1 (* x1 x1)))
            x1)))))
   (if (<= x1 -4.5e+153)
     t_2
     (if (<= x1 -5.6e+102)
       (+
        x1
        (+
         t_4
         (+
          x1
          (*
           x1
           (+ 2.0 (* x1 (- (+ (* x1 -4.0) (+ (* x2 6.0) (* x2 8.0))) 6.0)))))))
       (if (<= x1 -6.8e+30)
         t_5
         (if (<= x1 23000000000000.0)
           (+
            x1
            (-
             t_1
             (* x2 (+ 6.0 (- (* x1 (- 12.0 (* x1 6.0))) (* 8.0 (* x1 x2)))))))
           (if (<= x1 4.2e+144) t_5 t_2)))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = x1 * ((x1 * 9.0) - 2.0);
	double t_2 = x1 + ((x2 * -6.0) + t_1);
	double t_3 = -1.0 - (x1 * x1);
	double t_4 = 3.0 * ((x1 - (t_0 - (2.0 * x2))) / t_3);
	double t_5 = x1 + (t_4 - (((((((x1 * x1) * ((((x1 - (t_0 + (2.0 * x2))) / t_3) * 4.0) - 6.0)) + (x1 * 2.0)) * t_3) - (3.0 * t_0)) - (x1 * (x1 * x1))) - x1));
	double tmp;
	if (x1 <= -4.5e+153) {
		tmp = t_2;
	} else if (x1 <= -5.6e+102) {
		tmp = x1 + (t_4 + (x1 + (x1 * (2.0 + (x1 * (((x1 * -4.0) + ((x2 * 6.0) + (x2 * 8.0))) - 6.0))))));
	} else if (x1 <= -6.8e+30) {
		tmp = t_5;
	} else if (x1 <= 23000000000000.0) {
		tmp = x1 + (t_1 - (x2 * (6.0 + ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))));
	} else if (x1 <= 4.2e+144) {
		tmp = t_5;
	} 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) :: tmp
    t_0 = x1 * (x1 * 3.0d0)
    t_1 = x1 * ((x1 * 9.0d0) - 2.0d0)
    t_2 = x1 + ((x2 * (-6.0d0)) + t_1)
    t_3 = (-1.0d0) - (x1 * x1)
    t_4 = 3.0d0 * ((x1 - (t_0 - (2.0d0 * x2))) / t_3)
    t_5 = x1 + (t_4 - (((((((x1 * x1) * ((((x1 - (t_0 + (2.0d0 * x2))) / t_3) * 4.0d0) - 6.0d0)) + (x1 * 2.0d0)) * t_3) - (3.0d0 * t_0)) - (x1 * (x1 * x1))) - x1))
    if (x1 <= (-4.5d+153)) then
        tmp = t_2
    else if (x1 <= (-5.6d+102)) then
        tmp = x1 + (t_4 + (x1 + (x1 * (2.0d0 + (x1 * (((x1 * (-4.0d0)) + ((x2 * 6.0d0) + (x2 * 8.0d0))) - 6.0d0))))))
    else if (x1 <= (-6.8d+30)) then
        tmp = t_5
    else if (x1 <= 23000000000000.0d0) then
        tmp = x1 + (t_1 - (x2 * (6.0d0 + ((x1 * (12.0d0 - (x1 * 6.0d0))) - (8.0d0 * (x1 * x2))))))
    else if (x1 <= 4.2d+144) then
        tmp = t_5
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = x1 * ((x1 * 9.0) - 2.0);
	double t_2 = x1 + ((x2 * -6.0) + t_1);
	double t_3 = -1.0 - (x1 * x1);
	double t_4 = 3.0 * ((x1 - (t_0 - (2.0 * x2))) / t_3);
	double t_5 = x1 + (t_4 - (((((((x1 * x1) * ((((x1 - (t_0 + (2.0 * x2))) / t_3) * 4.0) - 6.0)) + (x1 * 2.0)) * t_3) - (3.0 * t_0)) - (x1 * (x1 * x1))) - x1));
	double tmp;
	if (x1 <= -4.5e+153) {
		tmp = t_2;
	} else if (x1 <= -5.6e+102) {
		tmp = x1 + (t_4 + (x1 + (x1 * (2.0 + (x1 * (((x1 * -4.0) + ((x2 * 6.0) + (x2 * 8.0))) - 6.0))))));
	} else if (x1 <= -6.8e+30) {
		tmp = t_5;
	} else if (x1 <= 23000000000000.0) {
		tmp = x1 + (t_1 - (x2 * (6.0 + ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))));
	} else if (x1 <= 4.2e+144) {
		tmp = t_5;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = x1 * ((x1 * 9.0) - 2.0)
	t_2 = x1 + ((x2 * -6.0) + t_1)
	t_3 = -1.0 - (x1 * x1)
	t_4 = 3.0 * ((x1 - (t_0 - (2.0 * x2))) / t_3)
	t_5 = x1 + (t_4 - (((((((x1 * x1) * ((((x1 - (t_0 + (2.0 * x2))) / t_3) * 4.0) - 6.0)) + (x1 * 2.0)) * t_3) - (3.0 * t_0)) - (x1 * (x1 * x1))) - x1))
	tmp = 0
	if x1 <= -4.5e+153:
		tmp = t_2
	elif x1 <= -5.6e+102:
		tmp = x1 + (t_4 + (x1 + (x1 * (2.0 + (x1 * (((x1 * -4.0) + ((x2 * 6.0) + (x2 * 8.0))) - 6.0))))))
	elif x1 <= -6.8e+30:
		tmp = t_5
	elif x1 <= 23000000000000.0:
		tmp = x1 + (t_1 - (x2 * (6.0 + ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))))
	elif x1 <= 4.2e+144:
		tmp = t_5
	else:
		tmp = t_2
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(x1 * Float64(Float64(x1 * 9.0) - 2.0))
	t_2 = Float64(x1 + Float64(Float64(x2 * -6.0) + t_1))
	t_3 = Float64(-1.0 - Float64(x1 * x1))
	t_4 = Float64(3.0 * Float64(Float64(x1 - Float64(t_0 - Float64(2.0 * x2))) / t_3))
	t_5 = Float64(x1 + Float64(t_4 - Float64(Float64(Float64(Float64(Float64(Float64(Float64(x1 * x1) * Float64(Float64(Float64(Float64(x1 - Float64(t_0 + Float64(2.0 * x2))) / t_3) * 4.0) - 6.0)) + Float64(x1 * 2.0)) * t_3) - Float64(3.0 * t_0)) - Float64(x1 * Float64(x1 * x1))) - x1)))
	tmp = 0.0
	if (x1 <= -4.5e+153)
		tmp = t_2;
	elseif (x1 <= -5.6e+102)
		tmp = Float64(x1 + Float64(t_4 + Float64(x1 + Float64(x1 * Float64(2.0 + Float64(x1 * Float64(Float64(Float64(x1 * -4.0) + Float64(Float64(x2 * 6.0) + Float64(x2 * 8.0))) - 6.0)))))));
	elseif (x1 <= -6.8e+30)
		tmp = t_5;
	elseif (x1 <= 23000000000000.0)
		tmp = Float64(x1 + Float64(t_1 - Float64(x2 * Float64(6.0 + Float64(Float64(x1 * Float64(12.0 - Float64(x1 * 6.0))) - Float64(8.0 * Float64(x1 * x2)))))));
	elseif (x1 <= 4.2e+144)
		tmp = t_5;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * 3.0);
	t_1 = x1 * ((x1 * 9.0) - 2.0);
	t_2 = x1 + ((x2 * -6.0) + t_1);
	t_3 = -1.0 - (x1 * x1);
	t_4 = 3.0 * ((x1 - (t_0 - (2.0 * x2))) / t_3);
	t_5 = x1 + (t_4 - (((((((x1 * x1) * ((((x1 - (t_0 + (2.0 * x2))) / t_3) * 4.0) - 6.0)) + (x1 * 2.0)) * t_3) - (3.0 * t_0)) - (x1 * (x1 * x1))) - x1));
	tmp = 0.0;
	if (x1 <= -4.5e+153)
		tmp = t_2;
	elseif (x1 <= -5.6e+102)
		tmp = x1 + (t_4 + (x1 + (x1 * (2.0 + (x1 * (((x1 * -4.0) + ((x2 * 6.0) + (x2 * 8.0))) - 6.0))))));
	elseif (x1 <= -6.8e+30)
		tmp = t_5;
	elseif (x1 <= 23000000000000.0)
		tmp = x1 + (t_1 - (x2 * (6.0 + ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))));
	elseif (x1 <= 4.2e+144)
		tmp = t_5;
	else
		tmp = t_2;
	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[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(3.0 * N[(N[(x1 - N[(t$95$0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(x1 + N[(t$95$4 - N[(N[(N[(N[(N[(N[(N[(x1 * x1), $MachinePrecision] * N[(N[(N[(N[(x1 - N[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$3), $MachinePrecision] * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] + N[(x1 * 2.0), $MachinePrecision]), $MachinePrecision] * t$95$3), $MachinePrecision] - N[(3.0 * t$95$0), $MachinePrecision]), $MachinePrecision] - N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -4.5e+153], t$95$2, If[LessEqual[x1, -5.6e+102], N[(x1 + N[(t$95$4 + N[(x1 + N[(x1 * N[(2.0 + N[(x1 * N[(N[(N[(x1 * -4.0), $MachinePrecision] + N[(N[(x2 * 6.0), $MachinePrecision] + N[(x2 * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -6.8e+30], t$95$5, If[LessEqual[x1, 23000000000000.0], N[(x1 + N[(t$95$1 - N[(x2 * N[(6.0 + N[(N[(x1 * N[(12.0 - N[(x1 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 4.2e+144], t$95$5, t$95$2]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -4.5000000000000001e153 or 4.19999999999999993e144 < 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 32.2%

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

   5. Taylor expanded in x1 around 0 66.1%

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

   6. Taylor expanded in x2 around 0 98.3%

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

      1. *-commutative 98.3%

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

   8. Simplified 98.3%

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

   if -4.5000000000000001e153 < x1 < -5.60000000000000037e102

   1. Initial program 0.0%

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

   3. Taylor expanded in x1 around 0 0.0%

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

      1. +-commutative 0.0%

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

      2. mul-1-neg 0.0%

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

      3. sub-neg 0.0%

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

   5. Simplified 0.0%

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

   6. Taylor expanded in x1 around inf 0.0%

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

      1. *-commutative 0.0%

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

   8. Simplified 0.0%

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

   9. Taylor expanded in x1 around 0 93.3%

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

   if -5.60000000000000037e102 < x1 < -6.8000000000000005e30 or 2.3e13 < x1 < 4.19999999999999993e144

