Rosa's FloatVsDoubleBenchmark

Percentage Accurate: 70.2% → 99.5%

Time: 56.2s

Alternatives: 27

Speedup: 1.4×

• 46.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 70.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.5% accurate, 0.1× speedup

Math

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

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (+ (* x1 x1) 1.0))
        (t_2 (/ (- (+ t_0 (* 2.0 x2)) x1) t_1))
        (t_3 (/ (fma x1 (* x1 3.0) (- (* 2.0 x2) x1)) (fma x1 x1 1.0))))
   (if (<=
        (+
         x1
         (+
          (+
           x1
           (+
            (+
             (*
              t_1
              (+
               (* (* (* x1 2.0) t_2) (- t_2 3.0))
               (* (* x1 x1) (- (* t_2 4.0) 6.0))))
             (* t_0 t_2))
            (* x1 (* x1 x1))))
          (* 3.0 (/ (- (- t_0 (* 2.0 x2)) x1) t_1))))
        INFINITY)
     (+
      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_3 4.0 -6.0)) (* t_3 (* (* x1 2.0) (+ t_3 -3.0))))
         (+
          (*
           (* 3.0 (* x1 x1))
           (/ (- (fma (* x1 3.0) x1 (+ x2 x2)) x1) (fma x1 x1 1.0)))
          (pow x1 3.0))))))
     (+ x1 (+ (+ x1 (* 6.0 (pow x1 4.0))) (* 3.0 (* x2 -2.0)))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = ((t_0 + (2.0 * x2)) - x1) / t_1;
	double t_3 = fma(x1, (x1 * 3.0), ((2.0 * x2) - x1)) / fma(x1, x1, 1.0);
	double tmp;
	if ((x1 + ((x1 + (((t_1 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((t_2 * 4.0) - 6.0)))) + (t_0 * t_2)) + (x1 * (x1 * x1)))) + (3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)))) <= ((double) INFINITY)) {
		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_3, 4.0, -6.0)), (t_3 * ((x1 * 2.0) * (t_3 + -3.0)))), (((3.0 * (x1 * x1)) * ((fma((x1 * 3.0), x1, (x2 + x2)) - x1) / fma(x1, x1, 1.0))) + pow(x1, 3.0)))));
	} else {
		tmp = x1 + ((x1 + (6.0 * pow(x1, 4.0))) + (3.0 * (x2 * -2.0)));
	}
	return tmp;
}

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(Float64(x1 * x1) + 1.0)
	t_2 = Float64(Float64(Float64(t_0 + Float64(2.0 * x2)) - x1) / t_1)
	t_3 = Float64(fma(x1, Float64(x1 * 3.0), Float64(Float64(2.0 * x2) - x1)) / fma(x1, x1, 1.0))
	tmp = 0.0
	if (Float64(x1 + Float64(Float64(x1 + Float64(Float64(Float64(t_1 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_2) * Float64(t_2 - 3.0)) + Float64(Float64(x1 * x1) * Float64(Float64(t_2 * 4.0) - 6.0)))) + Float64(t_0 * t_2)) + Float64(x1 * Float64(x1 * x1)))) + Float64(3.0 * Float64(Float64(Float64(t_0 - Float64(2.0 * x2)) - x1) / t_1)))) <= Inf)
		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_3, 4.0, -6.0)), Float64(t_3 * Float64(Float64(x1 * 2.0) * Float64(t_3 + -3.0)))), Float64(Float64(Float64(3.0 * Float64(x1 * x1)) * Float64(Float64(fma(Float64(x1 * 3.0), x1, Float64(x2 + x2)) - x1) / fma(x1, x1, 1.0))) + (x1 ^ 3.0))))));
	else
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(6.0 * (x1 ^ 4.0))) + Float64(3.0 * Float64(x2 * -2.0))));
	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[(N[(N[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$3 = 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[N[(x1 + N[(N[(x1 + N[(N[(N[(t$95$1 * N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$2), $MachinePrecision] * N[(t$95$2 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$2 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$0 * t$95$2), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(N[(N[(t$95$0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], 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$3 * 4.0 + -6.0), $MachinePrecision]), $MachinePrecision] + N[(t$95$3 * N[(N[(x1 * 2.0), $MachinePrecision] * N[(t$95$3 + -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(3.0 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] * N[(N[(N[(N[(x1 * 3.0), $MachinePrecision] * x1 + N[(x2 + x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[Power[x1, 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x1 + N[(6.0 * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

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 99.6%

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

   3. Simplified 99.8%

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

      1. fma-udef 99.8%

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

      2. *-commutative 99.8%

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

      3. *-commutative 99.8%

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

      4. fma-udef 99.8%

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

      5. *-commutative 99.8%

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

      6. *-commutative 99.8%

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

      7. associate--l+ 99.8%

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

      8. fma-def 99.8%

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

      9. associate-*l* 99.8%

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

      10. fma-def 99.8%

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

      11. count-2 99.8%

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

      12. fma-def 99.8%

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

   5. Applied egg-rr 99.8%

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

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

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around 0 0.0%

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

      1. *-commutative 0.0%

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

   4. Simplified 0.0%

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

   5. Taylor expanded in x1 around inf 97.4%

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

      1. *-commutative 97.4%

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

   7. Simplified 97.4%

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

4. Final simplification 99.0%

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

Alternative 2: 99.5% accurate, 0.1× speedup

Math

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

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (+ (* x1 x1) 1.0))
        (t_2 (/ (- (+ t_0 (* 2.0 x2)) x1) t_1))
        (t_3 (/ (fma x1 (* x1 3.0) (- (* 2.0 x2) x1)) (fma x1 x1 1.0))))
   (if (<=
        (+
         x1
         (+
          (+
           x1
           (+
            (+
             (*
              t_1
              (+
               (* (* (* x1 2.0) t_2) (- t_2 3.0))
               (* (* x1 x1) (- (* t_2 4.0) 6.0))))
             (* t_0 t_2))
            (* x1 (* x1 x1))))
          (* 3.0 (/ (- (- t_0 (* 2.0 x2)) x1) t_1))))
        INFINITY)
     (+
      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_3 4.0 -6.0)) (* t_3 (* (* x1 2.0) (+ t_3 -3.0))))
         (+
          (pow x1 3.0)
          (* (* 3.0 (* x1 x1)) (/ (- t_0 x1) (fma x1 x1 1.0))))))))
     (+ x1 (+ (+ x1 (* 6.0 (pow x1 4.0))) (* 3.0 (* x2 -2.0)))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = ((t_0 + (2.0 * x2)) - x1) / t_1;
	double t_3 = fma(x1, (x1 * 3.0), ((2.0 * x2) - x1)) / fma(x1, x1, 1.0);
	double tmp;
	if ((x1 + ((x1 + (((t_1 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((t_2 * 4.0) - 6.0)))) + (t_0 * t_2)) + (x1 * (x1 * x1)))) + (3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)))) <= ((double) INFINITY)) {
		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_3, 4.0, -6.0)), (t_3 * ((x1 * 2.0) * (t_3 + -3.0)))), (pow(x1, 3.0) + ((3.0 * (x1 * x1)) * ((t_0 - x1) / fma(x1, x1, 1.0)))))));
	} else {
		tmp = x1 + ((x1 + (6.0 * pow(x1, 4.0))) + (3.0 * (x2 * -2.0)));
	}
	return tmp;
}

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(Float64(x1 * x1) + 1.0)
	t_2 = Float64(Float64(Float64(t_0 + Float64(2.0 * x2)) - x1) / t_1)
	t_3 = Float64(fma(x1, Float64(x1 * 3.0), Float64(Float64(2.0 * x2) - x1)) / fma(x1, x1, 1.0))
	tmp = 0.0
	if (Float64(x1 + Float64(Float64(x1 + Float64(Float64(Float64(t_1 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_2) * Float64(t_2 - 3.0)) + Float64(Float64(x1 * x1) * Float64(Float64(t_2 * 4.0) - 6.0)))) + Float64(t_0 * t_2)) + Float64(x1 * Float64(x1 * x1)))) + Float64(3.0 * Float64(Float64(Float64(t_0 - Float64(2.0 * x2)) - x1) / t_1)))) <= Inf)
		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_3, 4.0, -6.0)), Float64(t_3 * Float64(Float64(x1 * 2.0) * Float64(t_3 + -3.0)))), Float64((x1 ^ 3.0) + Float64(Float64(3.0 * Float64(x1 * x1)) * Float64(Float64(t_0 - x1) / fma(x1, x1, 1.0))))))));
	else
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(6.0 * (x1 ^ 4.0))) + Float64(3.0 * Float64(x2 * -2.0))));
	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[(N[(N[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$3 = 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[N[(x1 + N[(N[(x1 + N[(N[(N[(t$95$1 * N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$2), $MachinePrecision] * N[(t$95$2 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$2 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$0 * t$95$2), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(N[(N[(t$95$0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], 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$3 * 4.0 + -6.0), $MachinePrecision]), $MachinePrecision] + N[(t$95$3 * N[(N[(x1 * 2.0), $MachinePrecision] * N[(t$95$3 + -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[Power[x1, 3.0], $MachinePrecision] + N[(N[(3.0 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] * N[(N[(t$95$0 - x1), $MachinePrecision] / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x1 + N[(6.0 * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

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 99.6%

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

   3. Simplified 99.8%

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

      1. fma-udef 99.8%

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

      2. *-commutative 99.8%

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

      3. *-commutative 99.8%

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

      4. fma-udef 99.8%

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

      5. *-commutative 99.8%

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

      6. *-commutative 99.8%

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

      7. associate--l+ 99.8%

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

      8. fma-def 99.8%

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

      9. associate-*l* 99.8%

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

      10. fma-def 99.8%

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

      11. count-2 99.8%

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

      12. fma-def 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in x2 around 0 99.7%

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

      1. unpow2 99.7%

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

      2. associate-*r* 99.7%

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

      3. *-commutative 99.7%

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

      4. +-commutative 99.7%

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

      5. unpow2 99.7%

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

      6. fma-udef 99.7%

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

   8. Simplified 99.7%

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

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

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around 0 0.0%

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

      1. *-commutative 0.0%

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

   4. Simplified 0.0%

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

   5. Taylor expanded in x1 around inf 97.4%

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

      1. *-commutative 97.4%

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

   7. Simplified 97.4%

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

4. Final simplification 99.0%

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

Alternative 3: 99.3% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (+.f64 x1 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 (+.f64 (*.f64 (*.f64 (*.f64 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 99.6%

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

   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 0.0%

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

      1. *-commutative 0.0%

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

   4. Simplified 0.0%

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

   5. Taylor expanded in x1 around inf 97.4%

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

      1. *-commutative 97.4%

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

   7. Simplified 97.4%

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

4. Final simplification 98.9%

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

Alternative 4: 98.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot {x1}^{4}\\ t_1 := x1 \cdot x1 + 1\\ t_2 := 3 \cdot \left(x2 \cdot -2\right)\\ t_3 := \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{t_1}\\ \mathbf{if}\;x1 \leq -5.5 \cdot 10^{+102}:\\ \;\;\;\;x1 \cdot 2 + t_0\\ \mathbf{elif}\;x1 \leq 2.4 \cdot 10^{+49}:\\ \;\;\;\;x1 + \left(t_2 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(t_1 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t_3\right) \cdot \left(t_3 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(t_3 \cdot 4 - 6\right)\right) + x1 \cdot \left(\left(x1 \cdot 3\right) \cdot \left(3 - \frac{1}{x1}\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 + t_0\right) + t_2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* 6.0 (pow x1 4.0)))
        (t_1 (+ (* x1 x1) 1.0))
        (t_2 (* 3.0 (* x2 -2.0)))
        (t_3 (/ (- (+ (* x1 (* x1 3.0)) (* 2.0 x2)) x1) t_1)))
   (if (<= x1 -5.5e+102)
     (+ (* x1 2.0) t_0)
     (if (<= x1 2.4e+49)
       (+
        x1
        (+
         t_2
         (+
          x1
          (+
           (* x1 (* x1 x1))
           (+
            (*
             t_1
             (+
              (* (* (* x1 2.0) t_3) (- t_3 3.0))
              (* (* x1 x1) (- (* t_3 4.0) 6.0))))
            (* x1 (* (* x1 3.0) (- 3.0 (/ 1.0 x1)))))))))
       (+ x1 (+ (+ x1 t_0) t_2))))))

C

double code(double x1, double x2) {
	double t_0 = 6.0 * pow(x1, 4.0);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = 3.0 * (x2 * -2.0);
	double t_3 = (((x1 * (x1 * 3.0)) + (2.0 * x2)) - x1) / t_1;
	double tmp;
	if (x1 <= -5.5e+102) {
		tmp = (x1 * 2.0) + t_0;
	} else if (x1 <= 2.4e+49) {
		tmp = x1 + (t_2 + (x1 + ((x1 * (x1 * x1)) + ((t_1 * ((((x1 * 2.0) * t_3) * (t_3 - 3.0)) + ((x1 * x1) * ((t_3 * 4.0) - 6.0)))) + (x1 * ((x1 * 3.0) * (3.0 - (1.0 / x1))))))));
	} else {
		tmp = x1 + ((x1 + t_0) + t_2);
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_0 = 6.0d0 * (x1 ** 4.0d0)
    t_1 = (x1 * x1) + 1.0d0
    t_2 = 3.0d0 * (x2 * (-2.0d0))
    t_3 = (((x1 * (x1 * 3.0d0)) + (2.0d0 * x2)) - x1) / t_1
    if (x1 <= (-5.5d+102)) then
        tmp = (x1 * 2.0d0) + t_0
    else if (x1 <= 2.4d+49) then
        tmp = x1 + (t_2 + (x1 + ((x1 * (x1 * x1)) + ((t_1 * ((((x1 * 2.0d0) * t_3) * (t_3 - 3.0d0)) + ((x1 * x1) * ((t_3 * 4.0d0) - 6.0d0)))) + (x1 * ((x1 * 3.0d0) * (3.0d0 - (1.0d0 / x1))))))))
    else
        tmp = x1 + ((x1 + t_0) + t_2)
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = 6.0 * Math.pow(x1, 4.0);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = 3.0 * (x2 * -2.0);
	double t_3 = (((x1 * (x1 * 3.0)) + (2.0 * x2)) - x1) / t_1;
	double tmp;
	if (x1 <= -5.5e+102) {
		tmp = (x1 * 2.0) + t_0;
	} else if (x1 <= 2.4e+49) {
		tmp = x1 + (t_2 + (x1 + ((x1 * (x1 * x1)) + ((t_1 * ((((x1 * 2.0) * t_3) * (t_3 - 3.0)) + ((x1 * x1) * ((t_3 * 4.0) - 6.0)))) + (x1 * ((x1 * 3.0) * (3.0 - (1.0 / x1))))))));
	} else {
		tmp = x1 + ((x1 + t_0) + t_2);
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = 6.0 * math.pow(x1, 4.0)
	t_1 = (x1 * x1) + 1.0
	t_2 = 3.0 * (x2 * -2.0)
	t_3 = (((x1 * (x1 * 3.0)) + (2.0 * x2)) - x1) / t_1
	tmp = 0
	if x1 <= -5.5e+102:
		tmp = (x1 * 2.0) + t_0
	elif x1 <= 2.4e+49:
		tmp = x1 + (t_2 + (x1 + ((x1 * (x1 * x1)) + ((t_1 * ((((x1 * 2.0) * t_3) * (t_3 - 3.0)) + ((x1 * x1) * ((t_3 * 4.0) - 6.0)))) + (x1 * ((x1 * 3.0) * (3.0 - (1.0 / x1))))))))
	else:
		tmp = x1 + ((x1 + t_0) + t_2)
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(6.0 * (x1 ^ 4.0))
	t_1 = Float64(Float64(x1 * x1) + 1.0)
	t_2 = Float64(3.0 * Float64(x2 * -2.0))
	t_3 = Float64(Float64(Float64(Float64(x1 * Float64(x1 * 3.0)) + Float64(2.0 * x2)) - x1) / t_1)
	tmp = 0.0
	if (x1 <= -5.5e+102)
		tmp = Float64(Float64(x1 * 2.0) + t_0);
	elseif (x1 <= 2.4e+49)
		tmp = Float64(x1 + Float64(t_2 + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(t_1 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_3) * Float64(t_3 - 3.0)) + Float64(Float64(x1 * x1) * Float64(Float64(t_3 * 4.0) - 6.0)))) + Float64(x1 * Float64(Float64(x1 * 3.0) * Float64(3.0 - Float64(1.0 / x1)))))))));
	else
		tmp = Float64(x1 + Float64(Float64(x1 + t_0) + t_2));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = 6.0 * (x1 ^ 4.0);
	t_1 = (x1 * x1) + 1.0;
	t_2 = 3.0 * (x2 * -2.0);
	t_3 = (((x1 * (x1 * 3.0)) + (2.0 * x2)) - x1) / t_1;
	tmp = 0.0;
	if (x1 <= -5.5e+102)
		tmp = (x1 * 2.0) + t_0;
	elseif (x1 <= 2.4e+49)
		tmp = x1 + (t_2 + (x1 + ((x1 * (x1 * x1)) + ((t_1 * ((((x1 * 2.0) * t_3) * (t_3 - 3.0)) + ((x1 * x1) * ((t_3 * 4.0) - 6.0)))) + (x1 * ((x1 * 3.0) * (3.0 - (1.0 / x1))))))));
	else
		tmp = x1 + ((x1 + t_0) + t_2);
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(6.0 * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$2 = N[(3.0 * N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision] + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[x1, -5.5e+102], N[(N[(x1 * 2.0), $MachinePrecision] + t$95$0), $MachinePrecision], If[LessEqual[x1, 2.4e+49], N[(x1 + N[(t$95$2 + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + 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[(t$95$3 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] * N[(3.0 - N[(1.0 / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x1 + t$95$0), $MachinePrecision] + t$95$2), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -5.49999999999999981e102

   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%

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

      1. *-commutative 0.0%

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

   4. Simplified 0.0%

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

   5. Taylor expanded in x1 around inf 100.0%

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

      1. *-commutative 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in x1 around inf 100.0%

      \[\leadsto \color{blue}{2 \cdot x1 + 6 \cdot {x1}^{4}} \]

   if -5.49999999999999981e102 < x1 < 2.4e49

   1. Initial program 99.5%

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

   2. Taylor expanded in x1 around 0 75.5%

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

      1. *-commutative 75.5%

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

   4. Simplified 75.5%

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

   5. Taylor expanded in x1 around inf 92.6%

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

      1. pow1 92.6%

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

      2. *-commutative 92.6%

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

      3. *-commutative 92.6%

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

   7. Applied egg-rr 92.6%

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

      1. unpow1 92.6%

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

      2. associate-*l* 99.4%

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

   9. Simplified 99.4%

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

   if 2.4e49 < x1

   1. Initial program 42.8%

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

   2. Taylor expanded in x1 around 0 42.8%

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

      1. *-commutative 42.8%

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

   4. Simplified 42.8%

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

   5. Taylor expanded in x1 around inf 96.4%

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

      1. *-commutative 96.4%

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

   7. Simplified 96.4%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.5 \cdot 10^{+102}:\\ \;\;\;\;x1 \cdot 2 + 6 \cdot {x1}^{4}\\ \mathbf{elif}\;x1 \leq 2.4 \cdot 10^{+49}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2\right) + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right)\right) + x1 \cdot \left(\left(x1 \cdot 3\right) \cdot \left(3 - \frac{1}{x1}\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 + 6 \cdot {x1}^{4}\right) + 3 \cdot \left(x2 \cdot -2\right)\right)\\ \end{array} \]

Alternative 5: 98.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{t_0}\\ \mathbf{if}\;x1 \leq -5.5 \cdot 10^{+102} \lor \neg \left(x1 \leq 2.4 \cdot 10^{+49}\right):\\ \;\;\;\;x1 \cdot 2 + 6 \cdot {x1}^{4}\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2\right) + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(t_0 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t_1\right) \cdot \left(t_1 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(t_1 \cdot 4 - 6\right)\right) + x1 \cdot \left(\left(x1 \cdot 3\right) \cdot \left(3 - \frac{1}{x1}\right)\right)\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ (* x1 x1) 1.0))
        (t_1 (/ (- (+ (* x1 (* x1 3.0)) (* 2.0 x2)) x1) t_0)))
   (if (or (<= x1 -5.5e+102) (not (<= x1 2.4e+49)))
     (+ (* x1 2.0) (* 6.0 (pow x1 4.0)))
     (+
      x1
      (+
       (* 3.0 (* x2 -2.0))
       (+
        x1
        (+
         (* x1 (* x1 x1))
         (+
          (*
           t_0
           (+
            (* (* (* x1 2.0) t_1) (- t_1 3.0))
            (* (* x1 x1) (- (* t_1 4.0) 6.0))))
          (* x1 (* (* x1 3.0) (- 3.0 (/ 1.0 x1))))))))))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = (((x1 * (x1 * 3.0)) + (2.0 * x2)) - x1) / t_0;
	double tmp;
	if ((x1 <= -5.5e+102) || !(x1 <= 2.4e+49)) {
		tmp = (x1 * 2.0) + (6.0 * pow(x1, 4.0));
	} else {
		tmp = x1 + ((3.0 * (x2 * -2.0)) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * ((((x1 * 2.0) * t_1) * (t_1 - 3.0)) + ((x1 * x1) * ((t_1 * 4.0) - 6.0)))) + (x1 * ((x1 * 3.0) * (3.0 - (1.0 / 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) :: tmp
    t_0 = (x1 * x1) + 1.0d0
    t_1 = (((x1 * (x1 * 3.0d0)) + (2.0d0 * x2)) - x1) / t_0
    if ((x1 <= (-5.5d+102)) .or. (.not. (x1 <= 2.4d+49))) then
        tmp = (x1 * 2.0d0) + (6.0d0 * (x1 ** 4.0d0))
    else
        tmp = x1 + ((3.0d0 * (x2 * (-2.0d0))) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * ((((x1 * 2.0d0) * t_1) * (t_1 - 3.0d0)) + ((x1 * x1) * ((t_1 * 4.0d0) - 6.0d0)))) + (x1 * ((x1 * 3.0d0) * (3.0d0 - (1.0d0 / x1))))))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = (((x1 * (x1 * 3.0)) + (2.0 * x2)) - x1) / t_0;
	double tmp;
	if ((x1 <= -5.5e+102) || !(x1 <= 2.4e+49)) {
		tmp = (x1 * 2.0) + (6.0 * Math.pow(x1, 4.0));
	} else {
		tmp = x1 + ((3.0 * (x2 * -2.0)) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * ((((x1 * 2.0) * t_1) * (t_1 - 3.0)) + ((x1 * x1) * ((t_1 * 4.0) - 6.0)))) + (x1 * ((x1 * 3.0) * (3.0 - (1.0 / x1))))))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x1 * x1) + 1.0
	t_1 = (((x1 * (x1 * 3.0)) + (2.0 * x2)) - x1) / t_0
	tmp = 0
	if (x1 <= -5.5e+102) or not (x1 <= 2.4e+49):
		tmp = (x1 * 2.0) + (6.0 * math.pow(x1, 4.0))
	else:
		tmp = x1 + ((3.0 * (x2 * -2.0)) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * ((((x1 * 2.0) * t_1) * (t_1 - 3.0)) + ((x1 * x1) * ((t_1 * 4.0) - 6.0)))) + (x1 * ((x1 * 3.0) * (3.0 - (1.0 / x1))))))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * x1) + 1.0)
	t_1 = Float64(Float64(Float64(Float64(x1 * Float64(x1 * 3.0)) + Float64(2.0 * x2)) - x1) / t_0)
	tmp = 0.0
	if ((x1 <= -5.5e+102) || !(x1 <= 2.4e+49))
		tmp = Float64(Float64(x1 * 2.0) + Float64(6.0 * (x1 ^ 4.0)));
	else
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(x2 * -2.0)) + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(t_0 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_1) * Float64(t_1 - 3.0)) + Float64(Float64(x1 * x1) * Float64(Float64(t_1 * 4.0) - 6.0)))) + Float64(x1 * Float64(Float64(x1 * 3.0) * Float64(3.0 - Float64(1.0 / x1)))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x1 * x1) + 1.0;
	t_1 = (((x1 * (x1 * 3.0)) + (2.0 * x2)) - x1) / t_0;
	tmp = 0.0;
	if ((x1 <= -5.5e+102) || ~((x1 <= 2.4e+49)))
		tmp = (x1 * 2.0) + (6.0 * (x1 ^ 4.0));
	else
		tmp = x1 + ((3.0 * (x2 * -2.0)) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * ((((x1 * 2.0) * t_1) * (t_1 - 3.0)) + ((x1 * x1) * ((t_1 * 4.0) - 6.0)))) + (x1 * ((x1 * 3.0) * (3.0 - (1.0 / x1))))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$1 = N[(N[(N[(N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision] + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]}, If[Or[LessEqual[x1, -5.5e+102], N[Not[LessEqual[x1, 2.4e+49]], $MachinePrecision]], N[(N[(x1 * 2.0), $MachinePrecision] + N[(6.0 * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(3.0 * N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$0 * N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$1), $MachinePrecision] * N[(t$95$1 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$1 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] * N[(3.0 - N[(1.0 / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if x1 < -5.49999999999999981e102 or 2.4e49 < x1

   1. Initial program 24.0%

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

   2. Taylor expanded in x1 around 0 24.0%

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

      1. *-commutative 24.0%

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

   4. Simplified 24.0%

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

   5. Taylor expanded in x1 around inf 98.0%

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

      1. *-commutative 98.0%

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

   7. Simplified 98.0%

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

   8. Taylor expanded in x1 around inf 98.0%

      \[\leadsto \color{blue}{2 \cdot x1 + 6 \cdot {x1}^{4}} \]

   if -5.49999999999999981e102 < x1 < 2.4e49

   1. Initial program 99.5%

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

   2. Taylor expanded in x1 around 0 75.5%

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

      1. *-commutative 75.5%

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

   4. Simplified 75.5%

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

   5. Taylor expanded in x1 around inf 92.6%

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

      1. pow1 92.6%

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

      2. *-commutative 92.6%

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

      3. *-commutative 92.6%

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

   7. Applied egg-rr 92.6%

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

      1. unpow1 92.6%

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

      2. associate-*l* 99.4%

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

   9. Simplified 99.4%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.5 \cdot 10^{+102} \lor \neg \left(x1 \leq 2.4 \cdot 10^{+49}\right):\\ \;\;\;\;x1 \cdot 2 + 6 \cdot {x1}^{4}\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2\right) + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right)\right) + x1 \cdot \left(\left(x1 \cdot 3\right) \cdot \left(3 - \frac{1}{x1}\right)\right)\right)\right)\right)\right)\\ \end{array} \]

Alternative 6: 86.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(x2 \cdot x2\right) \cdot 36\\ t_1 := x1 \cdot x1 + 1\\ t_2 := \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{t_1}\\ \mathbf{if}\;x1 \leq -2.7 \cdot 10^{+103}:\\ \;\;\;\;x1 + \left(\left(x1 + 4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right) + \frac{t_0 - \left(x1 \cdot x1\right) \cdot 9}{x2 \cdot -6 - x1 \cdot -3}\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2\right) + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(t_1 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t_2\right) \cdot \left(t_2 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(t_2 \cdot 4 - 6\right)\right) + x1 \cdot \left(\left(x1 \cdot 3\right) \cdot \left(3 - \frac{1}{x1}\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1 - t_0}{x1 - x2 \cdot -6}\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* (* x2 x2) 36.0))
        (t_1 (+ (* x1 x1) 1.0))
        (t_2 (/ (- (+ (* x1 (* x1 3.0)) (* 2.0 x2)) x1) t_1)))
   (if (<= x1 -2.7e+103)
     (+
      x1
      (+
       (+ x1 (* 4.0 (* x1 (* x2 (- (* 2.0 x2) 3.0)))))
       (/ (- t_0 (* (* x1 x1) 9.0)) (- (* x2 -6.0) (* x1 -3.0)))))
     (if (<= x1 1.35e+154)
       (+
        x1
        (+
         (* 3.0 (* x2 -2.0))
         (+
          x1
          (+
           (* x1 (* x1 x1))
           (+
            (*
             t_1
             (+
              (* (* (* x1 2.0) t_2) (- t_2 3.0))
              (* (* x1 x1) (- (* t_2 4.0) 6.0))))
            (* x1 (* (* x1 3.0) (- 3.0 (/ 1.0 x1)))))))))
       (/ (- (* x1 x1) t_0) (- x1 (* x2 -6.0)))))))

