Rosa's FloatVsDoubleBenchmark

Percentage Accurate: 70.0% → 98.5%

Time: 1.2min

Alternatives: 24

Speedup: 7.4×

• 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: 70.0% 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: 98.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := \frac{\mathsf{fma}\left(x1, x1 \cdot 3, 2 \cdot x2 - x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}\\ \mathbf{if}\;x1 \leq -2 \cdot 10^{+154}:\\ \;\;\;\;x1 + x1 \cdot \left(x1 \cdot 9\right)\\ \mathbf{elif}\;x1 \leq -9.5 \cdot 10^{+105}:\\ \;\;\;\;x1 + \left(\left(x1 + {x1}^{4} \cdot 6\right) + 3 \cdot \frac{\left(t_0 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right)\\ \mathbf{elif}\;x1 \leq 5.1 \cdot 10^{+140}:\\ \;\;\;\;x1 + \mathsf{fma}\left(3, \frac{t_0 - \mathsf{fma}\left(2, x2, x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}, x1 + \mathsf{fma}\left(\mathsf{fma}\left(x1, x1, 1\right), \mathsf{fma}\left(x1, x1 \cdot \mathsf{fma}\left(t_1, 4, -6\right), t_1 \cdot \left(\left(t_1 + -3\right) \cdot \left(x1 \cdot 2\right)\right)\right), \mathsf{fma}\left(t_0, t_1, {x1}^{3}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + \left(9 \cdot \left(x1 \cdot x1\right) - x1 \cdot \left(2 - 4 \cdot \left(2 \cdot \left(x2 \cdot x2\right)\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (/ (fma x1 (* x1 3.0) (- (* 2.0 x2) x1)) (fma x1 x1 1.0))))
   (if (<= x1 -2e+154)
     (+ x1 (* x1 (* x1 9.0)))
     (if (<= x1 -9.5e+105)
       (+
        x1
        (+
         (+ x1 (* (pow x1 4.0) 6.0))
         (* 3.0 (/ (- (- t_0 (* 2.0 x2)) x1) (+ (* x1 x1) 1.0)))))
       (if (<= x1 5.1e+140)
         (+
          x1
          (fma
           3.0
           (/ (- t_0 (fma 2.0 x2 x1)) (fma x1 x1 1.0))
           (+
            x1
            (fma
             (fma x1 x1 1.0)
             (fma
              x1
              (* x1 (fma t_1 4.0 -6.0))
              (* t_1 (* (+ t_1 -3.0) (* x1 2.0))))
             (fma t_0 t_1 (pow x1 3.0))))))
         (+
          x1
          (+
           (* x2 -6.0)
           (-
            (* 9.0 (* x1 x1))
            (* x1 (- 2.0 (* 4.0 (* 2.0 (* x2 x2)))))))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = fma(x1, (x1 * 3.0), ((2.0 * x2) - x1)) / fma(x1, x1, 1.0);
	double tmp;
	if (x1 <= -2e+154) {
		tmp = x1 + (x1 * (x1 * 9.0));
	} else if (x1 <= -9.5e+105) {
		tmp = x1 + ((x1 + (pow(x1, 4.0) * 6.0)) + (3.0 * (((t_0 - (2.0 * x2)) - x1) / ((x1 * x1) + 1.0))));
	} else if (x1 <= 5.1e+140) {
		tmp = x1 + fma(3.0, ((t_0 - fma(2.0, x2, x1)) / fma(x1, x1, 1.0)), (x1 + fma(fma(x1, x1, 1.0), fma(x1, (x1 * fma(t_1, 4.0, -6.0)), (t_1 * ((t_1 + -3.0) * (x1 * 2.0)))), fma(t_0, t_1, pow(x1, 3.0)))));
	} else {
		tmp = x1 + ((x2 * -6.0) + ((9.0 * (x1 * x1)) - (x1 * (2.0 - (4.0 * (2.0 * (x2 * x2)))))));
	}
	return tmp;
}

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(fma(x1, Float64(x1 * 3.0), Float64(Float64(2.0 * x2) - x1)) / fma(x1, x1, 1.0))
	tmp = 0.0
	if (x1 <= -2e+154)
		tmp = Float64(x1 + Float64(x1 * Float64(x1 * 9.0)));
	elseif (x1 <= -9.5e+105)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64((x1 ^ 4.0) * 6.0)) + Float64(3.0 * Float64(Float64(Float64(t_0 - Float64(2.0 * x2)) - x1) / Float64(Float64(x1 * x1) + 1.0)))));
	elseif (x1 <= 5.1e+140)
		tmp = Float64(x1 + fma(3.0, Float64(Float64(t_0 - fma(2.0, x2, x1)) / fma(x1, x1, 1.0)), Float64(x1 + fma(fma(x1, x1, 1.0), fma(x1, Float64(x1 * fma(t_1, 4.0, -6.0)), Float64(t_1 * Float64(Float64(t_1 + -3.0) * Float64(x1 * 2.0)))), fma(t_0, t_1, (x1 ^ 3.0))))));
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(Float64(9.0 * Float64(x1 * x1)) - Float64(x1 * Float64(2.0 - Float64(4.0 * Float64(2.0 * Float64(x2 * x2))))))));
	end
	return tmp
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x1 * N[(x1 * 3.0), $MachinePrecision] + N[(N[(2.0 * x2), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision] / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -2e+154], N[(x1 + N[(x1 * N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -9.5e+105], N[(x1 + N[(N[(x1 + N[(N[Power[x1, 4.0], $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(N[(N[(t$95$0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 5.1e+140], N[(x1 + N[(3.0 * N[(N[(t$95$0 - N[(2.0 * x2 + x1), $MachinePrecision]), $MachinePrecision] / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(N[(x1 * x1 + 1.0), $MachinePrecision] * N[(x1 * N[(x1 * N[(t$95$1 * 4.0 + -6.0), $MachinePrecision]), $MachinePrecision] + N[(t$95$1 * N[(N[(t$95$1 + -3.0), $MachinePrecision] * N[(x1 * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$0 * t$95$1 + N[Power[x1, 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(N[(9.0 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] - N[(x1 * N[(2.0 - N[(4.0 * N[(2.0 * N[(x2 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -2.00000000000000007e154

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around 0 0.0%

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

   3. Taylor expanded in x1 around 0 42.9%

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

   4. Taylor expanded in x1 around inf 57.1%

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

      1. associate-*r* 57.1%

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

      2. *-commutative 57.1%

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

      3. cancel-sign-sub-inv 57.1%

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

      4. unpow2 57.1%

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

      5. +-commutative 57.1%

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

      6. distribute-lft-neg-in 57.1%

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

      7. *-commutative 57.1%

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

      8. distribute-lft-neg-in 57.1%

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

      9. metadata-eval 57.1%

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

      10. count-2 57.1%

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

   6. Simplified 57.1%

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

   7. Taylor expanded in x2 around 0 100.0%

      \[\leadsto \color{blue}{x1 + 9 \cdot {x1}^{2}} \]
   8. Step-by-step derivation

      1. *-commutative 100.0%

         \[\leadsto x1 + \color{blue}{{x1}^{2} \cdot 9} \]

      2. unpow2 100.0%

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

      3. associate-*r* 100.0%

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

   9. Simplified 100.0%

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

   if -2.00000000000000007e154 < x1 < -9.4999999999999995e105

   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. Taylor expanded in x1 around inf 100.0%

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

      1. *-commutative 100.0%

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

   4. Simplified 100.0%

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

   if -9.4999999999999995e105 < x1 < 5.1e140

   1. Initial program 98.8%

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

   3. Simplified 99.1%

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

   if 5.1e140 < x1

   1. Initial program 3.1%

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

   2. Taylor expanded in x1 around 0 3.1%

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

   3. Taylor expanded in x1 around 0 81.3%

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

   4. Taylor expanded in x2 around 0 100.0%

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

      1. *-commutative 100.0%

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

      2. unpow2 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in x2 around inf 100.0%

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

      1. unpow2 100.0%

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

   9. Simplified 100.0%

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

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -2 \cdot 10^{+154}:\\ \;\;\;\;x1 + x1 \cdot \left(x1 \cdot 9\right)\\ \mathbf{elif}\;x1 \leq -9.5 \cdot 10^{+105}:\\ \;\;\;\;x1 + \left(\left(x1 + {x1}^{4} \cdot 6\right) + 3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right)\\ \mathbf{elif}\;x1 \leq 5.1 \cdot 10^{+140}:\\ \;\;\;\;x1 + \mathsf{fma}\left(3, \frac{x1 \cdot \left(x1 \cdot 3\right) - \mathsf{fma}\left(2, x2, x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}, x1 + \mathsf{fma}\left(\mathsf{fma}\left(x1, x1, 1\right), \mathsf{fma}\left(x1, x1 \cdot \mathsf{fma}\left(\frac{\mathsf{fma}\left(x1, x1 \cdot 3, 2 \cdot x2 - x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}, 4, -6\right), \frac{\mathsf{fma}\left(x1, x1 \cdot 3, 2 \cdot x2 - x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)} \cdot \left(\left(\frac{\mathsf{fma}\left(x1, x1 \cdot 3, 2 \cdot x2 - x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)} + -3\right) \cdot \left(x1 \cdot 2\right)\right)\right), \mathsf{fma}\left(x1 \cdot \left(x1 \cdot 3\right), \frac{\mathsf{fma}\left(x1, x1 \cdot 3, 2 \cdot x2 - x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}, {x1}^{3}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + \left(9 \cdot \left(x1 \cdot x1\right) - x1 \cdot \left(2 - 4 \cdot \left(2 \cdot \left(x2 \cdot x2\right)\right)\right)\right)\right)\\ \end{array} \]

Alternative 2: 98.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{\mathsf{fma}\left(x1, x1 \cdot 3, \left(x2 + x2\right) - x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := x1 \cdot x1 + 1\\ t_3 := x1 \cdot \left(x1 \cdot 9\right)\\ t_4 := \frac{\left(t_1 + 2 \cdot x2\right) - x1}{t_2}\\ \mathbf{if}\;x1 \leq -5 \cdot 10^{+153}:\\ \;\;\;\;x1 + t_3\\ \mathbf{elif}\;x1 \leq -1.35 \cdot 10^{-101}:\\ \;\;\;\;x1 + \mathsf{fma}\left(3, \frac{t_1 - \mathsf{fma}\left(2, x2, x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}, t_3 + \mathsf{fma}\left(x1, x1, 1\right) \cdot \left(x1 + x1 \cdot \left(2 \cdot \left(t_0 \cdot \left(-3 + t_0\right)\right) + x1 \cdot \mathsf{fma}\left(t_0, 4, -6\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 5.1 \cdot 10^{+140}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t_1 - 2 \cdot x2\right) - x1}{t_2} + \left(x1 + \left(\left(t_2 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t_4\right) \cdot \left(t_4 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \left(\frac{\mathsf{fma}\left(x1 \cdot 3, x1, x2 + x2\right)}{\mathsf{fma}\left(x1, x1, 1\right)} - \frac{x1}{\mathsf{fma}\left(x1, x1, 1\right)}\right) - 6\right)\right) + t_1 \cdot t_4\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + \left(9 \cdot \left(x1 \cdot x1\right) - x1 \cdot \left(2 - 4 \cdot \left(2 \cdot \left(x2 \cdot x2\right)\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (/ (fma x1 (* x1 3.0) (- (+ x2 x2) x1)) (fma x1 x1 1.0)))
        (t_1 (* x1 (* x1 3.0)))
        (t_2 (+ (* x1 x1) 1.0))
        (t_3 (* x1 (* x1 9.0)))
        (t_4 (/ (- (+ t_1 (* 2.0 x2)) x1) t_2)))
   (if (<= x1 -5e+153)
     (+ x1 t_3)
     (if (<= x1 -1.35e-101)
       (+
        x1
        (fma
         3.0
         (/ (- t_1 (fma 2.0 x2 x1)) (fma x1 x1 1.0))
         (+
          t_3
          (*
           (fma x1 x1 1.0)
           (+
            x1
            (*
             x1
             (+ (* 2.0 (* t_0 (+ -3.0 t_0))) (* x1 (fma t_0 4.0 -6.0)))))))))
       (if (<= x1 5.1e+140)
         (+
          x1
          (+
           (* 3.0 (/ (- (- t_1 (* 2.0 x2)) x1) t_2))
           (+
            x1
            (+
             (+
              (*
               t_2
               (+
                (* (* (* x1 2.0) t_4) (- t_4 3.0))
                (*
                 (* x1 x1)
                 (-
                  (*
                   4.0
                   (-
                    (/ (fma (* x1 3.0) x1 (+ x2 x2)) (fma x1 x1 1.0))
                    (/ x1 (fma x1 x1 1.0))))
                  6.0))))
              (* t_1 t_4))
             (* x1 (* x1 x1))))))
         (+
          x1
          (+
           (* x2 -6.0)
           (-
            (* 9.0 (* x1 x1))
            (* x1 (- 2.0 (* 4.0 (* 2.0 (* x2 x2)))))))))))))

C

double code(double x1, double x2) {
	double t_0 = fma(x1, (x1 * 3.0), ((x2 + x2) - x1)) / fma(x1, x1, 1.0);
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = x1 * (x1 * 9.0);
	double t_4 = ((t_1 + (2.0 * x2)) - x1) / t_2;
	double tmp;
	if (x1 <= -5e+153) {
		tmp = x1 + t_3;
	} else if (x1 <= -1.35e-101) {
		tmp = x1 + fma(3.0, ((t_1 - fma(2.0, x2, x1)) / fma(x1, x1, 1.0)), (t_3 + (fma(x1, x1, 1.0) * (x1 + (x1 * ((2.0 * (t_0 * (-3.0 + t_0))) + (x1 * fma(t_0, 4.0, -6.0))))))));
	} else if (x1 <= 5.1e+140) {
		tmp = x1 + ((3.0 * (((t_1 - (2.0 * x2)) - x1) / t_2)) + (x1 + (((t_2 * ((((x1 * 2.0) * t_4) * (t_4 - 3.0)) + ((x1 * x1) * ((4.0 * ((fma((x1 * 3.0), x1, (x2 + x2)) / fma(x1, x1, 1.0)) - (x1 / fma(x1, x1, 1.0)))) - 6.0)))) + (t_1 * t_4)) + (x1 * (x1 * x1)))));
	} else {
		tmp = x1 + ((x2 * -6.0) + ((9.0 * (x1 * x1)) - (x1 * (2.0 - (4.0 * (2.0 * (x2 * x2)))))));
	}
	return tmp;
}

Julia

function code(x1, x2)
	t_0 = Float64(fma(x1, Float64(x1 * 3.0), Float64(Float64(x2 + x2) - x1)) / fma(x1, x1, 1.0))
	t_1 = Float64(x1 * Float64(x1 * 3.0))
	t_2 = Float64(Float64(x1 * x1) + 1.0)
	t_3 = Float64(x1 * Float64(x1 * 9.0))
	t_4 = Float64(Float64(Float64(t_1 + Float64(2.0 * x2)) - x1) / t_2)
	tmp = 0.0
	if (x1 <= -5e+153)
		tmp = Float64(x1 + t_3);
	elseif (x1 <= -1.35e-101)
		tmp = Float64(x1 + fma(3.0, Float64(Float64(t_1 - fma(2.0, x2, x1)) / fma(x1, x1, 1.0)), Float64(t_3 + Float64(fma(x1, x1, 1.0) * Float64(x1 + Float64(x1 * Float64(Float64(2.0 * Float64(t_0 * Float64(-3.0 + t_0))) + Float64(x1 * fma(t_0, 4.0, -6.0)))))))));
	elseif (x1 <= 5.1e+140)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_1 - Float64(2.0 * x2)) - x1) / t_2)) + Float64(x1 + Float64(Float64(Float64(t_2 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_4) * Float64(t_4 - 3.0)) + Float64(Float64(x1 * x1) * Float64(Float64(4.0 * Float64(Float64(fma(Float64(x1 * 3.0), x1, Float64(x2 + x2)) / fma(x1, x1, 1.0)) - Float64(x1 / fma(x1, x1, 1.0)))) - 6.0)))) + Float64(t_1 * t_4)) + Float64(x1 * Float64(x1 * x1))))));
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(Float64(9.0 * Float64(x1 * x1)) - Float64(x1 * Float64(2.0 - Float64(4.0 * Float64(2.0 * Float64(x2 * x2))))))));
	end
	return tmp
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x1 * N[(x1 * 3.0), $MachinePrecision] + N[(N[(x2 + x2), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision] / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$3 = N[(x1 * N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(t$95$1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]}, If[LessEqual[x1, -5e+153], N[(x1 + t$95$3), $MachinePrecision], If[LessEqual[x1, -1.35e-101], N[(x1 + N[(3.0 * N[(N[(t$95$1 - N[(2.0 * x2 + x1), $MachinePrecision]), $MachinePrecision] / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision] + N[(t$95$3 + N[(N[(x1 * x1 + 1.0), $MachinePrecision] * N[(x1 + N[(x1 * N[(N[(2.0 * N[(t$95$0 * N[(-3.0 + t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(t$95$0 * 4.0 + -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 5.1e+140], N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$1 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(N[(N[(t$95$2 * N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$4), $MachinePrecision] * N[(t$95$4 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(4.0 * N[(N[(N[(N[(x1 * 3.0), $MachinePrecision] * x1 + N[(x2 + x2), $MachinePrecision]), $MachinePrecision] / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision] - N[(x1 / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$1 * t$95$4), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(N[(9.0 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] - N[(x1 * N[(2.0 - N[(4.0 * N[(2.0 * N[(x2 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -5.00000000000000018e153

   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. Taylor expanded in x1 around 0 0.0%

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

   3. Taylor expanded in x1 around 0 42.9%

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

   4. Taylor expanded in x1 around inf 57.1%

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

      1. associate-*r* 57.1%

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

      2. *-commutative 57.1%

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

      3. cancel-sign-sub-inv 57.1%

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

      4. unpow2 57.1%

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

      5. +-commutative 57.1%

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

      6. distribute-lft-neg-in 57.1%

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

      7. *-commutative 57.1%

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

      8. distribute-lft-neg-in 57.1%

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

      9. metadata-eval 57.1%

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

      10. count-2 57.1%

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

   6. Simplified 57.1%

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

   7. Taylor expanded in x2 around 0 100.0%

      \[\leadsto \color{blue}{x1 + 9 \cdot {x1}^{2}} \]
   8. Step-by-step derivation

      1. *-commutative 100.0%

         \[\leadsto x1 + \color{blue}{{x1}^{2} \cdot 9} \]

      2. unpow2 100.0%

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

      3. associate-*r* 100.0%

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

   9. Simplified 100.0%

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

   if -5.00000000000000018e153 < x1 < -1.3500000000000001e-101

   1. Initial program 78.8%

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

   3. Simplified 97.9%

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

   4. Taylor expanded in x1 around inf 97.9%

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

      1. *-commutative 97.9%

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

   6. Simplified 97.9%

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

   if -1.3500000000000001e-101 < x1 < 5.1e140

   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. Step-by-step derivation

      1. fma-def 99.4%

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

      2. div-sub 99.4%

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

      3. fma-def 99.4%

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

      4. count-2 99.4%

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

   3. Applied egg-rr 99.4%

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

   if 5.1e140 < x1

   1. Initial program 3.1%

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

   2. Taylor expanded in x1 around 0 3.1%

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

   3. Taylor expanded in x1 around 0 81.3%

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

   4. Taylor expanded in x2 around 0 100.0%

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

      1. *-commutative 100.0%

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

      2. unpow2 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in x2 around inf 100.0%

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

      1. unpow2 100.0%

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

   9. Simplified 100.0%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5 \cdot 10^{+153}:\\ \;\;\;\;x1 + x1 \cdot \left(x1 \cdot 9\right)\\ \mathbf{elif}\;x1 \leq -1.35 \cdot 10^{-101}:\\ \;\;\;\;x1 + \mathsf{fma}\left(3, \frac{x1 \cdot \left(x1 \cdot 3\right) - \mathsf{fma}\left(2, x2, x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}, x1 \cdot \left(x1 \cdot 9\right) + \mathsf{fma}\left(x1, x1, 1\right) \cdot \left(x1 + x1 \cdot \left(2 \cdot \left(\frac{\mathsf{fma}\left(x1, x1 \cdot 3, \left(x2 + x2\right) - x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)} \cdot \left(-3 + \frac{\mathsf{fma}\left(x1, x1 \cdot 3, \left(x2 + x2\right) - x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}\right)\right) + x1 \cdot \mathsf{fma}\left(\frac{\mathsf{fma}\left(x1, x1 \cdot 3, \left(x2 + x2\right) - x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}, 4, -6\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 5.1 \cdot 10^{+140}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(\left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \left(\frac{\mathsf{fma}\left(x1 \cdot 3, x1, x2 + x2\right)}{\mathsf{fma}\left(x1, x1, 1\right)} - \frac{x1}{\mathsf{fma}\left(x1, x1, 1\right)}\right) - 6\right)\right) + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + \left(9 \cdot \left(x1 \cdot x1\right) - x1 \cdot \left(2 - 4 \cdot \left(2 \cdot \left(x2 \cdot x2\right)\right)\right)\right)\right)\\ \end{array} \]

Alternative 3: 98.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := x1 \cdot x1 + 1\\ t_2 := 3 \cdot \frac{\left(t_0 - 2 \cdot x2\right) - x1}{t_1}\\ t_3 := \frac{\left(t_0 + 2 \cdot x2\right) - x1}{t_1}\\ \mathbf{if}\;x1 \leq -2 \cdot 10^{+154}:\\ \;\;\;\;x1 + x1 \cdot \left(x1 \cdot 9\right)\\ \mathbf{elif}\;x1 \leq -9.5 \cdot 10^{+105}:\\ \;\;\;\;x1 + \left(\left(x1 + {x1}^{4} \cdot 6\right) + t_2\right)\\ \mathbf{elif}\;x1 \leq 5.1 \cdot 10^{+140}:\\ \;\;\;\;x1 + \left(t_2 + \left(x1 + \left(\left(t_1 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t_3\right) \cdot \left(t_3 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \left(\frac{\mathsf{fma}\left(x1 \cdot 3, x1, x2 + x2\right)}{\mathsf{fma}\left(x1, x1, 1\right)} - \frac{x1}{\mathsf{fma}\left(x1, x1, 1\right)}\right) - 6\right)\right) + t_0 \cdot t_3\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + \left(9 \cdot \left(x1 \cdot x1\right) - x1 \cdot \left(2 - 4 \cdot \left(2 \cdot \left(x2 \cdot x2\right)\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (+ (* x1 x1) 1.0))
        (t_2 (* 3.0 (/ (- (- t_0 (* 2.0 x2)) x1) t_1)))
        (t_3 (/ (- (+ t_0 (* 2.0 x2)) x1) t_1)))
   (if (<= x1 -2e+154)
     (+ x1 (* x1 (* x1 9.0)))
     (if (<= x1 -9.5e+105)
       (+ x1 (+ (+ x1 (* (pow x1 4.0) 6.0)) t_2))
       (if (<= x1 5.1e+140)
         (+
          x1
          (+
           t_2
           (+
            x1
            (+
             (+
              (*
               t_1
               (+
                (* (* (* x1 2.0) t_3) (- t_3 3.0))
                (*
                 (* x1 x1)
                 (-
                  (*
                   4.0
                   (-
                    (/ (fma (* x1 3.0) x1 (+ x2 x2)) (fma x1 x1 1.0))
                    (/ x1 (fma x1 x1 1.0))))
                  6.0))))
              (* t_0 t_3))
             (* x1 (* x1 x1))))))
         (+
          x1
          (+
           (* x2 -6.0)
           (-
            (* 9.0 (* x1 x1))
            (* x1 (- 2.0 (* 4.0 (* 2.0 (* x2 x2)))))))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = 3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1);
	double t_3 = ((t_0 + (2.0 * x2)) - x1) / t_1;
	double tmp;
	if (x1 <= -2e+154) {
		tmp = x1 + (x1 * (x1 * 9.0));
	} else if (x1 <= -9.5e+105) {
		tmp = x1 + ((x1 + (pow(x1, 4.0) * 6.0)) + t_2);
	} else if (x1 <= 5.1e+140) {
		tmp = x1 + (t_2 + (x1 + (((t_1 * ((((x1 * 2.0) * t_3) * (t_3 - 3.0)) + ((x1 * x1) * ((4.0 * ((fma((x1 * 3.0), x1, (x2 + x2)) / fma(x1, x1, 1.0)) - (x1 / fma(x1, x1, 1.0)))) - 6.0)))) + (t_0 * t_3)) + (x1 * (x1 * x1)))));
	} else {
		tmp = x1 + ((x2 * -6.0) + ((9.0 * (x1 * x1)) - (x1 * (2.0 - (4.0 * (2.0 * (x2 * x2)))))));
	}
	return tmp;
}

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(Float64(x1 * x1) + 1.0)
	t_2 = Float64(3.0 * Float64(Float64(Float64(t_0 - Float64(2.0 * x2)) - x1) / t_1))
	t_3 = Float64(Float64(Float64(t_0 + Float64(2.0 * x2)) - x1) / t_1)
	tmp = 0.0
	if (x1 <= -2e+154)
		tmp = Float64(x1 + Float64(x1 * Float64(x1 * 9.0)));
	elseif (x1 <= -9.5e+105)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64((x1 ^ 4.0) * 6.0)) + t_2));
	elseif (x1 <= 5.1e+140)
		tmp = Float64(x1 + Float64(t_2 + Float64(x1 + Float64(Float64(Float64(t_1 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_3) * Float64(t_3 - 3.0)) + Float64(Float64(x1 * x1) * Float64(Float64(4.0 * Float64(Float64(fma(Float64(x1 * 3.0), x1, Float64(x2 + x2)) / fma(x1, x1, 1.0)) - Float64(x1 / fma(x1, x1, 1.0)))) - 6.0)))) + Float64(t_0 * t_3)) + Float64(x1 * Float64(x1 * x1))))));
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(Float64(9.0 * Float64(x1 * x1)) - Float64(x1 * Float64(2.0 - Float64(4.0 * Float64(2.0 * Float64(x2 * x2))))))));
	end
	return tmp
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$2 = N[(3.0 * N[(N[(N[(t$95$0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[x1, -2e+154], N[(x1 + N[(x1 * N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -9.5e+105], N[(x1 + N[(N[(x1 + N[(N[Power[x1, 4.0], $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 5.1e+140], N[(x1 + N[(t$95$2 + N[(x1 + N[(N[(N[(t$95$1 * N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$3), $MachinePrecision] * N[(t$95$3 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(4.0 * N[(N[(N[(N[(x1 * 3.0), $MachinePrecision] * x1 + N[(x2 + x2), $MachinePrecision]), $MachinePrecision] / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision] - N[(x1 / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$0 * t$95$3), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(N[(9.0 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] - N[(x1 * N[(2.0 - N[(4.0 * N[(2.0 * N[(x2 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -2.00000000000000007e154

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around 0 0.0%

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

   3. Taylor expanded in x1 around 0 42.9%

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

   4. Taylor expanded in x1 around inf 57.1%

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

      1. associate-*r* 57.1%

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

      2. *-commutative 57.1%

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

      3. cancel-sign-sub-inv 57.1%

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

      4. unpow2 57.1%

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

      5. +-commutative 57.1%

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

      6. distribute-lft-neg-in 57.1%

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

      7. *-commutative 57.1%

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

      8. distribute-lft-neg-in 57.1%

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

      9. metadata-eval 57.1%

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

      10. count-2 57.1%

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

   6. Simplified 57.1%

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

   7. Taylor expanded in x2 around 0 100.0%

      \[\leadsto \color{blue}{x1 + 9 \cdot {x1}^{2}} \]
   8. Step-by-step derivation

      1. *-commutative 100.0%

         \[\leadsto x1 + \color{blue}{{x1}^{2} \cdot 9} \]

      2. unpow2 100.0%

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

      3. associate-*r* 100.0%

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

   9. Simplified 100.0%

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

   if -2.00000000000000007e154 < x1 < -9.4999999999999995e105

   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. Taylor expanded in x1 around inf 100.0%

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

      1. *-commutative 100.0%

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

   4. Simplified 100.0%

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

   if -9.4999999999999995e105 < x1 < 5.1e140

   1. Initial program 98.8%

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

      1. fma-def 98.8%

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

      2. div-sub 98.8%

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

      3. fma-def 98.8%

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

      4. count-2 98.8%

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

   3. Applied egg-rr 98.8%

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

   if 5.1e140 < x1

   1. Initial program 3.1%

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

   2. Taylor expanded in x1 around 0 3.1%

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

   3. Taylor expanded in x1 around 0 81.3%

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

   4. Taylor expanded in x2 around 0 100.0%

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

      1. *-commutative 100.0%

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

      2. unpow2 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in x2 around inf 100.0%

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

      1. unpow2 100.0%

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

   9. Simplified 100.0%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -2 \cdot 10^{+154}:\\ \;\;\;\;x1 + x1 \cdot \left(x1 \cdot 9\right)\\ \mathbf{elif}\;x1 \leq -9.5 \cdot 10^{+105}:\\ \;\;\;\;x1 + \left(\left(x1 + {x1}^{4} \cdot 6\right) + 3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right)\\ \mathbf{elif}\;x1 \leq 5.1 \cdot 10^{+140}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(\left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \left(\frac{\mathsf{fma}\left(x1 \cdot 3, x1, x2 + x2\right)}{\mathsf{fma}\left(x1, x1, 1\right)} - \frac{x1}{\mathsf{fma}\left(x1, x1, 1\right)}\right) - 6\right)\right) + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + \left(9 \cdot \left(x1 \cdot x1\right) - x1 \cdot \left(2 - 4 \cdot \left(2 \cdot \left(x2 \cdot x2\right)\right)\right)\right)\right)\\ \end{array} \]

Alternative 4: 95.5% accurate, 0.5× speedup

Math

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

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

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);
	double t_3 = (t_2 - x1) / t_0;
	double t_4 = (x1 - t_2) / t_0;
	double t_5 = x1 + ((3.0 * (((t_1 - (2.0 * x2)) - x1) / t_0)) + (x1 - (((t_1 * t_4) + (t_0 * ((((x1 * 2.0) * t_3) * (3.0 + t_4)) + ((x1 * x1) * (6.0 - (4.0 * t_3)))))) - (x1 * (x1 * x1)))));
	double tmp;
	if (t_5 <= ((double) INFINITY)) {
		tmp = t_5;
	} else {
		tmp = x1 + ((x1 * (x1 * 9.0)) + (x2 * -6.0));
	}
	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);
	double t_3 = (t_2 - x1) / t_0;
	double t_4 = (x1 - t_2) / t_0;
	double t_5 = x1 + ((3.0 * (((t_1 - (2.0 * x2)) - x1) / t_0)) + (x1 - (((t_1 * t_4) + (t_0 * ((((x1 * 2.0) * t_3) * (3.0 + t_4)) + ((x1 * x1) * (6.0 - (4.0 * t_3)))))) - (x1 * (x1 * x1)))));
	double tmp;
	if (t_5 <= Double.POSITIVE_INFINITY) {
		tmp = t_5;
	} else {
		tmp = x1 + ((x1 * (x1 * 9.0)) + (x2 * -6.0));
	}
	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)
	t_3 = (t_2 - x1) / t_0
	t_4 = (x1 - t_2) / t_0
	t_5 = x1 + ((3.0 * (((t_1 - (2.0 * x2)) - x1) / t_0)) + (x1 - (((t_1 * t_4) + (t_0 * ((((x1 * 2.0) * t_3) * (3.0 + t_4)) + ((x1 * x1) * (6.0 - (4.0 * t_3)))))) - (x1 * (x1 * x1)))))
	tmp = 0
	if t_5 <= math.inf:
		tmp = t_5
	else:
		tmp = x1 + ((x1 * (x1 * 9.0)) + (x2 * -6.0))
	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(t_1 + Float64(2.0 * x2))
	t_3 = Float64(Float64(t_2 - x1) / t_0)
	t_4 = Float64(Float64(x1 - t_2) / t_0)
	t_5 = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_1 - Float64(2.0 * x2)) - x1) / t_0)) + Float64(x1 - Float64(Float64(Float64(t_1 * t_4) + Float64(t_0 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_3) * Float64(3.0 + t_4)) + Float64(Float64(x1 * x1) * Float64(6.0 - Float64(4.0 * t_3)))))) - Float64(x1 * Float64(x1 * x1))))))
	tmp = 0.0
	if (t_5 <= Inf)
		tmp = t_5;
	else
		tmp = Float64(x1 + Float64(Float64(x1 * Float64(x1 * 9.0)) + Float64(x2 * -6.0)));
	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);
	t_3 = (t_2 - x1) / t_0;
	t_4 = (x1 - t_2) / t_0;
	t_5 = x1 + ((3.0 * (((t_1 - (2.0 * x2)) - x1) / t_0)) + (x1 - (((t_1 * t_4) + (t_0 * ((((x1 * 2.0) * t_3) * (3.0 + t_4)) + ((x1 * x1) * (6.0 - (4.0 * t_3)))))) - (x1 * (x1 * x1)))));
	tmp = 0.0;
	if (t_5 <= Inf)
		tmp = t_5;
	else
		tmp = x1 + ((x1 * (x1 * 9.0)) + (x2 * -6.0));
	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[(t$95$1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t$95$2 - x1), $MachinePrecision] / t$95$0), $MachinePrecision]}, Block[{t$95$4 = N[(N[(x1 - t$95$2), $MachinePrecision] / t$95$0), $MachinePrecision]}, Block[{t$95$5 = N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$1 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision] + N[(x1 - N[(N[(N[(t$95$1 * t$95$4), $MachinePrecision] + N[(t$95$0 * N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$3), $MachinePrecision] * N[(3.0 + t$95$4), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 - N[(4.0 * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$5, Infinity], t$95$5, N[(x1 + N[(N[(x1 * N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision] + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 99.4%