   1. Initial program 97.3%

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

   3. Taylor expanded in x1 around 0 83.5%

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

      1. +-commutative 83.5%

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

      2. mul-1-neg 83.5%

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

      3. sub-neg 83.5%

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

   5. Simplified 83.5%

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

   6. Taylor expanded in x1 around inf 79.2%

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

      1. *-commutative 79.2%

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

   8. Simplified 79.2%

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

   9. Taylor expanded in x1 around inf 79.2%

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

   if -6.8000000000000005e30 < x1 < 2.3e13

   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 83.5%

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

   4. Taylor expanded in x1 around 0 83.5%

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

   5. Taylor expanded in x1 around 0 83.9%

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

   6. Taylor expanded in x2 around 0 95.2%

      \[\leadsto x1 + \color{blue}{\left(x1 \cdot \left(9 \cdot x1 - 2\right) + x2 \cdot \left(\left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(6 \cdot x1 - 12\right)\right) - 6\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4.5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 - 2\right)\right)\\ \mathbf{elif}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right)}{-1 - x1 \cdot x1} + \left(x1 + x1 \cdot \left(2 + x1 \cdot \left(\left(x1 \cdot -4 + \left(x2 \cdot 6 + x2 \cdot 8\right)\right) - 6\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -6.8 \cdot 10^{+30}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right)}{-1 - x1 \cdot x1} - \left(\left(\left(\left(\left(x1 \cdot x1\right) \cdot \left(\frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{-1 - x1 \cdot x1} \cdot 4 - 6\right) + x1 \cdot 2\right) \cdot \left(-1 - x1 \cdot x1\right) - 3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right)\right) - x1 \cdot \left(x1 \cdot x1\right)\right) - x1\right)\right)\\ \mathbf{elif}\;x1 \leq 23000000000000:\\ \;\;\;\;x1 + \left(x1 \cdot \left(x1 \cdot 9 - 2\right) - x2 \cdot \left(6 + \left(x1 \cdot \left(12 - x1 \cdot 6\right) - 8 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 4.2 \cdot 10^{+144}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right)}{-1 - x1 \cdot x1} - \left(\left(\left(\left(\left(x1 \cdot x1\right) \cdot \left(\frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{-1 - x1 \cdot x1} \cdot 4 - 6\right) + x1 \cdot 2\right) \cdot \left(-1 - x1 \cdot x1\right) - 3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right)\right) - x1 \cdot \left(x1 \cdot x1\right)\right) - x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 - 2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 88.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := x1 \cdot \left(x1 \cdot 9 - 2\right)\\ t_2 := x1 + \left(x2 \cdot -6 + t\_1\right)\\ t_3 := -1 - x1 \cdot x1\\ t_4 := 3 \cdot \frac{x1 - \left(t\_0 - 2 \cdot x2\right)}{t\_3}\\ t_5 := 3 - 2 \cdot x2\\ \mathbf{if}\;x1 \leq -4.5 \cdot 10^{+150}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x1 \leq -1.6 \cdot 10^{+84}:\\ \;\;\;\;x1 + \left(t\_4 + \left(x1 + x1 \cdot \left(2 - x1 \cdot \left(6 + \left(\left(x1 \cdot \left(4 - x1 \cdot \left(\left(3 \cdot t\_5 + \left(x2 \cdot 8 + 4 \cdot t\_5\right)\right) - 6\right)\right) - x2 \cdot 8\right) - x2 \cdot 6\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{+14}:\\ \;\;\;\;x1 + \left(t\_1 - x2 \cdot \left(6 + \left(x1 \cdot \left(12 - x1 \cdot 6\right) - 8 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 4.2 \cdot 10^{+144}:\\ \;\;\;\;x1 + \left(t\_4 - \left(\left(\left(\left(\left(x1 \cdot x1\right) \cdot 6 + x1 \cdot 2\right) \cdot t\_3 - t\_0 \cdot \frac{x1 - \left(t\_0 + 2 \cdot x2\right)}{t\_3}\right) - x1 \cdot \left(x1 \cdot x1\right)\right) - x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (* x1 (- (* x1 9.0) 2.0)))
        (t_2 (+ x1 (+ (* x2 -6.0) t_1)))
        (t_3 (- -1.0 (* x1 x1)))
        (t_4 (* 3.0 (/ (- x1 (- t_0 (* 2.0 x2))) t_3)))
        (t_5 (- 3.0 (* 2.0 x2))))
   (if (<= x1 -4.5e+150)
     t_2
     (if (<= x1 -1.6e+84)
       (+
        x1
        (+
         t_4
         (+
          x1
          (*
           x1
           (-
            2.0
            (*
             x1
             (+
              6.0
              (-
               (-
                (*
                 x1
                 (-
                  4.0
                  (* x1 (- (+ (* 3.0 t_5) (+ (* x2 8.0) (* 4.0 t_5))) 6.0))))
                (* x2 8.0))
               (* x2 6.0)))))))))
       (if (<= x1 2e+14)
         (+
          x1
          (-
           t_1
           (* x2 (+ 6.0 (- (* x1 (- 12.0 (* x1 6.0))) (* 8.0 (* x1 x2)))))))
         (if (<= x1 4.2e+144)
           (+
            x1
            (-
             t_4
             (-
              (-
               (-
                (* (+ (* (* x1 x1) 6.0) (* x1 2.0)) t_3)
                (* t_0 (/ (- x1 (+ t_0 (* 2.0 x2))) t_3)))
               (* x1 (* x1 x1)))
              x1)))
           t_2))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = x1 * ((x1 * 9.0) - 2.0);
	double t_2 = x1 + ((x2 * -6.0) + t_1);
	double t_3 = -1.0 - (x1 * x1);
	double t_4 = 3.0 * ((x1 - (t_0 - (2.0 * x2))) / t_3);
	double t_5 = 3.0 - (2.0 * x2);
	double tmp;
	if (x1 <= -4.5e+150) {
		tmp = t_2;
	} else if (x1 <= -1.6e+84) {
		tmp = x1 + (t_4 + (x1 + (x1 * (2.0 - (x1 * (6.0 + (((x1 * (4.0 - (x1 * (((3.0 * t_5) + ((x2 * 8.0) + (4.0 * t_5))) - 6.0)))) - (x2 * 8.0)) - (x2 * 6.0))))))));
	} else if (x1 <= 2e+14) {
		tmp = x1 + (t_1 - (x2 * (6.0 + ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))));
	} else if (x1 <= 4.2e+144) {
		tmp = x1 + (t_4 - (((((((x1 * x1) * 6.0) + (x1 * 2.0)) * t_3) - (t_0 * ((x1 - (t_0 + (2.0 * x2))) / t_3))) - (x1 * (x1 * x1))) - x1));
	} 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) :: tmp
    t_0 = x1 * (x1 * 3.0d0)
    t_1 = x1 * ((x1 * 9.0d0) - 2.0d0)
    t_2 = x1 + ((x2 * (-6.0d0)) + t_1)
    t_3 = (-1.0d0) - (x1 * x1)
    t_4 = 3.0d0 * ((x1 - (t_0 - (2.0d0 * x2))) / t_3)
    t_5 = 3.0d0 - (2.0d0 * x2)
    if (x1 <= (-4.5d+150)) then
        tmp = t_2
    else if (x1 <= (-1.6d+84)) then
        tmp = x1 + (t_4 + (x1 + (x1 * (2.0d0 - (x1 * (6.0d0 + (((x1 * (4.0d0 - (x1 * (((3.0d0 * t_5) + ((x2 * 8.0d0) + (4.0d0 * t_5))) - 6.0d0)))) - (x2 * 8.0d0)) - (x2 * 6.0d0))))))))
    else if (x1 <= 2d+14) then
        tmp = x1 + (t_1 - (x2 * (6.0d0 + ((x1 * (12.0d0 - (x1 * 6.0d0))) - (8.0d0 * (x1 * x2))))))
    else if (x1 <= 4.2d+144) then
        tmp = x1 + (t_4 - (((((((x1 * x1) * 6.0d0) + (x1 * 2.0d0)) * t_3) - (t_0 * ((x1 - (t_0 + (2.0d0 * x2))) / t_3))) - (x1 * (x1 * x1))) - x1))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = x1 * ((x1 * 9.0) - 2.0);
	double t_2 = x1 + ((x2 * -6.0) + t_1);
	double t_3 = -1.0 - (x1 * x1);
	double t_4 = 3.0 * ((x1 - (t_0 - (2.0 * x2))) / t_3);
	double t_5 = 3.0 - (2.0 * x2);
	double tmp;
	if (x1 <= -4.5e+150) {
		tmp = t_2;
	} else if (x1 <= -1.6e+84) {
		tmp = x1 + (t_4 + (x1 + (x1 * (2.0 - (x1 * (6.0 + (((x1 * (4.0 - (x1 * (((3.0 * t_5) + ((x2 * 8.0) + (4.0 * t_5))) - 6.0)))) - (x2 * 8.0)) - (x2 * 6.0))))))));
	} else if (x1 <= 2e+14) {
		tmp = x1 + (t_1 - (x2 * (6.0 + ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))));
	} else if (x1 <= 4.2e+144) {
		tmp = x1 + (t_4 - (((((((x1 * x1) * 6.0) + (x1 * 2.0)) * t_3) - (t_0 * ((x1 - (t_0 + (2.0 * x2))) / t_3))) - (x1 * (x1 * x1))) - x1));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = x1 * ((x1 * 9.0) - 2.0)
	t_2 = x1 + ((x2 * -6.0) + t_1)
	t_3 = -1.0 - (x1 * x1)
	t_4 = 3.0 * ((x1 - (t_0 - (2.0 * x2))) / t_3)
	t_5 = 3.0 - (2.0 * x2)
	tmp = 0
	if x1 <= -4.5e+150:
		tmp = t_2
	elif x1 <= -1.6e+84:
		tmp = x1 + (t_4 + (x1 + (x1 * (2.0 - (x1 * (6.0 + (((x1 * (4.0 - (x1 * (((3.0 * t_5) + ((x2 * 8.0) + (4.0 * t_5))) - 6.0)))) - (x2 * 8.0)) - (x2 * 6.0))))))))
	elif x1 <= 2e+14:
		tmp = x1 + (t_1 - (x2 * (6.0 + ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))))
	elif x1 <= 4.2e+144:
		tmp = x1 + (t_4 - (((((((x1 * x1) * 6.0) + (x1 * 2.0)) * t_3) - (t_0 * ((x1 - (t_0 + (2.0 * x2))) / t_3))) - (x1 * (x1 * x1))) - x1))
	else:
		tmp = t_2
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(x1 * Float64(Float64(x1 * 9.0) - 2.0))
	t_2 = Float64(x1 + Float64(Float64(x2 * -6.0) + t_1))
	t_3 = Float64(-1.0 - Float64(x1 * x1))
	t_4 = Float64(3.0 * Float64(Float64(x1 - Float64(t_0 - Float64(2.0 * x2))) / t_3))
	t_5 = Float64(3.0 - Float64(2.0 * x2))
	tmp = 0.0
	if (x1 <= -4.5e+150)
		tmp = t_2;
	elseif (x1 <= -1.6e+84)
		tmp = Float64(x1 + Float64(t_4 + Float64(x1 + Float64(x1 * Float64(2.0 - Float64(x1 * Float64(6.0 + Float64(Float64(Float64(x1 * Float64(4.0 - Float64(x1 * Float64(Float64(Float64(3.0 * t_5) + Float64(Float64(x2 * 8.0) + Float64(4.0 * t_5))) - 6.0)))) - Float64(x2 * 8.0)) - Float64(x2 * 6.0)))))))));
	elseif (x1 <= 2e+14)
		tmp = Float64(x1 + Float64(t_1 - Float64(x2 * Float64(6.0 + Float64(Float64(x1 * Float64(12.0 - Float64(x1 * 6.0))) - Float64(8.0 * Float64(x1 * x2)))))));
	elseif (x1 <= 4.2e+144)
		tmp = Float64(x1 + Float64(t_4 - Float64(Float64(Float64(Float64(Float64(Float64(Float64(x1 * x1) * 6.0) + Float64(x1 * 2.0)) * t_3) - Float64(t_0 * Float64(Float64(x1 - Float64(t_0 + Float64(2.0 * x2))) / t_3))) - Float64(x1 * Float64(x1 * x1))) - x1)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * 3.0);
	t_1 = x1 * ((x1 * 9.0) - 2.0);
	t_2 = x1 + ((x2 * -6.0) + t_1);
	t_3 = -1.0 - (x1 * x1);
	t_4 = 3.0 * ((x1 - (t_0 - (2.0 * x2))) / t_3);
	t_5 = 3.0 - (2.0 * x2);
	tmp = 0.0;
	if (x1 <= -4.5e+150)
		tmp = t_2;
	elseif (x1 <= -1.6e+84)
		tmp = x1 + (t_4 + (x1 + (x1 * (2.0 - (x1 * (6.0 + (((x1 * (4.0 - (x1 * (((3.0 * t_5) + ((x2 * 8.0) + (4.0 * t_5))) - 6.0)))) - (x2 * 8.0)) - (x2 * 6.0))))))));
	elseif (x1 <= 2e+14)
		tmp = x1 + (t_1 - (x2 * (6.0 + ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))));
	elseif (x1 <= 4.2e+144)
		tmp = x1 + (t_4 - (((((((x1 * x1) * 6.0) + (x1 * 2.0)) * t_3) - (t_0 * ((x1 - (t_0 + (2.0 * x2))) / t_3))) - (x1 * (x1 * x1))) - x1));
	else
		tmp = t_2;
	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[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(3.0 * N[(N[(x1 - N[(t$95$0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -4.5e+150], t$95$2, If[LessEqual[x1, -1.6e+84], N[(x1 + N[(t$95$4 + N[(x1 + N[(x1 * N[(2.0 - N[(x1 * N[(6.0 + N[(N[(N[(x1 * N[(4.0 - N[(x1 * N[(N[(N[(3.0 * t$95$5), $MachinePrecision] + N[(N[(x2 * 8.0), $MachinePrecision] + N[(4.0 * t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x2 * 8.0), $MachinePrecision]), $MachinePrecision] - N[(x2 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 2e+14], N[(x1 + N[(t$95$1 - N[(x2 * N[(6.0 + N[(N[(x1 * N[(12.0 - N[(x1 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 4.2e+144], N[(x1 + N[(t$95$4 - N[(N[(N[(N[(N[(N[(N[(x1 * x1), $MachinePrecision] * 6.0), $MachinePrecision] + N[(x1 * 2.0), $MachinePrecision]), $MachinePrecision] * t$95$3), $MachinePrecision] - N[(t$95$0 * N[(N[(x1 - N[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -4.5e150 or 4.19999999999999993e144 < 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 31.7%