C

double code(double x1, double x2) {
	double t_0 = (x2 * x2) * 36.0;
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = (((x1 * (x1 * 3.0)) + (2.0 * x2)) - x1) / t_1;
	double tmp;
	if (x1 <= -2.7e+103) {
		tmp = x1 + ((x1 + (4.0 * (x1 * (x2 * ((2.0 * x2) - 3.0))))) + ((t_0 - ((x1 * x1) * 9.0)) / ((x2 * -6.0) - (x1 * -3.0))));
	} else if (x1 <= 1.35e+154) {
		tmp = x1 + ((3.0 * (x2 * -2.0)) + (x1 + ((x1 * (x1 * x1)) + ((t_1 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((t_2 * 4.0) - 6.0)))) + (x1 * ((x1 * 3.0) * (3.0 - (1.0 / x1))))))));
	} else {
		tmp = ((x1 * x1) - t_0) / (x1 - (x2 * -6.0));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = (x2 * x2) * 36.0d0
    t_1 = (x1 * x1) + 1.0d0
    t_2 = (((x1 * (x1 * 3.0d0)) + (2.0d0 * x2)) - x1) / t_1
    if (x1 <= (-2.7d+103)) then
        tmp = x1 + ((x1 + (4.0d0 * (x1 * (x2 * ((2.0d0 * x2) - 3.0d0))))) + ((t_0 - ((x1 * x1) * 9.0d0)) / ((x2 * (-6.0d0)) - (x1 * (-3.0d0)))))
    else if (x1 <= 1.35d+154) then
        tmp = x1 + ((3.0d0 * (x2 * (-2.0d0))) + (x1 + ((x1 * (x1 * x1)) + ((t_1 * ((((x1 * 2.0d0) * t_2) * (t_2 - 3.0d0)) + ((x1 * x1) * ((t_2 * 4.0d0) - 6.0d0)))) + (x1 * ((x1 * 3.0d0) * (3.0d0 - (1.0d0 / x1))))))))
    else
        tmp = ((x1 * x1) - t_0) / (x1 - (x2 * (-6.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (x2 * x2) * 36.0;
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = (((x1 * (x1 * 3.0)) + (2.0 * x2)) - x1) / t_1;
	double tmp;
	if (x1 <= -2.7e+103) {
		tmp = x1 + ((x1 + (4.0 * (x1 * (x2 * ((2.0 * x2) - 3.0))))) + ((t_0 - ((x1 * x1) * 9.0)) / ((x2 * -6.0) - (x1 * -3.0))));
	} else if (x1 <= 1.35e+154) {
		tmp = x1 + ((3.0 * (x2 * -2.0)) + (x1 + ((x1 * (x1 * x1)) + ((t_1 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((t_2 * 4.0) - 6.0)))) + (x1 * ((x1 * 3.0) * (3.0 - (1.0 / x1))))))));
	} else {
		tmp = ((x1 * x1) - t_0) / (x1 - (x2 * -6.0));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x2 * x2) * 36.0
	t_1 = (x1 * x1) + 1.0
	t_2 = (((x1 * (x1 * 3.0)) + (2.0 * x2)) - x1) / t_1
	tmp = 0
	if x1 <= -2.7e+103:
		tmp = x1 + ((x1 + (4.0 * (x1 * (x2 * ((2.0 * x2) - 3.0))))) + ((t_0 - ((x1 * x1) * 9.0)) / ((x2 * -6.0) - (x1 * -3.0))))
	elif x1 <= 1.35e+154:
		tmp = x1 + ((3.0 * (x2 * -2.0)) + (x1 + ((x1 * (x1 * x1)) + ((t_1 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((t_2 * 4.0) - 6.0)))) + (x1 * ((x1 * 3.0) * (3.0 - (1.0 / x1))))))))
	else:
		tmp = ((x1 * x1) - t_0) / (x1 - (x2 * -6.0))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x2 * x2) * 36.0)
	t_1 = Float64(Float64(x1 * x1) + 1.0)
	t_2 = Float64(Float64(Float64(Float64(x1 * Float64(x1 * 3.0)) + Float64(2.0 * x2)) - x1) / t_1)
	tmp = 0.0
	if (x1 <= -2.7e+103)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(4.0 * Float64(x1 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0))))) + Float64(Float64(t_0 - Float64(Float64(x1 * x1) * 9.0)) / Float64(Float64(x2 * -6.0) - Float64(x1 * -3.0)))));
	elseif (x1 <= 1.35e+154)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(x2 * -2.0)) + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(t_1 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_2) * Float64(t_2 - 3.0)) + Float64(Float64(x1 * x1) * Float64(Float64(t_2 * 4.0) - 6.0)))) + Float64(x1 * Float64(Float64(x1 * 3.0) * Float64(3.0 - Float64(1.0 / x1)))))))));
	else
		tmp = Float64(Float64(Float64(x1 * x1) - t_0) / Float64(x1 - Float64(x2 * -6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x2 * x2) * 36.0;
	t_1 = (x1 * x1) + 1.0;
	t_2 = (((x1 * (x1 * 3.0)) + (2.0 * x2)) - x1) / t_1;
	tmp = 0.0;
	if (x1 <= -2.7e+103)
		tmp = x1 + ((x1 + (4.0 * (x1 * (x2 * ((2.0 * x2) - 3.0))))) + ((t_0 - ((x1 * x1) * 9.0)) / ((x2 * -6.0) - (x1 * -3.0))));
	elseif (x1 <= 1.35e+154)
		tmp = x1 + ((3.0 * (x2 * -2.0)) + (x1 + ((x1 * (x1 * x1)) + ((t_1 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((t_2 * 4.0) - 6.0)))) + (x1 * ((x1 * 3.0) * (3.0 - (1.0 / x1))))))));
	else
		tmp = ((x1 * x1) - t_0) / (x1 - (x2 * -6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x2 * x2), $MachinePrecision] * 36.0), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision] + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[x1, -2.7e+103], N[(x1 + N[(N[(x1 + N[(4.0 * N[(x1 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$0 - N[(N[(x1 * x1), $MachinePrecision] * 9.0), $MachinePrecision]), $MachinePrecision] / N[(N[(x2 * -6.0), $MachinePrecision] - N[(x1 * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.35e+154], N[(x1 + N[(N[(3.0 * N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$1 * N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$2), $MachinePrecision] * N[(t$95$2 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$2 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] * N[(3.0 - N[(1.0 / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x1 * x1), $MachinePrecision] - t$95$0), $MachinePrecision] / N[(x1 - N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -2.69999999999999993e103

   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 2.4%

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

      1. flip-+ 41.0%

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

      2. *-commutative 41.0%

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

      3. *-commutative 41.0%

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

      4. *-commutative 41.0%

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

      5. *-commutative 41.0%

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

      6. *-commutative 41.0%

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

      7. *-commutative 41.0%

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

   5. Applied egg-rr 41.0%

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

      1. swap-sqr 41.0%

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

      2. metadata-eval 41.0%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + \frac{\left(x2 \cdot x2\right) \cdot \color{blue}{36} - \left(x1 \cdot -3\right) \cdot \left(x1 \cdot -3\right)}{x2 \cdot -6 - x1 \cdot -3}\right) \]

      3. swap-sqr 41.0%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + \frac{\left(x2 \cdot x2\right) \cdot 36 - \color{blue}{\left(x1 \cdot x1\right) \cdot \left(-3 \cdot -3\right)}}{x2 \cdot -6 - x1 \cdot -3}\right) \]

      4. metadata-eval 41.0%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + \frac{\left(x2 \cdot x2\right) \cdot 36 - \left(x1 \cdot x1\right) \cdot \color{blue}{9}}{x2 \cdot -6 - x1 \cdot -3}\right) \]

      5. *-commutative 41.0%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + \frac{\left(x2 \cdot x2\right) \cdot 36 - \left(x1 \cdot x1\right) \cdot 9}{\color{blue}{-6 \cdot x2} - x1 \cdot -3}\right) \]

   7. Simplified 41.0%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + \color{blue}{\frac{\left(x2 \cdot x2\right) \cdot 36 - \left(x1 \cdot x1\right) \cdot 9}{-6 \cdot x2 - x1 \cdot -3}}\right) \]

   if -2.69999999999999993e103 < x1 < 1.35000000000000003e154

   1. Initial program 98.5%

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

   2. Taylor expanded in x1 around 0 77.9%

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

      1. *-commutative 77.9%

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

   4. Simplified 77.9%

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

   5. Taylor expanded in x1 around inf 92.5%

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

      1. pow1 92.5%

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

      2. *-commutative 92.5%

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

      3. *-commutative 92.5%

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

   7. Applied egg-rr 92.5%

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

      1. unpow1 92.5%

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

      2. associate-*l* 98.4%

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

   9. Simplified 98.4%

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

   if 1.35000000000000003e154 < 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 7.4%

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

      1. *-commutative 7.4%

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

   5. Simplified 7.4%

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

      1. flip-+ 66.7%

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

   7. Applied egg-rr 66.7%

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

      1. swap-sqr 66.7%

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

      2. metadata-eval 66.7%

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

      3. *-commutative 66.7%

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

   9. Simplified 66.7%

      \[\leadsto \color{blue}{\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - -6 \cdot x2}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 84.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -2.7 \cdot 10^{+103}:\\ \;\;\;\;x1 + \left(\left(x1 + 4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right) + \frac{\left(x2 \cdot x2\right) \cdot 36 - \left(x1 \cdot x1\right) \cdot 9}{x2 \cdot -6 - x1 \cdot -3}\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2\right) + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right)\right) + x1 \cdot \left(\left(x1 \cdot 3\right) \cdot \left(3 - \frac{1}{x1}\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - x2 \cdot -6}\\ \end{array} \]

Alternative 7: 79.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := 3 \cdot t_0\\ t_2 := x1 \cdot x1 + 1\\ t_3 := 3 \cdot \frac{\left(t_0 - 2 \cdot x2\right) - x1}{t_2}\\ t_4 := \frac{\left(t_0 + 2 \cdot x2\right) - x1}{t_2}\\ t_5 := t_4 - 3\\ t_6 := \left(\left(x1 \cdot 2\right) \cdot t_4\right) \cdot t_5\\ t_7 := \left(x2 \cdot x2\right) \cdot 36\\ t_8 := 3 \cdot \left(x2 \cdot -2\right)\\ t_9 := 4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ t_10 := x1 + t_9\\ t_11 := x1 \cdot \left(x1 \cdot x1\right)\\ \mathbf{if}\;x1 \leq -3.3 \cdot 10^{+94}:\\ \;\;\;\;x1 + \left(t_10 + \frac{t_7 - \left(x1 \cdot x1\right) \cdot 9}{x2 \cdot -6 - x1 \cdot -3}\right)\\ \mathbf{elif}\;x1 \leq -3.2 \cdot 10^{+21}:\\ \;\;\;\;x1 + \left(t_8 + \left(x1 + \left(t_11 + \left(t_1 + t_2 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(t_4 \cdot 4 - 6\right) + t_5 \cdot \left(\left(x1 \cdot 2\right) \cdot 3\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -2.7 \cdot 10^{-235}:\\ \;\;\;\;x1 + \left(t_3 + \left(x1 + \left(t_11 + \left(t_2 \cdot t_9 + t_0 \cdot \left(2 \cdot x2 - x1\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 3.4 \cdot 10^{-210}:\\ \;\;\;\;x1 + \left(t_8 + \left(x1 + \left(t_11 + \left(t_1 + t_2 \cdot \left(t_6 + x1 \cdot \left(x1 \cdot 6\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 0.00032:\\ \;\;\;\;x1 + \left(t_3 + t_10\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(t_8 + \left(x1 + \left(t_11 + \left(t_2 \cdot \left(t_6 + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \left(3 - \frac{1}{x1}\right) - 6\right)\right) + t_1\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1 - t_7}{x1 - x2 \cdot -6}\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (* 3.0 t_0))
        (t_2 (+ (* x1 x1) 1.0))
        (t_3 (* 3.0 (/ (- (- t_0 (* 2.0 x2)) x1) t_2)))
        (t_4 (/ (- (+ t_0 (* 2.0 x2)) x1) t_2))
        (t_5 (- t_4 3.0))
        (t_6 (* (* (* x1 2.0) t_4) t_5))
        (t_7 (* (* x2 x2) 36.0))
        (t_8 (* 3.0 (* x2 -2.0)))
        (t_9 (* 4.0 (* x1 (* x2 (- (* 2.0 x2) 3.0)))))
        (t_10 (+ x1 t_9))
        (t_11 (* x1 (* x1 x1))))
   (if (<= x1 -3.3e+94)
     (+ x1 (+ t_10 (/ (- t_7 (* (* x1 x1) 9.0)) (- (* x2 -6.0) (* x1 -3.0)))))
     (if (<= x1 -3.2e+21)
       (+
        x1
        (+
         t_8
         (+
          x1
          (+
           t_11
           (+
            t_1
            (*
             t_2
             (+
              (* (* x1 x1) (- (* t_4 4.0) 6.0))
              (* t_5 (* (* x1 2.0) 3.0)))))))))
       (if (<= x1 -2.7e-235)
         (+
          x1
          (+ t_3 (+ x1 (+ t_11 (+ (* t_2 t_9) (* t_0 (- (* 2.0 x2) x1)))))))
         (if (<= x1 3.4e-210)
           (+
            x1
            (+ t_8 (+ x1 (+ t_11 (+ t_1 (* t_2 (+ t_6 (* x1 (* x1 6.0)))))))))
           (if (<= x1 0.00032)
             (+ x1 (+ t_3 t_10))
             (if (<= x1 1.35e+154)
               (+
                x1
                (+
                 t_8
                 (+
                  x1
                  (+
                   t_11
                   (+
                    (*
                     t_2
                     (+ t_6 (* (* x1 x1) (- (* 4.0 (- 3.0 (/ 1.0 x1))) 6.0))))
                    t_1)))))
               (/ (- (* x1 x1) t_7) (- x1 (* x2 -6.0)))))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = 3.0 * t_0;
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = 3.0 * (((t_0 - (2.0 * x2)) - x1) / t_2);
	double t_4 = ((t_0 + (2.0 * x2)) - x1) / t_2;
	double t_5 = t_4 - 3.0;
	double t_6 = ((x1 * 2.0) * t_4) * t_5;
	double t_7 = (x2 * x2) * 36.0;
	double t_8 = 3.0 * (x2 * -2.0);
	double t_9 = 4.0 * (x1 * (x2 * ((2.0 * x2) - 3.0)));
	double t_10 = x1 + t_9;
	double t_11 = x1 * (x1 * x1);
	double tmp;
	if (x1 <= -3.3e+94) {
		tmp = x1 + (t_10 + ((t_7 - ((x1 * x1) * 9.0)) / ((x2 * -6.0) - (x1 * -3.0))));
	} else if (x1 <= -3.2e+21) {
		tmp = x1 + (t_8 + (x1 + (t_11 + (t_1 + (t_2 * (((x1 * x1) * ((t_4 * 4.0) - 6.0)) + (t_5 * ((x1 * 2.0) * 3.0))))))));
	} else if (x1 <= -2.7e-235) {
		tmp = x1 + (t_3 + (x1 + (t_11 + ((t_2 * t_9) + (t_0 * ((2.0 * x2) - x1))))));
	} else if (x1 <= 3.4e-210) {
		tmp = x1 + (t_8 + (x1 + (t_11 + (t_1 + (t_2 * (t_6 + (x1 * (x1 * 6.0))))))));
	} else if (x1 <= 0.00032) {
		tmp = x1 + (t_3 + t_10);
	} else if (x1 <= 1.35e+154) {
		tmp = x1 + (t_8 + (x1 + (t_11 + ((t_2 * (t_6 + ((x1 * x1) * ((4.0 * (3.0 - (1.0 / x1))) - 6.0)))) + t_1))));
	} else {
		tmp = ((x1 * x1) - t_7) / (x1 - (x2 * -6.0));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_10
    real(8) :: t_11
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: t_8
    real(8) :: t_9
    real(8) :: tmp
    t_0 = x1 * (x1 * 3.0d0)
    t_1 = 3.0d0 * t_0
    t_2 = (x1 * x1) + 1.0d0
    t_3 = 3.0d0 * (((t_0 - (2.0d0 * x2)) - x1) / t_2)
    t_4 = ((t_0 + (2.0d0 * x2)) - x1) / t_2
    t_5 = t_4 - 3.0d0
    t_6 = ((x1 * 2.0d0) * t_4) * t_5
    t_7 = (x2 * x2) * 36.0d0
    t_8 = 3.0d0 * (x2 * (-2.0d0))
    t_9 = 4.0d0 * (x1 * (x2 * ((2.0d0 * x2) - 3.0d0)))
    t_10 = x1 + t_9
    t_11 = x1 * (x1 * x1)
    if (x1 <= (-3.3d+94)) then
        tmp = x1 + (t_10 + ((t_7 - ((x1 * x1) * 9.0d0)) / ((x2 * (-6.0d0)) - (x1 * (-3.0d0)))))
    else if (x1 <= (-3.2d+21)) then
        tmp = x1 + (t_8 + (x1 + (t_11 + (t_1 + (t_2 * (((x1 * x1) * ((t_4 * 4.0d0) - 6.0d0)) + (t_5 * ((x1 * 2.0d0) * 3.0d0))))))))
    else if (x1 <= (-2.7d-235)) then
        tmp = x1 + (t_3 + (x1 + (t_11 + ((t_2 * t_9) + (t_0 * ((2.0d0 * x2) - x1))))))
    else if (x1 <= 3.4d-210) then
        tmp = x1 + (t_8 + (x1 + (t_11 + (t_1 + (t_2 * (t_6 + (x1 * (x1 * 6.0d0))))))))
    else if (x1 <= 0.00032d0) then
        tmp = x1 + (t_3 + t_10)
    else if (x1 <= 1.35d+154) then
        tmp = x1 + (t_8 + (x1 + (t_11 + ((t_2 * (t_6 + ((x1 * x1) * ((4.0d0 * (3.0d0 - (1.0d0 / x1))) - 6.0d0)))) + t_1))))
    else
        tmp = ((x1 * x1) - t_7) / (x1 - (x2 * (-6.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = 3.0 * t_0;
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = 3.0 * (((t_0 - (2.0 * x2)) - x1) / t_2);
	double t_4 = ((t_0 + (2.0 * x2)) - x1) / t_2;
	double t_5 = t_4 - 3.0;
	double t_6 = ((x1 * 2.0) * t_4) * t_5;
	double t_7 = (x2 * x2) * 36.0;
	double t_8 = 3.0 * (x2 * -2.0);
	double t_9 = 4.0 * (x1 * (x2 * ((2.0 * x2) - 3.0)));
	double t_10 = x1 + t_9;
	double t_11 = x1 * (x1 * x1);
	double tmp;
	if (x1 <= -3.3e+94) {
		tmp = x1 + (t_10 + ((t_7 - ((x1 * x1) * 9.0)) / ((x2 * -6.0) - (x1 * -3.0))));
	} else if (x1 <= -3.2e+21) {
		tmp = x1 + (t_8 + (x1 + (t_11 + (t_1 + (t_2 * (((x1 * x1) * ((t_4 * 4.0) - 6.0)) + (t_5 * ((x1 * 2.0) * 3.0))))))));
	} else if (x1 <= -2.7e-235) {
		tmp = x1 + (t_3 + (x1 + (t_11 + ((t_2 * t_9) + (t_0 * ((2.0 * x2) - x1))))));
	} else if (x1 <= 3.4e-210) {
		tmp = x1 + (t_8 + (x1 + (t_11 + (t_1 + (t_2 * (t_6 + (x1 * (x1 * 6.0))))))));
	} else if (x1 <= 0.00032) {
		tmp = x1 + (t_3 + t_10);
	} else if (x1 <= 1.35e+154) {
		tmp = x1 + (t_8 + (x1 + (t_11 + ((t_2 * (t_6 + ((x1 * x1) * ((4.0 * (3.0 - (1.0 / x1))) - 6.0)))) + t_1))));
	} else {
		tmp = ((x1 * x1) - t_7) / (x1 - (x2 * -6.0));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = 3.0 * t_0
	t_2 = (x1 * x1) + 1.0
	t_3 = 3.0 * (((t_0 - (2.0 * x2)) - x1) / t_2)
	t_4 = ((t_0 + (2.0 * x2)) - x1) / t_2
	t_5 = t_4 - 3.0
	t_6 = ((x1 * 2.0) * t_4) * t_5
	t_7 = (x2 * x2) * 36.0
	t_8 = 3.0 * (x2 * -2.0)
	t_9 = 4.0 * (x1 * (x2 * ((2.0 * x2) - 3.0)))
	t_10 = x1 + t_9
	t_11 = x1 * (x1 * x1)
	tmp = 0
	if x1 <= -3.3e+94:
		tmp = x1 + (t_10 + ((t_7 - ((x1 * x1) * 9.0)) / ((x2 * -6.0) - (x1 * -3.0))))
	elif x1 <= -3.2e+21:
		tmp = x1 + (t_8 + (x1 + (t_11 + (t_1 + (t_2 * (((x1 * x1) * ((t_4 * 4.0) - 6.0)) + (t_5 * ((x1 * 2.0) * 3.0))))))))
	elif x1 <= -2.7e-235:
		tmp = x1 + (t_3 + (x1 + (t_11 + ((t_2 * t_9) + (t_0 * ((2.0 * x2) - x1))))))
	elif x1 <= 3.4e-210:
		tmp = x1 + (t_8 + (x1 + (t_11 + (t_1 + (t_2 * (t_6 + (x1 * (x1 * 6.0))))))))
	elif x1 <= 0.00032:
		tmp = x1 + (t_3 + t_10)
	elif x1 <= 1.35e+154:
		tmp = x1 + (t_8 + (x1 + (t_11 + ((t_2 * (t_6 + ((x1 * x1) * ((4.0 * (3.0 - (1.0 / x1))) - 6.0)))) + t_1))))
	else:
		tmp = ((x1 * x1) - t_7) / (x1 - (x2 * -6.0))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(3.0 * t_0)
	t_2 = Float64(Float64(x1 * x1) + 1.0)
	t_3 = Float64(3.0 * Float64(Float64(Float64(t_0 - Float64(2.0 * x2)) - x1) / t_2))
	t_4 = Float64(Float64(Float64(t_0 + Float64(2.0 * x2)) - x1) / t_2)
	t_5 = Float64(t_4 - 3.0)
	t_6 = Float64(Float64(Float64(x1 * 2.0) * t_4) * t_5)
	t_7 = Float64(Float64(x2 * x2) * 36.0)
	t_8 = Float64(3.0 * Float64(x2 * -2.0))
	t_9 = Float64(4.0 * Float64(x1 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0))))
	t_10 = Float64(x1 + t_9)
	t_11 = Float64(x1 * Float64(x1 * x1))
	tmp = 0.0
	if (x1 <= -3.3e+94)
		tmp = Float64(x1 + Float64(t_10 + Float64(Float64(t_7 - Float64(Float64(x1 * x1) * 9.0)) / Float64(Float64(x2 * -6.0) - Float64(x1 * -3.0)))));
	elseif (x1 <= -3.2e+21)
		tmp = Float64(x1 + Float64(t_8 + Float64(x1 + Float64(t_11 + Float64(t_1 + Float64(t_2 * Float64(Float64(Float64(x1 * x1) * Float64(Float64(t_4 * 4.0) - 6.0)) + Float64(t_5 * Float64(Float64(x1 * 2.0) * 3.0)))))))));
	elseif (x1 <= -2.7e-235)
		tmp = Float64(x1 + Float64(t_3 + Float64(x1 + Float64(t_11 + Float64(Float64(t_2 * t_9) + Float64(t_0 * Float64(Float64(2.0 * x2) - x1)))))));
	elseif (x1 <= 3.4e-210)
		tmp = Float64(x1 + Float64(t_8 + Float64(x1 + Float64(t_11 + Float64(t_1 + Float64(t_2 * Float64(t_6 + Float64(x1 * Float64(x1 * 6.0)))))))));
	elseif (x1 <= 0.00032)
		tmp = Float64(x1 + Float64(t_3 + t_10));
	elseif (x1 <= 1.35e+154)
		tmp = Float64(x1 + Float64(t_8 + Float64(x1 + Float64(t_11 + Float64(Float64(t_2 * Float64(t_6 + Float64(Float64(x1 * x1) * Float64(Float64(4.0 * Float64(3.0 - Float64(1.0 / x1))) - 6.0)))) + t_1)))));
	else
		tmp = Float64(Float64(Float64(x1 * x1) - t_7) / Float64(x1 - Float64(x2 * -6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * 3.0);
	t_1 = 3.0 * t_0;
	t_2 = (x1 * x1) + 1.0;
	t_3 = 3.0 * (((t_0 - (2.0 * x2)) - x1) / t_2);
	t_4 = ((t_0 + (2.0 * x2)) - x1) / t_2;
	t_5 = t_4 - 3.0;
	t_6 = ((x1 * 2.0) * t_4) * t_5;
	t_7 = (x2 * x2) * 36.0;
	t_8 = 3.0 * (x2 * -2.0);
	t_9 = 4.0 * (x1 * (x2 * ((2.0 * x2) - 3.0)));
	t_10 = x1 + t_9;
	t_11 = x1 * (x1 * x1);
	tmp = 0.0;
	if (x1 <= -3.3e+94)
		tmp = x1 + (t_10 + ((t_7 - ((x1 * x1) * 9.0)) / ((x2 * -6.0) - (x1 * -3.0))));
	elseif (x1 <= -3.2e+21)
		tmp = x1 + (t_8 + (x1 + (t_11 + (t_1 + (t_2 * (((x1 * x1) * ((t_4 * 4.0) - 6.0)) + (t_5 * ((x1 * 2.0) * 3.0))))))));
	elseif (x1 <= -2.7e-235)
		tmp = x1 + (t_3 + (x1 + (t_11 + ((t_2 * t_9) + (t_0 * ((2.0 * x2) - x1))))));
	elseif (x1 <= 3.4e-210)
		tmp = x1 + (t_8 + (x1 + (t_11 + (t_1 + (t_2 * (t_6 + (x1 * (x1 * 6.0))))))));
	elseif (x1 <= 0.00032)
		tmp = x1 + (t_3 + t_10);
	elseif (x1 <= 1.35e+154)
		tmp = x1 + (t_8 + (x1 + (t_11 + ((t_2 * (t_6 + ((x1 * x1) * ((4.0 * (3.0 - (1.0 / x1))) - 6.0)))) + t_1))));
	else
		tmp = ((x1 * x1) - t_7) / (x1 - (x2 * -6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(3.0 * t$95$0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$3 = 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$4 = N[(N[(N[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]}, Block[{t$95$5 = N[(t$95$4 - 3.0), $MachinePrecision]}, Block[{t$95$6 = N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$4), $MachinePrecision] * t$95$5), $MachinePrecision]}, Block[{t$95$7 = N[(N[(x2 * x2), $MachinePrecision] * 36.0), $MachinePrecision]}, Block[{t$95$8 = N[(3.0 * N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$9 = N[(4.0 * N[(x1 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$10 = N[(x1 + t$95$9), $MachinePrecision]}, Block[{t$95$11 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -3.3e+94], N[(x1 + N[(t$95$10 + N[(N[(t$95$7 - N[(N[(x1 * x1), $MachinePrecision] * 9.0), $MachinePrecision]), $MachinePrecision] / N[(N[(x2 * -6.0), $MachinePrecision] - N[(x1 * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -3.2e+21], N[(x1 + N[(t$95$8 + N[(x1 + N[(t$95$11 + N[(t$95$1 + N[(t$95$2 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$4 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] + N[(t$95$5 * N[(N[(x1 * 2.0), $MachinePrecision] * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -2.7e-235], N[(x1 + N[(t$95$3 + N[(x1 + N[(t$95$11 + N[(N[(t$95$2 * t$95$9), $MachinePrecision] + N[(t$95$0 * N[(N[(2.0 * x2), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 3.4e-210], N[(x1 + N[(t$95$8 + N[(x1 + N[(t$95$11 + N[(t$95$1 + N[(t$95$2 * N[(t$95$6 + N[(x1 * N[(x1 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 0.00032], N[(x1 + N[(t$95$3 + t$95$10), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.35e+154], N[(x1 + N[(t$95$8 + N[(x1 + N[(t$95$11 + N[(N[(t$95$2 * N[(t$95$6 + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(4.0 * N[(3.0 - N[(1.0 / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x1 * x1), $MachinePrecision] - t$95$7), $MachinePrecision] / N[(x1 - N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if x1 < -3.3e94

   1. Initial program 4.3%

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

   2. Taylor expanded in x1 around 0 2.2%

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

   3. Taylor expanded in x1 around 0 4.5%

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

      1. flip-+ 41.5%

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

      2. *-commutative 41.5%

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

      3. *-commutative 41.5%

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

      4. *-commutative 41.5%

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

      5. *-commutative 41.5%

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

      6. *-commutative 41.5%

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

      7. *-commutative 41.5%

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

   5. Applied egg-rr 41.5%

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

      1. swap-sqr 41.5%

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

      2. metadata-eval 41.5%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + \frac{\left(x2 \cdot x2\right) \cdot \color{blue}{36} - \left(x1 \cdot -3\right) \cdot \left(x1 \cdot -3\right)}{x2 \cdot -6 - x1 \cdot -3}\right) \]

      3. swap-sqr 41.5%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + \frac{\left(x2 \cdot x2\right) \cdot 36 - \color{blue}{\left(x1 \cdot x1\right) \cdot \left(-3 \cdot -3\right)}}{x2 \cdot -6 - x1 \cdot -3}\right) \]

      4. metadata-eval 41.5%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + \frac{\left(x2 \cdot x2\right) \cdot 36 - \left(x1 \cdot x1\right) \cdot \color{blue}{9}}{x2 \cdot -6 - x1 \cdot -3}\right) \]

      5. *-commutative 41.5%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + \frac{\left(x2 \cdot x2\right) \cdot 36 - \left(x1 \cdot x1\right) \cdot 9}{\color{blue}{-6 \cdot x2} - x1 \cdot -3}\right) \]

   7. Simplified 41.5%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + \color{blue}{\frac{\left(x2 \cdot x2\right) \cdot 36 - \left(x1 \cdot x1\right) \cdot 9}{-6 \cdot x2 - x1 \cdot -3}}\right) \]

   if -3.3e94 < x1 < -3.2e21

   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 99.4%

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

      1. *-commutative 99.4%

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

   4. Simplified 99.4%

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

   5. Taylor expanded in x1 around inf 99.4%

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

   6. Taylor expanded in x1 around inf 96.4%

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

   if -3.2e21 < x1 < -2.7000000000000002e-235

   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 91.9%

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

   3. Taylor expanded in x1 around 0 89.0%

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

   4. Taylor expanded in x1 around 0 89.2%

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

   if -2.7000000000000002e-235 < x1 < 3.39999999999999974e-210

   1. Initial program 99.8%

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

   2. Taylor expanded in x1 around 0 93.4%

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

      1. *-commutative 93.4%

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

   4. Simplified 93.4%

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

   5. Taylor expanded in x1 around inf 93.4%

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

   6. Taylor expanded in x1 around inf 93.4%

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

      1. unpow2 93.4%

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

      2. associate-*r* 93.4%

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

   8. Simplified 93.4%

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

   if 3.39999999999999974e-210 < x1 < 3.20000000000000026e-4

   1. Initial program 99.5%

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

   2. Taylor expanded in x1 around 0 95.4%

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

   if 3.20000000000000026e-4 < x1 < 1.35000000000000003e154

   1. Initial program 93.9%

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

   2. Taylor expanded in x1 around 0 93.1%

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

      1. *-commutative 93.1%

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

   4. Simplified 93.1%

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

   5. Taylor expanded in x1 around inf 92.8%

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

   6. Taylor expanded in x1 around inf 92.3%

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

   if 1.35000000000000003e154 < 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 7.4%

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

      1. *-commutative 7.4%

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

   5. Simplified 7.4%

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

      1. flip-+ 66.7%

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

   7. Applied egg-rr 66.7%

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

      1. swap-sqr 66.7%

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

      2. metadata-eval 66.7%

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

      3. *-commutative 66.7%

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

   9. Simplified 66.7%

      \[\leadsto \color{blue}{\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - -6 \cdot x2}} \]
3. Recombined 7 regimes into one program.

