Rosa's FloatVsDoubleBenchmark

Percentage Accurate: 69.4% → 99.6%

Time: 1.5min

Alternatives: 25

Speedup: 3.7×

• 46.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 69.4% 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: 99.6% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 99.5%

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

   3. Simplified 99.6%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in x1 around -inf 15.1%

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

   4. Taylor expanded in x1 around 0 98.6%

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

      1. *-commutative 98.6%

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

   6. Simplified 98.6%

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

4. Final simplification 99.3%

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

Alternative 2: 99.4% accurate, 0.2× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 99.5%

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

   3. Taylor expanded in x2 around inf 99.5%

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

      1. +-commutative 99.5%

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

      2. associate--r+ 99.5%

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

      3. associate-*r/ 99.5%

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

      4. div-sub 99.5%

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

      5. fma-neg 99.5%

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

      6. +-commutative 99.5%

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

      7. unpow2 99.5%

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

      8. fma-undefine 99.5%

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

      9. associate-*r/ 99.5%

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

      10. metadata-eval 99.5%

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

      11. +-commutative 99.5%

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

      12. unpow2 99.5%

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

      13. fma-undefine 99.5%

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

   5. Simplified 99.5%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in x1 around -inf 15.1%

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

   4. Taylor expanded in x1 around 0 98.6%

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

      1. *-commutative 98.6%

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

   6. Simplified 98.6%

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

4. Final simplification 99.2%

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

Alternative 3: 99.4% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 99.5%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in x1 around -inf 15.1%

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

   4. Taylor expanded in x1 around 0 98.6%

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

      1. *-commutative 98.6%

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

   6. Simplified 98.6%

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

4. Final simplification 99.2%

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

Alternative 4: 98.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := \left(t\_1 + 2 \cdot x2\right) - x1\\ t_3 := 3 - 2 \cdot x2\\ t_4 := -1 - x1 \cdot x1\\ t_5 := \frac{t\_2}{t\_4}\\ t_6 := \frac{t\_2}{t\_0}\\ \mathbf{if}\;x1 \leq -1 \cdot 10^{+103}:\\ \;\;\;\;x1 + \left(6 + \left(x1 + x1 \cdot \left(x1 \cdot \left(x1 \cdot -6 - 12\right) - 16\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.9 \cdot 10^{+122}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(\left(\left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot t\_5\right) + \left(\left(x1 \cdot 2\right) \cdot t\_6\right) \cdot \left(3 + t\_5\right)\right) \cdot t\_4 + t\_1 \cdot t\_6\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 3 \cdot \frac{\left(t\_1 - 2 \cdot x2\right) - x1}{t\_0}\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 - \left(x1 \cdot \left(\left(x1 \cdot \left(3 \cdot \left(x2 \cdot -2 - 3\right) - x1 \cdot 3\right) + 2 \cdot \left(-1 + 3 \cdot t\_3\right)\right) - -1\right) + -2 \cdot t\_3\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ (* x1 x1) 1.0))
        (t_1 (* x1 (* x1 3.0)))
        (t_2 (- (+ t_1 (* 2.0 x2)) x1))
        (t_3 (- 3.0 (* 2.0 x2)))
        (t_4 (- -1.0 (* x1 x1)))
        (t_5 (/ t_2 t_4))
        (t_6 (/ t_2 t_0)))
   (if (<= x1 -1e+103)
     (+ x1 (+ 6.0 (+ x1 (* x1 (- (* x1 (- (* x1 -6.0) 12.0)) 16.0)))))
     (if (<= x1 1.9e+122)
       (+
        x1
        (+
         (+
          x1
          (+
           (+
            (*
             (+
              (* (* x1 x1) (+ 6.0 (* 4.0 t_5)))
              (* (* (* x1 2.0) t_6) (+ 3.0 t_5)))
             t_4)
            (* t_1 t_6))
           (* x1 (* x1 x1))))
         (* 3.0 (/ (- (- t_1 (* 2.0 x2)) x1) t_0))))
       (-
        (* x2 -6.0)
        (+
         (*
          x1
          (-
           (+
            (* x1 (- (* 3.0 (- (* x2 -2.0) 3.0)) (* x1 3.0)))
            (* 2.0 (+ -1.0 (* 3.0 t_3))))
           -1.0))
         (* -2.0 t_3)))))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = (t_1 + (2.0 * x2)) - x1;
	double t_3 = 3.0 - (2.0 * x2);
	double t_4 = -1.0 - (x1 * x1);
	double t_5 = t_2 / t_4;
	double t_6 = t_2 / t_0;
	double tmp;
	if (x1 <= -1e+103) {
		tmp = x1 + (6.0 + (x1 + (x1 * ((x1 * ((x1 * -6.0) - 12.0)) - 16.0))));
	} else if (x1 <= 1.9e+122) {
		tmp = x1 + ((x1 + ((((((x1 * x1) * (6.0 + (4.0 * t_5))) + (((x1 * 2.0) * t_6) * (3.0 + t_5))) * t_4) + (t_1 * t_6)) + (x1 * (x1 * x1)))) + (3.0 * (((t_1 - (2.0 * x2)) - x1) / t_0)));
	} else {
		tmp = (x2 * -6.0) - ((x1 * (((x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - (x1 * 3.0))) + (2.0 * (-1.0 + (3.0 * t_3)))) - -1.0)) + (-2.0 * t_3));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: tmp
    t_0 = (x1 * x1) + 1.0d0
    t_1 = x1 * (x1 * 3.0d0)
    t_2 = (t_1 + (2.0d0 * x2)) - x1
    t_3 = 3.0d0 - (2.0d0 * x2)
    t_4 = (-1.0d0) - (x1 * x1)
    t_5 = t_2 / t_4
    t_6 = t_2 / t_0
    if (x1 <= (-1d+103)) then
        tmp = x1 + (6.0d0 + (x1 + (x1 * ((x1 * ((x1 * (-6.0d0)) - 12.0d0)) - 16.0d0))))
    else if (x1 <= 1.9d+122) then
        tmp = x1 + ((x1 + ((((((x1 * x1) * (6.0d0 + (4.0d0 * t_5))) + (((x1 * 2.0d0) * t_6) * (3.0d0 + t_5))) * t_4) + (t_1 * t_6)) + (x1 * (x1 * x1)))) + (3.0d0 * (((t_1 - (2.0d0 * x2)) - x1) / t_0)))
    else
        tmp = (x2 * (-6.0d0)) - ((x1 * (((x1 * ((3.0d0 * ((x2 * (-2.0d0)) - 3.0d0)) - (x1 * 3.0d0))) + (2.0d0 * ((-1.0d0) + (3.0d0 * t_3)))) - (-1.0d0))) + ((-2.0d0) * t_3))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = (t_1 + (2.0 * x2)) - x1;
	double t_3 = 3.0 - (2.0 * x2);
	double t_4 = -1.0 - (x1 * x1);
	double t_5 = t_2 / t_4;
	double t_6 = t_2 / t_0;
	double tmp;
	if (x1 <= -1e+103) {
		tmp = x1 + (6.0 + (x1 + (x1 * ((x1 * ((x1 * -6.0) - 12.0)) - 16.0))));
	} else if (x1 <= 1.9e+122) {
		tmp = x1 + ((x1 + ((((((x1 * x1) * (6.0 + (4.0 * t_5))) + (((x1 * 2.0) * t_6) * (3.0 + t_5))) * t_4) + (t_1 * t_6)) + (x1 * (x1 * x1)))) + (3.0 * (((t_1 - (2.0 * x2)) - x1) / t_0)));
	} else {
		tmp = (x2 * -6.0) - ((x1 * (((x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - (x1 * 3.0))) + (2.0 * (-1.0 + (3.0 * t_3)))) - -1.0)) + (-2.0 * t_3));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x1 * x1) + 1.0
	t_1 = x1 * (x1 * 3.0)
	t_2 = (t_1 + (2.0 * x2)) - x1
	t_3 = 3.0 - (2.0 * x2)
	t_4 = -1.0 - (x1 * x1)
	t_5 = t_2 / t_4
	t_6 = t_2 / t_0
	tmp = 0
	if x1 <= -1e+103:
		tmp = x1 + (6.0 + (x1 + (x1 * ((x1 * ((x1 * -6.0) - 12.0)) - 16.0))))
	elif x1 <= 1.9e+122:
		tmp = x1 + ((x1 + ((((((x1 * x1) * (6.0 + (4.0 * t_5))) + (((x1 * 2.0) * t_6) * (3.0 + t_5))) * t_4) + (t_1 * t_6)) + (x1 * (x1 * x1)))) + (3.0 * (((t_1 - (2.0 * x2)) - x1) / t_0)))
	else:
		tmp = (x2 * -6.0) - ((x1 * (((x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - (x1 * 3.0))) + (2.0 * (-1.0 + (3.0 * t_3)))) - -1.0)) + (-2.0 * t_3))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * x1) + 1.0)
	t_1 = Float64(x1 * Float64(x1 * 3.0))
	t_2 = Float64(Float64(t_1 + Float64(2.0 * x2)) - x1)
	t_3 = Float64(3.0 - Float64(2.0 * x2))
	t_4 = Float64(-1.0 - Float64(x1 * x1))
	t_5 = Float64(t_2 / t_4)
	t_6 = Float64(t_2 / t_0)
	tmp = 0.0
	if (x1 <= -1e+103)
		tmp = Float64(x1 + Float64(6.0 + Float64(x1 + Float64(x1 * Float64(Float64(x1 * Float64(Float64(x1 * -6.0) - 12.0)) - 16.0)))));
	elseif (x1 <= 1.9e+122)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(Float64(Float64(Float64(Float64(Float64(x1 * x1) * Float64(6.0 + Float64(4.0 * t_5))) + Float64(Float64(Float64(x1 * 2.0) * t_6) * Float64(3.0 + t_5))) * t_4) + Float64(t_1 * t_6)) + Float64(x1 * Float64(x1 * x1)))) + Float64(3.0 * Float64(Float64(Float64(t_1 - Float64(2.0 * x2)) - x1) / t_0))));
	else
		tmp = Float64(Float64(x2 * -6.0) - Float64(Float64(x1 * Float64(Float64(Float64(x1 * Float64(Float64(3.0 * Float64(Float64(x2 * -2.0) - 3.0)) - Float64(x1 * 3.0))) + Float64(2.0 * Float64(-1.0 + Float64(3.0 * t_3)))) - -1.0)) + Float64(-2.0 * t_3)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x1 * x1) + 1.0;
	t_1 = x1 * (x1 * 3.0);
	t_2 = (t_1 + (2.0 * x2)) - x1;
	t_3 = 3.0 - (2.0 * x2);
	t_4 = -1.0 - (x1 * x1);
	t_5 = t_2 / t_4;
	t_6 = t_2 / t_0;
	tmp = 0.0;
	if (x1 <= -1e+103)
		tmp = x1 + (6.0 + (x1 + (x1 * ((x1 * ((x1 * -6.0) - 12.0)) - 16.0))));
	elseif (x1 <= 1.9e+122)
		tmp = x1 + ((x1 + ((((((x1 * x1) * (6.0 + (4.0 * t_5))) + (((x1 * 2.0) * t_6) * (3.0 + t_5))) * t_4) + (t_1 * t_6)) + (x1 * (x1 * x1)))) + (3.0 * (((t_1 - (2.0 * x2)) - x1) / t_0)));
	else
		tmp = (x2 * -6.0) - ((x1 * (((x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - (x1 * 3.0))) + (2.0 * (-1.0 + (3.0 * t_3)))) - -1.0)) + (-2.0 * t_3));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t$95$1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]}, Block[{t$95$3 = N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $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[(t$95$2 / t$95$0), $MachinePrecision]}, If[LessEqual[x1, -1e+103], N[(x1 + N[(6.0 + N[(x1 + N[(x1 * N[(N[(x1 * N[(N[(x1 * -6.0), $MachinePrecision] - 12.0), $MachinePrecision]), $MachinePrecision] - 16.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.9e+122], N[(x1 + N[(N[(x1 + N[(N[(N[(N[(N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 + N[(4.0 * t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$6), $MachinePrecision] * N[(3.0 + t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * t$95$4), $MachinePrecision] + N[(t$95$1 * t$95$6), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(N[(N[(t$95$1 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x2 * -6.0), $MachinePrecision] - N[(N[(x1 * N[(N[(N[(x1 * N[(N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision] - N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(2.0 * N[(-1.0 + N[(3.0 * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision] + N[(-2.0 * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -1e103

   1. Initial program 2.3%

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

   3. Taylor expanded in x1 around inf 2.3%

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

   4. Taylor expanded in x1 around 0 20.9%

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

   5. Taylor expanded in x1 around 0 88.4%

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

      1. *-commutative 97.7%

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

   7. Simplified 88.4%

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

   8. Taylor expanded in x2 around 0 97.7%

      \[\leadsto x1 + \color{blue}{\left(6 + \left(x1 + x1 \cdot \left(x1 \cdot \left(-6 \cdot x1 - 12\right) - 16\right)\right)\right)} \]

   if -1e103 < x1 < 1.8999999999999999e122

   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 1.8999999999999999e122 < x1

   1. Initial program 18.4%

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

   3. Taylor expanded in x1 around inf 18.4%

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

   4. Taylor expanded in x1 around 0 8.1%

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

   5. Taylor expanded in x1 around 0 97.4%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1 \cdot 10^{+103}:\\ \;\;\;\;x1 + \left(6 + \left(x1 + x1 \cdot \left(x1 \cdot \left(x1 \cdot -6 - 12\right) - 16\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.9 \cdot 10^{+122}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(\left(\left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1}\right) + \left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(3 + \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1}\right)\right) \cdot \left(-1 - x1 \cdot x1\right) + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 - \left(x1 \cdot \left(\left(x1 \cdot \left(3 \cdot \left(x2 \cdot -2 - 3\right) - x1 \cdot 3\right) + 2 \cdot \left(-1 + 3 \cdot \left(3 - 2 \cdot x2\right)\right)\right) - -1\right) + -2 \cdot \left(3 - 2 \cdot x2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 96.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := 3 - 2 \cdot x2\\ t_2 := x1 \cdot \left(x1 \cdot 3\right)\\ t_3 := \left(t\_2 + 2 \cdot x2\right) - x1\\ t_4 := \frac{t\_3}{t\_0}\\ \mathbf{if}\;x1 \leq -5 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(6 + \left(x1 + x1 \cdot \left(x1 \cdot \left(x1 \cdot -6 - 12\right) - 16\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{+122}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t\_2 - 2 \cdot x2\right) - x1}{t\_0} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(t\_2 \cdot t\_4 - t\_0 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t\_4\right) \cdot \left(3 + \frac{t\_3}{-1 - x1 \cdot x1}\right) - \left(x1 \cdot x1\right) \cdot 6\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 - \left(x1 \cdot \left(\left(x1 \cdot \left(3 \cdot \left(x2 \cdot -2 - 3\right) - x1 \cdot 3\right) + 2 \cdot \left(-1 + 3 \cdot t\_1\right)\right) - -1\right) + -2 \cdot t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ (* x1 x1) 1.0))
        (t_1 (- 3.0 (* 2.0 x2)))
        (t_2 (* x1 (* x1 3.0)))
        (t_3 (- (+ t_2 (* 2.0 x2)) x1))
        (t_4 (/ t_3 t_0)))
   (if (<= x1 -5e+102)
     (+ x1 (+ 6.0 (+ x1 (* x1 (- (* x1 (- (* x1 -6.0) 12.0)) 16.0)))))
     (if (<= x1 2e+122)
       (+
        x1
        (+
         (* 3.0 (/ (- (- t_2 (* 2.0 x2)) x1) t_0))
         (+
          x1
          (+
           (* x1 (* x1 x1))
           (-
            (* t_2 t_4)
            (*
             t_0
             (-
              (* (* (* x1 2.0) t_4) (+ 3.0 (/ t_3 (- -1.0 (* x1 x1)))))
              (* (* x1 x1) 6.0))))))))
       (-
        (* x2 -6.0)
        (+
         (*
          x1
          (-
           (+
            (* x1 (- (* 3.0 (- (* x2 -2.0) 3.0)) (* x1 3.0)))
            (* 2.0 (+ -1.0 (* 3.0 t_1))))
           -1.0))
         (* -2.0 t_1)))))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = 3.0 - (2.0 * x2);
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = (t_2 + (2.0 * x2)) - x1;
	double t_4 = t_3 / t_0;
	double tmp;
	if (x1 <= -5e+102) {
		tmp = x1 + (6.0 + (x1 + (x1 * ((x1 * ((x1 * -6.0) - 12.0)) - 16.0))));
	} else if (x1 <= 2e+122) {
		tmp = x1 + ((3.0 * (((t_2 - (2.0 * x2)) - x1) / t_0)) + (x1 + ((x1 * (x1 * x1)) + ((t_2 * t_4) - (t_0 * ((((x1 * 2.0) * t_4) * (3.0 + (t_3 / (-1.0 - (x1 * x1))))) - ((x1 * x1) * 6.0)))))));
	} else {
		tmp = (x2 * -6.0) - ((x1 * (((x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - (x1 * 3.0))) + (2.0 * (-1.0 + (3.0 * t_1)))) - -1.0)) + (-2.0 * 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) :: t_4
    real(8) :: tmp
    t_0 = (x1 * x1) + 1.0d0
    t_1 = 3.0d0 - (2.0d0 * x2)
    t_2 = x1 * (x1 * 3.0d0)
    t_3 = (t_2 + (2.0d0 * x2)) - x1
    t_4 = t_3 / t_0
    if (x1 <= (-5d+102)) then
        tmp = x1 + (6.0d0 + (x1 + (x1 * ((x1 * ((x1 * (-6.0d0)) - 12.0d0)) - 16.0d0))))
    else if (x1 <= 2d+122) then
        tmp = x1 + ((3.0d0 * (((t_2 - (2.0d0 * x2)) - x1) / t_0)) + (x1 + ((x1 * (x1 * x1)) + ((t_2 * t_4) - (t_0 * ((((x1 * 2.0d0) * t_4) * (3.0d0 + (t_3 / ((-1.0d0) - (x1 * x1))))) - ((x1 * x1) * 6.0d0)))))))
    else
        tmp = (x2 * (-6.0d0)) - ((x1 * (((x1 * ((3.0d0 * ((x2 * (-2.0d0)) - 3.0d0)) - (x1 * 3.0d0))) + (2.0d0 * ((-1.0d0) + (3.0d0 * t_1)))) - (-1.0d0))) + ((-2.0d0) * t_1))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = 3.0 - (2.0 * x2);
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = (t_2 + (2.0 * x2)) - x1;
	double t_4 = t_3 / t_0;
	double tmp;
	if (x1 <= -5e+102) {
		tmp = x1 + (6.0 + (x1 + (x1 * ((x1 * ((x1 * -6.0) - 12.0)) - 16.0))));
	} else if (x1 <= 2e+122) {
		tmp = x1 + ((3.0 * (((t_2 - (2.0 * x2)) - x1) / t_0)) + (x1 + ((x1 * (x1 * x1)) + ((t_2 * t_4) - (t_0 * ((((x1 * 2.0) * t_4) * (3.0 + (t_3 / (-1.0 - (x1 * x1))))) - ((x1 * x1) * 6.0)))))));
	} else {
		tmp = (x2 * -6.0) - ((x1 * (((x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - (x1 * 3.0))) + (2.0 * (-1.0 + (3.0 * t_1)))) - -1.0)) + (-2.0 * t_1));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x1 * x1) + 1.0
	t_1 = 3.0 - (2.0 * x2)
	t_2 = x1 * (x1 * 3.0)
	t_3 = (t_2 + (2.0 * x2)) - x1
	t_4 = t_3 / t_0
	tmp = 0
	if x1 <= -5e+102:
		tmp = x1 + (6.0 + (x1 + (x1 * ((x1 * ((x1 * -6.0) - 12.0)) - 16.0))))
	elif x1 <= 2e+122:
		tmp = x1 + ((3.0 * (((t_2 - (2.0 * x2)) - x1) / t_0)) + (x1 + ((x1 * (x1 * x1)) + ((t_2 * t_4) - (t_0 * ((((x1 * 2.0) * t_4) * (3.0 + (t_3 / (-1.0 - (x1 * x1))))) - ((x1 * x1) * 6.0)))))))
	else:
		tmp = (x2 * -6.0) - ((x1 * (((x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - (x1 * 3.0))) + (2.0 * (-1.0 + (3.0 * t_1)))) - -1.0)) + (-2.0 * t_1))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * x1) + 1.0)
	t_1 = Float64(3.0 - Float64(2.0 * x2))
	t_2 = Float64(x1 * Float64(x1 * 3.0))
	t_3 = Float64(Float64(t_2 + Float64(2.0 * x2)) - x1)
	t_4 = Float64(t_3 / t_0)
	tmp = 0.0
	if (x1 <= -5e+102)
		tmp = Float64(x1 + Float64(6.0 + Float64(x1 + Float64(x1 * Float64(Float64(x1 * Float64(Float64(x1 * -6.0) - 12.0)) - 16.0)))));
	elseif (x1 <= 2e+122)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_2 - Float64(2.0 * x2)) - x1) / t_0)) + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(t_2 * t_4) - Float64(t_0 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_4) * Float64(3.0 + Float64(t_3 / Float64(-1.0 - Float64(x1 * x1))))) - Float64(Float64(x1 * x1) * 6.0))))))));
	else
		tmp = Float64(Float64(x2 * -6.0) - Float64(Float64(x1 * Float64(Float64(Float64(x1 * Float64(Float64(3.0 * Float64(Float64(x2 * -2.0) - 3.0)) - Float64(x1 * 3.0))) + Float64(2.0 * Float64(-1.0 + Float64(3.0 * t_1)))) - -1.0)) + Float64(-2.0 * t_1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x1 * x1) + 1.0;
	t_1 = 3.0 - (2.0 * x2);
	t_2 = x1 * (x1 * 3.0);
	t_3 = (t_2 + (2.0 * x2)) - x1;
	t_4 = t_3 / t_0;
	tmp = 0.0;
	if (x1 <= -5e+102)
		tmp = x1 + (6.0 + (x1 + (x1 * ((x1 * ((x1 * -6.0) - 12.0)) - 16.0))));
	elseif (x1 <= 2e+122)
		tmp = x1 + ((3.0 * (((t_2 - (2.0 * x2)) - x1) / t_0)) + (x1 + ((x1 * (x1 * x1)) + ((t_2 * t_4) - (t_0 * ((((x1 * 2.0) * t_4) * (3.0 + (t_3 / (-1.0 - (x1 * x1))))) - ((x1 * x1) * 6.0)))))));
	else
		tmp = (x2 * -6.0) - ((x1 * (((x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - (x1 * 3.0))) + (2.0 * (-1.0 + (3.0 * t_1)))) - -1.0)) + (-2.0 * t_1));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$1 = N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t$95$2 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$3 / t$95$0), $MachinePrecision]}, If[LessEqual[x1, -5e+102], N[(x1 + N[(6.0 + N[(x1 + N[(x1 * N[(N[(x1 * N[(N[(x1 * -6.0), $MachinePrecision] - 12.0), $MachinePrecision]), $MachinePrecision] - 16.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 2e+122], N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$2 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$2 * t$95$4), $MachinePrecision] - N[(t$95$0 * N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$4), $MachinePrecision] * N[(3.0 + N[(t$95$3 / N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x1 * x1), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x2 * -6.0), $MachinePrecision] - N[(N[(x1 * N[(N[(N[(x1 * N[(N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision] - N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(2.0 * N[(-1.0 + N[(3.0 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision] + N[(-2.0 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -5e102