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

   5. Taylor expanded in x1 around 0 66.7%

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

   6. Taylor expanded in x2 around 0 96.9%

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

      1. *-commutative 96.9%

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

   8. Simplified 96.9%

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

   if -4.5e150 < x1 < -1.60000000000000005e84

   1. Initial program 17.6%

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

   3. Taylor expanded in x1 around 0 17.6%

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

      1. +-commutative 17.6%

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

      2. mul-1-neg 17.6%

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

      3. sub-neg 17.6%

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

   5. Simplified 17.6%

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

   6. Taylor expanded in x1 around inf 17.6%

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

      1. *-commutative 17.6%

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

   8. Simplified 17.6%

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

   9. Taylor expanded in x1 around 0 88.2%

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

   if -1.60000000000000005e84 < x1 < 2e14

   1. Initial program 98.7%

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

   3. Taylor expanded in x1 around 0 78.0%

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

   4. Taylor expanded in x1 around 0 75.9%

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

   5. Taylor expanded in x1 around 0 77.2%

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

   6. Taylor expanded in x2 around 0 89.3%

      \[\leadsto x1 + \color{blue}{\left(x1 \cdot \left(9 \cdot x1 - 2\right) + x2 \cdot \left(\left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(6 \cdot x1 - 12\right)\right) - 6\right)\right)} \]

   if 2e14 < x1 < 4.19999999999999993e144

   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 86.2%

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

      1. +-commutative 86.2%

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

      2. mul-1-neg 86.2%

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

      3. sub-neg 86.2%

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

   5. Simplified 86.2%

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

   6. Taylor expanded in x1 around inf 82.9%

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

      1. *-commutative 82.9%

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

   8. Simplified 82.9%

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

   9. Taylor expanded in x1 around inf 80.1%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4.5 \cdot 10^{+150}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 - 2\right)\right)\\ \mathbf{elif}\;x1 \leq -1.6 \cdot 10^{+84}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right)}{-1 - x1 \cdot x1} + \left(x1 + x1 \cdot \left(2 - x1 \cdot \left(6 + \left(\left(x1 \cdot \left(4 - x1 \cdot \left(\left(3 \cdot \left(3 - 2 \cdot x2\right) + \left(x2 \cdot 8 + 4 \cdot \left(3 - 2 \cdot x2\right)\right)\right) - 6\right)\right) - x2 \cdot 8\right) - x2 \cdot 6\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{+14}:\\ \;\;\;\;x1 + \left(x1 \cdot \left(x1 \cdot 9 - 2\right) - x2 \cdot \left(6 + \left(x1 \cdot \left(12 - x1 \cdot 6\right) - 8 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 4.2 \cdot 10^{+144}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right)}{-1 - x1 \cdot x1} - \left(\left(\left(\left(\left(x1 \cdot x1\right) \cdot 6 + x1 \cdot 2\right) \cdot \left(-1 - x1 \cdot x1\right) - \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{-1 - x1 \cdot x1}\right) - x1 \cdot \left(x1 \cdot x1\right)\right) - x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 - 2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 85.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 9 - 2\right)\\ t_1 := 3 - 2 \cdot x2\\ \mathbf{if}\;x1 \leq -4.5 \cdot 10^{+150}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + t\_0\right)\\ \mathbf{elif}\;x1 \leq -1.6 \cdot 10^{+84}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right)}{-1 - x1 \cdot x1} + \left(x1 + x1 \cdot \left(2 - x1 \cdot \left(6 + \left(\left(x1 \cdot \left(4 - x1 \cdot \left(\left(3 \cdot t\_1 + \left(x2 \cdot 8 + 4 \cdot t\_1\right)\right) - 6\right)\right) - x2 \cdot 8\right) - x2 \cdot 6\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 16500000000000:\\ \;\;\;\;x1 + \left(t\_0 - x2 \cdot \left(6 + \left(x1 \cdot \left(12 - x1 \cdot 6\right) - 8 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x1 \cdot \left(-1 + x1 \cdot \left(x1 + 3\right)\right)\right) + \left(x1 - 4 \cdot \left(x1 \cdot \left(x2 \cdot t\_1\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (- (* x1 9.0) 2.0))) (t_1 (- 3.0 (* 2.0 x2))))
   (if (<= x1 -4.5e+150)
     (+ x1 (+ (* x2 -6.0) t_0))
     (if (<= x1 -1.6e+84)
       (+
        x1
        (+
         (* 3.0 (/ (- x1 (- (* x1 (* x1 3.0)) (* 2.0 x2))) (- -1.0 (* x1 x1))))
         (+
          x1
          (*
           x1
           (-
            2.0
            (*
             x1
             (+
              6.0
              (-
               (-
                (*
                 x1
                 (-
                  4.0
                  (* x1 (- (+ (* 3.0 t_1) (+ (* x2 8.0) (* 4.0 t_1))) 6.0))))
                (* x2 8.0))
               (* x2 6.0)))))))))
       (if (<= x1 16500000000000.0)
         (+
          x1
          (-
           t_0
           (* x2 (+ 6.0 (- (* x1 (- 12.0 (* x1 6.0))) (* 8.0 (* x1 x2)))))))
         (+
          x1
          (+
           (* 3.0 (* x1 (+ -1.0 (* x1 (+ x1 3.0)))))
           (- x1 (* 4.0 (* x1 (* x2 t_1)))))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * ((x1 * 9.0) - 2.0);
	double t_1 = 3.0 - (2.0 * x2);
	double tmp;
	if (x1 <= -4.5e+150) {
		tmp = x1 + ((x2 * -6.0) + t_0);
	} else if (x1 <= -1.6e+84) {
		tmp = x1 + ((3.0 * ((x1 - ((x1 * (x1 * 3.0)) - (2.0 * x2))) / (-1.0 - (x1 * x1)))) + (x1 + (x1 * (2.0 - (x1 * (6.0 + (((x1 * (4.0 - (x1 * (((3.0 * t_1) + ((x2 * 8.0) + (4.0 * t_1))) - 6.0)))) - (x2 * 8.0)) - (x2 * 6.0))))))));
	} else if (x1 <= 16500000000000.0) {
		tmp = x1 + (t_0 - (x2 * (6.0 + ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))));
	} else {
		tmp = x1 + ((3.0 * (x1 * (-1.0 + (x1 * (x1 + 3.0))))) + (x1 - (4.0 * (x1 * (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) :: tmp
    t_0 = x1 * ((x1 * 9.0d0) - 2.0d0)
    t_1 = 3.0d0 - (2.0d0 * x2)
    if (x1 <= (-4.5d+150)) then
        tmp = x1 + ((x2 * (-6.0d0)) + t_0)
    else if (x1 <= (-1.6d+84)) then
        tmp = x1 + ((3.0d0 * ((x1 - ((x1 * (x1 * 3.0d0)) - (2.0d0 * x2))) / ((-1.0d0) - (x1 * x1)))) + (x1 + (x1 * (2.0d0 - (x1 * (6.0d0 + (((x1 * (4.0d0 - (x1 * (((3.0d0 * t_1) + ((x2 * 8.0d0) + (4.0d0 * t_1))) - 6.0d0)))) - (x2 * 8.0d0)) - (x2 * 6.0d0))))))))
    else if (x1 <= 16500000000000.0d0) then
        tmp = x1 + (t_0 - (x2 * (6.0d0 + ((x1 * (12.0d0 - (x1 * 6.0d0))) - (8.0d0 * (x1 * x2))))))
    else
        tmp = x1 + ((3.0d0 * (x1 * ((-1.0d0) + (x1 * (x1 + 3.0d0))))) + (x1 - (4.0d0 * (x1 * (x2 * t_1)))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * ((x1 * 9.0) - 2.0);
	double t_1 = 3.0 - (2.0 * x2);
	double tmp;
	if (x1 <= -4.5e+150) {
		tmp = x1 + ((x2 * -6.0) + t_0);
	} else if (x1 <= -1.6e+84) {
		tmp = x1 + ((3.0 * ((x1 - ((x1 * (x1 * 3.0)) - (2.0 * x2))) / (-1.0 - (x1 * x1)))) + (x1 + (x1 * (2.0 - (x1 * (6.0 + (((x1 * (4.0 - (x1 * (((3.0 * t_1) + ((x2 * 8.0) + (4.0 * t_1))) - 6.0)))) - (x2 * 8.0)) - (x2 * 6.0))))))));
	} else if (x1 <= 16500000000000.0) {
		tmp = x1 + (t_0 - (x2 * (6.0 + ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))));
	} else {
		tmp = x1 + ((3.0 * (x1 * (-1.0 + (x1 * (x1 + 3.0))))) + (x1 - (4.0 * (x1 * (x2 * t_1)))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * ((x1 * 9.0) - 2.0)
	t_1 = 3.0 - (2.0 * x2)
	tmp = 0
	if x1 <= -4.5e+150:
		tmp = x1 + ((x2 * -6.0) + t_0)
	elif x1 <= -1.6e+84:
		tmp = x1 + ((3.0 * ((x1 - ((x1 * (x1 * 3.0)) - (2.0 * x2))) / (-1.0 - (x1 * x1)))) + (x1 + (x1 * (2.0 - (x1 * (6.0 + (((x1 * (4.0 - (x1 * (((3.0 * t_1) + ((x2 * 8.0) + (4.0 * t_1))) - 6.0)))) - (x2 * 8.0)) - (x2 * 6.0))))))))
	elif x1 <= 16500000000000.0:
		tmp = x1 + (t_0 - (x2 * (6.0 + ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))))
	else:
		tmp = x1 + ((3.0 * (x1 * (-1.0 + (x1 * (x1 + 3.0))))) + (x1 - (4.0 * (x1 * (x2 * t_1)))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(Float64(x1 * 9.0) - 2.0))
	t_1 = Float64(3.0 - Float64(2.0 * x2))
	tmp = 0.0
	if (x1 <= -4.5e+150)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + t_0));
	elseif (x1 <= -1.6e+84)
		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(x1 * Float64(2.0 - Float64(x1 * Float64(6.0 + Float64(Float64(Float64(x1 * Float64(4.0 - Float64(x1 * Float64(Float64(Float64(3.0 * t_1) + Float64(Float64(x2 * 8.0) + Float64(4.0 * t_1))) - 6.0)))) - Float64(x2 * 8.0)) - Float64(x2 * 6.0)))))))));
	elseif (x1 <= 16500000000000.0)
		tmp = Float64(x1 + Float64(t_0 - Float64(x2 * Float64(6.0 + Float64(Float64(x1 * Float64(12.0 - Float64(x1 * 6.0))) - Float64(8.0 * Float64(x1 * x2)))))));
	else
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(x1 * Float64(-1.0 + Float64(x1 * Float64(x1 + 3.0))))) + Float64(x1 - Float64(4.0 * Float64(x1 * Float64(x2 * t_1))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * ((x1 * 9.0) - 2.0);
	t_1 = 3.0 - (2.0 * x2);
	tmp = 0.0;
	if (x1 <= -4.5e+150)
		tmp = x1 + ((x2 * -6.0) + t_0);
	elseif (x1 <= -1.6e+84)
		tmp = x1 + ((3.0 * ((x1 - ((x1 * (x1 * 3.0)) - (2.0 * x2))) / (-1.0 - (x1 * x1)))) + (x1 + (x1 * (2.0 - (x1 * (6.0 + (((x1 * (4.0 - (x1 * (((3.0 * t_1) + ((x2 * 8.0) + (4.0 * t_1))) - 6.0)))) - (x2 * 8.0)) - (x2 * 6.0))))))));
	elseif (x1 <= 16500000000000.0)
		tmp = x1 + (t_0 - (x2 * (6.0 + ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))));
	else
		tmp = x1 + ((3.0 * (x1 * (-1.0 + (x1 * (x1 + 3.0))))) + (x1 - (4.0 * (x1 * (x2 * t_1)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -4.5e+150], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + t$95$0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -1.6e+84], 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[(x1 * N[(2.0 - N[(x1 * N[(6.0 + N[(N[(N[(x1 * N[(4.0 - N[(x1 * N[(N[(N[(3.0 * t$95$1), $MachinePrecision] + N[(N[(x2 * 8.0), $MachinePrecision] + N[(4.0 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x2 * 8.0), $MachinePrecision]), $MachinePrecision] - N[(x2 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 16500000000000.0], N[(x1 + N[(t$95$0 - N[(x2 * N[(6.0 + N[(N[(x1 * N[(12.0 - N[(x1 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(3.0 * N[(x1 * N[(-1.0 + N[(x1 * N[(x1 + 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 - N[(4.0 * N[(x1 * N[(x2 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -4.5e150