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -3.3 \cdot 10^{+94}:\\ \;\;\;\;x1 + \left(\left(x1 + 4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right) + \frac{\left(x2 \cdot x2\right) \cdot 36 - \left(x1 \cdot x1\right) \cdot 9}{x2 \cdot -6 - x1 \cdot -3}\right)\\ \mathbf{elif}\;x1 \leq -3.2 \cdot 10^{+21}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2\right) + \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(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 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 3\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -2.7 \cdot 10^{-235}:\\ \;\;\;\;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(4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right) + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(2 \cdot x2 - x1\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 3.4 \cdot 10^{-210}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2\right) + \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(\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) + x1 \cdot \left(x1 \cdot 6\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 0.00032:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + 4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2\right) + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \left(3 - \frac{1}{x1}\right) - 6\right)\right) + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - x2 \cdot -6}\\ \end{array} \]

Alternative 8: 85.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(x2 \cdot x2\right) \cdot 36\\ t_1 := x1 \cdot x1 + 1\\ t_2 := \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{t_1}\\ \mathbf{if}\;x1 \leq -5.4 \cdot 10^{+103}:\\ \;\;\;\;x1 + \left(\left(x1 + 4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right) + \frac{t_0 - \left(x1 \cdot x1\right) \cdot 9}{x2 \cdot -6 - x1 \cdot -3}\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2\right) + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(t_1 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t_2\right) \cdot \left(t_2 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(t_2 \cdot 4 - 6\right)\right) + x1 \cdot -3\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1 - t_0}{x1 - x2 \cdot -6}\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* (* x2 x2) 36.0))
        (t_1 (+ (* x1 x1) 1.0))
        (t_2 (/ (- (+ (* x1 (* x1 3.0)) (* 2.0 x2)) x1) t_1)))
   (if (<= x1 -5.4e+103)
     (+
      x1
      (+
       (+ x1 (* 4.0 (* x1 (* x2 (- (* 2.0 x2) 3.0)))))
       (/ (- t_0 (* (* x1 x1) 9.0)) (- (* x2 -6.0) (* x1 -3.0)))))
     (if (<= x1 1.35e+154)
       (+
        x1
        (+
         (* 3.0 (* x2 -2.0))
         (+
          x1
          (+
           (* x1 (* x1 x1))
           (+
            (*
             t_1
             (+
              (* (* (* x1 2.0) t_2) (- t_2 3.0))
              (* (* x1 x1) (- (* t_2 4.0) 6.0))))
            (* x1 -3.0))))))
       (/ (- (* x1 x1) t_0) (- x1 (* x2 -6.0)))))))

C

double code(double x1, double x2) {
	double t_0 = (x2 * x2) * 36.0;
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = (((x1 * (x1 * 3.0)) + (2.0 * x2)) - x1) / t_1;
	double tmp;
	if (x1 <= -5.4e+103) {
		tmp = x1 + ((x1 + (4.0 * (x1 * (x2 * ((2.0 * x2) - 3.0))))) + ((t_0 - ((x1 * x1) * 9.0)) / ((x2 * -6.0) - (x1 * -3.0))));
	} else if (x1 <= 1.35e+154) {
		tmp = x1 + ((3.0 * (x2 * -2.0)) + (x1 + ((x1 * (x1 * x1)) + ((t_1 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((t_2 * 4.0) - 6.0)))) + (x1 * -3.0)))));
	} else {
		tmp = ((x1 * x1) - t_0) / (x1 - (x2 * -6.0));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = (x2 * x2) * 36.0d0
    t_1 = (x1 * x1) + 1.0d0
    t_2 = (((x1 * (x1 * 3.0d0)) + (2.0d0 * x2)) - x1) / t_1
    if (x1 <= (-5.4d+103)) then
        tmp = x1 + ((x1 + (4.0d0 * (x1 * (x2 * ((2.0d0 * x2) - 3.0d0))))) + ((t_0 - ((x1 * x1) * 9.0d0)) / ((x2 * (-6.0d0)) - (x1 * (-3.0d0)))))
    else if (x1 <= 1.35d+154) then
        tmp = x1 + ((3.0d0 * (x2 * (-2.0d0))) + (x1 + ((x1 * (x1 * x1)) + ((t_1 * ((((x1 * 2.0d0) * t_2) * (t_2 - 3.0d0)) + ((x1 * x1) * ((t_2 * 4.0d0) - 6.0d0)))) + (x1 * (-3.0d0))))))
    else
        tmp = ((x1 * x1) - t_0) / (x1 - (x2 * (-6.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (x2 * x2) * 36.0;
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = (((x1 * (x1 * 3.0)) + (2.0 * x2)) - x1) / t_1;
	double tmp;
	if (x1 <= -5.4e+103) {
		tmp = x1 + ((x1 + (4.0 * (x1 * (x2 * ((2.0 * x2) - 3.0))))) + ((t_0 - ((x1 * x1) * 9.0)) / ((x2 * -6.0) - (x1 * -3.0))));
	} else if (x1 <= 1.35e+154) {
		tmp = x1 + ((3.0 * (x2 * -2.0)) + (x1 + ((x1 * (x1 * x1)) + ((t_1 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((t_2 * 4.0) - 6.0)))) + (x1 * -3.0)))));
	} else {
		tmp = ((x1 * x1) - t_0) / (x1 - (x2 * -6.0));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x2 * x2) * 36.0
	t_1 = (x1 * x1) + 1.0
	t_2 = (((x1 * (x1 * 3.0)) + (2.0 * x2)) - x1) / t_1
	tmp = 0
	if x1 <= -5.4e+103:
		tmp = x1 + ((x1 + (4.0 * (x1 * (x2 * ((2.0 * x2) - 3.0))))) + ((t_0 - ((x1 * x1) * 9.0)) / ((x2 * -6.0) - (x1 * -3.0))))
	elif x1 <= 1.35e+154:
		tmp = x1 + ((3.0 * (x2 * -2.0)) + (x1 + ((x1 * (x1 * x1)) + ((t_1 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((t_2 * 4.0) - 6.0)))) + (x1 * -3.0)))))
	else:
		tmp = ((x1 * x1) - t_0) / (x1 - (x2 * -6.0))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x2 * x2) * 36.0)
	t_1 = Float64(Float64(x1 * x1) + 1.0)
	t_2 = Float64(Float64(Float64(Float64(x1 * Float64(x1 * 3.0)) + Float64(2.0 * x2)) - x1) / t_1)
	tmp = 0.0
	if (x1 <= -5.4e+103)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(4.0 * Float64(x1 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0))))) + Float64(Float64(t_0 - Float64(Float64(x1 * x1) * 9.0)) / Float64(Float64(x2 * -6.0) - Float64(x1 * -3.0)))));
	elseif (x1 <= 1.35e+154)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(x2 * -2.0)) + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(t_1 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_2) * Float64(t_2 - 3.0)) + Float64(Float64(x1 * x1) * Float64(Float64(t_2 * 4.0) - 6.0)))) + Float64(x1 * -3.0))))));
	else
		tmp = Float64(Float64(Float64(x1 * x1) - t_0) / Float64(x1 - Float64(x2 * -6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x2 * x2) * 36.0;
	t_1 = (x1 * x1) + 1.0;
	t_2 = (((x1 * (x1 * 3.0)) + (2.0 * x2)) - x1) / t_1;
	tmp = 0.0;
	if (x1 <= -5.4e+103)
		tmp = x1 + ((x1 + (4.0 * (x1 * (x2 * ((2.0 * x2) - 3.0))))) + ((t_0 - ((x1 * x1) * 9.0)) / ((x2 * -6.0) - (x1 * -3.0))));
	elseif (x1 <= 1.35e+154)
		tmp = x1 + ((3.0 * (x2 * -2.0)) + (x1 + ((x1 * (x1 * x1)) + ((t_1 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((t_2 * 4.0) - 6.0)))) + (x1 * -3.0)))));
	else
		tmp = ((x1 * x1) - t_0) / (x1 - (x2 * -6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x2 * x2), $MachinePrecision] * 36.0), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision] + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[x1, -5.4e+103], N[(x1 + N[(N[(x1 + N[(4.0 * N[(x1 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$0 - N[(N[(x1 * x1), $MachinePrecision] * 9.0), $MachinePrecision]), $MachinePrecision] / N[(N[(x2 * -6.0), $MachinePrecision] - N[(x1 * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.35e+154], N[(x1 + N[(N[(3.0 * N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$1 * N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$2), $MachinePrecision] * N[(t$95$2 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$2 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x1 * x1), $MachinePrecision] - t$95$0), $MachinePrecision] / N[(x1 - N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -5.39999999999999985e103

   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 2.4%

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

      1. flip-+ 41.0%

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

      2. *-commutative 41.0%

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

      3. *-commutative 41.0%

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

      4. *-commutative 41.0%

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

      5. *-commutative 41.0%

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

      6. *-commutative 41.0%

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

      7. *-commutative 41.0%

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

   5. Applied egg-rr 41.0%

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

      1. swap-sqr 41.0%

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

      2. metadata-eval 41.0%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + \frac{\left(x2 \cdot x2\right) \cdot \color{blue}{36} - \left(x1 \cdot -3\right) \cdot \left(x1 \cdot -3\right)}{x2 \cdot -6 - x1 \cdot -3}\right) \]

      3. swap-sqr 41.0%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + \frac{\left(x2 \cdot x2\right) \cdot 36 - \color{blue}{\left(x1 \cdot x1\right) \cdot \left(-3 \cdot -3\right)}}{x2 \cdot -6 - x1 \cdot -3}\right) \]

      4. metadata-eval 41.0%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + \frac{\left(x2 \cdot x2\right) \cdot 36 - \left(x1 \cdot x1\right) \cdot \color{blue}{9}}{x2 \cdot -6 - x1 \cdot -3}\right) \]

      5. *-commutative 41.0%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + \frac{\left(x2 \cdot x2\right) \cdot 36 - \left(x1 \cdot x1\right) \cdot 9}{\color{blue}{-6 \cdot x2} - x1 \cdot -3}\right) \]

   7. Simplified 41.0%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + \color{blue}{\frac{\left(x2 \cdot x2\right) \cdot 36 - \left(x1 \cdot x1\right) \cdot 9}{-6 \cdot x2 - x1 \cdot -3}}\right) \]

   if -5.39999999999999985e103 < x1 < 1.35000000000000003e154

   1. Initial program 98.5%

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

   2. Taylor expanded in x1 around 0 77.9%

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

      1. *-commutative 77.9%

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

   4. Simplified 77.9%

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

   5. Taylor expanded in x1 around inf 92.5%

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

   6. Taylor expanded in x1 around 0 96.9%

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

      1. *-commutative 96.9%

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

   8. Simplified 96.9%

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

   if 1.35000000000000003e154 < 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 7.4%

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

      1. *-commutative 7.4%

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

   5. Simplified 7.4%

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

      1. flip-+ 66.7%

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

   7. Applied egg-rr 66.7%

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

      1. swap-sqr 66.7%

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

      2. metadata-eval 66.7%

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

      3. *-commutative 66.7%

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

   9. Simplified 66.7%

      \[\leadsto \color{blue}{\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - -6 \cdot x2}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 83.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.4 \cdot 10^{+103}:\\ \;\;\;\;x1 + \left(\left(x1 + 4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right) + \frac{\left(x2 \cdot x2\right) \cdot 36 - \left(x1 \cdot x1\right) \cdot 9}{x2 \cdot -6 - x1 \cdot -3}\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2\right) + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right)\right) + x1 \cdot -3\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - x2 \cdot -6}\\ \end{array} \]

Alternative 9: 80.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := x1 \cdot x1 + 1\\ t_2 := \frac{\left(t_0 + 2 \cdot x2\right) - x1}{t_1}\\ t_3 := 3 - \frac{1}{x1}\\ t_4 := \left(x2 \cdot x2\right) \cdot 36\\ t_5 := 3 \cdot \left(x2 \cdot -2\right)\\ t_6 := x1 \cdot \left(x1 \cdot x1\right)\\ t_7 := \left(x1 \cdot 2\right) \cdot t_2\\ \mathbf{if}\;x1 \leq -3.2 \cdot 10^{+103}:\\ \;\;\;\;x1 + \left(\left(x1 + 4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right) + \frac{t_4 - \left(x1 \cdot x1\right) \cdot 9}{x2 \cdot -6 - x1 \cdot -3}\right)\\ \mathbf{elif}\;x1 \leq 0.00037:\\ \;\;\;\;x1 + \left(t_5 + \left(x1 + \left(t_6 + \left(t_1 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(t_2 \cdot 4 - 6\right) + t_7 \cdot \left(\left(x2 + x2\right) - 3\right)\right) + t_0 \cdot t_3\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(t_5 + \left(x1 + \left(t_6 + \left(t_1 \cdot \left(t_7 \cdot \left(t_2 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot t_3 - 6\right)\right) + 3 \cdot t_0\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1 - t_4}{x1 - x2 \cdot -6}\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (+ (* x1 x1) 1.0))
        (t_2 (/ (- (+ t_0 (* 2.0 x2)) x1) t_1))
        (t_3 (- 3.0 (/ 1.0 x1)))
        (t_4 (* (* x2 x2) 36.0))
        (t_5 (* 3.0 (* x2 -2.0)))
        (t_6 (* x1 (* x1 x1)))
        (t_7 (* (* x1 2.0) t_2)))
   (if (<= x1 -3.2e+103)
     (+
      x1
      (+
       (+ x1 (* 4.0 (* x1 (* x2 (- (* 2.0 x2) 3.0)))))
       (/ (- t_4 (* (* x1 x1) 9.0)) (- (* x2 -6.0) (* x1 -3.0)))))
     (if (<= x1 0.00037)
       (+
        x1
        (+
         t_5
         (+
          x1
          (+
           t_6
           (+
            (*
             t_1
             (+ (* (* x1 x1) (- (* t_2 4.0) 6.0)) (* t_7 (- (+ x2 x2) 3.0))))
            (* t_0 t_3))))))
       (if (<= x1 1.35e+154)
         (+
          x1
          (+
           t_5
           (+
            x1
            (+
             t_6
             (+
              (* t_1 (+ (* t_7 (- t_2 3.0)) (* (* x1 x1) (- (* 4.0 t_3) 6.0))))
              (* 3.0 t_0))))))
         (/ (- (* x1 x1) t_4) (- x1 (* x2 -6.0))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = ((t_0 + (2.0 * x2)) - x1) / t_1;
	double t_3 = 3.0 - (1.0 / x1);
	double t_4 = (x2 * x2) * 36.0;
	double t_5 = 3.0 * (x2 * -2.0);
	double t_6 = x1 * (x1 * x1);
	double t_7 = (x1 * 2.0) * t_2;
	double tmp;
	if (x1 <= -3.2e+103) {
		tmp = x1 + ((x1 + (4.0 * (x1 * (x2 * ((2.0 * x2) - 3.0))))) + ((t_4 - ((x1 * x1) * 9.0)) / ((x2 * -6.0) - (x1 * -3.0))));
	} else if (x1 <= 0.00037) {
		tmp = x1 + (t_5 + (x1 + (t_6 + ((t_1 * (((x1 * x1) * ((t_2 * 4.0) - 6.0)) + (t_7 * ((x2 + x2) - 3.0)))) + (t_0 * t_3)))));
	} else if (x1 <= 1.35e+154) {
		tmp = x1 + (t_5 + (x1 + (t_6 + ((t_1 * ((t_7 * (t_2 - 3.0)) + ((x1 * x1) * ((4.0 * t_3) - 6.0)))) + (3.0 * t_0)))));
	} else {
		tmp = ((x1 * x1) - t_4) / (x1 - (x2 * -6.0));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: 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 * 3.0d0)
    t_1 = (x1 * x1) + 1.0d0
    t_2 = ((t_0 + (2.0d0 * x2)) - x1) / t_1
    t_3 = 3.0d0 - (1.0d0 / x1)
    t_4 = (x2 * x2) * 36.0d0
    t_5 = 3.0d0 * (x2 * (-2.0d0))
    t_6 = x1 * (x1 * x1)
    t_7 = (x1 * 2.0d0) * t_2
    if (x1 <= (-3.2d+103)) then
        tmp = x1 + ((x1 + (4.0d0 * (x1 * (x2 * ((2.0d0 * x2) - 3.0d0))))) + ((t_4 - ((x1 * x1) * 9.0d0)) / ((x2 * (-6.0d0)) - (x1 * (-3.0d0)))))
    else if (x1 <= 0.00037d0) then
        tmp = x1 + (t_5 + (x1 + (t_6 + ((t_1 * (((x1 * x1) * ((t_2 * 4.0d0) - 6.0d0)) + (t_7 * ((x2 + x2) - 3.0d0)))) + (t_0 * t_3)))))
    else if (x1 <= 1.35d+154) then
        tmp = x1 + (t_5 + (x1 + (t_6 + ((t_1 * ((t_7 * (t_2 - 3.0d0)) + ((x1 * x1) * ((4.0d0 * t_3) - 6.0d0)))) + (3.0d0 * t_0)))))
    else
        tmp = ((x1 * x1) - t_4) / (x1 - (x2 * (-6.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = ((t_0 + (2.0 * x2)) - x1) / t_1;
	double t_3 = 3.0 - (1.0 / x1);
	double t_4 = (x2 * x2) * 36.0;
	double t_5 = 3.0 * (x2 * -2.0);
	double t_6 = x1 * (x1 * x1);
	double t_7 = (x1 * 2.0) * t_2;
	double tmp;
	if (x1 <= -3.2e+103) {
		tmp = x1 + ((x1 + (4.0 * (x1 * (x2 * ((2.0 * x2) - 3.0))))) + ((t_4 - ((x1 * x1) * 9.0)) / ((x2 * -6.0) - (x1 * -3.0))));
	} else if (x1 <= 0.00037) {
		tmp = x1 + (t_5 + (x1 + (t_6 + ((t_1 * (((x1 * x1) * ((t_2 * 4.0) - 6.0)) + (t_7 * ((x2 + x2) - 3.0)))) + (t_0 * t_3)))));
	} else if (x1 <= 1.35e+154) {
		tmp = x1 + (t_5 + (x1 + (t_6 + ((t_1 * ((t_7 * (t_2 - 3.0)) + ((x1 * x1) * ((4.0 * t_3) - 6.0)))) + (3.0 * t_0)))));
	} else {
		tmp = ((x1 * x1) - t_4) / (x1 - (x2 * -6.0));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = (x1 * x1) + 1.0
	t_2 = ((t_0 + (2.0 * x2)) - x1) / t_1
	t_3 = 3.0 - (1.0 / x1)
	t_4 = (x2 * x2) * 36.0
	t_5 = 3.0 * (x2 * -2.0)
	t_6 = x1 * (x1 * x1)
	t_7 = (x1 * 2.0) * t_2
	tmp = 0
	if x1 <= -3.2e+103:
		tmp = x1 + ((x1 + (4.0 * (x1 * (x2 * ((2.0 * x2) - 3.0))))) + ((t_4 - ((x1 * x1) * 9.0)) / ((x2 * -6.0) - (x1 * -3.0))))
	elif x1 <= 0.00037:
		tmp = x1 + (t_5 + (x1 + (t_6 + ((t_1 * (((x1 * x1) * ((t_2 * 4.0) - 6.0)) + (t_7 * ((x2 + x2) - 3.0)))) + (t_0 * t_3)))))
	elif x1 <= 1.35e+154:
		tmp = x1 + (t_5 + (x1 + (t_6 + ((t_1 * ((t_7 * (t_2 - 3.0)) + ((x1 * x1) * ((4.0 * t_3) - 6.0)))) + (3.0 * t_0)))))
	else:
		tmp = ((x1 * x1) - t_4) / (x1 - (x2 * -6.0))
	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(Float64(Float64(t_0 + Float64(2.0 * x2)) - x1) / t_1)
	t_3 = Float64(3.0 - Float64(1.0 / x1))
	t_4 = Float64(Float64(x2 * x2) * 36.0)
	t_5 = Float64(3.0 * Float64(x2 * -2.0))
	t_6 = Float64(x1 * Float64(x1 * x1))
	t_7 = Float64(Float64(x1 * 2.0) * t_2)
	tmp = 0.0
	if (x1 <= -3.2e+103)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(4.0 * Float64(x1 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0))))) + Float64(Float64(t_4 - Float64(Float64(x1 * x1) * 9.0)) / Float64(Float64(x2 * -6.0) - Float64(x1 * -3.0)))));
	elseif (x1 <= 0.00037)
		tmp = Float64(x1 + Float64(t_5 + Float64(x1 + Float64(t_6 + Float64(Float64(t_1 * Float64(Float64(Float64(x1 * x1) * Float64(Float64(t_2 * 4.0) - 6.0)) + Float64(t_7 * Float64(Float64(x2 + x2) - 3.0)))) + Float64(t_0 * t_3))))));
	elseif (x1 <= 1.35e+154)
		tmp = Float64(x1 + Float64(t_5 + Float64(x1 + Float64(t_6 + Float64(Float64(t_1 * Float64(Float64(t_7 * Float64(t_2 - 3.0)) + Float64(Float64(x1 * x1) * Float64(Float64(4.0 * t_3) - 6.0)))) + Float64(3.0 * t_0))))));
	else
		tmp = Float64(Float64(Float64(x1 * x1) - t_4) / Float64(x1 - Float64(x2 * -6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * 3.0);
	t_1 = (x1 * x1) + 1.0;
	t_2 = ((t_0 + (2.0 * x2)) - x1) / t_1;
	t_3 = 3.0 - (1.0 / x1);
	t_4 = (x2 * x2) * 36.0;
	t_5 = 3.0 * (x2 * -2.0);
	t_6 = x1 * (x1 * x1);
	t_7 = (x1 * 2.0) * t_2;
	tmp = 0.0;
	if (x1 <= -3.2e+103)
		tmp = x1 + ((x1 + (4.0 * (x1 * (x2 * ((2.0 * x2) - 3.0))))) + ((t_4 - ((x1 * x1) * 9.0)) / ((x2 * -6.0) - (x1 * -3.0))));
	elseif (x1 <= 0.00037)
		tmp = x1 + (t_5 + (x1 + (t_6 + ((t_1 * (((x1 * x1) * ((t_2 * 4.0) - 6.0)) + (t_7 * ((x2 + x2) - 3.0)))) + (t_0 * t_3)))));
	elseif (x1 <= 1.35e+154)
		tmp = x1 + (t_5 + (x1 + (t_6 + ((t_1 * ((t_7 * (t_2 - 3.0)) + ((x1 * x1) * ((4.0 * t_3) - 6.0)))) + (3.0 * t_0)))));
	else
		tmp = ((x1 * x1) - t_4) / (x1 - (x2 * -6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(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]}, Block[{t$95$3 = N[(3.0 - N[(1.0 / x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(x2 * x2), $MachinePrecision] * 36.0), $MachinePrecision]}, Block[{t$95$5 = N[(3.0 * N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(N[(x1 * 2.0), $MachinePrecision] * t$95$2), $MachinePrecision]}, If[LessEqual[x1, -3.2e+103], N[(x1 + N[(N[(x1 + N[(4.0 * N[(x1 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$4 - N[(N[(x1 * x1), $MachinePrecision] * 9.0), $MachinePrecision]), $MachinePrecision] / N[(N[(x2 * -6.0), $MachinePrecision] - N[(x1 * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 0.00037], N[(x1 + N[(t$95$5 + N[(x1 + N[(t$95$6 + N[(N[(t$95$1 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$2 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] + N[(t$95$7 * N[(N[(x2 + x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$0 * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.35e+154], N[(x1 + N[(t$95$5 + N[(x1 + N[(t$95$6 + N[(N[(t$95$1 * N[(N[(t$95$7 * N[(t$95$2 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(4.0 * t$95$3), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x1 * x1), $MachinePrecision] - t$95$4), $MachinePrecision] / N[(x1 - N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -3.19999999999999993e103

   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 2.4%

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

      1. flip-+ 41.0%

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

      2. *-commutative 41.0%

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

      3. *-commutative 41.0%

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

      4. *-commutative 41.0%

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

      5. *-commutative 41.0%

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

      6. *-commutative 41.0%

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

      7. *-commutative 41.0%

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

   5. Applied egg-rr 41.0%

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

      1. swap-sqr 41.0%

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

      2. metadata-eval 41.0%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + \frac{\left(x2 \cdot x2\right) \cdot \color{blue}{36} - \left(x1 \cdot -3\right) \cdot \left(x1 \cdot -3\right)}{x2 \cdot -6 - x1 \cdot -3}\right) \]

      3. swap-sqr 41.0%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + \frac{\left(x2 \cdot x2\right) \cdot 36 - \color{blue}{\left(x1 \cdot x1\right) \cdot \left(-3 \cdot -3\right)}}{x2 \cdot -6 - x1 \cdot -3}\right) \]

      4. metadata-eval 41.0%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + \frac{\left(x2 \cdot x2\right) \cdot 36 - \left(x1 \cdot x1\right) \cdot \color{blue}{9}}{x2 \cdot -6 - x1 \cdot -3}\right) \]

      5. *-commutative 41.0%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + \frac{\left(x2 \cdot x2\right) \cdot 36 - \left(x1 \cdot x1\right) \cdot 9}{\color{blue}{-6 \cdot x2} - x1 \cdot -3}\right) \]

   7. Simplified 41.0%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + \color{blue}{\frac{\left(x2 \cdot x2\right) \cdot 36 - \left(x1 \cdot x1\right) \cdot 9}{-6 \cdot x2 - x1 \cdot -3}}\right) \]

   if -3.19999999999999993e103 < x1 < 3.6999999999999999e-4

   1. Initial program 99.5%

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

   2. Taylor expanded in x1 around 0 74.5%

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

      1. *-commutative 74.5%

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

   4. Simplified 74.5%

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

   5. Taylor expanded in x1 around inf 92.2%

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

   6. Taylor expanded in x1 around 0 88.4%

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

      1. count-2 88.4%

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

   8. Simplified 88.4%

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

   if 3.6999999999999999e-4 < x1 < 1.35000000000000003e154

   1. Initial program 93.9%

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

   2. Taylor expanded in x1 around 0 93.1%

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

      1. *-commutative 93.1%

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

   4. Simplified 93.1%

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

   5. Taylor expanded in x1 around inf 92.8%

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

   6. Taylor expanded in x1 around inf 92.3%

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

   if 1.35000000000000003e154 < 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 7.4%

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

      1. *-commutative 7.4%

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

   5. Simplified 7.4%

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

      1. flip-+ 66.7%

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

   7. Applied egg-rr 66.7%

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

      1. swap-sqr 66.7%

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

      2. metadata-eval 66.7%

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

      3. *-commutative 66.7%

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

   9. Simplified 66.7%

      \[\leadsto \color{blue}{\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - -6 \cdot x2}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -3.2 \cdot 10^{+103}:\\ \;\;\;\;x1 + \left(\left(x1 + 4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right) + \frac{\left(x2 \cdot x2\right) \cdot 36 - \left(x1 \cdot x1\right) \cdot 9}{x2 \cdot -6 - x1 \cdot -3}\right)\\ \mathbf{elif}\;x1 \leq 0.00037:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2\right) + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right) + \left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\left(x2 + x2\right) - 3\right)\right) + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(3 - \frac{1}{x1}\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2\right) + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \left(3 - \frac{1}{x1}\right) - 6\right)\right) + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - x2 \cdot -6}\\ \end{array} \]

Alternative 10: 80.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(x2 \cdot x2\right) \cdot 36\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := x1 \cdot x1 + 1\\ t_3 := 3 \cdot \frac{\left(t_1 - 2 \cdot x2\right) - x1}{t_2}\\ t_4 := \frac{\left(t_1 + 2 \cdot x2\right) - x1}{t_2}\\ t_5 := 4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ t_6 := x1 + t_5\\ t_7 := x1 \cdot \left(x1 \cdot x1\right)\\ t_8 := x1 + \left(3 \cdot \left(x2 \cdot -2\right) + \left(x1 + \left(t_7 + \left(3 \cdot t_1 + t_2 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t_4\right) \cdot \left(t_4 - 3\right) + x1 \cdot \left(x1 \cdot 6\right)\right)\right)\right)\right)\right)\\ \mathbf{if}\;x1 \leq -3.6 \cdot 10^{+103}:\\ \;\;\;\;x1 + \left(t_6 + \frac{t_0 - \left(x1 \cdot x1\right) \cdot 9}{x2 \cdot -6 - x1 \cdot -3}\right)\\ \mathbf{elif}\;x1 \leq -0.0255:\\ \;\;\;\;t_8\\ \mathbf{elif}\;x1 \leq -3.2 \cdot 10^{-235}:\\ \;\;\;\;x1 + \left(t_3 + \left(x1 + \left(t_7 + \left(t_1 \cdot t_4 + t_2 \cdot t_5\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{-210}:\\ \;\;\;\;t_8\\ \mathbf{elif}\;x1 \leq 0.000385:\\ \;\;\;\;x1 + \left(t_3 + t_6\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;t_8\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1 - t_0}{x1 - x2 \cdot -6}\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* (* x2 x2) 36.0))
        (t_1 (* x1 (* x1 3.0)))
        (t_2 (+ (* x1 x1) 1.0))
        (t_3 (* 3.0 (/ (- (- t_1 (* 2.0 x2)) x1) t_2)))
        (t_4 (/ (- (+ t_1 (* 2.0 x2)) x1) t_2))
        (t_5 (* 4.0 (* x1 (* x2 (- (* 2.0 x2) 3.0)))))
        (t_6 (+ x1 t_5))
        (t_7 (* x1 (* x1 x1)))
        (t_8
         (+
          x1
          (+
           (* 3.0 (* x2 -2.0))
           (+
            x1
            (+
             t_7
             (+
              (* 3.0 t_1)
              (*
               t_2
               (+ (* (* (* x1 2.0) t_4) (- t_4 3.0)) (* x1 (* x1 6.0)))))))))))
   (if (<= x1 -3.6e+103)
     (+ x1 (+ t_6 (/ (- t_0 (* (* x1 x1) 9.0)) (- (* x2 -6.0) (* x1 -3.0)))))
     (if (<= x1 -0.0255)
       t_8
       (if (<= x1 -3.2e-235)
         (+ x1 (+ t_3 (+ x1 (+ t_7 (+ (* t_1 t_4) (* t_2 t_5))))))
         (if (<= x1 2e-210)
           t_8
           (if (<= x1 0.000385)
             (+ x1 (+ t_3 t_6))
             (if (<= x1 1.35e+154)
               t_8
               (/ (- (* x1 x1) t_0) (- x1 (* x2 -6.0)))))))))))