   1. Initial program 2.3%

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

   3. Taylor expanded in x1 around inf 2.3%

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

   4. Taylor expanded in x1 around 0 20.9%

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

   5. Taylor expanded in x1 around 0 88.4%

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

      1. *-commutative 97.7%

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

   7. Simplified 88.4%

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

   8. Taylor expanded in x2 around 0 97.7%

      \[\leadsto x1 + \color{blue}{\left(6 + \left(x1 + x1 \cdot \left(x1 \cdot \left(-6 \cdot x1 - 12\right) - 16\right)\right)\right)} \]

   if -5e102 < x1 < 2.00000000000000003e122

   1. Initial program 99.4%

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

   3. Taylor expanded in x1 around inf 98.3%

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

   if 2.00000000000000003e122 < x1

   1. Initial program 18.4%

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

   3. Taylor expanded in x1 around inf 18.4%

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

   4. Taylor expanded in x1 around 0 8.1%

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

   5. Taylor expanded in x1 around 0 97.4%

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

4. Final simplification 98.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(6 + \left(x1 + x1 \cdot \left(x1 \cdot \left(x1 \cdot -6 - 12\right) - 16\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{+122}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - \left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(3 + \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1}\right) - \left(x1 \cdot x1\right) \cdot 6\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 - \left(x1 \cdot \left(\left(x1 \cdot \left(3 \cdot \left(x2 \cdot -2 - 3\right) - x1 \cdot 3\right) + 2 \cdot \left(-1 + 3 \cdot \left(3 - 2 \cdot x2\right)\right)\right) - -1\right) + -2 \cdot \left(3 - 2 \cdot x2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 92.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := 3 - 2 \cdot x2\\ t_2 := -1 - x1 \cdot x1\\ t_3 := x1 \cdot \left(x1 \cdot 3\right)\\ t_4 := 3 \cdot \frac{\left(t\_3 - 2 \cdot x2\right) - x1}{t\_0}\\ t_5 := \left(t\_3 + 2 \cdot x2\right) - x1\\ t_6 := x1 + \left(t\_4 - \left(\left(\left(t\_3 \cdot \frac{t\_5}{t\_2} + \left(\left(x1 \cdot x1\right) \cdot 6 + \left(\frac{t\_5}{t\_0} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot 3\right)\right) \cdot t\_2\right) - x1 \cdot \left(x1 \cdot x1\right)\right) - x1\right)\right)\\ \mathbf{if}\;x1 \leq -1 \cdot 10^{+103}:\\ \;\;\;\;x1 + \left(6 + \left(x1 + x1 \cdot \left(x1 \cdot \left(x1 \cdot -6 - 12\right) - 16\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -31000000000000:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;x1 \leq 1.28 \cdot 10^{+35}:\\ \;\;\;\;x1 + \left(t\_4 + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot -3 + 2 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 4.5 \cdot 10^{+123}:\\ \;\;\;\;t\_6\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 - \left(x1 \cdot \left(\left(x1 \cdot \left(3 \cdot \left(x2 \cdot -2 - 3\right) - x1 \cdot 3\right) + 2 \cdot \left(-1 + 3 \cdot t\_1\right)\right) - -1\right) + -2 \cdot t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ (* x1 x1) 1.0))
        (t_1 (- 3.0 (* 2.0 x2)))
        (t_2 (- -1.0 (* x1 x1)))
        (t_3 (* x1 (* x1 3.0)))
        (t_4 (* 3.0 (/ (- (- t_3 (* 2.0 x2)) x1) t_0)))
        (t_5 (- (+ t_3 (* 2.0 x2)) x1))
        (t_6
         (+
          x1
          (-
           t_4
           (-
            (-
             (+
              (* t_3 (/ t_5 t_2))
              (*
               (+ (* (* x1 x1) 6.0) (* (- (/ t_5 t_0) 3.0) (* (* x1 2.0) 3.0)))
               t_2))
             (* x1 (* x1 x1)))
            x1)))))
   (if (<= x1 -1e+103)
     (+ x1 (+ 6.0 (+ x1 (* x1 (- (* x1 (- (* x1 -6.0) 12.0)) 16.0)))))
     (if (<= x1 -31000000000000.0)
       t_6
       (if (<= x1 1.28e+35)
         (+ x1 (+ t_4 (+ x1 (* 4.0 (* x2 (+ (* x1 -3.0) (* 2.0 (* x1 x2))))))))
         (if (<= x1 4.5e+123)
           t_6
           (-
            (* x2 -6.0)
            (+
             (*
              x1
              (-
               (+
                (* x1 (- (* 3.0 (- (* x2 -2.0) 3.0)) (* x1 3.0)))
                (* 2.0 (+ -1.0 (* 3.0 t_1))))
               -1.0))
             (* -2.0 t_1)))))))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = 3.0 - (2.0 * x2);
	double t_2 = -1.0 - (x1 * x1);
	double t_3 = x1 * (x1 * 3.0);
	double t_4 = 3.0 * (((t_3 - (2.0 * x2)) - x1) / t_0);
	double t_5 = (t_3 + (2.0 * x2)) - x1;
	double t_6 = x1 + (t_4 - ((((t_3 * (t_5 / t_2)) + ((((x1 * x1) * 6.0) + (((t_5 / t_0) - 3.0) * ((x1 * 2.0) * 3.0))) * t_2)) - (x1 * (x1 * x1))) - x1));
	double tmp;
	if (x1 <= -1e+103) {
		tmp = x1 + (6.0 + (x1 + (x1 * ((x1 * ((x1 * -6.0) - 12.0)) - 16.0))));
	} else if (x1 <= -31000000000000.0) {
		tmp = t_6;
	} else if (x1 <= 1.28e+35) {
		tmp = x1 + (t_4 + (x1 + (4.0 * (x2 * ((x1 * -3.0) + (2.0 * (x1 * x2)))))));
	} else if (x1 <= 4.5e+123) {
		tmp = t_6;
	} else {
		tmp = (x2 * -6.0) - ((x1 * (((x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - (x1 * 3.0))) + (2.0 * (-1.0 + (3.0 * t_1)))) - -1.0)) + (-2.0 * 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) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: tmp
    t_0 = (x1 * x1) + 1.0d0
    t_1 = 3.0d0 - (2.0d0 * x2)
    t_2 = (-1.0d0) - (x1 * x1)
    t_3 = x1 * (x1 * 3.0d0)
    t_4 = 3.0d0 * (((t_3 - (2.0d0 * x2)) - x1) / t_0)
    t_5 = (t_3 + (2.0d0 * x2)) - x1
    t_6 = x1 + (t_4 - ((((t_3 * (t_5 / t_2)) + ((((x1 * x1) * 6.0d0) + (((t_5 / t_0) - 3.0d0) * ((x1 * 2.0d0) * 3.0d0))) * t_2)) - (x1 * (x1 * x1))) - x1))
    if (x1 <= (-1d+103)) then
        tmp = x1 + (6.0d0 + (x1 + (x1 * ((x1 * ((x1 * (-6.0d0)) - 12.0d0)) - 16.0d0))))
    else if (x1 <= (-31000000000000.0d0)) then
        tmp = t_6
    else if (x1 <= 1.28d+35) then
        tmp = x1 + (t_4 + (x1 + (4.0d0 * (x2 * ((x1 * (-3.0d0)) + (2.0d0 * (x1 * x2)))))))
    else if (x1 <= 4.5d+123) then
        tmp = t_6
    else
        tmp = (x2 * (-6.0d0)) - ((x1 * (((x1 * ((3.0d0 * ((x2 * (-2.0d0)) - 3.0d0)) - (x1 * 3.0d0))) + (2.0d0 * ((-1.0d0) + (3.0d0 * t_1)))) - (-1.0d0))) + ((-2.0d0) * t_1))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = 3.0 - (2.0 * x2);
	double t_2 = -1.0 - (x1 * x1);
	double t_3 = x1 * (x1 * 3.0);
	double t_4 = 3.0 * (((t_3 - (2.0 * x2)) - x1) / t_0);
	double t_5 = (t_3 + (2.0 * x2)) - x1;
	double t_6 = x1 + (t_4 - ((((t_3 * (t_5 / t_2)) + ((((x1 * x1) * 6.0) + (((t_5 / t_0) - 3.0) * ((x1 * 2.0) * 3.0))) * t_2)) - (x1 * (x1 * x1))) - x1));
	double tmp;
	if (x1 <= -1e+103) {
		tmp = x1 + (6.0 + (x1 + (x1 * ((x1 * ((x1 * -6.0) - 12.0)) - 16.0))));
	} else if (x1 <= -31000000000000.0) {
		tmp = t_6;
	} else if (x1 <= 1.28e+35) {
		tmp = x1 + (t_4 + (x1 + (4.0 * (x2 * ((x1 * -3.0) + (2.0 * (x1 * x2)))))));
	} else if (x1 <= 4.5e+123) {
		tmp = t_6;
	} else {
		tmp = (x2 * -6.0) - ((x1 * (((x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - (x1 * 3.0))) + (2.0 * (-1.0 + (3.0 * t_1)))) - -1.0)) + (-2.0 * t_1));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x1 * x1) + 1.0
	t_1 = 3.0 - (2.0 * x2)
	t_2 = -1.0 - (x1 * x1)
	t_3 = x1 * (x1 * 3.0)
	t_4 = 3.0 * (((t_3 - (2.0 * x2)) - x1) / t_0)
	t_5 = (t_3 + (2.0 * x2)) - x1
	t_6 = x1 + (t_4 - ((((t_3 * (t_5 / t_2)) + ((((x1 * x1) * 6.0) + (((t_5 / t_0) - 3.0) * ((x1 * 2.0) * 3.0))) * t_2)) - (x1 * (x1 * x1))) - x1))
	tmp = 0
	if x1 <= -1e+103:
		tmp = x1 + (6.0 + (x1 + (x1 * ((x1 * ((x1 * -6.0) - 12.0)) - 16.0))))
	elif x1 <= -31000000000000.0:
		tmp = t_6
	elif x1 <= 1.28e+35:
		tmp = x1 + (t_4 + (x1 + (4.0 * (x2 * ((x1 * -3.0) + (2.0 * (x1 * x2)))))))
	elif x1 <= 4.5e+123:
		tmp = t_6
	else:
		tmp = (x2 * -6.0) - ((x1 * (((x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - (x1 * 3.0))) + (2.0 * (-1.0 + (3.0 * t_1)))) - -1.0)) + (-2.0 * t_1))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * x1) + 1.0)
	t_1 = Float64(3.0 - Float64(2.0 * x2))
	t_2 = Float64(-1.0 - Float64(x1 * x1))
	t_3 = Float64(x1 * Float64(x1 * 3.0))
	t_4 = Float64(3.0 * Float64(Float64(Float64(t_3 - Float64(2.0 * x2)) - x1) / t_0))
	t_5 = Float64(Float64(t_3 + Float64(2.0 * x2)) - x1)
	t_6 = Float64(x1 + Float64(t_4 - Float64(Float64(Float64(Float64(t_3 * Float64(t_5 / t_2)) + Float64(Float64(Float64(Float64(x1 * x1) * 6.0) + Float64(Float64(Float64(t_5 / t_0) - 3.0) * Float64(Float64(x1 * 2.0) * 3.0))) * t_2)) - Float64(x1 * Float64(x1 * x1))) - x1)))
	tmp = 0.0
	if (x1 <= -1e+103)
		tmp = Float64(x1 + Float64(6.0 + Float64(x1 + Float64(x1 * Float64(Float64(x1 * Float64(Float64(x1 * -6.0) - 12.0)) - 16.0)))));
	elseif (x1 <= -31000000000000.0)
		tmp = t_6;
	elseif (x1 <= 1.28e+35)
		tmp = Float64(x1 + Float64(t_4 + Float64(x1 + Float64(4.0 * Float64(x2 * Float64(Float64(x1 * -3.0) + Float64(2.0 * Float64(x1 * x2))))))));
	elseif (x1 <= 4.5e+123)
		tmp = t_6;
	else
		tmp = Float64(Float64(x2 * -6.0) - Float64(Float64(x1 * Float64(Float64(Float64(x1 * Float64(Float64(3.0 * Float64(Float64(x2 * -2.0) - 3.0)) - Float64(x1 * 3.0))) + Float64(2.0 * Float64(-1.0 + Float64(3.0 * t_1)))) - -1.0)) + Float64(-2.0 * t_1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x1 * x1) + 1.0;
	t_1 = 3.0 - (2.0 * x2);
	t_2 = -1.0 - (x1 * x1);
	t_3 = x1 * (x1 * 3.0);
	t_4 = 3.0 * (((t_3 - (2.0 * x2)) - x1) / t_0);
	t_5 = (t_3 + (2.0 * x2)) - x1;
	t_6 = x1 + (t_4 - ((((t_3 * (t_5 / t_2)) + ((((x1 * x1) * 6.0) + (((t_5 / t_0) - 3.0) * ((x1 * 2.0) * 3.0))) * t_2)) - (x1 * (x1 * x1))) - x1));
	tmp = 0.0;
	if (x1 <= -1e+103)
		tmp = x1 + (6.0 + (x1 + (x1 * ((x1 * ((x1 * -6.0) - 12.0)) - 16.0))));
	elseif (x1 <= -31000000000000.0)
		tmp = t_6;
	elseif (x1 <= 1.28e+35)
		tmp = x1 + (t_4 + (x1 + (4.0 * (x2 * ((x1 * -3.0) + (2.0 * (x1 * x2)))))));
	elseif (x1 <= 4.5e+123)
		tmp = t_6;
	else
		tmp = (x2 * -6.0) - ((x1 * (((x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - (x1 * 3.0))) + (2.0 * (-1.0 + (3.0 * t_1)))) - -1.0)) + (-2.0 * t_1));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$1 = N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(3.0 * N[(N[(N[(t$95$3 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(t$95$3 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]}, Block[{t$95$6 = N[(x1 + N[(t$95$4 - N[(N[(N[(N[(t$95$3 * N[(t$95$5 / t$95$2), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(N[(x1 * x1), $MachinePrecision] * 6.0), $MachinePrecision] + N[(N[(N[(t$95$5 / t$95$0), $MachinePrecision] - 3.0), $MachinePrecision] * N[(N[(x1 * 2.0), $MachinePrecision] * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * t$95$2), $MachinePrecision]), $MachinePrecision] - N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -1e+103], N[(x1 + N[(6.0 + N[(x1 + N[(x1 * N[(N[(x1 * N[(N[(x1 * -6.0), $MachinePrecision] - 12.0), $MachinePrecision]), $MachinePrecision] - 16.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -31000000000000.0], t$95$6, If[LessEqual[x1, 1.28e+35], N[(x1 + N[(t$95$4 + N[(x1 + N[(4.0 * N[(x2 * N[(N[(x1 * -3.0), $MachinePrecision] + N[(2.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 4.5e+123], t$95$6, N[(N[(x2 * -6.0), $MachinePrecision] - N[(N[(x1 * N[(N[(N[(x1 * N[(N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision] - N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(2.0 * N[(-1.0 + N[(3.0 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision] + N[(-2.0 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -1e103

