Rosa's FloatVsDoubleBenchmark

Percentage Accurate: 70.7% → 99.4%

Time: 37.9s

Alternatives: 22

Speedup: 2.9×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 70.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.4% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 99.4%

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

   3. Applied egg-rr 90.0%

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

   5. Simplified 99.4%

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

   if +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 97.3%

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

      1. *-commutative 97.3%

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

   7. Simplified 97.3%

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

   8. Taylor expanded in x1 around inf 97.3%

      \[\leadsto \color{blue}{2 \cdot x1 + 6 \cdot {x1}^{4}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.8%

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

Alternative 2: 99.4% accurate, 0.5× speedup

Math

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

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 2.0) (* 6.0 (pow x1 4.0))))))

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 * 2.0) + (6.0 * pow(x1, 4.0));
	}
	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 * 2.0) + (6.0 * Math.pow(x1, 4.0));
	}
	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 * 2.0) + (6.0 * math.pow(x1, 4.0))
	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(Float64(x1 * 2.0) + Float64(6.0 * (x1 ^ 4.0)));
	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 * 2.0) + (6.0 * (x1 ^ 4.0));
	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[(N[(x1 * 2.0), $MachinePrecision] + N[(6.0 * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 99.4%

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

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

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around 0 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 97.3%

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

      1. *-commutative 97.3%

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

   7. Simplified 97.3%

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

   8. Taylor expanded in x1 around inf 97.3%

      \[\leadsto \color{blue}{2 \cdot x1 + 6 \cdot {x1}^{4}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.8%

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

Alternative 3: 91.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := x1 \cdot \left(x1 \cdot x1\right)\\ t_2 := x1 + \left(x2 \cdot -6 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)\\ t_3 := x1 \cdot \left(x1 \cdot 3\right)\\ t_4 := \frac{\left(t_3 + 2 \cdot x2\right) - x1}{t_0}\\ t_5 := x1 + \left(\left(x1 + \left(\left(t_0 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t_4\right) \cdot \left(t_4 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(t_4 \cdot 4 - 6\right)\right) + t_3 \cdot t_4\right) + t_1\right)\right) + 9\right)\\ \mathbf{if}\;x1 \leq -1.22 \cdot 10^{+53}:\\ \;\;\;\;x1 \cdot 2 + 6 \cdot {x1}^{4}\\ \mathbf{elif}\;x1 \leq -0.00112:\\ \;\;\;\;t_5\\ \mathbf{elif}\;x1 \leq -8.4 \cdot 10^{-166}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x1 \leq 4.9 \cdot 10^{-285}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(x2 \cdot -12 + -1\right)\\ \mathbf{elif}\;x1 \leq 1.1 \cdot 10^{-27}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x1 \leq 4.2 \cdot 10^{+69}:\\ \;\;\;\;t_5\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(t_1 + \left(t_0 \cdot \left(\left(x1 \cdot x1\right) \cdot 6\right) + \left(x1 \cdot x1\right) \cdot 9\right)\right)\right) + 3 \cdot \left(x2 \cdot -2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ (* x1 x1) 1.0))
        (t_1 (* x1 (* x1 x1)))
        (t_2
         (+
          x1
          (+ (* x2 -6.0) (* x1 (- (* 4.0 (* x2 (- (* 2.0 x2) 3.0))) 2.0)))))
        (t_3 (* x1 (* x1 3.0)))
        (t_4 (/ (- (+ t_3 (* 2.0 x2)) x1) t_0))
        (t_5
         (+
          x1
          (+
           (+
            x1
            (+
             (+
              (*
               t_0
               (+
                (* (* (* x1 2.0) t_4) (- t_4 3.0))
                (* (* x1 x1) (- (* t_4 4.0) 6.0))))
              (* t_3 t_4))
             t_1))
           9.0))))
   (if (<= x1 -1.22e+53)
     (+ (* x1 2.0) (* 6.0 (pow x1 4.0)))
     (if (<= x1 -0.00112)
       t_5
       (if (<= x1 -8.4e-166)
         t_2
         (if (<= x1 4.9e-285)
           (+ (* x2 -6.0) (* x1 (+ (* x2 -12.0) -1.0)))
           (if (<= x1 1.1e-27)
             t_2
             (if (<= x1 4.2e+69)
               t_5
               (+
                x1
                (+
                 (+ x1 (+ t_1 (+ (* t_0 (* (* x1 x1) 6.0)) (* (* x1 x1) 9.0))))
                 (* 3.0 (* x2 -2.0))))))))))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = x1 * (x1 * x1);
	double t_2 = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)));
	double t_3 = x1 * (x1 * 3.0);
	double t_4 = ((t_3 + (2.0 * x2)) - x1) / t_0;
	double t_5 = x1 + ((x1 + (((t_0 * ((((x1 * 2.0) * t_4) * (t_4 - 3.0)) + ((x1 * x1) * ((t_4 * 4.0) - 6.0)))) + (t_3 * t_4)) + t_1)) + 9.0);
	double tmp;
	if (x1 <= -1.22e+53) {
		tmp = (x1 * 2.0) + (6.0 * pow(x1, 4.0));
	} else if (x1 <= -0.00112) {
		tmp = t_5;
	} else if (x1 <= -8.4e-166) {
		tmp = t_2;
	} else if (x1 <= 4.9e-285) {
		tmp = (x2 * -6.0) + (x1 * ((x2 * -12.0) + -1.0));
	} else if (x1 <= 1.1e-27) {
		tmp = t_2;
	} else if (x1 <= 4.2e+69) {
		tmp = t_5;
	} else {
		tmp = x1 + ((x1 + (t_1 + ((t_0 * ((x1 * x1) * 6.0)) + ((x1 * x1) * 9.0)))) + (3.0 * (x2 * -2.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_0 = (x1 * x1) + 1.0d0
    t_1 = x1 * (x1 * x1)
    t_2 = x1 + ((x2 * (-6.0d0)) + (x1 * ((4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0))) - 2.0d0)))
    t_3 = x1 * (x1 * 3.0d0)
    t_4 = ((t_3 + (2.0d0 * x2)) - x1) / t_0
    t_5 = x1 + ((x1 + (((t_0 * ((((x1 * 2.0d0) * t_4) * (t_4 - 3.0d0)) + ((x1 * x1) * ((t_4 * 4.0d0) - 6.0d0)))) + (t_3 * t_4)) + t_1)) + 9.0d0)
    if (x1 <= (-1.22d+53)) then
        tmp = (x1 * 2.0d0) + (6.0d0 * (x1 ** 4.0d0))
    else if (x1 <= (-0.00112d0)) then
        tmp = t_5
    else if (x1 <= (-8.4d-166)) then
        tmp = t_2
    else if (x1 <= 4.9d-285) then
        tmp = (x2 * (-6.0d0)) + (x1 * ((x2 * (-12.0d0)) + (-1.0d0)))
    else if (x1 <= 1.1d-27) then
        tmp = t_2
    else if (x1 <= 4.2d+69) then
        tmp = t_5
    else
        tmp = x1 + ((x1 + (t_1 + ((t_0 * ((x1 * x1) * 6.0d0)) + ((x1 * x1) * 9.0d0)))) + (3.0d0 * (x2 * (-2.0d0))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = x1 * (x1 * x1);
	double t_2 = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)));
	double t_3 = x1 * (x1 * 3.0);
	double t_4 = ((t_3 + (2.0 * x2)) - x1) / t_0;
	double t_5 = x1 + ((x1 + (((t_0 * ((((x1 * 2.0) * t_4) * (t_4 - 3.0)) + ((x1 * x1) * ((t_4 * 4.0) - 6.0)))) + (t_3 * t_4)) + t_1)) + 9.0);
	double tmp;
	if (x1 <= -1.22e+53) {
		tmp = (x1 * 2.0) + (6.0 * Math.pow(x1, 4.0));
	} else if (x1 <= -0.00112) {
		tmp = t_5;
	} else if (x1 <= -8.4e-166) {
		tmp = t_2;
	} else if (x1 <= 4.9e-285) {
		tmp = (x2 * -6.0) + (x1 * ((x2 * -12.0) + -1.0));
	} else if (x1 <= 1.1e-27) {
		tmp = t_2;
	} else if (x1 <= 4.2e+69) {
		tmp = t_5;
	} else {
		tmp = x1 + ((x1 + (t_1 + ((t_0 * ((x1 * x1) * 6.0)) + ((x1 * x1) * 9.0)))) + (3.0 * (x2 * -2.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x1 * x1) + 1.0
	t_1 = x1 * (x1 * x1)
	t_2 = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)))
	t_3 = x1 * (x1 * 3.0)
	t_4 = ((t_3 + (2.0 * x2)) - x1) / t_0
	t_5 = x1 + ((x1 + (((t_0 * ((((x1 * 2.0) * t_4) * (t_4 - 3.0)) + ((x1 * x1) * ((t_4 * 4.0) - 6.0)))) + (t_3 * t_4)) + t_1)) + 9.0)
	tmp = 0
	if x1 <= -1.22e+53:
		tmp = (x1 * 2.0) + (6.0 * math.pow(x1, 4.0))
	elif x1 <= -0.00112:
		tmp = t_5
	elif x1 <= -8.4e-166:
		tmp = t_2
	elif x1 <= 4.9e-285:
		tmp = (x2 * -6.0) + (x1 * ((x2 * -12.0) + -1.0))
	elif x1 <= 1.1e-27:
		tmp = t_2
	elif x1 <= 4.2e+69:
		tmp = t_5
	else:
		tmp = x1 + ((x1 + (t_1 + ((t_0 * ((x1 * x1) * 6.0)) + ((x1 * x1) * 9.0)))) + (3.0 * (x2 * -2.0)))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * x1) + 1.0)
	t_1 = Float64(x1 * Float64(x1 * x1))
	t_2 = 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_3 = Float64(x1 * Float64(x1 * 3.0))
	t_4 = Float64(Float64(Float64(t_3 + Float64(2.0 * x2)) - x1) / t_0)
	t_5 = Float64(x1 + Float64(Float64(x1 + Float64(Float64(Float64(t_0 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_4) * Float64(t_4 - 3.0)) + Float64(Float64(x1 * x1) * Float64(Float64(t_4 * 4.0) - 6.0)))) + Float64(t_3 * t_4)) + t_1)) + 9.0))
	tmp = 0.0
	if (x1 <= -1.22e+53)
		tmp = Float64(Float64(x1 * 2.0) + Float64(6.0 * (x1 ^ 4.0)));
	elseif (x1 <= -0.00112)
		tmp = t_5;
	elseif (x1 <= -8.4e-166)
		tmp = t_2;
	elseif (x1 <= 4.9e-285)
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(x2 * -12.0) + -1.0)));
	elseif (x1 <= 1.1e-27)
		tmp = t_2;
	elseif (x1 <= 4.2e+69)
		tmp = t_5;
	else
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(t_1 + Float64(Float64(t_0 * Float64(Float64(x1 * x1) * 6.0)) + Float64(Float64(x1 * x1) * 9.0)))) + Float64(3.0 * Float64(x2 * -2.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x1 * x1) + 1.0;
	t_1 = x1 * (x1 * x1);
	t_2 = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)));
	t_3 = x1 * (x1 * 3.0);
	t_4 = ((t_3 + (2.0 * x2)) - x1) / t_0;
	t_5 = x1 + ((x1 + (((t_0 * ((((x1 * 2.0) * t_4) * (t_4 - 3.0)) + ((x1 * x1) * ((t_4 * 4.0) - 6.0)))) + (t_3 * t_4)) + t_1)) + 9.0);
	tmp = 0.0;
	if (x1 <= -1.22e+53)
		tmp = (x1 * 2.0) + (6.0 * (x1 ^ 4.0));
	elseif (x1 <= -0.00112)
		tmp = t_5;
	elseif (x1 <= -8.4e-166)
		tmp = t_2;
	elseif (x1 <= 4.9e-285)
		tmp = (x2 * -6.0) + (x1 * ((x2 * -12.0) + -1.0));
	elseif (x1 <= 1.1e-27)
		tmp = t_2;
	elseif (x1 <= 4.2e+69)
		tmp = t_5;
	else
		tmp = x1 + ((x1 + (t_1 + ((t_0 * ((x1 * x1) * 6.0)) + ((x1 * x1) * 9.0)))) + (3.0 * (x2 * -2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = 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$3 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(t$95$3 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]}, Block[{t$95$5 = N[(x1 + N[(N[(x1 + N[(N[(N[(t$95$0 * N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$4), $MachinePrecision] * N[(t$95$4 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$4 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$3 * t$95$4), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision] + 9.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -1.22e+53], N[(N[(x1 * 2.0), $MachinePrecision] + N[(6.0 * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -0.00112], t$95$5, If[LessEqual[x1, -8.4e-166], t$95$2, If[LessEqual[x1, 4.9e-285], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(x2 * -12.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.1e-27], t$95$2, If[LessEqual[x1, 4.2e+69], t$95$5, N[(x1 + N[(N[(x1 + N[(t$95$1 + N[(N[(t$95$0 * N[(N[(x1 * x1), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x1 < -1.21999999999999999e53