C

double code(double x1, double x2) {
	double t_0 = (x2 * x2) * 36.0;
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = 3.0 * (((t_1 - (2.0 * x2)) - x1) / t_2);
	double t_4 = ((t_1 + (2.0 * x2)) - x1) / t_2;
	double t_5 = 4.0 * (x1 * (x2 * ((2.0 * x2) - 3.0)));
	double t_6 = x1 + t_5;
	double t_7 = x1 * (x1 * x1);
	double t_8 = x1 + ((3.0 * (x2 * -2.0)) + (x1 + (t_7 + ((3.0 * t_1) + (t_2 * ((((x1 * 2.0) * t_4) * (t_4 - 3.0)) + (x1 * (x1 * 6.0))))))));
	double tmp;
	if (x1 <= -3.6e+103) {
		tmp = x1 + (t_6 + ((t_0 - ((x1 * x1) * 9.0)) / ((x2 * -6.0) - (x1 * -3.0))));
	} else if (x1 <= -0.0255) {
		tmp = t_8;
	} else if (x1 <= -3.2e-235) {
		tmp = x1 + (t_3 + (x1 + (t_7 + ((t_1 * t_4) + (t_2 * t_5)))));
	} else if (x1 <= 2e-210) {
		tmp = t_8;
	} else if (x1 <= 0.000385) {
		tmp = x1 + (t_3 + t_6);
	} else if (x1 <= 1.35e+154) {
		tmp = t_8;
	} else {
		tmp = ((x1 * x1) - t_0) / (x1 - (x2 * -6.0));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: 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 = (x2 * x2) * 36.0d0
    t_1 = x1 * (x1 * 3.0d0)
    t_2 = (x1 * x1) + 1.0d0
    t_3 = 3.0d0 * (((t_1 - (2.0d0 * x2)) - x1) / t_2)
    t_4 = ((t_1 + (2.0d0 * x2)) - x1) / t_2
    t_5 = 4.0d0 * (x1 * (x2 * ((2.0d0 * x2) - 3.0d0)))
    t_6 = x1 + t_5
    t_7 = x1 * (x1 * x1)
    t_8 = x1 + ((3.0d0 * (x2 * (-2.0d0))) + (x1 + (t_7 + ((3.0d0 * t_1) + (t_2 * ((((x1 * 2.0d0) * t_4) * (t_4 - 3.0d0)) + (x1 * (x1 * 6.0d0))))))))
    if (x1 <= (-3.6d+103)) then
        tmp = x1 + (t_6 + ((t_0 - ((x1 * x1) * 9.0d0)) / ((x2 * (-6.0d0)) - (x1 * (-3.0d0)))))
    else if (x1 <= (-0.0255d0)) then
        tmp = t_8
    else if (x1 <= (-3.2d-235)) then
        tmp = x1 + (t_3 + (x1 + (t_7 + ((t_1 * t_4) + (t_2 * t_5)))))
    else if (x1 <= 2d-210) then
        tmp = t_8
    else if (x1 <= 0.000385d0) then
        tmp = x1 + (t_3 + t_6)
    else if (x1 <= 1.35d+154) then
        tmp = t_8
    else
        tmp = ((x1 * x1) - t_0) / (x1 - (x2 * (-6.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (x2 * x2) * 36.0;
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = 3.0 * (((t_1 - (2.0 * x2)) - x1) / t_2);
	double t_4 = ((t_1 + (2.0 * x2)) - x1) / t_2;
	double t_5 = 4.0 * (x1 * (x2 * ((2.0 * x2) - 3.0)));
	double t_6 = x1 + t_5;
	double t_7 = x1 * (x1 * x1);
	double t_8 = x1 + ((3.0 * (x2 * -2.0)) + (x1 + (t_7 + ((3.0 * t_1) + (t_2 * ((((x1 * 2.0) * t_4) * (t_4 - 3.0)) + (x1 * (x1 * 6.0))))))));
	double tmp;
	if (x1 <= -3.6e+103) {
		tmp = x1 + (t_6 + ((t_0 - ((x1 * x1) * 9.0)) / ((x2 * -6.0) - (x1 * -3.0))));
	} else if (x1 <= -0.0255) {
		tmp = t_8;
	} else if (x1 <= -3.2e-235) {
		tmp = x1 + (t_3 + (x1 + (t_7 + ((t_1 * t_4) + (t_2 * t_5)))));
	} else if (x1 <= 2e-210) {
		tmp = t_8;
	} else if (x1 <= 0.000385) {
		tmp = x1 + (t_3 + t_6);
	} else if (x1 <= 1.35e+154) {
		tmp = t_8;
	} else {
		tmp = ((x1 * x1) - t_0) / (x1 - (x2 * -6.0));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x2 * x2) * 36.0
	t_1 = x1 * (x1 * 3.0)
	t_2 = (x1 * x1) + 1.0
	t_3 = 3.0 * (((t_1 - (2.0 * x2)) - x1) / t_2)
	t_4 = ((t_1 + (2.0 * x2)) - x1) / t_2
	t_5 = 4.0 * (x1 * (x2 * ((2.0 * x2) - 3.0)))
	t_6 = x1 + t_5
	t_7 = x1 * (x1 * x1)
	t_8 = x1 + ((3.0 * (x2 * -2.0)) + (x1 + (t_7 + ((3.0 * t_1) + (t_2 * ((((x1 * 2.0) * t_4) * (t_4 - 3.0)) + (x1 * (x1 * 6.0))))))))
	tmp = 0
	if x1 <= -3.6e+103:
		tmp = x1 + (t_6 + ((t_0 - ((x1 * x1) * 9.0)) / ((x2 * -6.0) - (x1 * -3.0))))
	elif x1 <= -0.0255:
		tmp = t_8
	elif x1 <= -3.2e-235:
		tmp = x1 + (t_3 + (x1 + (t_7 + ((t_1 * t_4) + (t_2 * t_5)))))
	elif x1 <= 2e-210:
		tmp = t_8
	elif x1 <= 0.000385:
		tmp = x1 + (t_3 + t_6)
	elif x1 <= 1.35e+154:
		tmp = t_8
	else:
		tmp = ((x1 * x1) - t_0) / (x1 - (x2 * -6.0))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x2 * x2) * 36.0)
	t_1 = Float64(x1 * Float64(x1 * 3.0))
	t_2 = Float64(Float64(x1 * x1) + 1.0)
	t_3 = Float64(3.0 * Float64(Float64(Float64(t_1 - Float64(2.0 * x2)) - x1) / t_2))
	t_4 = Float64(Float64(Float64(t_1 + Float64(2.0 * x2)) - x1) / t_2)
	t_5 = Float64(4.0 * Float64(x1 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0))))
	t_6 = Float64(x1 + t_5)
	t_7 = Float64(x1 * Float64(x1 * x1))
	t_8 = Float64(x1 + Float64(Float64(3.0 * Float64(x2 * -2.0)) + Float64(x1 + Float64(t_7 + Float64(Float64(3.0 * t_1) + Float64(t_2 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_4) * Float64(t_4 - 3.0)) + Float64(x1 * Float64(x1 * 6.0)))))))))
	tmp = 0.0
	if (x1 <= -3.6e+103)
		tmp = Float64(x1 + Float64(t_6 + Float64(Float64(t_0 - Float64(Float64(x1 * x1) * 9.0)) / Float64(Float64(x2 * -6.0) - Float64(x1 * -3.0)))));
	elseif (x1 <= -0.0255)
		tmp = t_8;
	elseif (x1 <= -3.2e-235)
		tmp = Float64(x1 + Float64(t_3 + Float64(x1 + Float64(t_7 + Float64(Float64(t_1 * t_4) + Float64(t_2 * t_5))))));
	elseif (x1 <= 2e-210)
		tmp = t_8;
	elseif (x1 <= 0.000385)
		tmp = Float64(x1 + Float64(t_3 + t_6));
	elseif (x1 <= 1.35e+154)
		tmp = t_8;
	else
		tmp = Float64(Float64(Float64(x1 * x1) - t_0) / Float64(x1 - Float64(x2 * -6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x2 * x2) * 36.0;
	t_1 = x1 * (x1 * 3.0);
	t_2 = (x1 * x1) + 1.0;
	t_3 = 3.0 * (((t_1 - (2.0 * x2)) - x1) / t_2);
	t_4 = ((t_1 + (2.0 * x2)) - x1) / t_2;
	t_5 = 4.0 * (x1 * (x2 * ((2.0 * x2) - 3.0)));
	t_6 = x1 + t_5;
	t_7 = x1 * (x1 * x1);
	t_8 = x1 + ((3.0 * (x2 * -2.0)) + (x1 + (t_7 + ((3.0 * t_1) + (t_2 * ((((x1 * 2.0) * t_4) * (t_4 - 3.0)) + (x1 * (x1 * 6.0))))))));
	tmp = 0.0;
	if (x1 <= -3.6e+103)
		tmp = x1 + (t_6 + ((t_0 - ((x1 * x1) * 9.0)) / ((x2 * -6.0) - (x1 * -3.0))));
	elseif (x1 <= -0.0255)
		tmp = t_8;
	elseif (x1 <= -3.2e-235)
		tmp = x1 + (t_3 + (x1 + (t_7 + ((t_1 * t_4) + (t_2 * t_5)))));
	elseif (x1 <= 2e-210)
		tmp = t_8;
	elseif (x1 <= 0.000385)
		tmp = x1 + (t_3 + t_6);
	elseif (x1 <= 1.35e+154)
		tmp = t_8;
	else
		tmp = ((x1 * x1) - t_0) / (x1 - (x2 * -6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x2 * x2), $MachinePrecision] * 36.0), $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[(3.0 * N[(N[(N[(t$95$1 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(t$95$1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]}, Block[{t$95$5 = N[(4.0 * N[(x1 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(x1 + t$95$5), $MachinePrecision]}, Block[{t$95$7 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$8 = N[(x1 + N[(N[(3.0 * N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(t$95$7 + N[(N[(3.0 * t$95$1), $MachinePrecision] + 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[(x1 * N[(x1 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -3.6e+103], N[(x1 + N[(t$95$6 + N[(N[(t$95$0 - N[(N[(x1 * x1), $MachinePrecision] * 9.0), $MachinePrecision]), $MachinePrecision] / N[(N[(x2 * -6.0), $MachinePrecision] - N[(x1 * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -0.0255], t$95$8, If[LessEqual[x1, -3.2e-235], N[(x1 + N[(t$95$3 + N[(x1 + N[(t$95$7 + N[(N[(t$95$1 * t$95$4), $MachinePrecision] + N[(t$95$2 * t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 2e-210], t$95$8, If[LessEqual[x1, 0.000385], N[(x1 + N[(t$95$3 + t$95$6), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.35e+154], t$95$8, N[(N[(N[(x1 * x1), $MachinePrecision] - t$95$0), $MachinePrecision] / N[(x1 - N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x1 < -3.60000000000000017e103

   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 2.4%

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

      1. flip-+ 41.0%

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

      2. *-commutative 41.0%

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

      3. *-commutative 41.0%

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

      4. *-commutative 41.0%

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

      5. *-commutative 41.0%

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

      6. *-commutative 41.0%

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

      7. *-commutative 41.0%

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

   5. Applied egg-rr 41.0%

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

      1. swap-sqr 41.0%

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

      2. metadata-eval 41.0%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + \frac{\left(x2 \cdot x2\right) \cdot \color{blue}{36} - \left(x1 \cdot -3\right) \cdot \left(x1 \cdot -3\right)}{x2 \cdot -6 - x1 \cdot -3}\right) \]

      3. swap-sqr 41.0%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + \frac{\left(x2 \cdot x2\right) \cdot 36 - \color{blue}{\left(x1 \cdot x1\right) \cdot \left(-3 \cdot -3\right)}}{x2 \cdot -6 - x1 \cdot -3}\right) \]

      4. metadata-eval 41.0%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + \frac{\left(x2 \cdot x2\right) \cdot 36 - \left(x1 \cdot x1\right) \cdot \color{blue}{9}}{x2 \cdot -6 - x1 \cdot -3}\right) \]

      5. *-commutative 41.0%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + \frac{\left(x2 \cdot x2\right) \cdot 36 - \left(x1 \cdot x1\right) \cdot 9}{\color{blue}{-6 \cdot x2} - x1 \cdot -3}\right) \]

   7. Simplified 41.0%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + \color{blue}{\frac{\left(x2 \cdot x2\right) \cdot 36 - \left(x1 \cdot x1\right) \cdot 9}{-6 \cdot x2 - x1 \cdot -3}}\right) \]

   if -3.60000000000000017e103 < x1 < -0.0254999999999999984 or -3.2000000000000001e-235 < x1 < 2.0000000000000001e-210 or 3.8499999999999998e-4 < x1 < 1.35000000000000003e154

   1. Initial program 97.6%

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

   2. Taylor expanded in x1 around 0 94.0%

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

      1. *-commutative 94.0%

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

   4. Simplified 94.0%

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

   5. Taylor expanded in x1 around inf 93.9%

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

   6. Taylor expanded in x1 around inf 89.2%

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

      1. unpow2 89.2%

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

      2. associate-*r* 89.3%

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

   8. Simplified 89.3%

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

   if -0.0254999999999999984 < x1 < -3.2000000000000001e-235

   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 97.2%

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

   3. Taylor expanded in x1 around 0 94.2%

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

   if 2.0000000000000001e-210 < x1 < 3.8499999999999998e-4

   1. Initial program 99.5%

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

   2. Taylor expanded in x1 around 0 95.4%

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

   if 1.35000000000000003e154 < 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 7.4%

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

      1. *-commutative 7.4%

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

   5. Simplified 7.4%

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

      1. flip-+ 66.7%

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

   7. Applied egg-rr 66.7%

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

      1. swap-sqr 66.7%

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

      2. metadata-eval 66.7%

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

      3. *-commutative 66.7%

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

   9. Simplified 66.7%

      \[\leadsto \color{blue}{\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - -6 \cdot x2}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -3.6 \cdot 10^{+103}:\\ \;\;\;\;x1 + \left(\left(x1 + 4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right) + \frac{\left(x2 \cdot x2\right) \cdot 36 - \left(x1 \cdot x1\right) \cdot 9}{x2 \cdot -6 - x1 \cdot -3}\right)\\ \mathbf{elif}\;x1 \leq -0.0255:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2\right) + \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(\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) + x1 \cdot \left(x1 \cdot 6\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -3.2 \cdot 10^{-235}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 \cdot x1 + 1\right) \cdot \left(4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{-210}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2\right) + \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(\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) + x1 \cdot \left(x1 \cdot 6\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 0.000385:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + 4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2\right) + \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(\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) + x1 \cdot \left(x1 \cdot 6\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - x2 \cdot -6}\\ \end{array} \]

Alternative 11: 79.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := 3 \cdot t_0\\ t_2 := \left(x2 \cdot x2\right) \cdot 36\\ t_3 := 3 \cdot \left(x2 \cdot -2\right)\\ t_4 := 4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ t_5 := x1 + t_4\\ t_6 := x1 \cdot \left(x1 \cdot x1\right)\\ t_7 := x1 \cdot x1 + 1\\ t_8 := 3 \cdot \frac{\left(t_0 - 2 \cdot x2\right) - x1}{t_7}\\ t_9 := \frac{\left(t_0 + 2 \cdot x2\right) - x1}{t_7}\\ t_10 := t_9 - 3\\ t_11 := x1 + \left(t_3 + \left(x1 + \left(t_6 + \left(t_1 + t_7 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t_9\right) \cdot t_10 + x1 \cdot \left(x1 \cdot 6\right)\right)\right)\right)\right)\right)\\ \mathbf{if}\;x1 \leq -3.3 \cdot 10^{+94}:\\ \;\;\;\;x1 + \left(t_5 + \frac{t_2 - \left(x1 \cdot x1\right) \cdot 9}{x2 \cdot -6 - x1 \cdot -3}\right)\\ \mathbf{elif}\;x1 \leq -3.2 \cdot 10^{+21}:\\ \;\;\;\;x1 + \left(t_3 + \left(x1 + \left(t_6 + \left(t_1 + t_7 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(t_9 \cdot 4 - 6\right) + t_10 \cdot \left(\left(x1 \cdot 2\right) \cdot 3\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -2.45 \cdot 10^{-235}:\\ \;\;\;\;x1 + \left(t_8 + \left(x1 + \left(t_6 + \left(t_7 \cdot t_4 + t_0 \cdot \left(2 \cdot x2 - x1\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.25 \cdot 10^{-210}:\\ \;\;\;\;t_11\\ \mathbf{elif}\;x1 \leq 0.0003:\\ \;\;\;\;x1 + \left(t_8 + t_5\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;t_11\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1 - t_2}{x1 - x2 \cdot -6}\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (* 3.0 t_0))
        (t_2 (* (* x2 x2) 36.0))
        (t_3 (* 3.0 (* x2 -2.0)))
        (t_4 (* 4.0 (* x1 (* x2 (- (* 2.0 x2) 3.0)))))
        (t_5 (+ x1 t_4))
        (t_6 (* x1 (* x1 x1)))
        (t_7 (+ (* x1 x1) 1.0))
        (t_8 (* 3.0 (/ (- (- t_0 (* 2.0 x2)) x1) t_7)))
        (t_9 (/ (- (+ t_0 (* 2.0 x2)) x1) t_7))
        (t_10 (- t_9 3.0))
        (t_11
         (+
          x1
          (+
           t_3
           (+
            x1
            (+
             t_6
             (+
              t_1
              (* t_7 (+ (* (* (* x1 2.0) t_9) t_10) (* x1 (* x1 6.0)))))))))))
   (if (<= x1 -3.3e+94)
     (+ x1 (+ t_5 (/ (- t_2 (* (* x1 x1) 9.0)) (- (* x2 -6.0) (* x1 -3.0)))))
     (if (<= x1 -3.2e+21)
       (+
        x1
        (+
         t_3
         (+
          x1
          (+
           t_6
           (+
            t_1
            (*
             t_7
             (+
              (* (* x1 x1) (- (* t_9 4.0) 6.0))
              (* t_10 (* (* x1 2.0) 3.0)))))))))
       (if (<= x1 -2.45e-235)
         (+
          x1
          (+ t_8 (+ x1 (+ t_6 (+ (* t_7 t_4) (* t_0 (- (* 2.0 x2) x1)))))))
         (if (<= x1 1.25e-210)
           t_11
           (if (<= x1 0.0003)
             (+ x1 (+ t_8 t_5))
             (if (<= x1 1.35e+154)
               t_11
               (/ (- (* x1 x1) t_2) (- x1 (* x2 -6.0)))))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = 3.0 * t_0;
	double t_2 = (x2 * x2) * 36.0;
	double t_3 = 3.0 * (x2 * -2.0);
	double t_4 = 4.0 * (x1 * (x2 * ((2.0 * x2) - 3.0)));
	double t_5 = x1 + t_4;
	double t_6 = x1 * (x1 * x1);
	double t_7 = (x1 * x1) + 1.0;
	double t_8 = 3.0 * (((t_0 - (2.0 * x2)) - x1) / t_7);
	double t_9 = ((t_0 + (2.0 * x2)) - x1) / t_7;
	double t_10 = t_9 - 3.0;
	double t_11 = x1 + (t_3 + (x1 + (t_6 + (t_1 + (t_7 * ((((x1 * 2.0) * t_9) * t_10) + (x1 * (x1 * 6.0))))))));
	double tmp;
	if (x1 <= -3.3e+94) {
		tmp = x1 + (t_5 + ((t_2 - ((x1 * x1) * 9.0)) / ((x2 * -6.0) - (x1 * -3.0))));
	} else if (x1 <= -3.2e+21) {
		tmp = x1 + (t_3 + (x1 + (t_6 + (t_1 + (t_7 * (((x1 * x1) * ((t_9 * 4.0) - 6.0)) + (t_10 * ((x1 * 2.0) * 3.0))))))));
	} else if (x1 <= -2.45e-235) {
		tmp = x1 + (t_8 + (x1 + (t_6 + ((t_7 * t_4) + (t_0 * ((2.0 * x2) - x1))))));
	} else if (x1 <= 1.25e-210) {
		tmp = t_11;
	} else if (x1 <= 0.0003) {
		tmp = x1 + (t_8 + t_5);
	} else if (x1 <= 1.35e+154) {
		tmp = t_11;
	} else {
		tmp = ((x1 * x1) - t_2) / (x1 - (x2 * -6.0));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_10
    real(8) :: t_11
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: t_8
    real(8) :: t_9
    real(8) :: tmp
    t_0 = x1 * (x1 * 3.0d0)
    t_1 = 3.0d0 * t_0
    t_2 = (x2 * x2) * 36.0d0
    t_3 = 3.0d0 * (x2 * (-2.0d0))
    t_4 = 4.0d0 * (x1 * (x2 * ((2.0d0 * x2) - 3.0d0)))
    t_5 = x1 + t_4
    t_6 = x1 * (x1 * x1)
    t_7 = (x1 * x1) + 1.0d0
    t_8 = 3.0d0 * (((t_0 - (2.0d0 * x2)) - x1) / t_7)
    t_9 = ((t_0 + (2.0d0 * x2)) - x1) / t_7
    t_10 = t_9 - 3.0d0
    t_11 = x1 + (t_3 + (x1 + (t_6 + (t_1 + (t_7 * ((((x1 * 2.0d0) * t_9) * t_10) + (x1 * (x1 * 6.0d0))))))))
    if (x1 <= (-3.3d+94)) then
        tmp = x1 + (t_5 + ((t_2 - ((x1 * x1) * 9.0d0)) / ((x2 * (-6.0d0)) - (x1 * (-3.0d0)))))
    else if (x1 <= (-3.2d+21)) then
        tmp = x1 + (t_3 + (x1 + (t_6 + (t_1 + (t_7 * (((x1 * x1) * ((t_9 * 4.0d0) - 6.0d0)) + (t_10 * ((x1 * 2.0d0) * 3.0d0))))))))
    else if (x1 <= (-2.45d-235)) then
        tmp = x1 + (t_8 + (x1 + (t_6 + ((t_7 * t_4) + (t_0 * ((2.0d0 * x2) - x1))))))
    else if (x1 <= 1.25d-210) then
        tmp = t_11
    else if (x1 <= 0.0003d0) then
        tmp = x1 + (t_8 + t_5)
    else if (x1 <= 1.35d+154) then
        tmp = t_11
    else
        tmp = ((x1 * x1) - t_2) / (x1 - (x2 * (-6.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = 3.0 * t_0;
	double t_2 = (x2 * x2) * 36.0;
	double t_3 = 3.0 * (x2 * -2.0);
	double t_4 = 4.0 * (x1 * (x2 * ((2.0 * x2) - 3.0)));
	double t_5 = x1 + t_4;
	double t_6 = x1 * (x1 * x1);
	double t_7 = (x1 * x1) + 1.0;
	double t_8 = 3.0 * (((t_0 - (2.0 * x2)) - x1) / t_7);
	double t_9 = ((t_0 + (2.0 * x2)) - x1) / t_7;
	double t_10 = t_9 - 3.0;
	double t_11 = x1 + (t_3 + (x1 + (t_6 + (t_1 + (t_7 * ((((x1 * 2.0) * t_9) * t_10) + (x1 * (x1 * 6.0))))))));
	double tmp;
	if (x1 <= -3.3e+94) {
		tmp = x1 + (t_5 + ((t_2 - ((x1 * x1) * 9.0)) / ((x2 * -6.0) - (x1 * -3.0))));
	} else if (x1 <= -3.2e+21) {
		tmp = x1 + (t_3 + (x1 + (t_6 + (t_1 + (t_7 * (((x1 * x1) * ((t_9 * 4.0) - 6.0)) + (t_10 * ((x1 * 2.0) * 3.0))))))));
	} else if (x1 <= -2.45e-235) {
		tmp = x1 + (t_8 + (x1 + (t_6 + ((t_7 * t_4) + (t_0 * ((2.0 * x2) - x1))))));
	} else if (x1 <= 1.25e-210) {
		tmp = t_11;
	} else if (x1 <= 0.0003) {
		tmp = x1 + (t_8 + t_5);
	} else if (x1 <= 1.35e+154) {
		tmp = t_11;
	} else {
		tmp = ((x1 * x1) - t_2) / (x1 - (x2 * -6.0));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = 3.0 * t_0
	t_2 = (x2 * x2) * 36.0
	t_3 = 3.0 * (x2 * -2.0)
	t_4 = 4.0 * (x1 * (x2 * ((2.0 * x2) - 3.0)))
	t_5 = x1 + t_4
	t_6 = x1 * (x1 * x1)
	t_7 = (x1 * x1) + 1.0
	t_8 = 3.0 * (((t_0 - (2.0 * x2)) - x1) / t_7)
	t_9 = ((t_0 + (2.0 * x2)) - x1) / t_7
	t_10 = t_9 - 3.0
	t_11 = x1 + (t_3 + (x1 + (t_6 + (t_1 + (t_7 * ((((x1 * 2.0) * t_9) * t_10) + (x1 * (x1 * 6.0))))))))
	tmp = 0
	if x1 <= -3.3e+94:
		tmp = x1 + (t_5 + ((t_2 - ((x1 * x1) * 9.0)) / ((x2 * -6.0) - (x1 * -3.0))))
	elif x1 <= -3.2e+21:
		tmp = x1 + (t_3 + (x1 + (t_6 + (t_1 + (t_7 * (((x1 * x1) * ((t_9 * 4.0) - 6.0)) + (t_10 * ((x1 * 2.0) * 3.0))))))))
	elif x1 <= -2.45e-235:
		tmp = x1 + (t_8 + (x1 + (t_6 + ((t_7 * t_4) + (t_0 * ((2.0 * x2) - x1))))))
	elif x1 <= 1.25e-210:
		tmp = t_11
	elif x1 <= 0.0003:
		tmp = x1 + (t_8 + t_5)
	elif x1 <= 1.35e+154:
		tmp = t_11
	else:
		tmp = ((x1 * x1) - t_2) / (x1 - (x2 * -6.0))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(3.0 * t_0)
	t_2 = Float64(Float64(x2 * x2) * 36.0)
	t_3 = Float64(3.0 * Float64(x2 * -2.0))
	t_4 = Float64(4.0 * Float64(x1 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0))))
	t_5 = Float64(x1 + t_4)
	t_6 = Float64(x1 * Float64(x1 * x1))
	t_7 = Float64(Float64(x1 * x1) + 1.0)
	t_8 = Float64(3.0 * Float64(Float64(Float64(t_0 - Float64(2.0 * x2)) - x1) / t_7))
	t_9 = Float64(Float64(Float64(t_0 + Float64(2.0 * x2)) - x1) / t_7)
	t_10 = Float64(t_9 - 3.0)
	t_11 = Float64(x1 + Float64(t_3 + Float64(x1 + Float64(t_6 + Float64(t_1 + Float64(t_7 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_9) * t_10) + Float64(x1 * Float64(x1 * 6.0)))))))))
	tmp = 0.0
	if (x1 <= -3.3e+94)
		tmp = Float64(x1 + Float64(t_5 + Float64(Float64(t_2 - Float64(Float64(x1 * x1) * 9.0)) / Float64(Float64(x2 * -6.0) - Float64(x1 * -3.0)))));
	elseif (x1 <= -3.2e+21)
		tmp = Float64(x1 + Float64(t_3 + Float64(x1 + Float64(t_6 + Float64(t_1 + Float64(t_7 * Float64(Float64(Float64(x1 * x1) * Float64(Float64(t_9 * 4.0) - 6.0)) + Float64(t_10 * Float64(Float64(x1 * 2.0) * 3.0)))))))));
	elseif (x1 <= -2.45e-235)
		tmp = Float64(x1 + Float64(t_8 + Float64(x1 + Float64(t_6 + Float64(Float64(t_7 * t_4) + Float64(t_0 * Float64(Float64(2.0 * x2) - x1)))))));
	elseif (x1 <= 1.25e-210)
		tmp = t_11;
	elseif (x1 <= 0.0003)
		tmp = Float64(x1 + Float64(t_8 + t_5));
	elseif (x1 <= 1.35e+154)
		tmp = t_11;
	else
		tmp = Float64(Float64(Float64(x1 * x1) - t_2) / Float64(x1 - Float64(x2 * -6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * 3.0);
	t_1 = 3.0 * t_0;
	t_2 = (x2 * x2) * 36.0;
	t_3 = 3.0 * (x2 * -2.0);
	t_4 = 4.0 * (x1 * (x2 * ((2.0 * x2) - 3.0)));
	t_5 = x1 + t_4;
	t_6 = x1 * (x1 * x1);
	t_7 = (x1 * x1) + 1.0;
	t_8 = 3.0 * (((t_0 - (2.0 * x2)) - x1) / t_7);
	t_9 = ((t_0 + (2.0 * x2)) - x1) / t_7;
	t_10 = t_9 - 3.0;
	t_11 = x1 + (t_3 + (x1 + (t_6 + (t_1 + (t_7 * ((((x1 * 2.0) * t_9) * t_10) + (x1 * (x1 * 6.0))))))));
	tmp = 0.0;
	if (x1 <= -3.3e+94)
		tmp = x1 + (t_5 + ((t_2 - ((x1 * x1) * 9.0)) / ((x2 * -6.0) - (x1 * -3.0))));
	elseif (x1 <= -3.2e+21)
		tmp = x1 + (t_3 + (x1 + (t_6 + (t_1 + (t_7 * (((x1 * x1) * ((t_9 * 4.0) - 6.0)) + (t_10 * ((x1 * 2.0) * 3.0))))))));
	elseif (x1 <= -2.45e-235)
		tmp = x1 + (t_8 + (x1 + (t_6 + ((t_7 * t_4) + (t_0 * ((2.0 * x2) - x1))))));
	elseif (x1 <= 1.25e-210)
		tmp = t_11;
	elseif (x1 <= 0.0003)
		tmp = x1 + (t_8 + t_5);
	elseif (x1 <= 1.35e+154)
		tmp = t_11;
	else
		tmp = ((x1 * x1) - t_2) / (x1 - (x2 * -6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(3.0 * t$95$0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x2 * x2), $MachinePrecision] * 36.0), $MachinePrecision]}, Block[{t$95$3 = N[(3.0 * N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(4.0 * N[(x1 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(x1 + t$95$4), $MachinePrecision]}, Block[{t$95$6 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$8 = N[(3.0 * N[(N[(N[(t$95$0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$7), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$9 = N[(N[(N[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$7), $MachinePrecision]}, Block[{t$95$10 = N[(t$95$9 - 3.0), $MachinePrecision]}, Block[{t$95$11 = N[(x1 + N[(t$95$3 + N[(x1 + N[(t$95$6 + N[(t$95$1 + N[(t$95$7 * N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$9), $MachinePrecision] * t$95$10), $MachinePrecision] + N[(x1 * N[(x1 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -3.3e+94], N[(x1 + N[(t$95$5 + N[(N[(t$95$2 - N[(N[(x1 * x1), $MachinePrecision] * 9.0), $MachinePrecision]), $MachinePrecision] / N[(N[(x2 * -6.0), $MachinePrecision] - N[(x1 * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -3.2e+21], N[(x1 + N[(t$95$3 + N[(x1 + N[(t$95$6 + N[(t$95$1 + N[(t$95$7 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$9 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] + N[(t$95$10 * N[(N[(x1 * 2.0), $MachinePrecision] * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -2.45e-235], N[(x1 + N[(t$95$8 + N[(x1 + N[(t$95$6 + N[(N[(t$95$7 * t$95$4), $MachinePrecision] + N[(t$95$0 * N[(N[(2.0 * x2), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.25e-210], t$95$11, If[LessEqual[x1, 0.0003], N[(x1 + N[(t$95$8 + t$95$5), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.35e+154], t$95$11, N[(N[(N[(x1 * x1), $MachinePrecision] - t$95$2), $MachinePrecision] / N[(x1 - N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if x1 < -3.3e94