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

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

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around 0 1.3%

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

   3. Taylor expanded in x1 around 0 53.4%

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

   4. Taylor expanded in x2 around 0 63.6%

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

      1. *-commutative 63.6%

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

      2. unpow2 63.6%

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

   6. Simplified 63.6%

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

   7. Taylor expanded in x1 around inf 87.1%

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

      1. *-commutative 87.1%

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

      2. unpow2 87.1%

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

      3. associate-*r* 87.1%

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

   9. Simplified 87.1%

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

4. Final simplification 95.6%

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

Alternative 5: 98.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := t_0 + 2 \cdot x2\\ t_2 := x1 \cdot x1 + 1\\ t_3 := \frac{t_1 - x1}{t_2}\\ t_4 := 3 \cdot \frac{\left(t_0 - 2 \cdot x2\right) - x1}{t_2}\\ t_5 := \frac{x1 - t_1}{t_2}\\ \mathbf{if}\;x1 \leq -2 \cdot 10^{+154}:\\ \;\;\;\;x1 + x1 \cdot \left(x1 \cdot 9\right)\\ \mathbf{elif}\;x1 \leq -9.5 \cdot 10^{+105}:\\ \;\;\;\;x1 + \left(\left(x1 + {x1}^{4} \cdot 6\right) + t_4\right)\\ \mathbf{elif}\;x1 \leq 5.1 \cdot 10^{+140}:\\ \;\;\;\;x1 + \left(t_4 + \left(x1 - \left(\left(t_0 \cdot t_5 + t_2 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t_3\right) \cdot \left(3 + t_5\right) + \left(x1 \cdot x1\right) \cdot \left(6 - 4 \cdot t_3\right)\right)\right) - x1 \cdot \left(x1 \cdot x1\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + \left(9 \cdot \left(x1 \cdot x1\right) - x1 \cdot \left(2 - 4 \cdot \left(2 \cdot \left(x2 \cdot x2\right)\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (+ t_0 (* 2.0 x2)))
        (t_2 (+ (* x1 x1) 1.0))
        (t_3 (/ (- t_1 x1) t_2))
        (t_4 (* 3.0 (/ (- (- t_0 (* 2.0 x2)) x1) t_2)))
        (t_5 (/ (- x1 t_1) t_2)))
   (if (<= x1 -2e+154)
     (+ x1 (* x1 (* x1 9.0)))
     (if (<= x1 -9.5e+105)
       (+ x1 (+ (+ x1 (* (pow x1 4.0) 6.0)) t_4))
       (if (<= x1 5.1e+140)
         (+
          x1
          (+
           t_4
           (-
            x1
            (-
             (+
              (* t_0 t_5)
              (*
               t_2
               (+
                (* (* (* x1 2.0) t_3) (+ 3.0 t_5))
                (* (* x1 x1) (- 6.0 (* 4.0 t_3))))))
             (* x1 (* x1 x1))))))
         (+
          x1
          (+
           (* x2 -6.0)
           (-
            (* 9.0 (* x1 x1))
            (* x1 (- 2.0 (* 4.0 (* 2.0 (* x2 x2)))))))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = t_0 + (2.0 * x2);
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = (t_1 - x1) / t_2;
	double t_4 = 3.0 * (((t_0 - (2.0 * x2)) - x1) / t_2);
	double t_5 = (x1 - t_1) / t_2;
	double tmp;
	if (x1 <= -2e+154) {
		tmp = x1 + (x1 * (x1 * 9.0));
	} else if (x1 <= -9.5e+105) {
		tmp = x1 + ((x1 + (pow(x1, 4.0) * 6.0)) + t_4);
	} else if (x1 <= 5.1e+140) {
		tmp = x1 + (t_4 + (x1 - (((t_0 * t_5) + (t_2 * ((((x1 * 2.0) * t_3) * (3.0 + t_5)) + ((x1 * x1) * (6.0 - (4.0 * t_3)))))) - (x1 * (x1 * x1)))));
	} else {
		tmp = x1 + ((x2 * -6.0) + ((9.0 * (x1 * x1)) - (x1 * (2.0 - (4.0 * (2.0 * (x2 * x2)))))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_0 = x1 * (x1 * 3.0d0)
    t_1 = t_0 + (2.0d0 * x2)
    t_2 = (x1 * x1) + 1.0d0
    t_3 = (t_1 - x1) / t_2
    t_4 = 3.0d0 * (((t_0 - (2.0d0 * x2)) - x1) / t_2)
    t_5 = (x1 - t_1) / t_2
    if (x1 <= (-2d+154)) then
        tmp = x1 + (x1 * (x1 * 9.0d0))
    else if (x1 <= (-9.5d+105)) then
        tmp = x1 + ((x1 + ((x1 ** 4.0d0) * 6.0d0)) + t_4)
    else if (x1 <= 5.1d+140) then
        tmp = x1 + (t_4 + (x1 - (((t_0 * t_5) + (t_2 * ((((x1 * 2.0d0) * t_3) * (3.0d0 + t_5)) + ((x1 * x1) * (6.0d0 - (4.0d0 * t_3)))))) - (x1 * (x1 * x1)))))
    else
        tmp = x1 + ((x2 * (-6.0d0)) + ((9.0d0 * (x1 * x1)) - (x1 * (2.0d0 - (4.0d0 * (2.0d0 * (x2 * x2)))))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = t_0 + (2.0 * x2);
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = (t_1 - x1) / t_2;
	double t_4 = 3.0 * (((t_0 - (2.0 * x2)) - x1) / t_2);
	double t_5 = (x1 - t_1) / t_2;
	double tmp;
	if (x1 <= -2e+154) {
		tmp = x1 + (x1 * (x1 * 9.0));
	} else if (x1 <= -9.5e+105) {
		tmp = x1 + ((x1 + (Math.pow(x1, 4.0) * 6.0)) + t_4);
	} else if (x1 <= 5.1e+140) {
		tmp = x1 + (t_4 + (x1 - (((t_0 * t_5) + (t_2 * ((((x1 * 2.0) * t_3) * (3.0 + t_5)) + ((x1 * x1) * (6.0 - (4.0 * t_3)))))) - (x1 * (x1 * x1)))));
	} else {
		tmp = x1 + ((x2 * -6.0) + ((9.0 * (x1 * x1)) - (x1 * (2.0 - (4.0 * (2.0 * (x2 * x2)))))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = t_0 + (2.0 * x2)
	t_2 = (x1 * x1) + 1.0
	t_3 = (t_1 - x1) / t_2
	t_4 = 3.0 * (((t_0 - (2.0 * x2)) - x1) / t_2)
	t_5 = (x1 - t_1) / t_2
	tmp = 0
	if x1 <= -2e+154:
		tmp = x1 + (x1 * (x1 * 9.0))
	elif x1 <= -9.5e+105:
		tmp = x1 + ((x1 + (math.pow(x1, 4.0) * 6.0)) + t_4)
	elif x1 <= 5.1e+140:
		tmp = x1 + (t_4 + (x1 - (((t_0 * t_5) + (t_2 * ((((x1 * 2.0) * t_3) * (3.0 + t_5)) + ((x1 * x1) * (6.0 - (4.0 * t_3)))))) - (x1 * (x1 * x1)))))
	else:
		tmp = x1 + ((x2 * -6.0) + ((9.0 * (x1 * x1)) - (x1 * (2.0 - (4.0 * (2.0 * (x2 * x2)))))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(t_0 + Float64(2.0 * x2))
	t_2 = Float64(Float64(x1 * x1) + 1.0)
	t_3 = Float64(Float64(t_1 - x1) / t_2)
	t_4 = Float64(3.0 * Float64(Float64(Float64(t_0 - Float64(2.0 * x2)) - x1) / t_2))
	t_5 = Float64(Float64(x1 - t_1) / t_2)
	tmp = 0.0
	if (x1 <= -2e+154)
		tmp = Float64(x1 + Float64(x1 * Float64(x1 * 9.0)));
	elseif (x1 <= -9.5e+105)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64((x1 ^ 4.0) * 6.0)) + t_4));
	elseif (x1 <= 5.1e+140)
		tmp = Float64(x1 + Float64(t_4 + Float64(x1 - Float64(Float64(Float64(t_0 * t_5) + Float64(t_2 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_3) * Float64(3.0 + t_5)) + Float64(Float64(x1 * x1) * Float64(6.0 - Float64(4.0 * t_3)))))) - Float64(x1 * Float64(x1 * x1))))));
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(Float64(9.0 * Float64(x1 * x1)) - Float64(x1 * Float64(2.0 - Float64(4.0 * Float64(2.0 * Float64(x2 * x2))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * 3.0);
	t_1 = t_0 + (2.0 * x2);
	t_2 = (x1 * x1) + 1.0;
	t_3 = (t_1 - x1) / t_2;
	t_4 = 3.0 * (((t_0 - (2.0 * x2)) - x1) / t_2);
	t_5 = (x1 - t_1) / t_2;
	tmp = 0.0;
	if (x1 <= -2e+154)
		tmp = x1 + (x1 * (x1 * 9.0));
	elseif (x1 <= -9.5e+105)
		tmp = x1 + ((x1 + ((x1 ^ 4.0) * 6.0)) + t_4);
	elseif (x1 <= 5.1e+140)
		tmp = x1 + (t_4 + (x1 - (((t_0 * t_5) + (t_2 * ((((x1 * 2.0) * t_3) * (3.0 + t_5)) + ((x1 * x1) * (6.0 - (4.0 * t_3)))))) - (x1 * (x1 * x1)))));
	else
		tmp = x1 + ((x2 * -6.0) + ((9.0 * (x1 * x1)) - (x1 * (2.0 - (4.0 * (2.0 * (x2 * x2)))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t$95$1 - x1), $MachinePrecision] / t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(3.0 * N[(N[(N[(t$95$0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(x1 - t$95$1), $MachinePrecision] / t$95$2), $MachinePrecision]}, If[LessEqual[x1, -2e+154], N[(x1 + N[(x1 * N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -9.5e+105], N[(x1 + N[(N[(x1 + N[(N[Power[x1, 4.0], $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision] + t$95$4), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 5.1e+140], N[(x1 + N[(t$95$4 + N[(x1 - N[(N[(N[(t$95$0 * t$95$5), $MachinePrecision] + N[(t$95$2 * N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$3), $MachinePrecision] * N[(3.0 + t$95$5), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 - N[(4.0 * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(N[(9.0 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] - N[(x1 * N[(2.0 - N[(4.0 * N[(2.0 * N[(x2 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -2.00000000000000007e154

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around 0 0.0%

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

   3. Taylor expanded in x1 around 0 42.9%

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

   4. Taylor expanded in x1 around inf 57.1%

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

      1. associate-*r* 57.1%

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

      2. *-commutative 57.1%

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

      3. cancel-sign-sub-inv 57.1%

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

      4. unpow2 57.1%

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

      5. +-commutative 57.1%

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

      6. distribute-lft-neg-in 57.1%

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

      7. *-commutative 57.1%

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

      8. distribute-lft-neg-in 57.1%

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

      9. metadata-eval 57.1%

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

      10. count-2 57.1%

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

   6. Simplified 57.1%

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

   7. Taylor expanded in x2 around 0 100.0%

      \[\leadsto \color{blue}{x1 + 9 \cdot {x1}^{2}} \]
   8. Step-by-step derivation

      1. *-commutative 100.0%

         \[\leadsto x1 + \color{blue}{{x1}^{2} \cdot 9} \]

      2. unpow2 100.0%

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

      3. associate-*r* 100.0%

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

   9. Simplified 100.0%

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

   if -2.00000000000000007e154 < x1 < -9.4999999999999995e105

   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. Taylor expanded in x1 around inf 100.0%

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

      1. *-commutative 100.0%

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

   4. Simplified 100.0%

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

   if -9.4999999999999995e105 < x1 < 5.1e140

   1. Initial program 98.8%

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

   if 5.1e140 < x1

   1. Initial program 3.1%

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

   2. Taylor expanded in x1 around 0 3.1%

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

   3. Taylor expanded in x1 around 0 81.3%

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

   4. Taylor expanded in x2 around 0 100.0%

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

      1. *-commutative 100.0%

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

      2. unpow2 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in x2 around inf 100.0%

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

      1. unpow2 100.0%

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

   9. Simplified 100.0%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -2 \cdot 10^{+154}:\\ \;\;\;\;x1 + x1 \cdot \left(x1 \cdot 9\right)\\ \mathbf{elif}\;x1 \leq -9.5 \cdot 10^{+105}:\\ \;\;\;\;x1 + \left(\left(x1 + {x1}^{4} \cdot 6\right) + 3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right)\\ \mathbf{elif}\;x1 \leq 5.1 \cdot 10^{+140}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 - \left(\left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1} + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(3 + \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot \left(6 - 4 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right)\right)\right) - x1 \cdot \left(x1 \cdot x1\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + \left(9 \cdot \left(x1 \cdot x1\right) - x1 \cdot \left(2 - 4 \cdot \left(2 \cdot \left(x2 \cdot x2\right)\right)\right)\right)\right)\\ \end{array} \]

Alternative 6: 88.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot x1\right)\\ t_1 := x1 \cdot x1 + 1\\ t_2 := 3 - \frac{1}{x1}\\ t_3 := x1 \cdot \left(x1 \cdot 3\right)\\ t_4 := 3 \cdot \frac{\left(t_3 - 2 \cdot x2\right) - x1}{t_1}\\ t_5 := x2 + \left(3 + x2\right)\\ t_6 := \left(x1 \cdot x1\right) \cdot t_5\\ t_7 := \frac{\left(t_3 + 2 \cdot x2\right) - x1}{t_1}\\ t_8 := \left(x1 \cdot x1\right) \cdot \left(4 \cdot t_7 - 6\right)\\ \mathbf{if}\;x1 \leq -4.5 \cdot 10^{+153}:\\ \;\;\;\;x1 + x1 \cdot \left(x1 \cdot 9\right)\\ \mathbf{elif}\;x1 \leq -9.5 \cdot 10^{+105}:\\ \;\;\;\;x1 + \frac{\left(x2 \cdot x2\right) \cdot 36 - 9 \cdot \left(t_6 \cdot t_6\right)}{x2 \cdot -6 - t_3 \cdot t_5}\\ \mathbf{elif}\;x1 \leq -2050000:\\ \;\;\;\;x1 + \left(t_4 + \left(x1 + \left(t_0 + \left(t_1 \cdot \left(t_8 + \frac{1}{x1} \cdot \left(\left(x1 \cdot 2\right) \cdot \left(\frac{1}{x1} - 3\right)\right)\right) + 3 \cdot t_3\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -2.6 \cdot 10^{-239}:\\ \;\;\;\;x1 - \left(x1 \cdot \left(2 + 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right) - x2 \cdot -6\right)\\ \mathbf{elif}\;x1 \leq 9.6 \cdot 10^{-176}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + 8 \cdot \left(x2 \cdot \left(x1 \cdot x2\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 75 \lor \neg \left(x1 \leq 5.1 \cdot 10^{+140}\right):\\ \;\;\;\;x1 + \left(x2 \cdot -6 + \left(9 \cdot \left(x1 \cdot x1\right) - x1 \cdot \left(2 - 4 \cdot \left(2 \cdot \left(x2 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(t_4 + \left(x1 + \left(t_0 + \left(t_1 \cdot \left(t_8 + \left(t_7 - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot t_2\right)\right) + t_3 \cdot t_2\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 x1)))
        (t_1 (+ (* x1 x1) 1.0))
        (t_2 (- 3.0 (/ 1.0 x1)))
        (t_3 (* x1 (* x1 3.0)))
        (t_4 (* 3.0 (/ (- (- t_3 (* 2.0 x2)) x1) t_1)))
        (t_5 (+ x2 (+ 3.0 x2)))
        (t_6 (* (* x1 x1) t_5))
        (t_7 (/ (- (+ t_3 (* 2.0 x2)) x1) t_1))
        (t_8 (* (* x1 x1) (- (* 4.0 t_7) 6.0))))
   (if (<= x1 -4.5e+153)
     (+ x1 (* x1 (* x1 9.0)))
     (if (<= x1 -9.5e+105)
       (+
        x1
        (/
         (- (* (* x2 x2) 36.0) (* 9.0 (* t_6 t_6)))
         (- (* x2 -6.0) (* t_3 t_5))))
       (if (<= x1 -2050000.0)
         (+
          x1
          (+
           t_4
           (+
            x1
            (+
             t_0
             (+
              (* t_1 (+ t_8 (* (/ 1.0 x1) (* (* x1 2.0) (- (/ 1.0 x1) 3.0)))))
              (* 3.0 t_3))))))
         (if (<= x1 -2.6e-239)
           (-
            x1
            (- (* x1 (+ 2.0 (* 4.0 (* x2 (- 3.0 (* 2.0 x2)))))) (* x2 -6.0)))
           (if (<= x1 9.6e-176)
             (+ x1 (+ (* x2 -6.0) (* 8.0 (* x2 (* x1 x2)))))
             (if (or (<= x1 75.0) (not (<= x1 5.1e+140)))
               (+
                x1
                (+
                 (* x2 -6.0)
                 (-
                  (* 9.0 (* x1 x1))
                  (* x1 (- 2.0 (* 4.0 (* 2.0 (* x2 x2))))))))
               (+
                x1
                (+
                 t_4
                 (+
                  x1
                  (+
                   t_0
                   (+
                    (* t_1 (+ t_8 (* (- t_7 3.0) (* (* x1 2.0) t_2))))
                    (* t_3 t_2))))))))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * x1);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = 3.0 - (1.0 / x1);
	double t_3 = x1 * (x1 * 3.0);
	double t_4 = 3.0 * (((t_3 - (2.0 * x2)) - x1) / t_1);
	double t_5 = x2 + (3.0 + x2);
	double t_6 = (x1 * x1) * t_5;
	double t_7 = ((t_3 + (2.0 * x2)) - x1) / t_1;
	double t_8 = (x1 * x1) * ((4.0 * t_7) - 6.0);
	double tmp;
	if (x1 <= -4.5e+153) {
		tmp = x1 + (x1 * (x1 * 9.0));
	} else if (x1 <= -9.5e+105) {
		tmp = x1 + ((((x2 * x2) * 36.0) - (9.0 * (t_6 * t_6))) / ((x2 * -6.0) - (t_3 * t_5)));
	} else if (x1 <= -2050000.0) {
		tmp = x1 + (t_4 + (x1 + (t_0 + ((t_1 * (t_8 + ((1.0 / x1) * ((x1 * 2.0) * ((1.0 / x1) - 3.0))))) + (3.0 * t_3)))));
	} else if (x1 <= -2.6e-239) {
		tmp = x1 - ((x1 * (2.0 + (4.0 * (x2 * (3.0 - (2.0 * x2)))))) - (x2 * -6.0));
	} else if (x1 <= 9.6e-176) {
		tmp = x1 + ((x2 * -6.0) + (8.0 * (x2 * (x1 * x2))));
	} else if ((x1 <= 75.0) || !(x1 <= 5.1e+140)) {
		tmp = x1 + ((x2 * -6.0) + ((9.0 * (x1 * x1)) - (x1 * (2.0 - (4.0 * (2.0 * (x2 * x2)))))));
	} else {
		tmp = x1 + (t_4 + (x1 + (t_0 + ((t_1 * (t_8 + ((t_7 - 3.0) * ((x1 * 2.0) * t_2)))) + (t_3 * t_2)))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: t_8
    real(8) :: tmp
    t_0 = x1 * (x1 * x1)
    t_1 = (x1 * x1) + 1.0d0
    t_2 = 3.0d0 - (1.0d0 / x1)
    t_3 = x1 * (x1 * 3.0d0)
    t_4 = 3.0d0 * (((t_3 - (2.0d0 * x2)) - x1) / t_1)
    t_5 = x2 + (3.0d0 + x2)
    t_6 = (x1 * x1) * t_5
    t_7 = ((t_3 + (2.0d0 * x2)) - x1) / t_1
    t_8 = (x1 * x1) * ((4.0d0 * t_7) - 6.0d0)
    if (x1 <= (-4.5d+153)) then
        tmp = x1 + (x1 * (x1 * 9.0d0))
    else if (x1 <= (-9.5d+105)) then
        tmp = x1 + ((((x2 * x2) * 36.0d0) - (9.0d0 * (t_6 * t_6))) / ((x2 * (-6.0d0)) - (t_3 * t_5)))
    else if (x1 <= (-2050000.0d0)) then
        tmp = x1 + (t_4 + (x1 + (t_0 + ((t_1 * (t_8 + ((1.0d0 / x1) * ((x1 * 2.0d0) * ((1.0d0 / x1) - 3.0d0))))) + (3.0d0 * t_3)))))
    else if (x1 <= (-2.6d-239)) then
        tmp = x1 - ((x1 * (2.0d0 + (4.0d0 * (x2 * (3.0d0 - (2.0d0 * x2)))))) - (x2 * (-6.0d0)))
    else if (x1 <= 9.6d-176) then
        tmp = x1 + ((x2 * (-6.0d0)) + (8.0d0 * (x2 * (x1 * x2))))
    else if ((x1 <= 75.0d0) .or. (.not. (x1 <= 5.1d+140))) then
        tmp = x1 + ((x2 * (-6.0d0)) + ((9.0d0 * (x1 * x1)) - (x1 * (2.0d0 - (4.0d0 * (2.0d0 * (x2 * x2)))))))
    else
        tmp = x1 + (t_4 + (x1 + (t_0 + ((t_1 * (t_8 + ((t_7 - 3.0d0) * ((x1 * 2.0d0) * t_2)))) + (t_3 * t_2)))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * x1);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = 3.0 - (1.0 / x1);
	double t_3 = x1 * (x1 * 3.0);
	double t_4 = 3.0 * (((t_3 - (2.0 * x2)) - x1) / t_1);
	double t_5 = x2 + (3.0 + x2);
	double t_6 = (x1 * x1) * t_5;
	double t_7 = ((t_3 + (2.0 * x2)) - x1) / t_1;
	double t_8 = (x1 * x1) * ((4.0 * t_7) - 6.0);
	double tmp;
	if (x1 <= -4.5e+153) {
		tmp = x1 + (x1 * (x1 * 9.0));
	} else if (x1 <= -9.5e+105) {
		tmp = x1 + ((((x2 * x2) * 36.0) - (9.0 * (t_6 * t_6))) / ((x2 * -6.0) - (t_3 * t_5)));
	} else if (x1 <= -2050000.0) {
		tmp = x1 + (t_4 + (x1 + (t_0 + ((t_1 * (t_8 + ((1.0 / x1) * ((x1 * 2.0) * ((1.0 / x1) - 3.0))))) + (3.0 * t_3)))));
	} else if (x1 <= -2.6e-239) {
		tmp = x1 - ((x1 * (2.0 + (4.0 * (x2 * (3.0 - (2.0 * x2)))))) - (x2 * -6.0));
	} else if (x1 <= 9.6e-176) {
		tmp = x1 + ((x2 * -6.0) + (8.0 * (x2 * (x1 * x2))));
	} else if ((x1 <= 75.0) || !(x1 <= 5.1e+140)) {
		tmp = x1 + ((x2 * -6.0) + ((9.0 * (x1 * x1)) - (x1 * (2.0 - (4.0 * (2.0 * (x2 * x2)))))));
	} else {
		tmp = x1 + (t_4 + (x1 + (t_0 + ((t_1 * (t_8 + ((t_7 - 3.0) * ((x1 * 2.0) * t_2)))) + (t_3 * t_2)))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * x1)
	t_1 = (x1 * x1) + 1.0
	t_2 = 3.0 - (1.0 / x1)
	t_3 = x1 * (x1 * 3.0)
	t_4 = 3.0 * (((t_3 - (2.0 * x2)) - x1) / t_1)
	t_5 = x2 + (3.0 + x2)
	t_6 = (x1 * x1) * t_5
	t_7 = ((t_3 + (2.0 * x2)) - x1) / t_1
	t_8 = (x1 * x1) * ((4.0 * t_7) - 6.0)
	tmp = 0
	if x1 <= -4.5e+153:
		tmp = x1 + (x1 * (x1 * 9.0))
	elif x1 <= -9.5e+105:
		tmp = x1 + ((((x2 * x2) * 36.0) - (9.0 * (t_6 * t_6))) / ((x2 * -6.0) - (t_3 * t_5)))
	elif x1 <= -2050000.0:
		tmp = x1 + (t_4 + (x1 + (t_0 + ((t_1 * (t_8 + ((1.0 / x1) * ((x1 * 2.0) * ((1.0 / x1) - 3.0))))) + (3.0 * t_3)))))
	elif x1 <= -2.6e-239:
		tmp = x1 - ((x1 * (2.0 + (4.0 * (x2 * (3.0 - (2.0 * x2)))))) - (x2 * -6.0))
	elif x1 <= 9.6e-176:
		tmp = x1 + ((x2 * -6.0) + (8.0 * (x2 * (x1 * x2))))
	elif (x1 <= 75.0) or not (x1 <= 5.1e+140):
		tmp = x1 + ((x2 * -6.0) + ((9.0 * (x1 * x1)) - (x1 * (2.0 - (4.0 * (2.0 * (x2 * x2)))))))
	else:
		tmp = x1 + (t_4 + (x1 + (t_0 + ((t_1 * (t_8 + ((t_7 - 3.0) * ((x1 * 2.0) * t_2)))) + (t_3 * t_2)))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * x1))
	t_1 = Float64(Float64(x1 * x1) + 1.0)
	t_2 = Float64(3.0 - Float64(1.0 / 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_1))
	t_5 = Float64(x2 + Float64(3.0 + x2))
	t_6 = Float64(Float64(x1 * x1) * t_5)
	t_7 = Float64(Float64(Float64(t_3 + Float64(2.0 * x2)) - x1) / t_1)
	t_8 = Float64(Float64(x1 * x1) * Float64(Float64(4.0 * t_7) - 6.0))
	tmp = 0.0
	if (x1 <= -4.5e+153)
		tmp = Float64(x1 + Float64(x1 * Float64(x1 * 9.0)));
	elseif (x1 <= -9.5e+105)
		tmp = Float64(x1 + Float64(Float64(Float64(Float64(x2 * x2) * 36.0) - Float64(9.0 * Float64(t_6 * t_6))) / Float64(Float64(x2 * -6.0) - Float64(t_3 * t_5))));
	elseif (x1 <= -2050000.0)
		tmp = Float64(x1 + Float64(t_4 + Float64(x1 + Float64(t_0 + Float64(Float64(t_1 * Float64(t_8 + Float64(Float64(1.0 / x1) * Float64(Float64(x1 * 2.0) * Float64(Float64(1.0 / x1) - 3.0))))) + Float64(3.0 * t_3))))));
	elseif (x1 <= -2.6e-239)
		tmp = Float64(x1 - Float64(Float64(x1 * Float64(2.0 + Float64(4.0 * Float64(x2 * Float64(3.0 - Float64(2.0 * x2)))))) - Float64(x2 * -6.0)));
	elseif (x1 <= 9.6e-176)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(8.0 * Float64(x2 * Float64(x1 * x2)))));
	elseif ((x1 <= 75.0) || !(x1 <= 5.1e+140))
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(Float64(9.0 * Float64(x1 * x1)) - Float64(x1 * Float64(2.0 - Float64(4.0 * Float64(2.0 * Float64(x2 * x2))))))));
	else
		tmp = Float64(x1 + Float64(t_4 + Float64(x1 + Float64(t_0 + Float64(Float64(t_1 * Float64(t_8 + Float64(Float64(t_7 - 3.0) * Float64(Float64(x1 * 2.0) * t_2)))) + Float64(t_3 * t_2))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * x1);
	t_1 = (x1 * x1) + 1.0;
	t_2 = 3.0 - (1.0 / x1);
	t_3 = x1 * (x1 * 3.0);
	t_4 = 3.0 * (((t_3 - (2.0 * x2)) - x1) / t_1);
	t_5 = x2 + (3.0 + x2);
	t_6 = (x1 * x1) * t_5;
	t_7 = ((t_3 + (2.0 * x2)) - x1) / t_1;
	t_8 = (x1 * x1) * ((4.0 * t_7) - 6.0);
	tmp = 0.0;
	if (x1 <= -4.5e+153)
		tmp = x1 + (x1 * (x1 * 9.0));
	elseif (x1 <= -9.5e+105)
		tmp = x1 + ((((x2 * x2) * 36.0) - (9.0 * (t_6 * t_6))) / ((x2 * -6.0) - (t_3 * t_5)));
	elseif (x1 <= -2050000.0)
		tmp = x1 + (t_4 + (x1 + (t_0 + ((t_1 * (t_8 + ((1.0 / x1) * ((x1 * 2.0) * ((1.0 / x1) - 3.0))))) + (3.0 * t_3)))));
	elseif (x1 <= -2.6e-239)
		tmp = x1 - ((x1 * (2.0 + (4.0 * (x2 * (3.0 - (2.0 * x2)))))) - (x2 * -6.0));
	elseif (x1 <= 9.6e-176)
		tmp = x1 + ((x2 * -6.0) + (8.0 * (x2 * (x1 * x2))));
	elseif ((x1 <= 75.0) || ~((x1 <= 5.1e+140)))
		tmp = x1 + ((x2 * -6.0) + ((9.0 * (x1 * x1)) - (x1 * (2.0 - (4.0 * (2.0 * (x2 * x2)))))));
	else
		tmp = x1 + (t_4 + (x1 + (t_0 + ((t_1 * (t_8 + ((t_7 - 3.0) * ((x1 * 2.0) * t_2)))) + (t_3 * t_2)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$2 = N[(3.0 - N[(1.0 / 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$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(x2 + N[(3.0 + x2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(x1 * x1), $MachinePrecision] * t$95$5), $MachinePrecision]}, Block[{t$95$7 = N[(N[(N[(t$95$3 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$8 = N[(N[(x1 * x1), $MachinePrecision] * N[(N[(4.0 * t$95$7), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -4.5e+153], N[(x1 + N[(x1 * N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -9.5e+105], N[(x1 + N[(N[(N[(N[(x2 * x2), $MachinePrecision] * 36.0), $MachinePrecision] - N[(9.0 * N[(t$95$6 * t$95$6), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(x2 * -6.0), $MachinePrecision] - N[(t$95$3 * t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -2050000.0], N[(x1 + N[(t$95$4 + N[(x1 + N[(t$95$0 + N[(N[(t$95$1 * N[(t$95$8 + N[(N[(1.0 / x1), $MachinePrecision] * N[(N[(x1 * 2.0), $MachinePrecision] * N[(N[(1.0 / x1), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -2.6e-239], N[(x1 - N[(N[(x1 * N[(2.0 + N[(4.0 * N[(x2 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 9.6e-176], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(8.0 * N[(x2 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x1, 75.0], N[Not[LessEqual[x1, 5.1e+140]], $MachinePrecision]], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(N[(9.0 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] - N[(x1 * N[(2.0 - N[(4.0 * N[(2.0 * N[(x2 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(t$95$4 + N[(x1 + N[(t$95$0 + N[(N[(t$95$1 * N[(t$95$8 + N[(N[(t$95$7 - 3.0), $MachinePrecision] * N[(N[(x1 * 2.0), $MachinePrecision] * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$3 * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if x1 < -4.5000000000000001e153

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around 0 0.0%

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

   3. Taylor expanded in x1 around 0 42.9%

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

   4. Taylor expanded in x1 around inf 57.1%

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

      1. associate-*r* 57.1%

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

      2. *-commutative 57.1%

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

      3. cancel-sign-sub-inv 57.1%

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

      4. unpow2 57.1%

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

      5. +-commutative 57.1%

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

      6. distribute-lft-neg-in 57.1%

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

      7. *-commutative 57.1%

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

      8. distribute-lft-neg-in 57.1%

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

      9. metadata-eval 57.1%

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

      10. count-2 57.1%

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

   6. Simplified 57.1%

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

   7. Taylor expanded in x2 around 0 100.0%

      \[\leadsto \color{blue}{x1 + 9 \cdot {x1}^{2}} \]
   8. Step-by-step derivation

      1. *-commutative 100.0%

         \[\leadsto x1 + \color{blue}{{x1}^{2} \cdot 9} \]

      2. unpow2 100.0%

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

      3. associate-*r* 100.0%

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

   9. Simplified 100.0%

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

   if -4.5000000000000001e153 < x1 < -9.4999999999999995e105

   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. Taylor expanded in x1 around 0 0.2%

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

   3. Taylor expanded in x1 around 0 5.7%

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

   4. Taylor expanded in x1 around inf 23.9%

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

      1. associate-*r* 23.9%

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

      2. *-commutative 23.9%

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

      3. cancel-sign-sub-inv 23.9%

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

      4. unpow2 23.9%

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

      5. +-commutative 23.9%

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

      6. distribute-lft-neg-in 23.9%

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

      7. *-commutative 23.9%

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

      8. distribute-lft-neg-in 23.9%

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

      9. metadata-eval 23.9%

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

      10. count-2 23.9%

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

   6. Simplified 23.9%

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

      1. flip-+ 63.6%

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

      2. *-commutative 63.6%

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

      3. *-commutative 63.6%

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

      4. associate-*l* 63.6%

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

      5. associate-+l+ 63.6%

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

      6. associate-*l* 63.6%

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

      7. associate-+l+ 63.6%

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

      8. *-commutative 63.6%

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

   8. Applied egg-rr 63.6%

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

      1. swap-sqr 63.6%

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

      2. metadata-eval 63.6%

         \[\leadsto x1 + \frac{\left(x2 \cdot x2\right) \cdot \color{blue}{36} - \left(3 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right)\right) \cdot \left(3 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right)\right)}{x2 \cdot -6 - 3 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right)} \]

      3. swap-sqr 63.6%

         \[\leadsto x1 + \frac{\left(x2 \cdot x2\right) \cdot 36 - \color{blue}{\left(3 \cdot 3\right) \cdot \left(\left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right)\right)}}{x2 \cdot -6 - 3 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right)} \]

      4. metadata-eval 63.6%

         \[\leadsto x1 + \frac{\left(x2 \cdot x2\right) \cdot 36 - \color{blue}{9} \cdot \left(\left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right)\right)}{x2 \cdot -6 - 3 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right)} \]

      5. associate-*l* 63.6%

         \[\leadsto x1 + \frac{\left(x2 \cdot x2\right) \cdot 36 - 9 \cdot \left(\left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right)\right)}{x2 \cdot -6 - 3 \cdot \color{blue}{\left(x1 \cdot \left(x1 \cdot \left(x2 + \left(x2 + 3\right)\right)\right)\right)}} \]

      6. associate-*r* 63.6%

         \[\leadsto x1 + \frac{\left(x2 \cdot x2\right) \cdot 36 - 9 \cdot \left(\left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right)\right)}{x2 \cdot -6 - \color{blue}{\left(3 \cdot x1\right) \cdot \left(x1 \cdot \left(x2 + \left(x2 + 3\right)\right)\right)}} \]

      7. *-commutative 63.6%

         \[\leadsto x1 + \frac{\left(x2 \cdot x2\right) \cdot 36 - 9 \cdot \left(\left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right)\right)}{x2 \cdot -6 - \color{blue}{\left(x1 \cdot 3\right)} \cdot \left(x1 \cdot \left(x2 + \left(x2 + 3\right)\right)\right)} \]

      8. associate-*l* 63.6%

         \[\leadsto x1 + \frac{\left(x2 \cdot x2\right) \cdot 36 - 9 \cdot \left(\left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right)\right)}{x2 \cdot -6 - \color{blue}{\left(\left(x1 \cdot 3\right) \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)}} \]

      9. *-commutative 63.6%

         \[\leadsto x1 + \frac{\left(x2 \cdot x2\right) \cdot 36 - 9 \cdot \left(\left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right)\right)}{x2 \cdot -6 - \color{blue}{\left(x1 \cdot \left(x1 \cdot 3\right)\right)} \cdot \left(x2 + \left(x2 + 3\right)\right)} \]

   10. Simplified 63.6%

       \[\leadsto x1 + \color{blue}{\frac{\left(x2 \cdot x2\right) \cdot 36 - 9 \cdot \left(\left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right)\right)}{x2 \cdot -6 - \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(x2 + \left(x2 + 3\right)\right)}} \]

   if -9.4999999999999995e105 < x1 < -2.05e6

   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. Taylor expanded in x1 around inf 99.4%

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

   3. Taylor expanded in x1 around inf 99.4%

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

   4. Taylor expanded in x1 around inf 99.4%

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

   if -2.05e6 < x1 < -2.60000000000000003e-239

   1. Initial program 97.7%

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

   2. Taylor expanded in x1 around 0 88.1%

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

   3. Taylor expanded in x1 around 0 88.4%

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

   if -2.60000000000000003e-239 < x1 < 9.60000000000000024e-176

   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. Taylor expanded in x1 around 0 72.9%

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

   3. Taylor expanded in x1 around 0 72.9%

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

   4. Taylor expanded in x2 around 0 72.9%

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

      1. *-commutative 72.9%

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

      2. unpow2 72.9%

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

   6. Simplified 72.9%

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

   7. Taylor expanded in x2 around inf 71.0%

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

      1. *-commutative 71.0%

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

      2. unpow2 71.0%

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

      3. associate-*l* 97.8%

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

      4. *-commutative 97.8%

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

   9. Simplified 97.8%

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

   if 9.60000000000000024e-176 < x1 < 75 or 5.1e140 < x1

   1. Initial program 51.9%

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

   2. Taylor expanded in x1 around 0 48.3%

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

   3. Taylor expanded in x1 around 0 87.1%

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

   4. Taylor expanded in x2 around 0 96.3%

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

      1. *-commutative 96.3%

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

      2. unpow2 96.3%

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

   6. Simplified 96.3%

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

   7. Taylor expanded in x2 around inf 96.3%

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

      1. unpow2 96.3%

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

   9. Simplified 96.3%

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

   if 75 < x1 < 5.1e140

   1. Initial program 99.2%

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

   2. Taylor expanded in x1 around inf 87.3%

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

   3. Taylor expanded in x1 around inf 87.3%

      \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \left(3 - \frac{1}{x1}\right)\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \color{blue}{\left(3 - \frac{1}{x1}\right)}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
3. Recombined 7 regimes into one program.