   1. Initial program 2.3%

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

   3. Taylor expanded in x1 around inf 2.3%

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

   4. Taylor expanded in x1 around 0 20.9%

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

   5. Taylor expanded in x1 around 0 88.4%

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

      1. *-commutative 97.7%

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

   7. Simplified 88.4%

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

   8. Taylor expanded in x2 around 0 97.7%

      \[\leadsto x1 + \color{blue}{\left(6 + \left(x1 + x1 \cdot \left(x1 \cdot \left(-6 \cdot x1 - 12\right) - 16\right)\right)\right)} \]

   if -1e103 < x1 < -3.1e13 or 1.2799999999999999e35 < x1 < 4.49999999999999983e123

   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 96.5%

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

   4. Taylor expanded in x1 around inf 87.4%

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

   if -3.1e13 < x1 < 1.2799999999999999e35

   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 83.7%

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

   4. Taylor expanded in x2 around 0 95.7%

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

   if 4.49999999999999983e123 < x1

   1. Initial program 18.4%

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

   3. Taylor expanded in x1 around inf 18.4%

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

   4. Taylor expanded in x1 around 0 8.1%

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

   5. Taylor expanded in x1 around 0 97.4%

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

4. Final simplification 95.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1 \cdot 10^{+103}:\\ \;\;\;\;x1 + \left(6 + \left(x1 + x1 \cdot \left(x1 \cdot \left(x1 \cdot -6 - 12\right) - 16\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -31000000000000:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - \left(\left(\left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1} + \left(\left(x1 \cdot x1\right) \cdot 6 + \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot 3\right)\right) \cdot \left(-1 - x1 \cdot x1\right)\right) - x1 \cdot \left(x1 \cdot x1\right)\right) - x1\right)\right)\\ \mathbf{elif}\;x1 \leq 1.28 \cdot 10^{+35}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot -3 + 2 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 4.5 \cdot 10^{+123}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - \left(\left(\left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1} + \left(\left(x1 \cdot x1\right) \cdot 6 + \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot 3\right)\right) \cdot \left(-1 - x1 \cdot x1\right)\right) - x1 \cdot \left(x1 \cdot x1\right)\right) - x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 - \left(x1 \cdot \left(\left(x1 \cdot \left(3 \cdot \left(x2 \cdot -2 - 3\right) - x1 \cdot 3\right) + 2 \cdot \left(-1 + 3 \cdot \left(3 - 2 \cdot x2\right)\right)\right) - -1\right) + -2 \cdot \left(3 - 2 \cdot x2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 96.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := 3 - 2 \cdot x2\\ t_2 := x1 \cdot \left(x1 \cdot 3\right)\\ t_3 := \left(t\_2 + 2 \cdot x2\right) - x1\\ \mathbf{if}\;x1 \leq -5 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(6 + \left(x1 + x1 \cdot \left(x1 \cdot \left(x1 \cdot -6 - 12\right) - 16\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{+122}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t\_2 - 2 \cdot x2\right) - x1}{t\_0} + \left(x1 - \left(\left(t\_0 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{t\_3}{t\_0}\right) \cdot \left(3 + \frac{t\_3}{-1 - x1 \cdot x1}\right) - \left(x1 \cdot x1\right) \cdot 6\right) - 3 \cdot t\_2\right) - x1 \cdot \left(x1 \cdot x1\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 - \left(x1 \cdot \left(\left(x1 \cdot \left(3 \cdot \left(x2 \cdot -2 - 3\right) - x1 \cdot 3\right) + 2 \cdot \left(-1 + 3 \cdot t\_1\right)\right) - -1\right) + -2 \cdot t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ (* x1 x1) 1.0))
        (t_1 (- 3.0 (* 2.0 x2)))
        (t_2 (* x1 (* x1 3.0)))
        (t_3 (- (+ t_2 (* 2.0 x2)) x1)))
   (if (<= x1 -5e+102)
     (+ x1 (+ 6.0 (+ x1 (* x1 (- (* x1 (- (* x1 -6.0) 12.0)) 16.0)))))
     (if (<= x1 2e+122)
       (+
        x1
        (+
         (* 3.0 (/ (- (- t_2 (* 2.0 x2)) x1) t_0))
         (-
          x1
          (-
           (-
            (*
             t_0
             (-
              (* (* (* x1 2.0) (/ t_3 t_0)) (+ 3.0 (/ t_3 (- -1.0 (* x1 x1)))))
              (* (* x1 x1) 6.0)))
            (* 3.0 t_2))
           (* x1 (* x1 x1))))))
       (-
        (* x2 -6.0)
        (+
         (*
          x1
          (-
           (+
            (* x1 (- (* 3.0 (- (* x2 -2.0) 3.0)) (* x1 3.0)))
            (* 2.0 (+ -1.0 (* 3.0 t_1))))
           -1.0))
         (* -2.0 t_1)))))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = 3.0 - (2.0 * x2);
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = (t_2 + (2.0 * x2)) - x1;
	double tmp;
	if (x1 <= -5e+102) {
		tmp = x1 + (6.0 + (x1 + (x1 * ((x1 * ((x1 * -6.0) - 12.0)) - 16.0))));
	} else if (x1 <= 2e+122) {
		tmp = x1 + ((3.0 * (((t_2 - (2.0 * x2)) - x1) / t_0)) + (x1 - (((t_0 * ((((x1 * 2.0) * (t_3 / t_0)) * (3.0 + (t_3 / (-1.0 - (x1 * x1))))) - ((x1 * x1) * 6.0))) - (3.0 * t_2)) - (x1 * (x1 * x1)))));
	} else {
		tmp = (x2 * -6.0) - ((x1 * (((x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - (x1 * 3.0))) + (2.0 * (-1.0 + (3.0 * t_1)))) - -1.0)) + (-2.0 * 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 = (x1 * x1) + 1.0d0
    t_1 = 3.0d0 - (2.0d0 * x2)
    t_2 = x1 * (x1 * 3.0d0)
    t_3 = (t_2 + (2.0d0 * x2)) - x1
    if (x1 <= (-5d+102)) then
        tmp = x1 + (6.0d0 + (x1 + (x1 * ((x1 * ((x1 * (-6.0d0)) - 12.0d0)) - 16.0d0))))
    else if (x1 <= 2d+122) then
        tmp = x1 + ((3.0d0 * (((t_2 - (2.0d0 * x2)) - x1) / t_0)) + (x1 - (((t_0 * ((((x1 * 2.0d0) * (t_3 / t_0)) * (3.0d0 + (t_3 / ((-1.0d0) - (x1 * x1))))) - ((x1 * x1) * 6.0d0))) - (3.0d0 * t_2)) - (x1 * (x1 * x1)))))
    else
        tmp = (x2 * (-6.0d0)) - ((x1 * (((x1 * ((3.0d0 * ((x2 * (-2.0d0)) - 3.0d0)) - (x1 * 3.0d0))) + (2.0d0 * ((-1.0d0) + (3.0d0 * t_1)))) - (-1.0d0))) + ((-2.0d0) * t_1))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = 3.0 - (2.0 * x2);
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = (t_2 + (2.0 * x2)) - x1;
	double tmp;
	if (x1 <= -5e+102) {
		tmp = x1 + (6.0 + (x1 + (x1 * ((x1 * ((x1 * -6.0) - 12.0)) - 16.0))));
	} else if (x1 <= 2e+122) {
		tmp = x1 + ((3.0 * (((t_2 - (2.0 * x2)) - x1) / t_0)) + (x1 - (((t_0 * ((((x1 * 2.0) * (t_3 / t_0)) * (3.0 + (t_3 / (-1.0 - (x1 * x1))))) - ((x1 * x1) * 6.0))) - (3.0 * t_2)) - (x1 * (x1 * x1)))));
	} else {
		tmp = (x2 * -6.0) - ((x1 * (((x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - (x1 * 3.0))) + (2.0 * (-1.0 + (3.0 * t_1)))) - -1.0)) + (-2.0 * t_1));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x1 * x1) + 1.0
	t_1 = 3.0 - (2.0 * x2)
	t_2 = x1 * (x1 * 3.0)
	t_3 = (t_2 + (2.0 * x2)) - x1
	tmp = 0
	if x1 <= -5e+102:
		tmp = x1 + (6.0 + (x1 + (x1 * ((x1 * ((x1 * -6.0) - 12.0)) - 16.0))))
	elif x1 <= 2e+122:
		tmp = x1 + ((3.0 * (((t_2 - (2.0 * x2)) - x1) / t_0)) + (x1 - (((t_0 * ((((x1 * 2.0) * (t_3 / t_0)) * (3.0 + (t_3 / (-1.0 - (x1 * x1))))) - ((x1 * x1) * 6.0))) - (3.0 * t_2)) - (x1 * (x1 * x1)))))
	else:
		tmp = (x2 * -6.0) - ((x1 * (((x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - (x1 * 3.0))) + (2.0 * (-1.0 + (3.0 * t_1)))) - -1.0)) + (-2.0 * t_1))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * x1) + 1.0)
	t_1 = Float64(3.0 - Float64(2.0 * x2))
	t_2 = Float64(x1 * Float64(x1 * 3.0))
	t_3 = Float64(Float64(t_2 + Float64(2.0 * x2)) - x1)
	tmp = 0.0
	if (x1 <= -5e+102)
		tmp = Float64(x1 + Float64(6.0 + Float64(x1 + Float64(x1 * Float64(Float64(x1 * Float64(Float64(x1 * -6.0) - 12.0)) - 16.0)))));
	elseif (x1 <= 2e+122)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_2 - Float64(2.0 * x2)) - x1) / t_0)) + Float64(x1 - Float64(Float64(Float64(t_0 * Float64(Float64(Float64(Float64(x1 * 2.0) * Float64(t_3 / t_0)) * Float64(3.0 + Float64(t_3 / Float64(-1.0 - Float64(x1 * x1))))) - Float64(Float64(x1 * x1) * 6.0))) - Float64(3.0 * t_2)) - Float64(x1 * Float64(x1 * x1))))));
	else
		tmp = Float64(Float64(x2 * -6.0) - Float64(Float64(x1 * Float64(Float64(Float64(x1 * Float64(Float64(3.0 * Float64(Float64(x2 * -2.0) - 3.0)) - Float64(x1 * 3.0))) + Float64(2.0 * Float64(-1.0 + Float64(3.0 * t_1)))) - -1.0)) + Float64(-2.0 * t_1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x1 * x1) + 1.0;
	t_1 = 3.0 - (2.0 * x2);
	t_2 = x1 * (x1 * 3.0);
	t_3 = (t_2 + (2.0 * x2)) - x1;
	tmp = 0.0;
	if (x1 <= -5e+102)
		tmp = x1 + (6.0 + (x1 + (x1 * ((x1 * ((x1 * -6.0) - 12.0)) - 16.0))));
	elseif (x1 <= 2e+122)
		tmp = x1 + ((3.0 * (((t_2 - (2.0 * x2)) - x1) / t_0)) + (x1 - (((t_0 * ((((x1 * 2.0) * (t_3 / t_0)) * (3.0 + (t_3 / (-1.0 - (x1 * x1))))) - ((x1 * x1) * 6.0))) - (3.0 * t_2)) - (x1 * (x1 * x1)))));
	else
		tmp = (x2 * -6.0) - ((x1 * (((x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - (x1 * 3.0))) + (2.0 * (-1.0 + (3.0 * t_1)))) - -1.0)) + (-2.0 * t_1));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$1 = N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t$95$2 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]}, If[LessEqual[x1, -5e+102], N[(x1 + N[(6.0 + N[(x1 + N[(x1 * N[(N[(x1 * N[(N[(x1 * -6.0), $MachinePrecision] - 12.0), $MachinePrecision]), $MachinePrecision] - 16.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 2e+122], N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$2 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision] + N[(x1 - N[(N[(N[(t$95$0 * N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * N[(t$95$3 / t$95$0), $MachinePrecision]), $MachinePrecision] * N[(3.0 + N[(t$95$3 / N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x1 * x1), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(3.0 * t$95$2), $MachinePrecision]), $MachinePrecision] - N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x2 * -6.0), $MachinePrecision] - N[(N[(x1 * N[(N[(N[(x1 * N[(N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision] - N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(2.0 * N[(-1.0 + N[(3.0 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision] + N[(-2.0 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -5e102

   1. Initial program 2.3%

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

   3. Taylor expanded in x1 around inf 2.3%

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

   4. Taylor expanded in x1 around 0 20.9%

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

   5. Taylor expanded in x1 around 0 88.4%

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

      1. *-commutative 97.7%

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

   7. Simplified 88.4%

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

   8. Taylor expanded in x2 around 0 97.7%

      \[\leadsto x1 + \color{blue}{\left(6 + \left(x1 + x1 \cdot \left(x1 \cdot \left(-6 \cdot x1 - 12\right) - 16\right)\right)\right)} \]

   if -5e102 < x1 < 2.00000000000000003e122

   1. Initial program 99.4%

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

   3. Taylor expanded in x1 around inf 98.3%

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

   4. Taylor expanded in x1 around inf 98.3%

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

   if 2.00000000000000003e122 < x1

   1. Initial program 18.4%

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

   3. Taylor expanded in x1 around inf 18.4%

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

   4. Taylor expanded in x1 around 0 8.1%

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

   5. Taylor expanded in x1 around 0 97.4%

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

4. Final simplification 98.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(6 + \left(x1 + x1 \cdot \left(x1 \cdot \left(x1 \cdot -6 - 12\right) - 16\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{+122}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 - \left(\left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(3 + \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1}\right) - \left(x1 \cdot x1\right) \cdot 6\right) - 3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right)\right) - x1 \cdot \left(x1 \cdot x1\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 - \left(x1 \cdot \left(\left(x1 \cdot \left(3 \cdot \left(x2 \cdot -2 - 3\right) - x1 \cdot 3\right) + 2 \cdot \left(-1 + 3 \cdot \left(3 - 2 \cdot x2\right)\right)\right) - -1\right) + -2 \cdot \left(3 - 2 \cdot x2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 84.2% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 3 - 2 \cdot x2\\ \mathbf{if}\;x1 \leq -1.85 \cdot 10^{+94}:\\ \;\;\;\;x1 + \left(6 + \left(x1 + x1 \cdot \left(x1 \cdot \left(x1 \cdot -6 - 12\right) - 16\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.1 \cdot 10^{+122}:\\ \;\;\;\;x1 - \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1} - \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot -3 + 2 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 - \left(x1 \cdot \left(\left(x1 \cdot \left(3 \cdot \left(x2 \cdot -2 - 3\right) - x1 \cdot 3\right) + 2 \cdot \left(-1 + 3 \cdot t\_0\right)\right) - -1\right) + -2 \cdot t\_0\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (- 3.0 (* 2.0 x2))))
   (if (<= x1 -1.85e+94)
     (+ x1 (+ 6.0 (+ x1 (* x1 (- (* x1 (- (* x1 -6.0) 12.0)) 16.0)))))
     (if (<= x1 1.1e+122)
       (-
        x1
        (-
         (* 3.0 (/ (- (- (* x1 (* x1 3.0)) (* 2.0 x2)) x1) (- -1.0 (* x1 x1))))
         (+ x1 (* 4.0 (* x2 (+ (* x1 -3.0) (* 2.0 (* x1 x2))))))))
       (-
        (* x2 -6.0)
        (+
         (*
          x1
          (-
           (+
            (* x1 (- (* 3.0 (- (* x2 -2.0) 3.0)) (* x1 3.0)))
            (* 2.0 (+ -1.0 (* 3.0 t_0))))
           -1.0))
         (* -2.0 t_0)))))))

C

double code(double x1, double x2) {
	double t_0 = 3.0 - (2.0 * x2);
	double tmp;
	if (x1 <= -1.85e+94) {
		tmp = x1 + (6.0 + (x1 + (x1 * ((x1 * ((x1 * -6.0) - 12.0)) - 16.0))));
	} else if (x1 <= 1.1e+122) {
		tmp = x1 - ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / (-1.0 - (x1 * x1)))) - (x1 + (4.0 * (x2 * ((x1 * -3.0) + (2.0 * (x1 * x2)))))));
	} else {
		tmp = (x2 * -6.0) - ((x1 * (((x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - (x1 * 3.0))) + (2.0 * (-1.0 + (3.0 * t_0)))) - -1.0)) + (-2.0 * t_0));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 3.0d0 - (2.0d0 * x2)
    if (x1 <= (-1.85d+94)) then
        tmp = x1 + (6.0d0 + (x1 + (x1 * ((x1 * ((x1 * (-6.0d0)) - 12.0d0)) - 16.0d0))))
    else if (x1 <= 1.1d+122) then
        tmp = x1 - ((3.0d0 * ((((x1 * (x1 * 3.0d0)) - (2.0d0 * x2)) - x1) / ((-1.0d0) - (x1 * x1)))) - (x1 + (4.0d0 * (x2 * ((x1 * (-3.0d0)) + (2.0d0 * (x1 * x2)))))))
    else
        tmp = (x2 * (-6.0d0)) - ((x1 * (((x1 * ((3.0d0 * ((x2 * (-2.0d0)) - 3.0d0)) - (x1 * 3.0d0))) + (2.0d0 * ((-1.0d0) + (3.0d0 * t_0)))) - (-1.0d0))) + ((-2.0d0) * t_0))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = 3.0 - (2.0 * x2);
	double tmp;
	if (x1 <= -1.85e+94) {
		tmp = x1 + (6.0 + (x1 + (x1 * ((x1 * ((x1 * -6.0) - 12.0)) - 16.0))));
	} else if (x1 <= 1.1e+122) {
		tmp = x1 - ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / (-1.0 - (x1 * x1)))) - (x1 + (4.0 * (x2 * ((x1 * -3.0) + (2.0 * (x1 * x2)))))));
	} else {
		tmp = (x2 * -6.0) - ((x1 * (((x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - (x1 * 3.0))) + (2.0 * (-1.0 + (3.0 * t_0)))) - -1.0)) + (-2.0 * t_0));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = 3.0 - (2.0 * x2)
	tmp = 0
	if x1 <= -1.85e+94:
		tmp = x1 + (6.0 + (x1 + (x1 * ((x1 * ((x1 * -6.0) - 12.0)) - 16.0))))
	elif x1 <= 1.1e+122:
		tmp = x1 - ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / (-1.0 - (x1 * x1)))) - (x1 + (4.0 * (x2 * ((x1 * -3.0) + (2.0 * (x1 * x2)))))))
	else:
		tmp = (x2 * -6.0) - ((x1 * (((x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - (x1 * 3.0))) + (2.0 * (-1.0 + (3.0 * t_0)))) - -1.0)) + (-2.0 * t_0))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(3.0 - Float64(2.0 * x2))
	tmp = 0.0
	if (x1 <= -1.85e+94)
		tmp = Float64(x1 + Float64(6.0 + Float64(x1 + Float64(x1 * Float64(Float64(x1 * Float64(Float64(x1 * -6.0) - 12.0)) - 16.0)))));
	elseif (x1 <= 1.1e+122)
		tmp = Float64(x1 - Float64(Float64(3.0 * Float64(Float64(Float64(Float64(x1 * Float64(x1 * 3.0)) - Float64(2.0 * x2)) - x1) / Float64(-1.0 - Float64(x1 * x1)))) - Float64(x1 + Float64(4.0 * Float64(x2 * Float64(Float64(x1 * -3.0) + Float64(2.0 * Float64(x1 * x2))))))));
	else
		tmp = Float64(Float64(x2 * -6.0) - Float64(Float64(x1 * Float64(Float64(Float64(x1 * Float64(Float64(3.0 * Float64(Float64(x2 * -2.0) - 3.0)) - Float64(x1 * 3.0))) + Float64(2.0 * Float64(-1.0 + Float64(3.0 * t_0)))) - -1.0)) + Float64(-2.0 * t_0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = 3.0 - (2.0 * x2);
	tmp = 0.0;
	if (x1 <= -1.85e+94)
		tmp = x1 + (6.0 + (x1 + (x1 * ((x1 * ((x1 * -6.0) - 12.0)) - 16.0))));
	elseif (x1 <= 1.1e+122)
		tmp = x1 - ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / (-1.0 - (x1 * x1)))) - (x1 + (4.0 * (x2 * ((x1 * -3.0) + (2.0 * (x1 * x2)))))));
	else
		tmp = (x2 * -6.0) - ((x1 * (((x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - (x1 * 3.0))) + (2.0 * (-1.0 + (3.0 * t_0)))) - -1.0)) + (-2.0 * t_0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -1.85e+94], N[(x1 + N[(6.0 + N[(x1 + N[(x1 * N[(N[(x1 * N[(N[(x1 * -6.0), $MachinePrecision] - 12.0), $MachinePrecision]), $MachinePrecision] - 16.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.1e+122], N[(x1 - N[(N[(3.0 * N[(N[(N[(N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision] - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x1 + N[(4.0 * N[(x2 * N[(N[(x1 * -3.0), $MachinePrecision] + N[(2.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x2 * -6.0), $MachinePrecision] - N[(N[(x1 * N[(N[(N[(x1 * N[(N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision] - N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(2.0 * N[(-1.0 + N[(3.0 * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision] + N[(-2.0 * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -1.8500000000000001e94