   1. Initial program 4.3%

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

   2. Taylor expanded in x1 around 0 2.2%

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

   3. Taylor expanded in x1 around 0 4.5%

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

      1. flip-+ 41.5%

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

      2. *-commutative 41.5%

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

      3. *-commutative 41.5%

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

      4. *-commutative 41.5%

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

      5. *-commutative 41.5%

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

      6. *-commutative 41.5%

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

      7. *-commutative 41.5%

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

   5. Applied egg-rr 41.5%

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

      1. swap-sqr 41.5%

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

      2. metadata-eval 41.5%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + \frac{\left(x2 \cdot x2\right) \cdot \color{blue}{36} - \left(x1 \cdot -3\right) \cdot \left(x1 \cdot -3\right)}{x2 \cdot -6 - x1 \cdot -3}\right) \]

      3. swap-sqr 41.5%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + \frac{\left(x2 \cdot x2\right) \cdot 36 - \color{blue}{\left(x1 \cdot x1\right) \cdot \left(-3 \cdot -3\right)}}{x2 \cdot -6 - x1 \cdot -3}\right) \]

      4. metadata-eval 41.5%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + \frac{\left(x2 \cdot x2\right) \cdot 36 - \left(x1 \cdot x1\right) \cdot \color{blue}{9}}{x2 \cdot -6 - x1 \cdot -3}\right) \]

      5. *-commutative 41.5%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + \frac{\left(x2 \cdot x2\right) \cdot 36 - \left(x1 \cdot x1\right) \cdot 9}{\color{blue}{-6 \cdot x2} - x1 \cdot -3}\right) \]

   7. Simplified 41.5%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + \color{blue}{\frac{\left(x2 \cdot x2\right) \cdot 36 - \left(x1 \cdot x1\right) \cdot 9}{-6 \cdot x2 - x1 \cdot -3}}\right) \]

   if -3.3e94 < x1 < -3.2e21

   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 99.4%

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

      1. *-commutative 99.4%

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

   4. Simplified 99.4%

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

   5. Taylor expanded in x1 around inf 99.4%

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

   6. Taylor expanded in x1 around inf 96.4%

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

   if -3.2e21 < x1 < -2.44999999999999983e-235

   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 91.9%

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

   3. Taylor expanded in x1 around 0 89.0%

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

   4. Taylor expanded in x1 around 0 89.2%

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

   if -2.44999999999999983e-235 < x1 < 1.2500000000000001e-210 or 2.99999999999999974e-4 < x1 < 1.35000000000000003e154

   1. Initial program 97.0%

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

   2. Taylor expanded in x1 around 0 93.3%

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

      1. *-commutative 93.3%

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

   4. Simplified 93.3%

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

   5. Taylor expanded in x1 around inf 93.1%

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

   6. Taylor expanded in x1 around inf 92.5%

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

      1. unpow2 92.5%

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

      2. associate-*r* 92.5%

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

   8. Simplified 92.5%

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

   if 1.2500000000000001e-210 < x1 < 2.99999999999999974e-4

   1. Initial program 99.5%

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

   2. Taylor expanded in x1 around 0 95.4%

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

   if 1.35000000000000003e154 < 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 7.4%

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

      1. *-commutative 7.4%

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

   5. Simplified 7.4%

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

      1. flip-+ 66.7%

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

   7. Applied egg-rr 66.7%

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

      1. swap-sqr 66.7%

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

      2. metadata-eval 66.7%

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

      3. *-commutative 66.7%

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

   9. Simplified 66.7%

      \[\leadsto \color{blue}{\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - -6 \cdot x2}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -3.3 \cdot 10^{+94}:\\ \;\;\;\;x1 + \left(\left(x1 + 4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right) + \frac{\left(x2 \cdot x2\right) \cdot 36 - \left(x1 \cdot x1\right) \cdot 9}{x2 \cdot -6 - x1 \cdot -3}\right)\\ \mathbf{elif}\;x1 \leq -3.2 \cdot 10^{+21}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2\right) + \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(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 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 3\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -2.45 \cdot 10^{-235}:\\ \;\;\;\;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(4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right) + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(2 \cdot x2 - x1\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.25 \cdot 10^{-210}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2\right) + \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(\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) + x1 \cdot \left(x1 \cdot 6\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 0.0003:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + 4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2\right) + \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(\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) + x1 \cdot \left(x1 \cdot 6\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - x2 \cdot -6}\\ \end{array} \]

Alternative 12: 67.7% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := 4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ t_2 := x1 \cdot x1 + 1\\ t_3 := t_2 \cdot t_1\\ t_4 := x1 \cdot \left(x1 \cdot x1\right)\\ t_5 := \left(x2 \cdot x2\right) \cdot 36\\ t_6 := 3 \cdot \frac{\left(t_0 - 2 \cdot x2\right) - x1}{t_2}\\ \mathbf{if}\;x1 \leq -3.3 \cdot 10^{+94}:\\ \;\;\;\;x1 + \left(\left(x1 + t_1\right) + \frac{t_5 - \left(x1 \cdot x1\right) \cdot 9}{x2 \cdot -6 - x1 \cdot -3}\right)\\ \mathbf{elif}\;x1 \leq -2.1 \cdot 10^{-93}:\\ \;\;\;\;x1 + \left(t_6 + \left(x1 + \left(t_4 + \left(t_3 + t_0 \cdot \left(2 \cdot x2 - x1\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 8.2 \cdot 10^{-247}:\\ \;\;\;\;x1 + \left(t_6 + \left(x1 + 4 \cdot \left(-3 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(t_6 + \left(x1 + \left(t_4 + \left(t_0 \cdot \frac{\left(t_0 + 2 \cdot x2\right) - x1}{t_2} + t_3\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1 - t_5}{x1 - x2 \cdot -6}\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (* 4.0 (* x1 (* x2 (- (* 2.0 x2) 3.0)))))
        (t_2 (+ (* x1 x1) 1.0))
        (t_3 (* t_2 t_1))
        (t_4 (* x1 (* x1 x1)))
        (t_5 (* (* x2 x2) 36.0))
        (t_6 (* 3.0 (/ (- (- t_0 (* 2.0 x2)) x1) t_2))))
   (if (<= x1 -3.3e+94)
     (+
      x1
      (+ (+ x1 t_1) (/ (- t_5 (* (* x1 x1) 9.0)) (- (* x2 -6.0) (* x1 -3.0)))))
     (if (<= x1 -2.1e-93)
       (+ x1 (+ t_6 (+ x1 (+ t_4 (+ t_3 (* t_0 (- (* 2.0 x2) x1)))))))
       (if (<= x1 8.2e-247)
         (+ x1 (+ t_6 (+ x1 (* 4.0 (* -3.0 (* x1 x2))))))
         (if (<= x1 1.35e+154)
           (+
            x1
            (+
             t_6
             (+ x1 (+ t_4 (+ (* t_0 (/ (- (+ t_0 (* 2.0 x2)) x1) t_2)) t_3)))))
           (/ (- (* x1 x1) t_5) (- x1 (* x2 -6.0)))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = 4.0 * (x1 * (x2 * ((2.0 * x2) - 3.0)));
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = t_2 * t_1;
	double t_4 = x1 * (x1 * x1);
	double t_5 = (x2 * x2) * 36.0;
	double t_6 = 3.0 * (((t_0 - (2.0 * x2)) - x1) / t_2);
	double tmp;
	if (x1 <= -3.3e+94) {
		tmp = x1 + ((x1 + t_1) + ((t_5 - ((x1 * x1) * 9.0)) / ((x2 * -6.0) - (x1 * -3.0))));
	} else if (x1 <= -2.1e-93) {
		tmp = x1 + (t_6 + (x1 + (t_4 + (t_3 + (t_0 * ((2.0 * x2) - x1))))));
	} else if (x1 <= 8.2e-247) {
		tmp = x1 + (t_6 + (x1 + (4.0 * (-3.0 * (x1 * x2)))));
	} else if (x1 <= 1.35e+154) {
		tmp = x1 + (t_6 + (x1 + (t_4 + ((t_0 * (((t_0 + (2.0 * x2)) - x1) / t_2)) + t_3))));
	} else {
		tmp = ((x1 * x1) - t_5) / (x1 - (x2 * -6.0));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: tmp
    t_0 = x1 * (x1 * 3.0d0)
    t_1 = 4.0d0 * (x1 * (x2 * ((2.0d0 * x2) - 3.0d0)))
    t_2 = (x1 * x1) + 1.0d0
    t_3 = t_2 * t_1
    t_4 = x1 * (x1 * x1)
    t_5 = (x2 * x2) * 36.0d0
    t_6 = 3.0d0 * (((t_0 - (2.0d0 * x2)) - x1) / t_2)
    if (x1 <= (-3.3d+94)) then
        tmp = x1 + ((x1 + t_1) + ((t_5 - ((x1 * x1) * 9.0d0)) / ((x2 * (-6.0d0)) - (x1 * (-3.0d0)))))
    else if (x1 <= (-2.1d-93)) then
        tmp = x1 + (t_6 + (x1 + (t_4 + (t_3 + (t_0 * ((2.0d0 * x2) - x1))))))
    else if (x1 <= 8.2d-247) then
        tmp = x1 + (t_6 + (x1 + (4.0d0 * ((-3.0d0) * (x1 * x2)))))
    else if (x1 <= 1.35d+154) then
        tmp = x1 + (t_6 + (x1 + (t_4 + ((t_0 * (((t_0 + (2.0d0 * x2)) - x1) / t_2)) + t_3))))
    else
        tmp = ((x1 * x1) - t_5) / (x1 - (x2 * (-6.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = 4.0 * (x1 * (x2 * ((2.0 * x2) - 3.0)));
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = t_2 * t_1;
	double t_4 = x1 * (x1 * x1);
	double t_5 = (x2 * x2) * 36.0;
	double t_6 = 3.0 * (((t_0 - (2.0 * x2)) - x1) / t_2);
	double tmp;
	if (x1 <= -3.3e+94) {
		tmp = x1 + ((x1 + t_1) + ((t_5 - ((x1 * x1) * 9.0)) / ((x2 * -6.0) - (x1 * -3.0))));
	} else if (x1 <= -2.1e-93) {
		tmp = x1 + (t_6 + (x1 + (t_4 + (t_3 + (t_0 * ((2.0 * x2) - x1))))));
	} else if (x1 <= 8.2e-247) {
		tmp = x1 + (t_6 + (x1 + (4.0 * (-3.0 * (x1 * x2)))));
	} else if (x1 <= 1.35e+154) {
		tmp = x1 + (t_6 + (x1 + (t_4 + ((t_0 * (((t_0 + (2.0 * x2)) - x1) / t_2)) + t_3))));
	} else {
		tmp = ((x1 * x1) - t_5) / (x1 - (x2 * -6.0));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = 4.0 * (x1 * (x2 * ((2.0 * x2) - 3.0)))
	t_2 = (x1 * x1) + 1.0
	t_3 = t_2 * t_1
	t_4 = x1 * (x1 * x1)
	t_5 = (x2 * x2) * 36.0
	t_6 = 3.0 * (((t_0 - (2.0 * x2)) - x1) / t_2)
	tmp = 0
	if x1 <= -3.3e+94:
		tmp = x1 + ((x1 + t_1) + ((t_5 - ((x1 * x1) * 9.0)) / ((x2 * -6.0) - (x1 * -3.0))))
	elif x1 <= -2.1e-93:
		tmp = x1 + (t_6 + (x1 + (t_4 + (t_3 + (t_0 * ((2.0 * x2) - x1))))))
	elif x1 <= 8.2e-247:
		tmp = x1 + (t_6 + (x1 + (4.0 * (-3.0 * (x1 * x2)))))
	elif x1 <= 1.35e+154:
		tmp = x1 + (t_6 + (x1 + (t_4 + ((t_0 * (((t_0 + (2.0 * x2)) - x1) / t_2)) + t_3))))
	else:
		tmp = ((x1 * x1) - t_5) / (x1 - (x2 * -6.0))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(4.0 * Float64(x1 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0))))
	t_2 = Float64(Float64(x1 * x1) + 1.0)
	t_3 = Float64(t_2 * t_1)
	t_4 = Float64(x1 * Float64(x1 * x1))
	t_5 = Float64(Float64(x2 * x2) * 36.0)
	t_6 = Float64(3.0 * Float64(Float64(Float64(t_0 - Float64(2.0 * x2)) - x1) / t_2))
	tmp = 0.0
	if (x1 <= -3.3e+94)
		tmp = Float64(x1 + Float64(Float64(x1 + t_1) + Float64(Float64(t_5 - Float64(Float64(x1 * x1) * 9.0)) / Float64(Float64(x2 * -6.0) - Float64(x1 * -3.0)))));
	elseif (x1 <= -2.1e-93)
		tmp = Float64(x1 + Float64(t_6 + Float64(x1 + Float64(t_4 + Float64(t_3 + Float64(t_0 * Float64(Float64(2.0 * x2) - x1)))))));
	elseif (x1 <= 8.2e-247)
		tmp = Float64(x1 + Float64(t_6 + Float64(x1 + Float64(4.0 * Float64(-3.0 * Float64(x1 * x2))))));
	elseif (x1 <= 1.35e+154)
		tmp = Float64(x1 + Float64(t_6 + Float64(x1 + Float64(t_4 + Float64(Float64(t_0 * Float64(Float64(Float64(t_0 + Float64(2.0 * x2)) - x1) / t_2)) + t_3)))));
	else
		tmp = Float64(Float64(Float64(x1 * x1) - t_5) / Float64(x1 - Float64(x2 * -6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * 3.0);
	t_1 = 4.0 * (x1 * (x2 * ((2.0 * x2) - 3.0)));
	t_2 = (x1 * x1) + 1.0;
	t_3 = t_2 * t_1;
	t_4 = x1 * (x1 * x1);
	t_5 = (x2 * x2) * 36.0;
	t_6 = 3.0 * (((t_0 - (2.0 * x2)) - x1) / t_2);
	tmp = 0.0;
	if (x1 <= -3.3e+94)
		tmp = x1 + ((x1 + t_1) + ((t_5 - ((x1 * x1) * 9.0)) / ((x2 * -6.0) - (x1 * -3.0))));
	elseif (x1 <= -2.1e-93)
		tmp = x1 + (t_6 + (x1 + (t_4 + (t_3 + (t_0 * ((2.0 * x2) - x1))))));
	elseif (x1 <= 8.2e-247)
		tmp = x1 + (t_6 + (x1 + (4.0 * (-3.0 * (x1 * x2)))));
	elseif (x1 <= 1.35e+154)
		tmp = x1 + (t_6 + (x1 + (t_4 + ((t_0 * (((t_0 + (2.0 * x2)) - x1) / t_2)) + t_3))));
	else
		tmp = ((x1 * x1) - t_5) / (x1 - (x2 * -6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(4.0 * N[(x1 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 * t$95$1), $MachinePrecision]}, Block[{t$95$4 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(x2 * x2), $MachinePrecision] * 36.0), $MachinePrecision]}, Block[{t$95$6 = N[(3.0 * N[(N[(N[(t$95$0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -3.3e+94], N[(x1 + N[(N[(x1 + t$95$1), $MachinePrecision] + N[(N[(t$95$5 - N[(N[(x1 * x1), $MachinePrecision] * 9.0), $MachinePrecision]), $MachinePrecision] / N[(N[(x2 * -6.0), $MachinePrecision] - N[(x1 * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -2.1e-93], N[(x1 + N[(t$95$6 + N[(x1 + N[(t$95$4 + N[(t$95$3 + N[(t$95$0 * N[(N[(2.0 * x2), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 8.2e-247], N[(x1 + N[(t$95$6 + N[(x1 + N[(4.0 * N[(-3.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.35e+154], N[(x1 + N[(t$95$6 + N[(x1 + N[(t$95$4 + N[(N[(t$95$0 * N[(N[(N[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision] + t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x1 * x1), $MachinePrecision] - t$95$5), $MachinePrecision] / N[(x1 - N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x1 < -3.3e94

   1. Initial program 4.3%

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

   2. Taylor expanded in x1 around 0 2.2%

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

   3. Taylor expanded in x1 around 0 4.5%

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

      1. flip-+ 41.5%

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

      2. *-commutative 41.5%

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

      3. *-commutative 41.5%

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

      4. *-commutative 41.5%

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

      5. *-commutative 41.5%

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

      6. *-commutative 41.5%

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

      7. *-commutative 41.5%

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

   5. Applied egg-rr 41.5%

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

      1. swap-sqr 41.5%

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

      2. metadata-eval 41.5%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + \frac{\left(x2 \cdot x2\right) \cdot \color{blue}{36} - \left(x1 \cdot -3\right) \cdot \left(x1 \cdot -3\right)}{x2 \cdot -6 - x1 \cdot -3}\right) \]

      3. swap-sqr 41.5%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + \frac{\left(x2 \cdot x2\right) \cdot 36 - \color{blue}{\left(x1 \cdot x1\right) \cdot \left(-3 \cdot -3\right)}}{x2 \cdot -6 - x1 \cdot -3}\right) \]

      4. metadata-eval 41.5%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + \frac{\left(x2 \cdot x2\right) \cdot 36 - \left(x1 \cdot x1\right) \cdot \color{blue}{9}}{x2 \cdot -6 - x1 \cdot -3}\right) \]

      5. *-commutative 41.5%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + \frac{\left(x2 \cdot x2\right) \cdot 36 - \left(x1 \cdot x1\right) \cdot 9}{\color{blue}{-6 \cdot x2} - x1 \cdot -3}\right) \]

   7. Simplified 41.5%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + \color{blue}{\frac{\left(x2 \cdot x2\right) \cdot 36 - \left(x1 \cdot x1\right) \cdot 9}{-6 \cdot x2 - x1 \cdot -3}}\right) \]

   if -3.3e94 < x1 < -2.1000000000000001e-93

   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 0 46.4%

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

   3. Taylor expanded in x1 around 0 44.4%

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

   4. Taylor expanded in x1 around 0 46.7%

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

   if -2.1000000000000001e-93 < x1 < 8.1999999999999997e-247

   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 87.3%

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

   3. Taylor expanded in x2 around 0 96.2%

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

      1. *-commutative 96.2%

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

   5. Simplified 96.2%

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

   if 8.1999999999999997e-247 < x1 < 1.35000000000000003e154

   1. Initial program 97.4%

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

   2. Taylor expanded in x1 around 0 81.5%

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

   3. Taylor expanded in x1 around 0 82.2%

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

   if 1.35000000000000003e154 < 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 7.4%

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

      1. *-commutative 7.4%

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

   5. Simplified 7.4%

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

      1. flip-+ 66.7%

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

   7. Applied egg-rr 66.7%

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

      1. swap-sqr 66.7%

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

      2. metadata-eval 66.7%

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

      3. *-commutative 66.7%

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

   9. Simplified 66.7%

      \[\leadsto \color{blue}{\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - -6 \cdot x2}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -3.3 \cdot 10^{+94}:\\ \;\;\;\;x1 + \left(\left(x1 + 4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right) + \frac{\left(x2 \cdot x2\right) \cdot 36 - \left(x1 \cdot x1\right) \cdot 9}{x2 \cdot -6 - x1 \cdot -3}\right)\\ \mathbf{elif}\;x1 \leq -2.1 \cdot 10^{-93}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right) + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(2 \cdot x2 - x1\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 8.2 \cdot 10^{-247}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + 4 \cdot \left(-3 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 \cdot x1 + 1\right) \cdot \left(4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - x2 \cdot -6}\\ \end{array} \]

Alternative 13: 67.6% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(x1 \cdot x1\right) \cdot 9\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := 4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ t_3 := x1 \cdot x1 + 1\\ t_4 := t_3 \cdot t_2\\ t_5 := x1 \cdot \left(x1 \cdot x1\right)\\ t_6 := \left(x2 \cdot x2\right) \cdot 36\\ t_7 := 3 \cdot \frac{\left(t_1 - 2 \cdot x2\right) - x1}{t_3}\\ \mathbf{if}\;x1 \leq -3.3 \cdot 10^{+94}:\\ \;\;\;\;x1 + \left(\left(x1 + t_2\right) + \frac{t_6 - t_0}{x2 \cdot -6 - x1 \cdot -3}\right)\\ \mathbf{elif}\;x1 \leq -2.1 \cdot 10^{-93}:\\ \;\;\;\;x1 + \left(t_7 + \left(x1 + \left(t_5 + \left(t_4 + t_1 \cdot \left(2 \cdot x2 - x1\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 8 \cdot 10^{-247}:\\ \;\;\;\;x1 + \left(t_7 + \left(x1 + 4 \cdot \left(-3 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(t_7 + \left(x1 + \left(t_5 + \left(t_0 + t_4\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1 - t_6}{x1 - x2 \cdot -6}\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* (* x1 x1) 9.0))
        (t_1 (* x1 (* x1 3.0)))
        (t_2 (* 4.0 (* x1 (* x2 (- (* 2.0 x2) 3.0)))))
        (t_3 (+ (* x1 x1) 1.0))
        (t_4 (* t_3 t_2))
        (t_5 (* x1 (* x1 x1)))
        (t_6 (* (* x2 x2) 36.0))
        (t_7 (* 3.0 (/ (- (- t_1 (* 2.0 x2)) x1) t_3))))
   (if (<= x1 -3.3e+94)
     (+ x1 (+ (+ x1 t_2) (/ (- t_6 t_0) (- (* x2 -6.0) (* x1 -3.0)))))
     (if (<= x1 -2.1e-93)
       (+ x1 (+ t_7 (+ x1 (+ t_5 (+ t_4 (* t_1 (- (* 2.0 x2) x1)))))))
       (if (<= x1 8e-247)
         (+ x1 (+ t_7 (+ x1 (* 4.0 (* -3.0 (* x1 x2))))))
         (if (<= x1 1.35e+154)
           (+ x1 (+ t_7 (+ x1 (+ t_5 (+ t_0 t_4)))))
           (/ (- (* x1 x1) t_6) (- x1 (* x2 -6.0)))))))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * x1) * 9.0;
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = 4.0 * (x1 * (x2 * ((2.0 * x2) - 3.0)));
	double t_3 = (x1 * x1) + 1.0;
	double t_4 = t_3 * t_2;
	double t_5 = x1 * (x1 * x1);
	double t_6 = (x2 * x2) * 36.0;
	double t_7 = 3.0 * (((t_1 - (2.0 * x2)) - x1) / t_3);
	double tmp;
	if (x1 <= -3.3e+94) {
		tmp = x1 + ((x1 + t_2) + ((t_6 - t_0) / ((x2 * -6.0) - (x1 * -3.0))));
	} else if (x1 <= -2.1e-93) {
		tmp = x1 + (t_7 + (x1 + (t_5 + (t_4 + (t_1 * ((2.0 * x2) - x1))))));
	} else if (x1 <= 8e-247) {
		tmp = x1 + (t_7 + (x1 + (4.0 * (-3.0 * (x1 * x2)))));
	} else if (x1 <= 1.35e+154) {
		tmp = x1 + (t_7 + (x1 + (t_5 + (t_0 + t_4))));
	} else {
		tmp = ((x1 * x1) - t_6) / (x1 - (x2 * -6.0));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: 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) * 9.0d0
    t_1 = x1 * (x1 * 3.0d0)
    t_2 = 4.0d0 * (x1 * (x2 * ((2.0d0 * x2) - 3.0d0)))
    t_3 = (x1 * x1) + 1.0d0
    t_4 = t_3 * t_2
    t_5 = x1 * (x1 * x1)
    t_6 = (x2 * x2) * 36.0d0
    t_7 = 3.0d0 * (((t_1 - (2.0d0 * x2)) - x1) / t_3)
    if (x1 <= (-3.3d+94)) then
        tmp = x1 + ((x1 + t_2) + ((t_6 - t_0) / ((x2 * (-6.0d0)) - (x1 * (-3.0d0)))))
    else if (x1 <= (-2.1d-93)) then
        tmp = x1 + (t_7 + (x1 + (t_5 + (t_4 + (t_1 * ((2.0d0 * x2) - x1))))))
    else if (x1 <= 8d-247) then
        tmp = x1 + (t_7 + (x1 + (4.0d0 * ((-3.0d0) * (x1 * x2)))))
    else if (x1 <= 1.35d+154) then
        tmp = x1 + (t_7 + (x1 + (t_5 + (t_0 + t_4))))
    else
        tmp = ((x1 * x1) - t_6) / (x1 - (x2 * (-6.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (x1 * x1) * 9.0;
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = 4.0 * (x1 * (x2 * ((2.0 * x2) - 3.0)));
	double t_3 = (x1 * x1) + 1.0;
	double t_4 = t_3 * t_2;
	double t_5 = x1 * (x1 * x1);
	double t_6 = (x2 * x2) * 36.0;
	double t_7 = 3.0 * (((t_1 - (2.0 * x2)) - x1) / t_3);
	double tmp;
	if (x1 <= -3.3e+94) {
		tmp = x1 + ((x1 + t_2) + ((t_6 - t_0) / ((x2 * -6.0) - (x1 * -3.0))));
	} else if (x1 <= -2.1e-93) {
		tmp = x1 + (t_7 + (x1 + (t_5 + (t_4 + (t_1 * ((2.0 * x2) - x1))))));
	} else if (x1 <= 8e-247) {
		tmp = x1 + (t_7 + (x1 + (4.0 * (-3.0 * (x1 * x2)))));
	} else if (x1 <= 1.35e+154) {
		tmp = x1 + (t_7 + (x1 + (t_5 + (t_0 + t_4))));
	} else {
		tmp = ((x1 * x1) - t_6) / (x1 - (x2 * -6.0));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x1 * x1) * 9.0
	t_1 = x1 * (x1 * 3.0)
	t_2 = 4.0 * (x1 * (x2 * ((2.0 * x2) - 3.0)))
	t_3 = (x1 * x1) + 1.0
	t_4 = t_3 * t_2
	t_5 = x1 * (x1 * x1)
	t_6 = (x2 * x2) * 36.0
	t_7 = 3.0 * (((t_1 - (2.0 * x2)) - x1) / t_3)
	tmp = 0
	if x1 <= -3.3e+94:
		tmp = x1 + ((x1 + t_2) + ((t_6 - t_0) / ((x2 * -6.0) - (x1 * -3.0))))
	elif x1 <= -2.1e-93:
		tmp = x1 + (t_7 + (x1 + (t_5 + (t_4 + (t_1 * ((2.0 * x2) - x1))))))
	elif x1 <= 8e-247:
		tmp = x1 + (t_7 + (x1 + (4.0 * (-3.0 * (x1 * x2)))))
	elif x1 <= 1.35e+154:
		tmp = x1 + (t_7 + (x1 + (t_5 + (t_0 + t_4))))
	else:
		tmp = ((x1 * x1) - t_6) / (x1 - (x2 * -6.0))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * x1) * 9.0)
	t_1 = Float64(x1 * Float64(x1 * 3.0))
	t_2 = Float64(4.0 * Float64(x1 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0))))
	t_3 = Float64(Float64(x1 * x1) + 1.0)
	t_4 = Float64(t_3 * t_2)
	t_5 = Float64(x1 * Float64(x1 * x1))
	t_6 = Float64(Float64(x2 * x2) * 36.0)
	t_7 = Float64(3.0 * Float64(Float64(Float64(t_1 - Float64(2.0 * x2)) - x1) / t_3))
	tmp = 0.0
	if (x1 <= -3.3e+94)
		tmp = Float64(x1 + Float64(Float64(x1 + t_2) + Float64(Float64(t_6 - t_0) / Float64(Float64(x2 * -6.0) - Float64(x1 * -3.0)))));
	elseif (x1 <= -2.1e-93)
		tmp = Float64(x1 + Float64(t_7 + Float64(x1 + Float64(t_5 + Float64(t_4 + Float64(t_1 * Float64(Float64(2.0 * x2) - x1)))))));
	elseif (x1 <= 8e-247)
		tmp = Float64(x1 + Float64(t_7 + Float64(x1 + Float64(4.0 * Float64(-3.0 * Float64(x1 * x2))))));
	elseif (x1 <= 1.35e+154)
		tmp = Float64(x1 + Float64(t_7 + Float64(x1 + Float64(t_5 + Float64(t_0 + t_4)))));
	else
		tmp = Float64(Float64(Float64(x1 * x1) - t_6) / Float64(x1 - Float64(x2 * -6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x1 * x1) * 9.0;
	t_1 = x1 * (x1 * 3.0);
	t_2 = 4.0 * (x1 * (x2 * ((2.0 * x2) - 3.0)));
	t_3 = (x1 * x1) + 1.0;
	t_4 = t_3 * t_2;
	t_5 = x1 * (x1 * x1);
	t_6 = (x2 * x2) * 36.0;
	t_7 = 3.0 * (((t_1 - (2.0 * x2)) - x1) / t_3);
	tmp = 0.0;
	if (x1 <= -3.3e+94)
		tmp = x1 + ((x1 + t_2) + ((t_6 - t_0) / ((x2 * -6.0) - (x1 * -3.0))));
	elseif (x1 <= -2.1e-93)
		tmp = x1 + (t_7 + (x1 + (t_5 + (t_4 + (t_1 * ((2.0 * x2) - x1))))));
	elseif (x1 <= 8e-247)
		tmp = x1 + (t_7 + (x1 + (4.0 * (-3.0 * (x1 * x2)))));
	elseif (x1 <= 1.35e+154)
		tmp = x1 + (t_7 + (x1 + (t_5 + (t_0 + t_4))));
	else
		tmp = ((x1 * x1) - t_6) / (x1 - (x2 * -6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x1 * x1), $MachinePrecision] * 9.0), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(4.0 * N[(x1 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$3 * t$95$2), $MachinePrecision]}, Block[{t$95$5 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(x2 * x2), $MachinePrecision] * 36.0), $MachinePrecision]}, Block[{t$95$7 = N[(3.0 * N[(N[(N[(t$95$1 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$3), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -3.3e+94], N[(x1 + N[(N[(x1 + t$95$2), $MachinePrecision] + N[(N[(t$95$6 - t$95$0), $MachinePrecision] / N[(N[(x2 * -6.0), $MachinePrecision] - N[(x1 * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -2.1e-93], N[(x1 + N[(t$95$7 + N[(x1 + N[(t$95$5 + N[(t$95$4 + N[(t$95$1 * N[(N[(2.0 * x2), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 8e-247], N[(x1 + N[(t$95$7 + N[(x1 + N[(4.0 * N[(-3.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.35e+154], N[(x1 + N[(t$95$7 + N[(x1 + N[(t$95$5 + N[(t$95$0 + t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x1 * x1), $MachinePrecision] - t$95$6), $MachinePrecision] / N[(x1 - N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x1 < -3.3e94