4. Final simplification 93.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4.5 \cdot 10^{+153}:\\ \;\;\;\;x1 + x1 \cdot \left(x1 \cdot 9\right)\\ \mathbf{elif}\;x1 \leq -9.5 \cdot 10^{+105}:\\ \;\;\;\;x1 + \frac{\left(x2 \cdot x2\right) \cdot 36 - 9 \cdot \left(\left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(3 + x2\right)\right)\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(3 + x2\right)\right)\right)\right)}{x2 \cdot -6 - \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(x2 + \left(3 + x2\right)\right)}\\ \mathbf{elif}\;x1 \leq -2050000:\\ \;\;\;\;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 x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right) + \frac{1}{x1} \cdot \left(\left(x1 \cdot 2\right) \cdot \left(\frac{1}{x1} - 3\right)\right)\right) + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -2.6 \cdot 10^{-239}:\\ \;\;\;\;x1 - \left(x1 \cdot \left(2 + 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right) - x2 \cdot -6\right)\\ \mathbf{elif}\;x1 \leq 9.6 \cdot 10^{-176}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + 8 \cdot \left(x2 \cdot \left(x1 \cdot x2\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 75 \lor \neg \left(x1 \leq 5.1 \cdot 10^{+140}\right):\\ \;\;\;\;x1 + \left(x2 \cdot -6 + \left(9 \cdot \left(x1 \cdot x1\right) - x1 \cdot \left(2 - 4 \cdot \left(2 \cdot \left(x2 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right) + \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(3 - \frac{1}{x1}\right)\right)\right) + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(3 - \frac{1}{x1}\right)\right)\right)\right)\right)\\ \end{array} \]

Alternative 7: 94.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x2 + \left(3 + x2\right)\\ t_1 := \left(x1 \cdot x1\right) \cdot t_0\\ t_2 := x1 \cdot x1 + 1\\ t_3 := x1 \cdot \left(x1 \cdot 3\right)\\ t_4 := t_3 + 2 \cdot x2\\ t_5 := \frac{x1 - t_4}{t_2}\\ \mathbf{if}\;x1 \leq -4.5 \cdot 10^{+153}:\\ \;\;\;\;x1 + x1 \cdot \left(x1 \cdot 9\right)\\ \mathbf{elif}\;x1 \leq -9.5 \cdot 10^{+105}:\\ \;\;\;\;x1 + \frac{\left(x2 \cdot x2\right) \cdot 36 - 9 \cdot \left(t_1 \cdot t_1\right)}{x2 \cdot -6 - t_3 \cdot t_0}\\ \mathbf{elif}\;x1 \leq 5.1 \cdot 10^{+140}:\\ \;\;\;\;x1 - \left(3 \cdot \frac{x1 + \left(2 \cdot x2 - t_3\right)}{t_2} - \left(x1 - \left(\left(t_3 \cdot t_5 + t_2 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{t_4 - x1}{t_2}\right) \cdot \left(3 + t_5\right) - 6 \cdot \left(x1 \cdot x1\right)\right)\right) - x1 \cdot \left(x1 \cdot x1\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + \left(9 \cdot \left(x1 \cdot x1\right) - x1 \cdot \left(2 - 4 \cdot \left(2 \cdot \left(x2 \cdot x2\right)\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ x2 (+ 3.0 x2)))
        (t_1 (* (* x1 x1) t_0))
        (t_2 (+ (* x1 x1) 1.0))
        (t_3 (* x1 (* x1 3.0)))
        (t_4 (+ t_3 (* 2.0 x2)))
        (t_5 (/ (- x1 t_4) t_2)))
   (if (<= x1 -4.5e+153)
     (+ x1 (* x1 (* x1 9.0)))
     (if (<= x1 -9.5e+105)
       (+
        x1
        (/
         (- (* (* x2 x2) 36.0) (* 9.0 (* t_1 t_1)))
         (- (* x2 -6.0) (* t_3 t_0))))
       (if (<= x1 5.1e+140)
         (-
          x1
          (-
           (* 3.0 (/ (+ x1 (- (* 2.0 x2) t_3)) t_2))
           (-
            x1
            (-
             (+
              (* t_3 t_5)
              (*
               t_2
               (-
                (* (* (* x1 2.0) (/ (- t_4 x1) t_2)) (+ 3.0 t_5))
                (* 6.0 (* x1 x1)))))
             (* x1 (* x1 x1))))))
         (+
          x1
          (+
           (* x2 -6.0)
           (-
            (* 9.0 (* x1 x1))
            (* x1 (- 2.0 (* 4.0 (* 2.0 (* x2 x2)))))))))))))

C

double code(double x1, double x2) {
	double t_0 = x2 + (3.0 + x2);
	double t_1 = (x1 * x1) * t_0;
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = x1 * (x1 * 3.0);
	double t_4 = t_3 + (2.0 * x2);
	double t_5 = (x1 - t_4) / t_2;
	double tmp;
	if (x1 <= -4.5e+153) {
		tmp = x1 + (x1 * (x1 * 9.0));
	} else if (x1 <= -9.5e+105) {
		tmp = x1 + ((((x2 * x2) * 36.0) - (9.0 * (t_1 * t_1))) / ((x2 * -6.0) - (t_3 * t_0)));
	} else if (x1 <= 5.1e+140) {
		tmp = x1 - ((3.0 * ((x1 + ((2.0 * x2) - t_3)) / t_2)) - (x1 - (((t_3 * t_5) + (t_2 * ((((x1 * 2.0) * ((t_4 - x1) / t_2)) * (3.0 + t_5)) - (6.0 * (x1 * x1))))) - (x1 * (x1 * x1)))));
	} else {
		tmp = x1 + ((x2 * -6.0) + ((9.0 * (x1 * x1)) - (x1 * (2.0 - (4.0 * (2.0 * (x2 * x2)))))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_0 = x2 + (3.0d0 + x2)
    t_1 = (x1 * x1) * t_0
    t_2 = (x1 * x1) + 1.0d0
    t_3 = x1 * (x1 * 3.0d0)
    t_4 = t_3 + (2.0d0 * x2)
    t_5 = (x1 - t_4) / t_2
    if (x1 <= (-4.5d+153)) then
        tmp = x1 + (x1 * (x1 * 9.0d0))
    else if (x1 <= (-9.5d+105)) then
        tmp = x1 + ((((x2 * x2) * 36.0d0) - (9.0d0 * (t_1 * t_1))) / ((x2 * (-6.0d0)) - (t_3 * t_0)))
    else if (x1 <= 5.1d+140) then
        tmp = x1 - ((3.0d0 * ((x1 + ((2.0d0 * x2) - t_3)) / t_2)) - (x1 - (((t_3 * t_5) + (t_2 * ((((x1 * 2.0d0) * ((t_4 - x1) / t_2)) * (3.0d0 + t_5)) - (6.0d0 * (x1 * x1))))) - (x1 * (x1 * x1)))))
    else
        tmp = x1 + ((x2 * (-6.0d0)) + ((9.0d0 * (x1 * x1)) - (x1 * (2.0d0 - (4.0d0 * (2.0d0 * (x2 * x2)))))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x2 + (3.0 + x2);
	double t_1 = (x1 * x1) * t_0;
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = x1 * (x1 * 3.0);
	double t_4 = t_3 + (2.0 * x2);
	double t_5 = (x1 - t_4) / t_2;
	double tmp;
	if (x1 <= -4.5e+153) {
		tmp = x1 + (x1 * (x1 * 9.0));
	} else if (x1 <= -9.5e+105) {
		tmp = x1 + ((((x2 * x2) * 36.0) - (9.0 * (t_1 * t_1))) / ((x2 * -6.0) - (t_3 * t_0)));
	} else if (x1 <= 5.1e+140) {
		tmp = x1 - ((3.0 * ((x1 + ((2.0 * x2) - t_3)) / t_2)) - (x1 - (((t_3 * t_5) + (t_2 * ((((x1 * 2.0) * ((t_4 - x1) / t_2)) * (3.0 + t_5)) - (6.0 * (x1 * x1))))) - (x1 * (x1 * x1)))));
	} else {
		tmp = x1 + ((x2 * -6.0) + ((9.0 * (x1 * x1)) - (x1 * (2.0 - (4.0 * (2.0 * (x2 * x2)))))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x2 + (3.0 + x2)
	t_1 = (x1 * x1) * t_0
	t_2 = (x1 * x1) + 1.0
	t_3 = x1 * (x1 * 3.0)
	t_4 = t_3 + (2.0 * x2)
	t_5 = (x1 - t_4) / t_2
	tmp = 0
	if x1 <= -4.5e+153:
		tmp = x1 + (x1 * (x1 * 9.0))
	elif x1 <= -9.5e+105:
		tmp = x1 + ((((x2 * x2) * 36.0) - (9.0 * (t_1 * t_1))) / ((x2 * -6.0) - (t_3 * t_0)))
	elif x1 <= 5.1e+140:
		tmp = x1 - ((3.0 * ((x1 + ((2.0 * x2) - t_3)) / t_2)) - (x1 - (((t_3 * t_5) + (t_2 * ((((x1 * 2.0) * ((t_4 - x1) / t_2)) * (3.0 + t_5)) - (6.0 * (x1 * x1))))) - (x1 * (x1 * x1)))))
	else:
		tmp = x1 + ((x2 * -6.0) + ((9.0 * (x1 * x1)) - (x1 * (2.0 - (4.0 * (2.0 * (x2 * x2)))))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x2 + Float64(3.0 + x2))
	t_1 = Float64(Float64(x1 * x1) * t_0)
	t_2 = Float64(Float64(x1 * x1) + 1.0)
	t_3 = Float64(x1 * Float64(x1 * 3.0))
	t_4 = Float64(t_3 + Float64(2.0 * x2))
	t_5 = Float64(Float64(x1 - t_4) / t_2)
	tmp = 0.0
	if (x1 <= -4.5e+153)
		tmp = Float64(x1 + Float64(x1 * Float64(x1 * 9.0)));
	elseif (x1 <= -9.5e+105)
		tmp = Float64(x1 + Float64(Float64(Float64(Float64(x2 * x2) * 36.0) - Float64(9.0 * Float64(t_1 * t_1))) / Float64(Float64(x2 * -6.0) - Float64(t_3 * t_0))));
	elseif (x1 <= 5.1e+140)
		tmp = Float64(x1 - Float64(Float64(3.0 * Float64(Float64(x1 + Float64(Float64(2.0 * x2) - t_3)) / t_2)) - Float64(x1 - Float64(Float64(Float64(t_3 * t_5) + Float64(t_2 * Float64(Float64(Float64(Float64(x1 * 2.0) * Float64(Float64(t_4 - x1) / t_2)) * Float64(3.0 + t_5)) - Float64(6.0 * Float64(x1 * x1))))) - Float64(x1 * Float64(x1 * x1))))));
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(Float64(9.0 * Float64(x1 * x1)) - Float64(x1 * Float64(2.0 - Float64(4.0 * Float64(2.0 * Float64(x2 * x2))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x2 + (3.0 + x2);
	t_1 = (x1 * x1) * t_0;
	t_2 = (x1 * x1) + 1.0;
	t_3 = x1 * (x1 * 3.0);
	t_4 = t_3 + (2.0 * x2);
	t_5 = (x1 - t_4) / t_2;
	tmp = 0.0;
	if (x1 <= -4.5e+153)
		tmp = x1 + (x1 * (x1 * 9.0));
	elseif (x1 <= -9.5e+105)
		tmp = x1 + ((((x2 * x2) * 36.0) - (9.0 * (t_1 * t_1))) / ((x2 * -6.0) - (t_3 * t_0)));
	elseif (x1 <= 5.1e+140)
		tmp = x1 - ((3.0 * ((x1 + ((2.0 * x2) - t_3)) / t_2)) - (x1 - (((t_3 * t_5) + (t_2 * ((((x1 * 2.0) * ((t_4 - x1) / t_2)) * (3.0 + t_5)) - (6.0 * (x1 * x1))))) - (x1 * (x1 * x1)))));
	else
		tmp = x1 + ((x2 * -6.0) + ((9.0 * (x1 * x1)) - (x1 * (2.0 - (4.0 * (2.0 * (x2 * x2)))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x2 + N[(3.0 + x2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x1 * x1), $MachinePrecision] * t$95$0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$3 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$3 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(x1 - t$95$4), $MachinePrecision] / t$95$2), $MachinePrecision]}, If[LessEqual[x1, -4.5e+153], N[(x1 + N[(x1 * N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -9.5e+105], N[(x1 + N[(N[(N[(N[(x2 * x2), $MachinePrecision] * 36.0), $MachinePrecision] - N[(9.0 * N[(t$95$1 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(x2 * -6.0), $MachinePrecision] - N[(t$95$3 * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 5.1e+140], N[(x1 - N[(N[(3.0 * N[(N[(x1 + N[(N[(2.0 * x2), $MachinePrecision] - t$95$3), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision] - N[(x1 - N[(N[(N[(t$95$3 * t$95$5), $MachinePrecision] + N[(t$95$2 * N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * N[(N[(t$95$4 - x1), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision] * N[(3.0 + t$95$5), $MachinePrecision]), $MachinePrecision] - N[(6.0 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(N[(9.0 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] - N[(x1 * N[(2.0 - N[(4.0 * N[(2.0 * N[(x2 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -4.5000000000000001e153

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around 0 0.0%

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

   3. Taylor expanded in x1 around 0 42.9%

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

   4. Taylor expanded in x1 around inf 57.1%

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

      1. associate-*r* 57.1%

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

      2. *-commutative 57.1%

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

      3. cancel-sign-sub-inv 57.1%

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

      4. unpow2 57.1%

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

      5. +-commutative 57.1%

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

      6. distribute-lft-neg-in 57.1%

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

      7. *-commutative 57.1%

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

      8. distribute-lft-neg-in 57.1%

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

      9. metadata-eval 57.1%

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

      10. count-2 57.1%

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

   6. Simplified 57.1%

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

   7. Taylor expanded in x2 around 0 100.0%

      \[\leadsto \color{blue}{x1 + 9 \cdot {x1}^{2}} \]
   8. Step-by-step derivation

      1. *-commutative 100.0%

         \[\leadsto x1 + \color{blue}{{x1}^{2} \cdot 9} \]

      2. unpow2 100.0%

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

      3. associate-*r* 100.0%

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

   9. Simplified 100.0%

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

   if -4.5000000000000001e153 < x1 < -9.4999999999999995e105

   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. Taylor expanded in x1 around 0 0.2%

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

   3. Taylor expanded in x1 around 0 5.7%

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

   4. Taylor expanded in x1 around inf 23.9%

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

      1. associate-*r* 23.9%

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

      2. *-commutative 23.9%

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

      3. cancel-sign-sub-inv 23.9%

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

      4. unpow2 23.9%

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

      5. +-commutative 23.9%

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

      6. distribute-lft-neg-in 23.9%

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

      7. *-commutative 23.9%

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

      8. distribute-lft-neg-in 23.9%

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

      9. metadata-eval 23.9%

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

      10. count-2 23.9%

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

   6. Simplified 23.9%

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

      1. flip-+ 63.6%

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

      2. *-commutative 63.6%

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

      3. *-commutative 63.6%

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

      4. associate-*l* 63.6%

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

      5. associate-+l+ 63.6%

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

      6. associate-*l* 63.6%

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

      7. associate-+l+ 63.6%

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

      8. *-commutative 63.6%

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

   8. Applied egg-rr 63.6%

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

      1. swap-sqr 63.6%

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

      2. metadata-eval 63.6%

         \[\leadsto x1 + \frac{\left(x2 \cdot x2\right) \cdot \color{blue}{36} - \left(3 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right)\right) \cdot \left(3 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right)\right)}{x2 \cdot -6 - 3 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right)} \]

      3. swap-sqr 63.6%

         \[\leadsto x1 + \frac{\left(x2 \cdot x2\right) \cdot 36 - \color{blue}{\left(3 \cdot 3\right) \cdot \left(\left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right)\right)}}{x2 \cdot -6 - 3 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right)} \]

      4. metadata-eval 63.6%

         \[\leadsto x1 + \frac{\left(x2 \cdot x2\right) \cdot 36 - \color{blue}{9} \cdot \left(\left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right)\right)}{x2 \cdot -6 - 3 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right)} \]

      5. associate-*l* 63.6%

         \[\leadsto x1 + \frac{\left(x2 \cdot x2\right) \cdot 36 - 9 \cdot \left(\left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right)\right)}{x2 \cdot -6 - 3 \cdot \color{blue}{\left(x1 \cdot \left(x1 \cdot \left(x2 + \left(x2 + 3\right)\right)\right)\right)}} \]

      6. associate-*r* 63.6%

         \[\leadsto x1 + \frac{\left(x2 \cdot x2\right) \cdot 36 - 9 \cdot \left(\left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right)\right)}{x2 \cdot -6 - \color{blue}{\left(3 \cdot x1\right) \cdot \left(x1 \cdot \left(x2 + \left(x2 + 3\right)\right)\right)}} \]

      7. *-commutative 63.6%

         \[\leadsto x1 + \frac{\left(x2 \cdot x2\right) \cdot 36 - 9 \cdot \left(\left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right)\right)}{x2 \cdot -6 - \color{blue}{\left(x1 \cdot 3\right)} \cdot \left(x1 \cdot \left(x2 + \left(x2 + 3\right)\right)\right)} \]

      8. associate-*l* 63.6%

         \[\leadsto x1 + \frac{\left(x2 \cdot x2\right) \cdot 36 - 9 \cdot \left(\left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right)\right)}{x2 \cdot -6 - \color{blue}{\left(\left(x1 \cdot 3\right) \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)}} \]

      9. *-commutative 63.6%

         \[\leadsto x1 + \frac{\left(x2 \cdot x2\right) \cdot 36 - 9 \cdot \left(\left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right)\right)}{x2 \cdot -6 - \color{blue}{\left(x1 \cdot \left(x1 \cdot 3\right)\right)} \cdot \left(x2 + \left(x2 + 3\right)\right)} \]

   10. Simplified 63.6%

       \[\leadsto x1 + \color{blue}{\frac{\left(x2 \cdot x2\right) \cdot 36 - 9 \cdot \left(\left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right)\right)}{x2 \cdot -6 - \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(x2 + \left(x2 + 3\right)\right)}} \]

   if -9.4999999999999995e105 < x1 < 5.1e140

   1. Initial program 98.8%

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

   2. Taylor expanded in x1 around inf 97.1%

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

   if 5.1e140 < x1

   1. Initial program 3.1%

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

   2. Taylor expanded in x1 around 0 3.1%

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

   3. Taylor expanded in x1 around 0 81.3%

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

   4. Taylor expanded in x2 around 0 100.0%

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

      1. *-commutative 100.0%

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

      2. unpow2 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in x2 around inf 100.0%

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

      1. unpow2 100.0%

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

   9. Simplified 100.0%

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

4. Final simplification 96.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4.5 \cdot 10^{+153}:\\ \;\;\;\;x1 + x1 \cdot \left(x1 \cdot 9\right)\\ \mathbf{elif}\;x1 \leq -9.5 \cdot 10^{+105}:\\ \;\;\;\;x1 + \frac{\left(x2 \cdot x2\right) \cdot 36 - 9 \cdot \left(\left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(3 + x2\right)\right)\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(3 + x2\right)\right)\right)\right)}{x2 \cdot -6 - \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(x2 + \left(3 + x2\right)\right)}\\ \mathbf{elif}\;x1 \leq 5.1 \cdot 10^{+140}:\\ \;\;\;\;x1 - \left(3 \cdot \frac{x1 + \left(2 \cdot x2 - x1 \cdot \left(x1 \cdot 3\right)\right)}{x1 \cdot x1 + 1} - \left(x1 - \left(\left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1} + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(3 + \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right) - 6 \cdot \left(x1 \cdot x1\right)\right)\right) - x1 \cdot \left(x1 \cdot x1\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + \left(9 \cdot \left(x1 \cdot x1\right) - x1 \cdot \left(2 - 4 \cdot \left(2 \cdot \left(x2 \cdot x2\right)\right)\right)\right)\right)\\ \end{array} \]

Alternative 8: 88.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot x1\right)\\ t_1 := x1 \cdot x1 + 1\\ t_2 := x1 \cdot \left(x1 \cdot 3\right)\\ t_3 := 3 \cdot t_2\\ t_4 := x2 + \left(3 + x2\right)\\ t_5 := \left(x1 \cdot x1\right) \cdot t_4\\ t_6 := \frac{\left(t_2 + 2 \cdot x2\right) - x1}{t_1}\\ t_7 := \left(x1 \cdot x1\right) \cdot \left(4 \cdot t_6 - 6\right)\\ \mathbf{if}\;x1 \leq -4.5 \cdot 10^{+153}:\\ \;\;\;\;x1 + x1 \cdot \left(x1 \cdot 9\right)\\ \mathbf{elif}\;x1 \leq -9.5 \cdot 10^{+105}:\\ \;\;\;\;x1 + \frac{\left(x2 \cdot x2\right) \cdot 36 - 9 \cdot \left(t_5 \cdot t_5\right)}{x2 \cdot -6 - t_2 \cdot t_4}\\ \mathbf{elif}\;x1 \leq -650000:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t_2 - 2 \cdot x2\right) - x1}{t_1} + \left(x1 + \left(t_0 + \left(t_1 \cdot \left(t_7 + \frac{1}{x1} \cdot \left(\left(x1 \cdot 2\right) \cdot \left(\frac{1}{x1} - 3\right)\right)\right) + t_3\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -3.6 \cdot 10^{-241}:\\ \;\;\;\;x1 - \left(x1 \cdot \left(2 + 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right) - x2 \cdot -6\right)\\ \mathbf{elif}\;x1 \leq 4.2 \cdot 10^{-177}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + 8 \cdot \left(x2 \cdot \left(x1 \cdot x2\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 72 \lor \neg \left(x1 \leq 5.1 \cdot 10^{+140}\right):\\ \;\;\;\;x1 + \left(x2 \cdot -6 + \left(9 \cdot \left(x1 \cdot x1\right) - x1 \cdot \left(2 - 4 \cdot \left(2 \cdot \left(x2 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(t_0 + \left(t_3 + t_1 \cdot \left(t_7 + \left(t_6 - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(3 - \frac{1}{x1}\right)\right)\right)\right)\right)\right) + 3 \cdot \left(x2 \cdot -2 - x1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 x1)))
        (t_1 (+ (* x1 x1) 1.0))
        (t_2 (* x1 (* x1 3.0)))
        (t_3 (* 3.0 t_2))
        (t_4 (+ x2 (+ 3.0 x2)))
        (t_5 (* (* x1 x1) t_4))
        (t_6 (/ (- (+ t_2 (* 2.0 x2)) x1) t_1))
        (t_7 (* (* x1 x1) (- (* 4.0 t_6) 6.0))))
   (if (<= x1 -4.5e+153)
     (+ x1 (* x1 (* x1 9.0)))
     (if (<= x1 -9.5e+105)
       (+
        x1
        (/
         (- (* (* x2 x2) 36.0) (* 9.0 (* t_5 t_5)))
         (- (* x2 -6.0) (* t_2 t_4))))
       (if (<= x1 -650000.0)
         (+
          x1
          (+
           (* 3.0 (/ (- (- t_2 (* 2.0 x2)) x1) t_1))
           (+
            x1
            (+
             t_0
             (+
              (* t_1 (+ t_7 (* (/ 1.0 x1) (* (* x1 2.0) (- (/ 1.0 x1) 3.0)))))
              t_3)))))
         (if (<= x1 -3.6e-241)
           (-
            x1
            (- (* x1 (+ 2.0 (* 4.0 (* x2 (- 3.0 (* 2.0 x2)))))) (* x2 -6.0)))
           (if (<= x1 4.2e-177)
             (+ x1 (+ (* x2 -6.0) (* 8.0 (* x2 (* x1 x2)))))
             (if (or (<= x1 72.0) (not (<= x1 5.1e+140)))
               (+
                x1
                (+
                 (* x2 -6.0)
                 (-
                  (* 9.0 (* x1 x1))
                  (* x1 (- 2.0 (* 4.0 (* 2.0 (* x2 x2))))))))
               (+
                x1
                (+
                 (+
                  x1
                  (+
                   t_0
                   (+
                    t_3
                    (*
                     t_1
                     (+
                      t_7
                      (* (- t_6 3.0) (* (* x1 2.0) (- 3.0 (/ 1.0 x1)))))))))
                 (* 3.0 (- (* x2 -2.0) x1))))))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * x1);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = 3.0 * t_2;
	double t_4 = x2 + (3.0 + x2);
	double t_5 = (x1 * x1) * t_4;
	double t_6 = ((t_2 + (2.0 * x2)) - x1) / t_1;
	double t_7 = (x1 * x1) * ((4.0 * t_6) - 6.0);
	double tmp;
	if (x1 <= -4.5e+153) {
		tmp = x1 + (x1 * (x1 * 9.0));
	} else if (x1 <= -9.5e+105) {
		tmp = x1 + ((((x2 * x2) * 36.0) - (9.0 * (t_5 * t_5))) / ((x2 * -6.0) - (t_2 * t_4)));
	} else if (x1 <= -650000.0) {
		tmp = x1 + ((3.0 * (((t_2 - (2.0 * x2)) - x1) / t_1)) + (x1 + (t_0 + ((t_1 * (t_7 + ((1.0 / x1) * ((x1 * 2.0) * ((1.0 / x1) - 3.0))))) + t_3))));
	} else if (x1 <= -3.6e-241) {
		tmp = x1 - ((x1 * (2.0 + (4.0 * (x2 * (3.0 - (2.0 * x2)))))) - (x2 * -6.0));
	} else if (x1 <= 4.2e-177) {
		tmp = x1 + ((x2 * -6.0) + (8.0 * (x2 * (x1 * x2))));
	} else if ((x1 <= 72.0) || !(x1 <= 5.1e+140)) {
		tmp = x1 + ((x2 * -6.0) + ((9.0 * (x1 * x1)) - (x1 * (2.0 - (4.0 * (2.0 * (x2 * x2)))))));
	} else {
		tmp = x1 + ((x1 + (t_0 + (t_3 + (t_1 * (t_7 + ((t_6 - 3.0) * ((x1 * 2.0) * (3.0 - (1.0 / x1))))))))) + (3.0 * ((x2 * -2.0) - x1)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: tmp
    t_0 = x1 * (x1 * x1)
    t_1 = (x1 * x1) + 1.0d0
    t_2 = x1 * (x1 * 3.0d0)
    t_3 = 3.0d0 * t_2
    t_4 = x2 + (3.0d0 + x2)
    t_5 = (x1 * x1) * t_4
    t_6 = ((t_2 + (2.0d0 * x2)) - x1) / t_1
    t_7 = (x1 * x1) * ((4.0d0 * t_6) - 6.0d0)
    if (x1 <= (-4.5d+153)) then
        tmp = x1 + (x1 * (x1 * 9.0d0))
    else if (x1 <= (-9.5d+105)) then
        tmp = x1 + ((((x2 * x2) * 36.0d0) - (9.0d0 * (t_5 * t_5))) / ((x2 * (-6.0d0)) - (t_2 * t_4)))
    else if (x1 <= (-650000.0d0)) then
        tmp = x1 + ((3.0d0 * (((t_2 - (2.0d0 * x2)) - x1) / t_1)) + (x1 + (t_0 + ((t_1 * (t_7 + ((1.0d0 / x1) * ((x1 * 2.0d0) * ((1.0d0 / x1) - 3.0d0))))) + t_3))))
    else if (x1 <= (-3.6d-241)) then
        tmp = x1 - ((x1 * (2.0d0 + (4.0d0 * (x2 * (3.0d0 - (2.0d0 * x2)))))) - (x2 * (-6.0d0)))
    else if (x1 <= 4.2d-177) then
        tmp = x1 + ((x2 * (-6.0d0)) + (8.0d0 * (x2 * (x1 * x2))))
    else if ((x1 <= 72.0d0) .or. (.not. (x1 <= 5.1d+140))) then
        tmp = x1 + ((x2 * (-6.0d0)) + ((9.0d0 * (x1 * x1)) - (x1 * (2.0d0 - (4.0d0 * (2.0d0 * (x2 * x2)))))))
    else
        tmp = x1 + ((x1 + (t_0 + (t_3 + (t_1 * (t_7 + ((t_6 - 3.0d0) * ((x1 * 2.0d0) * (3.0d0 - (1.0d0 / x1))))))))) + (3.0d0 * ((x2 * (-2.0d0)) - x1)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * x1);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = 3.0 * t_2;
	double t_4 = x2 + (3.0 + x2);
	double t_5 = (x1 * x1) * t_4;
	double t_6 = ((t_2 + (2.0 * x2)) - x1) / t_1;
	double t_7 = (x1 * x1) * ((4.0 * t_6) - 6.0);
	double tmp;
	if (x1 <= -4.5e+153) {
		tmp = x1 + (x1 * (x1 * 9.0));
	} else if (x1 <= -9.5e+105) {
		tmp = x1 + ((((x2 * x2) * 36.0) - (9.0 * (t_5 * t_5))) / ((x2 * -6.0) - (t_2 * t_4)));
	} else if (x1 <= -650000.0) {
		tmp = x1 + ((3.0 * (((t_2 - (2.0 * x2)) - x1) / t_1)) + (x1 + (t_0 + ((t_1 * (t_7 + ((1.0 / x1) * ((x1 * 2.0) * ((1.0 / x1) - 3.0))))) + t_3))));
	} else if (x1 <= -3.6e-241) {
		tmp = x1 - ((x1 * (2.0 + (4.0 * (x2 * (3.0 - (2.0 * x2)))))) - (x2 * -6.0));
	} else if (x1 <= 4.2e-177) {
		tmp = x1 + ((x2 * -6.0) + (8.0 * (x2 * (x1 * x2))));
	} else if ((x1 <= 72.0) || !(x1 <= 5.1e+140)) {
		tmp = x1 + ((x2 * -6.0) + ((9.0 * (x1 * x1)) - (x1 * (2.0 - (4.0 * (2.0 * (x2 * x2)))))));
	} else {
		tmp = x1 + ((x1 + (t_0 + (t_3 + (t_1 * (t_7 + ((t_6 - 3.0) * ((x1 * 2.0) * (3.0 - (1.0 / x1))))))))) + (3.0 * ((x2 * -2.0) - x1)));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * x1)
	t_1 = (x1 * x1) + 1.0
	t_2 = x1 * (x1 * 3.0)
	t_3 = 3.0 * t_2
	t_4 = x2 + (3.0 + x2)
	t_5 = (x1 * x1) * t_4
	t_6 = ((t_2 + (2.0 * x2)) - x1) / t_1
	t_7 = (x1 * x1) * ((4.0 * t_6) - 6.0)
	tmp = 0
	if x1 <= -4.5e+153:
		tmp = x1 + (x1 * (x1 * 9.0))
	elif x1 <= -9.5e+105:
		tmp = x1 + ((((x2 * x2) * 36.0) - (9.0 * (t_5 * t_5))) / ((x2 * -6.0) - (t_2 * t_4)))
	elif x1 <= -650000.0:
		tmp = x1 + ((3.0 * (((t_2 - (2.0 * x2)) - x1) / t_1)) + (x1 + (t_0 + ((t_1 * (t_7 + ((1.0 / x1) * ((x1 * 2.0) * ((1.0 / x1) - 3.0))))) + t_3))))
	elif x1 <= -3.6e-241:
		tmp = x1 - ((x1 * (2.0 + (4.0 * (x2 * (3.0 - (2.0 * x2)))))) - (x2 * -6.0))
	elif x1 <= 4.2e-177:
		tmp = x1 + ((x2 * -6.0) + (8.0 * (x2 * (x1 * x2))))
	elif (x1 <= 72.0) or not (x1 <= 5.1e+140):
		tmp = x1 + ((x2 * -6.0) + ((9.0 * (x1 * x1)) - (x1 * (2.0 - (4.0 * (2.0 * (x2 * x2)))))))
	else:
		tmp = x1 + ((x1 + (t_0 + (t_3 + (t_1 * (t_7 + ((t_6 - 3.0) * ((x1 * 2.0) * (3.0 - (1.0 / x1))))))))) + (3.0 * ((x2 * -2.0) - x1)))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * x1))
	t_1 = Float64(Float64(x1 * x1) + 1.0)
	t_2 = Float64(x1 * Float64(x1 * 3.0))
	t_3 = Float64(3.0 * t_2)
	t_4 = Float64(x2 + Float64(3.0 + x2))
	t_5 = Float64(Float64(x1 * x1) * t_4)
	t_6 = Float64(Float64(Float64(t_2 + Float64(2.0 * x2)) - x1) / t_1)
	t_7 = Float64(Float64(x1 * x1) * Float64(Float64(4.0 * t_6) - 6.0))
	tmp = 0.0
	if (x1 <= -4.5e+153)
		tmp = Float64(x1 + Float64(x1 * Float64(x1 * 9.0)));
	elseif (x1 <= -9.5e+105)
		tmp = Float64(x1 + Float64(Float64(Float64(Float64(x2 * x2) * 36.0) - Float64(9.0 * Float64(t_5 * t_5))) / Float64(Float64(x2 * -6.0) - Float64(t_2 * t_4))));
	elseif (x1 <= -650000.0)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_2 - Float64(2.0 * x2)) - x1) / t_1)) + Float64(x1 + Float64(t_0 + Float64(Float64(t_1 * Float64(t_7 + Float64(Float64(1.0 / x1) * Float64(Float64(x1 * 2.0) * Float64(Float64(1.0 / x1) - 3.0))))) + t_3)))));
	elseif (x1 <= -3.6e-241)
		tmp = Float64(x1 - Float64(Float64(x1 * Float64(2.0 + Float64(4.0 * Float64(x2 * Float64(3.0 - Float64(2.0 * x2)))))) - Float64(x2 * -6.0)));
	elseif (x1 <= 4.2e-177)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(8.0 * Float64(x2 * Float64(x1 * x2)))));
	elseif ((x1 <= 72.0) || !(x1 <= 5.1e+140))
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(Float64(9.0 * Float64(x1 * x1)) - Float64(x1 * Float64(2.0 - Float64(4.0 * Float64(2.0 * Float64(x2 * x2))))))));
	else
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(t_0 + Float64(t_3 + Float64(t_1 * Float64(t_7 + Float64(Float64(t_6 - 3.0) * Float64(Float64(x1 * 2.0) * Float64(3.0 - Float64(1.0 / x1))))))))) + Float64(3.0 * Float64(Float64(x2 * -2.0) - x1))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * x1);
	t_1 = (x1 * x1) + 1.0;
	t_2 = x1 * (x1 * 3.0);
	t_3 = 3.0 * t_2;
	t_4 = x2 + (3.0 + x2);
	t_5 = (x1 * x1) * t_4;
	t_6 = ((t_2 + (2.0 * x2)) - x1) / t_1;
	t_7 = (x1 * x1) * ((4.0 * t_6) - 6.0);
	tmp = 0.0;
	if (x1 <= -4.5e+153)
		tmp = x1 + (x1 * (x1 * 9.0));
	elseif (x1 <= -9.5e+105)
		tmp = x1 + ((((x2 * x2) * 36.0) - (9.0 * (t_5 * t_5))) / ((x2 * -6.0) - (t_2 * t_4)));
	elseif (x1 <= -650000.0)
		tmp = x1 + ((3.0 * (((t_2 - (2.0 * x2)) - x1) / t_1)) + (x1 + (t_0 + ((t_1 * (t_7 + ((1.0 / x1) * ((x1 * 2.0) * ((1.0 / x1) - 3.0))))) + t_3))));
	elseif (x1 <= -3.6e-241)
		tmp = x1 - ((x1 * (2.0 + (4.0 * (x2 * (3.0 - (2.0 * x2)))))) - (x2 * -6.0));
	elseif (x1 <= 4.2e-177)
		tmp = x1 + ((x2 * -6.0) + (8.0 * (x2 * (x1 * x2))));
	elseif ((x1 <= 72.0) || ~((x1 <= 5.1e+140)))
		tmp = x1 + ((x2 * -6.0) + ((9.0 * (x1 * x1)) - (x1 * (2.0 - (4.0 * (2.0 * (x2 * x2)))))));
	else
		tmp = x1 + ((x1 + (t_0 + (t_3 + (t_1 * (t_7 + ((t_6 - 3.0) * ((x1 * 2.0) * (3.0 - (1.0 / x1))))))))) + (3.0 * ((x2 * -2.0) - x1)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$2 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(3.0 * t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(x2 + N[(3.0 + x2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(x1 * x1), $MachinePrecision] * t$95$4), $MachinePrecision]}, Block[{t$95$6 = N[(N[(N[(t$95$2 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$7 = N[(N[(x1 * x1), $MachinePrecision] * N[(N[(4.0 * t$95$6), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -4.5e+153], N[(x1 + N[(x1 * N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -9.5e+105], N[(x1 + N[(N[(N[(N[(x2 * x2), $MachinePrecision] * 36.0), $MachinePrecision] - N[(9.0 * N[(t$95$5 * t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(x2 * -6.0), $MachinePrecision] - N[(t$95$2 * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -650000.0], N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$2 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(t$95$0 + N[(N[(t$95$1 * N[(t$95$7 + N[(N[(1.0 / x1), $MachinePrecision] * N[(N[(x1 * 2.0), $MachinePrecision] * N[(N[(1.0 / x1), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -3.6e-241], N[(x1 - N[(N[(x1 * N[(2.0 + N[(4.0 * N[(x2 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 4.2e-177], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(8.0 * N[(x2 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x1, 72.0], N[Not[LessEqual[x1, 5.1e+140]], $MachinePrecision]], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(N[(9.0 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] - N[(x1 * N[(2.0 - N[(4.0 * N[(2.0 * N[(x2 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x1 + N[(t$95$0 + N[(t$95$3 + N[(t$95$1 * N[(t$95$7 + N[(N[(t$95$6 - 3.0), $MachinePrecision] * N[(N[(x1 * 2.0), $MachinePrecision] * N[(3.0 - N[(1.0 / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if x1 < -4.5000000000000001e153