   1. Initial program 8.7%

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

   3. Taylor expanded in x1 around inf 8.7%

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

   4. Taylor expanded in x1 around 0 20.2%

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

   5. Taylor expanded in x1 around 0 83.2%

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

      1. *-commutative 97.8%

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

   7. Simplified 83.2%

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

   8. Taylor expanded in x2 around 0 91.9%

      \[\leadsto x1 + \color{blue}{\left(6 + \left(x1 + x1 \cdot \left(x1 \cdot \left(-6 \cdot x1 - 12\right) - 16\right)\right)\right)} \]

   if -1.8500000000000001e94 < x1 < 1.1e122

   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 73.4%

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

   4. Taylor expanded in x2 around 0 83.3%

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

   if 1.1e122 < x1

   1. Initial program 18.4%

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

   3. Taylor expanded in x1 around inf 18.4%

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

   4. Taylor expanded in x1 around 0 8.1%

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

   5. Taylor expanded in x1 around 0 97.4%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.85 \cdot 10^{+94}:\\ \;\;\;\;x1 + \left(6 + \left(x1 + x1 \cdot \left(x1 \cdot \left(x1 \cdot -6 - 12\right) - 16\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.1 \cdot 10^{+122}:\\ \;\;\;\;x1 - \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1} - \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot -3 + 2 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 - \left(x1 \cdot \left(\left(x1 \cdot \left(3 \cdot \left(x2 \cdot -2 - 3\right) - x1 \cdot 3\right) + 2 \cdot \left(-1 + 3 \cdot \left(3 - 2 \cdot x2\right)\right)\right) - -1\right) + -2 \cdot \left(3 - 2 \cdot x2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 79.8% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 4 \cdot \left(x1 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\\ \mathbf{if}\;x1 \leq -1.46 \cdot 10^{+96}:\\ \;\;\;\;x1 + \left(6 + \left(x1 + x1 \cdot \left(x1 \cdot \left(x1 \cdot -6 - 12\right) - 16\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -2.05 \cdot 10^{-196}:\\ \;\;\;\;x1 - \left(\left(t\_0 - x1\right) + 3 \cdot \left(x1 \cdot \left(x1 \cdot \left(x2 \cdot -2 - 3\right) - -1\right) - x2 \cdot -2\right)\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{-265}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + 4 \cdot \left(x1 \cdot \left(x2 \cdot -3\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 - t\_0\right) - 3 \cdot \left(x1 \cdot \left(x1 \cdot \left(x2 \cdot -2 - \left(x1 + 3\right)\right) - -1\right) - x2 \cdot -2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* 4.0 (* x1 (* x2 (- 3.0 (* 2.0 x2)))))))
   (if (<= x1 -1.46e+96)
     (+ x1 (+ 6.0 (+ x1 (* x1 (- (* x1 (- (* x1 -6.0) 12.0)) 16.0)))))
     (if (<= x1 -2.05e-196)
       (-
        x1
        (+
         (- t_0 x1)
         (* 3.0 (- (* x1 (- (* x1 (- (* x2 -2.0) 3.0)) -1.0)) (* x2 -2.0)))))
       (if (<= x1 5e-265)
         (+
          x1
          (+
           (*
            3.0
            (/ (- (- (* x1 (* x1 3.0)) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0)))
           (+ x1 (* 4.0 (* x1 (* x2 -3.0))))))
         (+
          x1
          (-
           (- x1 t_0)
           (*
            3.0
            (-
             (* x1 (- (* x1 (- (* x2 -2.0) (+ x1 3.0))) -1.0))
             (* x2 -2.0))))))))))

C

double code(double x1, double x2) {
	double t_0 = 4.0 * (x1 * (x2 * (3.0 - (2.0 * x2))));
	double tmp;
	if (x1 <= -1.46e+96) {
		tmp = x1 + (6.0 + (x1 + (x1 * ((x1 * ((x1 * -6.0) - 12.0)) - 16.0))));
	} else if (x1 <= -2.05e-196) {
		tmp = x1 - ((t_0 - x1) + (3.0 * ((x1 * ((x1 * ((x2 * -2.0) - 3.0)) - -1.0)) - (x2 * -2.0))));
	} else if (x1 <= 5e-265) {
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / ((x1 * x1) + 1.0))) + (x1 + (4.0 * (x1 * (x2 * -3.0)))));
	} else {
		tmp = x1 + ((x1 - t_0) - (3.0 * ((x1 * ((x1 * ((x2 * -2.0) - (x1 + 3.0))) - -1.0)) - (x2 * -2.0))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 4.0d0 * (x1 * (x2 * (3.0d0 - (2.0d0 * x2))))
    if (x1 <= (-1.46d+96)) then
        tmp = x1 + (6.0d0 + (x1 + (x1 * ((x1 * ((x1 * (-6.0d0)) - 12.0d0)) - 16.0d0))))
    else if (x1 <= (-2.05d-196)) then
        tmp = x1 - ((t_0 - x1) + (3.0d0 * ((x1 * ((x1 * ((x2 * (-2.0d0)) - 3.0d0)) - (-1.0d0))) - (x2 * (-2.0d0)))))
    else if (x1 <= 5d-265) then
        tmp = x1 + ((3.0d0 * ((((x1 * (x1 * 3.0d0)) - (2.0d0 * x2)) - x1) / ((x1 * x1) + 1.0d0))) + (x1 + (4.0d0 * (x1 * (x2 * (-3.0d0))))))
    else
        tmp = x1 + ((x1 - t_0) - (3.0d0 * ((x1 * ((x1 * ((x2 * (-2.0d0)) - (x1 + 3.0d0))) - (-1.0d0))) - (x2 * (-2.0d0)))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = 4.0 * (x1 * (x2 * (3.0 - (2.0 * x2))));
	double tmp;
	if (x1 <= -1.46e+96) {
		tmp = x1 + (6.0 + (x1 + (x1 * ((x1 * ((x1 * -6.0) - 12.0)) - 16.0))));
	} else if (x1 <= -2.05e-196) {
		tmp = x1 - ((t_0 - x1) + (3.0 * ((x1 * ((x1 * ((x2 * -2.0) - 3.0)) - -1.0)) - (x2 * -2.0))));
	} else if (x1 <= 5e-265) {
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / ((x1 * x1) + 1.0))) + (x1 + (4.0 * (x1 * (x2 * -3.0)))));
	} else {
		tmp = x1 + ((x1 - t_0) - (3.0 * ((x1 * ((x1 * ((x2 * -2.0) - (x1 + 3.0))) - -1.0)) - (x2 * -2.0))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = 4.0 * (x1 * (x2 * (3.0 - (2.0 * x2))))
	tmp = 0
	if x1 <= -1.46e+96:
		tmp = x1 + (6.0 + (x1 + (x1 * ((x1 * ((x1 * -6.0) - 12.0)) - 16.0))))
	elif x1 <= -2.05e-196:
		tmp = x1 - ((t_0 - x1) + (3.0 * ((x1 * ((x1 * ((x2 * -2.0) - 3.0)) - -1.0)) - (x2 * -2.0))))
	elif x1 <= 5e-265:
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / ((x1 * x1) + 1.0))) + (x1 + (4.0 * (x1 * (x2 * -3.0)))))
	else:
		tmp = x1 + ((x1 - t_0) - (3.0 * ((x1 * ((x1 * ((x2 * -2.0) - (x1 + 3.0))) - -1.0)) - (x2 * -2.0))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(4.0 * Float64(x1 * Float64(x2 * Float64(3.0 - Float64(2.0 * x2)))))
	tmp = 0.0
	if (x1 <= -1.46e+96)
		tmp = Float64(x1 + Float64(6.0 + Float64(x1 + Float64(x1 * Float64(Float64(x1 * Float64(Float64(x1 * -6.0) - 12.0)) - 16.0)))));
	elseif (x1 <= -2.05e-196)
		tmp = Float64(x1 - Float64(Float64(t_0 - x1) + Float64(3.0 * Float64(Float64(x1 * Float64(Float64(x1 * Float64(Float64(x2 * -2.0) - 3.0)) - -1.0)) - Float64(x2 * -2.0)))));
	elseif (x1 <= 5e-265)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(Float64(x1 * Float64(x1 * 3.0)) - Float64(2.0 * x2)) - x1) / Float64(Float64(x1 * x1) + 1.0))) + Float64(x1 + Float64(4.0 * Float64(x1 * Float64(x2 * -3.0))))));
	else
		tmp = Float64(x1 + Float64(Float64(x1 - t_0) - Float64(3.0 * Float64(Float64(x1 * Float64(Float64(x1 * Float64(Float64(x2 * -2.0) - Float64(x1 + 3.0))) - -1.0)) - Float64(x2 * -2.0)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = 4.0 * (x1 * (x2 * (3.0 - (2.0 * x2))));
	tmp = 0.0;
	if (x1 <= -1.46e+96)
		tmp = x1 + (6.0 + (x1 + (x1 * ((x1 * ((x1 * -6.0) - 12.0)) - 16.0))));
	elseif (x1 <= -2.05e-196)
		tmp = x1 - ((t_0 - x1) + (3.0 * ((x1 * ((x1 * ((x2 * -2.0) - 3.0)) - -1.0)) - (x2 * -2.0))));
	elseif (x1 <= 5e-265)
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / ((x1 * x1) + 1.0))) + (x1 + (4.0 * (x1 * (x2 * -3.0)))));
	else
		tmp = x1 + ((x1 - t_0) - (3.0 * ((x1 * ((x1 * ((x2 * -2.0) - (x1 + 3.0))) - -1.0)) - (x2 * -2.0))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(4.0 * N[(x1 * N[(x2 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -1.46e+96], N[(x1 + N[(6.0 + N[(x1 + N[(x1 * N[(N[(x1 * N[(N[(x1 * -6.0), $MachinePrecision] - 12.0), $MachinePrecision]), $MachinePrecision] - 16.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -2.05e-196], N[(x1 - N[(N[(t$95$0 - x1), $MachinePrecision] + N[(3.0 * N[(N[(x1 * N[(N[(x1 * N[(N[(x2 * -2.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision] - N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 5e-265], N[(x1 + N[(N[(3.0 * N[(N[(N[(N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision] - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(4.0 * N[(x1 * N[(x2 * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x1 - t$95$0), $MachinePrecision] - N[(3.0 * N[(N[(x1 * N[(N[(x1 * N[(N[(x2 * -2.0), $MachinePrecision] - N[(x1 + 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision] - N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -1.4600000000000001e96

   1. Initial program 8.7%

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

   3. Taylor expanded in x1 around inf 8.7%

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

   4. Taylor expanded in x1 around 0 20.2%

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

   5. Taylor expanded in x1 around 0 83.2%

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

      1. *-commutative 97.8%

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

   7. Simplified 83.2%

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

   8. Taylor expanded in x2 around 0 91.9%

      \[\leadsto x1 + \color{blue}{\left(6 + \left(x1 + x1 \cdot \left(x1 \cdot \left(-6 \cdot x1 - 12\right) - 16\right)\right)\right)} \]

   if -1.4600000000000001e96 < x1 < -2.05000000000000011e-196

   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 67.0%

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

   4. Taylor expanded in x1 around 0 68.1%

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

   if -2.05000000000000011e-196 < x1 < 5.0000000000000001e-265

   1. Initial program 99.7%

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

   3. Taylor expanded in x1 around 0 76.1%

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

   4. Taylor expanded in x2 around 0 96.9%

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

      1. *-commutative 96.9%

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

   6. Simplified 96.9%

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

   if 5.0000000000000001e-265 < x1

   1. Initial program 71.7%

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

   3. Taylor expanded in x1 around 0 53.3%

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

   4. Taylor expanded in x1 around 0 82.1%

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

4. Final simplification 82.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.46 \cdot 10^{+96}:\\ \;\;\;\;x1 + \left(6 + \left(x1 + x1 \cdot \left(x1 \cdot \left(x1 \cdot -6 - 12\right) - 16\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -2.05 \cdot 10^{-196}:\\ \;\;\;\;x1 - \left(\left(4 \cdot \left(x1 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right) - x1\right) + 3 \cdot \left(x1 \cdot \left(x1 \cdot \left(x2 \cdot -2 - 3\right) - -1\right) - x2 \cdot -2\right)\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{-265}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + 4 \cdot \left(x1 \cdot \left(x2 \cdot -3\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 - 4 \cdot \left(x1 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right) - 3 \cdot \left(x1 \cdot \left(x1 \cdot \left(x2 \cdot -2 - \left(x1 + 3\right)\right) - -1\right) - x2 \cdot -2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 74.7% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -2.7 \cdot 10^{+95}:\\ \;\;\;\;x1 + \left(6 + \left(x1 + x1 \cdot \left(x1 \cdot \left(x1 \cdot -6 - 12\right) - 16\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -3.2 \cdot 10^{-198} \lor \neg \left(x1 \leq 5.6 \cdot 10^{-264}\right):\\ \;\;\;\;x1 - \left(\left(4 \cdot \left(x1 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right) - x1\right) + 3 \cdot \left(x1 \cdot \left(x1 \cdot \left(x2 \cdot -2 - 3\right) - -1\right) - x2 \cdot -2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + 4 \cdot \left(x1 \cdot \left(x2 \cdot -3\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -2.7e+95)
   (+ x1 (+ 6.0 (+ x1 (* x1 (- (* x1 (- (* x1 -6.0) 12.0)) 16.0)))))
   (if (or (<= x1 -3.2e-198) (not (<= x1 5.6e-264)))
     (-
      x1
      (+
       (- (* 4.0 (* x1 (* x2 (- 3.0 (* 2.0 x2))))) x1)
       (* 3.0 (- (* x1 (- (* x1 (- (* x2 -2.0) 3.0)) -1.0)) (* x2 -2.0)))))
     (+
      x1
      (+
       (* 3.0 (/ (- (- (* x1 (* x1 3.0)) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0)))
       (+ x1 (* 4.0 (* x1 (* x2 -3.0)))))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -2.7e+95) {
		tmp = x1 + (6.0 + (x1 + (x1 * ((x1 * ((x1 * -6.0) - 12.0)) - 16.0))));
	} else if ((x1 <= -3.2e-198) || !(x1 <= 5.6e-264)) {
		tmp = x1 - (((4.0 * (x1 * (x2 * (3.0 - (2.0 * x2))))) - x1) + (3.0 * ((x1 * ((x1 * ((x2 * -2.0) - 3.0)) - -1.0)) - (x2 * -2.0))));
	} else {
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / ((x1 * x1) + 1.0))) + (x1 + (4.0 * (x1 * (x2 * -3.0)))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x1 <= (-2.7d+95)) then
        tmp = x1 + (6.0d0 + (x1 + (x1 * ((x1 * ((x1 * (-6.0d0)) - 12.0d0)) - 16.0d0))))
    else if ((x1 <= (-3.2d-198)) .or. (.not. (x1 <= 5.6d-264))) then
        tmp = x1 - (((4.0d0 * (x1 * (x2 * (3.0d0 - (2.0d0 * x2))))) - x1) + (3.0d0 * ((x1 * ((x1 * ((x2 * (-2.0d0)) - 3.0d0)) - (-1.0d0))) - (x2 * (-2.0d0)))))
    else
        tmp = x1 + ((3.0d0 * ((((x1 * (x1 * 3.0d0)) - (2.0d0 * x2)) - x1) / ((x1 * x1) + 1.0d0))) + (x1 + (4.0d0 * (x1 * (x2 * (-3.0d0))))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= -2.7e+95) {
		tmp = x1 + (6.0 + (x1 + (x1 * ((x1 * ((x1 * -6.0) - 12.0)) - 16.0))));
	} else if ((x1 <= -3.2e-198) || !(x1 <= 5.6e-264)) {
		tmp = x1 - (((4.0 * (x1 * (x2 * (3.0 - (2.0 * x2))))) - x1) + (3.0 * ((x1 * ((x1 * ((x2 * -2.0) - 3.0)) - -1.0)) - (x2 * -2.0))));
	} else {
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / ((x1 * x1) + 1.0))) + (x1 + (4.0 * (x1 * (x2 * -3.0)))));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -2.7e+95:
		tmp = x1 + (6.0 + (x1 + (x1 * ((x1 * ((x1 * -6.0) - 12.0)) - 16.0))))
	elif (x1 <= -3.2e-198) or not (x1 <= 5.6e-264):
		tmp = x1 - (((4.0 * (x1 * (x2 * (3.0 - (2.0 * x2))))) - x1) + (3.0 * ((x1 * ((x1 * ((x2 * -2.0) - 3.0)) - -1.0)) - (x2 * -2.0))))
	else:
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / ((x1 * x1) + 1.0))) + (x1 + (4.0 * (x1 * (x2 * -3.0)))))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -2.7e+95)
		tmp = Float64(x1 + Float64(6.0 + Float64(x1 + Float64(x1 * Float64(Float64(x1 * Float64(Float64(x1 * -6.0) - 12.0)) - 16.0)))));
	elseif ((x1 <= -3.2e-198) || !(x1 <= 5.6e-264))
		tmp = Float64(x1 - Float64(Float64(Float64(4.0 * Float64(x1 * Float64(x2 * Float64(3.0 - Float64(2.0 * x2))))) - x1) + Float64(3.0 * Float64(Float64(x1 * Float64(Float64(x1 * Float64(Float64(x2 * -2.0) - 3.0)) - -1.0)) - Float64(x2 * -2.0)))));
	else
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(Float64(x1 * Float64(x1 * 3.0)) - Float64(2.0 * x2)) - x1) / Float64(Float64(x1 * x1) + 1.0))) + Float64(x1 + Float64(4.0 * Float64(x1 * Float64(x2 * -3.0))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -2.7e+95)
		tmp = x1 + (6.0 + (x1 + (x1 * ((x1 * ((x1 * -6.0) - 12.0)) - 16.0))));
	elseif ((x1 <= -3.2e-198) || ~((x1 <= 5.6e-264)))
		tmp = x1 - (((4.0 * (x1 * (x2 * (3.0 - (2.0 * x2))))) - x1) + (3.0 * ((x1 * ((x1 * ((x2 * -2.0) - 3.0)) - -1.0)) - (x2 * -2.0))));
	else
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / ((x1 * x1) + 1.0))) + (x1 + (4.0 * (x1 * (x2 * -3.0)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -2.7e+95], N[(x1 + N[(6.0 + N[(x1 + N[(x1 * N[(N[(x1 * N[(N[(x1 * -6.0), $MachinePrecision] - 12.0), $MachinePrecision]), $MachinePrecision] - 16.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x1, -3.2e-198], N[Not[LessEqual[x1, 5.6e-264]], $MachinePrecision]], N[(x1 - N[(N[(N[(4.0 * N[(x1 * N[(x2 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] + N[(3.0 * N[(N[(x1 * N[(N[(x1 * N[(N[(x2 * -2.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision] - N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(3.0 * N[(N[(N[(N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision] - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(4.0 * N[(x1 * N[(x2 * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -2.7e95

   1. Initial program 8.7%

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

   3. Taylor expanded in x1 around inf 8.7%

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

   4. Taylor expanded in x1 around 0 20.2%

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

   5. Taylor expanded in x1 around 0 83.2%

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

      1. *-commutative 97.8%

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

   7. Simplified 83.2%

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

   8. Taylor expanded in x2 around 0 91.9%

      \[\leadsto x1 + \color{blue}{\left(6 + \left(x1 + x1 \cdot \left(x1 \cdot \left(-6 \cdot x1 - 12\right) - 16\right)\right)\right)} \]