   1. Initial program 19.5%

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

   2. Taylor expanded in x1 around 0 19.5%

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

      1. *-commutative 19.5%

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

   4. Simplified 19.5%

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

   5. Taylor expanded in x1 around inf 98.2%

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

      1. *-commutative 98.2%

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

   7. Simplified 98.2%

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

   8. Taylor expanded in x1 around inf 98.2%

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

   if -1.21999999999999999e53 < x1 < -0.0011199999999999999 or 1.09999999999999993e-27 < x1 < 4.2000000000000003e69

   1. Initial program 96.2%

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

   2. Taylor expanded in x1 around inf 96.3%

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

   if -0.0011199999999999999 < x1 < -8.3999999999999998e-166 or 4.89999999999999975e-285 < x1 < 1.09999999999999993e-27

   1. Initial program 99.3%

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

   2. Taylor expanded in x1 around 0 90.7%

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

   3. Taylor expanded in x1 around 0 91.2%

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

   if -8.3999999999999998e-166 < x1 < 4.89999999999999975e-285

   1. Initial program 99.3%

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

   2. Taylor expanded in x1 around 0 78.3%

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

   3. Taylor expanded in x2 around 0 99.3%

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

      1. associate-*r* 99.3%

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

   5. Simplified 99.3%

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

   6. Taylor expanded in x1 around 0 99.7%

      \[\leadsto x1 + \color{blue}{\left(-6 \cdot x2 + x1 \cdot \left(-12 \cdot x2 - 2\right)\right)} \]
   7. Step-by-step derivation