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around 0 0.0%

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

   3. Taylor expanded in x1 around 0 42.9%

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

   4. Taylor expanded in x1 around inf 57.1%

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

      1. associate-*r* 57.1%

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

      2. *-commutative 57.1%

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

      3. cancel-sign-sub-inv 57.1%

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

      4. unpow2 57.1%

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

      5. +-commutative 57.1%

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

      6. distribute-lft-neg-in 57.1%

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

      7. *-commutative 57.1%

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

      8. distribute-lft-neg-in 57.1%

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

      9. metadata-eval 57.1%

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

      10. count-2 57.1%

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

   6. Simplified 57.1%

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

   7. Taylor expanded in x2 around 0 100.0%

      \[\leadsto \color{blue}{x1 + 9 \cdot {x1}^{2}} \]
   8. Step-by-step derivation

      1. *-commutative 100.0%

         \[\leadsto x1 + \color{blue}{{x1}^{2} \cdot 9} \]

      2. unpow2 100.0%

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

      3. associate-*r* 100.0%

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

   9. Simplified 100.0%

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

   if -4.5000000000000001e153 < x1 < -9.4999999999999995e105

   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. Taylor expanded in x1 around 0 0.2%

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

   3. Taylor expanded in x1 around 0 5.7%

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

   4. Taylor expanded in x1 around inf 23.9%

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

      1. associate-*r* 23.9%

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

      2. *-commutative 23.9%

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

      3. cancel-sign-sub-inv 23.9%

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

      4. unpow2 23.9%

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

      5. +-commutative 23.9%

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

      6. distribute-lft-neg-in 23.9%

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

      7. *-commutative 23.9%

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

      8. distribute-lft-neg-in 23.9%

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

      9. metadata-eval 23.9%

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

      10. count-2 23.9%

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

   6. Simplified 23.9%

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

      1. flip-+ 63.6%

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

      2. *-commutative 63.6%

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

      3. *-commutative 63.6%

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

      4. associate-*l* 63.6%

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

      5. associate-+l+ 63.6%

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

      6. associate-*l* 63.6%

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

      7. associate-+l+ 63.6%

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

      8. *-commutative 63.6%

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

   8. Applied egg-rr 63.6%

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

      1. swap-sqr 63.6%

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

      2. metadata-eval 63.6%

         \[\leadsto x1 + \frac{\left(x2 \cdot x2\right) \cdot \color{blue}{36} - \left(3 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right)\right) \cdot \left(3 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right)\right)}{x2 \cdot -6 - 3 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right)} \]

      3. swap-sqr 63.6%

         \[\leadsto x1 + \frac{\left(x2 \cdot x2\right) \cdot 36 - \color{blue}{\left(3 \cdot 3\right) \cdot \left(\left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right)\right)}}{x2 \cdot -6 - 3 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right)} \]

      4. metadata-eval 63.6%

         \[\leadsto x1 + \frac{\left(x2 \cdot x2\right) \cdot 36 - \color{blue}{9} \cdot \left(\left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right)\right)}{x2 \cdot -6 - 3 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right)} \]

      5. associate-*l* 63.6%

         \[\leadsto x1 + \frac{\left(x2 \cdot x2\right) \cdot 36 - 9 \cdot \left(\left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right)\right)}{x2 \cdot -6 - 3 \cdot \color{blue}{\left(x1 \cdot \left(x1 \cdot \left(x2 + \left(x2 + 3\right)\right)\right)\right)}} \]

      6. associate-*r* 63.6%

         \[\leadsto x1 + \frac{\left(x2 \cdot x2\right) \cdot 36 - 9 \cdot \left(\left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right)\right)}{x2 \cdot -6 - \color{blue}{\left(3 \cdot x1\right) \cdot \left(x1 \cdot \left(x2 + \left(x2 + 3\right)\right)\right)}} \]

      7. *-commutative 63.6%

         \[\leadsto x1 + \frac{\left(x2 \cdot x2\right) \cdot 36 - 9 \cdot \left(\left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right)\right)}{x2 \cdot -6 - \color{blue}{\left(x1 \cdot 3\right)} \cdot \left(x1 \cdot \left(x2 + \left(x2 + 3\right)\right)\right)} \]

      8. associate-*l* 63.6%

         \[\leadsto x1 + \frac{\left(x2 \cdot x2\right) \cdot 36 - 9 \cdot \left(\left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right)\right)}{x2 \cdot -6 - \color{blue}{\left(\left(x1 \cdot 3\right) \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)}} \]

      9. *-commutative 63.6%

         \[\leadsto x1 + \frac{\left(x2 \cdot x2\right) \cdot 36 - 9 \cdot \left(\left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right)\right)}{x2 \cdot -6 - \color{blue}{\left(x1 \cdot \left(x1 \cdot 3\right)\right)} \cdot \left(x2 + \left(x2 + 3\right)\right)} \]

   10. Simplified 63.6%

       \[\leadsto x1 + \color{blue}{\frac{\left(x2 \cdot x2\right) \cdot 36 - 9 \cdot \left(\left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right)\right)}{x2 \cdot -6 - \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(x2 + \left(x2 + 3\right)\right)}} \]

   if -9.4999999999999995e105 < x1 < -6.5e5

   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. Taylor expanded in x1 around inf 99.4%

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

   3. Taylor expanded in x1 around inf 99.4%

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

   4. Taylor expanded in x1 around inf 99.4%

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

   if -6.5e5 < x1 < -3.5999999999999999e-241

   1. Initial program 97.7%

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

   2. Taylor expanded in x1 around 0 88.1%

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

   3. Taylor expanded in x1 around 0 88.4%

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

   if -3.5999999999999999e-241 < x1 < 4.20000000000000002e-177

   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. Taylor expanded in x1 around 0 72.9%

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

   3. Taylor expanded in x1 around 0 72.9%

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

   4. Taylor expanded in x2 around 0 72.9%

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

      1. *-commutative 72.9%

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

      2. unpow2 72.9%

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

   6. Simplified 72.9%

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

   7. Taylor expanded in x2 around inf 71.0%

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

      1. *-commutative 71.0%

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

      2. unpow2 71.0%

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

      3. associate-*l* 97.8%

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

      4. *-commutative 97.8%

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

   9. Simplified 97.8%

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

   if 4.20000000000000002e-177 < x1 < 72 or 5.1e140 < x1

   1. Initial program 51.9%

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

   2. Taylor expanded in x1 around 0 48.3%

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

   3. Taylor expanded in x1 around 0 87.1%

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

   4. Taylor expanded in x2 around 0 96.3%

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

      1. *-commutative 96.3%

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

      2. unpow2 96.3%

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

   6. Simplified 96.3%

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

   7. Taylor expanded in x2 around inf 96.3%

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

      1. unpow2 96.3%

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

   9. Simplified 96.3%

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

   if 72 < x1 < 5.1e140

   1. Initial program 99.2%

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

   2. Taylor expanded in x1 around inf 87.3%

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

   3. Taylor expanded in x1 around inf 86.8%

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

   4. Taylor expanded in x1 around 0 87.3%

      \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \left(3 - \frac{1}{x1}\right)\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot 3\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \color{blue}{\left(-2 \cdot x2 + -1 \cdot x1\right)}\right) \]
3. Recombined 7 regimes into one program.

4. Final simplification 93.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4.5 \cdot 10^{+153}:\\ \;\;\;\;x1 + x1 \cdot \left(x1 \cdot 9\right)\\ \mathbf{elif}\;x1 \leq -9.5 \cdot 10^{+105}:\\ \;\;\;\;x1 + \frac{\left(x2 \cdot x2\right) \cdot 36 - 9 \cdot \left(\left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(3 + x2\right)\right)\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(3 + x2\right)\right)\right)\right)}{x2 \cdot -6 - \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(x2 + \left(3 + x2\right)\right)}\\ \mathbf{elif}\;x1 \leq -650000:\\ \;\;\;\;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 x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right) + \frac{1}{x1} \cdot \left(\left(x1 \cdot 2\right) \cdot \left(\frac{1}{x1} - 3\right)\right)\right) + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -3.6 \cdot 10^{-241}:\\ \;\;\;\;x1 - \left(x1 \cdot \left(2 + 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right) - x2 \cdot -6\right)\\ \mathbf{elif}\;x1 \leq 4.2 \cdot 10^{-177}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + 8 \cdot \left(x2 \cdot \left(x1 \cdot x2\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 72 \lor \neg \left(x1 \leq 5.1 \cdot 10^{+140}\right):\\ \;\;\;\;x1 + \left(x2 \cdot -6 + \left(9 \cdot \left(x1 \cdot x1\right) - x1 \cdot \left(2 - 4 \cdot \left(2 \cdot \left(x2 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right) + \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(3 - \frac{1}{x1}\right)\right)\right)\right)\right)\right) + 3 \cdot \left(x2 \cdot -2 - x1\right)\right)\\ \end{array} \]

Alternative 9: 88.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot x1\right)\\ t_1 := x1 \cdot x1 + 1\\ t_2 := x1 \cdot \left(x1 \cdot 3\right)\\ t_3 := 3 \cdot t_2\\ t_4 := x2 + \left(3 + x2\right)\\ t_5 := \left(x1 \cdot x1\right) \cdot t_4\\ t_6 := \frac{\left(t_2 + 2 \cdot x2\right) - x1}{t_1}\\ t_7 := \left(x1 \cdot x1\right) \cdot \left(4 \cdot t_6 - 6\right)\\ \mathbf{if}\;x1 \leq -4.5 \cdot 10^{+153}:\\ \;\;\;\;x1 + x1 \cdot \left(x1 \cdot 9\right)\\ \mathbf{elif}\;x1 \leq -9.5 \cdot 10^{+105}:\\ \;\;\;\;x1 + \frac{\left(x2 \cdot x2\right) \cdot 36 - 9 \cdot \left(t_5 \cdot t_5\right)}{x2 \cdot -6 - t_2 \cdot t_4}\\ \mathbf{elif}\;x1 \leq -900000:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t_2 - 2 \cdot x2\right) - x1}{t_1} + \left(x1 + \left(t_0 + \left(t_1 \cdot \left(t_7 + \frac{1}{x1} \cdot \left(\left(x1 \cdot 2\right) \cdot \left(\frac{1}{x1} - 3\right)\right)\right) + t_3\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -9.5 \cdot 10^{-240}:\\ \;\;\;\;x1 - \left(x1 \cdot \left(2 + 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right) - x2 \cdot -6\right)\\ \mathbf{elif}\;x1 \leq 8.6 \cdot 10^{-178}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + 8 \cdot \left(x2 \cdot \left(x1 \cdot x2\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 140 \lor \neg \left(x1 \leq 5.1 \cdot 10^{+140}\right):\\ \;\;\;\;x1 + \left(x2 \cdot -6 + \left(9 \cdot \left(x1 \cdot x1\right) - x1 \cdot \left(2 - 4 \cdot \left(2 \cdot \left(x2 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(t_0 + \left(t_3 + t_1 \cdot \left(t_7 + \left(t_6 - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(3 - \frac{1}{x1}\right)\right)\right)\right)\right)\right) + 3 \cdot \left(x2 \cdot -2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 x1)))
        (t_1 (+ (* x1 x1) 1.0))
        (t_2 (* x1 (* x1 3.0)))
        (t_3 (* 3.0 t_2))
        (t_4 (+ x2 (+ 3.0 x2)))
        (t_5 (* (* x1 x1) t_4))
        (t_6 (/ (- (+ t_2 (* 2.0 x2)) x1) t_1))
        (t_7 (* (* x1 x1) (- (* 4.0 t_6) 6.0))))
   (if (<= x1 -4.5e+153)
     (+ x1 (* x1 (* x1 9.0)))
     (if (<= x1 -9.5e+105)
       (+
        x1
        (/
         (- (* (* x2 x2) 36.0) (* 9.0 (* t_5 t_5)))
         (- (* x2 -6.0) (* t_2 t_4))))
       (if (<= x1 -900000.0)
         (+
          x1
          (+
           (* 3.0 (/ (- (- t_2 (* 2.0 x2)) x1) t_1))
           (+
            x1
            (+
             t_0
             (+
              (* t_1 (+ t_7 (* (/ 1.0 x1) (* (* x1 2.0) (- (/ 1.0 x1) 3.0)))))
              t_3)))))
         (if (<= x1 -9.5e-240)
           (-
            x1
            (- (* x1 (+ 2.0 (* 4.0 (* x2 (- 3.0 (* 2.0 x2)))))) (* x2 -6.0)))
           (if (<= x1 8.6e-178)
             (+ x1 (+ (* x2 -6.0) (* 8.0 (* x2 (* x1 x2)))))
             (if (or (<= x1 140.0) (not (<= x1 5.1e+140)))
               (+
                x1
                (+
                 (* x2 -6.0)
                 (-
                  (* 9.0 (* x1 x1))
                  (* x1 (- 2.0 (* 4.0 (* 2.0 (* x2 x2))))))))
               (+
                x1
                (+
                 (+
                  x1
                  (+
                   t_0
                   (+
                    t_3
                    (*
                     t_1
                     (+
                      t_7
                      (* (- t_6 3.0) (* (* x1 2.0) (- 3.0 (/ 1.0 x1)))))))))
                 (* 3.0 (* x2 -2.0))))))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * x1);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = 3.0 * t_2;
	double t_4 = x2 + (3.0 + x2);
	double t_5 = (x1 * x1) * t_4;
	double t_6 = ((t_2 + (2.0 * x2)) - x1) / t_1;
	double t_7 = (x1 * x1) * ((4.0 * t_6) - 6.0);
	double tmp;
	if (x1 <= -4.5e+153) {
		tmp = x1 + (x1 * (x1 * 9.0));
	} else if (x1 <= -9.5e+105) {
		tmp = x1 + ((((x2 * x2) * 36.0) - (9.0 * (t_5 * t_5))) / ((x2 * -6.0) - (t_2 * t_4)));
	} else if (x1 <= -900000.0) {
		tmp = x1 + ((3.0 * (((t_2 - (2.0 * x2)) - x1) / t_1)) + (x1 + (t_0 + ((t_1 * (t_7 + ((1.0 / x1) * ((x1 * 2.0) * ((1.0 / x1) - 3.0))))) + t_3))));
	} else if (x1 <= -9.5e-240) {
		tmp = x1 - ((x1 * (2.0 + (4.0 * (x2 * (3.0 - (2.0 * x2)))))) - (x2 * -6.0));
	} else if (x1 <= 8.6e-178) {
		tmp = x1 + ((x2 * -6.0) + (8.0 * (x2 * (x1 * x2))));
	} else if ((x1 <= 140.0) || !(x1 <= 5.1e+140)) {
		tmp = x1 + ((x2 * -6.0) + ((9.0 * (x1 * x1)) - (x1 * (2.0 - (4.0 * (2.0 * (x2 * x2)))))));
	} else {
		tmp = x1 + ((x1 + (t_0 + (t_3 + (t_1 * (t_7 + ((t_6 - 3.0) * ((x1 * 2.0) * (3.0 - (1.0 / x1))))))))) + (3.0 * (x2 * -2.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: tmp
    t_0 = x1 * (x1 * x1)
    t_1 = (x1 * x1) + 1.0d0
    t_2 = x1 * (x1 * 3.0d0)
    t_3 = 3.0d0 * t_2
    t_4 = x2 + (3.0d0 + x2)
    t_5 = (x1 * x1) * t_4
    t_6 = ((t_2 + (2.0d0 * x2)) - x1) / t_1
    t_7 = (x1 * x1) * ((4.0d0 * t_6) - 6.0d0)
    if (x1 <= (-4.5d+153)) then
        tmp = x1 + (x1 * (x1 * 9.0d0))
    else if (x1 <= (-9.5d+105)) then
        tmp = x1 + ((((x2 * x2) * 36.0d0) - (9.0d0 * (t_5 * t_5))) / ((x2 * (-6.0d0)) - (t_2 * t_4)))
    else if (x1 <= (-900000.0d0)) then
        tmp = x1 + ((3.0d0 * (((t_2 - (2.0d0 * x2)) - x1) / t_1)) + (x1 + (t_0 + ((t_1 * (t_7 + ((1.0d0 / x1) * ((x1 * 2.0d0) * ((1.0d0 / x1) - 3.0d0))))) + t_3))))
    else if (x1 <= (-9.5d-240)) then
        tmp = x1 - ((x1 * (2.0d0 + (4.0d0 * (x2 * (3.0d0 - (2.0d0 * x2)))))) - (x2 * (-6.0d0)))
    else if (x1 <= 8.6d-178) then
        tmp = x1 + ((x2 * (-6.0d0)) + (8.0d0 * (x2 * (x1 * x2))))
    else if ((x1 <= 140.0d0) .or. (.not. (x1 <= 5.1d+140))) then
        tmp = x1 + ((x2 * (-6.0d0)) + ((9.0d0 * (x1 * x1)) - (x1 * (2.0d0 - (4.0d0 * (2.0d0 * (x2 * x2)))))))
    else
        tmp = x1 + ((x1 + (t_0 + (t_3 + (t_1 * (t_7 + ((t_6 - 3.0d0) * ((x1 * 2.0d0) * (3.0d0 - (1.0d0 / x1))))))))) + (3.0d0 * (x2 * (-2.0d0))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * x1);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = 3.0 * t_2;
	double t_4 = x2 + (3.0 + x2);
	double t_5 = (x1 * x1) * t_4;
	double t_6 = ((t_2 + (2.0 * x2)) - x1) / t_1;
	double t_7 = (x1 * x1) * ((4.0 * t_6) - 6.0);
	double tmp;
	if (x1 <= -4.5e+153) {
		tmp = x1 + (x1 * (x1 * 9.0));
	} else if (x1 <= -9.5e+105) {
		tmp = x1 + ((((x2 * x2) * 36.0) - (9.0 * (t_5 * t_5))) / ((x2 * -6.0) - (t_2 * t_4)));
	} else if (x1 <= -900000.0) {
		tmp = x1 + ((3.0 * (((t_2 - (2.0 * x2)) - x1) / t_1)) + (x1 + (t_0 + ((t_1 * (t_7 + ((1.0 / x1) * ((x1 * 2.0) * ((1.0 / x1) - 3.0))))) + t_3))));
	} else if (x1 <= -9.5e-240) {
		tmp = x1 - ((x1 * (2.0 + (4.0 * (x2 * (3.0 - (2.0 * x2)))))) - (x2 * -6.0));
	} else if (x1 <= 8.6e-178) {
		tmp = x1 + ((x2 * -6.0) + (8.0 * (x2 * (x1 * x2))));
	} else if ((x1 <= 140.0) || !(x1 <= 5.1e+140)) {
		tmp = x1 + ((x2 * -6.0) + ((9.0 * (x1 * x1)) - (x1 * (2.0 - (4.0 * (2.0 * (x2 * x2)))))));
	} else {
		tmp = x1 + ((x1 + (t_0 + (t_3 + (t_1 * (t_7 + ((t_6 - 3.0) * ((x1 * 2.0) * (3.0 - (1.0 / x1))))))))) + (3.0 * (x2 * -2.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * x1)
	t_1 = (x1 * x1) + 1.0
	t_2 = x1 * (x1 * 3.0)
	t_3 = 3.0 * t_2
	t_4 = x2 + (3.0 + x2)
	t_5 = (x1 * x1) * t_4
	t_6 = ((t_2 + (2.0 * x2)) - x1) / t_1
	t_7 = (x1 * x1) * ((4.0 * t_6) - 6.0)
	tmp = 0
	if x1 <= -4.5e+153:
		tmp = x1 + (x1 * (x1 * 9.0))
	elif x1 <= -9.5e+105:
		tmp = x1 + ((((x2 * x2) * 36.0) - (9.0 * (t_5 * t_5))) / ((x2 * -6.0) - (t_2 * t_4)))
	elif x1 <= -900000.0:
		tmp = x1 + ((3.0 * (((t_2 - (2.0 * x2)) - x1) / t_1)) + (x1 + (t_0 + ((t_1 * (t_7 + ((1.0 / x1) * ((x1 * 2.0) * ((1.0 / x1) - 3.0))))) + t_3))))
	elif x1 <= -9.5e-240:
		tmp = x1 - ((x1 * (2.0 + (4.0 * (x2 * (3.0 - (2.0 * x2)))))) - (x2 * -6.0))
	elif x1 <= 8.6e-178:
		tmp = x1 + ((x2 * -6.0) + (8.0 * (x2 * (x1 * x2))))
	elif (x1 <= 140.0) or not (x1 <= 5.1e+140):
		tmp = x1 + ((x2 * -6.0) + ((9.0 * (x1 * x1)) - (x1 * (2.0 - (4.0 * (2.0 * (x2 * x2)))))))
	else:
		tmp = x1 + ((x1 + (t_0 + (t_3 + (t_1 * (t_7 + ((t_6 - 3.0) * ((x1 * 2.0) * (3.0 - (1.0 / x1))))))))) + (3.0 * (x2 * -2.0)))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * x1))
	t_1 = Float64(Float64(x1 * x1) + 1.0)
	t_2 = Float64(x1 * Float64(x1 * 3.0))
	t_3 = Float64(3.0 * t_2)
	t_4 = Float64(x2 + Float64(3.0 + x2))
	t_5 = Float64(Float64(x1 * x1) * t_4)
	t_6 = Float64(Float64(Float64(t_2 + Float64(2.0 * x2)) - x1) / t_1)
	t_7 = Float64(Float64(x1 * x1) * Float64(Float64(4.0 * t_6) - 6.0))
	tmp = 0.0
	if (x1 <= -4.5e+153)
		tmp = Float64(x1 + Float64(x1 * Float64(x1 * 9.0)));
	elseif (x1 <= -9.5e+105)
		tmp = Float64(x1 + Float64(Float64(Float64(Float64(x2 * x2) * 36.0) - Float64(9.0 * Float64(t_5 * t_5))) / Float64(Float64(x2 * -6.0) - Float64(t_2 * t_4))));
	elseif (x1 <= -900000.0)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_2 - Float64(2.0 * x2)) - x1) / t_1)) + Float64(x1 + Float64(t_0 + Float64(Float64(t_1 * Float64(t_7 + Float64(Float64(1.0 / x1) * Float64(Float64(x1 * 2.0) * Float64(Float64(1.0 / x1) - 3.0))))) + t_3)))));
	elseif (x1 <= -9.5e-240)
		tmp = Float64(x1 - Float64(Float64(x1 * Float64(2.0 + Float64(4.0 * Float64(x2 * Float64(3.0 - Float64(2.0 * x2)))))) - Float64(x2 * -6.0)));
	elseif (x1 <= 8.6e-178)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(8.0 * Float64(x2 * Float64(x1 * x2)))));
	elseif ((x1 <= 140.0) || !(x1 <= 5.1e+140))
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(Float64(9.0 * Float64(x1 * x1)) - Float64(x1 * Float64(2.0 - Float64(4.0 * Float64(2.0 * Float64(x2 * x2))))))));
	else
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(t_0 + Float64(t_3 + Float64(t_1 * Float64(t_7 + Float64(Float64(t_6 - 3.0) * Float64(Float64(x1 * 2.0) * Float64(3.0 - Float64(1.0 / x1))))))))) + Float64(3.0 * Float64(x2 * -2.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * x1);
	t_1 = (x1 * x1) + 1.0;
	t_2 = x1 * (x1 * 3.0);
	t_3 = 3.0 * t_2;
	t_4 = x2 + (3.0 + x2);
	t_5 = (x1 * x1) * t_4;
	t_6 = ((t_2 + (2.0 * x2)) - x1) / t_1;
	t_7 = (x1 * x1) * ((4.0 * t_6) - 6.0);
	tmp = 0.0;
	if (x1 <= -4.5e+153)
		tmp = x1 + (x1 * (x1 * 9.0));
	elseif (x1 <= -9.5e+105)
		tmp = x1 + ((((x2 * x2) * 36.0) - (9.0 * (t_5 * t_5))) / ((x2 * -6.0) - (t_2 * t_4)));
	elseif (x1 <= -900000.0)
		tmp = x1 + ((3.0 * (((t_2 - (2.0 * x2)) - x1) / t_1)) + (x1 + (t_0 + ((t_1 * (t_7 + ((1.0 / x1) * ((x1 * 2.0) * ((1.0 / x1) - 3.0))))) + t_3))));
	elseif (x1 <= -9.5e-240)
		tmp = x1 - ((x1 * (2.0 + (4.0 * (x2 * (3.0 - (2.0 * x2)))))) - (x2 * -6.0));
	elseif (x1 <= 8.6e-178)
		tmp = x1 + ((x2 * -6.0) + (8.0 * (x2 * (x1 * x2))));
	elseif ((x1 <= 140.0) || ~((x1 <= 5.1e+140)))
		tmp = x1 + ((x2 * -6.0) + ((9.0 * (x1 * x1)) - (x1 * (2.0 - (4.0 * (2.0 * (x2 * x2)))))));
	else
		tmp = x1 + ((x1 + (t_0 + (t_3 + (t_1 * (t_7 + ((t_6 - 3.0) * ((x1 * 2.0) * (3.0 - (1.0 / x1))))))))) + (3.0 * (x2 * -2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$2 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(3.0 * t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(x2 + N[(3.0 + x2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(x1 * x1), $MachinePrecision] * t$95$4), $MachinePrecision]}, Block[{t$95$6 = N[(N[(N[(t$95$2 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$7 = N[(N[(x1 * x1), $MachinePrecision] * N[(N[(4.0 * t$95$6), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -4.5e+153], N[(x1 + N[(x1 * N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -9.5e+105], N[(x1 + N[(N[(N[(N[(x2 * x2), $MachinePrecision] * 36.0), $MachinePrecision] - N[(9.0 * N[(t$95$5 * t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(x2 * -6.0), $MachinePrecision] - N[(t$95$2 * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -900000.0], N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$2 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(t$95$0 + N[(N[(t$95$1 * N[(t$95$7 + N[(N[(1.0 / x1), $MachinePrecision] * N[(N[(x1 * 2.0), $MachinePrecision] * N[(N[(1.0 / x1), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -9.5e-240], N[(x1 - N[(N[(x1 * N[(2.0 + N[(4.0 * N[(x2 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 8.6e-178], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(8.0 * N[(x2 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x1, 140.0], N[Not[LessEqual[x1, 5.1e+140]], $MachinePrecision]], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(N[(9.0 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] - N[(x1 * N[(2.0 - N[(4.0 * N[(2.0 * N[(x2 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x1 + N[(t$95$0 + N[(t$95$3 + N[(t$95$1 * N[(t$95$7 + N[(N[(t$95$6 - 3.0), $MachinePrecision] * N[(N[(x1 * 2.0), $MachinePrecision] * N[(3.0 - N[(1.0 / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if x1 < -4.5000000000000001e153

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around 0 0.0%

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

   3. Taylor expanded in x1 around 0 42.9%

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

   4. Taylor expanded in x1 around inf 57.1%

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

      1. associate-*r* 57.1%

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

      2. *-commutative 57.1%

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

      3. cancel-sign-sub-inv 57.1%

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

      4. unpow2 57.1%

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

      5. +-commutative 57.1%

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

      6. distribute-lft-neg-in 57.1%

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

      7. *-commutative 57.1%

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

      8. distribute-lft-neg-in 57.1%

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

      9. metadata-eval 57.1%

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

      10. count-2 57.1%

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

   6. Simplified 57.1%

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

   7. Taylor expanded in x2 around 0 100.0%

      \[\leadsto \color{blue}{x1 + 9 \cdot {x1}^{2}} \]
   8. Step-by-step derivation

      1. *-commutative 100.0%

         \[\leadsto x1 + \color{blue}{{x1}^{2} \cdot 9} \]

      2. unpow2 100.0%

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

      3. associate-*r* 100.0%

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

   9. Simplified 100.0%

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

   if -4.5000000000000001e153 < x1 < -9.4999999999999995e105

   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. Taylor expanded in x1 around 0 0.2%

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

   3. Taylor expanded in x1 around 0 5.7%

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

   4. Taylor expanded in x1 around inf 23.9%

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

      1. associate-*r* 23.9%

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

      2. *-commutative 23.9%

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

      3. cancel-sign-sub-inv 23.9%

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

      4. unpow2 23.9%

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

      5. +-commutative 23.9%

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

      6. distribute-lft-neg-in 23.9%

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

      7. *-commutative 23.9%

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

      8. distribute-lft-neg-in 23.9%

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

      9. metadata-eval 23.9%

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

      10. count-2 23.9%

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

   6. Simplified 23.9%

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

      1. flip-+ 63.6%

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

      2. *-commutative 63.6%

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

      3. *-commutative 63.6%

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

      4. associate-*l* 63.6%

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

      5. associate-+l+ 63.6%

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

      6. associate-*l* 63.6%

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

      7. associate-+l+ 63.6%

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

      8. *-commutative 63.6%

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

   8. Applied egg-rr 63.6%

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

      1. swap-sqr 63.6%

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

      2. metadata-eval 63.6%

         \[\leadsto x1 + \frac{\left(x2 \cdot x2\right) \cdot \color{blue}{36} - \left(3 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right)\right) \cdot \left(3 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right)\right)}{x2 \cdot -6 - 3 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right)} \]

      3. swap-sqr 63.6%

         \[\leadsto x1 + \frac{\left(x2 \cdot x2\right) \cdot 36 - \color{blue}{\left(3 \cdot 3\right) \cdot \left(\left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right)\right)}}{x2 \cdot -6 - 3 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right)} \]

      4. metadata-eval 63.6%

         \[\leadsto x1 + \frac{\left(x2 \cdot x2\right) \cdot 36 - \color{blue}{9} \cdot \left(\left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right)\right)}{x2 \cdot -6 - 3 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right)} \]

      5. associate-*l* 63.6%

         \[\leadsto x1 + \frac{\left(x2 \cdot x2\right) \cdot 36 - 9 \cdot \left(\left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right)\right)}{x2 \cdot -6 - 3 \cdot \color{blue}{\left(x1 \cdot \left(x1 \cdot \left(x2 + \left(x2 + 3\right)\right)\right)\right)}} \]

      6. associate-*r* 63.6%

         \[\leadsto x1 + \frac{\left(x2 \cdot x2\right) \cdot 36 - 9 \cdot \left(\left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right)\right)}{x2 \cdot -6 - \color{blue}{\left(3 \cdot x1\right) \cdot \left(x1 \cdot \left(x2 + \left(x2 + 3\right)\right)\right)}} \]

      7. *-commutative 63.6%

         \[\leadsto x1 + \frac{\left(x2 \cdot x2\right) \cdot 36 - 9 \cdot \left(\left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right)\right)}{x2 \cdot -6 - \color{blue}{\left(x1 \cdot 3\right)} \cdot \left(x1 \cdot \left(x2 + \left(x2 + 3\right)\right)\right)} \]

      8. associate-*l* 63.6%

         \[\leadsto x1 + \frac{\left(x2 \cdot x2\right) \cdot 36 - 9 \cdot \left(\left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right)\right)}{x2 \cdot -6 - \color{blue}{\left(\left(x1 \cdot 3\right) \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)}} \]

      9. *-commutative 63.6%

         \[\leadsto x1 + \frac{\left(x2 \cdot x2\right) \cdot 36 - 9 \cdot \left(\left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right)\right)}{x2 \cdot -6 - \color{blue}{\left(x1 \cdot \left(x1 \cdot 3\right)\right)} \cdot \left(x2 + \left(x2 + 3\right)\right)} \]

   10. Simplified 63.6%

       \[\leadsto x1 + \color{blue}{\frac{\left(x2 \cdot x2\right) \cdot 36 - 9 \cdot \left(\left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right)\right)}{x2 \cdot -6 - \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(x2 + \left(x2 + 3\right)\right)}} \]

   if -9.4999999999999995e105 < x1 < -9e5

   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. Taylor expanded in x1 around inf 99.4%

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

   3. Taylor expanded in x1 around inf 99.4%

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

   4. Taylor expanded in x1 around inf 99.4%

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

   if -9e5 < x1 < -9.5000000000000005e-240

   1. Initial program 97.7%

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

   2. Taylor expanded in x1 around 0 88.1%

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

   3. Taylor expanded in x1 around 0 88.4%

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

   if -9.5000000000000005e-240 < x1 < 8.6e-178

   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. Taylor expanded in x1 around 0 72.9%

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

   3. Taylor expanded in x1 around 0 72.9%

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

   4. Taylor expanded in x2 around 0 72.9%

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

      1. *-commutative 72.9%

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

      2. unpow2 72.9%

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

   6. Simplified 72.9%

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

   7. Taylor expanded in x2 around inf 71.0%

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

      1. *-commutative 71.0%

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

      2. unpow2 71.0%

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

      3. associate-*l* 97.8%

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

      4. *-commutative 97.8%

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

   9. Simplified 97.8%

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

   if 8.6e-178 < x1 < 140 or 5.1e140 < x1

   1. Initial program 51.9%

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

   2. Taylor expanded in x1 around 0 48.3%

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

   3. Taylor expanded in x1 around 0 87.1%

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

   4. Taylor expanded in x2 around 0 96.3%

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

      1. *-commutative 96.3%

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

      2. unpow2 96.3%

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

   6. Simplified 96.3%

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

   7. Taylor expanded in x2 around inf 96.3%

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

      1. unpow2 96.3%

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

   9. Simplified 96.3%

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

   if 140 < x1 < 5.1e140

   1. Initial program 99.2%

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

   2. Taylor expanded in x1 around inf 87.3%

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

   3. Taylor expanded in x1 around inf 86.8%

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

   4. Taylor expanded in x1 around 0 86.8%

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

      1. *-commutative 27.3%

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

   6. Simplified 86.8%

      \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \left(3 - \frac{1}{x1}\right)\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot 3\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \color{blue}{\left(x2 \cdot -2\right)}\right) \]
3. Recombined 7 regimes into one program.