   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 0.0%

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

   5. Taylor expanded in x1 around 0 68.6%

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

   6. Taylor expanded in x2 around 0 97.5%

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

      1. *-commutative 97.5%

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

   8. Simplified 97.5%

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

   if -4.5e150 < x1 < -1.60000000000000005e84

   1. Initial program 17.6%

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

   3. Taylor expanded in x1 around 0 17.6%

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

      1. +-commutative 17.6%

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

      2. mul-1-neg 17.6%

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

      3. sub-neg 17.6%

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

   5. Simplified 17.6%

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

   6. Taylor expanded in x1 around inf 17.6%

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

      1. *-commutative 17.6%

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

   8. Simplified 17.6%

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

   9. Taylor expanded in x1 around 0 88.2%

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

   if -1.60000000000000005e84 < x1 < 1.65e13

   1. Initial program 98.7%

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

   3. Taylor expanded in x1 around 0 78.0%

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

   4. Taylor expanded in x1 around 0 75.9%

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

   5. Taylor expanded in x1 around 0 77.2%

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

   6. Taylor expanded in x2 around 0 89.3%

      \[\leadsto x1 + \color{blue}{\left(x1 \cdot \left(9 \cdot x1 - 2\right) + x2 \cdot \left(\left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(6 \cdot x1 - 12\right)\right) - 6\right)\right)} \]

   if 1.65e13 < x1

   1. Initial program 54.2%

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

   3. Taylor expanded in x1 around 0 21.9%

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

   4. Taylor expanded in x1 around 0 58.6%

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

   5. Taylor expanded in x2 around 0 73.1%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4.5 \cdot 10^{+150}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 - 2\right)\right)\\ \mathbf{elif}\;x1 \leq -1.6 \cdot 10^{+84}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right)}{-1 - x1 \cdot x1} + \left(x1 + x1 \cdot \left(2 - x1 \cdot \left(6 + \left(\left(x1 \cdot \left(4 - x1 \cdot \left(\left(3 \cdot \left(3 - 2 \cdot x2\right) + \left(x2 \cdot 8 + 4 \cdot \left(3 - 2 \cdot x2\right)\right)\right) - 6\right)\right) - x2 \cdot 8\right) - x2 \cdot 6\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 16500000000000:\\ \;\;\;\;x1 + \left(x1 \cdot \left(x1 \cdot 9 - 2\right) - x2 \cdot \left(6 + \left(x1 \cdot \left(12 - x1 \cdot 6\right) - 8 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x1 \cdot \left(-1 + x1 \cdot \left(x1 + 3\right)\right)\right) + \left(x1 - 4 \cdot \left(x1 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 86.1% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 9 - 2\right)\\ \mathbf{if}\;x1 \leq -4.5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + t\_0\right)\\ \mathbf{elif}\;x1 \leq -9.6 \cdot 10^{+67}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right)}{-1 - x1 \cdot x1} + \left(x1 + x1 \cdot \left(2 + x1 \cdot \left(\left(x1 \cdot -4 + \left(x2 \cdot 6 + x2 \cdot 8\right)\right) - 6\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 16500000000000:\\ \;\;\;\;x1 + \left(t\_0 - x2 \cdot \left(6 + \left(x1 \cdot \left(12 - x1 \cdot 6\right) - 8 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x1 \cdot \left(-1 + x1 \cdot \left(x1 + 3\right)\right)\right) + \left(x1 - 4 \cdot \left(x1 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (- (* x1 9.0) 2.0))))
   (if (<= x1 -4.5e+153)
     (+ x1 (+ (* x2 -6.0) t_0))
     (if (<= x1 -9.6e+67)
       (+
        x1
        (+
         (* 3.0 (/ (- x1 (- (* x1 (* x1 3.0)) (* 2.0 x2))) (- -1.0 (* x1 x1))))
         (+
          x1
          (*
           x1
           (+ 2.0 (* x1 (- (+ (* x1 -4.0) (+ (* x2 6.0) (* x2 8.0))) 6.0)))))))
       (if (<= x1 16500000000000.0)
         (+
          x1
          (-
           t_0
           (* x2 (+ 6.0 (- (* x1 (- 12.0 (* x1 6.0))) (* 8.0 (* x1 x2)))))))
         (+
          x1
          (+
           (* 3.0 (* x1 (+ -1.0 (* x1 (+ x1 3.0)))))
           (- x1 (* 4.0 (* x1 (* x2 (- 3.0 (* 2.0 x2)))))))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * ((x1 * 9.0) - 2.0);
	double tmp;
	if (x1 <= -4.5e+153) {
		tmp = x1 + ((x2 * -6.0) + t_0);
	} else if (x1 <= -9.6e+67) {
		tmp = x1 + ((3.0 * ((x1 - ((x1 * (x1 * 3.0)) - (2.0 * x2))) / (-1.0 - (x1 * x1)))) + (x1 + (x1 * (2.0 + (x1 * (((x1 * -4.0) + ((x2 * 6.0) + (x2 * 8.0))) - 6.0))))));
	} else if (x1 <= 16500000000000.0) {
		tmp = x1 + (t_0 - (x2 * (6.0 + ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))));
	} else {
		tmp = x1 + ((3.0 * (x1 * (-1.0 + (x1 * (x1 + 3.0))))) + (x1 - (4.0 * (x1 * (x2 * (3.0 - (2.0 * x2)))))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x1 * ((x1 * 9.0d0) - 2.0d0)
    if (x1 <= (-4.5d+153)) then
        tmp = x1 + ((x2 * (-6.0d0)) + t_0)
    else if (x1 <= (-9.6d+67)) then
        tmp = x1 + ((3.0d0 * ((x1 - ((x1 * (x1 * 3.0d0)) - (2.0d0 * x2))) / ((-1.0d0) - (x1 * x1)))) + (x1 + (x1 * (2.0d0 + (x1 * (((x1 * (-4.0d0)) + ((x2 * 6.0d0) + (x2 * 8.0d0))) - 6.0d0))))))
    else if (x1 <= 16500000000000.0d0) then
        tmp = x1 + (t_0 - (x2 * (6.0d0 + ((x1 * (12.0d0 - (x1 * 6.0d0))) - (8.0d0 * (x1 * x2))))))
    else
        tmp = x1 + ((3.0d0 * (x1 * ((-1.0d0) + (x1 * (x1 + 3.0d0))))) + (x1 - (4.0d0 * (x1 * (x2 * (3.0d0 - (2.0d0 * x2)))))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * ((x1 * 9.0) - 2.0);
	double tmp;
	if (x1 <= -4.5e+153) {
		tmp = x1 + ((x2 * -6.0) + t_0);
	} else if (x1 <= -9.6e+67) {
		tmp = x1 + ((3.0 * ((x1 - ((x1 * (x1 * 3.0)) - (2.0 * x2))) / (-1.0 - (x1 * x1)))) + (x1 + (x1 * (2.0 + (x1 * (((x1 * -4.0) + ((x2 * 6.0) + (x2 * 8.0))) - 6.0))))));
	} else if (x1 <= 16500000000000.0) {
		tmp = x1 + (t_0 - (x2 * (6.0 + ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))));
	} else {
		tmp = x1 + ((3.0 * (x1 * (-1.0 + (x1 * (x1 + 3.0))))) + (x1 - (4.0 * (x1 * (x2 * (3.0 - (2.0 * x2)))))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * ((x1 * 9.0) - 2.0)
	tmp = 0
	if x1 <= -4.5e+153:
		tmp = x1 + ((x2 * -6.0) + t_0)
	elif x1 <= -9.6e+67:
		tmp = x1 + ((3.0 * ((x1 - ((x1 * (x1 * 3.0)) - (2.0 * x2))) / (-1.0 - (x1 * x1)))) + (x1 + (x1 * (2.0 + (x1 * (((x1 * -4.0) + ((x2 * 6.0) + (x2 * 8.0))) - 6.0))))))
	elif x1 <= 16500000000000.0:
		tmp = x1 + (t_0 - (x2 * (6.0 + ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))))
	else:
		tmp = x1 + ((3.0 * (x1 * (-1.0 + (x1 * (x1 + 3.0))))) + (x1 - (4.0 * (x1 * (x2 * (3.0 - (2.0 * x2)))))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(Float64(x1 * 9.0) - 2.0))
	tmp = 0.0
	if (x1 <= -4.5e+153)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + t_0));
	elseif (x1 <= -9.6e+67)
		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(x1 * Float64(2.0 + Float64(x1 * Float64(Float64(Float64(x1 * -4.0) + Float64(Float64(x2 * 6.0) + Float64(x2 * 8.0))) - 6.0)))))));
	elseif (x1 <= 16500000000000.0)
		tmp = Float64(x1 + Float64(t_0 - Float64(x2 * Float64(6.0 + Float64(Float64(x1 * Float64(12.0 - Float64(x1 * 6.0))) - Float64(8.0 * Float64(x1 * x2)))))));
	else
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(x1 * Float64(-1.0 + Float64(x1 * Float64(x1 + 3.0))))) + Float64(x1 - Float64(4.0 * Float64(x1 * Float64(x2 * Float64(3.0 - Float64(2.0 * x2))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * ((x1 * 9.0) - 2.0);
	tmp = 0.0;
	if (x1 <= -4.5e+153)
		tmp = x1 + ((x2 * -6.0) + t_0);
	elseif (x1 <= -9.6e+67)
		tmp = x1 + ((3.0 * ((x1 - ((x1 * (x1 * 3.0)) - (2.0 * x2))) / (-1.0 - (x1 * x1)))) + (x1 + (x1 * (2.0 + (x1 * (((x1 * -4.0) + ((x2 * 6.0) + (x2 * 8.0))) - 6.0))))));
	elseif (x1 <= 16500000000000.0)
		tmp = x1 + (t_0 - (x2 * (6.0 + ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))));
	else
		tmp = x1 + ((3.0 * (x1 * (-1.0 + (x1 * (x1 + 3.0))))) + (x1 - (4.0 * (x1 * (x2 * (3.0 - (2.0 * x2)))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -4.5e+153], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + t$95$0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -9.6e+67], 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[(x1 * N[(2.0 + N[(x1 * N[(N[(N[(x1 * -4.0), $MachinePrecision] + N[(N[(x2 * 6.0), $MachinePrecision] + N[(x2 * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 16500000000000.0], N[(x1 + N[(t$95$0 - N[(x2 * N[(6.0 + N[(N[(x1 * N[(12.0 - N[(x1 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(3.0 * N[(x1 * N[(-1.0 + N[(x1 * N[(x1 + 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 - N[(4.0 * N[(x1 * N[(x2 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -4.5000000000000001e153

   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 0.0%

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

   5. Taylor expanded in x1 around 0 67.6%

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

   6. Taylor expanded in x2 around 0 100.0%

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

      1. *-commutative 100.0%

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

   8. Simplified 100.0%

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

   if -4.5000000000000001e153 < x1 < -9.60000000000000007e67

   1. Initial program 31.7%

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

   3. Taylor expanded in x1 around 0 27.2%

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

      1. +-commutative 27.2%

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

      2. mul-1-neg 27.2%

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

      3. sub-neg 27.2%

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

   5. Simplified 27.2%

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

   6. Taylor expanded in x1 around inf 31.7%

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

      1. *-commutative 31.7%

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

   8. Simplified 31.7%

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

   9. Taylor expanded in x1 around 0 73.7%

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

   if -9.60000000000000007e67 < x1 < 1.65e13

   1. Initial program 98.7%

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

   3. Taylor expanded in x1 around 0 78.7%

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

   4. Taylor expanded in x1 around 0 76.7%

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

   5. Taylor expanded in x1 around 0 77.9%

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

   6. Taylor expanded in x2 around 0 90.4%

      \[\leadsto x1 + \color{blue}{\left(x1 \cdot \left(9 \cdot x1 - 2\right) + x2 \cdot \left(\left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(6 \cdot x1 - 12\right)\right) - 6\right)\right)} \]

   if 1.65e13 < x1

   1. Initial program 54.2%

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

   3. Taylor expanded in x1 around 0 21.9%

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

   4. Taylor expanded in x1 around 0 58.6%

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

   5. Taylor expanded in x2 around 0 73.1%

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

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4.5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 - 2\right)\right)\\ \mathbf{elif}\;x1 \leq -9.6 \cdot 10^{+67}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right)}{-1 - x1 \cdot x1} + \left(x1 + x1 \cdot \left(2 + x1 \cdot \left(\left(x1 \cdot -4 + \left(x2 \cdot 6 + x2 \cdot 8\right)\right) - 6\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 16500000000000:\\ \;\;\;\;x1 + \left(x1 \cdot \left(x1 \cdot 9 - 2\right) - x2 \cdot \left(6 + \left(x1 \cdot \left(12 - x1 \cdot 6\right) - 8 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x1 \cdot \left(-1 + x1 \cdot \left(x1 + 3\right)\right)\right) + \left(x1 - 4 \cdot \left(x1 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 83.6% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x2 \cdot \left(3 - 2 \cdot x2\right)\\ t_1 := x1 \cdot \left(x1 \cdot 9 - 2\right)\\ \mathbf{if}\;x1 \leq -2.2 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + t\_1\right)\\ \mathbf{elif}\;x1 \leq -1.26 \cdot 10^{+70}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(\left(x2 \cdot \left(x1 \cdot 6 + 9 \cdot \frac{x1}{x2}\right) - 4 \cdot t\_0\right) - 2\right)\right)\\ \mathbf{elif}\;x1 \leq 16500000000000:\\ \;\;\;\;x1 + \left(t\_1 - x2 \cdot \left(6 + \left(x1 \cdot \left(12 - x1 \cdot 6\right) - 8 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x1 \cdot \left(-1 + x1 \cdot \left(x1 + 3\right)\right)\right) + \left(x1 - 4 \cdot \left(x1 \cdot t\_0\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x2 (- 3.0 (* 2.0 x2)))) (t_1 (* x1 (- (* x1 9.0) 2.0))))
   (if (<= x1 -2.2e+154)
     (+ x1 (+ (* x2 -6.0) t_1))
     (if (<= x1 -1.26e+70)
       (+
        x1
        (+
         (* x2 -6.0)
         (*
          x1
          (- (- (* x2 (+ (* x1 6.0) (* 9.0 (/ x1 x2)))) (* 4.0 t_0)) 2.0))))
       (if (<= x1 16500000000000.0)
         (+
          x1
          (-
           t_1
           (* x2 (+ 6.0 (- (* x1 (- 12.0 (* x1 6.0))) (* 8.0 (* x1 x2)))))))
         (+
          x1
          (+
           (* 3.0 (* x1 (+ -1.0 (* x1 (+ x1 3.0)))))
           (- x1 (* 4.0 (* x1 t_0))))))))))