      1. fma-def 99.9%

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

      2. *-commutative 99.9%

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

      3. fma-neg 99.9%

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

      4. metadata-eval 99.9%

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

   8. Simplified 99.9%

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

   9. Taylor expanded in x1 around 0 99.8%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(-12 \cdot x2 - 1\right)} \]

   if 4.2000000000000003e69 < x1

   1. Initial program 47.1%

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

   2. Taylor expanded in x1 around 0 47.1%

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

      1. *-commutative 47.1%

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

   4. Simplified 47.1%

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

   5. Taylor expanded in x1 around inf 47.1%

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

      1. *-commutative 47.1%

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

      2. unpow2 47.1%

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

   7. Simplified 47.1%

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

   8. Taylor expanded in x1 around inf 98.1%

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

      1. *-commutative 98.1%

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

      2. unpow2 98.1%

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

   10. Simplified 98.1%

       \[\leadsto x1 + \left(\left(\left(\left(\left(\left(x1 \cdot x1\right) \cdot 6\right) \cdot \left(x1 \cdot x1 + 1\right) + \color{blue}{\left(x1 \cdot x1\right) \cdot 9}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]
3. Recombined 5 regimes into one program.

4. Final simplification 95.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.22 \cdot 10^{+53}:\\ \;\;\;\;x1 \cdot 2 + 6 \cdot {x1}^{4}\\ \mathbf{elif}\;x1 \leq -0.00112:\\ \;\;\;\;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) + 9\right)\\ \mathbf{elif}\;x1 \leq -8.4 \cdot 10^{-166}:\\ \;\;\;\;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 4.9 \cdot 10^{-285}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(x2 \cdot -12 + -1\right)\\ \mathbf{elif}\;x1 \leq 1.1 \cdot 10^{-27}:\\ \;\;\;\;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 4.2 \cdot 10^{+69}:\\ \;\;\;\;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) + 9\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\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 6\right) + \left(x1 \cdot x1\right) \cdot 9\right)\right)\right) + 3 \cdot \left(x2 \cdot -2\right)\right)\\ \end{array} \]

Alternative 4: 95.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot x1\right)\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := x1 \cdot x1 + 1\\ t_3 := \frac{\left(t_1 + 2 \cdot x2\right) - x1}{t_2}\\ \mathbf{if}\;x1 \leq -4 \cdot 10^{+101}:\\ \;\;\;\;x1 \cdot 2 + 6 \cdot {x1}^{4}\\ \mathbf{elif}\;x1 \leq 2.6 \cdot 10^{+67}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t_1 - 2 \cdot x2\right) - x1}{t_2} + \left(x1 + \left(t_0 + \left(t_1 \cdot t_3 + t_2 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(t_3 \cdot 4 - 6\right) + \left(t_3 - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(x2 + \left(x2 - x1\right)\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(t_0 + \left(t_2 \cdot \left(\left(x1 \cdot x1\right) \cdot 6\right) + \left(x1 \cdot x1\right) \cdot 9\right)\right)\right) + 3 \cdot \left(x2 \cdot -2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 x1)))
        (t_1 (* x1 (* x1 3.0)))
        (t_2 (+ (* x1 x1) 1.0))
        (t_3 (/ (- (+ t_1 (* 2.0 x2)) x1) t_2)))
   (if (<= x1 -4e+101)
     (+ (* x1 2.0) (* 6.0 (pow x1 4.0)))
     (if (<= x1 2.6e+67)
       (+
        x1
        (+
         (* 3.0 (/ (- (- t_1 (* 2.0 x2)) x1) t_2))
         (+
          x1
          (+
           t_0
           (+
            (* t_1 t_3)
            (*
             t_2
             (+
              (* (* x1 x1) (- (* t_3 4.0) 6.0))
              (* (- t_3 3.0) (* (* x1 2.0) (+ x2 (- x2 x1)))))))))))
       (+
        x1
        (+
         (+ x1 (+ t_0 (+ (* t_2 (* (* x1 x1) 6.0)) (* (* x1 x1) 9.0))))
         (* 3.0 (* x2 -2.0))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * x1);
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = ((t_1 + (2.0 * x2)) - x1) / t_2;
	double tmp;
	if (x1 <= -4e+101) {
		tmp = (x1 * 2.0) + (6.0 * pow(x1, 4.0));
	} else if (x1 <= 2.6e+67) {
		tmp = x1 + ((3.0 * (((t_1 - (2.0 * x2)) - x1) / t_2)) + (x1 + (t_0 + ((t_1 * t_3) + (t_2 * (((x1 * x1) * ((t_3 * 4.0) - 6.0)) + ((t_3 - 3.0) * ((x1 * 2.0) * (x2 + (x2 - x1))))))))));
	} else {
		tmp = x1 + ((x1 + (t_0 + ((t_2 * ((x1 * x1) * 6.0)) + ((x1 * x1) * 9.0)))) + (3.0 * (x2 * -2.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_0 = x1 * (x1 * x1)
    t_1 = x1 * (x1 * 3.0d0)
    t_2 = (x1 * x1) + 1.0d0
    t_3 = ((t_1 + (2.0d0 * x2)) - x1) / t_2
    if (x1 <= (-4d+101)) then
        tmp = (x1 * 2.0d0) + (6.0d0 * (x1 ** 4.0d0))
    else if (x1 <= 2.6d+67) then
        tmp = x1 + ((3.0d0 * (((t_1 - (2.0d0 * x2)) - x1) / t_2)) + (x1 + (t_0 + ((t_1 * t_3) + (t_2 * (((x1 * x1) * ((t_3 * 4.0d0) - 6.0d0)) + ((t_3 - 3.0d0) * ((x1 * 2.0d0) * (x2 + (x2 - x1))))))))))
    else
        tmp = x1 + ((x1 + (t_0 + ((t_2 * ((x1 * x1) * 6.0d0)) + ((x1 * x1) * 9.0d0)))) + (3.0d0 * (x2 * (-2.0d0))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * x1);
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = ((t_1 + (2.0 * x2)) - x1) / t_2;
	double tmp;
	if (x1 <= -4e+101) {
		tmp = (x1 * 2.0) + (6.0 * Math.pow(x1, 4.0));
	} else if (x1 <= 2.6e+67) {
		tmp = x1 + ((3.0 * (((t_1 - (2.0 * x2)) - x1) / t_2)) + (x1 + (t_0 + ((t_1 * t_3) + (t_2 * (((x1 * x1) * ((t_3 * 4.0) - 6.0)) + ((t_3 - 3.0) * ((x1 * 2.0) * (x2 + (x2 - x1))))))))));
	} else {
		tmp = x1 + ((x1 + (t_0 + ((t_2 * ((x1 * x1) * 6.0)) + ((x1 * x1) * 9.0)))) + (3.0 * (x2 * -2.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * x1)
	t_1 = x1 * (x1 * 3.0)
	t_2 = (x1 * x1) + 1.0
	t_3 = ((t_1 + (2.0 * x2)) - x1) / t_2
	tmp = 0
	if x1 <= -4e+101:
		tmp = (x1 * 2.0) + (6.0 * math.pow(x1, 4.0))
	elif x1 <= 2.6e+67:
		tmp = x1 + ((3.0 * (((t_1 - (2.0 * x2)) - x1) / t_2)) + (x1 + (t_0 + ((t_1 * t_3) + (t_2 * (((x1 * x1) * ((t_3 * 4.0) - 6.0)) + ((t_3 - 3.0) * ((x1 * 2.0) * (x2 + (x2 - x1))))))))))
	else:
		tmp = x1 + ((x1 + (t_0 + ((t_2 * ((x1 * x1) * 6.0)) + ((x1 * x1) * 9.0)))) + (3.0 * (x2 * -2.0)))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * x1))
	t_1 = Float64(x1 * Float64(x1 * 3.0))
	t_2 = Float64(Float64(x1 * x1) + 1.0)
	t_3 = Float64(Float64(Float64(t_1 + Float64(2.0 * x2)) - x1) / t_2)
	tmp = 0.0
	if (x1 <= -4e+101)
		tmp = Float64(Float64(x1 * 2.0) + Float64(6.0 * (x1 ^ 4.0)));
	elseif (x1 <= 2.6e+67)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_1 - Float64(2.0 * x2)) - x1) / t_2)) + Float64(x1 + Float64(t_0 + Float64(Float64(t_1 * t_3) + Float64(t_2 * Float64(Float64(Float64(x1 * x1) * Float64(Float64(t_3 * 4.0) - 6.0)) + Float64(Float64(t_3 - 3.0) * Float64(Float64(x1 * 2.0) * Float64(x2 + Float64(x2 - x1)))))))))));
	else
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(t_0 + Float64(Float64(t_2 * Float64(Float64(x1 * x1) * 6.0)) + Float64(Float64(x1 * x1) * 9.0)))) + Float64(3.0 * Float64(x2 * -2.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * x1);
	t_1 = x1 * (x1 * 3.0);
	t_2 = (x1 * x1) + 1.0;
	t_3 = ((t_1 + (2.0 * x2)) - x1) / t_2;
	tmp = 0.0;
	if (x1 <= -4e+101)
		tmp = (x1 * 2.0) + (6.0 * (x1 ^ 4.0));
	elseif (x1 <= 2.6e+67)
		tmp = x1 + ((3.0 * (((t_1 - (2.0 * x2)) - x1) / t_2)) + (x1 + (t_0 + ((t_1 * t_3) + (t_2 * (((x1 * x1) * ((t_3 * 4.0) - 6.0)) + ((t_3 - 3.0) * ((x1 * 2.0) * (x2 + (x2 - x1))))))))));
	else
		tmp = x1 + ((x1 + (t_0 + ((t_2 * ((x1 * x1) * 6.0)) + ((x1 * x1) * 9.0)))) + (3.0 * (x2 * -2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(t$95$1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]}, If[LessEqual[x1, -4e+101], N[(N[(x1 * 2.0), $MachinePrecision] + N[(6.0 * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 2.6e+67], N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$1 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(t$95$0 + N[(N[(t$95$1 * t$95$3), $MachinePrecision] + N[(t$95$2 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$3 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$3 - 3.0), $MachinePrecision] * N[(N[(x1 * 2.0), $MachinePrecision] * N[(x2 + N[(x2 - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x1 + N[(t$95$0 + N[(N[(t$95$2 * N[(N[(x1 * x1), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -3.9999999999999999e101