4. Final simplification 93.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4.5 \cdot 10^{+153}:\\ \;\;\;\;x1 + x1 \cdot \left(x1 \cdot 9\right)\\ \mathbf{elif}\;x1 \leq -9.5 \cdot 10^{+105}:\\ \;\;\;\;x1 + \frac{\left(x2 \cdot x2\right) \cdot 36 - 9 \cdot \left(\left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(3 + x2\right)\right)\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(3 + x2\right)\right)\right)\right)}{x2 \cdot -6 - \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(x2 + \left(3 + x2\right)\right)}\\ \mathbf{elif}\;x1 \leq -900000:\\ \;\;\;\;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 x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right) + \frac{1}{x1} \cdot \left(\left(x1 \cdot 2\right) \cdot \left(\frac{1}{x1} - 3\right)\right)\right) + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -9.5 \cdot 10^{-240}:\\ \;\;\;\;x1 - \left(x1 \cdot \left(2 + 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right) - x2 \cdot -6\right)\\ \mathbf{elif}\;x1 \leq 8.6 \cdot 10^{-178}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + 8 \cdot \left(x2 \cdot \left(x1 \cdot x2\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 140 \lor \neg \left(x1 \leq 5.1 \cdot 10^{+140}\right):\\ \;\;\;\;x1 + \left(x2 \cdot -6 + \left(9 \cdot \left(x1 \cdot x1\right) - x1 \cdot \left(2 - 4 \cdot \left(2 \cdot \left(x2 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right) + \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(3 - \frac{1}{x1}\right)\right)\right)\right)\right)\right) + 3 \cdot \left(x2 \cdot -2\right)\right)\\ \end{array} \]

Alternative 10: 88.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x2 + \left(3 + x2\right)\\ t_1 := \left(x1 \cdot x1\right) \cdot t_0\\ t_2 := x1 \cdot x1 + 1\\ t_3 := x1 \cdot \left(x1 \cdot 3\right)\\ t_4 := x1 + \left(3 \cdot \frac{\left(t_3 - 2 \cdot x2\right) - x1}{t_2} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(t_2 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(t_3 + 2 \cdot x2\right) - x1}{t_2} - 6\right) + \frac{1}{x1} \cdot \left(\left(x1 \cdot 2\right) \cdot \left(\frac{1}{x1} - 3\right)\right)\right) + 3 \cdot t_3\right)\right)\right)\right)\\ \mathbf{if}\;x1 \leq -4.5 \cdot 10^{+153}:\\ \;\;\;\;x1 + x1 \cdot \left(x1 \cdot 9\right)\\ \mathbf{elif}\;x1 \leq -9.5 \cdot 10^{+105}:\\ \;\;\;\;x1 + \frac{\left(x2 \cdot x2\right) \cdot 36 - 9 \cdot \left(t_1 \cdot t_1\right)}{x2 \cdot -6 - t_3 \cdot t_0}\\ \mathbf{elif}\;x1 \leq -600000:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x1 \leq -1.3 \cdot 10^{-242}:\\ \;\;\;\;x1 - \left(x1 \cdot \left(2 + 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right) - x2 \cdot -6\right)\\ \mathbf{elif}\;x1 \leq 2.1 \cdot 10^{-177}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + 8 \cdot \left(x2 \cdot \left(x1 \cdot x2\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 520 \lor \neg \left(x1 \leq 5.1 \cdot 10^{+140}\right):\\ \;\;\;\;x1 + \left(x2 \cdot -6 + \left(9 \cdot \left(x1 \cdot x1\right) - x1 \cdot \left(2 - 4 \cdot \left(2 \cdot \left(x2 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ x2 (+ 3.0 x2)))
        (t_1 (* (* x1 x1) t_0))
        (t_2 (+ (* x1 x1) 1.0))
        (t_3 (* x1 (* x1 3.0)))
        (t_4
         (+
          x1
          (+
           (* 3.0 (/ (- (- t_3 (* 2.0 x2)) x1) t_2))
           (+
            x1
            (+
             (* x1 (* x1 x1))
             (+
              (*
               t_2
               (+
                (* (* x1 x1) (- (* 4.0 (/ (- (+ t_3 (* 2.0 x2)) x1) t_2)) 6.0))
                (* (/ 1.0 x1) (* (* x1 2.0) (- (/ 1.0 x1) 3.0)))))
              (* 3.0 t_3))))))))
   (if (<= x1 -4.5e+153)
     (+ x1 (* x1 (* x1 9.0)))
     (if (<= x1 -9.5e+105)
       (+
        x1
        (/
         (- (* (* x2 x2) 36.0) (* 9.0 (* t_1 t_1)))
         (- (* x2 -6.0) (* t_3 t_0))))
       (if (<= x1 -600000.0)
         t_4
         (if (<= x1 -1.3e-242)
           (-
            x1
            (- (* x1 (+ 2.0 (* 4.0 (* x2 (- 3.0 (* 2.0 x2)))))) (* x2 -6.0)))
           (if (<= x1 2.1e-177)
             (+ x1 (+ (* x2 -6.0) (* 8.0 (* x2 (* x1 x2)))))
             (if (or (<= x1 520.0) (not (<= x1 5.1e+140)))
               (+
                x1
                (+
                 (* x2 -6.0)
                 (-
                  (* 9.0 (* x1 x1))
                  (* x1 (- 2.0 (* 4.0 (* 2.0 (* x2 x2))))))))
               t_4))))))))

C

double code(double x1, double x2) {
	double t_0 = x2 + (3.0 + x2);
	double t_1 = (x1 * x1) * t_0;
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = x1 * (x1 * 3.0);
	double t_4 = x1 + ((3.0 * (((t_3 - (2.0 * x2)) - x1) / t_2)) + (x1 + ((x1 * (x1 * x1)) + ((t_2 * (((x1 * x1) * ((4.0 * (((t_3 + (2.0 * x2)) - x1) / t_2)) - 6.0)) + ((1.0 / x1) * ((x1 * 2.0) * ((1.0 / x1) - 3.0))))) + (3.0 * t_3)))));
	double tmp;
	if (x1 <= -4.5e+153) {
		tmp = x1 + (x1 * (x1 * 9.0));
	} else if (x1 <= -9.5e+105) {
		tmp = x1 + ((((x2 * x2) * 36.0) - (9.0 * (t_1 * t_1))) / ((x2 * -6.0) - (t_3 * t_0)));
	} else if (x1 <= -600000.0) {
		tmp = t_4;
	} else if (x1 <= -1.3e-242) {
		tmp = x1 - ((x1 * (2.0 + (4.0 * (x2 * (3.0 - (2.0 * x2)))))) - (x2 * -6.0));
	} else if (x1 <= 2.1e-177) {
		tmp = x1 + ((x2 * -6.0) + (8.0 * (x2 * (x1 * x2))));
	} else if ((x1 <= 520.0) || !(x1 <= 5.1e+140)) {
		tmp = x1 + ((x2 * -6.0) + ((9.0 * (x1 * x1)) - (x1 * (2.0 - (4.0 * (2.0 * (x2 * x2)))))));
	} else {
		tmp = t_4;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_0 = x2 + (3.0d0 + x2)
    t_1 = (x1 * x1) * t_0
    t_2 = (x1 * x1) + 1.0d0
    t_3 = x1 * (x1 * 3.0d0)
    t_4 = x1 + ((3.0d0 * (((t_3 - (2.0d0 * x2)) - x1) / t_2)) + (x1 + ((x1 * (x1 * x1)) + ((t_2 * (((x1 * x1) * ((4.0d0 * (((t_3 + (2.0d0 * x2)) - x1) / t_2)) - 6.0d0)) + ((1.0d0 / x1) * ((x1 * 2.0d0) * ((1.0d0 / x1) - 3.0d0))))) + (3.0d0 * t_3)))))
    if (x1 <= (-4.5d+153)) then
        tmp = x1 + (x1 * (x1 * 9.0d0))
    else if (x1 <= (-9.5d+105)) then
        tmp = x1 + ((((x2 * x2) * 36.0d0) - (9.0d0 * (t_1 * t_1))) / ((x2 * (-6.0d0)) - (t_3 * t_0)))
    else if (x1 <= (-600000.0d0)) then
        tmp = t_4
    else if (x1 <= (-1.3d-242)) then
        tmp = x1 - ((x1 * (2.0d0 + (4.0d0 * (x2 * (3.0d0 - (2.0d0 * x2)))))) - (x2 * (-6.0d0)))
    else if (x1 <= 2.1d-177) then
        tmp = x1 + ((x2 * (-6.0d0)) + (8.0d0 * (x2 * (x1 * x2))))
    else if ((x1 <= 520.0d0) .or. (.not. (x1 <= 5.1d+140))) then
        tmp = x1 + ((x2 * (-6.0d0)) + ((9.0d0 * (x1 * x1)) - (x1 * (2.0d0 - (4.0d0 * (2.0d0 * (x2 * x2)))))))
    else
        tmp = t_4
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x2 + (3.0 + x2);
	double t_1 = (x1 * x1) * t_0;
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = x1 * (x1 * 3.0);
	double t_4 = x1 + ((3.0 * (((t_3 - (2.0 * x2)) - x1) / t_2)) + (x1 + ((x1 * (x1 * x1)) + ((t_2 * (((x1 * x1) * ((4.0 * (((t_3 + (2.0 * x2)) - x1) / t_2)) - 6.0)) + ((1.0 / x1) * ((x1 * 2.0) * ((1.0 / x1) - 3.0))))) + (3.0 * t_3)))));
	double tmp;
	if (x1 <= -4.5e+153) {
		tmp = x1 + (x1 * (x1 * 9.0));
	} else if (x1 <= -9.5e+105) {
		tmp = x1 + ((((x2 * x2) * 36.0) - (9.0 * (t_1 * t_1))) / ((x2 * -6.0) - (t_3 * t_0)));
	} else if (x1 <= -600000.0) {
		tmp = t_4;
	} else if (x1 <= -1.3e-242) {
		tmp = x1 - ((x1 * (2.0 + (4.0 * (x2 * (3.0 - (2.0 * x2)))))) - (x2 * -6.0));
	} else if (x1 <= 2.1e-177) {
		tmp = x1 + ((x2 * -6.0) + (8.0 * (x2 * (x1 * x2))));
	} else if ((x1 <= 520.0) || !(x1 <= 5.1e+140)) {
		tmp = x1 + ((x2 * -6.0) + ((9.0 * (x1 * x1)) - (x1 * (2.0 - (4.0 * (2.0 * (x2 * x2)))))));
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x2 + (3.0 + x2)
	t_1 = (x1 * x1) * t_0
	t_2 = (x1 * x1) + 1.0
	t_3 = x1 * (x1 * 3.0)
	t_4 = x1 + ((3.0 * (((t_3 - (2.0 * x2)) - x1) / t_2)) + (x1 + ((x1 * (x1 * x1)) + ((t_2 * (((x1 * x1) * ((4.0 * (((t_3 + (2.0 * x2)) - x1) / t_2)) - 6.0)) + ((1.0 / x1) * ((x1 * 2.0) * ((1.0 / x1) - 3.0))))) + (3.0 * t_3)))))
	tmp = 0
	if x1 <= -4.5e+153:
		tmp = x1 + (x1 * (x1 * 9.0))
	elif x1 <= -9.5e+105:
		tmp = x1 + ((((x2 * x2) * 36.0) - (9.0 * (t_1 * t_1))) / ((x2 * -6.0) - (t_3 * t_0)))
	elif x1 <= -600000.0:
		tmp = t_4
	elif x1 <= -1.3e-242:
		tmp = x1 - ((x1 * (2.0 + (4.0 * (x2 * (3.0 - (2.0 * x2)))))) - (x2 * -6.0))
	elif x1 <= 2.1e-177:
		tmp = x1 + ((x2 * -6.0) + (8.0 * (x2 * (x1 * x2))))
	elif (x1 <= 520.0) or not (x1 <= 5.1e+140):
		tmp = x1 + ((x2 * -6.0) + ((9.0 * (x1 * x1)) - (x1 * (2.0 - (4.0 * (2.0 * (x2 * x2)))))))
	else:
		tmp = t_4
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x2 + Float64(3.0 + x2))
	t_1 = Float64(Float64(x1 * x1) * t_0)
	t_2 = Float64(Float64(x1 * x1) + 1.0)
	t_3 = Float64(x1 * Float64(x1 * 3.0))
	t_4 = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_3 - Float64(2.0 * x2)) - x1) / t_2)) + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(t_2 * Float64(Float64(Float64(x1 * x1) * Float64(Float64(4.0 * Float64(Float64(Float64(t_3 + Float64(2.0 * x2)) - x1) / t_2)) - 6.0)) + Float64(Float64(1.0 / x1) * Float64(Float64(x1 * 2.0) * Float64(Float64(1.0 / x1) - 3.0))))) + Float64(3.0 * t_3))))))
	tmp = 0.0
	if (x1 <= -4.5e+153)
		tmp = Float64(x1 + Float64(x1 * Float64(x1 * 9.0)));
	elseif (x1 <= -9.5e+105)
		tmp = Float64(x1 + Float64(Float64(Float64(Float64(x2 * x2) * 36.0) - Float64(9.0 * Float64(t_1 * t_1))) / Float64(Float64(x2 * -6.0) - Float64(t_3 * t_0))));
	elseif (x1 <= -600000.0)
		tmp = t_4;
	elseif (x1 <= -1.3e-242)
		tmp = Float64(x1 - Float64(Float64(x1 * Float64(2.0 + Float64(4.0 * Float64(x2 * Float64(3.0 - Float64(2.0 * x2)))))) - Float64(x2 * -6.0)));
	elseif (x1 <= 2.1e-177)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(8.0 * Float64(x2 * Float64(x1 * x2)))));
	elseif ((x1 <= 520.0) || !(x1 <= 5.1e+140))
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(Float64(9.0 * Float64(x1 * x1)) - Float64(x1 * Float64(2.0 - Float64(4.0 * Float64(2.0 * Float64(x2 * x2))))))));
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x2 + (3.0 + x2);
	t_1 = (x1 * x1) * t_0;
	t_2 = (x1 * x1) + 1.0;
	t_3 = x1 * (x1 * 3.0);
	t_4 = x1 + ((3.0 * (((t_3 - (2.0 * x2)) - x1) / t_2)) + (x1 + ((x1 * (x1 * x1)) + ((t_2 * (((x1 * x1) * ((4.0 * (((t_3 + (2.0 * x2)) - x1) / t_2)) - 6.0)) + ((1.0 / x1) * ((x1 * 2.0) * ((1.0 / x1) - 3.0))))) + (3.0 * t_3)))));
	tmp = 0.0;
	if (x1 <= -4.5e+153)
		tmp = x1 + (x1 * (x1 * 9.0));
	elseif (x1 <= -9.5e+105)
		tmp = x1 + ((((x2 * x2) * 36.0) - (9.0 * (t_1 * t_1))) / ((x2 * -6.0) - (t_3 * t_0)));
	elseif (x1 <= -600000.0)
		tmp = t_4;
	elseif (x1 <= -1.3e-242)
		tmp = x1 - ((x1 * (2.0 + (4.0 * (x2 * (3.0 - (2.0 * x2)))))) - (x2 * -6.0));
	elseif (x1 <= 2.1e-177)
		tmp = x1 + ((x2 * -6.0) + (8.0 * (x2 * (x1 * x2))));
	elseif ((x1 <= 520.0) || ~((x1 <= 5.1e+140)))
		tmp = x1 + ((x2 * -6.0) + ((9.0 * (x1 * x1)) - (x1 * (2.0 - (4.0 * (2.0 * (x2 * x2)))))));
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x2 + N[(3.0 + x2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x1 * x1), $MachinePrecision] * t$95$0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$3 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$3 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$2 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(N[(4.0 * N[(N[(N[(t$95$3 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] + N[(N[(1.0 / x1), $MachinePrecision] * N[(N[(x1 * 2.0), $MachinePrecision] * N[(N[(1.0 / x1), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -4.5e+153], N[(x1 + N[(x1 * N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -9.5e+105], N[(x1 + N[(N[(N[(N[(x2 * x2), $MachinePrecision] * 36.0), $MachinePrecision] - N[(9.0 * N[(t$95$1 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(x2 * -6.0), $MachinePrecision] - N[(t$95$3 * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -600000.0], t$95$4, If[LessEqual[x1, -1.3e-242], N[(x1 - N[(N[(x1 * N[(2.0 + N[(4.0 * N[(x2 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 2.1e-177], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(8.0 * N[(x2 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x1, 520.0], N[Not[LessEqual[x1, 5.1e+140]], $MachinePrecision]], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(N[(9.0 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] - N[(x1 * N[(2.0 - N[(4.0 * N[(2.0 * N[(x2 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$4]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if x1 < -4.5000000000000001e153

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around 0 0.0%

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

   3. Taylor expanded in x1 around 0 42.9%

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

   4. Taylor expanded in x1 around inf 57.1%

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

      1. associate-*r* 57.1%

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

      2. *-commutative 57.1%

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

      3. cancel-sign-sub-inv 57.1%

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

      4. unpow2 57.1%

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

      5. +-commutative 57.1%

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

      6. distribute-lft-neg-in 57.1%

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

      7. *-commutative 57.1%

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

      8. distribute-lft-neg-in 57.1%

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

      9. metadata-eval 57.1%

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

      10. count-2 57.1%

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

   6. Simplified 57.1%

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

   7. Taylor expanded in x2 around 0 100.0%

      \[\leadsto \color{blue}{x1 + 9 \cdot {x1}^{2}} \]
   8. Step-by-step derivation

      1. *-commutative 100.0%

         \[\leadsto x1 + \color{blue}{{x1}^{2} \cdot 9} \]

      2. unpow2 100.0%

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

      3. associate-*r* 100.0%

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

   9. Simplified 100.0%

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

   if -4.5000000000000001e153 < x1 < -9.4999999999999995e105

   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. Taylor expanded in x1 around 0 0.2%

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

   3. Taylor expanded in x1 around 0 5.7%

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

   4. Taylor expanded in x1 around inf 23.9%

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

      1. associate-*r* 23.9%

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

      2. *-commutative 23.9%

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

      3. cancel-sign-sub-inv 23.9%

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

      4. unpow2 23.9%

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

      5. +-commutative 23.9%

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

      6. distribute-lft-neg-in 23.9%

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

      7. *-commutative 23.9%

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

      8. distribute-lft-neg-in 23.9%

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

      9. metadata-eval 23.9%

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

      10. count-2 23.9%

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

   6. Simplified 23.9%

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

      1. flip-+ 63.6%

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

      2. *-commutative 63.6%

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

      3. *-commutative 63.6%

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

      4. associate-*l* 63.6%

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

      5. associate-+l+ 63.6%

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

      6. associate-*l* 63.6%

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

      7. associate-+l+ 63.6%

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

      8. *-commutative 63.6%

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

   8. Applied egg-rr 63.6%

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

      1. swap-sqr 63.6%

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

      2. metadata-eval 63.6%

         \[\leadsto x1 + \frac{\left(x2 \cdot x2\right) \cdot \color{blue}{36} - \left(3 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right)\right) \cdot \left(3 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right)\right)}{x2 \cdot -6 - 3 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right)} \]

      3. swap-sqr 63.6%

         \[\leadsto x1 + \frac{\left(x2 \cdot x2\right) \cdot 36 - \color{blue}{\left(3 \cdot 3\right) \cdot \left(\left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right)\right)}}{x2 \cdot -6 - 3 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right)} \]

      4. metadata-eval 63.6%

         \[\leadsto x1 + \frac{\left(x2 \cdot x2\right) \cdot 36 - \color{blue}{9} \cdot \left(\left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right)\right)}{x2 \cdot -6 - 3 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right)} \]

      5. associate-*l* 63.6%

         \[\leadsto x1 + \frac{\left(x2 \cdot x2\right) \cdot 36 - 9 \cdot \left(\left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right)\right)}{x2 \cdot -6 - 3 \cdot \color{blue}{\left(x1 \cdot \left(x1 \cdot \left(x2 + \left(x2 + 3\right)\right)\right)\right)}} \]

      6. associate-*r* 63.6%

         \[\leadsto x1 + \frac{\left(x2 \cdot x2\right) \cdot 36 - 9 \cdot \left(\left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right)\right)}{x2 \cdot -6 - \color{blue}{\left(3 \cdot x1\right) \cdot \left(x1 \cdot \left(x2 + \left(x2 + 3\right)\right)\right)}} \]

      7. *-commutative 63.6%

         \[\leadsto x1 + \frac{\left(x2 \cdot x2\right) \cdot 36 - 9 \cdot \left(\left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right)\right)}{x2 \cdot -6 - \color{blue}{\left(x1 \cdot 3\right)} \cdot \left(x1 \cdot \left(x2 + \left(x2 + 3\right)\right)\right)} \]

      8. associate-*l* 63.6%

         \[\leadsto x1 + \frac{\left(x2 \cdot x2\right) \cdot 36 - 9 \cdot \left(\left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right)\right)}{x2 \cdot -6 - \color{blue}{\left(\left(x1 \cdot 3\right) \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)}} \]

      9. *-commutative 63.6%

         \[\leadsto x1 + \frac{\left(x2 \cdot x2\right) \cdot 36 - 9 \cdot \left(\left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right)\right)}{x2 \cdot -6 - \color{blue}{\left(x1 \cdot \left(x1 \cdot 3\right)\right)} \cdot \left(x2 + \left(x2 + 3\right)\right)} \]

   10. Simplified 63.6%

       \[\leadsto x1 + \color{blue}{\frac{\left(x2 \cdot x2\right) \cdot 36 - 9 \cdot \left(\left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right)\right)}{x2 \cdot -6 - \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(x2 + \left(x2 + 3\right)\right)}} \]

   if -9.4999999999999995e105 < x1 < -6e5 or 520 < x1 < 5.1e140

   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. Taylor expanded in x1 around inf 92.3%

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

   3. Taylor expanded in x1 around inf 92.0%

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

   4. Taylor expanded in x1 around inf 91.9%

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

   if -6e5 < x1 < -1.30000000000000009e-242

   1. Initial program 97.7%

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

   2. Taylor expanded in x1 around 0 88.1%

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

   3. Taylor expanded in x1 around 0 88.4%

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

   if -1.30000000000000009e-242 < x1 < 2.10000000000000001e-177

   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. Taylor expanded in x1 around 0 72.9%

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

   3. Taylor expanded in x1 around 0 72.9%

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

   4. Taylor expanded in x2 around 0 72.9%

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

      1. *-commutative 72.9%

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

      2. unpow2 72.9%

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

   6. Simplified 72.9%

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

   7. Taylor expanded in x2 around inf 71.0%

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

      1. *-commutative 71.0%

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

      2. unpow2 71.0%

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

      3. associate-*l* 97.8%

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

      4. *-commutative 97.8%

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

   9. Simplified 97.8%

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

   if 2.10000000000000001e-177 < x1 < 520 or 5.1e140 < x1

   1. Initial program 51.9%

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

   2. Taylor expanded in x1 around 0 48.3%

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

   3. Taylor expanded in x1 around 0 87.1%

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

   4. Taylor expanded in x2 around 0 96.3%

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

      1. *-commutative 96.3%

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

      2. unpow2 96.3%

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

   6. Simplified 96.3%

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

   7. Taylor expanded in x2 around inf 96.3%

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

      1. unpow2 96.3%

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

   9. Simplified 96.3%

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

4. Final simplification 93.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4.5 \cdot 10^{+153}:\\ \;\;\;\;x1 + x1 \cdot \left(x1 \cdot 9\right)\\ \mathbf{elif}\;x1 \leq -9.5 \cdot 10^{+105}:\\ \;\;\;\;x1 + \frac{\left(x2 \cdot x2\right) \cdot 36 - 9 \cdot \left(\left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(3 + x2\right)\right)\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(3 + x2\right)\right)\right)\right)}{x2 \cdot -6 - \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(x2 + \left(3 + x2\right)\right)}\\ \mathbf{elif}\;x1 \leq -600000:\\ \;\;\;\;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 x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right) + \frac{1}{x1} \cdot \left(\left(x1 \cdot 2\right) \cdot \left(\frac{1}{x1} - 3\right)\right)\right) + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -1.3 \cdot 10^{-242}:\\ \;\;\;\;x1 - \left(x1 \cdot \left(2 + 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right) - x2 \cdot -6\right)\\ \mathbf{elif}\;x1 \leq 2.1 \cdot 10^{-177}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + 8 \cdot \left(x2 \cdot \left(x1 \cdot x2\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 520 \lor \neg \left(x1 \leq 5.1 \cdot 10^{+140}\right):\\ \;\;\;\;x1 + \left(x2 \cdot -6 + \left(9 \cdot \left(x1 \cdot x1\right) - x1 \cdot \left(2 - 4 \cdot \left(2 \cdot \left(x2 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right) + \frac{1}{x1} \cdot \left(\left(x1 \cdot 2\right) \cdot \left(\frac{1}{x1} - 3\right)\right)\right) + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right)\right)\right)\right)\right)\\ \end{array} \]

Alternative 11: 87.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x2 + \left(3 + x2\right)\\ t_1 := \left(x1 \cdot x1\right) \cdot t_0\\ t_2 := x1 \cdot x1 + 1\\ t_3 := x1 \cdot \left(x1 \cdot 3\right)\\ t_4 := x1 + \left(3 \cdot \frac{\left(t_3 - 2 \cdot x2\right) - x1}{t_2} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot t_3 + t_2 \cdot \left(6 \cdot \left(x1 \cdot x1\right) + \left(\frac{\left(t_3 + 2 \cdot x2\right) - x1}{t_2} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(3 - \frac{1}{x1}\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{if}\;x1 \leq -4.5 \cdot 10^{+153}:\\ \;\;\;\;x1 + x1 \cdot \left(x1 \cdot 9\right)\\ \mathbf{elif}\;x1 \leq -9.5 \cdot 10^{+105}:\\ \;\;\;\;x1 + \frac{\left(x2 \cdot x2\right) \cdot 36 - 9 \cdot \left(t_1 \cdot t_1\right)}{x2 \cdot -6 - t_3 \cdot t_0}\\ \mathbf{elif}\;x1 \leq -2000000:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x1 \leq -3.4 \cdot 10^{-239}:\\ \;\;\;\;x1 - \left(x1 \cdot \left(2 + 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right) - x2 \cdot -6\right)\\ \mathbf{elif}\;x1 \leq 2.5 \cdot 10^{-178}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + 8 \cdot \left(x2 \cdot \left(x1 \cdot x2\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 112 \lor \neg \left(x1 \leq 5.1 \cdot 10^{+140}\right):\\ \;\;\;\;x1 + \left(x2 \cdot -6 + \left(9 \cdot \left(x1 \cdot x1\right) - x1 \cdot \left(2 - 4 \cdot \left(2 \cdot \left(x2 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ x2 (+ 3.0 x2)))
        (t_1 (* (* x1 x1) t_0))
        (t_2 (+ (* x1 x1) 1.0))
        (t_3 (* x1 (* x1 3.0)))
        (t_4
         (+
          x1
          (+
           (* 3.0 (/ (- (- t_3 (* 2.0 x2)) x1) t_2))
           (+
            x1
            (+
             (* x1 (* x1 x1))
             (+
              (* 3.0 t_3)
              (*
               t_2
               (+
                (* 6.0 (* x1 x1))
                (*
                 (- (/ (- (+ t_3 (* 2.0 x2)) x1) t_2) 3.0)
                 (* (* x1 2.0) (- 3.0 (/ 1.0 x1)))))))))))))
   (if (<= x1 -4.5e+153)
     (+ x1 (* x1 (* x1 9.0)))
     (if (<= x1 -9.5e+105)
       (+
        x1
        (/
         (- (* (* x2 x2) 36.0) (* 9.0 (* t_1 t_1)))
         (- (* x2 -6.0) (* t_3 t_0))))
       (if (<= x1 -2000000.0)
         t_4
         (if (<= x1 -3.4e-239)
           (-
            x1
            (- (* x1 (+ 2.0 (* 4.0 (* x2 (- 3.0 (* 2.0 x2)))))) (* x2 -6.0)))
           (if (<= x1 2.5e-178)
             (+ x1 (+ (* x2 -6.0) (* 8.0 (* x2 (* x1 x2)))))
             (if (or (<= x1 112.0) (not (<= x1 5.1e+140)))
               (+
                x1
                (+
                 (* x2 -6.0)
                 (-
                  (* 9.0 (* x1 x1))
                  (* x1 (- 2.0 (* 4.0 (* 2.0 (* x2 x2))))))))
               t_4))))))))

C

double code(double x1, double x2) {
	double t_0 = x2 + (3.0 + x2);
	double t_1 = (x1 * x1) * t_0;
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = x1 * (x1 * 3.0);
	double t_4 = x1 + ((3.0 * (((t_3 - (2.0 * x2)) - x1) / t_2)) + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_3) + (t_2 * ((6.0 * (x1 * x1)) + (((((t_3 + (2.0 * x2)) - x1) / t_2) - 3.0) * ((x1 * 2.0) * (3.0 - (1.0 / x1))))))))));
	double tmp;
	if (x1 <= -4.5e+153) {
		tmp = x1 + (x1 * (x1 * 9.0));
	} else if (x1 <= -9.5e+105) {
		tmp = x1 + ((((x2 * x2) * 36.0) - (9.0 * (t_1 * t_1))) / ((x2 * -6.0) - (t_3 * t_0)));
	} else if (x1 <= -2000000.0) {
		tmp = t_4;
	} else if (x1 <= -3.4e-239) {
		tmp = x1 - ((x1 * (2.0 + (4.0 * (x2 * (3.0 - (2.0 * x2)))))) - (x2 * -6.0));
	} else if (x1 <= 2.5e-178) {
		tmp = x1 + ((x2 * -6.0) + (8.0 * (x2 * (x1 * x2))));
	} else if ((x1 <= 112.0) || !(x1 <= 5.1e+140)) {
		tmp = x1 + ((x2 * -6.0) + ((9.0 * (x1 * x1)) - (x1 * (2.0 - (4.0 * (2.0 * (x2 * x2)))))));
	} else {
		tmp = t_4;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_0 = x2 + (3.0d0 + x2)
    t_1 = (x1 * x1) * t_0
    t_2 = (x1 * x1) + 1.0d0
    t_3 = x1 * (x1 * 3.0d0)
    t_4 = x1 + ((3.0d0 * (((t_3 - (2.0d0 * x2)) - x1) / t_2)) + (x1 + ((x1 * (x1 * x1)) + ((3.0d0 * t_3) + (t_2 * ((6.0d0 * (x1 * x1)) + (((((t_3 + (2.0d0 * x2)) - x1) / t_2) - 3.0d0) * ((x1 * 2.0d0) * (3.0d0 - (1.0d0 / x1))))))))))
    if (x1 <= (-4.5d+153)) then
        tmp = x1 + (x1 * (x1 * 9.0d0))
    else if (x1 <= (-9.5d+105)) then
        tmp = x1 + ((((x2 * x2) * 36.0d0) - (9.0d0 * (t_1 * t_1))) / ((x2 * (-6.0d0)) - (t_3 * t_0)))
    else if (x1 <= (-2000000.0d0)) then
        tmp = t_4
    else if (x1 <= (-3.4d-239)) then
        tmp = x1 - ((x1 * (2.0d0 + (4.0d0 * (x2 * (3.0d0 - (2.0d0 * x2)))))) - (x2 * (-6.0d0)))
    else if (x1 <= 2.5d-178) then
        tmp = x1 + ((x2 * (-6.0d0)) + (8.0d0 * (x2 * (x1 * x2))))
    else if ((x1 <= 112.0d0) .or. (.not. (x1 <= 5.1d+140))) then
        tmp = x1 + ((x2 * (-6.0d0)) + ((9.0d0 * (x1 * x1)) - (x1 * (2.0d0 - (4.0d0 * (2.0d0 * (x2 * x2)))))))
    else
        tmp = t_4
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x2 + (3.0 + x2);
	double t_1 = (x1 * x1) * t_0;
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = x1 * (x1 * 3.0);
	double t_4 = x1 + ((3.0 * (((t_3 - (2.0 * x2)) - x1) / t_2)) + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_3) + (t_2 * ((6.0 * (x1 * x1)) + (((((t_3 + (2.0 * x2)) - x1) / t_2) - 3.0) * ((x1 * 2.0) * (3.0 - (1.0 / x1))))))))));
	double tmp;
	if (x1 <= -4.5e+153) {
		tmp = x1 + (x1 * (x1 * 9.0));
	} else if (x1 <= -9.5e+105) {
		tmp = x1 + ((((x2 * x2) * 36.0) - (9.0 * (t_1 * t_1))) / ((x2 * -6.0) - (t_3 * t_0)));
	} else if (x1 <= -2000000.0) {
		tmp = t_4;
	} else if (x1 <= -3.4e-239) {
		tmp = x1 - ((x1 * (2.0 + (4.0 * (x2 * (3.0 - (2.0 * x2)))))) - (x2 * -6.0));
	} else if (x1 <= 2.5e-178) {
		tmp = x1 + ((x2 * -6.0) + (8.0 * (x2 * (x1 * x2))));
	} else if ((x1 <= 112.0) || !(x1 <= 5.1e+140)) {
		tmp = x1 + ((x2 * -6.0) + ((9.0 * (x1 * x1)) - (x1 * (2.0 - (4.0 * (2.0 * (x2 * x2)))))));
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x2 + (3.0 + x2)
	t_1 = (x1 * x1) * t_0
	t_2 = (x1 * x1) + 1.0
	t_3 = x1 * (x1 * 3.0)
	t_4 = x1 + ((3.0 * (((t_3 - (2.0 * x2)) - x1) / t_2)) + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_3) + (t_2 * ((6.0 * (x1 * x1)) + (((((t_3 + (2.0 * x2)) - x1) / t_2) - 3.0) * ((x1 * 2.0) * (3.0 - (1.0 / x1))))))))))
	tmp = 0
	if x1 <= -4.5e+153:
		tmp = x1 + (x1 * (x1 * 9.0))
	elif x1 <= -9.5e+105:
		tmp = x1 + ((((x2 * x2) * 36.0) - (9.0 * (t_1 * t_1))) / ((x2 * -6.0) - (t_3 * t_0)))
	elif x1 <= -2000000.0:
		tmp = t_4
	elif x1 <= -3.4e-239:
		tmp = x1 - ((x1 * (2.0 + (4.0 * (x2 * (3.0 - (2.0 * x2)))))) - (x2 * -6.0))
	elif x1 <= 2.5e-178:
		tmp = x1 + ((x2 * -6.0) + (8.0 * (x2 * (x1 * x2))))
	elif (x1 <= 112.0) or not (x1 <= 5.1e+140):
		tmp = x1 + ((x2 * -6.0) + ((9.0 * (x1 * x1)) - (x1 * (2.0 - (4.0 * (2.0 * (x2 * x2)))))))
	else:
		tmp = t_4
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x2 + Float64(3.0 + x2))
	t_1 = Float64(Float64(x1 * x1) * t_0)
	t_2 = Float64(Float64(x1 * x1) + 1.0)
	t_3 = Float64(x1 * Float64(x1 * 3.0))
	t_4 = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_3 - Float64(2.0 * x2)) - x1) / t_2)) + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(3.0 * t_3) + Float64(t_2 * Float64(Float64(6.0 * Float64(x1 * x1)) + Float64(Float64(Float64(Float64(Float64(t_3 + Float64(2.0 * x2)) - x1) / t_2) - 3.0) * Float64(Float64(x1 * 2.0) * Float64(3.0 - Float64(1.0 / x1)))))))))))
	tmp = 0.0
	if (x1 <= -4.5e+153)
		tmp = Float64(x1 + Float64(x1 * Float64(x1 * 9.0)));
	elseif (x1 <= -9.5e+105)
		tmp = Float64(x1 + Float64(Float64(Float64(Float64(x2 * x2) * 36.0) - Float64(9.0 * Float64(t_1 * t_1))) / Float64(Float64(x2 * -6.0) - Float64(t_3 * t_0))));
	elseif (x1 <= -2000000.0)
		tmp = t_4;
	elseif (x1 <= -3.4e-239)
		tmp = Float64(x1 - Float64(Float64(x1 * Float64(2.0 + Float64(4.0 * Float64(x2 * Float64(3.0 - Float64(2.0 * x2)))))) - Float64(x2 * -6.0)));
	elseif (x1 <= 2.5e-178)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(8.0 * Float64(x2 * Float64(x1 * x2)))));
	elseif ((x1 <= 112.0) || !(x1 <= 5.1e+140))
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(Float64(9.0 * Float64(x1 * x1)) - Float64(x1 * Float64(2.0 - Float64(4.0 * Float64(2.0 * Float64(x2 * x2))))))));
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x2 + (3.0 + x2);
	t_1 = (x1 * x1) * t_0;
	t_2 = (x1 * x1) + 1.0;
	t_3 = x1 * (x1 * 3.0);
	t_4 = x1 + ((3.0 * (((t_3 - (2.0 * x2)) - x1) / t_2)) + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_3) + (t_2 * ((6.0 * (x1 * x1)) + (((((t_3 + (2.0 * x2)) - x1) / t_2) - 3.0) * ((x1 * 2.0) * (3.0 - (1.0 / x1))))))))));
	tmp = 0.0;
	if (x1 <= -4.5e+153)
		tmp = x1 + (x1 * (x1 * 9.0));
	elseif (x1 <= -9.5e+105)
		tmp = x1 + ((((x2 * x2) * 36.0) - (9.0 * (t_1 * t_1))) / ((x2 * -6.0) - (t_3 * t_0)));
	elseif (x1 <= -2000000.0)
		tmp = t_4;
	elseif (x1 <= -3.4e-239)
		tmp = x1 - ((x1 * (2.0 + (4.0 * (x2 * (3.0 - (2.0 * x2)))))) - (x2 * -6.0));
	elseif (x1 <= 2.5e-178)
		tmp = x1 + ((x2 * -6.0) + (8.0 * (x2 * (x1 * x2))));
	elseif ((x1 <= 112.0) || ~((x1 <= 5.1e+140)))
		tmp = x1 + ((x2 * -6.0) + ((9.0 * (x1 * x1)) - (x1 * (2.0 - (4.0 * (2.0 * (x2 * x2)))))));
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x2 + N[(3.0 + x2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x1 * x1), $MachinePrecision] * t$95$0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$3 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$3 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(3.0 * t$95$3), $MachinePrecision] + N[(t$95$2 * N[(N[(6.0 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(N[(N[(t$95$3 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision] - 3.0), $MachinePrecision] * N[(N[(x1 * 2.0), $MachinePrecision] * N[(3.0 - N[(1.0 / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -4.5e+153], N[(x1 + N[(x1 * N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -9.5e+105], N[(x1 + N[(N[(N[(N[(x2 * x2), $MachinePrecision] * 36.0), $MachinePrecision] - N[(9.0 * N[(t$95$1 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(x2 * -6.0), $MachinePrecision] - N[(t$95$3 * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -2000000.0], t$95$4, If[LessEqual[x1, -3.4e-239], N[(x1 - N[(N[(x1 * N[(2.0 + N[(4.0 * N[(x2 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 2.5e-178], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(8.0 * N[(x2 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x1, 112.0], N[Not[LessEqual[x1, 5.1e+140]], $MachinePrecision]], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(N[(9.0 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] - N[(x1 * N[(2.0 - N[(4.0 * N[(2.0 * N[(x2 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$4]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if x1 < -4.5000000000000001e153