C

double code(double x1, double x2) {
	double t_0 = x2 * (3.0 - (2.0 * x2));
	double t_1 = x1 * ((x1 * 9.0) - 2.0);
	double tmp;
	if (x1 <= -2.2e+154) {
		tmp = x1 + ((x2 * -6.0) + t_1);
	} else if (x1 <= -1.26e+70) {
		tmp = x1 + ((x2 * -6.0) + (x1 * (((x2 * ((x1 * 6.0) + (9.0 * (x1 / x2)))) - (4.0 * t_0)) - 2.0)));
	} else if (x1 <= 16500000000000.0) {
		tmp = x1 + (t_1 - (x2 * (6.0 + ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))));
	} else {
		tmp = x1 + ((3.0 * (x1 * (-1.0 + (x1 * (x1 + 3.0))))) + (x1 - (4.0 * (x1 * t_0))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x2 * (3.0d0 - (2.0d0 * x2))
    t_1 = x1 * ((x1 * 9.0d0) - 2.0d0)
    if (x1 <= (-2.2d+154)) then
        tmp = x1 + ((x2 * (-6.0d0)) + t_1)
    else if (x1 <= (-1.26d+70)) then
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * (((x2 * ((x1 * 6.0d0) + (9.0d0 * (x1 / x2)))) - (4.0d0 * t_0)) - 2.0d0)))
    else if (x1 <= 16500000000000.0d0) then
        tmp = x1 + (t_1 - (x2 * (6.0d0 + ((x1 * (12.0d0 - (x1 * 6.0d0))) - (8.0d0 * (x1 * x2))))))
    else
        tmp = x1 + ((3.0d0 * (x1 * ((-1.0d0) + (x1 * (x1 + 3.0d0))))) + (x1 - (4.0d0 * (x1 * t_0))))
    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 t_1 = x1 * ((x1 * 9.0) - 2.0);
	double tmp;
	if (x1 <= -2.2e+154) {
		tmp = x1 + ((x2 * -6.0) + t_1);
	} else if (x1 <= -1.26e+70) {
		tmp = x1 + ((x2 * -6.0) + (x1 * (((x2 * ((x1 * 6.0) + (9.0 * (x1 / x2)))) - (4.0 * t_0)) - 2.0)));
	} else if (x1 <= 16500000000000.0) {
		tmp = x1 + (t_1 - (x2 * (6.0 + ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))));
	} else {
		tmp = x1 + ((3.0 * (x1 * (-1.0 + (x1 * (x1 + 3.0))))) + (x1 - (4.0 * (x1 * t_0))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x2 * (3.0 - (2.0 * x2))
	t_1 = x1 * ((x1 * 9.0) - 2.0)
	tmp = 0
	if x1 <= -2.2e+154:
		tmp = x1 + ((x2 * -6.0) + t_1)
	elif x1 <= -1.26e+70:
		tmp = x1 + ((x2 * -6.0) + (x1 * (((x2 * ((x1 * 6.0) + (9.0 * (x1 / x2)))) - (4.0 * t_0)) - 2.0)))
	elif x1 <= 16500000000000.0:
		tmp = x1 + (t_1 - (x2 * (6.0 + ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))))
	else:
		tmp = x1 + ((3.0 * (x1 * (-1.0 + (x1 * (x1 + 3.0))))) + (x1 - (4.0 * (x1 * t_0))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x2 * Float64(3.0 - Float64(2.0 * x2)))
	t_1 = Float64(x1 * Float64(Float64(x1 * 9.0) - 2.0))
	tmp = 0.0
	if (x1 <= -2.2e+154)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + t_1));
	elseif (x1 <= -1.26e+70)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(Float64(x2 * Float64(Float64(x1 * 6.0) + Float64(9.0 * Float64(x1 / x2)))) - Float64(4.0 * t_0)) - 2.0))));
	elseif (x1 <= 16500000000000.0)
		tmp = Float64(x1 + Float64(t_1 - Float64(x2 * Float64(6.0 + Float64(Float64(x1 * Float64(12.0 - Float64(x1 * 6.0))) - Float64(8.0 * Float64(x1 * x2)))))));
	else
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(x1 * Float64(-1.0 + Float64(x1 * Float64(x1 + 3.0))))) + Float64(x1 - Float64(4.0 * Float64(x1 * t_0)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x2 * (3.0 - (2.0 * x2));
	t_1 = x1 * ((x1 * 9.0) - 2.0);
	tmp = 0.0;
	if (x1 <= -2.2e+154)
		tmp = x1 + ((x2 * -6.0) + t_1);
	elseif (x1 <= -1.26e+70)
		tmp = x1 + ((x2 * -6.0) + (x1 * (((x2 * ((x1 * 6.0) + (9.0 * (x1 / x2)))) - (4.0 * t_0)) - 2.0)));
	elseif (x1 <= 16500000000000.0)
		tmp = x1 + (t_1 - (x2 * (6.0 + ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))));
	else
		tmp = x1 + ((3.0 * (x1 * (-1.0 + (x1 * (x1 + 3.0))))) + (x1 - (4.0 * (x1 * t_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]}, Block[{t$95$1 = N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -2.2e+154], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -1.26e+70], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(N[(x2 * N[(N[(x1 * 6.0), $MachinePrecision] + N[(9.0 * N[(x1 / x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * t$95$0), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 16500000000000.0], N[(x1 + N[(t$95$1 - N[(x2 * N[(6.0 + N[(N[(x1 * N[(12.0 - N[(x1 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(3.0 * N[(x1 * N[(-1.0 + N[(x1 * N[(x1 + 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 - N[(4.0 * N[(x1 * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -2.2000000000000001e154

   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 0.0%

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

   5. Taylor expanded in x1 around 0 66.7%

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

   6. Taylor expanded in x2 around 0 100.0%

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

      1. *-commutative 100.0%

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

   8. Simplified 100.0%

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

   if -2.2000000000000001e154 < x1 < -1.26000000000000001e70

   1. Initial program 30.4%

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

   3. Taylor expanded in x1 around 0 8.9%

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

   4. Taylor expanded in x1 around 0 8.7%

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

   5. Taylor expanded in x1 around 0 21.2%

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

   6. Taylor expanded in x2 around inf 41.6%

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

   if -1.26000000000000001e70 < x1 < 1.65e13

   1. Initial program 98.7%

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

   3. Taylor expanded in x1 around 0 78.7%

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

   4. Taylor expanded in x1 around 0 76.7%

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

   5. Taylor expanded in x1 around 0 77.9%

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

   6. Taylor expanded in x2 around 0 90.4%

      \[\leadsto x1 + \color{blue}{\left(x1 \cdot \left(9 \cdot x1 - 2\right) + x2 \cdot \left(\left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(6 \cdot x1 - 12\right)\right) - 6\right)\right)} \]

   if 1.65e13 < x1

   1. Initial program 54.2%

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

   3. Taylor expanded in x1 around 0 21.9%

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

   4. Taylor expanded in x1 around 0 58.6%

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

   5. Taylor expanded in x2 around 0 73.1%

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

4. Final simplification 83.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -2.2 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 - 2\right)\right)\\ \mathbf{elif}\;x1 \leq -1.26 \cdot 10^{+70}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(\left(x2 \cdot \left(x1 \cdot 6 + 9 \cdot \frac{x1}{x2}\right) - 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right) - 2\right)\right)\\ \mathbf{elif}\;x1 \leq 16500000000000:\\ \;\;\;\;x1 + \left(x1 \cdot \left(x1 \cdot 9 - 2\right) - x2 \cdot \left(6 + \left(x1 \cdot \left(12 - x1 \cdot 6\right) - 8 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x1 \cdot \left(-1 + x1 \cdot \left(x1 + 3\right)\right)\right) + \left(x1 - 4 \cdot \left(x1 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 77.0% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 + 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right)\\ t_1 := x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 - 2\right)\right)\\ \mathbf{if}\;x1 \leq -2.5 \cdot 10^{+84}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x1 \leq -3.8 \cdot 10^{-157}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x1 \leq 2.3 \cdot 10^{-212}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x1 \leq 4.6 \cdot 10^{+91}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(-1 + x1 \cdot \left(x1 + 3\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0
         (+
          x1
          (- (* x2 -6.0) (* x1 (+ 2.0 (* 4.0 (* x2 (- 3.0 (* 2.0 x2)))))))))
        (t_1 (+ x1 (+ (* x2 -6.0) (* x1 (- (* x1 9.0) 2.0))))))
   (if (<= x1 -2.5e+84)
     t_1
     (if (<= x1 -3.8e-157)
       t_0
       (if (<= x1 2.3e-212)
         t_1
         (if (<= x1 4.6e+91)
           t_0
           (+ x1 (+ x1 (* 3.0 (* x1 (+ -1.0 (* x1 (+ x1 3.0)))))))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 + ((x2 * -6.0) - (x1 * (2.0 + (4.0 * (x2 * (3.0 - (2.0 * x2)))))));
	double t_1 = x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) - 2.0)));
	double tmp;
	if (x1 <= -2.5e+84) {
		tmp = t_1;
	} else if (x1 <= -3.8e-157) {
		tmp = t_0;
	} else if (x1 <= 2.3e-212) {
		tmp = t_1;
	} else if (x1 <= 4.6e+91) {
		tmp = t_0;
	} else {
		tmp = x1 + (x1 + (3.0 * (x1 * (-1.0 + (x1 * (x1 + 3.0))))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x1 + ((x2 * (-6.0d0)) - (x1 * (2.0d0 + (4.0d0 * (x2 * (3.0d0 - (2.0d0 * x2)))))))
    t_1 = x1 + ((x2 * (-6.0d0)) + (x1 * ((x1 * 9.0d0) - 2.0d0)))
    if (x1 <= (-2.5d+84)) then
        tmp = t_1
    else if (x1 <= (-3.8d-157)) then
        tmp = t_0
    else if (x1 <= 2.3d-212) then
        tmp = t_1
    else if (x1 <= 4.6d+91) then
        tmp = t_0
    else
        tmp = x1 + (x1 + (3.0d0 * (x1 * ((-1.0d0) + (x1 * (x1 + 3.0d0))))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 + ((x2 * -6.0) - (x1 * (2.0 + (4.0 * (x2 * (3.0 - (2.0 * x2)))))));
	double t_1 = x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) - 2.0)));
	double tmp;
	if (x1 <= -2.5e+84) {
		tmp = t_1;
	} else if (x1 <= -3.8e-157) {
		tmp = t_0;
	} else if (x1 <= 2.3e-212) {
		tmp = t_1;
	} else if (x1 <= 4.6e+91) {
		tmp = t_0;
	} else {
		tmp = x1 + (x1 + (3.0 * (x1 * (-1.0 + (x1 * (x1 + 3.0))))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 + ((x2 * -6.0) - (x1 * (2.0 + (4.0 * (x2 * (3.0 - (2.0 * x2)))))))
	t_1 = x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) - 2.0)))
	tmp = 0
	if x1 <= -2.5e+84:
		tmp = t_1
	elif x1 <= -3.8e-157:
		tmp = t_0
	elif x1 <= 2.3e-212:
		tmp = t_1
	elif x1 <= 4.6e+91:
		tmp = t_0
	else:
		tmp = x1 + (x1 + (3.0 * (x1 * (-1.0 + (x1 * (x1 + 3.0))))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 + Float64(Float64(x2 * -6.0) - Float64(x1 * Float64(2.0 + Float64(4.0 * Float64(x2 * Float64(3.0 - Float64(2.0 * x2))))))))
	t_1 = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(x1 * 9.0) - 2.0))))
	tmp = 0.0
	if (x1 <= -2.5e+84)
		tmp = t_1;
	elseif (x1 <= -3.8e-157)
		tmp = t_0;
	elseif (x1 <= 2.3e-212)
		tmp = t_1;
	elseif (x1 <= 4.6e+91)
		tmp = t_0;
	else
		tmp = Float64(x1 + Float64(x1 + Float64(3.0 * Float64(x1 * Float64(-1.0 + Float64(x1 * Float64(x1 + 3.0)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 + ((x2 * -6.0) - (x1 * (2.0 + (4.0 * (x2 * (3.0 - (2.0 * x2)))))));
	t_1 = x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) - 2.0)));
	tmp = 0.0;
	if (x1 <= -2.5e+84)
		tmp = t_1;
	elseif (x1 <= -3.8e-157)
		tmp = t_0;
	elseif (x1 <= 2.3e-212)
		tmp = t_1;
	elseif (x1 <= 4.6e+91)
		tmp = t_0;
	else
		tmp = x1 + (x1 + (3.0 * (x1 * (-1.0 + (x1 * (x1 + 3.0))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] - N[(x1 * N[(2.0 + N[(4.0 * N[(x2 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -2.5e+84], t$95$1, If[LessEqual[x1, -3.8e-157], t$95$0, If[LessEqual[x1, 2.3e-212], t$95$1, If[LessEqual[x1, 4.6e+91], t$95$0, N[(x1 + N[(x1 + N[(3.0 * N[(x1 * N[(-1.0 + N[(x1 * N[(x1 + 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -2.5e84 or -3.8000000000000002e-157 < x1 < 2.3000000000000001e-212