   1. Initial program 2.2%

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

   2. Taylor expanded in x1 around 0 2.2%

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

      1. *-commutative 2.2%

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

   4. Simplified 2.2%

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

   5. Taylor expanded in x1 around inf 97.8%

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

      1. *-commutative 97.8%

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

   7. Simplified 97.8%

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

   8. Taylor expanded in x1 around inf 97.8%

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

   if -3.9999999999999999e101 < x1 < 2.6e67

   1. Initial program 98.7%

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

   2. Taylor expanded in x1 around 0 95.2%

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

      1. +-commutative 95.2%

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

      2. count-2 95.2%

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

      3. associate-+l+ 95.2%

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

      4. mul-1-neg 95.2%

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

      5. unsub-neg 95.2%

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

   4. Simplified 95.2%

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

   if 2.6e67 < x1

   1. Initial program 49.0%

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

   2. Taylor expanded in x1 around 0 49.0%

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

      1. *-commutative 49.0%

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

   4. Simplified 49.0%

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

   5. Taylor expanded in x1 around inf 47.4%

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

      1. *-commutative 47.4%

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

      2. unpow2 47.4%

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

   7. Simplified 47.4%

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

   8. Taylor expanded in x1 around inf 96.5%

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

      1. *-commutative 96.5%

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

      2. unpow2 96.5%

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

   10. Simplified 96.5%

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

4. Final simplification 96.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4 \cdot 10^{+101}:\\ \;\;\;\;x1 \cdot 2 + 6 \cdot {x1}^{4}\\ \mathbf{elif}\;x1 \leq 2.6 \cdot 10^{+67}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right) + \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(x2 + \left(x2 - x1\right)\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot 6\right) + \left(x1 \cdot x1\right) \cdot 9\right)\right)\right) + 3 \cdot \left(x2 \cdot -2\right)\right)\\ \end{array} \]