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around 0 0.0%

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

   3. Taylor expanded in x1 around 0 42.9%

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

   4. Taylor expanded in x1 around inf 57.1%

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

      1. associate-*r* 57.1%

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

      2. *-commutative 57.1%

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

      3. cancel-sign-sub-inv 57.1%

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

      4. unpow2 57.1%

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

      5. +-commutative 57.1%

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

      6. distribute-lft-neg-in 57.1%

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

      7. *-commutative 57.1%

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

      8. distribute-lft-neg-in 57.1%

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

      9. metadata-eval 57.1%

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

      10. count-2 57.1%

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

   6. Simplified 57.1%

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

   7. Taylor expanded in x2 around 0 100.0%

      \[\leadsto \color{blue}{x1 + 9 \cdot {x1}^{2}} \]
   8. Step-by-step derivation

      1. *-commutative 100.0%

         \[\leadsto x1 + \color{blue}{{x1}^{2} \cdot 9} \]

      2. unpow2 100.0%

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

      3. associate-*r* 100.0%

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

   9. Simplified 100.0%

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

   if -4.5000000000000001e153 < x1 < -9.4999999999999995e105

   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. Taylor expanded in x1 around 0 0.2%

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

   3. Taylor expanded in x1 around 0 5.7%

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

   4. Taylor expanded in x1 around inf 23.9%

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

      1. associate-*r* 23.9%

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

      2. *-commutative 23.9%

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

      3. cancel-sign-sub-inv 23.9%

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

      4. unpow2 23.9%

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

      5. +-commutative 23.9%

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

      6. distribute-lft-neg-in 23.9%

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

      7. *-commutative 23.9%

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

      8. distribute-lft-neg-in 23.9%

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

      9. metadata-eval 23.9%

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

      10. count-2 23.9%

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

   6. Simplified 23.9%

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

      1. flip-+ 63.6%

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

      2. *-commutative 63.6%

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

      3. *-commutative 63.6%

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

      4. associate-*l* 63.6%

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

      5. associate-+l+ 63.6%

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

      6. associate-*l* 63.6%

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

      7. associate-+l+ 63.6%

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

      8. *-commutative 63.6%

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

   8. Applied egg-rr 63.6%

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

      1. swap-sqr 63.6%

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

      2. metadata-eval 63.6%

         \[\leadsto x1 + \frac{\left(x2 \cdot x2\right) \cdot \color{blue}{36} - \left(3 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right)\right) \cdot \left(3 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right)\right)}{x2 \cdot -6 - 3 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right)} \]

      3. swap-sqr 63.6%

         \[\leadsto x1 + \frac{\left(x2 \cdot x2\right) \cdot 36 - \color{blue}{\left(3 \cdot 3\right) \cdot \left(\left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right)\right)}}{x2 \cdot -6 - 3 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right)} \]

      4. metadata-eval 63.6%

         \[\leadsto x1 + \frac{\left(x2 \cdot x2\right) \cdot 36 - \color{blue}{9} \cdot \left(\left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right)\right)}{x2 \cdot -6 - 3 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right)} \]

      5. associate-*l* 63.6%

         \[\leadsto x1 + \frac{\left(x2 \cdot x2\right) \cdot 36 - 9 \cdot \left(\left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right)\right)}{x2 \cdot -6 - 3 \cdot \color{blue}{\left(x1 \cdot \left(x1 \cdot \left(x2 + \left(x2 + 3\right)\right)\right)\right)}} \]

      6. associate-*r* 63.6%

         \[\leadsto x1 + \frac{\left(x2 \cdot x2\right) \cdot 36 - 9 \cdot \left(\left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right)\right)}{x2 \cdot -6 - \color{blue}{\left(3 \cdot x1\right) \cdot \left(x1 \cdot \left(x2 + \left(x2 + 3\right)\right)\right)}} \]

      7. *-commutative 63.6%

         \[\leadsto x1 + \frac{\left(x2 \cdot x2\right) \cdot 36 - 9 \cdot \left(\left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right)\right)}{x2 \cdot -6 - \color{blue}{\left(x1 \cdot 3\right)} \cdot \left(x1 \cdot \left(x2 + \left(x2 + 3\right)\right)\right)} \]

      8. associate-*l* 63.6%

         \[\leadsto x1 + \frac{\left(x2 \cdot x2\right) \cdot 36 - 9 \cdot \left(\left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right)\right)}{x2 \cdot -6 - \color{blue}{\left(\left(x1 \cdot 3\right) \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)}} \]

      9. *-commutative 63.6%

         \[\leadsto x1 + \frac{\left(x2 \cdot x2\right) \cdot 36 - 9 \cdot \left(\left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right)\right)}{x2 \cdot -6 - \color{blue}{\left(x1 \cdot \left(x1 \cdot 3\right)\right)} \cdot \left(x2 + \left(x2 + 3\right)\right)} \]

   10. Simplified 63.6%

       \[\leadsto x1 + \color{blue}{\frac{\left(x2 \cdot x2\right) \cdot 36 - 9 \cdot \left(\left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right)\right)}{x2 \cdot -6 - \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(x2 + \left(x2 + 3\right)\right)}} \]

   if -9.4999999999999995e105 < x1 < -2e6 or 112 < x1 < 5.1e140

   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. Taylor expanded in x1 around inf 92.3%

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

   3. Taylor expanded in x1 around inf 92.0%

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

   4. Taylor expanded in x1 around inf 78.6%

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

   if -2e6 < x1 < -3.4e-239

   1. Initial program 97.7%

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

   2. Taylor expanded in x1 around 0 88.1%

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

   3. Taylor expanded in x1 around 0 88.4%

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

   if -3.4e-239 < x1 < 2.49999999999999988e-178

   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. Taylor expanded in x1 around 0 72.9%

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

   3. Taylor expanded in x1 around 0 72.9%

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

   4. Taylor expanded in x2 around 0 72.9%

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

      1. *-commutative 72.9%

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

      2. unpow2 72.9%

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

   6. Simplified 72.9%

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

   7. Taylor expanded in x2 around inf 71.0%

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

      1. *-commutative 71.0%

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

      2. unpow2 71.0%

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

      3. associate-*l* 97.8%

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

      4. *-commutative 97.8%

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

   9. Simplified 97.8%

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

   if 2.49999999999999988e-178 < x1 < 112 or 5.1e140 < x1

   1. Initial program 51.9%

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

   2. Taylor expanded in x1 around 0 48.3%

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

   3. Taylor expanded in x1 around 0 87.1%

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

   4. Taylor expanded in x2 around 0 96.3%

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

      1. *-commutative 96.3%

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

      2. unpow2 96.3%

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

   6. Simplified 96.3%

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

   7. Taylor expanded in x2 around inf 96.3%

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

      1. unpow2 96.3%

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

   9. Simplified 96.3%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4.5 \cdot 10^{+153}:\\ \;\;\;\;x1 + x1 \cdot \left(x1 \cdot 9\right)\\ \mathbf{elif}\;x1 \leq -9.5 \cdot 10^{+105}:\\ \;\;\;\;x1 + \frac{\left(x2 \cdot x2\right) \cdot 36 - 9 \cdot \left(\left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(3 + x2\right)\right)\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(3 + x2\right)\right)\right)\right)}{x2 \cdot -6 - \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(x2 + \left(3 + x2\right)\right)}\\ \mathbf{elif}\;x1 \leq -2000000:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(6 \cdot \left(x1 \cdot x1\right) + \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(3 - \frac{1}{x1}\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -3.4 \cdot 10^{-239}:\\ \;\;\;\;x1 - \left(x1 \cdot \left(2 + 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right) - x2 \cdot -6\right)\\ \mathbf{elif}\;x1 \leq 2.5 \cdot 10^{-178}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + 8 \cdot \left(x2 \cdot \left(x1 \cdot x2\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 112 \lor \neg \left(x1 \leq 5.1 \cdot 10^{+140}\right):\\ \;\;\;\;x1 + \left(x2 \cdot -6 + \left(9 \cdot \left(x1 \cdot x1\right) - x1 \cdot \left(2 - 4 \cdot \left(2 \cdot \left(x2 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(6 \cdot \left(x1 \cdot x1\right) + \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(3 - \frac{1}{x1}\right)\right)\right)\right)\right)\right)\right)\\ \end{array} \]

Alternative 12: 78.6% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 9 \cdot \left(x1 \cdot x1\right)\\ t_1 := x2 + \left(3 + x2\right)\\ t_2 := \left(x1 \cdot x1\right) \cdot t_1\\ \mathbf{if}\;x1 \leq -4.5 \cdot 10^{+153}:\\ \;\;\;\;x1 + x1 \cdot \left(x1 \cdot 9\right)\\ \mathbf{elif}\;x1 \leq -9.5 \cdot 10^{+105}:\\ \;\;\;\;x1 + \frac{\left(x2 \cdot x2\right) \cdot 36 - 9 \cdot \left(t_2 \cdot t_2\right)}{x2 \cdot -6 - \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot t_1}\\ \mathbf{elif}\;x1 \leq -2.9 \cdot 10^{-239}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + \left(t_0 - x1 \cdot \left(2 - 4 \cdot \left(2 \cdot \left(x2 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 3.8 \cdot 10^{-178}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + 8 \cdot \left(x2 \cdot \left(x1 \cdot x2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 - \left(\left(x1 \cdot \left(2 + 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right) - t_0\right) - x2 \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* 9.0 (* x1 x1)))
        (t_1 (+ x2 (+ 3.0 x2)))
        (t_2 (* (* x1 x1) t_1)))
   (if (<= x1 -4.5e+153)
     (+ x1 (* x1 (* x1 9.0)))
     (if (<= x1 -9.5e+105)
       (+
        x1
        (/
         (- (* (* x2 x2) 36.0) (* 9.0 (* t_2 t_2)))
         (- (* x2 -6.0) (* (* x1 (* x1 3.0)) t_1))))
       (if (<= x1 -2.9e-239)
         (+
          x1
          (+ (* x2 -6.0) (- t_0 (* x1 (- 2.0 (* 4.0 (* 2.0 (* x2 x2))))))))
         (if (<= x1 3.8e-178)
           (+ x1 (+ (* x2 -6.0) (* 8.0 (* x2 (* x1 x2)))))
           (-
            x1
            (-
             (- (* x1 (+ 2.0 (* 4.0 (* x2 (- 3.0 (* 2.0 x2)))))) t_0)
             (* x2 -6.0)))))))))

C

double code(double x1, double x2) {
	double t_0 = 9.0 * (x1 * x1);
	double t_1 = x2 + (3.0 + x2);
	double t_2 = (x1 * x1) * t_1;
	double tmp;
	if (x1 <= -4.5e+153) {
		tmp = x1 + (x1 * (x1 * 9.0));
	} else if (x1 <= -9.5e+105) {
		tmp = x1 + ((((x2 * x2) * 36.0) - (9.0 * (t_2 * t_2))) / ((x2 * -6.0) - ((x1 * (x1 * 3.0)) * t_1)));
	} else if (x1 <= -2.9e-239) {
		tmp = x1 + ((x2 * -6.0) + (t_0 - (x1 * (2.0 - (4.0 * (2.0 * (x2 * x2)))))));
	} else if (x1 <= 3.8e-178) {
		tmp = x1 + ((x2 * -6.0) + (8.0 * (x2 * (x1 * x2))));
	} else {
		tmp = x1 - (((x1 * (2.0 + (4.0 * (x2 * (3.0 - (2.0 * x2)))))) - t_0) - (x2 * -6.0));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = 9.0d0 * (x1 * x1)
    t_1 = x2 + (3.0d0 + x2)
    t_2 = (x1 * x1) * t_1
    if (x1 <= (-4.5d+153)) then
        tmp = x1 + (x1 * (x1 * 9.0d0))
    else if (x1 <= (-9.5d+105)) then
        tmp = x1 + ((((x2 * x2) * 36.0d0) - (9.0d0 * (t_2 * t_2))) / ((x2 * (-6.0d0)) - ((x1 * (x1 * 3.0d0)) * t_1)))
    else if (x1 <= (-2.9d-239)) then
        tmp = x1 + ((x2 * (-6.0d0)) + (t_0 - (x1 * (2.0d0 - (4.0d0 * (2.0d0 * (x2 * x2)))))))
    else if (x1 <= 3.8d-178) then
        tmp = x1 + ((x2 * (-6.0d0)) + (8.0d0 * (x2 * (x1 * x2))))
    else
        tmp = x1 - (((x1 * (2.0d0 + (4.0d0 * (x2 * (3.0d0 - (2.0d0 * x2)))))) - t_0) - (x2 * (-6.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = 9.0 * (x1 * x1);
	double t_1 = x2 + (3.0 + x2);
	double t_2 = (x1 * x1) * t_1;
	double tmp;
	if (x1 <= -4.5e+153) {
		tmp = x1 + (x1 * (x1 * 9.0));
	} else if (x1 <= -9.5e+105) {
		tmp = x1 + ((((x2 * x2) * 36.0) - (9.0 * (t_2 * t_2))) / ((x2 * -6.0) - ((x1 * (x1 * 3.0)) * t_1)));
	} else if (x1 <= -2.9e-239) {
		tmp = x1 + ((x2 * -6.0) + (t_0 - (x1 * (2.0 - (4.0 * (2.0 * (x2 * x2)))))));
	} else if (x1 <= 3.8e-178) {
		tmp = x1 + ((x2 * -6.0) + (8.0 * (x2 * (x1 * x2))));
	} else {
		tmp = x1 - (((x1 * (2.0 + (4.0 * (x2 * (3.0 - (2.0 * x2)))))) - t_0) - (x2 * -6.0));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = 9.0 * (x1 * x1)
	t_1 = x2 + (3.0 + x2)
	t_2 = (x1 * x1) * t_1
	tmp = 0
	if x1 <= -4.5e+153:
		tmp = x1 + (x1 * (x1 * 9.0))
	elif x1 <= -9.5e+105:
		tmp = x1 + ((((x2 * x2) * 36.0) - (9.0 * (t_2 * t_2))) / ((x2 * -6.0) - ((x1 * (x1 * 3.0)) * t_1)))
	elif x1 <= -2.9e-239:
		tmp = x1 + ((x2 * -6.0) + (t_0 - (x1 * (2.0 - (4.0 * (2.0 * (x2 * x2)))))))
	elif x1 <= 3.8e-178:
		tmp = x1 + ((x2 * -6.0) + (8.0 * (x2 * (x1 * x2))))
	else:
		tmp = x1 - (((x1 * (2.0 + (4.0 * (x2 * (3.0 - (2.0 * x2)))))) - t_0) - (x2 * -6.0))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(9.0 * Float64(x1 * x1))
	t_1 = Float64(x2 + Float64(3.0 + x2))
	t_2 = Float64(Float64(x1 * x1) * t_1)
	tmp = 0.0
	if (x1 <= -4.5e+153)
		tmp = Float64(x1 + Float64(x1 * Float64(x1 * 9.0)));
	elseif (x1 <= -9.5e+105)
		tmp = Float64(x1 + Float64(Float64(Float64(Float64(x2 * x2) * 36.0) - Float64(9.0 * Float64(t_2 * t_2))) / Float64(Float64(x2 * -6.0) - Float64(Float64(x1 * Float64(x1 * 3.0)) * t_1))));
	elseif (x1 <= -2.9e-239)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(t_0 - Float64(x1 * Float64(2.0 - Float64(4.0 * Float64(2.0 * Float64(x2 * x2))))))));
	elseif (x1 <= 3.8e-178)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(8.0 * Float64(x2 * Float64(x1 * x2)))));
	else
		tmp = Float64(x1 - Float64(Float64(Float64(x1 * Float64(2.0 + Float64(4.0 * Float64(x2 * Float64(3.0 - Float64(2.0 * x2)))))) - t_0) - Float64(x2 * -6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = 9.0 * (x1 * x1);
	t_1 = x2 + (3.0 + x2);
	t_2 = (x1 * x1) * t_1;
	tmp = 0.0;
	if (x1 <= -4.5e+153)
		tmp = x1 + (x1 * (x1 * 9.0));
	elseif (x1 <= -9.5e+105)
		tmp = x1 + ((((x2 * x2) * 36.0) - (9.0 * (t_2 * t_2))) / ((x2 * -6.0) - ((x1 * (x1 * 3.0)) * t_1)));
	elseif (x1 <= -2.9e-239)
		tmp = x1 + ((x2 * -6.0) + (t_0 - (x1 * (2.0 - (4.0 * (2.0 * (x2 * x2)))))));
	elseif (x1 <= 3.8e-178)
		tmp = x1 + ((x2 * -6.0) + (8.0 * (x2 * (x1 * x2))));
	else
		tmp = x1 - (((x1 * (2.0 + (4.0 * (x2 * (3.0 - (2.0 * x2)))))) - t_0) - (x2 * -6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(9.0 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x2 + N[(3.0 + x2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x1 * x1), $MachinePrecision] * t$95$1), $MachinePrecision]}, If[LessEqual[x1, -4.5e+153], N[(x1 + N[(x1 * N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -9.5e+105], N[(x1 + N[(N[(N[(N[(x2 * x2), $MachinePrecision] * 36.0), $MachinePrecision] - N[(9.0 * N[(t$95$2 * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(x2 * -6.0), $MachinePrecision] - N[(N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision] * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -2.9e-239], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(t$95$0 - N[(x1 * N[(2.0 - N[(4.0 * N[(2.0 * N[(x2 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 3.8e-178], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(8.0 * N[(x2 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 - N[(N[(N[(x1 * N[(2.0 + N[(4.0 * N[(x2 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$0), $MachinePrecision] - N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x1 < -4.5000000000000001e153

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around 0 0.0%

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

   3. Taylor expanded in x1 around 0 42.9%

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

   4. Taylor expanded in x1 around inf 57.1%

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

      1. associate-*r* 57.1%

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

      2. *-commutative 57.1%

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

      3. cancel-sign-sub-inv 57.1%

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

      4. unpow2 57.1%

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

      5. +-commutative 57.1%

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

      6. distribute-lft-neg-in 57.1%

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

      7. *-commutative 57.1%

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

      8. distribute-lft-neg-in 57.1%

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

      9. metadata-eval 57.1%

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

      10. count-2 57.1%

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

   6. Simplified 57.1%

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

   7. Taylor expanded in x2 around 0 100.0%

      \[\leadsto \color{blue}{x1 + 9 \cdot {x1}^{2}} \]
   8. Step-by-step derivation

      1. *-commutative 100.0%

         \[\leadsto x1 + \color{blue}{{x1}^{2} \cdot 9} \]

      2. unpow2 100.0%

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

      3. associate-*r* 100.0%

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

   9. Simplified 100.0%

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

   if -4.5000000000000001e153 < x1 < -9.4999999999999995e105

   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. Taylor expanded in x1 around 0 0.2%

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

   3. Taylor expanded in x1 around 0 5.7%

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

   4. Taylor expanded in x1 around inf 23.9%

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

      1. associate-*r* 23.9%

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

      2. *-commutative 23.9%

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

      3. cancel-sign-sub-inv 23.9%

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

      4. unpow2 23.9%

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

      5. +-commutative 23.9%

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

      6. distribute-lft-neg-in 23.9%

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

      7. *-commutative 23.9%

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

      8. distribute-lft-neg-in 23.9%

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

      9. metadata-eval 23.9%

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

      10. count-2 23.9%

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

   6. Simplified 23.9%

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

      1. flip-+ 63.6%

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

      2. *-commutative 63.6%

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

      3. *-commutative 63.6%

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

      4. associate-*l* 63.6%

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

      5. associate-+l+ 63.6%

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

      6. associate-*l* 63.6%

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

      7. associate-+l+ 63.6%

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

      8. *-commutative 63.6%

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

   8. Applied egg-rr 63.6%

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

      1. swap-sqr 63.6%

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

      2. metadata-eval 63.6%

         \[\leadsto x1 + \frac{\left(x2 \cdot x2\right) \cdot \color{blue}{36} - \left(3 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right)\right) \cdot \left(3 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right)\right)}{x2 \cdot -6 - 3 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right)} \]

      3. swap-sqr 63.6%

         \[\leadsto x1 + \frac{\left(x2 \cdot x2\right) \cdot 36 - \color{blue}{\left(3 \cdot 3\right) \cdot \left(\left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right)\right)}}{x2 \cdot -6 - 3 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right)} \]

      4. metadata-eval 63.6%

         \[\leadsto x1 + \frac{\left(x2 \cdot x2\right) \cdot 36 - \color{blue}{9} \cdot \left(\left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right)\right)}{x2 \cdot -6 - 3 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right)} \]

      5. associate-*l* 63.6%

         \[\leadsto x1 + \frac{\left(x2 \cdot x2\right) \cdot 36 - 9 \cdot \left(\left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right)\right)}{x2 \cdot -6 - 3 \cdot \color{blue}{\left(x1 \cdot \left(x1 \cdot \left(x2 + \left(x2 + 3\right)\right)\right)\right)}} \]

      6. associate-*r* 63.6%

         \[\leadsto x1 + \frac{\left(x2 \cdot x2\right) \cdot 36 - 9 \cdot \left(\left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right)\right)}{x2 \cdot -6 - \color{blue}{\left(3 \cdot x1\right) \cdot \left(x1 \cdot \left(x2 + \left(x2 + 3\right)\right)\right)}} \]

      7. *-commutative 63.6%

         \[\leadsto x1 + \frac{\left(x2 \cdot x2\right) \cdot 36 - 9 \cdot \left(\left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right)\right)}{x2 \cdot -6 - \color{blue}{\left(x1 \cdot 3\right)} \cdot \left(x1 \cdot \left(x2 + \left(x2 + 3\right)\right)\right)} \]

      8. associate-*l* 63.6%

         \[\leadsto x1 + \frac{\left(x2 \cdot x2\right) \cdot 36 - 9 \cdot \left(\left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right)\right)}{x2 \cdot -6 - \color{blue}{\left(\left(x1 \cdot 3\right) \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)}} \]

      9. *-commutative 63.6%

         \[\leadsto x1 + \frac{\left(x2 \cdot x2\right) \cdot 36 - 9 \cdot \left(\left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right)\right)}{x2 \cdot -6 - \color{blue}{\left(x1 \cdot \left(x1 \cdot 3\right)\right)} \cdot \left(x2 + \left(x2 + 3\right)\right)} \]

   10. Simplified 63.6%

       \[\leadsto x1 + \color{blue}{\frac{\left(x2 \cdot x2\right) \cdot 36 - 9 \cdot \left(\left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(x2 + 3\right)\right)\right)\right)}{x2 \cdot -6 - \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(x2 + \left(x2 + 3\right)\right)}} \]

   if -9.4999999999999995e105 < x1 < -2.9000000000000002e-239

   1. Initial program 98.1%

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

   2. Taylor expanded in x1 around 0 72.6%

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

   3. Taylor expanded in x1 around 0 73.6%

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

   4. Taylor expanded in x2 around 0 73.6%

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

      1. *-commutative 73.6%

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

      2. unpow2 73.6%

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

   6. Simplified 73.6%

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

   7. Taylor expanded in x2 around inf 73.6%

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

      1. unpow2 73.6%

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

   9. Simplified 73.6%

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

   if -2.9000000000000002e-239 < x1 < 3.80000000000000015e-178

   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. Taylor expanded in x1 around 0 72.9%

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

   3. Taylor expanded in x1 around 0 72.9%

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

   4. Taylor expanded in x2 around 0 72.9%

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

      1. *-commutative 72.9%

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

      2. unpow2 72.9%

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

   6. Simplified 72.9%

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

   7. Taylor expanded in x2 around inf 71.0%

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

      1. *-commutative 71.0%

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

      2. unpow2 71.0%

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

      3. associate-*l* 97.8%

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

      4. *-commutative 97.8%

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

   9. Simplified 97.8%

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

   if 3.80000000000000015e-178 < x1

   1. Initial program 65.4%

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

   2. Taylor expanded in x1 around 0 42.3%

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

   3. Taylor expanded in x1 around 0 66.7%

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

   4. Taylor expanded in x2 around 0 76.8%

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

      1. *-commutative 76.8%

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

      2. unpow2 76.8%

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

   6. Simplified 76.8%

      \[\leadsto x1 + \left(-6 \cdot x2 + \left(\color{blue}{\left(x1 \cdot x1\right) \cdot 9} + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)\right) \]
3. Recombined 5 regimes into one program.

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4.5 \cdot 10^{+153}:\\ \;\;\;\;x1 + x1 \cdot \left(x1 \cdot 9\right)\\ \mathbf{elif}\;x1 \leq -9.5 \cdot 10^{+105}:\\ \;\;\;\;x1 + \frac{\left(x2 \cdot x2\right) \cdot 36 - 9 \cdot \left(\left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(3 + x2\right)\right)\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x2 + \left(3 + x2\right)\right)\right)\right)}{x2 \cdot -6 - \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(x2 + \left(3 + x2\right)\right)}\\ \mathbf{elif}\;x1 \leq -2.9 \cdot 10^{-239}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + \left(9 \cdot \left(x1 \cdot x1\right) - x1 \cdot \left(2 - 4 \cdot \left(2 \cdot \left(x2 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 3.8 \cdot 10^{-178}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + 8 \cdot \left(x2 \cdot \left(x1 \cdot x2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 - \left(\left(x1 \cdot \left(2 + 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right) - 9 \cdot \left(x1 \cdot x1\right)\right) - x2 \cdot -6\right)\\ \end{array} \]

Alternative 13: 76.7% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 9 \cdot \left(x1 \cdot x1\right)\\ \mathbf{if}\;x1 \leq -8.2 \cdot 10^{+114}:\\ \;\;\;\;x1 + \left(x1 \cdot \left(x1 \cdot 9\right) + x2 \cdot -6\right)\\ \mathbf{elif}\;x1 \leq -5.2 \cdot 10^{-239}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + \left(t_0 - x1 \cdot \left(2 - 4 \cdot \left(2 \cdot \left(x2 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.6 \cdot 10^{-174}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + 8 \cdot \left(x2 \cdot \left(x1 \cdot x2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 - \left(\left(x1 \cdot \left(2 + 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right) - t_0\right) - x2 \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* 9.0 (* x1 x1))))
   (if (<= x1 -8.2e+114)
     (+ x1 (+ (* x1 (* x1 9.0)) (* x2 -6.0)))
     (if (<= x1 -5.2e-239)
       (+ x1 (+ (* x2 -6.0) (- t_0 (* x1 (- 2.0 (* 4.0 (* 2.0 (* x2 x2))))))))
       (if (<= x1 1.6e-174)
         (+ x1 (+ (* x2 -6.0) (* 8.0 (* x2 (* x1 x2)))))
         (-
          x1
          (-
           (- (* x1 (+ 2.0 (* 4.0 (* x2 (- 3.0 (* 2.0 x2)))))) t_0)
           (* x2 -6.0))))))))

C

double code(double x1, double x2) {
	double t_0 = 9.0 * (x1 * x1);
	double tmp;
	if (x1 <= -8.2e+114) {
		tmp = x1 + ((x1 * (x1 * 9.0)) + (x2 * -6.0));
	} else if (x1 <= -5.2e-239) {
		tmp = x1 + ((x2 * -6.0) + (t_0 - (x1 * (2.0 - (4.0 * (2.0 * (x2 * x2)))))));
	} else if (x1 <= 1.6e-174) {
		tmp = x1 + ((x2 * -6.0) + (8.0 * (x2 * (x1 * x2))));
	} else {
		tmp = x1 - (((x1 * (2.0 + (4.0 * (x2 * (3.0 - (2.0 * x2)))))) - t_0) - (x2 * -6.0));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 9.0d0 * (x1 * x1)
    if (x1 <= (-8.2d+114)) then
        tmp = x1 + ((x1 * (x1 * 9.0d0)) + (x2 * (-6.0d0)))
    else if (x1 <= (-5.2d-239)) then
        tmp = x1 + ((x2 * (-6.0d0)) + (t_0 - (x1 * (2.0d0 - (4.0d0 * (2.0d0 * (x2 * x2)))))))
    else if (x1 <= 1.6d-174) then
        tmp = x1 + ((x2 * (-6.0d0)) + (8.0d0 * (x2 * (x1 * x2))))
    else
        tmp = x1 - (((x1 * (2.0d0 + (4.0d0 * (x2 * (3.0d0 - (2.0d0 * x2)))))) - t_0) - (x2 * (-6.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = 9.0 * (x1 * x1);
	double tmp;
	if (x1 <= -8.2e+114) {
		tmp = x1 + ((x1 * (x1 * 9.0)) + (x2 * -6.0));
	} else if (x1 <= -5.2e-239) {
		tmp = x1 + ((x2 * -6.0) + (t_0 - (x1 * (2.0 - (4.0 * (2.0 * (x2 * x2)))))));
	} else if (x1 <= 1.6e-174) {
		tmp = x1 + ((x2 * -6.0) + (8.0 * (x2 * (x1 * x2))));
	} else {
		tmp = x1 - (((x1 * (2.0 + (4.0 * (x2 * (3.0 - (2.0 * x2)))))) - t_0) - (x2 * -6.0));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = 9.0 * (x1 * x1)
	tmp = 0
	if x1 <= -8.2e+114:
		tmp = x1 + ((x1 * (x1 * 9.0)) + (x2 * -6.0))
	elif x1 <= -5.2e-239:
		tmp = x1 + ((x2 * -6.0) + (t_0 - (x1 * (2.0 - (4.0 * (2.0 * (x2 * x2)))))))
	elif x1 <= 1.6e-174:
		tmp = x1 + ((x2 * -6.0) + (8.0 * (x2 * (x1 * x2))))
	else:
		tmp = x1 - (((x1 * (2.0 + (4.0 * (x2 * (3.0 - (2.0 * x2)))))) - t_0) - (x2 * -6.0))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(9.0 * Float64(x1 * x1))
	tmp = 0.0
	if (x1 <= -8.2e+114)
		tmp = Float64(x1 + Float64(Float64(x1 * Float64(x1 * 9.0)) + Float64(x2 * -6.0)));
	elseif (x1 <= -5.2e-239)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(t_0 - Float64(x1 * Float64(2.0 - Float64(4.0 * Float64(2.0 * Float64(x2 * x2))))))));
	elseif (x1 <= 1.6e-174)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(8.0 * Float64(x2 * Float64(x1 * x2)))));
	else
		tmp = Float64(x1 - Float64(Float64(Float64(x1 * Float64(2.0 + Float64(4.0 * Float64(x2 * Float64(3.0 - Float64(2.0 * x2)))))) - t_0) - Float64(x2 * -6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = 9.0 * (x1 * x1);
	tmp = 0.0;
	if (x1 <= -8.2e+114)
		tmp = x1 + ((x1 * (x1 * 9.0)) + (x2 * -6.0));
	elseif (x1 <= -5.2e-239)
		tmp = x1 + ((x2 * -6.0) + (t_0 - (x1 * (2.0 - (4.0 * (2.0 * (x2 * x2)))))));
	elseif (x1 <= 1.6e-174)
		tmp = x1 + ((x2 * -6.0) + (8.0 * (x2 * (x1 * x2))));
	else
		tmp = x1 - (((x1 * (2.0 + (4.0 * (x2 * (3.0 - (2.0 * x2)))))) - t_0) - (x2 * -6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(9.0 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -8.2e+114], N[(x1 + N[(N[(x1 * N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision] + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -5.2e-239], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(t$95$0 - N[(x1 * N[(2.0 - N[(4.0 * N[(2.0 * N[(x2 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.6e-174], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(8.0 * N[(x2 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 - N[(N[(N[(x1 * N[(2.0 + N[(4.0 * N[(x2 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$0), $MachinePrecision] - N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -8.2000000000000001e114

   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. Taylor expanded in x1 around 0 0.0%

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

   3. Taylor expanded in x1 around 0 34.6%

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

   4. Taylor expanded in x2 around 0 39.0%

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

      1. *-commutative 39.0%

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

      2. unpow2 39.0%

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

   6. Simplified 39.0%

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

   7. Taylor expanded in x1 around inf 79.7%

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

      1. *-commutative 79.7%

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

      2. unpow2 79.7%

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

      3. associate-*r* 79.7%

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

   9. Simplified 79.7%

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

   if -8.2000000000000001e114 < x1 < -5.20000000000000005e-239

   1. Initial program 96.8%

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

   2. Taylor expanded in x1 around 0 71.7%

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

   3. Taylor expanded in x1 around 0 72.7%

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

   4. Taylor expanded in x2 around 0 72.7%

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

      1. *-commutative 72.7%

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

      2. unpow2 72.7%

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

   6. Simplified 72.7%

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

   7. Taylor expanded in x2 around inf 72.7%

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

      1. unpow2 72.7%

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

   9. Simplified 72.7%

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

   if -5.20000000000000005e-239 < x1 < 1.6e-174

   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. Taylor expanded in x1 around 0 72.9%

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

   3. Taylor expanded in x1 around 0 72.9%

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

   4. Taylor expanded in x2 around 0 72.9%

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

      1. *-commutative 72.9%

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

      2. unpow2 72.9%

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

   6. Simplified 72.9%

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

   7. Taylor expanded in x2 around inf 71.0%

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

      1. *-commutative 71.0%

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

      2. unpow2 71.0%

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

      3. associate-*l* 97.8%

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

      4. *-commutative 97.8%

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

   9. Simplified 97.8%

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

   if 1.6e-174 < x1

   1. Initial program 65.4%

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

   2. Taylor expanded in x1 around 0 42.3%

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

   3. Taylor expanded in x1 around 0 66.7%

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

   4. Taylor expanded in x2 around 0 76.8%

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

      1. *-commutative 76.8%

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

      2. unpow2 76.8%

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

   6. Simplified 76.8%

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

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -8.2 \cdot 10^{+114}:\\ \;\;\;\;x1 + \left(x1 \cdot \left(x1 \cdot 9\right) + x2 \cdot -6\right)\\ \mathbf{elif}\;x1 \leq -5.2 \cdot 10^{-239}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + \left(9 \cdot \left(x1 \cdot x1\right) - x1 \cdot \left(2 - 4 \cdot \left(2 \cdot \left(x2 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.6 \cdot 10^{-174}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + 8 \cdot \left(x2 \cdot \left(x1 \cdot x2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 - \left(\left(x1 \cdot \left(2 + 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right) - 9 \cdot \left(x1 \cdot x1\right)\right) - x2 \cdot -6\right)\\ \end{array} \]