   1. Initial program 48.3%

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

   3. Taylor expanded in x1 around 0 34.1%

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

   4. Taylor expanded in x1 around 0 34.1%

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

   5. Taylor expanded in x1 around 0 60.2%

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

   6. Taylor expanded in x2 around 0 78.9%

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

      1. *-commutative 78.9%

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

   8. Simplified 78.9%

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

   if -2.5e84 < x1 < -3.8000000000000002e-157 or 2.3000000000000001e-212 < x1 < 4.59999999999999982e91

   1. Initial program 98.4%

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

   3. Taylor expanded in x1 around 0 73.0%

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

   4. Taylor expanded in x1 around 0 69.1%

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

   5. Taylor expanded in x1 around 0 73.2%

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

   if 4.59999999999999982e91 < x1

   1. Initial program 32.4%

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

   3. Taylor expanded in x1 around 0 14.4%

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

   4. Taylor expanded in x1 around 0 73.7%

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

   5. Taylor expanded in x2 around 0 89.9%

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

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -2.5 \cdot 10^{+84}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 - 2\right)\right)\\ \mathbf{elif}\;x1 \leq -3.8 \cdot 10^{-157}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 + 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 2.3 \cdot 10^{-212}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 - 2\right)\right)\\ \mathbf{elif}\;x1 \leq 4.6 \cdot 10^{+91}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 + 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(-1 + x1 \cdot \left(x1 + 3\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 77.0% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 + 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right)\\ \mathbf{if}\;x1 \leq -2.4 \cdot 10^{+84}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 - 2\right)\right)\\ \mathbf{elif}\;x1 \leq -3.8 \cdot 10^{-157}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x1 \leq 1.2 \cdot 10^{-212}:\\ \;\;\;\;x1 - \left(x1 \cdot \left(2 - x1 \cdot 9\right) + x2 \cdot \left(6 + x1 \cdot \left(12 - x1 \cdot 6\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 4.6 \cdot 10^{+91}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(-1 + x1 \cdot \left(x1 + 3\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0
         (+
          x1
          (- (* x2 -6.0) (* x1 (+ 2.0 (* 4.0 (* x2 (- 3.0 (* 2.0 x2))))))))))
   (if (<= x1 -2.4e+84)
     (+ x1 (+ (* x2 -6.0) (* x1 (- (* x1 9.0) 2.0))))
     (if (<= x1 -3.8e-157)
       t_0
       (if (<= x1 1.2e-212)
         (-
          x1
          (+
           (* x1 (- 2.0 (* x1 9.0)))
           (* x2 (+ 6.0 (* x1 (- 12.0 (* x1 6.0)))))))
         (if (<= x1 4.6e+91)
           t_0
           (+ x1 (+ x1 (* 3.0 (* x1 (+ -1.0 (* x1 (+ x1 3.0)))))))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 + ((x2 * -6.0) - (x1 * (2.0 + (4.0 * (x2 * (3.0 - (2.0 * x2)))))));
	double tmp;
	if (x1 <= -2.4e+84) {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) - 2.0)));
	} else if (x1 <= -3.8e-157) {
		tmp = t_0;
	} else if (x1 <= 1.2e-212) {
		tmp = x1 - ((x1 * (2.0 - (x1 * 9.0))) + (x2 * (6.0 + (x1 * (12.0 - (x1 * 6.0))))));
	} else if (x1 <= 4.6e+91) {
		tmp = t_0;
	} else {
		tmp = x1 + (x1 + (3.0 * (x1 * (-1.0 + (x1 * (x1 + 3.0))))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x1 + ((x2 * (-6.0d0)) - (x1 * (2.0d0 + (4.0d0 * (x2 * (3.0d0 - (2.0d0 * x2)))))))
    if (x1 <= (-2.4d+84)) then
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * ((x1 * 9.0d0) - 2.0d0)))
    else if (x1 <= (-3.8d-157)) then
        tmp = t_0
    else if (x1 <= 1.2d-212) then
        tmp = x1 - ((x1 * (2.0d0 - (x1 * 9.0d0))) + (x2 * (6.0d0 + (x1 * (12.0d0 - (x1 * 6.0d0))))))
    else if (x1 <= 4.6d+91) then
        tmp = t_0
    else
        tmp = x1 + (x1 + (3.0d0 * (x1 * ((-1.0d0) + (x1 * (x1 + 3.0d0))))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 + ((x2 * -6.0) - (x1 * (2.0 + (4.0 * (x2 * (3.0 - (2.0 * x2)))))));
	double tmp;
	if (x1 <= -2.4e+84) {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) - 2.0)));
	} else if (x1 <= -3.8e-157) {
		tmp = t_0;
	} else if (x1 <= 1.2e-212) {
		tmp = x1 - ((x1 * (2.0 - (x1 * 9.0))) + (x2 * (6.0 + (x1 * (12.0 - (x1 * 6.0))))));
	} else if (x1 <= 4.6e+91) {
		tmp = t_0;
	} else {
		tmp = x1 + (x1 + (3.0 * (x1 * (-1.0 + (x1 * (x1 + 3.0))))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 + ((x2 * -6.0) - (x1 * (2.0 + (4.0 * (x2 * (3.0 - (2.0 * x2)))))))
	tmp = 0
	if x1 <= -2.4e+84:
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) - 2.0)))
	elif x1 <= -3.8e-157:
		tmp = t_0
	elif x1 <= 1.2e-212:
		tmp = x1 - ((x1 * (2.0 - (x1 * 9.0))) + (x2 * (6.0 + (x1 * (12.0 - (x1 * 6.0))))))
	elif x1 <= 4.6e+91:
		tmp = t_0
	else:
		tmp = x1 + (x1 + (3.0 * (x1 * (-1.0 + (x1 * (x1 + 3.0))))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 + Float64(Float64(x2 * -6.0) - Float64(x1 * Float64(2.0 + Float64(4.0 * Float64(x2 * Float64(3.0 - Float64(2.0 * x2))))))))
	tmp = 0.0
	if (x1 <= -2.4e+84)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(x1 * 9.0) - 2.0))));
	elseif (x1 <= -3.8e-157)
		tmp = t_0;
	elseif (x1 <= 1.2e-212)
		tmp = Float64(x1 - Float64(Float64(x1 * Float64(2.0 - Float64(x1 * 9.0))) + Float64(x2 * Float64(6.0 + Float64(x1 * Float64(12.0 - Float64(x1 * 6.0)))))));
	elseif (x1 <= 4.6e+91)
		tmp = t_0;
	else
		tmp = Float64(x1 + Float64(x1 + Float64(3.0 * Float64(x1 * Float64(-1.0 + Float64(x1 * Float64(x1 + 3.0)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 + ((x2 * -6.0) - (x1 * (2.0 + (4.0 * (x2 * (3.0 - (2.0 * x2)))))));
	tmp = 0.0;
	if (x1 <= -2.4e+84)
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) - 2.0)));
	elseif (x1 <= -3.8e-157)
		tmp = t_0;
	elseif (x1 <= 1.2e-212)
		tmp = x1 - ((x1 * (2.0 - (x1 * 9.0))) + (x2 * (6.0 + (x1 * (12.0 - (x1 * 6.0))))));
	elseif (x1 <= 4.6e+91)
		tmp = t_0;
	else
		tmp = x1 + (x1 + (3.0 * (x1 * (-1.0 + (x1 * (x1 + 3.0))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] - N[(x1 * N[(2.0 + N[(4.0 * N[(x2 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -2.4e+84], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -3.8e-157], t$95$0, If[LessEqual[x1, 1.2e-212], N[(x1 - N[(N[(x1 * N[(2.0 - N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x2 * N[(6.0 + N[(x1 * N[(12.0 - N[(x1 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 4.6e+91], t$95$0, N[(x1 + N[(x1 + N[(3.0 * N[(x1 * N[(-1.0 + N[(x1 * N[(x1 + 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -2.4e84

   1. Initial program 5.8%

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

   3. Taylor expanded in x1 around 0 0.1%

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

   4. Taylor expanded in x1 around 0 0.0%

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

   5. Taylor expanded in x1 around 0 47.7%

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

   6. Taylor expanded in x2 around 0 67.9%

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

      1. *-commutative 67.9%

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

   8. Simplified 67.9%

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

   if -2.4e84 < x1 < -3.8000000000000002e-157 or 1.19999999999999995e-212 < x1 < 4.59999999999999982e91

   1. Initial program 98.4%

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

   3. Taylor expanded in x1 around 0 73.0%

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

   4. Taylor expanded in x1 around 0 69.1%

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

   5. Taylor expanded in x1 around 0 73.2%

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

   if -3.8000000000000002e-157 < x1 < 1.19999999999999995e-212

   1. Initial program 99.6%

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

   3. Taylor expanded in x1 around 0 75.3%

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

   4. Taylor expanded in x1 around 0 75.3%

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

   5. Taylor expanded in x1 around 0 75.3%

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

   6. Taylor expanded in x2 around 0 92.3%

      \[\leadsto x1 + \color{blue}{\left(x1 \cdot \left(9 \cdot x1 - 2\right) + x2 \cdot \left(x1 \cdot \left(6 \cdot x1 - 12\right) - 6\right)\right)} \]

   if 4.59999999999999982e91 < x1

   1. Initial program 32.4%

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

   3. Taylor expanded in x1 around 0 14.4%

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

   4. Taylor expanded in x1 around 0 73.7%

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

   5. Taylor expanded in x2 around 0 89.9%

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

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -2.4 \cdot 10^{+84}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 - 2\right)\right)\\ \mathbf{elif}\;x1 \leq -3.8 \cdot 10^{-157}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 + 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.2 \cdot 10^{-212}:\\ \;\;\;\;x1 - \left(x1 \cdot \left(2 - x1 \cdot 9\right) + x2 \cdot \left(6 + x1 \cdot \left(12 - x1 \cdot 6\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 4.6 \cdot 10^{+91}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 + 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(-1 + x1 \cdot \left(x1 + 3\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 82.3% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 9 - 2\right)\\ \mathbf{if}\;x1 \leq -2.2 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + t\_0\right)\\ \mathbf{elif}\;x1 \leq 4.6 \cdot 10^{+91}:\\ \;\;\;\;x1 + \left(t\_0 - x2 \cdot \left(6 + \left(x1 \cdot \left(12 - x1 \cdot 6\right) - 8 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(-1 + x1 \cdot \left(x1 + 3\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (- (* x1 9.0) 2.0))))
   (if (<= x1 -2.2e+154)
     (+ x1 (+ (* x2 -6.0) t_0))
     (if (<= x1 4.6e+91)
       (+
        x1
        (-
         t_0
         (* x2 (+ 6.0 (- (* x1 (- 12.0 (* x1 6.0))) (* 8.0 (* x1 x2)))))))
       (+ x1 (+ x1 (* 3.0 (* x1 (+ -1.0 (* x1 (+ x1 3.0)))))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * ((x1 * 9.0) - 2.0);
	double tmp;
	if (x1 <= -2.2e+154) {
		tmp = x1 + ((x2 * -6.0) + t_0);
	} else if (x1 <= 4.6e+91) {
		tmp = x1 + (t_0 - (x2 * (6.0 + ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))));
	} else {
		tmp = x1 + (x1 + (3.0 * (x1 * (-1.0 + (x1 * (x1 + 3.0))))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x1 * ((x1 * 9.0d0) - 2.0d0)
    if (x1 <= (-2.2d+154)) then
        tmp = x1 + ((x2 * (-6.0d0)) + t_0)
    else if (x1 <= 4.6d+91) then
        tmp = x1 + (t_0 - (x2 * (6.0d0 + ((x1 * (12.0d0 - (x1 * 6.0d0))) - (8.0d0 * (x1 * x2))))))
    else
        tmp = x1 + (x1 + (3.0d0 * (x1 * ((-1.0d0) + (x1 * (x1 + 3.0d0))))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * ((x1 * 9.0) - 2.0);
	double tmp;
	if (x1 <= -2.2e+154) {
		tmp = x1 + ((x2 * -6.0) + t_0);
	} else if (x1 <= 4.6e+91) {
		tmp = x1 + (t_0 - (x2 * (6.0 + ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))));
	} else {
		tmp = x1 + (x1 + (3.0 * (x1 * (-1.0 + (x1 * (x1 + 3.0))))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * ((x1 * 9.0) - 2.0)
	tmp = 0
	if x1 <= -2.2e+154:
		tmp = x1 + ((x2 * -6.0) + t_0)
	elif x1 <= 4.6e+91:
		tmp = x1 + (t_0 - (x2 * (6.0 + ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))))
	else:
		tmp = x1 + (x1 + (3.0 * (x1 * (-1.0 + (x1 * (x1 + 3.0))))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(Float64(x1 * 9.0) - 2.0))
	tmp = 0.0
	if (x1 <= -2.2e+154)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + t_0));
	elseif (x1 <= 4.6e+91)
		tmp = Float64(x1 + Float64(t_0 - Float64(x2 * Float64(6.0 + Float64(Float64(x1 * Float64(12.0 - Float64(x1 * 6.0))) - Float64(8.0 * Float64(x1 * x2)))))));
	else
		tmp = Float64(x1 + Float64(x1 + Float64(3.0 * Float64(x1 * Float64(-1.0 + Float64(x1 * Float64(x1 + 3.0)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * ((x1 * 9.0) - 2.0);
	tmp = 0.0;
	if (x1 <= -2.2e+154)
		tmp = x1 + ((x2 * -6.0) + t_0);
	elseif (x1 <= 4.6e+91)
		tmp = x1 + (t_0 - (x2 * (6.0 + ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))));
	else
		tmp = x1 + (x1 + (3.0 * (x1 * (-1.0 + (x1 * (x1 + 3.0))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -2.2e+154], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + t$95$0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 4.6e+91], N[(x1 + N[(t$95$0 - N[(x2 * N[(6.0 + N[(N[(x1 * N[(12.0 - N[(x1 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(x1 + N[(3.0 * N[(x1 * N[(-1.0 + N[(x1 * N[(x1 + 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -2.2000000000000001e154