   if -2.7e95 < x1 < -3.19999999999999994e-198 or 5.60000000000000024e-264 < x1

   1. Initial program 82.0%

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

   3. Taylor expanded in x1 around 0 58.4%

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

   4. Taylor expanded in x1 around 0 74.1%

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

   if -3.19999999999999994e-198 < x1 < 5.60000000000000024e-264

   1. Initial program 99.7%

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

   3. Taylor expanded in x1 around 0 76.1%

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

   4. Taylor expanded in x2 around 0 96.9%

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

      1. *-commutative 96.9%

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

   6. Simplified 96.9%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -2.7 \cdot 10^{+95}:\\ \;\;\;\;x1 + \left(6 + \left(x1 + x1 \cdot \left(x1 \cdot \left(x1 \cdot -6 - 12\right) - 16\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -3.2 \cdot 10^{-198} \lor \neg \left(x1 \leq 5.6 \cdot 10^{-264}\right):\\ \;\;\;\;x1 - \left(\left(4 \cdot \left(x1 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right) - x1\right) + 3 \cdot \left(x1 \cdot \left(x1 \cdot \left(x2 \cdot -2 - 3\right) - -1\right) - x2 \cdot -2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + 4 \cdot \left(x1 \cdot \left(x2 \cdot -3\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 84.0% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -3 \cdot 10^{+94}:\\ \;\;\;\;x1 + \left(6 + \left(x1 + x1 \cdot \left(x1 \cdot \left(x1 \cdot -6 - 12\right) - 16\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.1 \cdot 10^{+122}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot -3 + 2 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 - 4 \cdot \left(x1 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right) - 3 \cdot \left(x1 \cdot \left(x1 \cdot \left(x2 \cdot -2 - \left(x1 + 3\right)\right) - -1\right) - x2 \cdot -2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -3e+94)
   (+ x1 (+ 6.0 (+ x1 (* x1 (- (* x1 (- (* x1 -6.0) 12.0)) 16.0)))))
   (if (<= x1 1.1e+122)
     (+
      x1
      (+
       (* 3.0 (/ (- (- (* x1 (* x1 3.0)) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0)))
       (+ x1 (* 4.0 (* x2 (+ (* x1 -3.0) (* 2.0 (* x1 x2))))))))
     (+
      x1
      (-
       (- x1 (* 4.0 (* x1 (* x2 (- 3.0 (* 2.0 x2))))))
       (*
        3.0
        (- (* x1 (- (* x1 (- (* x2 -2.0) (+ x1 3.0))) -1.0)) (* x2 -2.0))))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -3e+94) {
		tmp = x1 + (6.0 + (x1 + (x1 * ((x1 * ((x1 * -6.0) - 12.0)) - 16.0))));
	} else if (x1 <= 1.1e+122) {
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / ((x1 * x1) + 1.0))) + (x1 + (4.0 * (x2 * ((x1 * -3.0) + (2.0 * (x1 * x2)))))));
	} else {
		tmp = x1 + ((x1 - (4.0 * (x1 * (x2 * (3.0 - (2.0 * x2)))))) - (3.0 * ((x1 * ((x1 * ((x2 * -2.0) - (x1 + 3.0))) - -1.0)) - (x2 * -2.0))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x1 <= (-3d+94)) then
        tmp = x1 + (6.0d0 + (x1 + (x1 * ((x1 * ((x1 * (-6.0d0)) - 12.0d0)) - 16.0d0))))
    else if (x1 <= 1.1d+122) then
        tmp = x1 + ((3.0d0 * ((((x1 * (x1 * 3.0d0)) - (2.0d0 * x2)) - x1) / ((x1 * x1) + 1.0d0))) + (x1 + (4.0d0 * (x2 * ((x1 * (-3.0d0)) + (2.0d0 * (x1 * x2)))))))
    else
        tmp = x1 + ((x1 - (4.0d0 * (x1 * (x2 * (3.0d0 - (2.0d0 * x2)))))) - (3.0d0 * ((x1 * ((x1 * ((x2 * (-2.0d0)) - (x1 + 3.0d0))) - (-1.0d0))) - (x2 * (-2.0d0)))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= -3e+94) {
		tmp = x1 + (6.0 + (x1 + (x1 * ((x1 * ((x1 * -6.0) - 12.0)) - 16.0))));
	} else if (x1 <= 1.1e+122) {
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / ((x1 * x1) + 1.0))) + (x1 + (4.0 * (x2 * ((x1 * -3.0) + (2.0 * (x1 * x2)))))));
	} else {
		tmp = x1 + ((x1 - (4.0 * (x1 * (x2 * (3.0 - (2.0 * x2)))))) - (3.0 * ((x1 * ((x1 * ((x2 * -2.0) - (x1 + 3.0))) - -1.0)) - (x2 * -2.0))));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -3e+94:
		tmp = x1 + (6.0 + (x1 + (x1 * ((x1 * ((x1 * -6.0) - 12.0)) - 16.0))))
	elif x1 <= 1.1e+122:
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / ((x1 * x1) + 1.0))) + (x1 + (4.0 * (x2 * ((x1 * -3.0) + (2.0 * (x1 * x2)))))))
	else:
		tmp = x1 + ((x1 - (4.0 * (x1 * (x2 * (3.0 - (2.0 * x2)))))) - (3.0 * ((x1 * ((x1 * ((x2 * -2.0) - (x1 + 3.0))) - -1.0)) - (x2 * -2.0))))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -3e+94)
		tmp = Float64(x1 + Float64(6.0 + Float64(x1 + Float64(x1 * Float64(Float64(x1 * Float64(Float64(x1 * -6.0) - 12.0)) - 16.0)))));
	elseif (x1 <= 1.1e+122)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(Float64(x1 * Float64(x1 * 3.0)) - Float64(2.0 * x2)) - x1) / Float64(Float64(x1 * x1) + 1.0))) + Float64(x1 + Float64(4.0 * Float64(x2 * Float64(Float64(x1 * -3.0) + Float64(2.0 * Float64(x1 * x2))))))));
	else
		tmp = Float64(x1 + Float64(Float64(x1 - Float64(4.0 * Float64(x1 * Float64(x2 * Float64(3.0 - Float64(2.0 * x2)))))) - Float64(3.0 * Float64(Float64(x1 * Float64(Float64(x1 * Float64(Float64(x2 * -2.0) - Float64(x1 + 3.0))) - -1.0)) - Float64(x2 * -2.0)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -3e+94)
		tmp = x1 + (6.0 + (x1 + (x1 * ((x1 * ((x1 * -6.0) - 12.0)) - 16.0))));
	elseif (x1 <= 1.1e+122)
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / ((x1 * x1) + 1.0))) + (x1 + (4.0 * (x2 * ((x1 * -3.0) + (2.0 * (x1 * x2)))))));
	else
		tmp = x1 + ((x1 - (4.0 * (x1 * (x2 * (3.0 - (2.0 * x2)))))) - (3.0 * ((x1 * ((x1 * ((x2 * -2.0) - (x1 + 3.0))) - -1.0)) - (x2 * -2.0))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -3e+94], N[(x1 + N[(6.0 + N[(x1 + N[(x1 * N[(N[(x1 * N[(N[(x1 * -6.0), $MachinePrecision] - 12.0), $MachinePrecision]), $MachinePrecision] - 16.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.1e+122], N[(x1 + N[(N[(3.0 * N[(N[(N[(N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision] - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(4.0 * N[(x2 * N[(N[(x1 * -3.0), $MachinePrecision] + N[(2.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x1 - N[(4.0 * N[(x1 * N[(x2 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(3.0 * N[(N[(x1 * N[(N[(x1 * N[(N[(x2 * -2.0), $MachinePrecision] - N[(x1 + 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision] - N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -3.0000000000000001e94

   1. Initial program 8.7%

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

   3. Taylor expanded in x1 around inf 8.7%

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

   4. Taylor expanded in x1 around 0 20.2%

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

   5. Taylor expanded in x1 around 0 83.2%

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

      1. *-commutative 97.8%

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

   7. Simplified 83.2%

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

   8. Taylor expanded in x2 around 0 91.9%

      \[\leadsto x1 + \color{blue}{\left(6 + \left(x1 + x1 \cdot \left(x1 \cdot \left(-6 \cdot x1 - 12\right) - 16\right)\right)\right)} \]

   if -3.0000000000000001e94 < x1 < 1.1e122

   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 73.4%

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

   4. Taylor expanded in x2 around 0 83.3%

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

   if 1.1e122 < x1

   1. Initial program 18.4%

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

   3. Taylor expanded in x1 around 0 6.0%

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

   4. Taylor expanded in x1 around 0 94.7%

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

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -3 \cdot 10^{+94}:\\ \;\;\;\;x1 + \left(6 + \left(x1 + x1 \cdot \left(x1 \cdot \left(x1 \cdot -6 - 12\right) - 16\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.1 \cdot 10^{+122}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot -3 + 2 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 - 4 \cdot \left(x1 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right) - 3 \cdot \left(x1 \cdot \left(x1 \cdot \left(x2 \cdot -2 - \left(x1 + 3\right)\right) - -1\right) - x2 \cdot -2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 72.1% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x2 \cdot \left(3 - 2 \cdot x2\right)\\ \mathbf{if}\;x1 \leq -1.46 \cdot 10^{+96}:\\ \;\;\;\;x1 + \left(6 + \left(x1 + x1 \cdot \left(x1 \cdot \left(x1 \cdot -6 - 12\right) - 16\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -1 \cdot 10^{-192}:\\ \;\;\;\;x1 + \left(\left(x1 - 4 \cdot \left(x1 \cdot t\_0\right)\right) - 3 \cdot \left(x2 \cdot \left(2 + \frac{x1}{x2}\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 2.35 \cdot 10^{-262}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + 4 \cdot \left(x1 \cdot \left(x2 \cdot -3\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 + 4 \cdot t\_0\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x2 (- 3.0 (* 2.0 x2)))))
   (if (<= x1 -1.46e+96)
     (+ x1 (+ 6.0 (+ x1 (* x1 (- (* x1 (- (* x1 -6.0) 12.0)) 16.0)))))
     (if (<= x1 -1e-192)
       (+ x1 (- (- x1 (* 4.0 (* x1 t_0))) (* 3.0 (* x2 (+ 2.0 (/ x1 x2))))))
       (if (<= x1 2.35e-262)
         (+
          x1
          (+
           (*
            3.0
            (/ (- (- (* x1 (* x1 3.0)) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0)))
           (+ x1 (* 4.0 (* x1 (* x2 -3.0))))))
         (+ x1 (- (* x2 -6.0) (* x1 (+ 2.0 (* 4.0 t_0))))))))))

C

double code(double x1, double x2) {
	double t_0 = x2 * (3.0 - (2.0 * x2));
	double tmp;
	if (x1 <= -1.46e+96) {
		tmp = x1 + (6.0 + (x1 + (x1 * ((x1 * ((x1 * -6.0) - 12.0)) - 16.0))));
	} else if (x1 <= -1e-192) {
		tmp = x1 + ((x1 - (4.0 * (x1 * t_0))) - (3.0 * (x2 * (2.0 + (x1 / x2)))));
	} else if (x1 <= 2.35e-262) {
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / ((x1 * x1) + 1.0))) + (x1 + (4.0 * (x1 * (x2 * -3.0)))));
	} else {
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + (4.0 * t_0))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x2 * (3.0d0 - (2.0d0 * x2))
    if (x1 <= (-1.46d+96)) then
        tmp = x1 + (6.0d0 + (x1 + (x1 * ((x1 * ((x1 * (-6.0d0)) - 12.0d0)) - 16.0d0))))
    else if (x1 <= (-1d-192)) then
        tmp = x1 + ((x1 - (4.0d0 * (x1 * t_0))) - (3.0d0 * (x2 * (2.0d0 + (x1 / x2)))))
    else if (x1 <= 2.35d-262) then
        tmp = x1 + ((3.0d0 * ((((x1 * (x1 * 3.0d0)) - (2.0d0 * x2)) - x1) / ((x1 * x1) + 1.0d0))) + (x1 + (4.0d0 * (x1 * (x2 * (-3.0d0))))))
    else
        tmp = x1 + ((x2 * (-6.0d0)) - (x1 * (2.0d0 + (4.0d0 * 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 tmp;
	if (x1 <= -1.46e+96) {
		tmp = x1 + (6.0 + (x1 + (x1 * ((x1 * ((x1 * -6.0) - 12.0)) - 16.0))));
	} else if (x1 <= -1e-192) {
		tmp = x1 + ((x1 - (4.0 * (x1 * t_0))) - (3.0 * (x2 * (2.0 + (x1 / x2)))));
	} else if (x1 <= 2.35e-262) {
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / ((x1 * x1) + 1.0))) + (x1 + (4.0 * (x1 * (x2 * -3.0)))));
	} else {
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + (4.0 * t_0))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x2 * (3.0 - (2.0 * x2))
	tmp = 0
	if x1 <= -1.46e+96:
		tmp = x1 + (6.0 + (x1 + (x1 * ((x1 * ((x1 * -6.0) - 12.0)) - 16.0))))
	elif x1 <= -1e-192:
		tmp = x1 + ((x1 - (4.0 * (x1 * t_0))) - (3.0 * (x2 * (2.0 + (x1 / x2)))))
	elif x1 <= 2.35e-262:
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / ((x1 * x1) + 1.0))) + (x1 + (4.0 * (x1 * (x2 * -3.0)))))
	else:
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + (4.0 * t_0))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x2 * Float64(3.0 - Float64(2.0 * x2)))
	tmp = 0.0
	if (x1 <= -1.46e+96)
		tmp = Float64(x1 + Float64(6.0 + Float64(x1 + Float64(x1 * Float64(Float64(x1 * Float64(Float64(x1 * -6.0) - 12.0)) - 16.0)))));
	elseif (x1 <= -1e-192)
		tmp = Float64(x1 + Float64(Float64(x1 - Float64(4.0 * Float64(x1 * t_0))) - Float64(3.0 * Float64(x2 * Float64(2.0 + Float64(x1 / x2))))));
	elseif (x1 <= 2.35e-262)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(Float64(x1 * Float64(x1 * 3.0)) - Float64(2.0 * x2)) - x1) / Float64(Float64(x1 * x1) + 1.0))) + Float64(x1 + Float64(4.0 * Float64(x1 * Float64(x2 * -3.0))))));
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) - Float64(x1 * Float64(2.0 + Float64(4.0 * t_0)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x2 * (3.0 - (2.0 * x2));
	tmp = 0.0;
	if (x1 <= -1.46e+96)
		tmp = x1 + (6.0 + (x1 + (x1 * ((x1 * ((x1 * -6.0) - 12.0)) - 16.0))));
	elseif (x1 <= -1e-192)
		tmp = x1 + ((x1 - (4.0 * (x1 * t_0))) - (3.0 * (x2 * (2.0 + (x1 / x2)))));
	elseif (x1 <= 2.35e-262)
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / ((x1 * x1) + 1.0))) + (x1 + (4.0 * (x1 * (x2 * -3.0)))));
	else
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + (4.0 * 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]}, If[LessEqual[x1, -1.46e+96], N[(x1 + N[(6.0 + N[(x1 + N[(x1 * N[(N[(x1 * N[(N[(x1 * -6.0), $MachinePrecision] - 12.0), $MachinePrecision]), $MachinePrecision] - 16.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -1e-192], N[(x1 + N[(N[(x1 - N[(4.0 * N[(x1 * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(3.0 * N[(x2 * N[(2.0 + N[(x1 / x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 2.35e-262], N[(x1 + N[(N[(3.0 * N[(N[(N[(N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision] - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(4.0 * N[(x1 * N[(x2 * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] - N[(x1 * N[(2.0 + N[(4.0 * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -1.4600000000000001e96

   1. Initial program 8.7%

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

   3. Taylor expanded in x1 around inf 8.7%

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

   4. Taylor expanded in x1 around 0 20.2%

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

   5. Taylor expanded in x1 around 0 83.2%

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

      1. *-commutative 97.8%

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

   7. Simplified 83.2%

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

   8. Taylor expanded in x2 around 0 91.9%

      \[\leadsto x1 + \color{blue}{\left(6 + \left(x1 + x1 \cdot \left(x1 \cdot \left(-6 \cdot x1 - 12\right) - 16\right)\right)\right)} \]

   if -1.4600000000000001e96 < x1 < -1.0000000000000001e-192

   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 x2 around inf 99.4%

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

      1. +-commutative 99.4%

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

      2. associate--r+ 99.4%

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

      3. associate-*r/ 99.4%

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

      4. div-sub 99.4%

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

      5. fma-neg 99.4%

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

      6. +-commutative 99.4%

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

      7. unpow2 99.4%

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

      8. fma-undefine 99.4%

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

      9. associate-*r/ 99.4%

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

      10. metadata-eval 99.4%

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

      11. +-commutative 99.4%

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

      12. unpow2 99.4%

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

      13. fma-undefine 99.4%

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

   5. Simplified 99.4%

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

   6. Taylor expanded in x1 around 0 98.0%

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

      1. associate-*r/ 98.0%

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

      2. neg-mul-1 98.0%

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

   8. Simplified 98.0%

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

   9. Taylor expanded in x1 around 0 66.9%

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

   10. Taylor expanded in x1 around 0 66.9%

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

   if -1.0000000000000001e-192 < x1 < 2.3499999999999999e-262

   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 77.4%

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

   4. Taylor expanded in x2 around 0 97.0%

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

      1. *-commutative 97.0%

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

   6. Simplified 97.0%

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

   if 2.3499999999999999e-262 < x1

   1. Initial program 71.7%

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

   3. Taylor expanded in x2 around inf 71.6%

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

      1. +-commutative 71.6%

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

      2. associate--r+ 71.6%

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

      3. associate-*r/ 71.6%

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

      4. div-sub 71.6%

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

      5. fma-neg 71.6%

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

      6. +-commutative 71.6%

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

      7. unpow2 71.6%

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

      8. fma-undefine 71.6%

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

      9. associate-*r/ 71.6%

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

      10. metadata-eval 71.6%

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

      11. +-commutative 71.6%

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

      12. unpow2 71.6%

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

      13. fma-undefine 71.6%

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

   5. Simplified 71.6%

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

   6. Taylor expanded in x1 around 0 71.1%

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

      1. associate-*r/ 71.1%

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

      2. neg-mul-1 71.1%

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

   8. Simplified 71.1%

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

   9. Taylor expanded in x1 around 0 59.2%

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

   10. Taylor expanded in x1 around 0 59.4%

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

4. Final simplification 72.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.46 \cdot 10^{+96}:\\ \;\;\;\;x1 + \left(6 + \left(x1 + x1 \cdot \left(x1 \cdot \left(x1 \cdot -6 - 12\right) - 16\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -1 \cdot 10^{-192}:\\ \;\;\;\;x1 + \left(\left(x1 - 4 \cdot \left(x1 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right) - 3 \cdot \left(x2 \cdot \left(2 + \frac{x1}{x2}\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 2.35 \cdot 10^{-262}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + 4 \cdot \left(x1 \cdot \left(x2 \cdot -3\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 + 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 71.1% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x2 \cdot \left(3 - 2 \cdot x2\right)\\ \mathbf{if}\;x1 \leq -5.1 \cdot 10^{+95}:\\ \;\;\;\;x1 + \left(6 + \left(x1 + x1 \cdot \left(x1 \cdot \left(x1 \cdot -6 - 12\right) - 16\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -5.1 \cdot 10^{-200}:\\ \;\;\;\;x1 + \left(\left(x1 - 4 \cdot \left(x1 \cdot t\_0\right)\right) - 3 \cdot \left(x2 \cdot \left(2 + \frac{x1}{x2}\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -3.6 \cdot 10^{-291}:\\ \;\;\;\;x1 + \left(x1 + x2 \cdot \left(\left(x1 \cdot -12 + \left(x1 \cdot x2\right) \cdot 8\right) - 6\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 + 4 \cdot t\_0\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x2 (- 3.0 (* 2.0 x2)))))
   (if (<= x1 -5.1e+95)
     (+ x1 (+ 6.0 (+ x1 (* x1 (- (* x1 (- (* x1 -6.0) 12.0)) 16.0)))))
     (if (<= x1 -5.1e-200)
       (+ x1 (- (- x1 (* 4.0 (* x1 t_0))) (* 3.0 (* x2 (+ 2.0 (/ x1 x2))))))
       (if (<= x1 -3.6e-291)
         (+ x1 (+ x1 (* x2 (- (+ (* x1 -12.0) (* (* x1 x2) 8.0)) 6.0))))
         (+ x1 (- (* x2 -6.0) (* x1 (+ 2.0 (* 4.0 t_0))))))))))