Alternative 14: 76.7% accurate, 4.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -2.3 \cdot 10^{+110}:\\ \;\;\;\;x1 + \left(x1 \cdot \left(x1 \cdot 9\right) + x2 \cdot -6\right)\\ \mathbf{elif}\;x1 \leq -8.5 \cdot 10^{-240} \lor \neg \left(x1 \leq 1.15 \cdot 10^{-174}\right):\\ \;\;\;\;x1 + \left(x2 \cdot -6 + \left(9 \cdot \left(x1 \cdot x1\right) - x1 \cdot \left(2 - 4 \cdot \left(2 \cdot \left(x2 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + 8 \cdot \left(x2 \cdot \left(x1 \cdot x2\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -2.3e+110)
   (+ x1 (+ (* x1 (* x1 9.0)) (* x2 -6.0)))
   (if (or (<= x1 -8.5e-240) (not (<= x1 1.15e-174)))
     (+
      x1
      (+
       (* x2 -6.0)
       (- (* 9.0 (* x1 x1)) (* x1 (- 2.0 (* 4.0 (* 2.0 (* x2 x2))))))))
     (+ x1 (+ (* x2 -6.0) (* 8.0 (* x2 (* x1 x2))))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -2.3e+110) {
		tmp = x1 + ((x1 * (x1 * 9.0)) + (x2 * -6.0));
	} else if ((x1 <= -8.5e-240) || !(x1 <= 1.15e-174)) {
		tmp = x1 + ((x2 * -6.0) + ((9.0 * (x1 * x1)) - (x1 * (2.0 - (4.0 * (2.0 * (x2 * x2)))))));
	} else {
		tmp = x1 + ((x2 * -6.0) + (8.0 * (x2 * (x1 * x2))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x1 <= (-2.3d+110)) then
        tmp = x1 + ((x1 * (x1 * 9.0d0)) + (x2 * (-6.0d0)))
    else if ((x1 <= (-8.5d-240)) .or. (.not. (x1 <= 1.15d-174))) then
        tmp = x1 + ((x2 * (-6.0d0)) + ((9.0d0 * (x1 * x1)) - (x1 * (2.0d0 - (4.0d0 * (2.0d0 * (x2 * x2)))))))
    else
        tmp = x1 + ((x2 * (-6.0d0)) + (8.0d0 * (x2 * (x1 * x2))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= -2.3e+110) {
		tmp = x1 + ((x1 * (x1 * 9.0)) + (x2 * -6.0));
	} else if ((x1 <= -8.5e-240) || !(x1 <= 1.15e-174)) {
		tmp = x1 + ((x2 * -6.0) + ((9.0 * (x1 * x1)) - (x1 * (2.0 - (4.0 * (2.0 * (x2 * x2)))))));
	} else {
		tmp = x1 + ((x2 * -6.0) + (8.0 * (x2 * (x1 * x2))));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -2.3e+110:
		tmp = x1 + ((x1 * (x1 * 9.0)) + (x2 * -6.0))
	elif (x1 <= -8.5e-240) or not (x1 <= 1.15e-174):
		tmp = x1 + ((x2 * -6.0) + ((9.0 * (x1 * x1)) - (x1 * (2.0 - (4.0 * (2.0 * (x2 * x2)))))))
	else:
		tmp = x1 + ((x2 * -6.0) + (8.0 * (x2 * (x1 * x2))))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -2.3e+110)
		tmp = Float64(x1 + Float64(Float64(x1 * Float64(x1 * 9.0)) + Float64(x2 * -6.0)));
	elseif ((x1 <= -8.5e-240) || !(x1 <= 1.15e-174))
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(Float64(9.0 * Float64(x1 * x1)) - Float64(x1 * Float64(2.0 - Float64(4.0 * Float64(2.0 * Float64(x2 * x2))))))));
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(8.0 * Float64(x2 * Float64(x1 * x2)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -2.3e+110)
		tmp = x1 + ((x1 * (x1 * 9.0)) + (x2 * -6.0));
	elseif ((x1 <= -8.5e-240) || ~((x1 <= 1.15e-174)))
		tmp = x1 + ((x2 * -6.0) + ((9.0 * (x1 * x1)) - (x1 * (2.0 - (4.0 * (2.0 * (x2 * x2)))))));
	else
		tmp = x1 + ((x2 * -6.0) + (8.0 * (x2 * (x1 * x2))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -2.3e+110], N[(x1 + N[(N[(x1 * N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision] + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x1, -8.5e-240], N[Not[LessEqual[x1, 1.15e-174]], $MachinePrecision]], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(N[(9.0 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] - N[(x1 * N[(2.0 - N[(4.0 * N[(2.0 * N[(x2 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(8.0 * N[(x2 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -2.3e110

   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. Taylor expanded in x1 around 0 0.0%

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

   3. Taylor expanded in x1 around 0 34.6%

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

   4. Taylor expanded in x2 around 0 39.0%

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

      1. *-commutative 39.0%

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

      2. unpow2 39.0%

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

   6. Simplified 39.0%

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

   7. Taylor expanded in x1 around inf 79.7%

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

      1. *-commutative 79.7%

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

      2. unpow2 79.7%

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

      3. associate-*r* 79.7%

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

   9. Simplified 79.7%

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

   if -2.3e110 < x1 < -8.5e-240 or 1.1499999999999999e-174 < x1

   1. Initial program 79.8%

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

   2. Taylor expanded in x1 around 0 55.8%

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

   3. Taylor expanded in x1 around 0 69.5%

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

   4. Taylor expanded in x2 around 0 74.9%

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

      1. *-commutative 74.9%

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

      2. unpow2 74.9%

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

   6. Simplified 74.9%

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

   7. Taylor expanded in x2 around inf 74.9%

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

      1. unpow2 74.9%

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

   9. Simplified 74.9%

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

   if -8.5e-240 < x1 < 1.1499999999999999e-174

   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. Taylor expanded in x1 around 0 72.9%

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

   3. Taylor expanded in x1 around 0 72.9%

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

   4. Taylor expanded in x2 around 0 72.9%

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

      1. *-commutative 72.9%

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

      2. unpow2 72.9%

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

   6. Simplified 72.9%

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

   7. Taylor expanded in x2 around inf 71.0%

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

      1. *-commutative 71.0%

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

      2. unpow2 71.0%

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

      3. associate-*l* 97.8%

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

      4. *-commutative 97.8%

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

   9. Simplified 97.8%

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

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -2.3 \cdot 10^{+110}:\\ \;\;\;\;x1 + \left(x1 \cdot \left(x1 \cdot 9\right) + x2 \cdot -6\right)\\ \mathbf{elif}\;x1 \leq -8.5 \cdot 10^{-240} \lor \neg \left(x1 \leq 1.15 \cdot 10^{-174}\right):\\ \;\;\;\;x1 + \left(x2 \cdot -6 + \left(9 \cdot \left(x1 \cdot x1\right) - x1 \cdot \left(2 - 4 \cdot \left(2 \cdot \left(x2 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + 8 \cdot \left(x2 \cdot \left(x1 \cdot x2\right)\right)\right)\\ \end{array} \]

Alternative 15: 55.7% accurate, 6.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 + \left(x2 \cdot 8\right) \cdot \left(x1 \cdot x2\right)\\ \mathbf{if}\;x2 \leq -4.4 \cdot 10^{+170}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x2 \leq 6.2 \cdot 10^{+72}:\\ \;\;\;\;x1 + \left(x1 \cdot \left(x1 \cdot 9\right) + x2 \cdot -6\right)\\ \mathbf{elif}\;x2 \leq 1.8 \cdot 10^{+228} \lor \neg \left(x2 \leq 3.8 \cdot 10^{+246}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot 2 + x2 \cdot \left(x1 \cdot -12 - 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ x1 (* (* x2 8.0) (* x1 x2)))))
   (if (<= x2 -4.4e+170)
     t_0
     (if (<= x2 6.2e+72)
       (+ x1 (+ (* x1 (* x1 9.0)) (* x2 -6.0)))
       (if (or (<= x2 1.8e+228) (not (<= x2 3.8e+246)))
         t_0
         (+ (* x1 2.0) (* x2 (- (* x1 -12.0) 6.0))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 + ((x2 * 8.0) * (x1 * x2));
	double tmp;
	if (x2 <= -4.4e+170) {
		tmp = t_0;
	} else if (x2 <= 6.2e+72) {
		tmp = x1 + ((x1 * (x1 * 9.0)) + (x2 * -6.0));
	} else if ((x2 <= 1.8e+228) || !(x2 <= 3.8e+246)) {
		tmp = t_0;
	} else {
		tmp = (x1 * 2.0) + (x2 * ((x1 * -12.0) - 6.0));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x1 + ((x2 * 8.0d0) * (x1 * x2))
    if (x2 <= (-4.4d+170)) then
        tmp = t_0
    else if (x2 <= 6.2d+72) then
        tmp = x1 + ((x1 * (x1 * 9.0d0)) + (x2 * (-6.0d0)))
    else if ((x2 <= 1.8d+228) .or. (.not. (x2 <= 3.8d+246))) then
        tmp = t_0
    else
        tmp = (x1 * 2.0d0) + (x2 * ((x1 * (-12.0d0)) - 6.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 + ((x2 * 8.0) * (x1 * x2));
	double tmp;
	if (x2 <= -4.4e+170) {
		tmp = t_0;
	} else if (x2 <= 6.2e+72) {
		tmp = x1 + ((x1 * (x1 * 9.0)) + (x2 * -6.0));
	} else if ((x2 <= 1.8e+228) || !(x2 <= 3.8e+246)) {
		tmp = t_0;
	} else {
		tmp = (x1 * 2.0) + (x2 * ((x1 * -12.0) - 6.0));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 + ((x2 * 8.0) * (x1 * x2))
	tmp = 0
	if x2 <= -4.4e+170:
		tmp = t_0
	elif x2 <= 6.2e+72:
		tmp = x1 + ((x1 * (x1 * 9.0)) + (x2 * -6.0))
	elif (x2 <= 1.8e+228) or not (x2 <= 3.8e+246):
		tmp = t_0
	else:
		tmp = (x1 * 2.0) + (x2 * ((x1 * -12.0) - 6.0))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 + Float64(Float64(x2 * 8.0) * Float64(x1 * x2)))
	tmp = 0.0
	if (x2 <= -4.4e+170)
		tmp = t_0;
	elseif (x2 <= 6.2e+72)
		tmp = Float64(x1 + Float64(Float64(x1 * Float64(x1 * 9.0)) + Float64(x2 * -6.0)));
	elseif ((x2 <= 1.8e+228) || !(x2 <= 3.8e+246))
		tmp = t_0;
	else
		tmp = Float64(Float64(x1 * 2.0) + Float64(x2 * Float64(Float64(x1 * -12.0) - 6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 + ((x2 * 8.0) * (x1 * x2));
	tmp = 0.0;
	if (x2 <= -4.4e+170)
		tmp = t_0;
	elseif (x2 <= 6.2e+72)
		tmp = x1 + ((x1 * (x1 * 9.0)) + (x2 * -6.0));
	elseif ((x2 <= 1.8e+228) || ~((x2 <= 3.8e+246)))
		tmp = t_0;
	else
		tmp = (x1 * 2.0) + (x2 * ((x1 * -12.0) - 6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 + N[(N[(x2 * 8.0), $MachinePrecision] * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x2, -4.4e+170], t$95$0, If[LessEqual[x2, 6.2e+72], N[(x1 + N[(N[(x1 * N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision] + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x2, 1.8e+228], N[Not[LessEqual[x2, 3.8e+246]], $MachinePrecision]], t$95$0, N[(N[(x1 * 2.0), $MachinePrecision] + N[(x2 * N[(N[(x1 * -12.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x2 < -4.39999999999999978e170 or 6.19999999999999977e72 < x2 < 1.8e228 or 3.79999999999999976e246 < x2

   1. Initial program 73.5%

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

   2. Taylor expanded in x1 around 0 51.8%

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

   3. Taylor expanded in x2 around inf 59.8%

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

      1. *-commutative 59.8%

         \[\leadsto x1 + 8 \cdot \color{blue}{\left({x2}^{2} \cdot x1\right)} \]

      2. associate-*r* 59.8%

         \[\leadsto x1 + \color{blue}{\left(8 \cdot {x2}^{2}\right) \cdot x1} \]

      3. unpow2 59.8%

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

      4. associate-*r* 59.8%

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

      5. associate-*r* 70.8%

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

      6. *-commutative 70.8%

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

   5. Simplified 70.8%

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

   if -4.39999999999999978e170 < x2 < 6.19999999999999977e72

   1. Initial program 68.9%

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

   2. Taylor expanded in x1 around 0 49.5%

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

   3. Taylor expanded in x1 around 0 69.1%

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

   4. Taylor expanded in x2 around 0 72.6%

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

      1. *-commutative 72.6%

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

      2. unpow2 72.6%

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

   6. Simplified 72.6%

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

   7. Taylor expanded in x1 around inf 57.4%

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

      1. *-commutative 57.4%

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

      2. unpow2 57.4%

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

      3. associate-*r* 57.4%

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

   9. Simplified 57.4%

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

   if 1.8e228 < x2 < 3.79999999999999976e246

   1. Initial program 28.3%

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

   2. Taylor expanded in x1 around 0 1.0%

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

   3. Taylor expanded in x1 around 0 15.3%

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

      1. *-commutative 15.3%

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

   5. Simplified 15.3%

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

   6. Taylor expanded in x2 around 0 77.0%

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

4. Final simplification 61.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq -4.4 \cdot 10^{+170}:\\ \;\;\;\;x1 + \left(x2 \cdot 8\right) \cdot \left(x1 \cdot x2\right)\\ \mathbf{elif}\;x2 \leq 6.2 \cdot 10^{+72}:\\ \;\;\;\;x1 + \left(x1 \cdot \left(x1 \cdot 9\right) + x2 \cdot -6\right)\\ \mathbf{elif}\;x2 \leq 1.8 \cdot 10^{+228} \lor \neg \left(x2 \leq 3.8 \cdot 10^{+246}\right):\\ \;\;\;\;x1 + \left(x2 \cdot 8\right) \cdot \left(x1 \cdot x2\right)\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot 2 + x2 \cdot \left(x1 \cdot -12 - 6\right)\\ \end{array} \]

Alternative 16: 55.9% accurate, 6.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 + \left(x2 \cdot 8\right) \cdot \left(x1 \cdot x2\right)\\ \mathbf{if}\;x2 \leq -1.12 \cdot 10^{+170}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x2 \leq 5.1 \cdot 10^{+72}:\\ \;\;\;\;x1 + \left(x1 \cdot \left(x1 \cdot 9\right) + x2 \cdot -6\right)\\ \mathbf{elif}\;x2 \leq 2.65 \cdot 10^{+221} \lor \neg \left(x2 \leq 7 \cdot 10^{+247}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;x1 - x2 \cdot \left(6 + \left(x1 \cdot x1\right) \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ x1 (* (* x2 8.0) (* x1 x2)))))
   (if (<= x2 -1.12e+170)
     t_0
     (if (<= x2 5.1e+72)
       (+ x1 (+ (* x1 (* x1 9.0)) (* x2 -6.0)))
       (if (or (<= x2 2.65e+221) (not (<= x2 7e+247)))
         t_0
         (- x1 (* x2 (+ 6.0 (* (* x1 x1) -6.0)))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 + ((x2 * 8.0) * (x1 * x2));
	double tmp;
	if (x2 <= -1.12e+170) {
		tmp = t_0;
	} else if (x2 <= 5.1e+72) {
		tmp = x1 + ((x1 * (x1 * 9.0)) + (x2 * -6.0));
	} else if ((x2 <= 2.65e+221) || !(x2 <= 7e+247)) {
		tmp = t_0;
	} else {
		tmp = x1 - (x2 * (6.0 + ((x1 * x1) * -6.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x1 + ((x2 * 8.0d0) * (x1 * x2))
    if (x2 <= (-1.12d+170)) then
        tmp = t_0
    else if (x2 <= 5.1d+72) then
        tmp = x1 + ((x1 * (x1 * 9.0d0)) + (x2 * (-6.0d0)))
    else if ((x2 <= 2.65d+221) .or. (.not. (x2 <= 7d+247))) then
        tmp = t_0
    else
        tmp = x1 - (x2 * (6.0d0 + ((x1 * x1) * (-6.0d0))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 + ((x2 * 8.0) * (x1 * x2));
	double tmp;
	if (x2 <= -1.12e+170) {
		tmp = t_0;
	} else if (x2 <= 5.1e+72) {
		tmp = x1 + ((x1 * (x1 * 9.0)) + (x2 * -6.0));
	} else if ((x2 <= 2.65e+221) || !(x2 <= 7e+247)) {
		tmp = t_0;
	} else {
		tmp = x1 - (x2 * (6.0 + ((x1 * x1) * -6.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 + ((x2 * 8.0) * (x1 * x2))
	tmp = 0
	if x2 <= -1.12e+170:
		tmp = t_0
	elif x2 <= 5.1e+72:
		tmp = x1 + ((x1 * (x1 * 9.0)) + (x2 * -6.0))
	elif (x2 <= 2.65e+221) or not (x2 <= 7e+247):
		tmp = t_0
	else:
		tmp = x1 - (x2 * (6.0 + ((x1 * x1) * -6.0)))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 + Float64(Float64(x2 * 8.0) * Float64(x1 * x2)))
	tmp = 0.0
	if (x2 <= -1.12e+170)
		tmp = t_0;
	elseif (x2 <= 5.1e+72)
		tmp = Float64(x1 + Float64(Float64(x1 * Float64(x1 * 9.0)) + Float64(x2 * -6.0)));
	elseif ((x2 <= 2.65e+221) || !(x2 <= 7e+247))
		tmp = t_0;
	else
		tmp = Float64(x1 - Float64(x2 * Float64(6.0 + Float64(Float64(x1 * x1) * -6.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 + ((x2 * 8.0) * (x1 * x2));
	tmp = 0.0;
	if (x2 <= -1.12e+170)
		tmp = t_0;
	elseif (x2 <= 5.1e+72)
		tmp = x1 + ((x1 * (x1 * 9.0)) + (x2 * -6.0));
	elseif ((x2 <= 2.65e+221) || ~((x2 <= 7e+247)))
		tmp = t_0;
	else
		tmp = x1 - (x2 * (6.0 + ((x1 * x1) * -6.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 + N[(N[(x2 * 8.0), $MachinePrecision] * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x2, -1.12e+170], t$95$0, If[LessEqual[x2, 5.1e+72], N[(x1 + N[(N[(x1 * N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision] + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x2, 2.65e+221], N[Not[LessEqual[x2, 7e+247]], $MachinePrecision]], t$95$0, N[(x1 - N[(x2 * N[(6.0 + N[(N[(x1 * x1), $MachinePrecision] * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x2 < -1.1200000000000001e170 or 5.09999999999999977e72 < x2 < 2.6499999999999998e221 or 7.0000000000000004e247 < x2

   1. Initial program 74.6%

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

   2. Taylor expanded in x1 around 0 52.5%

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

   3. Taylor expanded in x2 around inf 59.2%

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

      1. *-commutative 59.2%

         \[\leadsto x1 + 8 \cdot \color{blue}{\left({x2}^{2} \cdot x1\right)} \]

      2. associate-*r* 59.2%

         \[\leadsto x1 + \color{blue}{\left(8 \cdot {x2}^{2}\right) \cdot x1} \]

      3. unpow2 59.2%

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

      4. associate-*r* 59.2%

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

      5. associate-*r* 70.4%

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

      6. *-commutative 70.4%

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

   5. Simplified 70.4%

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

   if -1.1200000000000001e170 < x2 < 5.09999999999999977e72

   1. Initial program 68.9%

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

   2. Taylor expanded in x1 around 0 49.5%

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

   3. Taylor expanded in x1 around 0 69.1%

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

   4. Taylor expanded in x2 around 0 72.6%

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

      1. *-commutative 72.6%

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

      2. unpow2 72.6%

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

   6. Simplified 72.6%

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

   7. Taylor expanded in x1 around inf 57.4%

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

      1. *-commutative 57.4%

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

      2. unpow2 57.4%

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

      3. associate-*r* 57.4%

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

   9. Simplified 57.4%

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

   if 2.6499999999999998e221 < x2 < 7.0000000000000004e247

   1. Initial program 24.8%

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

   2. Taylor expanded in x1 around 0 0.9%

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

   3. Taylor expanded in x1 around 0 25.9%

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

   4. Taylor expanded in x1 around inf 92.4%

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

      1. associate-*r* 92.4%

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

      2. *-commutative 92.4%

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

      3. cancel-sign-sub-inv 92.4%

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

      4. unpow2 92.4%

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

      5. +-commutative 92.4%

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

      6. distribute-lft-neg-in 92.4%

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

      7. *-commutative 92.4%

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

      8. distribute-lft-neg-in 92.4%

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

      9. metadata-eval 92.4%

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

      10. count-2 92.4%

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

   6. Simplified 92.4%

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

   7. Taylor expanded in x2 around -inf 92.4%

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

      1. mul-1-neg 92.4%

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

      2. *-commutative 92.4%

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

      3. unpow2 92.4%

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

   9. Simplified 92.4%

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

4. Final simplification 62.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq -1.12 \cdot 10^{+170}:\\ \;\;\;\;x1 + \left(x2 \cdot 8\right) \cdot \left(x1 \cdot x2\right)\\ \mathbf{elif}\;x2 \leq 5.1 \cdot 10^{+72}:\\ \;\;\;\;x1 + \left(x1 \cdot \left(x1 \cdot 9\right) + x2 \cdot -6\right)\\ \mathbf{elif}\;x2 \leq 2.65 \cdot 10^{+221} \lor \neg \left(x2 \leq 7 \cdot 10^{+247}\right):\\ \;\;\;\;x1 + \left(x2 \cdot 8\right) \cdot \left(x1 \cdot x2\right)\\ \mathbf{else}:\\ \;\;\;\;x1 - x2 \cdot \left(6 + \left(x1 \cdot x1\right) \cdot -6\right)\\ \end{array} \]

Alternative 17: 57.5% accurate, 7.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 + x1 \cdot \left(x1 \cdot 9\right)\\ t_1 := x1 + 8 \cdot \left(x1 \cdot \left(x2 \cdot x2\right)\right)\\ \mathbf{if}\;x1 \leq -4.8 \cdot 10^{+108}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x1 \leq -4.2 \cdot 10^{-159}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x1 \leq 1.05 \cdot 10^{-90}:\\ \;\;\;\;x2 \cdot -6\\ \mathbf{elif}\;x1 \leq 4.5 \cdot 10^{+153}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ x1 (* x1 (* x1 9.0)))) (t_1 (+ x1 (* 8.0 (* x1 (* x2 x2))))))
   (if (<= x1 -4.8e+108)
     t_0
     (if (<= x1 -4.2e-159)
       t_1
       (if (<= x1 1.05e-90) (* x2 -6.0) (if (<= x1 4.5e+153) t_1 t_0))))))

C

double code(double x1, double x2) {
	double t_0 = x1 + (x1 * (x1 * 9.0));
	double t_1 = x1 + (8.0 * (x1 * (x2 * x2)));
	double tmp;
	if (x1 <= -4.8e+108) {
		tmp = t_0;
	} else if (x1 <= -4.2e-159) {
		tmp = t_1;
	} else if (x1 <= 1.05e-90) {
		tmp = x2 * -6.0;
	} else if (x1 <= 4.5e+153) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x1 + (x1 * (x1 * 9.0d0))
    t_1 = x1 + (8.0d0 * (x1 * (x2 * x2)))
    if (x1 <= (-4.8d+108)) then
        tmp = t_0
    else if (x1 <= (-4.2d-159)) then
        tmp = t_1
    else if (x1 <= 1.05d-90) then
        tmp = x2 * (-6.0d0)
    else if (x1 <= 4.5d+153) then
        tmp = t_1
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 + (x1 * (x1 * 9.0));
	double t_1 = x1 + (8.0 * (x1 * (x2 * x2)));
	double tmp;
	if (x1 <= -4.8e+108) {
		tmp = t_0;
	} else if (x1 <= -4.2e-159) {
		tmp = t_1;
	} else if (x1 <= 1.05e-90) {
		tmp = x2 * -6.0;
	} else if (x1 <= 4.5e+153) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 + (x1 * (x1 * 9.0))
	t_1 = x1 + (8.0 * (x1 * (x2 * x2)))
	tmp = 0
	if x1 <= -4.8e+108:
		tmp = t_0
	elif x1 <= -4.2e-159:
		tmp = t_1
	elif x1 <= 1.05e-90:
		tmp = x2 * -6.0
	elif x1 <= 4.5e+153:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 + Float64(x1 * Float64(x1 * 9.0)))
	t_1 = Float64(x1 + Float64(8.0 * Float64(x1 * Float64(x2 * x2))))
	tmp = 0.0
	if (x1 <= -4.8e+108)
		tmp = t_0;
	elseif (x1 <= -4.2e-159)
		tmp = t_1;
	elseif (x1 <= 1.05e-90)
		tmp = Float64(x2 * -6.0);
	elseif (x1 <= 4.5e+153)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 + (x1 * (x1 * 9.0));
	t_1 = x1 + (8.0 * (x1 * (x2 * x2)));
	tmp = 0.0;
	if (x1 <= -4.8e+108)
		tmp = t_0;
	elseif (x1 <= -4.2e-159)
		tmp = t_1;
	elseif (x1 <= 1.05e-90)
		tmp = x2 * -6.0;
	elseif (x1 <= 4.5e+153)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 + N[(x1 * N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 + N[(8.0 * N[(x1 * N[(x2 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -4.8e+108], t$95$0, If[LessEqual[x1, -4.2e-159], t$95$1, If[LessEqual[x1, 1.05e-90], N[(x2 * -6.0), $MachinePrecision], If[LessEqual[x1, 4.5e+153], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -4.80000000000000037e108 or 4.5000000000000001e153 < x1

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around 0 0.0%

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

   3. Taylor expanded in x1 around 0 52.8%

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

   4. Taylor expanded in x1 around inf 61.9%

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

      1. associate-*r* 61.9%

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

      2. *-commutative 61.9%

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

      3. cancel-sign-sub-inv 61.9%

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

      4. unpow2 61.9%

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

      5. +-commutative 61.9%

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

      6. distribute-lft-neg-in 61.9%

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

      7. *-commutative 61.9%

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

      8. distribute-lft-neg-in 61.9%

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

      9. metadata-eval 61.9%

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

      10. count-2 61.9%

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

   6. Simplified 61.9%

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

   7. Taylor expanded in x2 around 0 86.9%

      \[\leadsto \color{blue}{x1 + 9 \cdot {x1}^{2}} \]
   8. Step-by-step derivation

      1. *-commutative 86.9%

         \[\leadsto x1 + \color{blue}{{x1}^{2} \cdot 9} \]

      2. unpow2 86.9%

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

      3. associate-*r* 86.9%

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

   9. Simplified 86.9%

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

   if -4.80000000000000037e108 < x1 < -4.1999999999999998e-159 or 1.05e-90 < x1 < 4.5000000000000001e153

   1. Initial program 98.4%

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

   2. Taylor expanded in x1 around 0 62.9%

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

   3. Taylor expanded in x2 around inf 34.1%

      \[\leadsto x1 + \color{blue}{8 \cdot \left(x1 \cdot {x2}^{2}\right)} \]
   4. Step-by-step derivation

      1. *-commutative 34.1%

         \[\leadsto x1 + \color{blue}{\left(x1 \cdot {x2}^{2}\right) \cdot 8} \]

      2. unpow2 34.1%

         \[\leadsto x1 + \left(x1 \cdot \color{blue}{\left(x2 \cdot x2\right)}\right) \cdot 8 \]

   5. Simplified 34.1%

      \[\leadsto x1 + \color{blue}{\left(x1 \cdot \left(x2 \cdot x2\right)\right) \cdot 8} \]

   if -4.1999999999999998e-159 < x1 < 1.05e-90

   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. Taylor expanded in x1 around 0 78.2%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 66.9%

      \[\leadsto x1 + \color{blue}{-6 \cdot x2} \]
   4. Step-by-step derivation

      1. *-commutative 66.9%

         \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]

   5. Simplified 66.9%

      \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]

   6. Taylor expanded in x1 around 0 67.4%

      \[\leadsto \color{blue}{-6 \cdot x2} \]
   7. Step-by-step derivation

      1. *-commutative 67.4%

         \[\leadsto \color{blue}{x2 \cdot -6} \]

   8. Simplified 67.4%

      \[\leadsto \color{blue}{x2 \cdot -6} \]
3. Recombined 3 regimes into one program.

4. Final simplification 60.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4.8 \cdot 10^{+108}:\\ \;\;\;\;x1 + x1 \cdot \left(x1 \cdot 9\right)\\ \mathbf{elif}\;x1 \leq -4.2 \cdot 10^{-159}:\\ \;\;\;\;x1 + 8 \cdot \left(x1 \cdot \left(x2 \cdot x2\right)\right)\\ \mathbf{elif}\;x1 \leq 1.05 \cdot 10^{-90}:\\ \;\;\;\;x2 \cdot -6\\ \mathbf{elif}\;x1 \leq 4.5 \cdot 10^{+153}:\\ \;\;\;\;x1 + 8 \cdot \left(x1 \cdot \left(x2 \cdot x2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot \left(x1 \cdot 9\right)\\ \end{array} \]

Alternative 18: 58.4% accurate, 7.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 + x1 \cdot \left(x1 \cdot 9\right)\\ t_1 := x1 + \left(x2 \cdot 8\right) \cdot \left(x1 \cdot x2\right)\\ \mathbf{if}\;x1 \leq -6 \cdot 10^{+108}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x1 \leq -4.2 \cdot 10^{-159}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x1 \leq 1.25 \cdot 10^{-90}:\\ \;\;\;\;x2 \cdot -6\\ \mathbf{elif}\;x1 \leq 4.5 \cdot 10^{+153}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ x1 (* x1 (* x1 9.0)))) (t_1 (+ x1 (* (* x2 8.0) (* x1 x2)))))
   (if (<= x1 -6e+108)
     t_0
     (if (<= x1 -4.2e-159)
       t_1
       (if (<= x1 1.25e-90) (* x2 -6.0) (if (<= x1 4.5e+153) t_1 t_0))))))

C

double code(double x1, double x2) {
	double t_0 = x1 + (x1 * (x1 * 9.0));
	double t_1 = x1 + ((x2 * 8.0) * (x1 * x2));
	double tmp;
	if (x1 <= -6e+108) {
		tmp = t_0;
	} else if (x1 <= -4.2e-159) {
		tmp = t_1;
	} else if (x1 <= 1.25e-90) {
		tmp = x2 * -6.0;
	} else if (x1 <= 4.5e+153) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x1 + (x1 * (x1 * 9.0d0))
    t_1 = x1 + ((x2 * 8.0d0) * (x1 * x2))
    if (x1 <= (-6d+108)) then
        tmp = t_0
    else if (x1 <= (-4.2d-159)) then
        tmp = t_1
    else if (x1 <= 1.25d-90) then
        tmp = x2 * (-6.0d0)
    else if (x1 <= 4.5d+153) then
        tmp = t_1
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 + (x1 * (x1 * 9.0));
	double t_1 = x1 + ((x2 * 8.0) * (x1 * x2));
	double tmp;
	if (x1 <= -6e+108) {
		tmp = t_0;
	} else if (x1 <= -4.2e-159) {
		tmp = t_1;
	} else if (x1 <= 1.25e-90) {
		tmp = x2 * -6.0;
	} else if (x1 <= 4.5e+153) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 + (x1 * (x1 * 9.0))
	t_1 = x1 + ((x2 * 8.0) * (x1 * x2))
	tmp = 0
	if x1 <= -6e+108:
		tmp = t_0
	elif x1 <= -4.2e-159:
		tmp = t_1
	elif x1 <= 1.25e-90:
		tmp = x2 * -6.0
	elif x1 <= 4.5e+153:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 + Float64(x1 * Float64(x1 * 9.0)))
	t_1 = Float64(x1 + Float64(Float64(x2 * 8.0) * Float64(x1 * x2)))
	tmp = 0.0
	if (x1 <= -6e+108)
		tmp = t_0;
	elseif (x1 <= -4.2e-159)
		tmp = t_1;
	elseif (x1 <= 1.25e-90)
		tmp = Float64(x2 * -6.0);
	elseif (x1 <= 4.5e+153)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 + (x1 * (x1 * 9.0));
	t_1 = x1 + ((x2 * 8.0) * (x1 * x2));
	tmp = 0.0;
	if (x1 <= -6e+108)
		tmp = t_0;
	elseif (x1 <= -4.2e-159)
		tmp = t_1;
	elseif (x1 <= 1.25e-90)
		tmp = x2 * -6.0;
	elseif (x1 <= 4.5e+153)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 + N[(x1 * N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 + N[(N[(x2 * 8.0), $MachinePrecision] * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -6e+108], t$95$0, If[LessEqual[x1, -4.2e-159], t$95$1, If[LessEqual[x1, 1.25e-90], N[(x2 * -6.0), $MachinePrecision], If[LessEqual[x1, 4.5e+153], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -5.99999999999999968e108 or 4.5000000000000001e153 < x1

   1. Initial program 0.0%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 0.0%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 52.8%

      \[\leadsto x1 + \color{blue}{\left(-6 \cdot x2 + \left(3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right) + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)\right)} \]

   4. Taylor expanded in x1 around inf 61.9%

      \[\leadsto x1 + \left(-6 \cdot x2 + \color{blue}{3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)}\right) \]
   5. Step-by-step derivation

      1. associate-*r* 61.9%

         \[\leadsto x1 + \left(-6 \cdot x2 + \color{blue}{\left(3 \cdot {x1}^{2}\right) \cdot \left(3 - -2 \cdot x2\right)}\right) \]

      2. *-commutative 61.9%

         \[\leadsto x1 + \left(-6 \cdot x2 + \left(3 \cdot {x1}^{2}\right) \cdot \left(3 - \color{blue}{x2 \cdot -2}\right)\right) \]

      3. cancel-sign-sub-inv 61.9%

         \[\leadsto x1 + \left(-6 \cdot x2 + \left(3 \cdot {x1}^{2}\right) \cdot \color{blue}{\left(3 + \left(-x2\right) \cdot -2\right)}\right) \]

      4. unpow2 61.9%

         \[\leadsto x1 + \left(-6 \cdot x2 + \left(3 \cdot \color{blue}{\left(x1 \cdot x1\right)}\right) \cdot \left(3 + \left(-x2\right) \cdot -2\right)\right) \]

      5. +-commutative 61.9%

         \[\leadsto x1 + \left(-6 \cdot x2 + \left(3 \cdot \left(x1 \cdot x1\right)\right) \cdot \color{blue}{\left(\left(-x2\right) \cdot -2 + 3\right)}\right) \]

      6. distribute-lft-neg-in 61.9%

         \[\leadsto x1 + \left(-6 \cdot x2 + \left(3 \cdot \left(x1 \cdot x1\right)\right) \cdot \left(\color{blue}{\left(-x2 \cdot -2\right)} + 3\right)\right) \]

      7. *-commutative 61.9%

         \[\leadsto x1 + \left(-6 \cdot x2 + \left(3 \cdot \left(x1 \cdot x1\right)\right) \cdot \left(\left(-\color{blue}{-2 \cdot x2}\right) + 3\right)\right) \]

      8. distribute-lft-neg-in 61.9%

         \[\leadsto x1 + \left(-6 \cdot x2 + \left(3 \cdot \left(x1 \cdot x1\right)\right) \cdot \left(\color{blue}{\left(--2\right) \cdot x2} + 3\right)\right) \]

      9. metadata-eval 61.9%

         \[\leadsto x1 + \left(-6 \cdot x2 + \left(3 \cdot \left(x1 \cdot x1\right)\right) \cdot \left(\color{blue}{2} \cdot x2 + 3\right)\right) \]

      10. count-2 61.9%

          \[\leadsto x1 + \left(-6 \cdot x2 + \left(3 \cdot \left(x1 \cdot x1\right)\right) \cdot \left(\color{blue}{\left(x2 + x2\right)} + 3\right)\right) \]

   6. Simplified 61.9%

      \[\leadsto x1 + \left(-6 \cdot x2 + \color{blue}{\left(3 \cdot \left(x1 \cdot x1\right)\right) \cdot \left(\left(x2 + x2\right) + 3\right)}\right) \]

   7. Taylor expanded in x2 around 0 86.9%

      \[\leadsto \color{blue}{x1 + 9 \cdot {x1}^{2}} \]
   8. Step-by-step derivation

      1. *-commutative 86.9%

         \[\leadsto x1 + \color{blue}{{x1}^{2} \cdot 9} \]

      2. unpow2 86.9%

         \[\leadsto x1 + \color{blue}{\left(x1 \cdot x1\right)} \cdot 9 \]

      3. associate-*r* 86.9%

         \[\leadsto x1 + \color{blue}{x1 \cdot \left(x1 \cdot 9\right)} \]

   9. Simplified 86.9%

      \[\leadsto \color{blue}{x1 + x1 \cdot \left(x1 \cdot 9\right)} \]

   if -5.99999999999999968e108 < x1 < -4.1999999999999998e-159 or 1.25000000000000005e-90 < x1 < 4.5000000000000001e153

   1. Initial program 98.4%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 62.9%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x2 around inf 34.1%

      \[\leadsto x1 + \color{blue}{8 \cdot \left(x1 \cdot {x2}^{2}\right)} \]
   4. Step-by-step derivation

      1. *-commutative 34.1%

         \[\leadsto x1 + 8 \cdot \color{blue}{\left({x2}^{2} \cdot x1\right)} \]

      2. associate-*r* 34.1%

         \[\leadsto x1 + \color{blue}{\left(8 \cdot {x2}^{2}\right) \cdot x1} \]

      3. unpow2 34.1%

         \[\leadsto x1 + \left(8 \cdot \color{blue}{\left(x2 \cdot x2\right)}\right) \cdot x1 \]

      4. associate-*r* 34.1%

         \[\leadsto x1 + \color{blue}{\left(\left(8 \cdot x2\right) \cdot x2\right)} \cdot x1 \]

      5. associate-*r* 36.0%

         \[\leadsto x1 + \color{blue}{\left(8 \cdot x2\right) \cdot \left(x2 \cdot x1\right)} \]

      6. *-commutative 36.0%

         \[\leadsto x1 + \color{blue}{\left(x2 \cdot 8\right)} \cdot \left(x2 \cdot x1\right) \]

   5. Simplified 36.0%

      \[\leadsto x1 + \color{blue}{\left(x2 \cdot 8\right) \cdot \left(x2 \cdot x1\right)} \]

   if -4.1999999999999998e-159 < x1 < 1.25000000000000005e-90

   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. Taylor expanded in x1 around 0 78.2%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 66.9%

      \[\leadsto x1 + \color{blue}{-6 \cdot x2} \]
   4. Step-by-step derivation

      1. *-commutative 66.9%

         \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]

   5. Simplified 66.9%

      \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]

   6. Taylor expanded in x1 around 0 67.4%

      \[\leadsto \color{blue}{-6 \cdot x2} \]
   7. Step-by-step derivation

      1. *-commutative 67.4%

         \[\leadsto \color{blue}{x2 \cdot -6} \]

   8. Simplified 67.4%

      \[\leadsto \color{blue}{x2 \cdot -6} \]
3. Recombined 3 regimes into one program.