   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 0.0%

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

   5. Taylor expanded in x1 around 0 66.7%

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

   6. Taylor expanded in x2 around 0 100.0%

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

      1. *-commutative 100.0%

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

   8. Simplified 100.0%

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

   if -2.2000000000000001e154 < x1 < 4.59999999999999982e91

   1. Initial program 90.3%

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

   3. Taylor expanded in x1 around 0 66.1%

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

   4. Taylor expanded in x1 around 0 63.5%

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

   5. Taylor expanded in x1 around 0 66.4%

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

   6. Taylor expanded in x2 around 0 76.6%

      \[\leadsto x1 + \color{blue}{\left(x1 \cdot \left(9 \cdot x1 - 2\right) + x2 \cdot \left(\left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(6 \cdot x1 - 12\right)\right) - 6\right)\right)} \]

   if 4.59999999999999982e91 < x1

   1. Initial program 32.4%

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

   3. Taylor expanded in x1 around 0 14.4%

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

   4. Taylor expanded in x1 around 0 73.7%

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

   5. Taylor expanded in x2 around 0 89.9%

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

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -2.2 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 - 2\right)\right)\\ \mathbf{elif}\;x1 \leq 4.6 \cdot 10^{+91}:\\ \;\;\;\;x1 + \left(x1 \cdot \left(x1 \cdot 9 - 2\right) - x2 \cdot \left(6 + \left(x1 \cdot \left(12 - x1 \cdot 6\right) - 8 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(-1 + x1 \cdot \left(x1 + 3\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 82.7% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 9 - 2\right)\\ \mathbf{if}\;x1 \leq -2.2 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + t\_0\right)\\ \mathbf{elif}\;x1 \leq 16500000000000:\\ \;\;\;\;x1 + \left(t\_0 - x2 \cdot \left(6 + \left(x1 \cdot \left(12 - x1 \cdot 6\right) - 8 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x1 \cdot \left(-1 + x1 \cdot \left(x1 + 3\right)\right)\right) + \left(x1 - 4 \cdot \left(x1 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (- (* x1 9.0) 2.0))))
   (if (<= x1 -2.2e+154)
     (+ x1 (+ (* x2 -6.0) t_0))
     (if (<= x1 16500000000000.0)
       (+
        x1
        (-
         t_0
         (* x2 (+ 6.0 (- (* x1 (- 12.0 (* x1 6.0))) (* 8.0 (* x1 x2)))))))
       (+
        x1
        (+
         (* 3.0 (* x1 (+ -1.0 (* x1 (+ x1 3.0)))))
         (- x1 (* 4.0 (* x1 (* x2 (- 3.0 (* 2.0 x2))))))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * ((x1 * 9.0) - 2.0);
	double tmp;
	if (x1 <= -2.2e+154) {
		tmp = x1 + ((x2 * -6.0) + t_0);
	} else if (x1 <= 16500000000000.0) {
		tmp = x1 + (t_0 - (x2 * (6.0 + ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))));
	} else {
		tmp = x1 + ((3.0 * (x1 * (-1.0 + (x1 * (x1 + 3.0))))) + (x1 - (4.0 * (x1 * (x2 * (3.0 - (2.0 * x2)))))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x1 * ((x1 * 9.0d0) - 2.0d0)
    if (x1 <= (-2.2d+154)) then
        tmp = x1 + ((x2 * (-6.0d0)) + t_0)
    else if (x1 <= 16500000000000.0d0) then
        tmp = x1 + (t_0 - (x2 * (6.0d0 + ((x1 * (12.0d0 - (x1 * 6.0d0))) - (8.0d0 * (x1 * x2))))))
    else
        tmp = x1 + ((3.0d0 * (x1 * ((-1.0d0) + (x1 * (x1 + 3.0d0))))) + (x1 - (4.0d0 * (x1 * (x2 * (3.0d0 - (2.0d0 * x2)))))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * ((x1 * 9.0) - 2.0);
	double tmp;
	if (x1 <= -2.2e+154) {
		tmp = x1 + ((x2 * -6.0) + t_0);
	} else if (x1 <= 16500000000000.0) {
		tmp = x1 + (t_0 - (x2 * (6.0 + ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))));
	} else {
		tmp = x1 + ((3.0 * (x1 * (-1.0 + (x1 * (x1 + 3.0))))) + (x1 - (4.0 * (x1 * (x2 * (3.0 - (2.0 * x2)))))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * ((x1 * 9.0) - 2.0)
	tmp = 0
	if x1 <= -2.2e+154:
		tmp = x1 + ((x2 * -6.0) + t_0)
	elif x1 <= 16500000000000.0:
		tmp = x1 + (t_0 - (x2 * (6.0 + ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))))
	else:
		tmp = x1 + ((3.0 * (x1 * (-1.0 + (x1 * (x1 + 3.0))))) + (x1 - (4.0 * (x1 * (x2 * (3.0 - (2.0 * x2)))))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(Float64(x1 * 9.0) - 2.0))
	tmp = 0.0
	if (x1 <= -2.2e+154)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + t_0));
	elseif (x1 <= 16500000000000.0)
		tmp = Float64(x1 + Float64(t_0 - Float64(x2 * Float64(6.0 + Float64(Float64(x1 * Float64(12.0 - Float64(x1 * 6.0))) - Float64(8.0 * Float64(x1 * x2)))))));
	else
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(x1 * Float64(-1.0 + Float64(x1 * Float64(x1 + 3.0))))) + Float64(x1 - Float64(4.0 * Float64(x1 * Float64(x2 * Float64(3.0 - Float64(2.0 * x2))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * ((x1 * 9.0) - 2.0);
	tmp = 0.0;
	if (x1 <= -2.2e+154)
		tmp = x1 + ((x2 * -6.0) + t_0);
	elseif (x1 <= 16500000000000.0)
		tmp = x1 + (t_0 - (x2 * (6.0 + ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))));
	else
		tmp = x1 + ((3.0 * (x1 * (-1.0 + (x1 * (x1 + 3.0))))) + (x1 - (4.0 * (x1 * (x2 * (3.0 - (2.0 * x2)))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -2.2e+154], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + t$95$0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 16500000000000.0], N[(x1 + N[(t$95$0 - N[(x2 * N[(6.0 + N[(N[(x1 * N[(12.0 - N[(x1 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(3.0 * N[(x1 * N[(-1.0 + N[(x1 * N[(x1 + 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 - N[(4.0 * N[(x1 * N[(x2 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -2.2000000000000001e154

   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 0.0%

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

   5. Taylor expanded in x1 around 0 66.7%

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

   6. Taylor expanded in x2 around 0 100.0%

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

      1. *-commutative 100.0%

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

   8. Simplified 100.0%

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

   if -2.2000000000000001e154 < x1 < 1.65e13

   1. Initial program 89.4%

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

   3. Taylor expanded in x1 around 0 69.2%

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

   4. Taylor expanded in x1 around 0 67.4%

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

   5. Taylor expanded in x1 around 0 70.1%

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

   6. Taylor expanded in x2 around 0 80.9%

      \[\leadsto x1 + \color{blue}{\left(x1 \cdot \left(9 \cdot x1 - 2\right) + x2 \cdot \left(\left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(6 \cdot x1 - 12\right)\right) - 6\right)\right)} \]

   if 1.65e13 < x1

   1. Initial program 54.2%

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

   3. Taylor expanded in x1 around 0 21.9%

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

   4. Taylor expanded in x1 around 0 58.6%

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

   5. Taylor expanded in x2 around 0 73.1%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -2.2 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 - 2\right)\right)\\ \mathbf{elif}\;x1 \leq 16500000000000:\\ \;\;\;\;x1 + \left(x1 \cdot \left(x1 \cdot 9 - 2\right) - x2 \cdot \left(6 + \left(x1 \cdot \left(12 - x1 \cdot 6\right) - 8 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x1 \cdot \left(-1 + x1 \cdot \left(x1 + 3\right)\right)\right) + \left(x1 - 4 \cdot \left(x1 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 40.7% accurate, 4.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -1.65 \cdot 10^{+84}:\\ \;\;\;\;x1 + \left(9 + \left(x1 + x1 \cdot \left(x2 \cdot -12\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -5.5 \cdot 10^{-77} \lor \neg \left(x1 \leq 2.1 \cdot 10^{-106}\right):\\ \;\;\;\;x1 \cdot \left(2 - 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x2 \cdot -6\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -1.65e+84)
   (+ x1 (+ 9.0 (+ x1 (* x1 (* x2 -12.0)))))
   (if (or (<= x1 -5.5e-77) (not (<= x1 2.1e-106)))
     (* x1 (- 2.0 (* 4.0 (* x2 (- 3.0 (* 2.0 x2))))))
     (+ x1 (* x2 -6.0)))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -1.65e+84) {
		tmp = x1 + (9.0 + (x1 + (x1 * (x2 * -12.0))));
	} else if ((x1 <= -5.5e-77) || !(x1 <= 2.1e-106)) {
		tmp = x1 * (2.0 - (4.0 * (x2 * (3.0 - (2.0 * x2)))));
	} else {
		tmp = x1 + (x2 * -6.0);
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x1 <= (-1.65d+84)) then
        tmp = x1 + (9.0d0 + (x1 + (x1 * (x2 * (-12.0d0)))))
    else if ((x1 <= (-5.5d-77)) .or. (.not. (x1 <= 2.1d-106))) then
        tmp = x1 * (2.0d0 - (4.0d0 * (x2 * (3.0d0 - (2.0d0 * x2)))))
    else
        tmp = x1 + (x2 * (-6.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= -1.65e+84) {
		tmp = x1 + (9.0 + (x1 + (x1 * (x2 * -12.0))));
	} else if ((x1 <= -5.5e-77) || !(x1 <= 2.1e-106)) {
		tmp = x1 * (2.0 - (4.0 * (x2 * (3.0 - (2.0 * x2)))));
	} else {
		tmp = x1 + (x2 * -6.0);
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -1.65e+84:
		tmp = x1 + (9.0 + (x1 + (x1 * (x2 * -12.0))))
	elif (x1 <= -5.5e-77) or not (x1 <= 2.1e-106):
		tmp = x1 * (2.0 - (4.0 * (x2 * (3.0 - (2.0 * x2)))))
	else:
		tmp = x1 + (x2 * -6.0)
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -1.65e+84)
		tmp = Float64(x1 + Float64(9.0 + Float64(x1 + Float64(x1 * Float64(x2 * -12.0)))));
	elseif ((x1 <= -5.5e-77) || !(x1 <= 2.1e-106))
		tmp = Float64(x1 * Float64(2.0 - Float64(4.0 * Float64(x2 * Float64(3.0 - Float64(2.0 * x2))))));
	else
		tmp = Float64(x1 + Float64(x2 * -6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -1.65e+84)
		tmp = x1 + (9.0 + (x1 + (x1 * (x2 * -12.0))));
	elseif ((x1 <= -5.5e-77) || ~((x1 <= 2.1e-106)))
		tmp = x1 * (2.0 - (4.0 * (x2 * (3.0 - (2.0 * x2)))));
	else
		tmp = x1 + (x2 * -6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -1.65e+84], N[(x1 + N[(9.0 + N[(x1 + N[(x1 * N[(x2 * -12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x1, -5.5e-77], N[Not[LessEqual[x1, 2.1e-106]], $MachinePrecision]], N[(x1 * N[(2.0 - N[(4.0 * N[(x2 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -1.65000000000000008e84