Alternative 5: 90.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := x1 \cdot x1 + 1\\ t_2 := 3 \cdot \left(x2 \cdot -2\right)\\ t_3 := \frac{\left(t_0 + 2 \cdot x2\right) - x1}{t_1}\\ t_4 := \left(x1 \cdot 2\right) \cdot t_3\\ t_5 := x1 \cdot \left(x1 \cdot x1\right)\\ t_6 := \left(x1 \cdot x1\right) \cdot \left(t_3 \cdot 4 - 6\right)\\ \mathbf{if}\;x1 \leq -1.7 \cdot 10^{+51}:\\ \;\;\;\;x1 \cdot 2 + 6 \cdot {x1}^{4}\\ \mathbf{elif}\;x1 \leq -0.00063:\\ \;\;\;\;x1 + \left(t_2 + \left(x1 + \left(t_5 + \left(t_1 \cdot \left(t_4 \cdot \left(t_3 - 3\right) + t_6\right) + t_0 \cdot \left(x2 + x2\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -1.05 \cdot 10^{-165}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)\\ \mathbf{elif}\;x1 \leq 4.9 \cdot 10^{-285}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(x2 \cdot -12 + -1\right)\\ \mathbf{elif}\;x1 \leq 41000:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t_0 - 2 \cdot x2\right) - x1}{t_1} + \left(x1 + 4 \cdot \left(x1 \cdot \left(2 \cdot \left(x2 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 4.2 \cdot 10^{+69}:\\ \;\;\;\;x1 + \left(t_2 + \left(x1 + \left(t_5 + \left(t_0 \cdot t_3 + t_1 \cdot \left(t_6 + t_4 \cdot \frac{-1}{x1}\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(t_5 + \left(t_1 \cdot \left(\left(x1 \cdot x1\right) \cdot 6\right) + \left(x1 \cdot x1\right) \cdot 9\right)\right)\right) + t_2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (+ (* x1 x1) 1.0))
        (t_2 (* 3.0 (* x2 -2.0)))
        (t_3 (/ (- (+ t_0 (* 2.0 x2)) x1) t_1))
        (t_4 (* (* x1 2.0) t_3))
        (t_5 (* x1 (* x1 x1)))
        (t_6 (* (* x1 x1) (- (* t_3 4.0) 6.0))))
   (if (<= x1 -1.7e+51)
     (+ (* x1 2.0) (* 6.0 (pow x1 4.0)))
     (if (<= x1 -0.00063)
       (+
        x1
        (+
         t_2
         (+
          x1
          (+ t_5 (+ (* t_1 (+ (* t_4 (- t_3 3.0)) t_6)) (* t_0 (+ x2 x2)))))))
       (if (<= x1 -1.05e-165)
         (+
          x1
          (+ (* x2 -6.0) (* x1 (- (* 4.0 (* x2 (- (* 2.0 x2) 3.0))) 2.0))))
         (if (<= x1 4.9e-285)
           (+ (* x2 -6.0) (* x1 (+ (* x2 -12.0) -1.0)))
           (if (<= x1 41000.0)
             (+
              x1
              (+
               (* 3.0 (/ (- (- t_0 (* 2.0 x2)) x1) t_1))
               (+ x1 (* 4.0 (* x1 (* 2.0 (* x2 x2)))))))
             (if (<= x1 4.2e+69)
               (+
                x1
                (+
                 t_2
                 (+
                  x1
                  (+
                   t_5
                   (+ (* t_0 t_3) (* t_1 (+ t_6 (* t_4 (/ -1.0 x1)))))))))
               (+
                x1
                (+
                 (+ x1 (+ t_5 (+ (* t_1 (* (* x1 x1) 6.0)) (* (* x1 x1) 9.0))))
                 t_2))))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = 3.0 * (x2 * -2.0);
	double t_3 = ((t_0 + (2.0 * x2)) - x1) / t_1;
	double t_4 = (x1 * 2.0) * t_3;
	double t_5 = x1 * (x1 * x1);
	double t_6 = (x1 * x1) * ((t_3 * 4.0) - 6.0);
	double tmp;
	if (x1 <= -1.7e+51) {
		tmp = (x1 * 2.0) + (6.0 * pow(x1, 4.0));
	} else if (x1 <= -0.00063) {
		tmp = x1 + (t_2 + (x1 + (t_5 + ((t_1 * ((t_4 * (t_3 - 3.0)) + t_6)) + (t_0 * (x2 + x2))))));
	} else if (x1 <= -1.05e-165) {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)));
	} else if (x1 <= 4.9e-285) {
		tmp = (x2 * -6.0) + (x1 * ((x2 * -12.0) + -1.0));
	} else if (x1 <= 41000.0) {
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)) + (x1 + (4.0 * (x1 * (2.0 * (x2 * x2))))));
	} else if (x1 <= 4.2e+69) {
		tmp = x1 + (t_2 + (x1 + (t_5 + ((t_0 * t_3) + (t_1 * (t_6 + (t_4 * (-1.0 / x1))))))));
	} else {
		tmp = x1 + ((x1 + (t_5 + ((t_1 * ((x1 * x1) * 6.0)) + ((x1 * x1) * 9.0)))) + 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) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: tmp
    t_0 = x1 * (x1 * 3.0d0)
    t_1 = (x1 * x1) + 1.0d0
    t_2 = 3.0d0 * (x2 * (-2.0d0))
    t_3 = ((t_0 + (2.0d0 * x2)) - x1) / t_1
    t_4 = (x1 * 2.0d0) * t_3
    t_5 = x1 * (x1 * x1)
    t_6 = (x1 * x1) * ((t_3 * 4.0d0) - 6.0d0)
    if (x1 <= (-1.7d+51)) then
        tmp = (x1 * 2.0d0) + (6.0d0 * (x1 ** 4.0d0))
    else if (x1 <= (-0.00063d0)) then
        tmp = x1 + (t_2 + (x1 + (t_5 + ((t_1 * ((t_4 * (t_3 - 3.0d0)) + t_6)) + (t_0 * (x2 + x2))))))
    else if (x1 <= (-1.05d-165)) then
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * ((4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0))) - 2.0d0)))
    else if (x1 <= 4.9d-285) then
        tmp = (x2 * (-6.0d0)) + (x1 * ((x2 * (-12.0d0)) + (-1.0d0)))
    else if (x1 <= 41000.0d0) then
        tmp = x1 + ((3.0d0 * (((t_0 - (2.0d0 * x2)) - x1) / t_1)) + (x1 + (4.0d0 * (x1 * (2.0d0 * (x2 * x2))))))
    else if (x1 <= 4.2d+69) then
        tmp = x1 + (t_2 + (x1 + (t_5 + ((t_0 * t_3) + (t_1 * (t_6 + (t_4 * ((-1.0d0) / x1))))))))
    else
        tmp = x1 + ((x1 + (t_5 + ((t_1 * ((x1 * x1) * 6.0d0)) + ((x1 * x1) * 9.0d0)))) + t_2)
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = 3.0 * (x2 * -2.0);
	double t_3 = ((t_0 + (2.0 * x2)) - x1) / t_1;
	double t_4 = (x1 * 2.0) * t_3;
	double t_5 = x1 * (x1 * x1);
	double t_6 = (x1 * x1) * ((t_3 * 4.0) - 6.0);
	double tmp;
	if (x1 <= -1.7e+51) {
		tmp = (x1 * 2.0) + (6.0 * Math.pow(x1, 4.0));