   1. Initial program 4.3%

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

   2. Taylor expanded in x1 around 0 2.2%

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

   3. Taylor expanded in x1 around 0 4.5%

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

      1. flip-+ 41.5%

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

      2. *-commutative 41.5%

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

      3. *-commutative 41.5%

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

      4. *-commutative 41.5%

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

      5. *-commutative 41.5%

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

      6. *-commutative 41.5%

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

      7. *-commutative 41.5%

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

   5. Applied egg-rr 41.5%

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

      1. swap-sqr 41.5%

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

      2. metadata-eval 41.5%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + \frac{\left(x2 \cdot x2\right) \cdot \color{blue}{36} - \left(x1 \cdot -3\right) \cdot \left(x1 \cdot -3\right)}{x2 \cdot -6 - x1 \cdot -3}\right) \]

      3. swap-sqr 41.5%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + \frac{\left(x2 \cdot x2\right) \cdot 36 - \color{blue}{\left(x1 \cdot x1\right) \cdot \left(-3 \cdot -3\right)}}{x2 \cdot -6 - x1 \cdot -3}\right) \]

      4. metadata-eval 41.5%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + \frac{\left(x2 \cdot x2\right) \cdot 36 - \left(x1 \cdot x1\right) \cdot \color{blue}{9}}{x2 \cdot -6 - x1 \cdot -3}\right) \]

      5. *-commutative 41.5%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + \frac{\left(x2 \cdot x2\right) \cdot 36 - \left(x1 \cdot x1\right) \cdot 9}{\color{blue}{-6 \cdot x2} - x1 \cdot -3}\right) \]

   7. Simplified 41.5%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + \color{blue}{\frac{\left(x2 \cdot x2\right) \cdot 36 - \left(x1 \cdot x1\right) \cdot 9}{-6 \cdot x2 - x1 \cdot -3}}\right) \]

   if -3.3e94 < x1 < -2.1000000000000001e-93

   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 0 46.4%

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

   3. Taylor expanded in x1 around 0 44.4%

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

   4. Taylor expanded in x1 around 0 46.7%

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

   if -2.1000000000000001e-93 < x1 < 8.0000000000000002e-247

   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 87.3%

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

   3. Taylor expanded in x2 around 0 96.2%

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

      1. *-commutative 96.2%

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

   5. Simplified 96.2%

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

   if 8.0000000000000002e-247 < x1 < 1.35000000000000003e154

   1. Initial program 97.4%

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

   2. Taylor expanded in x1 around 0 81.5%

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

   3. Taylor expanded in x1 around 0 82.2%

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

   4. Taylor expanded in x1 around inf 82.1%

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

      1. *-commutative 82.1%

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

      2. unpow2 82.1%

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

   6. Simplified 82.1%

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

   if 1.35000000000000003e154 < 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 7.4%

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

      1. *-commutative 7.4%

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

   5. Simplified 7.4%

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

      1. flip-+ 66.7%

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

   7. Applied egg-rr 66.7%

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

      1. swap-sqr 66.7%

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

      2. metadata-eval 66.7%

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

      3. *-commutative 66.7%

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

   9. Simplified 66.7%

      \[\leadsto \color{blue}{\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - -6 \cdot x2}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -3.3 \cdot 10^{+94}:\\ \;\;\;\;x1 + \left(\left(x1 + 4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right) + \frac{\left(x2 \cdot x2\right) \cdot 36 - \left(x1 \cdot x1\right) \cdot 9}{x2 \cdot -6 - x1 \cdot -3}\right)\\ \mathbf{elif}\;x1 \leq -2.1 \cdot 10^{-93}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right) + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(2 \cdot x2 - x1\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 8 \cdot 10^{-247}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + 4 \cdot \left(-3 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot x1\right) \cdot 9 + \left(x1 \cdot x1 + 1\right) \cdot \left(4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - x2 \cdot -6}\\ \end{array} \]

Alternative 14: 69.4% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := \left(x2 \cdot x2\right) \cdot 36\\ t_2 := \left(x1 \cdot x1\right) \cdot 9\\ t_3 := x2 \cdot \left(2 \cdot x2 - 3\right)\\ t_4 := 4 \cdot \left(x1 \cdot t_3\right)\\ t_5 := 3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{t_0}\\ \mathbf{if}\;x1 \leq -3.8 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(\left(x1 + t_4\right) + \frac{t_1 - t_2}{x2 \cdot -6 - x1 \cdot -3}\right)\\ \mathbf{elif}\;x1 \leq -2.1 \cdot 10^{-226}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(4 \cdot t_3 - 2\right)\right)\\ \mathbf{elif}\;x1 \leq 6 \cdot 10^{-247}:\\ \;\;\;\;x1 + \left(t_5 + \left(x1 + 4 \cdot \left(-3 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(t_5 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(t_2 + t_0 \cdot t_4\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1 - t_1}{x1 - x2 \cdot -6}\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ (* x1 x1) 1.0))
        (t_1 (* (* x2 x2) 36.0))
        (t_2 (* (* x1 x1) 9.0))
        (t_3 (* x2 (- (* 2.0 x2) 3.0)))
        (t_4 (* 4.0 (* x1 t_3)))
        (t_5 (* 3.0 (/ (- (- (* x1 (* x1 3.0)) (* 2.0 x2)) x1) t_0))))
   (if (<= x1 -3.8e+154)
     (+ x1 (+ (+ x1 t_4) (/ (- t_1 t_2) (- (* x2 -6.0) (* x1 -3.0)))))
     (if (<= x1 -2.1e-226)
       (+ x1 (+ (* x2 -6.0) (* x1 (- (* 4.0 t_3) 2.0))))
       (if (<= x1 6e-247)
         (+ x1 (+ t_5 (+ x1 (* 4.0 (* -3.0 (* x1 x2))))))
         (if (<= x1 1.35e+154)
           (+ x1 (+ t_5 (+ x1 (+ (* x1 (* x1 x1)) (+ t_2 (* t_0 t_4))))))
           (/ (- (* x1 x1) t_1) (- x1 (* x2 -6.0)))))))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = (x2 * x2) * 36.0;
	double t_2 = (x1 * x1) * 9.0;
	double t_3 = x2 * ((2.0 * x2) - 3.0);
	double t_4 = 4.0 * (x1 * t_3);
	double t_5 = 3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / t_0);
	double tmp;
	if (x1 <= -3.8e+154) {
		tmp = x1 + ((x1 + t_4) + ((t_1 - t_2) / ((x2 * -6.0) - (x1 * -3.0))));
	} else if (x1 <= -2.1e-226) {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((4.0 * t_3) - 2.0)));
	} else if (x1 <= 6e-247) {
		tmp = x1 + (t_5 + (x1 + (4.0 * (-3.0 * (x1 * x2)))));
	} else if (x1 <= 1.35e+154) {
		tmp = x1 + (t_5 + (x1 + ((x1 * (x1 * x1)) + (t_2 + (t_0 * t_4)))));
	} else {
		tmp = ((x1 * x1) - t_1) / (x1 - (x2 * -6.0));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_0 = (x1 * x1) + 1.0d0
    t_1 = (x2 * x2) * 36.0d0
    t_2 = (x1 * x1) * 9.0d0
    t_3 = x2 * ((2.0d0 * x2) - 3.0d0)
    t_4 = 4.0d0 * (x1 * t_3)
    t_5 = 3.0d0 * ((((x1 * (x1 * 3.0d0)) - (2.0d0 * x2)) - x1) / t_0)
    if (x1 <= (-3.8d+154)) then
        tmp = x1 + ((x1 + t_4) + ((t_1 - t_2) / ((x2 * (-6.0d0)) - (x1 * (-3.0d0)))))
    else if (x1 <= (-2.1d-226)) then
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * ((4.0d0 * t_3) - 2.0d0)))
    else if (x1 <= 6d-247) then
        tmp = x1 + (t_5 + (x1 + (4.0d0 * ((-3.0d0) * (x1 * x2)))))
    else if (x1 <= 1.35d+154) then
        tmp = x1 + (t_5 + (x1 + ((x1 * (x1 * x1)) + (t_2 + (t_0 * t_4)))))
    else
        tmp = ((x1 * x1) - t_1) / (x1 - (x2 * (-6.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = (x2 * x2) * 36.0;
	double t_2 = (x1 * x1) * 9.0;
	double t_3 = x2 * ((2.0 * x2) - 3.0);
	double t_4 = 4.0 * (x1 * t_3);
	double t_5 = 3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / t_0);
	double tmp;
	if (x1 <= -3.8e+154) {
		tmp = x1 + ((x1 + t_4) + ((t_1 - t_2) / ((x2 * -6.0) - (x1 * -3.0))));
	} else if (x1 <= -2.1e-226) {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((4.0 * t_3) - 2.0)));
	} else if (x1 <= 6e-247) {
		tmp = x1 + (t_5 + (x1 + (4.0 * (-3.0 * (x1 * x2)))));
	} else if (x1 <= 1.35e+154) {
		tmp = x1 + (t_5 + (x1 + ((x1 * (x1 * x1)) + (t_2 + (t_0 * t_4)))));
	} else {
		tmp = ((x1 * x1) - t_1) / (x1 - (x2 * -6.0));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x1 * x1) + 1.0
	t_1 = (x2 * x2) * 36.0
	t_2 = (x1 * x1) * 9.0
	t_3 = x2 * ((2.0 * x2) - 3.0)
	t_4 = 4.0 * (x1 * t_3)
	t_5 = 3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / t_0)
	tmp = 0
	if x1 <= -3.8e+154:
		tmp = x1 + ((x1 + t_4) + ((t_1 - t_2) / ((x2 * -6.0) - (x1 * -3.0))))
	elif x1 <= -2.1e-226:
		tmp = x1 + ((x2 * -6.0) + (x1 * ((4.0 * t_3) - 2.0)))
	elif x1 <= 6e-247:
		tmp = x1 + (t_5 + (x1 + (4.0 * (-3.0 * (x1 * x2)))))
	elif x1 <= 1.35e+154:
		tmp = x1 + (t_5 + (x1 + ((x1 * (x1 * x1)) + (t_2 + (t_0 * t_4)))))
	else:
		tmp = ((x1 * x1) - t_1) / (x1 - (x2 * -6.0))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * x1) + 1.0)
	t_1 = Float64(Float64(x2 * x2) * 36.0)
	t_2 = Float64(Float64(x1 * x1) * 9.0)
	t_3 = Float64(x2 * Float64(Float64(2.0 * x2) - 3.0))
	t_4 = Float64(4.0 * Float64(x1 * t_3))
	t_5 = Float64(3.0 * Float64(Float64(Float64(Float64(x1 * Float64(x1 * 3.0)) - Float64(2.0 * x2)) - x1) / t_0))
	tmp = 0.0
	if (x1 <= -3.8e+154)
		tmp = Float64(x1 + Float64(Float64(x1 + t_4) + Float64(Float64(t_1 - t_2) / Float64(Float64(x2 * -6.0) - Float64(x1 * -3.0)))));
	elseif (x1 <= -2.1e-226)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(4.0 * t_3) - 2.0))));
	elseif (x1 <= 6e-247)
		tmp = Float64(x1 + Float64(t_5 + Float64(x1 + Float64(4.0 * Float64(-3.0 * Float64(x1 * x2))))));
	elseif (x1 <= 1.35e+154)
		tmp = Float64(x1 + Float64(t_5 + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(t_2 + Float64(t_0 * t_4))))));
	else
		tmp = Float64(Float64(Float64(x1 * x1) - t_1) / Float64(x1 - Float64(x2 * -6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x1 * x1) + 1.0;
	t_1 = (x2 * x2) * 36.0;
	t_2 = (x1 * x1) * 9.0;
	t_3 = x2 * ((2.0 * x2) - 3.0);
	t_4 = 4.0 * (x1 * t_3);
	t_5 = 3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / t_0);
	tmp = 0.0;
	if (x1 <= -3.8e+154)
		tmp = x1 + ((x1 + t_4) + ((t_1 - t_2) / ((x2 * -6.0) - (x1 * -3.0))));
	elseif (x1 <= -2.1e-226)
		tmp = x1 + ((x2 * -6.0) + (x1 * ((4.0 * t_3) - 2.0)));
	elseif (x1 <= 6e-247)
		tmp = x1 + (t_5 + (x1 + (4.0 * (-3.0 * (x1 * x2)))));
	elseif (x1 <= 1.35e+154)
		tmp = x1 + (t_5 + (x1 + ((x1 * (x1 * x1)) + (t_2 + (t_0 * t_4)))));
	else
		tmp = ((x1 * x1) - t_1) / (x1 - (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[(N[(x2 * x2), $MachinePrecision] * 36.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x1 * x1), $MachinePrecision] * 9.0), $MachinePrecision]}, Block[{t$95$3 = N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(4.0 * N[(x1 * t$95$3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(3.0 * N[(N[(N[(N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision] - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -3.8e+154], N[(x1 + N[(N[(x1 + t$95$4), $MachinePrecision] + N[(N[(t$95$1 - t$95$2), $MachinePrecision] / N[(N[(x2 * -6.0), $MachinePrecision] - N[(x1 * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -2.1e-226], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(4.0 * t$95$3), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 6e-247], N[(x1 + N[(t$95$5 + N[(x1 + N[(4.0 * N[(-3.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.35e+154], N[(x1 + N[(t$95$5 + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(t$95$2 + N[(t$95$0 * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x1 * x1), $MachinePrecision] - t$95$1), $MachinePrecision] / N[(x1 - N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x1 < -3.7999999999999998e154

   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 2.8%

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

      1. flip-+ 50.0%

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

      2. *-commutative 50.0%

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

      3. *-commutative 50.0%

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

      4. *-commutative 50.0%

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

      5. *-commutative 50.0%

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

      6. *-commutative 50.0%

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

      7. *-commutative 50.0%

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

   5. Applied egg-rr 50.0%

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

      1. swap-sqr 50.0%

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

      2. metadata-eval 50.0%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + \frac{\left(x2 \cdot x2\right) \cdot \color{blue}{36} - \left(x1 \cdot -3\right) \cdot \left(x1 \cdot -3\right)}{x2 \cdot -6 - x1 \cdot -3}\right) \]

      3. swap-sqr 50.0%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + \frac{\left(x2 \cdot x2\right) \cdot 36 - \color{blue}{\left(x1 \cdot x1\right) \cdot \left(-3 \cdot -3\right)}}{x2 \cdot -6 - x1 \cdot -3}\right) \]

      4. metadata-eval 50.0%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + \frac{\left(x2 \cdot x2\right) \cdot 36 - \left(x1 \cdot x1\right) \cdot \color{blue}{9}}{x2 \cdot -6 - x1 \cdot -3}\right) \]

      5. *-commutative 50.0%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + \frac{\left(x2 \cdot x2\right) \cdot 36 - \left(x1 \cdot x1\right) \cdot 9}{\color{blue}{-6 \cdot x2} - x1 \cdot -3}\right) \]

   7. Simplified 50.0%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + \color{blue}{\frac{\left(x2 \cdot x2\right) \cdot 36 - \left(x1 \cdot x1\right) \cdot 9}{-6 \cdot x2 - x1 \cdot -3}}\right) \]

   if -3.7999999999999998e154 < x1 < -2.1000000000000002e-226

   1. Initial program 88.2%

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

   2. Taylor expanded in x1 around 0 59.2%

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

   3. Taylor expanded in x1 around 0 59.9%

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

   if -2.1000000000000002e-226 < x1 < 5.9999999999999995e-247

   1. Initial program 99.7%

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

   2. Taylor expanded in x1 around 0 79.1%

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

   3. Taylor expanded in x2 around 0 96.3%

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

      1. *-commutative 96.3%

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

   5. Simplified 96.3%

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

   if 5.9999999999999995e-247 < x1 < 1.35000000000000003e154

   1. Initial program 97.4%

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

   2. Taylor expanded in x1 around 0 81.5%

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

   3. Taylor expanded in x1 around 0 82.2%

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

   4. Taylor expanded in x1 around inf 82.1%

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

      1. *-commutative 82.1%

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

      2. unpow2 82.1%

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

   6. Simplified 82.1%

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

   if 1.35000000000000003e154 < 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 7.4%

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

      1. *-commutative 7.4%

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

   5. Simplified 7.4%

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

      1. flip-+ 66.7%

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

   7. Applied egg-rr 66.7%

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

      1. swap-sqr 66.7%

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

      2. metadata-eval 66.7%

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

      3. *-commutative 66.7%

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

   9. Simplified 66.7%

      \[\leadsto \color{blue}{\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - -6 \cdot x2}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 71.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -3.8 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(\left(x1 + 4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right) + \frac{\left(x2 \cdot x2\right) \cdot 36 - \left(x1 \cdot x1\right) \cdot 9}{x2 \cdot -6 - x1 \cdot -3}\right)\\ \mathbf{elif}\;x1 \leq -2.1 \cdot 10^{-226}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)\\ \mathbf{elif}\;x1 \leq 6 \cdot 10^{-247}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + 4 \cdot \left(-3 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot x1\right) \cdot 9 + \left(x1 \cdot x1 + 1\right) \cdot \left(4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - x2 \cdot -6}\\ \end{array} \]

Alternative 15: 69.6% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(x2 \cdot x2\right) \cdot 36\\ t_1 := x2 \cdot \left(2 \cdot x2 - 3\right)\\ t_2 := 4 \cdot \left(x1 \cdot t_1\right)\\ t_3 := 3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\\ \mathbf{if}\;x1 \leq -3.8 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(\left(x1 + t_2\right) + \frac{t_0 - \left(x1 \cdot x1\right) \cdot 9}{x2 \cdot -6 - x1 \cdot -3}\right)\\ \mathbf{elif}\;x1 \leq -4.5 \cdot 10^{-230}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(4 \cdot t_1 - 2\right)\right)\\ \mathbf{elif}\;x1 \leq 8.2 \cdot 10^{-247}:\\ \;\;\;\;x1 + \left(t_3 + \left(x1 + 4 \cdot \left(-3 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(t_3 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + t_2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1 - t_0}{x1 - x2 \cdot -6}\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* (* x2 x2) 36.0))
        (t_1 (* x2 (- (* 2.0 x2) 3.0)))
        (t_2 (* 4.0 (* x1 t_1)))
        (t_3
         (*
          3.0
          (/ (- (- (* x1 (* x1 3.0)) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0)))))
   (if (<= x1 -3.8e+154)
     (+
      x1
      (+ (+ x1 t_2) (/ (- t_0 (* (* x1 x1) 9.0)) (- (* x2 -6.0) (* x1 -3.0)))))
     (if (<= x1 -4.5e-230)
       (+ x1 (+ (* x2 -6.0) (* x1 (- (* 4.0 t_1) 2.0))))
       (if (<= x1 8.2e-247)
         (+ x1 (+ t_3 (+ x1 (* 4.0 (* -3.0 (* x1 x2))))))
         (if (<= x1 1.35e+154)
           (+ x1 (+ t_3 (+ x1 (+ (* x1 (* x1 x1)) t_2))))
           (/ (- (* x1 x1) t_0) (- x1 (* x2 -6.0)))))))))

C

double code(double x1, double x2) {
	double t_0 = (x2 * x2) * 36.0;
	double t_1 = x2 * ((2.0 * x2) - 3.0);
	double t_2 = 4.0 * (x1 * t_1);
	double t_3 = 3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / ((x1 * x1) + 1.0));
	double tmp;
	if (x1 <= -3.8e+154) {
		tmp = x1 + ((x1 + t_2) + ((t_0 - ((x1 * x1) * 9.0)) / ((x2 * -6.0) - (x1 * -3.0))));
	} else if (x1 <= -4.5e-230) {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((4.0 * t_1) - 2.0)));
	} else if (x1 <= 8.2e-247) {
		tmp = x1 + (t_3 + (x1 + (4.0 * (-3.0 * (x1 * x2)))));
	} else if (x1 <= 1.35e+154) {
		tmp = x1 + (t_3 + (x1 + ((x1 * (x1 * x1)) + t_2)));
	} else {
		tmp = ((x1 * x1) - t_0) / (x1 - (x2 * -6.0));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_0 = (x2 * x2) * 36.0d0
    t_1 = x2 * ((2.0d0 * x2) - 3.0d0)
    t_2 = 4.0d0 * (x1 * t_1)
    t_3 = 3.0d0 * ((((x1 * (x1 * 3.0d0)) - (2.0d0 * x2)) - x1) / ((x1 * x1) + 1.0d0))
    if (x1 <= (-3.8d+154)) then
        tmp = x1 + ((x1 + t_2) + ((t_0 - ((x1 * x1) * 9.0d0)) / ((x2 * (-6.0d0)) - (x1 * (-3.0d0)))))
    else if (x1 <= (-4.5d-230)) then
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * ((4.0d0 * t_1) - 2.0d0)))
    else if (x1 <= 8.2d-247) then
        tmp = x1 + (t_3 + (x1 + (4.0d0 * ((-3.0d0) * (x1 * x2)))))
    else if (x1 <= 1.35d+154) then
        tmp = x1 + (t_3 + (x1 + ((x1 * (x1 * x1)) + t_2)))
    else
        tmp = ((x1 * x1) - t_0) / (x1 - (x2 * (-6.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (x2 * x2) * 36.0;
	double t_1 = x2 * ((2.0 * x2) - 3.0);
	double t_2 = 4.0 * (x1 * t_1);
	double t_3 = 3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / ((x1 * x1) + 1.0));
	double tmp;
	if (x1 <= -3.8e+154) {
		tmp = x1 + ((x1 + t_2) + ((t_0 - ((x1 * x1) * 9.0)) / ((x2 * -6.0) - (x1 * -3.0))));
	} else if (x1 <= -4.5e-230) {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((4.0 * t_1) - 2.0)));
	} else if (x1 <= 8.2e-247) {
		tmp = x1 + (t_3 + (x1 + (4.0 * (-3.0 * (x1 * x2)))));
	} else if (x1 <= 1.35e+154) {
		tmp = x1 + (t_3 + (x1 + ((x1 * (x1 * x1)) + t_2)));
	} else {
		tmp = ((x1 * x1) - t_0) / (x1 - (x2 * -6.0));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x2 * x2) * 36.0
	t_1 = x2 * ((2.0 * x2) - 3.0)
	t_2 = 4.0 * (x1 * t_1)
	t_3 = 3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / ((x1 * x1) + 1.0))
	tmp = 0
	if x1 <= -3.8e+154:
		tmp = x1 + ((x1 + t_2) + ((t_0 - ((x1 * x1) * 9.0)) / ((x2 * -6.0) - (x1 * -3.0))))
	elif x1 <= -4.5e-230:
		tmp = x1 + ((x2 * -6.0) + (x1 * ((4.0 * t_1) - 2.0)))
	elif x1 <= 8.2e-247:
		tmp = x1 + (t_3 + (x1 + (4.0 * (-3.0 * (x1 * x2)))))
	elif x1 <= 1.35e+154:
		tmp = x1 + (t_3 + (x1 + ((x1 * (x1 * x1)) + t_2)))
	else:
		tmp = ((x1 * x1) - t_0) / (x1 - (x2 * -6.0))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x2 * x2) * 36.0)
	t_1 = Float64(x2 * Float64(Float64(2.0 * x2) - 3.0))
	t_2 = Float64(4.0 * Float64(x1 * t_1))
	t_3 = Float64(3.0 * Float64(Float64(Float64(Float64(x1 * Float64(x1 * 3.0)) - Float64(2.0 * x2)) - x1) / Float64(Float64(x1 * x1) + 1.0)))
	tmp = 0.0
	if (x1 <= -3.8e+154)
		tmp = Float64(x1 + Float64(Float64(x1 + t_2) + Float64(Float64(t_0 - Float64(Float64(x1 * x1) * 9.0)) / Float64(Float64(x2 * -6.0) - Float64(x1 * -3.0)))));
	elseif (x1 <= -4.5e-230)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(4.0 * t_1) - 2.0))));
	elseif (x1 <= 8.2e-247)
		tmp = Float64(x1 + Float64(t_3 + Float64(x1 + Float64(4.0 * Float64(-3.0 * Float64(x1 * x2))))));
	elseif (x1 <= 1.35e+154)
		tmp = Float64(x1 + Float64(t_3 + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + t_2))));
	else
		tmp = Float64(Float64(Float64(x1 * x1) - t_0) / Float64(x1 - Float64(x2 * -6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x2 * x2) * 36.0;
	t_1 = x2 * ((2.0 * x2) - 3.0);
	t_2 = 4.0 * (x1 * t_1);
	t_3 = 3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / ((x1 * x1) + 1.0));
	tmp = 0.0;
	if (x1 <= -3.8e+154)
		tmp = x1 + ((x1 + t_2) + ((t_0 - ((x1 * x1) * 9.0)) / ((x2 * -6.0) - (x1 * -3.0))));
	elseif (x1 <= -4.5e-230)
		tmp = x1 + ((x2 * -6.0) + (x1 * ((4.0 * t_1) - 2.0)));
	elseif (x1 <= 8.2e-247)
		tmp = x1 + (t_3 + (x1 + (4.0 * (-3.0 * (x1 * x2)))));
	elseif (x1 <= 1.35e+154)
		tmp = x1 + (t_3 + (x1 + ((x1 * (x1 * x1)) + t_2)));
	else
		tmp = ((x1 * x1) - t_0) / (x1 - (x2 * -6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x2 * x2), $MachinePrecision] * 36.0), $MachinePrecision]}, Block[{t$95$1 = N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(4.0 * N[(x1 * t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(3.0 * N[(N[(N[(N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision] - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -3.8e+154], N[(x1 + N[(N[(x1 + t$95$2), $MachinePrecision] + N[(N[(t$95$0 - N[(N[(x1 * x1), $MachinePrecision] * 9.0), $MachinePrecision]), $MachinePrecision] / N[(N[(x2 * -6.0), $MachinePrecision] - N[(x1 * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -4.5e-230], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(4.0 * t$95$1), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 8.2e-247], N[(x1 + N[(t$95$3 + N[(x1 + N[(4.0 * N[(-3.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.35e+154], N[(x1 + N[(t$95$3 + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x1 * x1), $MachinePrecision] - t$95$0), $MachinePrecision] / N[(x1 - N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x1 < -3.7999999999999998e154

   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 2.8%

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

      1. flip-+ 50.0%

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

      2. *-commutative 50.0%

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

      3. *-commutative 50.0%

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

      4. *-commutative 50.0%

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

      5. *-commutative 50.0%

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

      6. *-commutative 50.0%

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

      7. *-commutative 50.0%

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

   5. Applied egg-rr 50.0%

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

      1. swap-sqr 50.0%

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

      2. metadata-eval 50.0%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + \frac{\left(x2 \cdot x2\right) \cdot \color{blue}{36} - \left(x1 \cdot -3\right) \cdot \left(x1 \cdot -3\right)}{x2 \cdot -6 - x1 \cdot -3}\right) \]

      3. swap-sqr 50.0%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + \frac{\left(x2 \cdot x2\right) \cdot 36 - \color{blue}{\left(x1 \cdot x1\right) \cdot \left(-3 \cdot -3\right)}}{x2 \cdot -6 - x1 \cdot -3}\right) \]

      4. metadata-eval 50.0%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + \frac{\left(x2 \cdot x2\right) \cdot 36 - \left(x1 \cdot x1\right) \cdot \color{blue}{9}}{x2 \cdot -6 - x1 \cdot -3}\right) \]

      5. *-commutative 50.0%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + \frac{\left(x2 \cdot x2\right) \cdot 36 - \left(x1 \cdot x1\right) \cdot 9}{\color{blue}{-6 \cdot x2} - x1 \cdot -3}\right) \]

   7. Simplified 50.0%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + \color{blue}{\frac{\left(x2 \cdot x2\right) \cdot 36 - \left(x1 \cdot x1\right) \cdot 9}{-6 \cdot x2 - x1 \cdot -3}}\right) \]

   if -3.7999999999999998e154 < x1 < -4.50000000000000004e-230

   1. Initial program 88.2%

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

   2. Taylor expanded in x1 around 0 59.2%

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

   3. Taylor expanded in x1 around 0 59.9%

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

   if -4.50000000000000004e-230 < x1 < 8.1999999999999997e-247

   1. Initial program 99.7%

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

   2. Taylor expanded in x1 around 0 79.1%

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

   3. Taylor expanded in x2 around 0 96.3%

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

      1. *-commutative 96.3%

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

   5. Simplified 96.3%

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

   if 8.1999999999999997e-247 < x1 < 1.35000000000000003e154

   1. Initial program 97.4%

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

   2. Taylor expanded in x1 around 0 81.5%

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

   3. Taylor expanded in x1 around 0 82.2%

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

   4. Taylor expanded in x1 around 0 79.2%

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

   if 1.35000000000000003e154 < 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 7.4%