C

double code(double x1, double x2) {
	double t_0 = x2 * (3.0 - (2.0 * x2));
	double tmp;
	if (x1 <= -5.1e+95) {
		tmp = x1 + (6.0 + (x1 + (x1 * ((x1 * ((x1 * -6.0) - 12.0)) - 16.0))));
	} else if (x1 <= -5.1e-200) {
		tmp = x1 + ((x1 - (4.0 * (x1 * t_0))) - (3.0 * (x2 * (2.0 + (x1 / x2)))));
	} else if (x1 <= -3.6e-291) {
		tmp = x1 + (x1 + (x2 * (((x1 * -12.0) + ((x1 * x2) * 8.0)) - 6.0)));
	} else {
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + (4.0 * t_0))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x2 * (3.0d0 - (2.0d0 * x2))
    if (x1 <= (-5.1d+95)) then
        tmp = x1 + (6.0d0 + (x1 + (x1 * ((x1 * ((x1 * (-6.0d0)) - 12.0d0)) - 16.0d0))))
    else if (x1 <= (-5.1d-200)) then
        tmp = x1 + ((x1 - (4.0d0 * (x1 * t_0))) - (3.0d0 * (x2 * (2.0d0 + (x1 / x2)))))
    else if (x1 <= (-3.6d-291)) then
        tmp = x1 + (x1 + (x2 * (((x1 * (-12.0d0)) + ((x1 * x2) * 8.0d0)) - 6.0d0)))
    else
        tmp = x1 + ((x2 * (-6.0d0)) - (x1 * (2.0d0 + (4.0d0 * 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 tmp;
	if (x1 <= -5.1e+95) {
		tmp = x1 + (6.0 + (x1 + (x1 * ((x1 * ((x1 * -6.0) - 12.0)) - 16.0))));
	} else if (x1 <= -5.1e-200) {
		tmp = x1 + ((x1 - (4.0 * (x1 * t_0))) - (3.0 * (x2 * (2.0 + (x1 / x2)))));
	} else if (x1 <= -3.6e-291) {
		tmp = x1 + (x1 + (x2 * (((x1 * -12.0) + ((x1 * x2) * 8.0)) - 6.0)));
	} else {
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + (4.0 * t_0))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x2 * (3.0 - (2.0 * x2))
	tmp = 0
	if x1 <= -5.1e+95:
		tmp = x1 + (6.0 + (x1 + (x1 * ((x1 * ((x1 * -6.0) - 12.0)) - 16.0))))
	elif x1 <= -5.1e-200:
		tmp = x1 + ((x1 - (4.0 * (x1 * t_0))) - (3.0 * (x2 * (2.0 + (x1 / x2)))))
	elif x1 <= -3.6e-291:
		tmp = x1 + (x1 + (x2 * (((x1 * -12.0) + ((x1 * x2) * 8.0)) - 6.0)))
	else:
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + (4.0 * t_0))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x2 * Float64(3.0 - Float64(2.0 * x2)))
	tmp = 0.0
	if (x1 <= -5.1e+95)
		tmp = Float64(x1 + Float64(6.0 + Float64(x1 + Float64(x1 * Float64(Float64(x1 * Float64(Float64(x1 * -6.0) - 12.0)) - 16.0)))));
	elseif (x1 <= -5.1e-200)
		tmp = Float64(x1 + Float64(Float64(x1 - Float64(4.0 * Float64(x1 * t_0))) - Float64(3.0 * Float64(x2 * Float64(2.0 + Float64(x1 / x2))))));
	elseif (x1 <= -3.6e-291)
		tmp = Float64(x1 + Float64(x1 + Float64(x2 * Float64(Float64(Float64(x1 * -12.0) + Float64(Float64(x1 * x2) * 8.0)) - 6.0))));
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) - Float64(x1 * Float64(2.0 + Float64(4.0 * t_0)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x2 * (3.0 - (2.0 * x2));
	tmp = 0.0;
	if (x1 <= -5.1e+95)
		tmp = x1 + (6.0 + (x1 + (x1 * ((x1 * ((x1 * -6.0) - 12.0)) - 16.0))));
	elseif (x1 <= -5.1e-200)
		tmp = x1 + ((x1 - (4.0 * (x1 * t_0))) - (3.0 * (x2 * (2.0 + (x1 / x2)))));
	elseif (x1 <= -3.6e-291)
		tmp = x1 + (x1 + (x2 * (((x1 * -12.0) + ((x1 * x2) * 8.0)) - 6.0)));
	else
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + (4.0 * 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]}, If[LessEqual[x1, -5.1e+95], N[(x1 + N[(6.0 + N[(x1 + N[(x1 * N[(N[(x1 * N[(N[(x1 * -6.0), $MachinePrecision] - 12.0), $MachinePrecision]), $MachinePrecision] - 16.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -5.1e-200], N[(x1 + N[(N[(x1 - N[(4.0 * N[(x1 * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(3.0 * N[(x2 * N[(2.0 + N[(x1 / x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -3.6e-291], N[(x1 + N[(x1 + N[(x2 * N[(N[(N[(x1 * -12.0), $MachinePrecision] + N[(N[(x1 * x2), $MachinePrecision] * 8.0), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] - N[(x1 * N[(2.0 + N[(4.0 * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -5.10000000000000003e95

   1. Initial program 8.7%

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

   3. Taylor expanded in x1 around inf 8.7%

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

   4. Taylor expanded in x1 around 0 20.2%

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

   5. Taylor expanded in x1 around 0 83.2%

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

      1. *-commutative 97.8%

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

   7. Simplified 83.2%

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

   8. Taylor expanded in x2 around 0 91.9%

      \[\leadsto x1 + \color{blue}{\left(6 + \left(x1 + x1 \cdot \left(x1 \cdot \left(-6 \cdot x1 - 12\right) - 16\right)\right)\right)} \]

   if -5.10000000000000003e95 < x1 < -5.0999999999999999e-200

   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 x2 around inf 99.4%

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

      1. +-commutative 99.4%

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

      2. associate--r+ 99.4%

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

      3. associate-*r/ 99.4%

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

      4. div-sub 99.4%

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

      5. fma-neg 99.4%

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

      6. +-commutative 99.4%

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

      7. unpow2 99.4%

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

      8. fma-undefine 99.4%

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

      9. associate-*r/ 99.4%

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

      10. metadata-eval 99.4%

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

      11. +-commutative 99.4%

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

      12. unpow2 99.4%

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

      13. fma-undefine 99.4%

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

   5. Simplified 99.4%

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

   6. Taylor expanded in x1 around 0 98.1%

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

      1. associate-*r/ 98.1%

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

      2. neg-mul-1 98.1%

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

   8. Simplified 98.1%

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

   9. Taylor expanded in x1 around 0 68.4%

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

   10. Taylor expanded in x1 around 0 68.4%

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

   if -5.0999999999999999e-200 < x1 < -3.59999999999999965e-291

   1. Initial program 99.9%

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

   3. Taylor expanded in x1 around 0 67.2%

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

   4. Taylor expanded in x1 around 0 64.2%

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

      1. *-commutative 0.0%

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

   6. Simplified 64.2%

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

   7. Taylor expanded in x2 around 0 96.8%

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

   if -3.59999999999999965e-291 < x1

   1. Initial program 74.1%

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

   3. Taylor expanded in x2 around inf 74.1%

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

      1. +-commutative 74.1%

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

      2. associate--r+ 74.1%

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

      3. associate-*r/ 74.1%

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

      4. div-sub 74.1%

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

      5. fma-neg 74.1%

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

      6. +-commutative 74.1%

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

      7. unpow2 74.1%

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

      8. fma-undefine 74.1%

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

      9. associate-*r/ 74.1%

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

      10. metadata-eval 74.1%

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

      11. +-commutative 74.1%

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

      12. unpow2 74.1%

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

      13. fma-undefine 74.1%

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

   5. Simplified 74.1%

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

   6. Taylor expanded in x1 around 0 73.6%

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

      1. associate-*r/ 73.6%

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

      2. neg-mul-1 73.6%

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

   8. Simplified 73.6%

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

   9. Taylor expanded in x1 around 0 62.1%

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

   10. Taylor expanded in x1 around 0 62.2%

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

4. Final simplification 72.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.1 \cdot 10^{+95}:\\ \;\;\;\;x1 + \left(6 + \left(x1 + x1 \cdot \left(x1 \cdot \left(x1 \cdot -6 - 12\right) - 16\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -5.1 \cdot 10^{-200}:\\ \;\;\;\;x1 + \left(\left(x1 - 4 \cdot \left(x1 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right) - 3 \cdot \left(x2 \cdot \left(2 + \frac{x1}{x2}\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -3.6 \cdot 10^{-291}:\\ \;\;\;\;x1 + \left(x1 + x2 \cdot \left(\left(x1 \cdot -12 + \left(x1 \cdot x2\right) \cdot 8\right) - 6\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 + 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 70.9% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -9.5 \cdot 10^{+95}:\\ \;\;\;\;x1 + \left(6 + \left(x1 + x1 \cdot \left(x1 \cdot \left(x1 \cdot -6 - 12\right) - 16\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -5.9 \cdot 10^{-200} \lor \neg \left(x1 \leq -3.6 \cdot 10^{-291}\right):\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 + 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + x2 \cdot \left(\left(x1 \cdot -12 + \left(x1 \cdot x2\right) \cdot 8\right) - 6\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -9.5e+95)
   (+ x1 (+ 6.0 (+ x1 (* x1 (- (* x1 (- (* x1 -6.0) 12.0)) 16.0)))))
   (if (or (<= x1 -5.9e-200) (not (<= x1 -3.6e-291)))
     (+ x1 (- (* x2 -6.0) (* x1 (+ 2.0 (* 4.0 (* x2 (- 3.0 (* 2.0 x2))))))))
     (+ x1 (+ x1 (* x2 (- (+ (* x1 -12.0) (* (* x1 x2) 8.0)) 6.0)))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -9.5e+95) {
		tmp = x1 + (6.0 + (x1 + (x1 * ((x1 * ((x1 * -6.0) - 12.0)) - 16.0))));
	} else if ((x1 <= -5.9e-200) || !(x1 <= -3.6e-291)) {
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + (4.0 * (x2 * (3.0 - (2.0 * x2)))))));
	} else {
		tmp = x1 + (x1 + (x2 * (((x1 * -12.0) + ((x1 * x2) * 8.0)) - 6.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x1 <= (-9.5d+95)) then
        tmp = x1 + (6.0d0 + (x1 + (x1 * ((x1 * ((x1 * (-6.0d0)) - 12.0d0)) - 16.0d0))))
    else if ((x1 <= (-5.9d-200)) .or. (.not. (x1 <= (-3.6d-291)))) then
        tmp = x1 + ((x2 * (-6.0d0)) - (x1 * (2.0d0 + (4.0d0 * (x2 * (3.0d0 - (2.0d0 * x2)))))))
    else
        tmp = x1 + (x1 + (x2 * (((x1 * (-12.0d0)) + ((x1 * x2) * 8.0d0)) - 6.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= -9.5e+95) {
		tmp = x1 + (6.0 + (x1 + (x1 * ((x1 * ((x1 * -6.0) - 12.0)) - 16.0))));
	} else if ((x1 <= -5.9e-200) || !(x1 <= -3.6e-291)) {
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + (4.0 * (x2 * (3.0 - (2.0 * x2)))))));
	} else {
		tmp = x1 + (x1 + (x2 * (((x1 * -12.0) + ((x1 * x2) * 8.0)) - 6.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -9.5e+95:
		tmp = x1 + (6.0 + (x1 + (x1 * ((x1 * ((x1 * -6.0) - 12.0)) - 16.0))))
	elif (x1 <= -5.9e-200) or not (x1 <= -3.6e-291):
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + (4.0 * (x2 * (3.0 - (2.0 * x2)))))))
	else:
		tmp = x1 + (x1 + (x2 * (((x1 * -12.0) + ((x1 * x2) * 8.0)) - 6.0)))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -9.5e+95)
		tmp = Float64(x1 + Float64(6.0 + Float64(x1 + Float64(x1 * Float64(Float64(x1 * Float64(Float64(x1 * -6.0) - 12.0)) - 16.0)))));
	elseif ((x1 <= -5.9e-200) || !(x1 <= -3.6e-291))
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) - Float64(x1 * Float64(2.0 + Float64(4.0 * Float64(x2 * Float64(3.0 - Float64(2.0 * x2))))))));
	else
		tmp = Float64(x1 + Float64(x1 + Float64(x2 * Float64(Float64(Float64(x1 * -12.0) + Float64(Float64(x1 * x2) * 8.0)) - 6.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -9.5e+95)
		tmp = x1 + (6.0 + (x1 + (x1 * ((x1 * ((x1 * -6.0) - 12.0)) - 16.0))));
	elseif ((x1 <= -5.9e-200) || ~((x1 <= -3.6e-291)))
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + (4.0 * (x2 * (3.0 - (2.0 * x2)))))));
	else
		tmp = x1 + (x1 + (x2 * (((x1 * -12.0) + ((x1 * x2) * 8.0)) - 6.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -9.5e+95], N[(x1 + N[(6.0 + N[(x1 + N[(x1 * N[(N[(x1 * N[(N[(x1 * -6.0), $MachinePrecision] - 12.0), $MachinePrecision]), $MachinePrecision] - 16.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x1, -5.9e-200], N[Not[LessEqual[x1, -3.6e-291]], $MachinePrecision]], 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], N[(x1 + N[(x1 + N[(x2 * N[(N[(N[(x1 * -12.0), $MachinePrecision] + N[(N[(x1 * x2), $MachinePrecision] * 8.0), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -9.5000000000000004e95

   1. Initial program 8.7%

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

   3. Taylor expanded in x1 around inf 8.7%

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

   4. Taylor expanded in x1 around 0 20.2%

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

   5. Taylor expanded in x1 around 0 83.2%

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

      1. *-commutative 97.8%

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

   7. Simplified 83.2%

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

   8. Taylor expanded in x2 around 0 91.9%

      \[\leadsto x1 + \color{blue}{\left(6 + \left(x1 + x1 \cdot \left(x1 \cdot \left(-6 \cdot x1 - 12\right) - 16\right)\right)\right)} \]

   if -9.5000000000000004e95 < x1 < -5.90000000000000053e-200 or -3.59999999999999965e-291 < x1

   1. Initial program 83.1%

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

   3. Taylor expanded in x2 around inf 83.1%

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

      1. +-commutative 83.1%

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

      2. associate--r+ 83.1%

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

      3. associate-*r/ 83.1%

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

      4. div-sub 83.1%

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

      5. fma-neg 83.1%

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

      6. +-commutative 83.1%

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

      7. unpow2 83.1%

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

      8. fma-undefine 83.1%

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

      9. associate-*r/ 83.1%

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

      10. metadata-eval 83.1%

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

      11. +-commutative 83.1%

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

      12. unpow2 83.1%

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

      13. fma-undefine 83.1%

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

   5. Simplified 83.1%

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

   6. Taylor expanded in x1 around 0 82.3%

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

      1. associate-*r/ 82.3%

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

      2. neg-mul-1 82.3%

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

   8. Simplified 82.3%

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

   9. Taylor expanded in x1 around 0 64.3%

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

   10. Taylor expanded in x1 around 0 64.0%

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

   if -5.90000000000000053e-200 < x1 < -3.59999999999999965e-291

   1. Initial program 99.9%

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

   3. Taylor expanded in x1 around 0 67.2%

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

   4. Taylor expanded in x1 around 0 64.2%

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

      1. *-commutative 0.0%

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

   6. Simplified 64.2%

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

   7. Taylor expanded in x2 around 0 96.8%

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

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -9.5 \cdot 10^{+95}:\\ \;\;\;\;x1 + \left(6 + \left(x1 + x1 \cdot \left(x1 \cdot \left(x1 \cdot -6 - 12\right) - 16\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -5.9 \cdot 10^{-200} \lor \neg \left(x1 \leq -3.6 \cdot 10^{-291}\right):\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 + 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + x2 \cdot \left(\left(x1 \cdot -12 + \left(x1 \cdot x2\right) \cdot 8\right) - 6\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 70.9% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x2 \cdot \left(3 - 2 \cdot x2\right)\\ \mathbf{if}\;x1 \leq -2.25 \cdot 10^{+95}:\\ \;\;\;\;x1 + \left(6 + \left(x1 + x1 \cdot \left(x1 \cdot \left(x1 \cdot -6 - 12\right) - 16\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -1.52 \cdot 10^{-200}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2 - x1\right) - \left(4 \cdot \left(x1 \cdot t\_0\right) - x1\right)\right)\\ \mathbf{elif}\;x1 \leq -5.8 \cdot 10^{-291}:\\ \;\;\;\;x1 + \left(x1 + x2 \cdot \left(\left(x1 \cdot -12 + \left(x1 \cdot x2\right) \cdot 8\right) - 6\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 + 4 \cdot t\_0\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x2 (- 3.0 (* 2.0 x2)))))
   (if (<= x1 -2.25e+95)
     (+ x1 (+ 6.0 (+ x1 (* x1 (- (* x1 (- (* x1 -6.0) 12.0)) 16.0)))))
     (if (<= x1 -1.52e-200)
       (+ x1 (- (* 3.0 (- (* x2 -2.0) x1)) (- (* 4.0 (* x1 t_0)) x1)))
       (if (<= x1 -5.8e-291)
         (+ x1 (+ x1 (* x2 (- (+ (* x1 -12.0) (* (* x1 x2) 8.0)) 6.0))))
         (+ x1 (- (* x2 -6.0) (* x1 (+ 2.0 (* 4.0 t_0))))))))))

C

double code(double x1, double x2) {
	double t_0 = x2 * (3.0 - (2.0 * x2));
	double tmp;
	if (x1 <= -2.25e+95) {
		tmp = x1 + (6.0 + (x1 + (x1 * ((x1 * ((x1 * -6.0) - 12.0)) - 16.0))));
	} else if (x1 <= -1.52e-200) {
		tmp = x1 + ((3.0 * ((x2 * -2.0) - x1)) - ((4.0 * (x1 * t_0)) - x1));
	} else if (x1 <= -5.8e-291) {
		tmp = x1 + (x1 + (x2 * (((x1 * -12.0) + ((x1 * x2) * 8.0)) - 6.0)));
	} else {
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + (4.0 * t_0))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x2 * (3.0d0 - (2.0d0 * x2))
    if (x1 <= (-2.25d+95)) then
        tmp = x1 + (6.0d0 + (x1 + (x1 * ((x1 * ((x1 * (-6.0d0)) - 12.0d0)) - 16.0d0))))
    else if (x1 <= (-1.52d-200)) then
        tmp = x1 + ((3.0d0 * ((x2 * (-2.0d0)) - x1)) - ((4.0d0 * (x1 * t_0)) - x1))
    else if (x1 <= (-5.8d-291)) then
        tmp = x1 + (x1 + (x2 * (((x1 * (-12.0d0)) + ((x1 * x2) * 8.0d0)) - 6.0d0)))
    else
        tmp = x1 + ((x2 * (-6.0d0)) - (x1 * (2.0d0 + (4.0d0 * 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 tmp;
	if (x1 <= -2.25e+95) {
		tmp = x1 + (6.0 + (x1 + (x1 * ((x1 * ((x1 * -6.0) - 12.0)) - 16.0))));
	} else if (x1 <= -1.52e-200) {
		tmp = x1 + ((3.0 * ((x2 * -2.0) - x1)) - ((4.0 * (x1 * t_0)) - x1));
	} else if (x1 <= -5.8e-291) {
		tmp = x1 + (x1 + (x2 * (((x1 * -12.0) + ((x1 * x2) * 8.0)) - 6.0)));
	} else {
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + (4.0 * t_0))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x2 * (3.0 - (2.0 * x2))
	tmp = 0
	if x1 <= -2.25e+95:
		tmp = x1 + (6.0 + (x1 + (x1 * ((x1 * ((x1 * -6.0) - 12.0)) - 16.0))))
	elif x1 <= -1.52e-200:
		tmp = x1 + ((3.0 * ((x2 * -2.0) - x1)) - ((4.0 * (x1 * t_0)) - x1))
	elif x1 <= -5.8e-291:
		tmp = x1 + (x1 + (x2 * (((x1 * -12.0) + ((x1 * x2) * 8.0)) - 6.0)))
	else:
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + (4.0 * t_0))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x2 * Float64(3.0 - Float64(2.0 * x2)))
	tmp = 0.0
	if (x1 <= -2.25e+95)
		tmp = Float64(x1 + Float64(6.0 + Float64(x1 + Float64(x1 * Float64(Float64(x1 * Float64(Float64(x1 * -6.0) - 12.0)) - 16.0)))));
	elseif (x1 <= -1.52e-200)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(x2 * -2.0) - x1)) - Float64(Float64(4.0 * Float64(x1 * t_0)) - x1)));
	elseif (x1 <= -5.8e-291)
		tmp = Float64(x1 + Float64(x1 + Float64(x2 * Float64(Float64(Float64(x1 * -12.0) + Float64(Float64(x1 * x2) * 8.0)) - 6.0))));
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) - Float64(x1 * Float64(2.0 + Float64(4.0 * t_0)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x2 * (3.0 - (2.0 * x2));
	tmp = 0.0;
	if (x1 <= -2.25e+95)
		tmp = x1 + (6.0 + (x1 + (x1 * ((x1 * ((x1 * -6.0) - 12.0)) - 16.0))));
	elseif (x1 <= -1.52e-200)
		tmp = x1 + ((3.0 * ((x2 * -2.0) - x1)) - ((4.0 * (x1 * t_0)) - x1));
	elseif (x1 <= -5.8e-291)
		tmp = x1 + (x1 + (x2 * (((x1 * -12.0) + ((x1 * x2) * 8.0)) - 6.0)));
	else
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + (4.0 * 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]}, If[LessEqual[x1, -2.25e+95], N[(x1 + N[(6.0 + N[(x1 + N[(x1 * N[(N[(x1 * N[(N[(x1 * -6.0), $MachinePrecision] - 12.0), $MachinePrecision]), $MachinePrecision] - 16.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -1.52e-200], N[(x1 + N[(N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision] - N[(N[(4.0 * N[(x1 * t$95$0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -5.8e-291], N[(x1 + N[(x1 + N[(x2 * N[(N[(N[(x1 * -12.0), $MachinePrecision] + N[(N[(x1 * x2), $MachinePrecision] * 8.0), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] - N[(x1 * N[(2.0 + N[(4.0 * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -2.25000000000000008e95