	} else if (x1 <= -0.00063) {
		tmp = x1 + (t_2 + (x1 + (t_5 + ((t_1 * ((t_4 * (t_3 - 3.0)) + t_6)) + (t_0 * (x2 + x2))))));
	} else if (x1 <= -1.05e-165) {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)));
	} else if (x1 <= 4.9e-285) {
		tmp = (x2 * -6.0) + (x1 * ((x2 * -12.0) + -1.0));
	} else if (x1 <= 41000.0) {
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)) + (x1 + (4.0 * (x1 * (2.0 * (x2 * x2))))));
	} else if (x1 <= 4.2e+69) {
		tmp = x1 + (t_2 + (x1 + (t_5 + ((t_0 * t_3) + (t_1 * (t_6 + (t_4 * (-1.0 / x1))))))));
	} else {
		tmp = x1 + ((x1 + (t_5 + ((t_1 * ((x1 * x1) * 6.0)) + ((x1 * x1) * 9.0)))) + t_2);
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = (x1 * x1) + 1.0
	t_2 = 3.0 * (x2 * -2.0)
	t_3 = ((t_0 + (2.0 * x2)) - x1) / t_1
	t_4 = (x1 * 2.0) * t_3
	t_5 = x1 * (x1 * x1)
	t_6 = (x1 * x1) * ((t_3 * 4.0) - 6.0)
	tmp = 0
	if x1 <= -1.7e+51:
		tmp = (x1 * 2.0) + (6.0 * math.pow(x1, 4.0))
	elif x1 <= -0.00063:
		tmp = x1 + (t_2 + (x1 + (t_5 + ((t_1 * ((t_4 * (t_3 - 3.0)) + t_6)) + (t_0 * (x2 + x2))))))
	elif x1 <= -1.05e-165:
		tmp = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)))
	elif x1 <= 4.9e-285:
		tmp = (x2 * -6.0) + (x1 * ((x2 * -12.0) + -1.0))
	elif x1 <= 41000.0:
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)) + (x1 + (4.0 * (x1 * (2.0 * (x2 * x2))))))
	elif x1 <= 4.2e+69:
		tmp = x1 + (t_2 + (x1 + (t_5 + ((t_0 * t_3) + (t_1 * (t_6 + (t_4 * (-1.0 / x1))))))))
	else:
		tmp = x1 + ((x1 + (t_5 + ((t_1 * ((x1 * x1) * 6.0)) + ((x1 * x1) * 9.0)))) + t_2)
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(Float64(x1 * x1) + 1.0)
	t_2 = Float64(3.0 * Float64(x2 * -2.0))
	t_3 = Float64(Float64(Float64(t_0 + Float64(2.0 * x2)) - x1) / t_1)
	t_4 = Float64(Float64(x1 * 2.0) * t_3)
	t_5 = Float64(x1 * Float64(x1 * x1))
	t_6 = Float64(Float64(x1 * x1) * Float64(Float64(t_3 * 4.0) - 6.0))
	tmp = 0.0
	if (x1 <= -1.7e+51)
		tmp = Float64(Float64(x1 * 2.0) + Float64(6.0 * (x1 ^ 4.0)));
	elseif (x1 <= -0.00063)
		tmp = Float64(x1 + Float64(t_2 + Float64(x1 + Float64(t_5 + Float64(Float64(t_1 * Float64(Float64(t_4 * Float64(t_3 - 3.0)) + t_6)) + Float64(t_0 * Float64(x2 + x2)))))));
	elseif (x1 <= -1.05e-165)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0))) - 2.0))));
	elseif (x1 <= 4.9e-285)
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(x2 * -12.0) + -1.0)));
	elseif (x1 <= 41000.0)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_0 - Float64(2.0 * x2)) - x1) / t_1)) + Float64(x1 + Float64(4.0 * Float64(x1 * Float64(2.0 * Float64(x2 * x2)))))));
	elseif (x1 <= 4.2e+69)
		tmp = Float64(x1 + Float64(t_2 + Float64(x1 + Float64(t_5 + Float64(Float64(t_0 * t_3) + Float64(t_1 * Float64(t_6 + Float64(t_4 * Float64(-1.0 / x1)))))))));
	else
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(t_5 + Float64(Float64(t_1 * Float64(Float64(x1 * x1) * 6.0)) + Float64(Float64(x1 * x1) * 9.0)))) + t_2));
	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 = 3.0 * (x2 * -2.0);
	t_3 = ((t_0 + (2.0 * x2)) - x1) / t_1;
	t_4 = (x1 * 2.0) * t_3;
	t_5 = x1 * (x1 * x1);
	t_6 = (x1 * x1) * ((t_3 * 4.0) - 6.0);
	tmp = 0.0;
	if (x1 <= -1.7e+51)
		tmp = (x1 * 2.0) + (6.0 * (x1 ^ 4.0));
	elseif (x1 <= -0.00063)
		tmp = x1 + (t_2 + (x1 + (t_5 + ((t_1 * ((t_4 * (t_3 - 3.0)) + t_6)) + (t_0 * (x2 + x2))))));
	elseif (x1 <= -1.05e-165)
		tmp = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)));
	elseif (x1 <= 4.9e-285)
		tmp = (x2 * -6.0) + (x1 * ((x2 * -12.0) + -1.0));
	elseif (x1 <= 41000.0)
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)) + (x1 + (4.0 * (x1 * (2.0 * (x2 * x2))))));
	elseif (x1 <= 4.2e+69)
		tmp = x1 + (t_2 + (x1 + (t_5 + ((t_0 * t_3) + (t_1 * (t_6 + (t_4 * (-1.0 / x1))))))));
	else
		tmp = x1 + ((x1 + (t_5 + ((t_1 * ((x1 * x1) * 6.0)) + ((x1 * x1) * 9.0)))) + t_2);
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(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[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$4 = N[(N[(x1 * 2.0), $MachinePrecision] * t$95$3), $MachinePrecision]}, Block[{t$95$5 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$3 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -1.7e+51], N[(N[(x1 * 2.0), $MachinePrecision] + N[(6.0 * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -0.00063], N[(x1 + N[(t$95$2 + N[(x1 + N[(t$95$5 + N[(N[(t$95$1 * N[(N[(t$95$4 * N[(t$95$3 - 3.0), $MachinePrecision]), $MachinePrecision] + t$95$6), $MachinePrecision]), $MachinePrecision] + N[(t$95$0 * N[(x2 + x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -1.05e-165], 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, 4.9e-285], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(x2 * -12.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 41000.0], N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(4.0 * N[(x1 * N[(2.0 * N[(x2 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 4.2e+69], N[(x1 + N[(t$95$2 + N[(x1 + N[(t$95$5 + N[(N[(t$95$0 * t$95$3), $MachinePrecision] + N[(t$95$1 * N[(t$95$6 + N[(t$95$4 * N[(-1.0 / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x1 + N[(t$95$5 + N[(N[(t$95$1 * N[(N[(x1 * x1), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if x1 < -1.69999999999999992e51