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

      1. *-commutative 7.4%

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

   5. Simplified 7.4%

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

      1. flip-+ 66.7%

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

   7. Applied egg-rr 66.7%

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

      1. swap-sqr 66.7%

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

      2. metadata-eval 66.7%

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

      3. *-commutative 66.7%

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

   9. Simplified 66.7%

      \[\leadsto \color{blue}{\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - -6 \cdot x2}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 70.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -3.8 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(\left(x1 + 4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right) + \frac{\left(x2 \cdot x2\right) \cdot 36 - \left(x1 \cdot x1\right) \cdot 9}{x2 \cdot -6 - x1 \cdot -3}\right)\\ \mathbf{elif}\;x1 \leq -4.5 \cdot 10^{-230}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)\\ \mathbf{elif}\;x1 \leq 8.2 \cdot 10^{-247}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + 4 \cdot \left(-3 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + 4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - x2 \cdot -6}\\ \end{array} \]

Alternative 16: 63.3% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\\ t_1 := x2 \cdot \left(2 \cdot x2 - 3\right)\\ \mathbf{if}\;x1 \leq -4.6 \cdot 10^{+101}:\\ \;\;\;\;x1 + \left(x1 + \left(x1 \cdot -3 + x2 \cdot \left(x1 \cdot -12 - 6\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -5.4 \cdot 10^{-226}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(4 \cdot t_1 - 2\right)\right)\\ \mathbf{elif}\;x1 \leq 8.2 \cdot 10^{-247}:\\ \;\;\;\;x1 + \left(t_0 + \left(x1 + 4 \cdot \left(-3 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(t_0 + \left(x1 + 4 \cdot \left(x1 \cdot t_1\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - x2 \cdot -6}\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0
         (* 3.0 (/ (- (- (* x1 (* x1 3.0)) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0))))
        (t_1 (* x2 (- (* 2.0 x2) 3.0))))
   (if (<= x1 -4.6e+101)
     (+ x1 (+ x1 (+ (* x1 -3.0) (* x2 (- (* x1 -12.0) 6.0)))))
     (if (<= x1 -5.4e-226)
       (+ x1 (+ (* x2 -6.0) (* x1 (- (* 4.0 t_1) 2.0))))
       (if (<= x1 8.2e-247)
         (+ x1 (+ t_0 (+ x1 (* 4.0 (* -3.0 (* x1 x2))))))
         (if (<= x1 1.35e+154)
           (+ x1 (+ t_0 (+ x1 (* 4.0 (* x1 t_1)))))
           (/ (- (* x1 x1) (* (* x2 x2) 36.0)) (- x1 (* x2 -6.0)))))))))

C

double code(double x1, double x2) {
	double t_0 = 3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / ((x1 * x1) + 1.0));
	double t_1 = x2 * ((2.0 * x2) - 3.0);
	double tmp;
	if (x1 <= -4.6e+101) {
		tmp = x1 + (x1 + ((x1 * -3.0) + (x2 * ((x1 * -12.0) - 6.0))));
	} else if (x1 <= -5.4e-226) {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((4.0 * t_1) - 2.0)));
	} else if (x1 <= 8.2e-247) {
		tmp = x1 + (t_0 + (x1 + (4.0 * (-3.0 * (x1 * x2)))));
	} else if (x1 <= 1.35e+154) {
		tmp = x1 + (t_0 + (x1 + (4.0 * (x1 * t_1))));
	} else {
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = 3.0d0 * ((((x1 * (x1 * 3.0d0)) - (2.0d0 * x2)) - x1) / ((x1 * x1) + 1.0d0))
    t_1 = x2 * ((2.0d0 * x2) - 3.0d0)
    if (x1 <= (-4.6d+101)) then
        tmp = x1 + (x1 + ((x1 * (-3.0d0)) + (x2 * ((x1 * (-12.0d0)) - 6.0d0))))
    else if (x1 <= (-5.4d-226)) then
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * ((4.0d0 * t_1) - 2.0d0)))
    else if (x1 <= 8.2d-247) then
        tmp = x1 + (t_0 + (x1 + (4.0d0 * ((-3.0d0) * (x1 * x2)))))
    else if (x1 <= 1.35d+154) then
        tmp = x1 + (t_0 + (x1 + (4.0d0 * (x1 * t_1))))
    else
        tmp = ((x1 * x1) - ((x2 * x2) * 36.0d0)) / (x1 - (x2 * (-6.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = 3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / ((x1 * x1) + 1.0));
	double t_1 = x2 * ((2.0 * x2) - 3.0);
	double tmp;
	if (x1 <= -4.6e+101) {
		tmp = x1 + (x1 + ((x1 * -3.0) + (x2 * ((x1 * -12.0) - 6.0))));
	} else if (x1 <= -5.4e-226) {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((4.0 * t_1) - 2.0)));
	} else if (x1 <= 8.2e-247) {
		tmp = x1 + (t_0 + (x1 + (4.0 * (-3.0 * (x1 * x2)))));
	} else if (x1 <= 1.35e+154) {
		tmp = x1 + (t_0 + (x1 + (4.0 * (x1 * t_1))));
	} else {
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = 3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / ((x1 * x1) + 1.0))
	t_1 = x2 * ((2.0 * x2) - 3.0)
	tmp = 0
	if x1 <= -4.6e+101:
		tmp = x1 + (x1 + ((x1 * -3.0) + (x2 * ((x1 * -12.0) - 6.0))))
	elif x1 <= -5.4e-226:
		tmp = x1 + ((x2 * -6.0) + (x1 * ((4.0 * t_1) - 2.0)))
	elif x1 <= 8.2e-247:
		tmp = x1 + (t_0 + (x1 + (4.0 * (-3.0 * (x1 * x2)))))
	elif x1 <= 1.35e+154:
		tmp = x1 + (t_0 + (x1 + (4.0 * (x1 * t_1))))
	else:
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(3.0 * Float64(Float64(Float64(Float64(x1 * Float64(x1 * 3.0)) - Float64(2.0 * x2)) - x1) / Float64(Float64(x1 * x1) + 1.0)))
	t_1 = Float64(x2 * Float64(Float64(2.0 * x2) - 3.0))
	tmp = 0.0
	if (x1 <= -4.6e+101)
		tmp = Float64(x1 + Float64(x1 + Float64(Float64(x1 * -3.0) + Float64(x2 * Float64(Float64(x1 * -12.0) - 6.0)))));
	elseif (x1 <= -5.4e-226)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(4.0 * t_1) - 2.0))));
	elseif (x1 <= 8.2e-247)
		tmp = Float64(x1 + Float64(t_0 + Float64(x1 + Float64(4.0 * Float64(-3.0 * Float64(x1 * x2))))));
	elseif (x1 <= 1.35e+154)
		tmp = Float64(x1 + Float64(t_0 + Float64(x1 + Float64(4.0 * Float64(x1 * t_1)))));
	else
		tmp = Float64(Float64(Float64(x1 * x1) - Float64(Float64(x2 * x2) * 36.0)) / Float64(x1 - Float64(x2 * -6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = 3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / ((x1 * x1) + 1.0));
	t_1 = x2 * ((2.0 * x2) - 3.0);
	tmp = 0.0;
	if (x1 <= -4.6e+101)
		tmp = x1 + (x1 + ((x1 * -3.0) + (x2 * ((x1 * -12.0) - 6.0))));
	elseif (x1 <= -5.4e-226)
		tmp = x1 + ((x2 * -6.0) + (x1 * ((4.0 * t_1) - 2.0)));
	elseif (x1 <= 8.2e-247)
		tmp = x1 + (t_0 + (x1 + (4.0 * (-3.0 * (x1 * x2)))));
	elseif (x1 <= 1.35e+154)
		tmp = x1 + (t_0 + (x1 + (4.0 * (x1 * t_1))));
	else
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(3.0 * N[(N[(N[(N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision] - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -4.6e+101], N[(x1 + N[(x1 + N[(N[(x1 * -3.0), $MachinePrecision] + N[(x2 * N[(N[(x1 * -12.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -5.4e-226], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(4.0 * t$95$1), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 8.2e-247], N[(x1 + N[(t$95$0 + N[(x1 + N[(4.0 * N[(-3.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.35e+154], N[(x1 + N[(t$95$0 + N[(x1 + N[(4.0 * N[(x1 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x1 * x1), $MachinePrecision] - N[(N[(x2 * x2), $MachinePrecision] * 36.0), $MachinePrecision]), $MachinePrecision] / N[(x1 - N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x1 < -4.6000000000000003e101

   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 2.4%

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

   4. Taylor expanded in x2 around 0 18.8%

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

   if -4.6000000000000003e101 < x1 < -5.40000000000000029e-226

   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 66.8%

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

   3. Taylor expanded in x1 around 0 67.5%

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

   if -5.40000000000000029e-226 < x1 < 8.1999999999999997e-247

   1. Initial program 99.7%

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

   2. Taylor expanded in x1 around 0 79.1%

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

   3. Taylor expanded in x2 around 0 96.3%

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

      1. *-commutative 96.3%

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

   5. Simplified 96.3%

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

   if 8.1999999999999997e-247 < x1 < 1.35000000000000003e154

   1. Initial program 97.4%

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

   2. Taylor expanded in x1 around 0 65.1%

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

   if 1.35000000000000003e154 < 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 7.4%

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

      1. *-commutative 7.4%

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

   5. Simplified 7.4%

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

      1. flip-+ 66.7%

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

   7. Applied egg-rr 66.7%

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

      1. swap-sqr 66.7%

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

      2. metadata-eval 66.7%

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

      3. *-commutative 66.7%

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

   9. Simplified 66.7%

      \[\leadsto \color{blue}{\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - -6 \cdot x2}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 61.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4.6 \cdot 10^{+101}:\\ \;\;\;\;x1 + \left(x1 + \left(x1 \cdot -3 + x2 \cdot \left(x1 \cdot -12 - 6\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -5.4 \cdot 10^{-226}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)\\ \mathbf{elif}\;x1 \leq 8.2 \cdot 10^{-247}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + 4 \cdot \left(-3 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + 4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - x2 \cdot -6}\\ \end{array} \]

Alternative 17: 67.1% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(x2 \cdot x2\right) \cdot 36\\ t_1 := x2 \cdot \left(2 \cdot x2 - 3\right)\\ t_2 := x1 + 4 \cdot \left(x1 \cdot t_1\right)\\ t_3 := 3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\\ \mathbf{if}\;x1 \leq -3.8 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(t_2 + \frac{t_0 - \left(x1 \cdot x1\right) \cdot 9}{x2 \cdot -6 - x1 \cdot -3}\right)\\ \mathbf{elif}\;x1 \leq -3 \cdot 10^{-227}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(4 \cdot t_1 - 2\right)\right)\\ \mathbf{elif}\;x1 \leq 1.05 \cdot 10^{-248}:\\ \;\;\;\;x1 + \left(t_3 + \left(x1 + 4 \cdot \left(-3 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(t_3 + t_2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1 - t_0}{x1 - x2 \cdot -6}\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* (* x2 x2) 36.0))
        (t_1 (* x2 (- (* 2.0 x2) 3.0)))
        (t_2 (+ x1 (* 4.0 (* x1 t_1))))
        (t_3
         (*
          3.0
          (/ (- (- (* x1 (* x1 3.0)) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0)))))
   (if (<= x1 -3.8e+154)
     (+ x1 (+ t_2 (/ (- t_0 (* (* x1 x1) 9.0)) (- (* x2 -6.0) (* x1 -3.0)))))
     (if (<= x1 -3e-227)
       (+ x1 (+ (* x2 -6.0) (* x1 (- (* 4.0 t_1) 2.0))))
       (if (<= x1 1.05e-248)
         (+ x1 (+ t_3 (+ x1 (* 4.0 (* -3.0 (* x1 x2))))))
         (if (<= x1 1.35e+154)
           (+ x1 (+ t_3 t_2))
           (/ (- (* x1 x1) t_0) (- x1 (* x2 -6.0)))))))))

C

double code(double x1, double x2) {
	double t_0 = (x2 * x2) * 36.0;
	double t_1 = x2 * ((2.0 * x2) - 3.0);
	double t_2 = x1 + (4.0 * (x1 * t_1));
	double t_3 = 3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / ((x1 * x1) + 1.0));
	double tmp;
	if (x1 <= -3.8e+154) {
		tmp = x1 + (t_2 + ((t_0 - ((x1 * x1) * 9.0)) / ((x2 * -6.0) - (x1 * -3.0))));
	} else if (x1 <= -3e-227) {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((4.0 * t_1) - 2.0)));
	} else if (x1 <= 1.05e-248) {
		tmp = x1 + (t_3 + (x1 + (4.0 * (-3.0 * (x1 * x2)))));
	} else if (x1 <= 1.35e+154) {
		tmp = x1 + (t_3 + t_2);
	} else {
		tmp = ((x1 * x1) - t_0) / (x1 - (x2 * -6.0));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_0 = (x2 * x2) * 36.0d0
    t_1 = x2 * ((2.0d0 * x2) - 3.0d0)
    t_2 = x1 + (4.0d0 * (x1 * t_1))
    t_3 = 3.0d0 * ((((x1 * (x1 * 3.0d0)) - (2.0d0 * x2)) - x1) / ((x1 * x1) + 1.0d0))
    if (x1 <= (-3.8d+154)) then
        tmp = x1 + (t_2 + ((t_0 - ((x1 * x1) * 9.0d0)) / ((x2 * (-6.0d0)) - (x1 * (-3.0d0)))))
    else if (x1 <= (-3d-227)) then
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * ((4.0d0 * t_1) - 2.0d0)))
    else if (x1 <= 1.05d-248) then
        tmp = x1 + (t_3 + (x1 + (4.0d0 * ((-3.0d0) * (x1 * x2)))))
    else if (x1 <= 1.35d+154) then
        tmp = x1 + (t_3 + t_2)
    else
        tmp = ((x1 * x1) - t_0) / (x1 - (x2 * (-6.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (x2 * x2) * 36.0;
	double t_1 = x2 * ((2.0 * x2) - 3.0);
	double t_2 = x1 + (4.0 * (x1 * t_1));
	double t_3 = 3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / ((x1 * x1) + 1.0));
	double tmp;
	if (x1 <= -3.8e+154) {
		tmp = x1 + (t_2 + ((t_0 - ((x1 * x1) * 9.0)) / ((x2 * -6.0) - (x1 * -3.0))));
	} else if (x1 <= -3e-227) {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((4.0 * t_1) - 2.0)));
	} else if (x1 <= 1.05e-248) {
		tmp = x1 + (t_3 + (x1 + (4.0 * (-3.0 * (x1 * x2)))));
	} else if (x1 <= 1.35e+154) {
		tmp = x1 + (t_3 + t_2);
	} else {
		tmp = ((x1 * x1) - t_0) / (x1 - (x2 * -6.0));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x2 * x2) * 36.0
	t_1 = x2 * ((2.0 * x2) - 3.0)
	t_2 = x1 + (4.0 * (x1 * t_1))
	t_3 = 3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / ((x1 * x1) + 1.0))
	tmp = 0
	if x1 <= -3.8e+154:
		tmp = x1 + (t_2 + ((t_0 - ((x1 * x1) * 9.0)) / ((x2 * -6.0) - (x1 * -3.0))))
	elif x1 <= -3e-227:
		tmp = x1 + ((x2 * -6.0) + (x1 * ((4.0 * t_1) - 2.0)))
	elif x1 <= 1.05e-248:
		tmp = x1 + (t_3 + (x1 + (4.0 * (-3.0 * (x1 * x2)))))
	elif x1 <= 1.35e+154:
		tmp = x1 + (t_3 + t_2)
	else:
		tmp = ((x1 * x1) - t_0) / (x1 - (x2 * -6.0))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x2 * x2) * 36.0)
	t_1 = Float64(x2 * Float64(Float64(2.0 * x2) - 3.0))
	t_2 = Float64(x1 + Float64(4.0 * Float64(x1 * t_1)))
	t_3 = Float64(3.0 * Float64(Float64(Float64(Float64(x1 * Float64(x1 * 3.0)) - Float64(2.0 * x2)) - x1) / Float64(Float64(x1 * x1) + 1.0)))
	tmp = 0.0
	if (x1 <= -3.8e+154)
		tmp = Float64(x1 + Float64(t_2 + Float64(Float64(t_0 - Float64(Float64(x1 * x1) * 9.0)) / Float64(Float64(x2 * -6.0) - Float64(x1 * -3.0)))));
	elseif (x1 <= -3e-227)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(4.0 * t_1) - 2.0))));
	elseif (x1 <= 1.05e-248)
		tmp = Float64(x1 + Float64(t_3 + Float64(x1 + Float64(4.0 * Float64(-3.0 * Float64(x1 * x2))))));
	elseif (x1 <= 1.35e+154)
		tmp = Float64(x1 + Float64(t_3 + t_2));
	else
		tmp = Float64(Float64(Float64(x1 * x1) - t_0) / Float64(x1 - Float64(x2 * -6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x2 * x2) * 36.0;
	t_1 = x2 * ((2.0 * x2) - 3.0);
	t_2 = x1 + (4.0 * (x1 * t_1));
	t_3 = 3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / ((x1 * x1) + 1.0));
	tmp = 0.0;
	if (x1 <= -3.8e+154)
		tmp = x1 + (t_2 + ((t_0 - ((x1 * x1) * 9.0)) / ((x2 * -6.0) - (x1 * -3.0))));
	elseif (x1 <= -3e-227)
		tmp = x1 + ((x2 * -6.0) + (x1 * ((4.0 * t_1) - 2.0)));
	elseif (x1 <= 1.05e-248)
		tmp = x1 + (t_3 + (x1 + (4.0 * (-3.0 * (x1 * x2)))));
	elseif (x1 <= 1.35e+154)
		tmp = x1 + (t_3 + t_2);
	else
		tmp = ((x1 * x1) - t_0) / (x1 - (x2 * -6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x2 * x2), $MachinePrecision] * 36.0), $MachinePrecision]}, Block[{t$95$1 = N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x1 + N[(4.0 * N[(x1 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(3.0 * N[(N[(N[(N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision] - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -3.8e+154], N[(x1 + N[(t$95$2 + N[(N[(t$95$0 - N[(N[(x1 * x1), $MachinePrecision] * 9.0), $MachinePrecision]), $MachinePrecision] / N[(N[(x2 * -6.0), $MachinePrecision] - N[(x1 * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -3e-227], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(4.0 * t$95$1), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.05e-248], N[(x1 + N[(t$95$3 + N[(x1 + N[(4.0 * N[(-3.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.35e+154], N[(x1 + N[(t$95$3 + t$95$2), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x1 * x1), $MachinePrecision] - t$95$0), $MachinePrecision] / N[(x1 - N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x1 < -3.7999999999999998e154

   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 2.8%

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

      1. flip-+ 50.0%

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

      2. *-commutative 50.0%

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

      3. *-commutative 50.0%

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

      4. *-commutative 50.0%

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

      5. *-commutative 50.0%

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

      6. *-commutative 50.0%

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

      7. *-commutative 50.0%

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

   5. Applied egg-rr 50.0%

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

      1. swap-sqr 50.0%

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

      2. metadata-eval 50.0%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + \frac{\left(x2 \cdot x2\right) \cdot \color{blue}{36} - \left(x1 \cdot -3\right) \cdot \left(x1 \cdot -3\right)}{x2 \cdot -6 - x1 \cdot -3}\right) \]

      3. swap-sqr 50.0%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + \frac{\left(x2 \cdot x2\right) \cdot 36 - \color{blue}{\left(x1 \cdot x1\right) \cdot \left(-3 \cdot -3\right)}}{x2 \cdot -6 - x1 \cdot -3}\right) \]

      4. metadata-eval 50.0%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + \frac{\left(x2 \cdot x2\right) \cdot 36 - \left(x1 \cdot x1\right) \cdot \color{blue}{9}}{x2 \cdot -6 - x1 \cdot -3}\right) \]

      5. *-commutative 50.0%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + \frac{\left(x2 \cdot x2\right) \cdot 36 - \left(x1 \cdot x1\right) \cdot 9}{\color{blue}{-6 \cdot x2} - x1 \cdot -3}\right) \]

   7. Simplified 50.0%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + \color{blue}{\frac{\left(x2 \cdot x2\right) \cdot 36 - \left(x1 \cdot x1\right) \cdot 9}{-6 \cdot x2 - x1 \cdot -3}}\right) \]

   if -3.7999999999999998e154 < x1 < -3e-227

   1. Initial program 88.2%

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

   2. Taylor expanded in x1 around 0 59.2%

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

   3. Taylor expanded in x1 around 0 59.9%

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

   if -3e-227 < x1 < 1.05e-248

   1. Initial program 99.7%

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

   2. Taylor expanded in x1 around 0 79.1%

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

   3. Taylor expanded in x2 around 0 96.3%

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

      1. *-commutative 96.3%

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

   5. Simplified 96.3%

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

   if 1.05e-248 < x1 < 1.35000000000000003e154

   1. Initial program 97.4%

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

   2. Taylor expanded in x1 around 0 65.1%

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

   if 1.35000000000000003e154 < 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 7.4%

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

      1. *-commutative 7.4%

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

   5. Simplified 7.4%

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

      1. flip-+ 66.7%

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

   7. Applied egg-rr 66.7%

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

      1. swap-sqr 66.7%

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

      2. metadata-eval 66.7%

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

      3. *-commutative 66.7%

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

   9. Simplified 66.7%

      \[\leadsto \color{blue}{\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - -6 \cdot x2}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -3.8 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(\left(x1 + 4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right) + \frac{\left(x2 \cdot x2\right) \cdot 36 - \left(x1 \cdot x1\right) \cdot 9}{x2 \cdot -6 - x1 \cdot -3}\right)\\ \mathbf{elif}\;x1 \leq -3 \cdot 10^{-227}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)\\ \mathbf{elif}\;x1 \leq 1.05 \cdot 10^{-248}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + 4 \cdot \left(-3 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + 4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - x2 \cdot -6}\\ \end{array} \]

Alternative 18: 62.3% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 + \left(x2 \cdot -6 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)\\ \mathbf{if}\;x1 \leq -4.6 \cdot 10^{+101}:\\ \;\;\;\;x1 + \left(x1 + \left(x1 \cdot -3 + x2 \cdot \left(x1 \cdot -12 - 6\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -3.9 \cdot 10^{-228}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x1 \leq 6.5 \cdot 10^{-247}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + 4 \cdot \left(-3 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.04 \cdot 10^{+121}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - x2 \cdot -6}\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0
         (+
          x1
          (+ (* x2 -6.0) (* x1 (- (* 4.0 (* x2 (- (* 2.0 x2) 3.0))) 2.0))))))
   (if (<= x1 -4.6e+101)
     (+ x1 (+ x1 (+ (* x1 -3.0) (* x2 (- (* x1 -12.0) 6.0)))))
     (if (<= x1 -3.9e-228)
       t_0
       (if (<= x1 6.5e-247)
         (+
          x1
          (+
           (*
            3.0
            (/ (- (- (* x1 (* x1 3.0)) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0)))
           (+ x1 (* 4.0 (* -3.0 (* x1 x2))))))
         (if (<= x1 1.04e+121)
           t_0
           (/ (- (* x1 x1) (* (* x2 x2) 36.0)) (- x1 (* x2 -6.0)))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)));
	double tmp;
	if (x1 <= -4.6e+101) {
		tmp = x1 + (x1 + ((x1 * -3.0) + (x2 * ((x1 * -12.0) - 6.0))));
	} else if (x1 <= -3.9e-228) {
		tmp = t_0;
	} else if (x1 <= 6.5e-247) {
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / ((x1 * x1) + 1.0))) + (x1 + (4.0 * (-3.0 * (x1 * x2)))));
	} else if (x1 <= 1.04e+121) {
		tmp = t_0;
	} else {
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x1 + ((x2 * (-6.0d0)) + (x1 * ((4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0))) - 2.0d0)))
    if (x1 <= (-4.6d+101)) then
        tmp = x1 + (x1 + ((x1 * (-3.0d0)) + (x2 * ((x1 * (-12.0d0)) - 6.0d0))))
    else if (x1 <= (-3.9d-228)) then
        tmp = t_0
    else if (x1 <= 6.5d-247) then
        tmp = x1 + ((3.0d0 * ((((x1 * (x1 * 3.0d0)) - (2.0d0 * x2)) - x1) / ((x1 * x1) + 1.0d0))) + (x1 + (4.0d0 * ((-3.0d0) * (x1 * x2)))))
    else if (x1 <= 1.04d+121) then
        tmp = t_0
    else
        tmp = ((x1 * x1) - ((x2 * x2) * 36.0d0)) / (x1 - (x2 * (-6.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)));
	double tmp;
	if (x1 <= -4.6e+101) {
		tmp = x1 + (x1 + ((x1 * -3.0) + (x2 * ((x1 * -12.0) - 6.0))));
	} else if (x1 <= -3.9e-228) {
		tmp = t_0;
	} else if (x1 <= 6.5e-247) {
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / ((x1 * x1) + 1.0))) + (x1 + (4.0 * (-3.0 * (x1 * x2)))));
	} else if (x1 <= 1.04e+121) {
		tmp = t_0;
	} else {
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)))
	tmp = 0
	if x1 <= -4.6e+101:
		tmp = x1 + (x1 + ((x1 * -3.0) + (x2 * ((x1 * -12.0) - 6.0))))
	elif x1 <= -3.9e-228:
		tmp = t_0
	elif x1 <= 6.5e-247:
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / ((x1 * x1) + 1.0))) + (x1 + (4.0 * (-3.0 * (x1 * x2)))))
	elif x1 <= 1.04e+121:
		tmp = t_0
	else:
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0))) - 2.0))))
	tmp = 0.0
	if (x1 <= -4.6e+101)
		tmp = Float64(x1 + Float64(x1 + Float64(Float64(x1 * -3.0) + Float64(x2 * Float64(Float64(x1 * -12.0) - 6.0)))));
	elseif (x1 <= -3.9e-228)
		tmp = t_0;
	elseif (x1 <= 6.5e-247)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(Float64(x1 * Float64(x1 * 3.0)) - Float64(2.0 * x2)) - x1) / Float64(Float64(x1 * x1) + 1.0))) + Float64(x1 + Float64(4.0 * Float64(-3.0 * Float64(x1 * x2))))));
	elseif (x1 <= 1.04e+121)
		tmp = t_0;
	else
		tmp = Float64(Float64(Float64(x1 * x1) - Float64(Float64(x2 * x2) * 36.0)) / Float64(x1 - Float64(x2 * -6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)));
	tmp = 0.0;
	if (x1 <= -4.6e+101)
		tmp = x1 + (x1 + ((x1 * -3.0) + (x2 * ((x1 * -12.0) - 6.0))));
	elseif (x1 <= -3.9e-228)
		tmp = t_0;
	elseif (x1 <= 6.5e-247)
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / ((x1 * x1) + 1.0))) + (x1 + (4.0 * (-3.0 * (x1 * x2)))));
	elseif (x1 <= 1.04e+121)
		tmp = t_0;
	else
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(4.0 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -4.6e+101], N[(x1 + N[(x1 + N[(N[(x1 * -3.0), $MachinePrecision] + N[(x2 * N[(N[(x1 * -12.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -3.9e-228], t$95$0, If[LessEqual[x1, 6.5e-247], N[(x1 + N[(N[(3.0 * N[(N[(N[(N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision] - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(4.0 * N[(-3.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.04e+121], t$95$0, N[(N[(N[(x1 * x1), $MachinePrecision] - N[(N[(x2 * x2), $MachinePrecision] * 36.0), $MachinePrecision]), $MachinePrecision] / N[(x1 - N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -4.6000000000000003e101

   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 2.4%

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

   4. Taylor expanded in x2 around 0 18.8%

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

   if -4.6000000000000003e101 < x1 < -3.90000000000000029e-228 or 6.4999999999999996e-247 < x1 < 1.04e121

   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 69.2%

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

   3. Taylor expanded in x1 around 0 69.1%

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

   if -3.90000000000000029e-228 < x1 < 6.4999999999999996e-247

   1. Initial program 99.7%

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

   2. Taylor expanded in x1 around 0 79.1%

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

   3. Taylor expanded in x2 around 0 96.3%

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

      1. *-commutative 96.3%

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

   5. Simplified 96.3%

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

   if 1.04e121 < x1

   1. Initial program 18.4%

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

   2. 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 6.6%

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

      1. *-commutative 6.6%

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

   5. Simplified 6.6%

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

      1. flip-+ 53.4%

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

   7. Applied egg-rr 53.4%

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

      1. swap-sqr 53.4%

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

      2. metadata-eval 53.4%

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

      3. *-commutative 53.4%

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

   9. Simplified 53.4%

      \[\leadsto \color{blue}{\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - -6 \cdot x2}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 61.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4.6 \cdot 10^{+101}:\\ \;\;\;\;x1 + \left(x1 + \left(x1 \cdot -3 + x2 \cdot \left(x1 \cdot -12 - 6\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -3.9 \cdot 10^{-228}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)\\ \mathbf{elif}\;x1 \leq 6.5 \cdot 10^{-247}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + 4 \cdot \left(-3 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.04 \cdot 10^{+121}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - x2 \cdot -6}\\ \end{array} \]