   1. Initial program 8.7%

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

   3. Taylor expanded in x1 around inf 8.7%

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

   4. Taylor expanded in x1 around 0 20.2%

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

   5. Taylor expanded in x1 around 0 83.2%

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

      1. *-commutative 97.8%

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

   7. Simplified 83.2%

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

   8. Taylor expanded in x2 around 0 91.9%

      \[\leadsto x1 + \color{blue}{\left(6 + \left(x1 + x1 \cdot \left(x1 \cdot \left(-6 \cdot x1 - 12\right) - 16\right)\right)\right)} \]

   if -2.25000000000000008e95 < x1 < -1.52e-200

   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 67.5%

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

   4. Taylor expanded in x1 around 0 68.3%

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

      1. neg-mul-1 68.3%

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

      2. unsub-neg 68.3%

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

      3. *-commutative 68.3%

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

   6. Simplified 68.3%

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

   if -1.52e-200 < x1 < -5.80000000000000003e-291

   1. Initial program 99.9%

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

   3. Taylor expanded in x1 around 0 67.2%

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

   4. Taylor expanded in x1 around 0 64.2%

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

      1. *-commutative 0.0%

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

   6. Simplified 64.2%

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

   7. Taylor expanded in x2 around 0 96.8%

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

   if -5.80000000000000003e-291 < x1

   1. Initial program 74.1%

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

   3. Taylor expanded in x2 around inf 74.1%

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

      1. +-commutative 74.1%

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

      2. associate--r+ 74.1%

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

      3. associate-*r/ 74.1%

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

      4. div-sub 74.1%

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

      5. fma-neg 74.1%

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

      6. +-commutative 74.1%

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

      7. unpow2 74.1%

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

      8. fma-undefine 74.1%

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

      9. associate-*r/ 74.1%

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

      10. metadata-eval 74.1%

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

      11. +-commutative 74.1%

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

      12. unpow2 74.1%

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

      13. fma-undefine 74.1%

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

   5. Simplified 74.1%

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

   6. Taylor expanded in x1 around 0 73.6%

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

      1. associate-*r/ 73.6%

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

      2. neg-mul-1 73.6%

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

   8. Simplified 73.6%

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

   9. Taylor expanded in x1 around 0 62.1%

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

   10. Taylor expanded in x1 around 0 62.2%

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

4. Final simplification 72.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -2.25 \cdot 10^{+95}:\\ \;\;\;\;x1 + \left(6 + \left(x1 + x1 \cdot \left(x1 \cdot \left(x1 \cdot -6 - 12\right) - 16\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -1.52 \cdot 10^{-200}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2 - x1\right) - \left(4 \cdot \left(x1 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right) - x1\right)\right)\\ \mathbf{elif}\;x1 \leq -5.8 \cdot 10^{-291}:\\ \;\;\;\;x1 + \left(x1 + x2 \cdot \left(\left(x1 \cdot -12 + \left(x1 \cdot x2\right) \cdot 8\right) - 6\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 + 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 56.1% accurate, 4.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -7.8 \cdot 10^{+95}:\\ \;\;\;\;x1 + \left(6 + \left(x1 + x1 \cdot \left(x1 \cdot \left(x1 \cdot -6 - 12\right) - 16\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -1.6 \cdot 10^{-69} \lor \neg \left(x1 \leq 3 \cdot 10^{-93}\right):\\ \;\;\;\;x1 + x1 \cdot \left(1 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x2 \cdot -6\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -7.8e+95)
   (+ x1 (+ 6.0 (+ x1 (* x1 (- (* x1 (- (* x1 -6.0) 12.0)) 16.0)))))
   (if (or (<= x1 -1.6e-69) (not (<= x1 3e-93)))
     (+ x1 (* x1 (+ 1.0 (* 4.0 (* x2 (- (* 2.0 x2) 3.0))))))
     (+ x1 (* x2 -6.0)))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -7.8e+95) {
		tmp = x1 + (6.0 + (x1 + (x1 * ((x1 * ((x1 * -6.0) - 12.0)) - 16.0))));
	} else if ((x1 <= -1.6e-69) || !(x1 <= 3e-93)) {
		tmp = x1 + (x1 * (1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0)))));
	} 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 <= (-7.8d+95)) then
        tmp = x1 + (6.0d0 + (x1 + (x1 * ((x1 * ((x1 * (-6.0d0)) - 12.0d0)) - 16.0d0))))
    else if ((x1 <= (-1.6d-69)) .or. (.not. (x1 <= 3d-93))) then
        tmp = x1 + (x1 * (1.0d0 + (4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0)))))
    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 <= -7.8e+95) {
		tmp = x1 + (6.0 + (x1 + (x1 * ((x1 * ((x1 * -6.0) - 12.0)) - 16.0))));
	} else if ((x1 <= -1.6e-69) || !(x1 <= 3e-93)) {
		tmp = x1 + (x1 * (1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0)))));
	} else {
		tmp = x1 + (x2 * -6.0);
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -7.8e+95:
		tmp = x1 + (6.0 + (x1 + (x1 * ((x1 * ((x1 * -6.0) - 12.0)) - 16.0))))
	elif (x1 <= -1.6e-69) or not (x1 <= 3e-93):
		tmp = x1 + (x1 * (1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0)))))
	else:
		tmp = x1 + (x2 * -6.0)
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -7.8e+95)
		tmp = Float64(x1 + Float64(6.0 + Float64(x1 + Float64(x1 * Float64(Float64(x1 * Float64(Float64(x1 * -6.0) - 12.0)) - 16.0)))));
	elseif ((x1 <= -1.6e-69) || !(x1 <= 3e-93))
		tmp = Float64(x1 + Float64(x1 * Float64(1.0 + Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0))))));
	else
		tmp = Float64(x1 + Float64(x2 * -6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -7.8e+95)
		tmp = x1 + (6.0 + (x1 + (x1 * ((x1 * ((x1 * -6.0) - 12.0)) - 16.0))));
	elseif ((x1 <= -1.6e-69) || ~((x1 <= 3e-93)))
		tmp = x1 + (x1 * (1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0)))));
	else
		tmp = x1 + (x2 * -6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -7.8e+95], N[(x1 + N[(6.0 + N[(x1 + N[(x1 * N[(N[(x1 * N[(N[(x1 * -6.0), $MachinePrecision] - 12.0), $MachinePrecision]), $MachinePrecision] - 16.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x1, -1.6e-69], N[Not[LessEqual[x1, 3e-93]], $MachinePrecision]], N[(x1 + N[(x1 * N[(1.0 + N[(4.0 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -7.7999999999999994e95

   1. Initial program 8.7%

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

   3. Taylor expanded in x1 around inf 8.7%

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

   4. Taylor expanded in x1 around 0 20.2%

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

   5. Taylor expanded in x1 around 0 83.2%

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

      1. *-commutative 97.8%

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

   7. Simplified 83.2%

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

   8. Taylor expanded in x2 around 0 91.9%

      \[\leadsto x1 + \color{blue}{\left(6 + \left(x1 + x1 \cdot \left(x1 \cdot \left(-6 \cdot x1 - 12\right) - 16\right)\right)\right)} \]

   if -7.7999999999999994e95 < x1 < -1.59999999999999999e-69 or 3.0000000000000001e-93 < x1

   1. Initial program 69.7%

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

   3. Taylor expanded in x1 around 0 35.9%

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

   4. Taylor expanded in x1 around 0 39.0%

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

      1. *-commutative 74.6%

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

   6. Simplified 39.0%

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

   7. Taylor expanded in x1 around inf 34.6%

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

   if -1.59999999999999999e-69 < x1 < 3.0000000000000001e-93

   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 86.1%

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

   4. Taylor expanded in x1 around 0 68.9%

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

      1. *-commutative 12.5%

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

   6. Simplified 68.9%

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

   7. Taylor expanded in x1 around 0 69.1%

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

      1. *-commutative 69.1%

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

   9. Simplified 69.1%

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

4. Final simplification 59.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -7.8 \cdot 10^{+95}:\\ \;\;\;\;x1 + \left(6 + \left(x1 + x1 \cdot \left(x1 \cdot \left(x1 \cdot -6 - 12\right) - 16\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -1.6 \cdot 10^{-69} \lor \neg \left(x1 \leq 3 \cdot 10^{-93}\right):\\ \;\;\;\;x1 + x1 \cdot \left(1 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x2 \cdot -6\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 47.3% accurate, 4.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -2.45 \cdot 10^{+65}:\\ \;\;\;\;x1 + x2 \cdot \left(x1 \cdot \left(12 + x1 \cdot 14\right) - 10\right)\\ \mathbf{elif}\;x1 \leq -1.75 \cdot 10^{-68} \lor \neg \left(x1 \leq 9.5 \cdot 10^{-93}\right):\\ \;\;\;\;x1 + x1 \cdot \left(1 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x2 \cdot -6\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -2.45e+65)
   (+ x1 (* x2 (- (* x1 (+ 12.0 (* x1 14.0))) 10.0)))
   (if (or (<= x1 -1.75e-68) (not (<= x1 9.5e-93)))
     (+ x1 (* x1 (+ 1.0 (* 4.0 (* x2 (- (* 2.0 x2) 3.0))))))
     (+ x1 (* x2 -6.0)))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -2.45e+65) {
		tmp = x1 + (x2 * ((x1 * (12.0 + (x1 * 14.0))) - 10.0));
	} else if ((x1 <= -1.75e-68) || !(x1 <= 9.5e-93)) {
		tmp = x1 + (x1 * (1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0)))));
	} 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 <= (-2.45d+65)) then
        tmp = x1 + (x2 * ((x1 * (12.0d0 + (x1 * 14.0d0))) - 10.0d0))
    else if ((x1 <= (-1.75d-68)) .or. (.not. (x1 <= 9.5d-93))) then
        tmp = x1 + (x1 * (1.0d0 + (4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0)))))
    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 <= -2.45e+65) {
		tmp = x1 + (x2 * ((x1 * (12.0 + (x1 * 14.0))) - 10.0));
	} else if ((x1 <= -1.75e-68) || !(x1 <= 9.5e-93)) {
		tmp = x1 + (x1 * (1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0)))));
	} else {
		tmp = x1 + (x2 * -6.0);
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -2.45e+65:
		tmp = x1 + (x2 * ((x1 * (12.0 + (x1 * 14.0))) - 10.0))
	elif (x1 <= -1.75e-68) or not (x1 <= 9.5e-93):
		tmp = x1 + (x1 * (1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0)))))
	else:
		tmp = x1 + (x2 * -6.0)
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -2.45e+65)
		tmp = Float64(x1 + Float64(x2 * Float64(Float64(x1 * Float64(12.0 + Float64(x1 * 14.0))) - 10.0)));
	elseif ((x1 <= -1.75e-68) || !(x1 <= 9.5e-93))
		tmp = Float64(x1 + Float64(x1 * Float64(1.0 + Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0))))));
	else
		tmp = Float64(x1 + Float64(x2 * -6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -2.45e+65)
		tmp = x1 + (x2 * ((x1 * (12.0 + (x1 * 14.0))) - 10.0));
	elseif ((x1 <= -1.75e-68) || ~((x1 <= 9.5e-93)))
		tmp = x1 + (x1 * (1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0)))));
	else
		tmp = x1 + (x2 * -6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -2.45e+65], N[(x1 + N[(x2 * N[(N[(x1 * N[(12.0 + N[(x1 * 14.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 10.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x1, -1.75e-68], N[Not[LessEqual[x1, 9.5e-93]], $MachinePrecision]], N[(x1 + N[(x1 * N[(1.0 + N[(4.0 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -2.44999999999999978e65

   1. Initial program 20.7%

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

   3. Taylor expanded in x1 around inf 20.7%

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

   4. Taylor expanded in x1 around 0 22.0%

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

   5. Taylor expanded in x1 around 0 76.7%

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

      1. *-commutative 98.1%

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

   7. Simplified 76.7%

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

   8. Taylor expanded in x2 around inf 42.2%

      \[\leadsto x1 + \color{blue}{x2 \cdot \left(x1 \cdot \left(12 + 14 \cdot x1\right) - 10\right)} \]

   if -2.44999999999999978e65 < x1 < -1.75000000000000006e-68 or 9.5000000000000001e-93 < x1

   1. Initial program 67.6%

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

   3. Taylor expanded in x1 around 0 37.4%

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

   4. Taylor expanded in x1 around 0 40.8%

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

      1. *-commutative 72.8%

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

   6. Simplified 40.8%

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

   7. Taylor expanded in x1 around inf 36.0%

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

   if -1.75000000000000006e-68 < x1 < 9.5000000000000001e-93

   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 86.1%

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

   4. Taylor expanded in x1 around 0 68.9%

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

      1. *-commutative 12.5%

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

   6. Simplified 68.9%

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

   7. Taylor expanded in x1 around 0 69.1%

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

      1. *-commutative 69.1%

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

   9. Simplified 69.1%

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

4. Final simplification 51.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -2.45 \cdot 10^{+65}:\\ \;\;\;\;x1 + x2 \cdot \left(x1 \cdot \left(12 + x1 \cdot 14\right) - 10\right)\\ \mathbf{elif}\;x1 \leq -1.75 \cdot 10^{-68} \lor \neg \left(x1 \leq 9.5 \cdot 10^{-93}\right):\\ \;\;\;\;x1 + x1 \cdot \left(1 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x2 \cdot -6\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 42.4% accurate, 4.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 + x2 \cdot \left(x1 \cdot \left(12 + x1 \cdot 14\right) - 10\right)\\ \mathbf{if}\;x1 \leq -3.8 \cdot 10^{-42}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x1 \leq 6.2 \cdot 10^{-94}:\\ \;\;\;\;x1 + x2 \cdot -6\\ \mathbf{elif}\;x1 \leq 10^{-29}:\\ \;\;\;\;x1 + x1 \cdot -2\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ x1 (* x2 (- (* x1 (+ 12.0 (* x1 14.0))) 10.0)))))
   (if (<= x1 -3.8e-42)
     t_0
     (if (<= x1 6.2e-94)
       (+ x1 (* x2 -6.0))
       (if (<= x1 1e-29) (+ x1 (* x1 -2.0)) t_0)))))

C

double code(double x1, double x2) {
	double t_0 = x1 + (x2 * ((x1 * (12.0 + (x1 * 14.0))) - 10.0));
	double tmp;
	if (x1 <= -3.8e-42) {
		tmp = t_0;
	} else if (x1 <= 6.2e-94) {
		tmp = x1 + (x2 * -6.0);
	} else if (x1 <= 1e-29) {
		tmp = x1 + (x1 * -2.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x1 + (x2 * ((x1 * (12.0d0 + (x1 * 14.0d0))) - 10.0d0))
    if (x1 <= (-3.8d-42)) then
        tmp = t_0
    else if (x1 <= 6.2d-94) then
        tmp = x1 + (x2 * (-6.0d0))
    else if (x1 <= 1d-29) then
        tmp = x1 + (x1 * (-2.0d0))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 + (x2 * ((x1 * (12.0 + (x1 * 14.0))) - 10.0));
	double tmp;
	if (x1 <= -3.8e-42) {
		tmp = t_0;
	} else if (x1 <= 6.2e-94) {
		tmp = x1 + (x2 * -6.0);
	} else if (x1 <= 1e-29) {
		tmp = x1 + (x1 * -2.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 + (x2 * ((x1 * (12.0 + (x1 * 14.0))) - 10.0))
	tmp = 0
	if x1 <= -3.8e-42:
		tmp = t_0
	elif x1 <= 6.2e-94:
		tmp = x1 + (x2 * -6.0)
	elif x1 <= 1e-29:
		tmp = x1 + (x1 * -2.0)
	else:
		tmp = t_0
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 + Float64(x2 * Float64(Float64(x1 * Float64(12.0 + Float64(x1 * 14.0))) - 10.0)))
	tmp = 0.0
	if (x1 <= -3.8e-42)
		tmp = t_0;
	elseif (x1 <= 6.2e-94)
		tmp = Float64(x1 + Float64(x2 * -6.0));
	elseif (x1 <= 1e-29)
		tmp = Float64(x1 + Float64(x1 * -2.0));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 + (x2 * ((x1 * (12.0 + (x1 * 14.0))) - 10.0));
	tmp = 0.0;
	if (x1 <= -3.8e-42)
		tmp = t_0;
	elseif (x1 <= 6.2e-94)
		tmp = x1 + (x2 * -6.0);
	elseif (x1 <= 1e-29)
		tmp = x1 + (x1 * -2.0);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 + N[(x2 * N[(N[(x1 * N[(12.0 + N[(x1 * 14.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 10.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -3.8e-42], t$95$0, If[LessEqual[x1, 6.2e-94], N[(x1 + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1e-29], N[(x1 + N[(x1 * -2.0), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -3.80000000000000017e-42 or 9.99999999999999943e-30 < x1

   1. Initial program 43.1%

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

   3. Taylor expanded in x1 around inf 34.5%

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

   4. Taylor expanded in x1 around 0 15.0%

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

   5. Taylor expanded in x1 around 0 39.8%

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

      1. *-commutative 91.2%

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

   7. Simplified 39.8%

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

   8. Taylor expanded in x2 around inf 30.8%

      \[\leadsto x1 + \color{blue}{x2 \cdot \left(x1 \cdot \left(12 + 14 \cdot x1\right) - 10\right)} \]

   if -3.80000000000000017e-42 < x1 < 6.1999999999999996e-94

   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 86.9%

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

   4. Taylor expanded in x1 around 0 70.8%

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

      1. *-commutative 15.3%

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

   6. Simplified 70.8%

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

   7. Taylor expanded in x1 around 0 66.8%

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

      1. *-commutative 66.8%

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

   9. Simplified 66.8%

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

   if 6.1999999999999996e-94 < x1 < 9.99999999999999943e-30

   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 x2 around inf 98.7%

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

      1. +-commutative 98.7%

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

      2. associate--r+ 98.7%

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

      3. associate-*r/ 98.7%

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

      4. div-sub 98.7%

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

      5. fma-neg 98.7%

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

      6. +-commutative 98.7%

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

      7. unpow2 98.7%

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

      8. fma-undefine 98.7%

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

      9. associate-*r/ 98.7%

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

      10. metadata-eval 98.7%

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

      11. +-commutative 98.7%

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

      12. unpow2 98.7%

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

      13. fma-undefine 98.7%

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

   5. Simplified 98.7%

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

   6. Taylor expanded in x1 around 0 98.7%

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

      1. associate-*r/ 98.7%

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

      2. neg-mul-1 98.7%

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

   8. Simplified 98.7%

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

   9. Taylor expanded in x1 around 0 79.5%

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

   10. Taylor expanded in x2 around 0 36.7%

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

       1. distribute-rgt1-in 37.1%

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

       2. metadata-eval 37.1%

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

   12. Simplified 37.1%

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

4. Final simplification 47.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -3.8 \cdot 10^{-42}:\\ \;\;\;\;x1 + x2 \cdot \left(x1 \cdot \left(12 + x1 \cdot 14\right) - 10\right)\\ \mathbf{elif}\;x1 \leq 6.2 \cdot 10^{-94}:\\ \;\;\;\;x1 + x2 \cdot -6\\ \mathbf{elif}\;x1 \leq 10^{-29}:\\ \;\;\;\;x1 + x1 \cdot -2\\ \mathbf{else}:\\ \;\;\;\;x1 + x2 \cdot \left(x1 \cdot \left(12 + x1 \cdot 14\right) - 10\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 32.7% accurate, 4.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x2 \cdot \left(x1 \cdot 12 - 10\right)\\ \mathbf{if}\;x1 \leq -1.15 \cdot 10^{-42}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{-94}:\\ \;\;\;\;x1 + x2 \cdot -6\\ \mathbf{elif}\;x1 \leq 10^{-29}:\\ \;\;\;\;x1 + x1 \cdot -2\\ \mathbf{elif}\;x1 \leq 8.6 \cdot 10^{+53}:\\ \;\;\;\;x1 + x1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x2 (- (* x1 12.0) 10.0))))
   (if (<= x1 -1.15e-42)
     t_0
     (if (<= x1 5e-94)
       (+ x1 (* x2 -6.0))
       (if (<= x1 1e-29)
         (+ x1 (* x1 -2.0))
         (if (<= x1 8.6e+53) (+ x1 x1) t_0))))))