   1. Initial program 21.0%

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

   2. Taylor expanded in x1 around 0 21.0%

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

      1. *-commutative 21.0%

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

   4. Simplified 21.0%

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

   5. Taylor expanded in x1 around inf 96.7%

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

      1. *-commutative 96.7%

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

   7. Simplified 96.7%

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

   8. Taylor expanded in x1 around inf 96.5%

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

   if -1.69999999999999992e51 < x1 < -6.30000000000000026e-4

   1. Initial program 99.3%

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

   2. Taylor expanded in x1 around 0 98.2%

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

      1. *-commutative 98.2%

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

   4. Simplified 98.2%

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

   5. Taylor expanded in x1 around 0 86.6%

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

      1. count-2 86.6%

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

   7. Simplified 86.6%

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

   if -6.30000000000000026e-4 < x1 < -1.04999999999999997e-165

   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 86.6%

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

   3. Taylor expanded in x1 around 0 87.2%

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

   if -1.04999999999999997e-165 < x1 < 4.89999999999999975e-285

   1. Initial program 99.3%

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

   2. Taylor expanded in x1 around 0 78.3%

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

   3. Taylor expanded in x2 around 0 99.3%

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

      1. associate-*r* 99.3%

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

   5. Simplified 99.3%

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

   6. Taylor expanded in x1 around 0 99.7%

      \[\leadsto x1 + \color{blue}{\left(-6 \cdot x2 + x1 \cdot \left(-12 \cdot x2 - 2\right)\right)} \]
   7. Step-by-step derivation

      1. fma-def 99.9%

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

      2. *-commutative 99.9%

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

      3. fma-neg 99.9%

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

      4. metadata-eval 99.9%

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

   8. Simplified 99.9%

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

   9. Taylor expanded in x1 around 0 99.8%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(-12 \cdot x2 - 1\right)} \]

   if 4.89999999999999975e-285 < x1 < 41000

   1. Initial program 97.8%

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

   2. Taylor expanded in x1 around 0 91.7%

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

   3. Taylor expanded in x2 around inf 91.7%

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

      1. associate-*r* 91.7%

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

      2. *-commutative 91.7%

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

      3. associate-*l* 91.7%

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

      4. unpow2 91.7%

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

   5. Simplified 91.7%

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

   if 41000 < x1 < 4.2000000000000003e69

   1. Initial program 99.1%

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

   2. Taylor expanded in x1 around 0 99.1%

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

      1. *-commutative 99.1%

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

   4. Simplified 99.1%

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

   5. Taylor expanded in x1 around inf 88.7%

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

   if 4.2000000000000003e69 < x1

   1. Initial program 47.1%

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

   2. Taylor expanded in x1 around 0 47.1%

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

      1. *-commutative 47.1%

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

   4. Simplified 47.1%

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

   5. Taylor expanded in x1 around inf 47.1%

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

      1. *-commutative 47.1%

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

      2. unpow2 47.1%

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

   7. Simplified 47.1%

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

   8. Taylor expanded in x1 around inf 98.1%

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

      1. *-commutative 98.1%

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

      2. unpow2 98.1%

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

   10. Simplified 98.1%

       \[\leadsto x1 + \left(\left(\left(\left(\left(\left(x1 \cdot x1\right) \cdot 6\right) \cdot \left(x1 \cdot x1 + 1\right) + \color{blue}{\left(x1 \cdot x1\right) \cdot 9}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]
3. Recombined 7 regimes into one program.