4. Final simplification 61.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -6 \cdot 10^{+108}:\\ \;\;\;\;x1 + x1 \cdot \left(x1 \cdot 9\right)\\ \mathbf{elif}\;x1 \leq -4.2 \cdot 10^{-159}:\\ \;\;\;\;x1 + \left(x2 \cdot 8\right) \cdot \left(x1 \cdot x2\right)\\ \mathbf{elif}\;x1 \leq 1.25 \cdot 10^{-90}:\\ \;\;\;\;x2 \cdot -6\\ \mathbf{elif}\;x1 \leq 4.5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(x2 \cdot 8\right) \cdot \left(x1 \cdot x2\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot \left(x1 \cdot 9\right)\\ \end{array} \]

Alternative 19: 74.7% accurate, 7.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x2 \leq -1.68 \cdot 10^{+149} \lor \neg \left(x2 \leq 1.55 \cdot 10^{+63}\right):\\ \;\;\;\;x1 + \left(x2 \cdot -6 + 8 \cdot \left(x2 \cdot \left(x1 \cdot x2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 + -2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x2 -1.68e+149) (not (<= x2 1.55e+63)))
   (+ x1 (+ (* x2 -6.0) (* 8.0 (* x2 (* x1 x2)))))
   (+ x1 (+ (* x2 -6.0) (* x1 (+ (* x1 9.0) -2.0))))))

C

double code(double x1, double x2) {
	double tmp;
	if ((x2 <= -1.68e+149) || !(x2 <= 1.55e+63)) {
		tmp = x1 + ((x2 * -6.0) + (8.0 * (x2 * (x1 * x2))));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) + -2.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if ((x2 <= (-1.68d+149)) .or. (.not. (x2 <= 1.55d+63))) then
        tmp = x1 + ((x2 * (-6.0d0)) + (8.0d0 * (x2 * (x1 * x2))))
    else
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * ((x1 * 9.0d0) + (-2.0d0))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x2 <= -1.68e+149) || !(x2 <= 1.55e+63)) {
		tmp = x1 + ((x2 * -6.0) + (8.0 * (x2 * (x1 * x2))));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) + -2.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x2 <= -1.68e+149) or not (x2 <= 1.55e+63):
		tmp = x1 + ((x2 * -6.0) + (8.0 * (x2 * (x1 * x2))))
	else:
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) + -2.0)))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x2 <= -1.68e+149) || !(x2 <= 1.55e+63))
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(8.0 * Float64(x2 * Float64(x1 * x2)))));
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(x1 * 9.0) + -2.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x2 <= -1.68e+149) || ~((x2 <= 1.55e+63)))
		tmp = x1 + ((x2 * -6.0) + (8.0 * (x2 * (x1 * x2))));
	else
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) + -2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x2, -1.68e+149], N[Not[LessEqual[x2, 1.55e+63]], $MachinePrecision]], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(8.0 * N[(x2 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x2 < -1.67999999999999999e149 or 1.55e63 < x2

   1. Initial program 70.1%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 45.8%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 50.6%

      \[\leadsto x1 + \color{blue}{\left(-6 \cdot x2 + \left(3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right) + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)\right)} \]

   4. Taylor expanded in x2 around 0 57.7%

      \[\leadsto x1 + \left(-6 \cdot x2 + \left(\color{blue}{9 \cdot {x1}^{2}} + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)\right) \]
   5. Step-by-step derivation

      1. *-commutative 57.7%

         \[\leadsto x1 + \left(-6 \cdot x2 + \left(\color{blue}{{x1}^{2} \cdot 9} + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)\right) \]

      2. unpow2 57.7%

         \[\leadsto x1 + \left(-6 \cdot x2 + \left(\color{blue}{\left(x1 \cdot x1\right)} \cdot 9 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)\right) \]

   6. Simplified 57.7%

      \[\leadsto x1 + \left(-6 \cdot x2 + \left(\color{blue}{\left(x1 \cdot x1\right) \cdot 9} + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)\right) \]

   7. Taylor expanded in x2 around inf 58.9%

      \[\leadsto x1 + \left(-6 \cdot x2 + \color{blue}{8 \cdot \left(x1 \cdot {x2}^{2}\right)}\right) \]
   8. Step-by-step derivation

      1. *-commutative 58.9%

         \[\leadsto x1 + \left(-6 \cdot x2 + 8 \cdot \color{blue}{\left({x2}^{2} \cdot x1\right)}\right) \]

      2. unpow2 58.9%

         \[\leadsto x1 + \left(-6 \cdot x2 + 8 \cdot \left(\color{blue}{\left(x2 \cdot x2\right)} \cdot x1\right)\right) \]

      3. associate-*l* 80.3%

         \[\leadsto x1 + \left(-6 \cdot x2 + 8 \cdot \color{blue}{\left(x2 \cdot \left(x2 \cdot x1\right)\right)}\right) \]

      4. *-commutative 80.3%

         \[\leadsto x1 + \left(-6 \cdot x2 + 8 \cdot \left(x2 \cdot \color{blue}{\left(x1 \cdot x2\right)}\right)\right) \]

   9. Simplified 80.3%

      \[\leadsto x1 + \left(-6 \cdot x2 + \color{blue}{8 \cdot \left(x2 \cdot \left(x1 \cdot x2\right)\right)}\right) \]

   if -1.67999999999999999e149 < x2 < 1.55e63

   1. Initial program 68.6%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 50.3%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 70.4%

      \[\leadsto x1 + \color{blue}{\left(-6 \cdot x2 + \left(3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right) + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)\right)} \]

   4. Taylor expanded in x2 around 0 73.4%

      \[\leadsto x1 + \left(-6 \cdot x2 + \left(\color{blue}{9 \cdot {x1}^{2}} + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)\right) \]
   5. Step-by-step derivation

      1. *-commutative 73.4%

         \[\leadsto x1 + \left(-6 \cdot x2 + \left(\color{blue}{{x1}^{2} \cdot 9} + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)\right) \]

      2. unpow2 73.4%

         \[\leadsto x1 + \left(-6 \cdot x2 + \left(\color{blue}{\left(x1 \cdot x1\right)} \cdot 9 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)\right) \]

   6. Simplified 73.4%

      \[\leadsto x1 + \left(-6 \cdot x2 + \left(\color{blue}{\left(x1 \cdot x1\right) \cdot 9} + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)\right) \]

   7. Taylor expanded in x2 around 0 76.1%

      \[\leadsto x1 + \left(-6 \cdot x2 + \color{blue}{\left(-2 \cdot x1 + 9 \cdot {x1}^{2}\right)}\right) \]
   8. Step-by-step derivation

      1. +-commutative 76.1%

         \[\leadsto x1 + \left(-6 \cdot x2 + \color{blue}{\left(9 \cdot {x1}^{2} + -2 \cdot x1\right)}\right) \]

      2. *-commutative 76.1%

         \[\leadsto x1 + \left(-6 \cdot x2 + \left(\color{blue}{{x1}^{2} \cdot 9} + -2 \cdot x1\right)\right) \]

      3. unpow2 76.1%

         \[\leadsto x1 + \left(-6 \cdot x2 + \left(\color{blue}{\left(x1 \cdot x1\right)} \cdot 9 + -2 \cdot x1\right)\right) \]

      4. associate-*r* 76.1%

         \[\leadsto x1 + \left(-6 \cdot x2 + \left(\color{blue}{x1 \cdot \left(x1 \cdot 9\right)} + -2 \cdot x1\right)\right) \]

      5. *-commutative 76.1%

         \[\leadsto x1 + \left(-6 \cdot x2 + \left(x1 \cdot \left(x1 \cdot 9\right) + \color{blue}{x1 \cdot -2}\right)\right) \]

      6. distribute-lft-out 76.1%

         \[\leadsto x1 + \left(-6 \cdot x2 + \color{blue}{x1 \cdot \left(x1 \cdot 9 + -2\right)}\right) \]

   9. Simplified 76.1%

      \[\leadsto x1 + \left(-6 \cdot x2 + \color{blue}{x1 \cdot \left(x1 \cdot 9 + -2\right)}\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq -1.68 \cdot 10^{+149} \lor \neg \left(x2 \leq 1.55 \cdot 10^{+63}\right):\\ \;\;\;\;x1 + \left(x2 \cdot -6 + 8 \cdot \left(x2 \cdot \left(x1 \cdot x2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 + -2\right)\right)\\ \end{array} \]

Alternative 20: 67.2% accurate, 7.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 9\right)\\ \mathbf{if}\;x1 \leq -6 \cdot 10^{+108}:\\ \;\;\;\;x1 + \left(t_0 + x2 \cdot -6\right)\\ \mathbf{elif}\;x1 \leq 4.5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + 8 \cdot \left(x2 \cdot \left(x1 \cdot x2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 9.0))))
   (if (<= x1 -6e+108)
     (+ x1 (+ t_0 (* x2 -6.0)))
     (if (<= x1 4.5e+153)
       (+ x1 (+ (* x2 -6.0) (* 8.0 (* x2 (* x1 x2)))))
       (+ x1 t_0)))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 9.0);
	double tmp;
	if (x1 <= -6e+108) {
		tmp = x1 + (t_0 + (x2 * -6.0));
	} else if (x1 <= 4.5e+153) {
		tmp = x1 + ((x2 * -6.0) + (8.0 * (x2 * (x1 * x2))));
	} else {
		tmp = x1 + t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x1 * (x1 * 9.0d0)
    if (x1 <= (-6d+108)) then
        tmp = x1 + (t_0 + (x2 * (-6.0d0)))
    else if (x1 <= 4.5d+153) then
        tmp = x1 + ((x2 * (-6.0d0)) + (8.0d0 * (x2 * (x1 * x2))))
    else
        tmp = x1 + t_0
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 9.0);
	double tmp;
	if (x1 <= -6e+108) {
		tmp = x1 + (t_0 + (x2 * -6.0));
	} else if (x1 <= 4.5e+153) {
		tmp = x1 + ((x2 * -6.0) + (8.0 * (x2 * (x1 * x2))));
	} else {
		tmp = x1 + t_0;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 9.0)
	tmp = 0
	if x1 <= -6e+108:
		tmp = x1 + (t_0 + (x2 * -6.0))
	elif x1 <= 4.5e+153:
		tmp = x1 + ((x2 * -6.0) + (8.0 * (x2 * (x1 * x2))))
	else:
		tmp = x1 + t_0
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 9.0))
	tmp = 0.0
	if (x1 <= -6e+108)
		tmp = Float64(x1 + Float64(t_0 + Float64(x2 * -6.0)));
	elseif (x1 <= 4.5e+153)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(8.0 * Float64(x2 * Float64(x1 * x2)))));
	else
		tmp = Float64(x1 + t_0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * 9.0);
	tmp = 0.0;
	if (x1 <= -6e+108)
		tmp = x1 + (t_0 + (x2 * -6.0));
	elseif (x1 <= 4.5e+153)
		tmp = x1 + ((x2 * -6.0) + (8.0 * (x2 * (x1 * x2))));
	else
		tmp = x1 + t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -6e+108], N[(x1 + N[(t$95$0 + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 4.5e+153], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(8.0 * N[(x2 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + t$95$0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -5.99999999999999968e108

   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. Taylor expanded in x1 around 0 0.1%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 34.0%

      \[\leadsto x1 + \color{blue}{\left(-6 \cdot x2 + \left(3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right) + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)\right)} \]

   4. Taylor expanded in x2 around 0 38.3%

      \[\leadsto x1 + \left(-6 \cdot x2 + \left(\color{blue}{9 \cdot {x1}^{2}} + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)\right) \]
   5. Step-by-step derivation

      1. *-commutative 38.3%

         \[\leadsto x1 + \left(-6 \cdot x2 + \left(\color{blue}{{x1}^{2} \cdot 9} + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)\right) \]

      2. unpow2 38.3%

         \[\leadsto x1 + \left(-6 \cdot x2 + \left(\color{blue}{\left(x1 \cdot x1\right)} \cdot 9 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)\right) \]

   6. Simplified 38.3%

      \[\leadsto x1 + \left(-6 \cdot x2 + \left(\color{blue}{\left(x1 \cdot x1\right) \cdot 9} + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)\right) \]

   7. Taylor expanded in x1 around inf 78.1%

      \[\leadsto x1 + \left(-6 \cdot x2 + \color{blue}{9 \cdot {x1}^{2}}\right) \]
   8. Step-by-step derivation

      1. *-commutative 78.1%

         \[\leadsto x1 + \left(-6 \cdot x2 + \color{blue}{{x1}^{2} \cdot 9}\right) \]

      2. unpow2 78.1%

         \[\leadsto x1 + \left(-6 \cdot x2 + \color{blue}{\left(x1 \cdot x1\right)} \cdot 9\right) \]

      3. associate-*r* 78.1%

         \[\leadsto x1 + \left(-6 \cdot x2 + \color{blue}{x1 \cdot \left(x1 \cdot 9\right)}\right) \]

   9. Simplified 78.1%

      \[\leadsto x1 + \left(-6 \cdot x2 + \color{blue}{x1 \cdot \left(x1 \cdot 9\right)}\right) \]

   if -5.99999999999999968e108 < x1 < 4.5000000000000001e153

   1. Initial program 98.8%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 69.8%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 68.7%

      \[\leadsto x1 + \color{blue}{\left(-6 \cdot x2 + \left(3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right) + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)\right)} \]

   4. Taylor expanded in x2 around 0 70.5%

      \[\leadsto x1 + \left(-6 \cdot x2 + \left(\color{blue}{9 \cdot {x1}^{2}} + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)\right) \]
   5. Step-by-step derivation

      1. *-commutative 70.5%

         \[\leadsto x1 + \left(-6 \cdot x2 + \left(\color{blue}{{x1}^{2} \cdot 9} + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)\right) \]

      2. unpow2 70.5%

         \[\leadsto x1 + \left(-6 \cdot x2 + \left(\color{blue}{\left(x1 \cdot x1\right)} \cdot 9 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)\right) \]

   6. Simplified 70.5%

      \[\leadsto x1 + \left(-6 \cdot x2 + \left(\color{blue}{\left(x1 \cdot x1\right) \cdot 9} + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)\right) \]

   7. Taylor expanded in x2 around inf 52.1%

      \[\leadsto x1 + \left(-6 \cdot x2 + \color{blue}{8 \cdot \left(x1 \cdot {x2}^{2}\right)}\right) \]
   8. Step-by-step derivation

      1. *-commutative 52.1%

         \[\leadsto x1 + \left(-6 \cdot x2 + 8 \cdot \color{blue}{\left({x2}^{2} \cdot x1\right)}\right) \]

      2. unpow2 52.1%

         \[\leadsto x1 + \left(-6 \cdot x2 + 8 \cdot \left(\color{blue}{\left(x2 \cdot x2\right)} \cdot x1\right)\right) \]

      3. associate-*l* 62.2%

         \[\leadsto x1 + \left(-6 \cdot x2 + 8 \cdot \color{blue}{\left(x2 \cdot \left(x2 \cdot x1\right)\right)}\right) \]

      4. *-commutative 62.2%

         \[\leadsto x1 + \left(-6 \cdot x2 + 8 \cdot \left(x2 \cdot \color{blue}{\left(x1 \cdot x2\right)}\right)\right) \]

   9. Simplified 62.2%

      \[\leadsto x1 + \left(-6 \cdot x2 + \color{blue}{8 \cdot \left(x2 \cdot \left(x1 \cdot x2\right)\right)}\right) \]

   if 4.5000000000000001e153 < x1

   1. Initial program 0.0%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 0.0%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 80.6%

      \[\leadsto x1 + \color{blue}{\left(-6 \cdot x2 + \left(3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right) + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)\right)} \]

   4. Taylor expanded in x1 around inf 80.6%

      \[\leadsto x1 + \left(-6 \cdot x2 + \color{blue}{3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)}\right) \]
   5. Step-by-step derivation

      1. associate-*r* 80.6%

         \[\leadsto x1 + \left(-6 \cdot x2 + \color{blue}{\left(3 \cdot {x1}^{2}\right) \cdot \left(3 - -2 \cdot x2\right)}\right) \]

      2. *-commutative 80.6%

         \[\leadsto x1 + \left(-6 \cdot x2 + \left(3 \cdot {x1}^{2}\right) \cdot \left(3 - \color{blue}{x2 \cdot -2}\right)\right) \]

      3. cancel-sign-sub-inv 80.6%

         \[\leadsto x1 + \left(-6 \cdot x2 + \left(3 \cdot {x1}^{2}\right) \cdot \color{blue}{\left(3 + \left(-x2\right) \cdot -2\right)}\right) \]

      4. unpow2 80.6%

         \[\leadsto x1 + \left(-6 \cdot x2 + \left(3 \cdot \color{blue}{\left(x1 \cdot x1\right)}\right) \cdot \left(3 + \left(-x2\right) \cdot -2\right)\right) \]

      5. +-commutative 80.6%

         \[\leadsto x1 + \left(-6 \cdot x2 + \left(3 \cdot \left(x1 \cdot x1\right)\right) \cdot \color{blue}{\left(\left(-x2\right) \cdot -2 + 3\right)}\right) \]

      6. distribute-lft-neg-in 80.6%

         \[\leadsto x1 + \left(-6 \cdot x2 + \left(3 \cdot \left(x1 \cdot x1\right)\right) \cdot \left(\color{blue}{\left(-x2 \cdot -2\right)} + 3\right)\right) \]

      7. *-commutative 80.6%

         \[\leadsto x1 + \left(-6 \cdot x2 + \left(3 \cdot \left(x1 \cdot x1\right)\right) \cdot \left(\left(-\color{blue}{-2 \cdot x2}\right) + 3\right)\right) \]

      8. distribute-lft-neg-in 80.6%

         \[\leadsto x1 + \left(-6 \cdot x2 + \left(3 \cdot \left(x1 \cdot x1\right)\right) \cdot \left(\color{blue}{\left(--2\right) \cdot x2} + 3\right)\right) \]

      9. metadata-eval 80.6%

         \[\leadsto x1 + \left(-6 \cdot x2 + \left(3 \cdot \left(x1 \cdot x1\right)\right) \cdot \left(\color{blue}{2} \cdot x2 + 3\right)\right) \]

      10. count-2 80.6%

          \[\leadsto x1 + \left(-6 \cdot x2 + \left(3 \cdot \left(x1 \cdot x1\right)\right) \cdot \left(\color{blue}{\left(x2 + x2\right)} + 3\right)\right) \]

   6. Simplified 80.6%

      \[\leadsto x1 + \left(-6 \cdot x2 + \color{blue}{\left(3 \cdot \left(x1 \cdot x1\right)\right) \cdot \left(\left(x2 + x2\right) + 3\right)}\right) \]

   7. Taylor expanded in x2 around 0 100.0%

      \[\leadsto \color{blue}{x1 + 9 \cdot {x1}^{2}} \]
   8. Step-by-step derivation

      1. *-commutative 100.0%

         \[\leadsto x1 + \color{blue}{{x1}^{2} \cdot 9} \]

      2. unpow2 100.0%

         \[\leadsto x1 + \color{blue}{\left(x1 \cdot x1\right)} \cdot 9 \]

      3. associate-*r* 100.0%

         \[\leadsto x1 + \color{blue}{x1 \cdot \left(x1 \cdot 9\right)} \]

   9. Simplified 100.0%

      \[\leadsto \color{blue}{x1 + x1 \cdot \left(x1 \cdot 9\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -6 \cdot 10^{+108}:\\ \;\;\;\;x1 + \left(x1 \cdot \left(x1 \cdot 9\right) + x2 \cdot -6\right)\\ \mathbf{elif}\;x1 \leq 4.5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + 8 \cdot \left(x2 \cdot \left(x1 \cdot x2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot \left(x1 \cdot 9\right)\\ \end{array} \]

Alternative 21: 56.3% accurate, 8.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x2 \leq -5 \cdot 10^{+170} \lor \neg \left(x2 \leq 6.2 \cdot 10^{+72}\right):\\ \;\;\;\;x1 + \left(x2 \cdot 8\right) \cdot \left(x1 \cdot x2\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 \cdot \left(x1 \cdot 9\right) + x2 \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x2 -5e+170) (not (<= x2 6.2e+72)))
   (+ x1 (* (* x2 8.0) (* x1 x2)))
   (+ x1 (+ (* x1 (* x1 9.0)) (* x2 -6.0)))))

C

double code(double x1, double x2) {
	double tmp;
	if ((x2 <= -5e+170) || !(x2 <= 6.2e+72)) {
		tmp = x1 + ((x2 * 8.0) * (x1 * x2));
	} else {
		tmp = x1 + ((x1 * (x1 * 9.0)) + (x2 * -6.0));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if ((x2 <= (-5d+170)) .or. (.not. (x2 <= 6.2d+72))) then
        tmp = x1 + ((x2 * 8.0d0) * (x1 * x2))
    else
        tmp = x1 + ((x1 * (x1 * 9.0d0)) + (x2 * (-6.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x2 <= -5e+170) || !(x2 <= 6.2e+72)) {
		tmp = x1 + ((x2 * 8.0) * (x1 * x2));
	} else {
		tmp = x1 + ((x1 * (x1 * 9.0)) + (x2 * -6.0));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x2 <= -5e+170) or not (x2 <= 6.2e+72):
		tmp = x1 + ((x2 * 8.0) * (x1 * x2))
	else:
		tmp = x1 + ((x1 * (x1 * 9.0)) + (x2 * -6.0))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x2 <= -5e+170) || !(x2 <= 6.2e+72))
		tmp = Float64(x1 + Float64(Float64(x2 * 8.0) * Float64(x1 * x2)));
	else
		tmp = Float64(x1 + Float64(Float64(x1 * Float64(x1 * 9.0)) + Float64(x2 * -6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x2 <= -5e+170) || ~((x2 <= 6.2e+72)))
		tmp = x1 + ((x2 * 8.0) * (x1 * x2));
	else
		tmp = x1 + ((x1 * (x1 * 9.0)) + (x2 * -6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x2, -5e+170], N[Not[LessEqual[x2, 6.2e+72]], $MachinePrecision]], N[(x1 + N[(N[(x2 * 8.0), $MachinePrecision] * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x1 * N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision] + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x2 < -4.99999999999999977e170 or 6.19999999999999977e72 < x2

   1. Initial program 69.5%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 47.3%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x2 around inf 55.8%

      \[\leadsto x1 + \color{blue}{8 \cdot \left(x1 \cdot {x2}^{2}\right)} \]
   4. Step-by-step derivation

      1. *-commutative 55.8%

         \[\leadsto x1 + 8 \cdot \color{blue}{\left({x2}^{2} \cdot x1\right)} \]

      2. associate-*r* 55.8%

         \[\leadsto x1 + \color{blue}{\left(8 \cdot {x2}^{2}\right) \cdot x1} \]

      3. unpow2 55.8%

         \[\leadsto x1 + \left(8 \cdot \color{blue}{\left(x2 \cdot x2\right)}\right) \cdot x1 \]

      4. associate-*r* 55.8%

         \[\leadsto x1 + \color{blue}{\left(\left(8 \cdot x2\right) \cdot x2\right)} \cdot x1 \]

      5. associate-*r* 65.9%

         \[\leadsto x1 + \color{blue}{\left(8 \cdot x2\right) \cdot \left(x2 \cdot x1\right)} \]

      6. *-commutative 65.9%

         \[\leadsto x1 + \color{blue}{\left(x2 \cdot 8\right)} \cdot \left(x2 \cdot x1\right) \]

   5. Simplified 65.9%

      \[\leadsto x1 + \color{blue}{\left(x2 \cdot 8\right) \cdot \left(x2 \cdot x1\right)} \]

   if -4.99999999999999977e170 < x2 < 6.19999999999999977e72

   1. Initial program 68.9%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 49.5%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 69.1%

      \[\leadsto x1 + \color{blue}{\left(-6 \cdot x2 + \left(3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right) + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)\right)} \]

   4. Taylor expanded in x2 around 0 72.6%

      \[\leadsto x1 + \left(-6 \cdot x2 + \left(\color{blue}{9 \cdot {x1}^{2}} + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)\right) \]
   5. Step-by-step derivation

      1. *-commutative 72.6%

         \[\leadsto x1 + \left(-6 \cdot x2 + \left(\color{blue}{{x1}^{2} \cdot 9} + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)\right) \]

      2. unpow2 72.6%

         \[\leadsto x1 + \left(-6 \cdot x2 + \left(\color{blue}{\left(x1 \cdot x1\right)} \cdot 9 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)\right) \]

   6. Simplified 72.6%

      \[\leadsto x1 + \left(-6 \cdot x2 + \left(\color{blue}{\left(x1 \cdot x1\right) \cdot 9} + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)\right) \]

   7. Taylor expanded in x1 around inf 57.4%

      \[\leadsto x1 + \left(-6 \cdot x2 + \color{blue}{9 \cdot {x1}^{2}}\right) \]
   8. Step-by-step derivation

      1. *-commutative 57.4%

         \[\leadsto x1 + \left(-6 \cdot x2 + \color{blue}{{x1}^{2} \cdot 9}\right) \]

      2. unpow2 57.4%

         \[\leadsto x1 + \left(-6 \cdot x2 + \color{blue}{\left(x1 \cdot x1\right)} \cdot 9\right) \]

      3. associate-*r* 57.4%

         \[\leadsto x1 + \left(-6 \cdot x2 + \color{blue}{x1 \cdot \left(x1 \cdot 9\right)}\right) \]

   9. Simplified 57.4%

      \[\leadsto x1 + \left(-6 \cdot x2 + \color{blue}{x1 \cdot \left(x1 \cdot 9\right)}\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 60.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq -5 \cdot 10^{+170} \lor \neg \left(x2 \leq 6.2 \cdot 10^{+72}\right):\\ \;\;\;\;x1 + \left(x2 \cdot 8\right) \cdot \left(x1 \cdot x2\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 \cdot \left(x1 \cdot 9\right) + x2 \cdot -6\right)\\ \end{array} \]

Alternative 22: 51.5% accurate, 11.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -9.4 \cdot 10^{-17} \lor \neg \left(x1 \leq 0.0019\right):\\ \;\;\;\;x1 + x1 \cdot \left(x1 \cdot 9\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x1 -9.4e-17) (not (<= x1 0.0019)))
   (+ x1 (* x1 (* x1 9.0)))
   (* x2 -6.0)))

C

double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -9.4e-17) || !(x1 <= 0.0019)) {
		tmp = x1 + (x1 * (x1 * 9.0));
	} else {
		tmp = x2 * -6.0;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if ((x1 <= (-9.4d-17)) .or. (.not. (x1 <= 0.0019d0))) then
        tmp = x1 + (x1 * (x1 * 9.0d0))
    else
        tmp = x2 * (-6.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -9.4e-17) || !(x1 <= 0.0019)) {
		tmp = x1 + (x1 * (x1 * 9.0));
	} else {
		tmp = x2 * -6.0;
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x1 <= -9.4e-17) or not (x1 <= 0.0019):
		tmp = x1 + (x1 * (x1 * 9.0))
	else:
		tmp = x2 * -6.0
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x1 <= -9.4e-17) || !(x1 <= 0.0019))
		tmp = Float64(x1 + Float64(x1 * Float64(x1 * 9.0)));
	else
		tmp = Float64(x2 * -6.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x1 <= -9.4e-17) || ~((x1 <= 0.0019)))
		tmp = x1 + (x1 * (x1 * 9.0));
	else
		tmp = x2 * -6.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x1, -9.4e-17], N[Not[LessEqual[x1, 0.0019]], $MachinePrecision]], N[(x1 + N[(x1 * N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x2 * -6.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x1 < -9.3999999999999999e-17 or 0.0019 < x1

   1. Initial program 39.1%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 12.4%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 42.5%

      \[\leadsto x1 + \color{blue}{\left(-6 \cdot x2 + \left(3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right) + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)\right)} \]

   4. Taylor expanded in x1 around inf 44.7%

      \[\leadsto x1 + \left(-6 \cdot x2 + \color{blue}{3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)}\right) \]
   5. Step-by-step derivation

      1. associate-*r* 44.7%

         \[\leadsto x1 + \left(-6 \cdot x2 + \color{blue}{\left(3 \cdot {x1}^{2}\right) \cdot \left(3 - -2 \cdot x2\right)}\right) \]

      2. *-commutative 44.7%

         \[\leadsto x1 + \left(-6 \cdot x2 + \left(3 \cdot {x1}^{2}\right) \cdot \left(3 - \color{blue}{x2 \cdot -2}\right)\right) \]

      3. cancel-sign-sub-inv 44.7%

         \[\leadsto x1 + \left(-6 \cdot x2 + \left(3 \cdot {x1}^{2}\right) \cdot \color{blue}{\left(3 + \left(-x2\right) \cdot -2\right)}\right) \]

      4. unpow2 44.7%

         \[\leadsto x1 + \left(-6 \cdot x2 + \left(3 \cdot \color{blue}{\left(x1 \cdot x1\right)}\right) \cdot \left(3 + \left(-x2\right) \cdot -2\right)\right) \]

      5. +-commutative 44.7%

         \[\leadsto x1 + \left(-6 \cdot x2 + \left(3 \cdot \left(x1 \cdot x1\right)\right) \cdot \color{blue}{\left(\left(-x2\right) \cdot -2 + 3\right)}\right) \]

      6. distribute-lft-neg-in 44.7%

         \[\leadsto x1 + \left(-6 \cdot x2 + \left(3 \cdot \left(x1 \cdot x1\right)\right) \cdot \left(\color{blue}{\left(-x2 \cdot -2\right)} + 3\right)\right) \]

      7. *-commutative 44.7%

         \[\leadsto x1 + \left(-6 \cdot x2 + \left(3 \cdot \left(x1 \cdot x1\right)\right) \cdot \left(\left(-\color{blue}{-2 \cdot x2}\right) + 3\right)\right) \]

      8. distribute-lft-neg-in 44.7%

         \[\leadsto x1 + \left(-6 \cdot x2 + \left(3 \cdot \left(x1 \cdot x1\right)\right) \cdot \left(\color{blue}{\left(--2\right) \cdot x2} + 3\right)\right) \]

      9. metadata-eval 44.7%

         \[\leadsto x1 + \left(-6 \cdot x2 + \left(3 \cdot \left(x1 \cdot x1\right)\right) \cdot \left(\color{blue}{2} \cdot x2 + 3\right)\right) \]

      10. count-2 44.7%

          \[\leadsto x1 + \left(-6 \cdot x2 + \left(3 \cdot \left(x1 \cdot x1\right)\right) \cdot \left(\color{blue}{\left(x2 + x2\right)} + 3\right)\right) \]

   6. Simplified 44.7%

      \[\leadsto x1 + \left(-6 \cdot x2 + \color{blue}{\left(3 \cdot \left(x1 \cdot x1\right)\right) \cdot \left(\left(x2 + x2\right) + 3\right)}\right) \]

   7. Taylor expanded in x2 around 0 54.8%

      \[\leadsto \color{blue}{x1 + 9 \cdot {x1}^{2}} \]
   8. Step-by-step derivation

      1. *-commutative 54.8%

         \[\leadsto x1 + \color{blue}{{x1}^{2} \cdot 9} \]

      2. unpow2 54.8%

         \[\leadsto x1 + \color{blue}{\left(x1 \cdot x1\right)} \cdot 9 \]

      3. associate-*r* 54.8%

         \[\leadsto x1 + \color{blue}{x1 \cdot \left(x1 \cdot 9\right)} \]

   9. Simplified 54.8%

      \[\leadsto \color{blue}{x1 + x1 \cdot \left(x1 \cdot 9\right)} \]

   if -9.3999999999999999e-17 < x1 < 0.0019

   1. Initial program 98.7%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 84.7%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 50.1%

      \[\leadsto x1 + \color{blue}{-6 \cdot x2} \]
   4. Step-by-step derivation

      1. *-commutative 50.1%

         \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]

   5. Simplified 50.1%

      \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]

   6. Taylor expanded in x1 around 0 50.7%

      \[\leadsto \color{blue}{-6 \cdot x2} \]
   7. Step-by-step derivation

      1. *-commutative 50.7%

         \[\leadsto \color{blue}{x2 \cdot -6} \]

   8. Simplified 50.7%

      \[\leadsto \color{blue}{x2 \cdot -6} \]
3. Recombined 2 regimes into one program.

4. Final simplification 52.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -9.4 \cdot 10^{-17} \lor \neg \left(x1 \leq 0.0019\right):\\ \;\;\;\;x1 + x1 \cdot \left(x1 \cdot 9\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6\\ \end{array} \]

Alternative 23: 26.1% accurate, 42.3× speedup

Math

\[\begin{array}{l} \\ x2 \cdot -6 \end{array} \]

FPCore

(FPCore (x1 x2) :precision binary64 (* x2 -6.0))

C

double code(double x1, double x2) {
	return x2 * -6.0;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    code = x2 * (-6.0d0)
end function

Java

public static double code(double x1, double x2) {
	return x2 * -6.0;
}

Python

def code(x1, x2):
	return x2 * -6.0

Julia

function code(x1, x2)
	return Float64(x2 * -6.0)
end

MATLAB

function tmp = code(x1, x2)
	tmp = x2 * -6.0;
end

Wolfram

code[x1_, x2_] := N[(x2 * -6.0), $MachinePrecision]

Derivation

1. Initial program 69.1%

   \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

2. Taylor expanded in x1 around 0 48.8%

   \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

3. Taylor expanded in x1 around 0 26.7%

   \[\leadsto x1 + \color{blue}{-6 \cdot x2} \]
4. Step-by-step derivation

   1. *-commutative 26.7%

      \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]

5. Simplified 26.7%

   \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]

6. Taylor expanded in x1 around 0 26.7%

   \[\leadsto \color{blue}{-6 \cdot x2} \]
7. Step-by-step derivation

   1. *-commutative 26.7%

      \[\leadsto \color{blue}{x2 \cdot -6} \]

8. Simplified 26.7%

   \[\leadsto \color{blue}{x2 \cdot -6} \]

9. Final simplification 26.7%

   \[\leadsto x2 \cdot -6 \]

Alternative 24: 3.2% accurate, 127.0× speedup

Math

\[\begin{array}{l} \\ x1 \end{array} \]

FPCore

(FPCore (x1 x2) :precision binary64 x1)

C

double code(double x1, double x2) {
	return x1;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    code = x1
end function

Java

public static double code(double x1, double x2) {
	return x1;
}

Python

def code(x1, x2):
	return x1

Julia

function code(x1, x2)
	return x1
end

MATLAB

function tmp = code(x1, x2)
	tmp = x1;
end

Wolfram

code[x1_, x2_] := x1

Derivation

1. Initial program 69.1%

   \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

2. Taylor expanded in x1 around 0 48.8%

   \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

3. Taylor expanded in x1 around 0 26.7%

   \[\leadsto x1 + \color{blue}{-6 \cdot x2} \]
4. Step-by-step derivation

   1. *-commutative 26.7%

      \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]

5. Simplified 26.7%

   \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]

6. Taylor expanded in x1 around inf 3.2%

   \[\leadsto \color{blue}{x1} \]

7. Final simplification 3.2%

   \[\leadsto x1 \]

Reproduce

herbie shell --seed 2023279 
(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))))))