C

double code(double x1, double x2) {
	double t_0 = x2 * ((x1 * 12.0) - 10.0);
	double tmp;
	if (x1 <= -1.15e-42) {
		tmp = t_0;
	} else if (x1 <= 5e-94) {
		tmp = x1 + (x2 * -6.0);
	} else if (x1 <= 1e-29) {
		tmp = x1 + (x1 * -2.0);
	} else if (x1 <= 8.6e+53) {
		tmp = x1 + x1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x2 * ((x1 * 12.0d0) - 10.0d0)
    if (x1 <= (-1.15d-42)) then
        tmp = t_0
    else if (x1 <= 5d-94) then
        tmp = x1 + (x2 * (-6.0d0))
    else if (x1 <= 1d-29) then
        tmp = x1 + (x1 * (-2.0d0))
    else if (x1 <= 8.6d+53) then
        tmp = x1 + x1
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x2 * ((x1 * 12.0) - 10.0);
	double tmp;
	if (x1 <= -1.15e-42) {
		tmp = t_0;
	} else if (x1 <= 5e-94) {
		tmp = x1 + (x2 * -6.0);
	} else if (x1 <= 1e-29) {
		tmp = x1 + (x1 * -2.0);
	} else if (x1 <= 8.6e+53) {
		tmp = x1 + x1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x2 * ((x1 * 12.0) - 10.0)
	tmp = 0
	if x1 <= -1.15e-42:
		tmp = t_0
	elif x1 <= 5e-94:
		tmp = x1 + (x2 * -6.0)
	elif x1 <= 1e-29:
		tmp = x1 + (x1 * -2.0)
	elif x1 <= 8.6e+53:
		tmp = x1 + x1
	else:
		tmp = t_0
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x2 * Float64(Float64(x1 * 12.0) - 10.0))
	tmp = 0.0
	if (x1 <= -1.15e-42)
		tmp = t_0;
	elseif (x1 <= 5e-94)
		tmp = Float64(x1 + Float64(x2 * -6.0));
	elseif (x1 <= 1e-29)
		tmp = Float64(x1 + Float64(x1 * -2.0));
	elseif (x1 <= 8.6e+53)
		tmp = Float64(x1 + x1);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x2 * ((x1 * 12.0) - 10.0);
	tmp = 0.0;
	if (x1 <= -1.15e-42)
		tmp = t_0;
	elseif (x1 <= 5e-94)
		tmp = x1 + (x2 * -6.0);
	elseif (x1 <= 1e-29)
		tmp = x1 + (x1 * -2.0);
	elseif (x1 <= 8.6e+53)
		tmp = x1 + x1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x2 * N[(N[(x1 * 12.0), $MachinePrecision] - 10.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -1.15e-42], t$95$0, If[LessEqual[x1, 5e-94], N[(x1 + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1e-29], N[(x1 + N[(x1 * -2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 8.6e+53], N[(x1 + x1), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -1.15000000000000002e-42 or 8.5999999999999995e53 < x1

   1. Initial program 36.9%

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

   3. Taylor expanded in x1 around inf 32.8%

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

   4. Taylor expanded in x1 around 0 6.5%

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

   5. Taylor expanded in x1 around 0 17.3%

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

   6. Taylor expanded in x2 around inf 16.4%

      \[\leadsto \color{blue}{x2 \cdot \left(12 \cdot x1 - 10\right)} \]

   if -1.15000000000000002e-42 < x1 < 4.9999999999999995e-94

   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 86.8%

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

   4. Taylor expanded in x1 around 0 71.4%

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

      1. *-commutative 15.4%

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

   6. Simplified 71.4%

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

   7. Taylor expanded in x1 around 0 67.3%

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

      1. *-commutative 67.3%

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

   9. Simplified 67.3%

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

   if 4.9999999999999995e-94 < x1 < 9.99999999999999943e-30

   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 x2 around inf 98.7%

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

      1. +-commutative 98.7%

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

      2. associate--r+ 98.7%

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

      3. associate-*r/ 98.7%

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

      4. div-sub 98.7%

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

      5. fma-neg 98.7%

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

      6. +-commutative 98.7%

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

      7. unpow2 98.7%

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

      8. fma-undefine 98.7%

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

      9. associate-*r/ 98.7%

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

      10. metadata-eval 98.7%

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

      11. +-commutative 98.7%

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

      12. unpow2 98.7%

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

      13. fma-undefine 98.7%

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

   5. Simplified 98.7%

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

   6. Taylor expanded in x1 around 0 98.7%

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

      1. associate-*r/ 98.7%

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

      2. neg-mul-1 98.7%

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

   8. Simplified 98.7%

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

   9. Taylor expanded in x1 around 0 79.5%

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

   10. Taylor expanded in x2 around 0 36.7%

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

       1. distribute-rgt1-in 37.1%

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

       2. metadata-eval 37.1%

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

   12. Simplified 37.1%

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

   if 9.99999999999999943e-30 < x1 < 8.5999999999999995e53

   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 40.4%

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

   4. Taylor expanded in x1 around 0 40.4%

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

      1. *-commutative 54.0%

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

   6. Simplified 40.4%

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

   7. Taylor expanded in x2 around 0 5.0%

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

4. Final simplification 39.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.15 \cdot 10^{-42}:\\ \;\;\;\;x2 \cdot \left(x1 \cdot 12 - 10\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{-94}:\\ \;\;\;\;x1 + x2 \cdot -6\\ \mathbf{elif}\;x1 \leq 10^{-29}:\\ \;\;\;\;x1 + x1 \cdot -2\\ \mathbf{elif}\;x1 \leq 8.6 \cdot 10^{+53}:\\ \;\;\;\;x1 + x1\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot \left(x1 \cdot 12 - 10\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 65.0% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -1.22 \cdot 10^{+95}:\\ \;\;\;\;x1 + \left(6 + \left(x1 + x1 \cdot \left(x1 \cdot \left(x1 \cdot -6 - 12\right) - 16\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + x2 \cdot \left(\left(x1 \cdot -12 + \left(x1 \cdot x2\right) \cdot 8\right) - 6\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -1.22e+95)
   (+ x1 (+ 6.0 (+ x1 (* x1 (- (* x1 (- (* x1 -6.0) 12.0)) 16.0)))))
   (+ x1 (+ x1 (* x2 (- (+ (* x1 -12.0) (* (* x1 x2) 8.0)) 6.0))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -1.22e+95) {
		tmp = x1 + (6.0 + (x1 + (x1 * ((x1 * ((x1 * -6.0) - 12.0)) - 16.0))));
	} else {
		tmp = x1 + (x1 + (x2 * (((x1 * -12.0) + ((x1 * x2) * 8.0)) - 6.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x1 <= (-1.22d+95)) then
        tmp = x1 + (6.0d0 + (x1 + (x1 * ((x1 * ((x1 * (-6.0d0)) - 12.0d0)) - 16.0d0))))
    else
        tmp = x1 + (x1 + (x2 * (((x1 * (-12.0d0)) + ((x1 * x2) * 8.0d0)) - 6.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= -1.22e+95) {
		tmp = x1 + (6.0 + (x1 + (x1 * ((x1 * ((x1 * -6.0) - 12.0)) - 16.0))));
	} else {
		tmp = x1 + (x1 + (x2 * (((x1 * -12.0) + ((x1 * x2) * 8.0)) - 6.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -1.22e+95:
		tmp = x1 + (6.0 + (x1 + (x1 * ((x1 * ((x1 * -6.0) - 12.0)) - 16.0))))
	else:
		tmp = x1 + (x1 + (x2 * (((x1 * -12.0) + ((x1 * x2) * 8.0)) - 6.0)))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -1.22e+95)
		tmp = Float64(x1 + Float64(6.0 + Float64(x1 + Float64(x1 * Float64(Float64(x1 * Float64(Float64(x1 * -6.0) - 12.0)) - 16.0)))));
	else
		tmp = Float64(x1 + Float64(x1 + Float64(x2 * Float64(Float64(Float64(x1 * -12.0) + Float64(Float64(x1 * x2) * 8.0)) - 6.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -1.22e+95)
		tmp = x1 + (6.0 + (x1 + (x1 * ((x1 * ((x1 * -6.0) - 12.0)) - 16.0))));
	else
		tmp = x1 + (x1 + (x2 * (((x1 * -12.0) + ((x1 * x2) * 8.0)) - 6.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -1.22e+95], N[(x1 + N[(6.0 + N[(x1 + N[(x1 * N[(N[(x1 * N[(N[(x1 * -6.0), $MachinePrecision] - 12.0), $MachinePrecision]), $MachinePrecision] - 16.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(x1 + N[(x2 * N[(N[(N[(x1 * -12.0), $MachinePrecision] + N[(N[(x1 * x2), $MachinePrecision] * 8.0), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x1 < -1.22000000000000007e95

   1. Initial program 8.7%

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

   3. Taylor expanded in x1 around inf 8.7%

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

   4. Taylor expanded in x1 around 0 20.2%

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

   5. Taylor expanded in x1 around 0 83.2%

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

      1. *-commutative 97.8%

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

   7. Simplified 83.2%

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

   8. Taylor expanded in x2 around 0 91.9%

      \[\leadsto x1 + \color{blue}{\left(6 + \left(x1 + x1 \cdot \left(x1 \cdot \left(-6 \cdot x1 - 12\right) - 16\right)\right)\right)} \]

   if -1.22000000000000007e95 < x1

   1. Initial program 84.8%

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

   3. Taylor expanded in x1 around 0 61.2%

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

   4. Taylor expanded in x1 around 0 54.1%

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

      1. *-commutative 43.3%

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

   6. Simplified 54.1%

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

   7. Taylor expanded in x2 around 0 62.2%

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

4. Final simplification 67.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.22 \cdot 10^{+95}:\\ \;\;\;\;x1 + \left(6 + \left(x1 + x1 \cdot \left(x1 \cdot \left(x1 \cdot -6 - 12\right) - 16\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + x2 \cdot \left(\left(x1 \cdot -12 + \left(x1 \cdot x2\right) \cdot 8\right) - 6\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 36.4% accurate, 6.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x2 \leq -3.4 \cdot 10^{-266} \lor \neg \left(x2 \leq 2.95 \cdot 10^{-120}\right):\\ \;\;\;\;x1 - \left(x2 \cdot \left(6 - x1 \cdot -12\right) - x1\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x2 -3.4e-266) (not (<= x2 2.95e-120)))
   (- x1 (- (* x2 (- 6.0 (* x1 -12.0))) x1))
   (+ x1 (* x1 -2.0))))

C

double code(double x1, double x2) {
	double tmp;
	if ((x2 <= -3.4e-266) || !(x2 <= 2.95e-120)) {
		tmp = x1 - ((x2 * (6.0 - (x1 * -12.0))) - x1);
	} else {
		tmp = x1 + (x1 * -2.0);
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if ((x2 <= (-3.4d-266)) .or. (.not. (x2 <= 2.95d-120))) then
        tmp = x1 - ((x2 * (6.0d0 - (x1 * (-12.0d0)))) - x1)
    else
        tmp = x1 + (x1 * (-2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x2 <= -3.4e-266) || !(x2 <= 2.95e-120)) {
		tmp = x1 - ((x2 * (6.0 - (x1 * -12.0))) - x1);
	} else {
		tmp = x1 + (x1 * -2.0);
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x2 <= -3.4e-266) or not (x2 <= 2.95e-120):
		tmp = x1 - ((x2 * (6.0 - (x1 * -12.0))) - x1)
	else:
		tmp = x1 + (x1 * -2.0)
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x2 <= -3.4e-266) || !(x2 <= 2.95e-120))
		tmp = Float64(x1 - Float64(Float64(x2 * Float64(6.0 - Float64(x1 * -12.0))) - x1));
	else
		tmp = Float64(x1 + Float64(x1 * -2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x2 <= -3.4e-266) || ~((x2 <= 2.95e-120)))
		tmp = x1 - ((x2 * (6.0 - (x1 * -12.0))) - x1);
	else
		tmp = x1 + (x1 * -2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x2, -3.4e-266], N[Not[LessEqual[x2, 2.95e-120]], $MachinePrecision]], N[(x1 - N[(N[(x2 * N[(6.0 - N[(x1 * -12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(x1 * -2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x2 < -3.39999999999999995e-266 or 2.94999999999999989e-120 < x2

   1. Initial program 69.7%

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

   3. Taylor expanded in x1 around 0 48.5%

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

   4. Taylor expanded in x1 around 0 49.1%

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

      1. *-commutative 55.8%

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

   6. Simplified 49.1%

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

   7. Taylor expanded in x2 around 0 38.7%

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

   if -3.39999999999999995e-266 < x2 < 2.94999999999999989e-120

   1. Initial program 79.6%

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

   3. Taylor expanded in x2 around inf 79.6%

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

      1. +-commutative 79.6%

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

      2. associate--r+ 79.6%

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

      3. associate-*r/ 79.6%

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

      4. div-sub 79.6%

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

      5. fma-neg 79.6%

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

      6. +-commutative 79.6%

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

      7. unpow2 79.6%

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

      8. fma-undefine 79.6%

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

      9. associate-*r/ 79.6%

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

      10. metadata-eval 79.6%

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

      11. +-commutative 79.6%

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

      12. unpow2 79.6%

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

      13. fma-undefine 79.6%

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

   5. Simplified 79.6%

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

   6. Taylor expanded in x1 around 0 77.0%

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

      1. associate-*r/ 77.0%

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

      2. neg-mul-1 77.0%

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

   8. Simplified 77.0%

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

   9. Taylor expanded in x1 around 0 77.7%

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

   10. Taylor expanded in x2 around 0 38.4%

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

       1. distribute-rgt1-in 38.7%

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

       2. metadata-eval 38.7%

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

   12. Simplified 38.7%

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

4. Final simplification 38.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq -3.4 \cdot 10^{-266} \lor \neg \left(x2 \leq 2.95 \cdot 10^{-120}\right):\\ \;\;\;\;x1 - \left(x2 \cdot \left(6 - x1 \cdot -12\right) - x1\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot -2\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 30.2% accurate, 8.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x2 \leq -3.4 \cdot 10^{-266} \lor \neg \left(x2 \leq 6.5 \cdot 10^{-121}\right):\\ \;\;\;\;x1 + x2 \cdot -6\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x2 -3.4e-266) (not (<= x2 6.5e-121)))
   (+ x1 (* x2 -6.0))
   (+ x1 (* x1 -2.0))))

C

double code(double x1, double x2) {
	double tmp;
	if ((x2 <= -3.4e-266) || !(x2 <= 6.5e-121)) {
		tmp = x1 + (x2 * -6.0);
	} else {
		tmp = x1 + (x1 * -2.0);
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if ((x2 <= (-3.4d-266)) .or. (.not. (x2 <= 6.5d-121))) then
        tmp = x1 + (x2 * (-6.0d0))
    else
        tmp = x1 + (x1 * (-2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x2 <= -3.4e-266) || !(x2 <= 6.5e-121)) {
		tmp = x1 + (x2 * -6.0);
	} else {
		tmp = x1 + (x1 * -2.0);
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x2 <= -3.4e-266) or not (x2 <= 6.5e-121):
		tmp = x1 + (x2 * -6.0)
	else:
		tmp = x1 + (x1 * -2.0)
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x2 <= -3.4e-266) || !(x2 <= 6.5e-121))
		tmp = Float64(x1 + Float64(x2 * -6.0));
	else
		tmp = Float64(x1 + Float64(x1 * -2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x2 <= -3.4e-266) || ~((x2 <= 6.5e-121)))
		tmp = x1 + (x2 * -6.0);
	else
		tmp = x1 + (x1 * -2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x2, -3.4e-266], N[Not[LessEqual[x2, 6.5e-121]], $MachinePrecision]], N[(x1 + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(x1 * -2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x2 < -3.39999999999999995e-266 or 6.5000000000000003e-121 < x2

   1. Initial program 69.7%

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

   3. Taylor expanded in x1 around 0 48.5%

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

   4. Taylor expanded in x1 around 0 49.1%

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

      1. *-commutative 55.8%

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

   6. Simplified 49.1%

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

   7. Taylor expanded in x1 around 0 33.8%

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

      1. *-commutative 33.8%

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

   9. Simplified 33.8%

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

   if -3.39999999999999995e-266 < x2 < 6.5000000000000003e-121

   1. Initial program 79.6%

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

   3. Taylor expanded in x2 around inf 79.6%

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

      1. +-commutative 79.6%

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

      2. associate--r+ 79.6%

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

      3. associate-*r/ 79.6%

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

      4. div-sub 79.6%

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

      5. fma-neg 79.6%

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

      6. +-commutative 79.6%

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

      7. unpow2 79.6%

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

      8. fma-undefine 79.6%

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

      9. associate-*r/ 79.6%

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

      10. metadata-eval 79.6%

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

      11. +-commutative 79.6%

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

      12. unpow2 79.6%

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

      13. fma-undefine 79.6%

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

   5. Simplified 79.6%

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

   6. Taylor expanded in x1 around 0 77.0%

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

      1. associate-*r/ 77.0%

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

      2. neg-mul-1 77.0%

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

   8. Simplified 77.0%

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

   9. Taylor expanded in x1 around 0 77.7%

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

   10. Taylor expanded in x2 around 0 38.4%

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

       1. distribute-rgt1-in 38.7%

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

       2. metadata-eval 38.7%

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

   12. Simplified 38.7%

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

4. Final simplification 34.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq -3.4 \cdot 10^{-266} \lor \neg \left(x2 \leq 6.5 \cdot 10^{-121}\right):\\ \;\;\;\;x1 + x2 \cdot -6\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot -2\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 13.8% accurate, 25.4× speedup

Math

\[\begin{array}{l} \\ x1 + x1 \cdot -2 \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 71.1%

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

3. Taylor expanded in x2 around inf 71.1%

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

   1. +-commutative 71.1%

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

   2. associate--r+ 71.1%

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

   3. associate-*r/ 71.1%

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

   4. div-sub 71.1%

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

   5. fma-neg 71.1%

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

   6. +-commutative 71.1%

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

   7. unpow2 71.1%

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

   8. fma-undefine 71.1%

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

   9. associate-*r/ 71.1%

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

   10. metadata-eval 71.1%

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

   11. +-commutative 71.1%

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

   12. unpow2 71.1%

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

   13. fma-undefine 71.1%

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

5. Simplified 71.1%

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

6. Taylor expanded in x1 around 0 70.5%

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

   1. associate-*r/ 70.5%

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

   2. neg-mul-1 70.5%

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

8. Simplified 70.5%

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

9. Taylor expanded in x1 around 0 59.0%

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

10. Taylor expanded in x2 around 0 10.3%

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

    1. distribute-rgt1-in 10.3%

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

    2. metadata-eval 10.3%

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

12. Simplified 10.3%

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

13. Final simplification 10.3%

    \[\leadsto x1 + x1 \cdot -2 \]
14. Add Preprocessing

Alternative 24: 3.3% accurate, 25.4× speedup

Math

\[\begin{array}{l} \\ 6 + x1 \cdot -17 \end{array} \]

FPCore

(FPCore (x1 x2) :precision binary64 (+ 6.0 (* x1 -17.0)))

C

double code(double x1, double x2) {
	return 6.0 + (x1 * -17.0);
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    code = 6.0d0 + (x1 * (-17.0d0))
end function

Java

public static double code(double x1, double x2) {
	return 6.0 + (x1 * -17.0);
}

Python

def code(x1, x2):
	return 6.0 + (x1 * -17.0)

Julia

function code(x1, x2)
	return Float64(6.0 + Float64(x1 * -17.0))
end

MATLAB

function tmp = code(x1, x2)
	tmp = 6.0 + (x1 * -17.0);
end

Wolfram

code[x1_, x2_] := N[(6.0 + N[(x1 * -17.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 71.1%

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

3. Taylor expanded in x1 around inf 21.6%

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

4. Taylor expanded in x1 around 0 7.2%

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

5. Taylor expanded in x1 around 0 12.2%

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

6. Taylor expanded in x2 around 0 3.5%

   \[\leadsto \color{blue}{6 + -17 \cdot x1} \]
7. Step-by-step derivation

   1. *-commutative 3.5%

      \[\leadsto 6 + \color{blue}{x1 \cdot -17} \]

8. Simplified 3.5%

   \[\leadsto \color{blue}{6 + x1 \cdot -17} \]
9. Add Preprocessing

Alternative 25: 3.4% accurate, 42.3× speedup

Math

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

FPCore

(FPCore (x1 x2) :precision binary64 (+ x1 x1))

C

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

Fortran

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

Java

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

Python

def code(x1, x2):
	return x1 + x1

Julia

function code(x1, x2)
	return Float64(x1 + x1)
end

MATLAB

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

Wolfram

code[x1_, x2_] := N[(x1 + x1), $MachinePrecision]

Derivation

1. Initial program 71.1%

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

3. Taylor expanded in x1 around 0 50.6%

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

4. Taylor expanded in x1 around 0 44.8%

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

   1. *-commutative 53.1%

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

6. Simplified 44.8%

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

7. Taylor expanded in x2 around 0 3.3%

   \[\leadsto x1 + \color{blue}{x1} \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2024100 
(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))))))