Alternative 19: 62.3% accurate, 4.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 + \left(x2 \cdot -6 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)\\ t_1 := x1 + \left(x1 + \left(x1 \cdot -3 + x2 \cdot \left(x1 \cdot -12 - 6\right)\right)\right)\\ \mathbf{if}\;x1 \leq -4.6 \cdot 10^{+101}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x1 \leq -1.65 \cdot 10^{-227}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x1 \leq 8.2 \cdot 10^{-247}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x1 \leq 1.04 \cdot 10^{+121}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - x2 \cdot -6}\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0
         (+
          x1
          (+ (* x2 -6.0) (* x1 (- (* 4.0 (* x2 (- (* 2.0 x2) 3.0))) 2.0)))))
        (t_1 (+ x1 (+ x1 (+ (* x1 -3.0) (* x2 (- (* x1 -12.0) 6.0)))))))
   (if (<= x1 -4.6e+101)
     t_1
     (if (<= x1 -1.65e-227)
       t_0
       (if (<= x1 8.2e-247)
         t_1
         (if (<= x1 1.04e+121)
           t_0
           (/ (- (* x1 x1) (* (* x2 x2) 36.0)) (- x1 (* x2 -6.0)))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)));
	double t_1 = x1 + (x1 + ((x1 * -3.0) + (x2 * ((x1 * -12.0) - 6.0))));
	double tmp;
	if (x1 <= -4.6e+101) {
		tmp = t_1;
	} else if (x1 <= -1.65e-227) {
		tmp = t_0;
	} else if (x1 <= 8.2e-247) {
		tmp = t_1;
	} else if (x1 <= 1.04e+121) {
		tmp = t_0;
	} else {
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x1 + ((x2 * (-6.0d0)) + (x1 * ((4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0))) - 2.0d0)))
    t_1 = x1 + (x1 + ((x1 * (-3.0d0)) + (x2 * ((x1 * (-12.0d0)) - 6.0d0))))
    if (x1 <= (-4.6d+101)) then
        tmp = t_1
    else if (x1 <= (-1.65d-227)) then
        tmp = t_0
    else if (x1 <= 8.2d-247) then
        tmp = t_1
    else if (x1 <= 1.04d+121) then
        tmp = t_0
    else
        tmp = ((x1 * x1) - ((x2 * x2) * 36.0d0)) / (x1 - (x2 * (-6.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)));
	double t_1 = x1 + (x1 + ((x1 * -3.0) + (x2 * ((x1 * -12.0) - 6.0))));
	double tmp;
	if (x1 <= -4.6e+101) {
		tmp = t_1;
	} else if (x1 <= -1.65e-227) {
		tmp = t_0;
	} else if (x1 <= 8.2e-247) {
		tmp = t_1;
	} else if (x1 <= 1.04e+121) {
		tmp = t_0;
	} else {
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)))
	t_1 = x1 + (x1 + ((x1 * -3.0) + (x2 * ((x1 * -12.0) - 6.0))))
	tmp = 0
	if x1 <= -4.6e+101:
		tmp = t_1
	elif x1 <= -1.65e-227:
		tmp = t_0
	elif x1 <= 8.2e-247:
		tmp = t_1
	elif x1 <= 1.04e+121:
		tmp = t_0
	else:
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0))) - 2.0))))
	t_1 = Float64(x1 + Float64(x1 + Float64(Float64(x1 * -3.0) + Float64(x2 * Float64(Float64(x1 * -12.0) - 6.0)))))
	tmp = 0.0
	if (x1 <= -4.6e+101)
		tmp = t_1;
	elseif (x1 <= -1.65e-227)
		tmp = t_0;
	elseif (x1 <= 8.2e-247)
		tmp = t_1;
	elseif (x1 <= 1.04e+121)
		tmp = t_0;
	else
		tmp = Float64(Float64(Float64(x1 * x1) - Float64(Float64(x2 * x2) * 36.0)) / Float64(x1 - Float64(x2 * -6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)));
	t_1 = x1 + (x1 + ((x1 * -3.0) + (x2 * ((x1 * -12.0) - 6.0))));
	tmp = 0.0;
	if (x1 <= -4.6e+101)
		tmp = t_1;
	elseif (x1 <= -1.65e-227)
		tmp = t_0;
	elseif (x1 <= 8.2e-247)
		tmp = t_1;
	elseif (x1 <= 1.04e+121)
		tmp = t_0;
	else
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(4.0 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 + N[(x1 + N[(N[(x1 * -3.0), $MachinePrecision] + N[(x2 * N[(N[(x1 * -12.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -4.6e+101], t$95$1, If[LessEqual[x1, -1.65e-227], t$95$0, If[LessEqual[x1, 8.2e-247], t$95$1, If[LessEqual[x1, 1.04e+121], t$95$0, N[(N[(N[(x1 * x1), $MachinePrecision] - N[(N[(x2 * x2), $MachinePrecision] * 36.0), $MachinePrecision]), $MachinePrecision] / N[(x1 - N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -4.6000000000000003e101 or -1.65e-227 < x1 < 8.1999999999999997e-247

   1. Initial program 39.6%

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

   2. Taylor expanded in x1 around 0 31.4%

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

   3. Taylor expanded in x1 around 0 32.8%

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

   4. Taylor expanded in x2 around 0 49.6%

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

   if -4.6000000000000003e101 < x1 < -1.65e-227 or 8.1999999999999997e-247 < x1 < 1.04e121

   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 69.2%

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

   3. Taylor expanded in x1 around 0 69.1%

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

   if 1.04e121 < x1

   1. Initial program 18.4%

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

   2. 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 6.6%

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

      1. *-commutative 6.6%

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

   5. Simplified 6.6%

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

      1. flip-+ 53.4%

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

   7. Applied egg-rr 53.4%

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

      1. swap-sqr 53.4%

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

      2. metadata-eval 53.4%

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

      3. *-commutative 53.4%

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

   9. Simplified 53.4%

      \[\leadsto \color{blue}{\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - -6 \cdot x2}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 61.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4.6 \cdot 10^{+101}:\\ \;\;\;\;x1 + \left(x1 + \left(x1 \cdot -3 + x2 \cdot \left(x1 \cdot -12 - 6\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -1.65 \cdot 10^{-227}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)\\ \mathbf{elif}\;x1 \leq 8.2 \cdot 10^{-247}:\\ \;\;\;\;x1 + \left(x1 + \left(x1 \cdot -3 + x2 \cdot \left(x1 \cdot -12 - 6\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.04 \cdot 10^{+121}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - x2 \cdot -6}\\ \end{array} \]

Alternative 20: 53.3% accurate, 5.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - x2 \cdot -6}\\ t_1 := x1 + \left(x1 + \left(x1 \cdot -3 + x2 \cdot \left(x1 \cdot -12 - 6\right)\right)\right)\\ \mathbf{if}\;x1 \leq -2.6 \cdot 10^{+140}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x1 \leq -320000000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x1 \leq 2.6 \cdot 10^{-48}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + x1 \cdot \left(1 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (/ (- (* x1 x1) (* (* x2 x2) 36.0)) (- x1 (* x2 -6.0))))
        (t_1 (+ x1 (+ x1 (+ (* x1 -3.0) (* x2 (- (* x1 -12.0) 6.0)))))))
   (if (<= x1 -2.6e+140)
     t_1
     (if (<= x1 -320000000.0)
       t_0
       (if (<= x1 2.6e-48)
         t_1
         (if (<= x1 1.35e+154)
           (+ x1 (* x1 (+ 1.0 (* 4.0 (* x2 (- (* 2.0 x2) 3.0))))))
           t_0))))))

C

double code(double x1, double x2) {
	double t_0 = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0));
	double t_1 = x1 + (x1 + ((x1 * -3.0) + (x2 * ((x1 * -12.0) - 6.0))));
	double tmp;
	if (x1 <= -2.6e+140) {
		tmp = t_1;
	} else if (x1 <= -320000000.0) {
		tmp = t_0;
	} else if (x1 <= 2.6e-48) {
		tmp = t_1;
	} else if (x1 <= 1.35e+154) {
		tmp = x1 + (x1 * (1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0)))));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = ((x1 * x1) - ((x2 * x2) * 36.0d0)) / (x1 - (x2 * (-6.0d0)))
    t_1 = x1 + (x1 + ((x1 * (-3.0d0)) + (x2 * ((x1 * (-12.0d0)) - 6.0d0))))
    if (x1 <= (-2.6d+140)) then
        tmp = t_1
    else if (x1 <= (-320000000.0d0)) then
        tmp = t_0
    else if (x1 <= 2.6d-48) then
        tmp = t_1
    else if (x1 <= 1.35d+154) then
        tmp = x1 + (x1 * (1.0d0 + (4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0)))))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0));
	double t_1 = x1 + (x1 + ((x1 * -3.0) + (x2 * ((x1 * -12.0) - 6.0))));
	double tmp;
	if (x1 <= -2.6e+140) {
		tmp = t_1;
	} else if (x1 <= -320000000.0) {
		tmp = t_0;
	} else if (x1 <= 2.6e-48) {
		tmp = t_1;
	} else if (x1 <= 1.35e+154) {
		tmp = x1 + (x1 * (1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0)))));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0))
	t_1 = x1 + (x1 + ((x1 * -3.0) + (x2 * ((x1 * -12.0) - 6.0))))
	tmp = 0
	if x1 <= -2.6e+140:
		tmp = t_1
	elif x1 <= -320000000.0:
		tmp = t_0
	elif x1 <= 2.6e-48:
		tmp = t_1
	elif x1 <= 1.35e+154:
		tmp = x1 + (x1 * (1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0)))))
	else:
		tmp = t_0
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(Float64(x1 * x1) - Float64(Float64(x2 * x2) * 36.0)) / Float64(x1 - Float64(x2 * -6.0)))
	t_1 = Float64(x1 + Float64(x1 + Float64(Float64(x1 * -3.0) + Float64(x2 * Float64(Float64(x1 * -12.0) - 6.0)))))
	tmp = 0.0
	if (x1 <= -2.6e+140)
		tmp = t_1;
	elseif (x1 <= -320000000.0)
		tmp = t_0;
	elseif (x1 <= 2.6e-48)
		tmp = t_1;
	elseif (x1 <= 1.35e+154)
		tmp = Float64(x1 + Float64(x1 * Float64(1.0 + Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0))))));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0));
	t_1 = x1 + (x1 + ((x1 * -3.0) + (x2 * ((x1 * -12.0) - 6.0))));
	tmp = 0.0;
	if (x1 <= -2.6e+140)
		tmp = t_1;
	elseif (x1 <= -320000000.0)
		tmp = t_0;
	elseif (x1 <= 2.6e-48)
		tmp = t_1;
	elseif (x1 <= 1.35e+154)
		tmp = x1 + (x1 * (1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0)))));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(N[(x1 * x1), $MachinePrecision] - N[(N[(x2 * x2), $MachinePrecision] * 36.0), $MachinePrecision]), $MachinePrecision] / N[(x1 - N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 + N[(x1 + N[(N[(x1 * -3.0), $MachinePrecision] + N[(x2 * N[(N[(x1 * -12.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -2.6e+140], t$95$1, If[LessEqual[x1, -320000000.0], t$95$0, If[LessEqual[x1, 2.6e-48], t$95$1, If[LessEqual[x1, 1.35e+154], N[(x1 + N[(x1 * N[(1.0 + N[(4.0 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -2.6000000000000001e140 or -3.2e8 < x1 < 2.59999999999999987e-48

   1. Initial program 75.1%

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

   2. Taylor expanded in x1 around 0 65.4%

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

   3. Taylor expanded in x1 around 0 65.9%

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

   4. Taylor expanded in x2 around 0 67.1%

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

   if -2.6000000000000001e140 < x1 < -3.2e8 or 1.35000000000000003e154 < x1

   1. Initial program 37.3%

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

   2. Taylor expanded in x1 around 0 7.6%

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

   3. Taylor expanded in x1 around 0 4.8%

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

      1. *-commutative 4.8%

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

   5. Simplified 4.8%

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

      1. flip-+ 44.9%

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

   7. Applied egg-rr 44.9%

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

      1. swap-sqr 44.9%

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

      2. metadata-eval 44.9%

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

      3. *-commutative 44.9%

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

   9. Simplified 44.9%

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

   if 2.59999999999999987e-48 < x1 < 1.35000000000000003e154

   1. Initial program 94.9%

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

   2. Taylor expanded in x1 around 0 37.5%

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

   3. Taylor expanded in x1 around inf 32.7%

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

4. Final simplification 56.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -2.6 \cdot 10^{+140}:\\ \;\;\;\;x1 + \left(x1 + \left(x1 \cdot -3 + x2 \cdot \left(x1 \cdot -12 - 6\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -320000000:\\ \;\;\;\;\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - x2 \cdot -6}\\ \mathbf{elif}\;x1 \leq 2.6 \cdot 10^{-48}:\\ \;\;\;\;x1 + \left(x1 + \left(x1 \cdot -3 + x2 \cdot \left(x1 \cdot -12 - 6\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + x1 \cdot \left(1 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - x2 \cdot -6}\\ \end{array} \]

Alternative 21: 50.2% accurate, 7.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq 10^{-44}:\\ \;\;\;\;x1 + \left(x1 + \left(x1 \cdot -3 + x2 \cdot \left(x1 \cdot -12 - 6\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot \left(1 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 1e-44)
   (+ x1 (+ x1 (+ (* x1 -3.0) (* x2 (- (* x1 -12.0) 6.0)))))
   (+ x1 (* x1 (+ 1.0 (* 4.0 (* x2 (- (* 2.0 x2) 3.0))))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= 1e-44) {
		tmp = x1 + (x1 + ((x1 * -3.0) + (x2 * ((x1 * -12.0) - 6.0))));
	} else {
		tmp = x1 + (x1 * (1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0)))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x1 <= 1d-44) then
        tmp = x1 + (x1 + ((x1 * (-3.0d0)) + (x2 * ((x1 * (-12.0d0)) - 6.0d0))))
    else
        tmp = x1 + (x1 * (1.0d0 + (4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0)))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= 1e-44) {
		tmp = x1 + (x1 + ((x1 * -3.0) + (x2 * ((x1 * -12.0) - 6.0))));
	} else {
		tmp = x1 + (x1 * (1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0)))));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= 1e-44:
		tmp = x1 + (x1 + ((x1 * -3.0) + (x2 * ((x1 * -12.0) - 6.0))))
	else:
		tmp = x1 + (x1 * (1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0)))))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= 1e-44)
		tmp = Float64(x1 + Float64(x1 + Float64(Float64(x1 * -3.0) + Float64(x2 * Float64(Float64(x1 * -12.0) - 6.0)))));
	else
		tmp = Float64(x1 + Float64(x1 * Float64(1.0 + Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= 1e-44)
		tmp = x1 + (x1 + ((x1 * -3.0) + (x2 * ((x1 * -12.0) - 6.0))));
	else
		tmp = x1 + (x1 * (1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, 1e-44], N[(x1 + N[(x1 + N[(N[(x1 * -3.0), $MachinePrecision] + N[(x2 * N[(N[(x1 * -12.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(x1 * N[(1.0 + N[(4.0 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x1 < 9.99999999999999953e-45

   1. Initial program 75.8%

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

   2. Taylor expanded in x1 around 0 58.5%

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

   3. Taylor expanded in x1 around 0 59.2%

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

   4. Taylor expanded in x2 around 0 58.2%

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

   if 9.99999999999999953e-45 < x1

   1. Initial program 54.8%

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

   2. Taylor expanded in x1 around 0 21.7%

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

   3. Taylor expanded in x1 around inf 39.1%

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

4. Final simplification 52.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq 10^{-44}:\\ \;\;\;\;x1 + \left(x1 + \left(x1 \cdot -3 + x2 \cdot \left(x1 \cdot -12 - 6\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot \left(1 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ \end{array} \]

Alternative 22: 41.6% accurate, 8.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(x2 \cdot x2\right) \cdot \left(x1 \cdot 8\right)\\ t_1 := x1 + x2 \cdot -6\\ \mathbf{if}\;x2 \leq -7 \cdot 10^{+196}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x2 \leq -5.5 \cdot 10^{-177}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x2 \leq 9 \cdot 10^{-177}:\\ \;\;\;\;x1 + x1 \cdot -2\\ \mathbf{elif}\;x2 \leq 6.6 \cdot 10^{+136}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* (* x2 x2) (* x1 8.0))) (t_1 (+ x1 (* x2 -6.0))))
   (if (<= x2 -7e+196)
     t_0
     (if (<= x2 -5.5e-177)
       t_1
       (if (<= x2 9e-177) (+ x1 (* x1 -2.0)) (if (<= x2 6.6e+136) t_1 t_0))))))

C

double code(double x1, double x2) {
	double t_0 = (x2 * x2) * (x1 * 8.0);
	double t_1 = x1 + (x2 * -6.0);
	double tmp;
	if (x2 <= -7e+196) {
		tmp = t_0;
	} else if (x2 <= -5.5e-177) {
		tmp = t_1;
	} else if (x2 <= 9e-177) {
		tmp = x1 + (x1 * -2.0);
	} else if (x2 <= 6.6e+136) {
		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 = (x2 * x2) * (x1 * 8.0d0)
    t_1 = x1 + (x2 * (-6.0d0))
    if (x2 <= (-7d+196)) then
        tmp = t_0
    else if (x2 <= (-5.5d-177)) then
        tmp = t_1
    else if (x2 <= 9d-177) then
        tmp = x1 + (x1 * (-2.0d0))
    else if (x2 <= 6.6d+136) 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 = (x2 * x2) * (x1 * 8.0);
	double t_1 = x1 + (x2 * -6.0);
	double tmp;
	if (x2 <= -7e+196) {
		tmp = t_0;
	} else if (x2 <= -5.5e-177) {
		tmp = t_1;
	} else if (x2 <= 9e-177) {
		tmp = x1 + (x1 * -2.0);
	} else if (x2 <= 6.6e+136) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x2 * x2) * (x1 * 8.0)
	t_1 = x1 + (x2 * -6.0)
	tmp = 0
	if x2 <= -7e+196:
		tmp = t_0
	elif x2 <= -5.5e-177:
		tmp = t_1
	elif x2 <= 9e-177:
		tmp = x1 + (x1 * -2.0)
	elif x2 <= 6.6e+136:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x2 * x2) * Float64(x1 * 8.0))
	t_1 = Float64(x1 + Float64(x2 * -6.0))
	tmp = 0.0
	if (x2 <= -7e+196)
		tmp = t_0;
	elseif (x2 <= -5.5e-177)
		tmp = t_1;
	elseif (x2 <= 9e-177)
		tmp = Float64(x1 + Float64(x1 * -2.0));
	elseif (x2 <= 6.6e+136)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x2 * x2) * (x1 * 8.0);
	t_1 = x1 + (x2 * -6.0);
	tmp = 0.0;
	if (x2 <= -7e+196)
		tmp = t_0;
	elseif (x2 <= -5.5e-177)
		tmp = t_1;
	elseif (x2 <= 9e-177)
		tmp = x1 + (x1 * -2.0);
	elseif (x2 <= 6.6e+136)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x2 * x2), $MachinePrecision] * N[(x1 * 8.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x2, -7e+196], t$95$0, If[LessEqual[x2, -5.5e-177], t$95$1, If[LessEqual[x2, 9e-177], N[(x1 + N[(x1 * -2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x2, 6.6e+136], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if x2 < -6.9999999999999997e196 or 6.59999999999999984e136 < x2

   1. Initial program 62.2%

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

   2. Taylor expanded in x1 around 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 inf 59.4%

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

   4. Taylor expanded in x2 around inf 59.4%

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

      1. associate-*r* 59.4%

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

      2. unpow2 59.4%

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

   6. Simplified 59.4%

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

   if -6.9999999999999997e196 < x2 < -5.4999999999999996e-177 or 9.0000000000000007e-177 < x2 < 6.59999999999999984e136

   1. Initial program 73.1%

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

   2. Taylor expanded in x1 around 0 48.7%

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

   3. Taylor expanded in x1 around 0 42.3%

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

      1. *-commutative 42.3%

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

   5. Simplified 42.3%

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

   if -5.4999999999999996e-177 < x2 < 9.0000000000000007e-177

   1. Initial program 69.8%

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

   2. Taylor expanded in x1 around 0 52.3%

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

   3. Taylor expanded in x1 around 0 52.9%

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

   4. Taylor expanded in x2 around 0 46.3%

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

      1. distribute-rgt1-in 46.7%

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

      2. metadata-eval 46.7%

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

      3. *-commutative 46.7%

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

   6. Simplified 46.7%

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

4. Final simplification 46.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq -7 \cdot 10^{+196}:\\ \;\;\;\;\left(x2 \cdot x2\right) \cdot \left(x1 \cdot 8\right)\\ \mathbf{elif}\;x2 \leq -5.5 \cdot 10^{-177}:\\ \;\;\;\;x1 + x2 \cdot -6\\ \mathbf{elif}\;x2 \leq 9 \cdot 10^{-177}:\\ \;\;\;\;x1 + x1 \cdot -2\\ \mathbf{elif}\;x2 \leq 6.6 \cdot 10^{+136}:\\ \;\;\;\;x1 + x2 \cdot -6\\ \mathbf{else}:\\ \;\;\;\;\left(x2 \cdot x2\right) \cdot \left(x1 \cdot 8\right)\\ \end{array} \]

Alternative 23: 41.6% accurate, 8.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(x2 \cdot x2\right) \cdot \left(x1 \cdot 8\right)\\ t_1 := x1 + \left(x1 + x2 \cdot -6\right)\\ \mathbf{if}\;x2 \leq -7.5 \cdot 10^{+196}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x2 \leq -6.8 \cdot 10^{-174}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x2 \leq 1.8 \cdot 10^{-172}:\\ \;\;\;\;x1 + x1 \cdot -2\\ \mathbf{elif}\;x2 \leq 4.6 \cdot 10^{+138}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* (* x2 x2) (* x1 8.0))) (t_1 (+ x1 (+ x1 (* x2 -6.0)))))
   (if (<= x2 -7.5e+196)
     t_0
     (if (<= x2 -6.8e-174)
       t_1
       (if (<= x2 1.8e-172)
         (+ x1 (* x1 -2.0))
         (if (<= x2 4.6e+138) t_1 t_0))))))

C

double code(double x1, double x2) {
	double t_0 = (x2 * x2) * (x1 * 8.0);
	double t_1 = x1 + (x1 + (x2 * -6.0));
	double tmp;
	if (x2 <= -7.5e+196) {
		tmp = t_0;
	} else if (x2 <= -6.8e-174) {
		tmp = t_1;
	} else if (x2 <= 1.8e-172) {
		tmp = x1 + (x1 * -2.0);
	} else if (x2 <= 4.6e+138) {
		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 = (x2 * x2) * (x1 * 8.0d0)
    t_1 = x1 + (x1 + (x2 * (-6.0d0)))
    if (x2 <= (-7.5d+196)) then
        tmp = t_0
    else if (x2 <= (-6.8d-174)) then
        tmp = t_1
    else if (x2 <= 1.8d-172) then
        tmp = x1 + (x1 * (-2.0d0))
    else if (x2 <= 4.6d+138) 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 = (x2 * x2) * (x1 * 8.0);
	double t_1 = x1 + (x1 + (x2 * -6.0));
	double tmp;
	if (x2 <= -7.5e+196) {
		tmp = t_0;
	} else if (x2 <= -6.8e-174) {
		tmp = t_1;
	} else if (x2 <= 1.8e-172) {
		tmp = x1 + (x1 * -2.0);
	} else if (x2 <= 4.6e+138) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x2 * x2) * (x1 * 8.0)
	t_1 = x1 + (x1 + (x2 * -6.0))
	tmp = 0
	if x2 <= -7.5e+196:
		tmp = t_0
	elif x2 <= -6.8e-174:
		tmp = t_1
	elif x2 <= 1.8e-172:
		tmp = x1 + (x1 * -2.0)
	elif x2 <= 4.6e+138:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x2 * x2) * Float64(x1 * 8.0))
	t_1 = Float64(x1 + Float64(x1 + Float64(x2 * -6.0)))
	tmp = 0.0
	if (x2 <= -7.5e+196)
		tmp = t_0;
	elseif (x2 <= -6.8e-174)
		tmp = t_1;
	elseif (x2 <= 1.8e-172)
		tmp = Float64(x1 + Float64(x1 * -2.0));
	elseif (x2 <= 4.6e+138)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x2 * x2) * (x1 * 8.0);
	t_1 = x1 + (x1 + (x2 * -6.0));
	tmp = 0.0;
	if (x2 <= -7.5e+196)
		tmp = t_0;
	elseif (x2 <= -6.8e-174)
		tmp = t_1;
	elseif (x2 <= 1.8e-172)
		tmp = x1 + (x1 * -2.0);
	elseif (x2 <= 4.6e+138)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x2 * x2), $MachinePrecision] * N[(x1 * 8.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 + N[(x1 + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x2, -7.5e+196], t$95$0, If[LessEqual[x2, -6.8e-174], t$95$1, If[LessEqual[x2, 1.8e-172], N[(x1 + N[(x1 * -2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x2, 4.6e+138], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if x2 < -7.5000000000000005e196 or 4.60000000000000015e138 < x2

   1. Initial program 62.2%

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

   2. Taylor expanded in x1 around 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 inf 59.4%

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

   4. Taylor expanded in x2 around inf 59.4%

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

      1. associate-*r* 59.4%

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

      2. unpow2 59.4%

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

   6. Simplified 59.4%

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

   if -7.5000000000000005e196 < x2 < -6.8000000000000004e-174 or 1.80000000000000007e-172 < x2 < 4.60000000000000015e138

   1. Initial program 73.1%

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

   2. Taylor expanded in x1 around 0 67.6%

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

      1. *-commutative 67.6%

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

   4. Simplified 67.6%

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

   5. Taylor expanded in x1 around inf 87.7%

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

      1. *-commutative 87.7%

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

   7. Simplified 87.7%

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

   8. Taylor expanded in x1 around 0 42.3%

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

   if -6.8000000000000004e-174 < x2 < 1.80000000000000007e-172

   1. Initial program 69.8%

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

   2. Taylor expanded in x1 around 0 52.3%

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

   3. Taylor expanded in x1 around 0 52.9%

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

   4. Taylor expanded in x2 around 0 46.3%

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

      1. distribute-rgt1-in 46.7%

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

      2. metadata-eval 46.7%

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

      3. *-commutative 46.7%

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

   6. Simplified 46.7%

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

4. Final simplification 47.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq -7.5 \cdot 10^{+196}:\\ \;\;\;\;\left(x2 \cdot x2\right) \cdot \left(x1 \cdot 8\right)\\ \mathbf{elif}\;x2 \leq -6.8 \cdot 10^{-174}:\\ \;\;\;\;x1 + \left(x1 + x2 \cdot -6\right)\\ \mathbf{elif}\;x2 \leq 1.8 \cdot 10^{-172}:\\ \;\;\;\;x1 + x1 \cdot -2\\ \mathbf{elif}\;x2 \leq 4.6 \cdot 10^{+138}:\\ \;\;\;\;x1 + \left(x1 + x2 \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x2 \cdot x2\right) \cdot \left(x1 \cdot 8\right)\\ \end{array} \]

Alternative 24: 31.8% accurate, 13.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x2 \leq -7.4 \cdot 10^{-174} \lor \neg \left(x2 \leq 1.6 \cdot 10^{-172}\right):\\ \;\;\;\;x1 + x2 \cdot -6\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x2 -7.4e-174) (not (<= x2 1.6e-172)))
   (+ x1 (* x2 -6.0))
   (+ x1 (* x1 -2.0))))

C

double code(double x1, double x2) {
	double tmp;
	if ((x2 <= -7.4e-174) || !(x2 <= 1.6e-172)) {
		tmp = x1 + (x2 * -6.0);
	} else {
		tmp = x1 + (x1 * -2.0);
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if ((x2 <= (-7.4d-174)) .or. (.not. (x2 <= 1.6d-172))) then
        tmp = x1 + (x2 * (-6.0d0))
    else
        tmp = x1 + (x1 * (-2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x2 <= -7.4e-174) || !(x2 <= 1.6e-172)) {
		tmp = x1 + (x2 * -6.0);
	} else {
		tmp = x1 + (x1 * -2.0);
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x2 <= -7.4e-174) or not (x2 <= 1.6e-172):
		tmp = x1 + (x2 * -6.0)
	else:
		tmp = x1 + (x1 * -2.0)
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x2 <= -7.4e-174) || !(x2 <= 1.6e-172))
		tmp = Float64(x1 + Float64(x2 * -6.0));
	else
		tmp = Float64(x1 + Float64(x1 * -2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x2 <= -7.4e-174) || ~((x2 <= 1.6e-172)))
		tmp = x1 + (x2 * -6.0);
	else
		tmp = x1 + (x1 * -2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x2, -7.4e-174], N[Not[LessEqual[x2, 1.6e-172]], $MachinePrecision]], N[(x1 + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(x1 * -2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x2 < -7.40000000000000019e-174 or 1.6000000000000001e-172 < 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 47.0%

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

   3. Taylor expanded in x1 around 0 33.7%

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

      1. *-commutative 33.7%

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

   5. Simplified 33.7%

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

   if -7.40000000000000019e-174 < x2 < 1.6000000000000001e-172

   1. Initial program 69.8%

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

   2. Taylor expanded in x1 around 0 52.3%

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

   3. Taylor expanded in x1 around 0 52.9%

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

   4. Taylor expanded in x2 around 0 46.3%

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

      1. distribute-rgt1-in 46.7%

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

      2. metadata-eval 46.7%

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

      3. *-commutative 46.7%

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

   6. Simplified 46.7%

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

4. Final simplification 36.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq -7.4 \cdot 10^{-174} \lor \neg \left(x2 \leq 1.6 \cdot 10^{-172}\right):\\ \;\;\;\;x1 + x2 \cdot -6\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot -2\\ \end{array} \]

Alternative 25: 3.4% accurate, 25.4× speedup

Math

\[\begin{array}{l} \\ x1 \cdot 2 + 9 \end{array} \]

FPCore

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

C

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

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    code = (x1 * 2.0d0) + 9.0d0
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 70.0%

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

2. Taylor expanded in x1 around 0 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 inf 19.1%

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

4. Taylor expanded in x2 around 0 3.6%

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

5. Final simplification 3.6%

   \[\leadsto x1 \cdot 2 + 9 \]

Alternative 26: 14.3% accurate, 25.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 70.0%

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

2. Taylor expanded in x1 around 0 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 53.5%

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

4. Taylor expanded in x2 around 0 15.2%

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

   1. distribute-rgt1-in 15.3%

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

   2. metadata-eval 15.3%

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

   3. *-commutative 15.3%

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

6. Simplified 15.3%

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

7. Final simplification 15.3%

   \[\leadsto x1 + x1 \cdot -2 \]

Alternative 27: 3.5% accurate, 127.0× speedup

Math

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

FPCore

(FPCore (x1 x2) :precision binary64 9.0)

C

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

Fortran

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

Java

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

Python

def code(x1, x2):
	return 9.0

Julia

function code(x1, x2)
	return 9.0
end

MATLAB

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

Wolfram

code[x1_, x2_] := 9.0

Derivation

1. Initial program 70.0%

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

2. Taylor expanded in x1 around 0 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 inf 19.1%

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

4. Taylor expanded in x1 around 0 3.6%

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

5. Final simplification 3.6%

   \[\leadsto 9 \]

Reproduce

herbie shell --seed 2023277 
(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))))))