   1. Initial program 5.8%

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

   3. Taylor expanded in x1 around 0 0.1%

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

   4. Taylor expanded in x1 around inf 0.1%

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

   5. Taylor expanded in x2 around 0 14.2%

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

      1. associate-*r* 14.2%

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

      2. *-commutative 14.2%

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

      3. associate-*l* 14.2%

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

   7. Simplified 14.2%

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

   if -1.65000000000000008e84 < x1 < -5.49999999999999998e-77 or 2.10000000000000003e-106 < x1

   1. Initial program 77.3%

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

   3. Taylor expanded in x1 around 0 47.8%

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

   4. Taylor expanded in x1 around inf 49.8%

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

   5. Taylor expanded in x1 around inf 49.6%

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

   if -5.49999999999999998e-77 < x1 < 2.10000000000000003e-106

   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 83.2%

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

   4. Taylor expanded in x1 around 0 83.2%

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

   5. Taylor expanded in x1 around 0 61.9%

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

      1. *-commutative 61.9%

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

   7. Simplified 61.9%

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

4. Final simplification 46.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.65 \cdot 10^{+84}:\\ \;\;\;\;x1 + \left(9 + \left(x1 + x1 \cdot \left(x2 \cdot -12\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -5.5 \cdot 10^{-77} \lor \neg \left(x1 \leq 2.1 \cdot 10^{-106}\right):\\ \;\;\;\;x1 \cdot \left(2 - 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x2 \cdot -6\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 68.7% accurate, 4.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x2 \leq -3.35 \cdot 10^{+133} \lor \neg \left(x2 \leq 5.4 \cdot 10^{+96}\right):\\ \;\;\;\;x1 + \left(9 + \left(x1 + x2 \cdot \left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot -12\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 - 2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x2 -3.35e+133) (not (<= x2 5.4e+96)))
   (+ x1 (+ 9.0 (+ x1 (* x2 (+ (* 8.0 (* x1 x2)) (* x1 -12.0))))))
   (+ x1 (+ (* x2 -6.0) (* x1 (- (* x1 9.0) 2.0))))))

C

double code(double x1, double x2) {
	double tmp;
	if ((x2 <= -3.35e+133) || !(x2 <= 5.4e+96)) {
		tmp = x1 + (9.0 + (x1 + (x2 * ((8.0 * (x1 * x2)) + (x1 * -12.0)))));
	} 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) :: tmp
    if ((x2 <= (-3.35d+133)) .or. (.not. (x2 <= 5.4d+96))) then
        tmp = x1 + (9.0d0 + (x1 + (x2 * ((8.0d0 * (x1 * x2)) + (x1 * (-12.0d0))))))
    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 tmp;
	if ((x2 <= -3.35e+133) || !(x2 <= 5.4e+96)) {
		tmp = x1 + (9.0 + (x1 + (x2 * ((8.0 * (x1 * x2)) + (x1 * -12.0)))));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) - 2.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x2 <= -3.35e+133) or not (x2 <= 5.4e+96):
		tmp = x1 + (9.0 + (x1 + (x2 * ((8.0 * (x1 * x2)) + (x1 * -12.0)))))
	else:
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) - 2.0)))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x2 <= -3.35e+133) || !(x2 <= 5.4e+96))
		tmp = Float64(x1 + Float64(9.0 + Float64(x1 + Float64(x2 * Float64(Float64(8.0 * Float64(x1 * x2)) + Float64(x1 * -12.0))))));
	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)
	tmp = 0.0;
	if ((x2 <= -3.35e+133) || ~((x2 <= 5.4e+96)))
		tmp = x1 + (9.0 + (x1 + (x2 * ((8.0 * (x1 * x2)) + (x1 * -12.0)))));
	else
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) - 2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x2, -3.35e+133], N[Not[LessEqual[x2, 5.4e+96]], $MachinePrecision]], N[(x1 + N[(9.0 + N[(x1 + N[(x2 * N[(N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision] + N[(x1 * -12.0), $MachinePrecision]), $MachinePrecision]), $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 2 regimes

2. if x2 < -3.35000000000000015e133 or 5.40000000000000044e96 < x2

   1. Initial program 75.7%

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

   3. Taylor expanded in x1 around 0 52.2%

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

   4. Taylor expanded in x1 around inf 62.6%

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

   5. Taylor expanded in x2 around 0 70.2%

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

   if -3.35000000000000015e133 < x2 < 5.40000000000000044e96

   1. Initial program 67.5%

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

   3. Taylor expanded in x1 around 0 49.0%

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

   4. Taylor expanded in x1 around 0 60.3%

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

   5. Taylor expanded in x1 around 0 70.0%

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

   6. Taylor expanded in x2 around 0 71.8%

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

      1. *-commutative 71.8%

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

   8. Simplified 71.8%

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

4. Final simplification 71.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq -3.35 \cdot 10^{+133} \lor \neg \left(x2 \leq 5.4 \cdot 10^{+96}\right):\\ \;\;\;\;x1 + \left(9 + \left(x1 + x2 \cdot \left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot -12\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 - 2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 65.9% accurate, 5.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x2 \leq -3.35 \cdot 10^{+133} \lor \neg \left(x2 \leq 5.4 \cdot 10^{+96}\right):\\ \;\;\;\;x1 \cdot \left(2 - 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 - 2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x2 -3.35e+133) (not (<= x2 5.4e+96)))
   (* x1 (- 2.0 (* 4.0 (* x2 (- 3.0 (* 2.0 x2))))))
   (+ x1 (+ (* x2 -6.0) (* x1 (- (* x1 9.0) 2.0))))))

C

double code(double x1, double x2) {
	double tmp;
	if ((x2 <= -3.35e+133) || !(x2 <= 5.4e+96)) {
		tmp = x1 * (2.0 - (4.0 * (x2 * (3.0 - (2.0 * x2)))));
	} 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) :: tmp
    if ((x2 <= (-3.35d+133)) .or. (.not. (x2 <= 5.4d+96))) then
        tmp = x1 * (2.0d0 - (4.0d0 * (x2 * (3.0d0 - (2.0d0 * x2)))))
    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 tmp;
	if ((x2 <= -3.35e+133) || !(x2 <= 5.4e+96)) {
		tmp = x1 * (2.0 - (4.0 * (x2 * (3.0 - (2.0 * x2)))));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) - 2.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x2 <= -3.35e+133) or not (x2 <= 5.4e+96):
		tmp = x1 * (2.0 - (4.0 * (x2 * (3.0 - (2.0 * x2)))))
	else:
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) - 2.0)))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x2 <= -3.35e+133) || !(x2 <= 5.4e+96))
		tmp = Float64(x1 * Float64(2.0 - Float64(4.0 * Float64(x2 * Float64(3.0 - Float64(2.0 * x2))))));
	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)
	tmp = 0.0;
	if ((x2 <= -3.35e+133) || ~((x2 <= 5.4e+96)))
		tmp = x1 * (2.0 - (4.0 * (x2 * (3.0 - (2.0 * x2)))));
	else
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) - 2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x2, -3.35e+133], N[Not[LessEqual[x2, 5.4e+96]], $MachinePrecision]], N[(x1 * N[(2.0 - N[(4.0 * N[(x2 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $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 2 regimes

2. if x2 < -3.35000000000000015e133 or 5.40000000000000044e96 < x2

   1. Initial program 75.7%

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

   3. Taylor expanded in x1 around 0 52.2%

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

   4. Taylor expanded in x1 around inf 62.6%

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

   5. Taylor expanded in x1 around inf 62.6%

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

   if -3.35000000000000015e133 < x2 < 5.40000000000000044e96

   1. Initial program 67.5%

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

   3. Taylor expanded in x1 around 0 49.0%

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

   4. Taylor expanded in x1 around 0 60.3%

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

   5. Taylor expanded in x1 around 0 70.0%

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

   6. Taylor expanded in x2 around 0 71.8%

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

      1. *-commutative 71.8%

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

   8. Simplified 71.8%

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

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq -3.35 \cdot 10^{+133} \lor \neg \left(x2 \leq 5.4 \cdot 10^{+96}\right):\\ \;\;\;\;x1 \cdot \left(2 - 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 - 2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 30.5% accurate, 6.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -4.1 \cdot 10^{-70} \lor \neg \left(x1 \leq 1.5\right):\\ \;\;\;\;x1 + \left(9 + \left(x1 + x1 \cdot \left(x2 \cdot -12\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x2 \cdot -6\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x1 -4.1e-70) (not (<= x1 1.5)))
   (+ x1 (+ 9.0 (+ x1 (* x1 (* x2 -12.0)))))
   (+ x1 (* x2 -6.0))))

C

double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -4.1e-70) || !(x1 <= 1.5)) {
		tmp = x1 + (9.0 + (x1 + (x1 * (x2 * -12.0))));
	} else {
		tmp = x1 + (x2 * -6.0);
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if ((x1 <= (-4.1d-70)) .or. (.not. (x1 <= 1.5d0))) then
        tmp = x1 + (9.0d0 + (x1 + (x1 * (x2 * (-12.0d0)))))
    else
        tmp = x1 + (x2 * (-6.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -4.1e-70) || !(x1 <= 1.5)) {
		tmp = x1 + (9.0 + (x1 + (x1 * (x2 * -12.0))));
	} else {
		tmp = x1 + (x2 * -6.0);
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x1 <= -4.1e-70) or not (x1 <= 1.5):
		tmp = x1 + (9.0 + (x1 + (x1 * (x2 * -12.0))))
	else:
		tmp = x1 + (x2 * -6.0)
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x1 <= -4.1e-70) || !(x1 <= 1.5))
		tmp = Float64(x1 + Float64(9.0 + Float64(x1 + Float64(x1 * Float64(x2 * -12.0)))));
	else
		tmp = Float64(x1 + Float64(x2 * -6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x1 <= -4.1e-70) || ~((x1 <= 1.5)))
		tmp = x1 + (9.0 + (x1 + (x1 * (x2 * -12.0))));
	else
		tmp = x1 + (x2 * -6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x1, -4.1e-70], N[Not[LessEqual[x1, 1.5]], $MachinePrecision]], N[(x1 + N[(9.0 + N[(x1 + N[(x1 * N[(x2 * -12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x1 < -4.09999999999999977e-70 or 1.5 < x1

   1. Initial program 48.7%

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

   3. Taylor expanded in x1 around 0 23.8%

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

   4. Taylor expanded in x1 around inf 30.6%

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

   5. Taylor expanded in x2 around 0 14.3%

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

      1. associate-*r* 14.1%

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

      2. *-commutative 14.1%

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

      3. associate-*l* 14.3%

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

   7. Simplified 14.3%

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

   if -4.09999999999999977e-70 < x1 < 1.5

   1. Initial program 99.4%

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

   3. Taylor expanded in x1 around 0 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 85.6%

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

   5. Taylor expanded in x1 around 0 52.8%

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

      1. *-commutative 52.8%

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

   7. Simplified 52.8%

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

4. Final simplification 30.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4.1 \cdot 10^{-70} \lor \neg \left(x1 \leq 1.5\right):\\ \;\;\;\;x1 + \left(9 + \left(x1 + x1 \cdot \left(x2 \cdot -12\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x2 \cdot -6\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 25.2% 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 70.3%

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

3. Taylor expanded in x1 around 0 50.1%

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

4. Taylor expanded in x1 around 0 56.8%

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

5. Taylor expanded in x1 around 0 24.2%

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

   1. *-commutative 24.2%

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

7. Simplified 24.2%

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

8. Final simplification 24.2%

   \[\leadsto x1 + x2 \cdot -6 \]
9. Add Preprocessing

Alternative 25: 3.5% accurate, 127.0× speedup

Math

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

FPCore

(FPCore (x1 x2) :precision binary64 9.0)

C

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

Fortran

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

Java

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

Python

def code(x1, x2):
	return 9.0

Julia

function code(x1, x2)
	return 9.0
end

MATLAB

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

Wolfram

code[x1_, x2_] := 9.0

Derivation

1. Initial program 70.3%

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

3. Taylor expanded in x1 around 0 50.1%

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

4. Taylor expanded in x1 around inf 26.6%

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

5. Taylor expanded in x1 around 0 3.3%

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

6. Final simplification 3.3%

   \[\leadsto 9 \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024076 
(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))))))