4. Final simplification 94.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.7 \cdot 10^{+51}:\\ \;\;\;\;x1 \cdot 2 + 6 \cdot {x1}^{4}\\ \mathbf{elif}\;x1 \leq -0.00063:\\ \;\;\;\;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) + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(x2 + x2\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -1.05 \cdot 10^{-165}:\\ \;\;\;\;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 4.9 \cdot 10^{-285}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(x2 \cdot -12 + -1\right)\\ \mathbf{elif}\;x1 \leq 41000:\\ \;\;\;\;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(2 \cdot \left(x2 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 4.2 \cdot 10^{+69}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2\right) + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right) + \left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \frac{-1}{x1}\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\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 6\right) + \left(x1 \cdot x1\right) \cdot 9\right)\right)\right) + 3 \cdot \left(x2 \cdot -2\right)\right)\\ \end{array} \]

Alternative 6: 84.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := 3 \cdot \left(x2 \cdot -2\right)\\ t_2 := x1 \cdot \left(x1 \cdot x1\right)\\ t_3 := x1 \cdot \left(x1 \cdot 3\right)\\ t_4 := \frac{\left(t_3 + 2 \cdot x2\right) - x1}{t_0}\\ t_5 := x1 + \left(t_1 + \left(x1 + \left(t_2 + \left(t_3 \cdot t_4 + t_0 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(t_4 \cdot 4 - 6\right) + \left(\left(x1 \cdot 2\right) \cdot t_4\right) \cdot \frac{-1}{x1}\right)\right)\right)\right)\right)\\ \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(t_1 + \left(x1 + \left(x1 \cdot x1\right) \cdot \left(6 + x2 \cdot 6\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -1.02 \cdot 10^{+15}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;x1 \leq -8.4 \cdot 10^{-166}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)\\ \mathbf{elif}\;x1 \leq 4.4 \cdot 10^{-285}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(x2 \cdot -12 + -1\right)\\ \mathbf{elif}\;x1 \leq 8200000000:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t_3 - 2 \cdot x2\right) - x1}{t_0} + \left(x1 + 4 \cdot \left(x1 \cdot \left(2 \cdot \left(x2 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 4.2 \cdot 10^{+69}:\\ \;\;\;\;t_5\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(t_2 + \left(t_0 \cdot \left(\left(x1 \cdot x1\right) \cdot 6\right) + \left(x1 \cdot x1\right) \cdot 9\right)\right)\right) + t_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ (* x1 x1) 1.0))
        (t_1 (* 3.0 (* x2 -2.0)))
        (t_2 (* x1 (* x1 x1)))
        (t_3 (* x1 (* x1 3.0)))
        (t_4 (/ (- (+ t_3 (* 2.0 x2)) x1) t_0))
        (t_5
         (+
          x1
          (+
           t_1
           (+
            x1
            (+
             t_2
             (+
              (* t_3 t_4)
              (*
               t_0
               (+
                (* (* x1 x1) (- (* t_4 4.0) 6.0))
                (* (* (* x1 2.0) t_4) (/ -1.0 x1)))))))))))
   (if (<= x1 -5.6e+102)
     (+ x1 (+ t_1 (+ x1 (* (* x1 x1) (+ 6.0 (* x2 6.0))))))
     (if (<= x1 -1.02e+15)
       t_5
       (if (<= x1 -8.4e-166)
         (+
          x1
          (+ (* x2 -6.0) (* x1 (- (* 4.0 (* x2 (- (* 2.0 x2) 3.0))) 2.0))))
         (if (<= x1 4.4e-285)
           (+ (* x2 -6.0) (* x1 (+ (* x2 -12.0) -1.0)))
           (if (<= x1 8200000000.0)
             (+
              x1
              (+
               (* 3.0 (/ (- (- t_3 (* 2.0 x2)) x1) t_0))
               (+ x1 (* 4.0 (* x1 (* 2.0 (* x2 x2)))))))
             (if (<= x1 4.2e+69)
               t_5
               (+
                x1
                (+
                 (+ x1 (+ t_2 (+ (* t_0 (* (* x1 x1) 6.0)) (* (* x1 x1) 9.0))))
                 t_1))))))))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = 3.0 * (x2 * -2.0);
	double t_2 = x1 * (x1 * x1);
	double t_3 = x1 * (x1 * 3.0);
	double t_4 = ((t_3 + (2.0 * x2)) - x1) / t_0;
	double t_5 = x1 + (t_1 + (x1 + (t_2 + ((t_3 * t_4) + (t_0 * (((x1 * x1) * ((t_4 * 4.0) - 6.0)) + (((x1 * 2.0) * t_4) * (-1.0 / x1))))))));
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = x1 + (t_1 + (x1 + ((x1 * x1) * (6.0 + (x2 * 6.0)))));
	} else if (x1 <= -1.02e+15) {
		tmp = t_5;
	} else if (x1 <= -8.4e-166) {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)));
	} else if (x1 <= 4.4e-285) {
		tmp = (x2 * -6.0) + (x1 * ((x2 * -12.0) + -1.0));
	} else if (x1 <= 8200000000.0) {
		tmp = x1 + ((3.0 * (((t_3 - (2.0 * x2)) - x1) / t_0)) + (x1 + (4.0 * (x1 * (2.0 * (x2 * x2))))));
	} else if (x1 <= 4.2e+69) {
		tmp = t_5;
	} else {
		tmp = x1 + ((x1 + (t_2 + ((t_0 * ((x1 * x1) * 6.0)) + ((x1 * x1) * 9.0)))) + t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_0 = (x1 * x1) + 1.0d0
    t_1 = 3.0d0 * (x2 * (-2.0d0))
    t_2 = x1 * (x1 * x1)
    t_3 = x1 * (x1 * 3.0d0)
    t_4 = ((t_3 + (2.0d0 * x2)) - x1) / t_0
    t_5 = x1 + (t_1 + (x1 + (t_2 + ((t_3 * t_4) + (t_0 * (((x1 * x1) * ((t_4 * 4.0d0) - 6.0d0)) + (((x1 * 2.0d0) * t_4) * ((-1.0d0) / x1))))))))
    if (x1 <= (-5.6d+102)) then
        tmp = x1 + (t_1 + (x1 + ((x1 * x1) * (6.0d0 + (x2 * 6.0d0)))))
    else if (x1 <= (-1.02d+15)) then
        tmp = t_5
    else if (x1 <= (-8.4d-166)) then
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * ((4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0))) - 2.0d0)))
    else if (x1 <= 4.4d-285) then
        tmp = (x2 * (-6.0d0)) + (x1 * ((x2 * (-12.0d0)) + (-1.0d0)))
    else if (x1 <= 8200000000.0d0) then
        tmp = x1 + ((3.0d0 * (((t_3 - (2.0d0 * x2)) - x1) / t_0)) + (x1 + (4.0d0 * (x1 * (2.0d0 * (x2 * x2))))))
    else if (x1 <= 4.2d+69) then
        tmp = t_5
    else
        tmp = x1 + ((x1 + (t_2 + ((t_0 * ((x1 * x1) * 6.0d0)) + ((x1 * x1) * 9.0d0)))) + t_1)
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = 3.0 * (x2 * -2.0);
	double t_2 = x1 * (x1 * x1);
	double t_3 = x1 * (x1 * 3.0);
	double t_4 = ((t_3 + (2.0 * x2)) - x1) / t_0;
	double t_5 = x1 + (t_1 + (x1 + (t_2 + ((t_3 * t_4) + (t_0 * (((x1 * x1) * ((t_4 * 4.0) - 6.0)) + (((x1 * 2.0) * t_4) * (-1.0 / x1))))))));
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = x1 + (t_1 + (x1 + ((x1 * x1) * (6.0 + (x2 * 6.0)))));
	} else if (x1 <= -1.02e+15) {
		tmp = t_5;
	} else if (x1 <= -8.4e-166) {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)));
	} else if (x1 <= 4.4e-285) {
		tmp = (x2 * -6.0) + (x1 * ((x2 * -12.0) + -1.0));
	} else if (x1 <= 8200000000.0) {
		tmp = x1 + ((3.0 * (((t_3 - (2.0 * x2)) - x1) / t_0)) + (x1 + (4.0 * (x1 * (2.0 * (x2 * x2))))));
	} else if (x1 <= 4.2e+69) {
		tmp = t_5;
	} else {
		tmp = x1 + ((x1 + (t_2 + ((t_0 * ((x1 * x1) * 6.0)) + ((x1 * x1) * 9.0)))) + t_1);
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x1 * x1) + 1.0
	t_1 = 3.0 * (x2 * -2.0)
	t_2 = x1 * (x1 * x1)
	t_3 = x1 * (x1 * 3.0)
	t_4 = ((t_3 + (2.0 * x2)) - x1) / t_0
	t_5 = x1 + (t_1 + (x1 + (t_2 + ((t_3 * t_4) + (t_0 * (((x1 * x1) * ((t_4 * 4.0) - 6.0)) + (((x1 * 2.0) * t_4) * (-1.0 / x1))))))))
	tmp = 0
	if x1 <= -5.6e+102:
		tmp = x1 + (t_1 + (x1 + ((x1 * x1) * (6.0 + (x2 * 6.0)))))
	elif x1 <= -1.02e+15:
		tmp = t_5
	elif x1 <= -8.4e-166:
		tmp = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)))
	elif x1 <= 4.4e-285:
		tmp = (x2 * -6.0) + (x1 * ((x2 * -12.0) + -1.0))
	elif x1 <= 8200000000.0:
		tmp = x1 + ((3.0 * (((t_3 - (2.0 * x2)) - x1) / t_0)) + (x1 + (4.0 * (x1 * (2.0 * (x2 * x2))))))
	elif x1 <= 4.2e+69:
		tmp = t_5
	else:
		tmp = x1 + ((x1 + (t_2 + ((t_0 * ((x1 * x1) * 6.0)) + ((x1 * x1) * 9.0)))) + t_1)
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * x1) + 1.0)
	t_1 = Float64(3.0 * Float64(x2 * -2.0))
	t_2 = Float64(x1 * Float64(x1 * x1))
	t_3 = Float64(x1 * Float64(x1 * 3.0))
	t_4 = Float64(Float64(Float64(t_3 + Float64(2.0 * x2)) - x1) / t_0)
	t_5 = Float64(x1 + Float64(t_1 + Float64(x1 + Float64(t_2 + Float64(Float64(t_3 * t_4) + Float64(t_0 * Float64(Float64(Float64(x1 * x1) * Float64(Float64(t_4 * 4.0) - 6.0)) + Float64(Float64(Float64(x1 * 2.0) * t_4) * Float64(-1.0 / x1)))))))))
	tmp = 0.0
	if (x1 <= -5.6e+102)
		tmp = Float64(x1 + Float64(t_1 + Float64(x1 + Float64(Float64(x1 * x1) * Float64(6.0 + Float64(x2 * 6.0))))));
	elseif (x1 <= -1.02e+15)
		tmp = t_5;
	elseif (x1 <= -8.4e-166)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0))) - 2.0))));
	elseif (x1 <= 4.4e-285)
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(x2 * -12.0) + -1.0)));
	elseif (x1 <= 8200000000.0)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_3 - Float64(2.0 * x2)) - x1) / t_0)) + Float64(x1 + Float64(4.0 * Float64(x1 * Float64(2.0 * Float64(x2 * x2)))))));
	elseif (x1 <= 4.2e+69)
		tmp = t_5;
	else
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(t_2 + Float64(Float64(t_0 * Float64(Float64(x1 * x1) * 6.0)) + Float64(Float64(x1 * x1) * 9.0)))) + t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x1 * x1) + 1.0;
	t_1 = 3.0 * (x2 * -2.0);
	t_2 = x1 * (x1 * x1);
	t_3 = x1 * (x1 * 3.0);
	t_4 = ((t_3 + (2.0 * x2)) - x1) / t_0;
	t_5 = x1 + (t_1 + (x1 + (t_2 + ((t_3 * t_4) + (t_0 * (((x1 * x1) * ((t_4 * 4.0) - 6.0)) + (((x1 * 2.0) * t_4) * (-1.0 / x1))))))));
	tmp = 0.0;
	if (x1 <= -5.6e+102)
		tmp = x1 + (t_1 + (x1 + ((x1 * x1) * (6.0 + (x2 * 6.0)))));
	elseif (x1 <= -1.02e+15)
		tmp = t_5;
	elseif (x1 <= -8.4e-166)
		tmp = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)));
	elseif (x1 <= 4.4e-285)
		tmp = (x2 * -6.0) + (x1 * ((x2 * -12.0) + -1.0));
	elseif (x1 <= 8200000000.0)
		tmp = x1 + ((3.0 * (((t_3 - (2.0 * x2)) - x1) / t_0)) + (x1 + (4.0 * (x1 * (2.0 * (x2 * x2))))));
	elseif (x1 <= 4.2e+69)
		tmp = t_5;
	else
		tmp = x1 + ((x1 + (t_2 + ((t_0 * ((x1 * x1) * 6.0)) + ((x1 * x1) * 9.0)))) + t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$1 = N[(3.0 * N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(t$95$3 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]}, Block[{t$95$5 = N[(x1 + N[(t$95$1 + N[(x1 + N[(t$95$2 + N[(N[(t$95$3 * t$95$4), $MachinePrecision] + N[(t$95$0 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$4 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$4), $MachinePrecision] * N[(-1.0 / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -5.6e+102], N[(x1 + N[(t$95$1 + N[(x1 + N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 + N[(x2 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -1.02e+15], t$95$5, If[LessEqual[x1, -8.4e-166], 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, 4.4e-285], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(x2 * -12.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 8200000000.0], N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$3 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(4.0 * N[(x1 * N[(2.0 * N[(x2 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 4.2e+69], t$95$5, N[(x1 + N[(N[(x1 + N[(t$95$2 + N[(N[(t$95$0 * N[(N[(x1 * x1), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if x1 < -5.60000000000000037e102

   1. Initial program 2.2%

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

   2. Taylor expanded in x1 around 0 2.2%

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

      1. *-commutative 2.2%

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

   4. Simplified 2.2%

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

   5. Taylor expanded in x1 around inf 0.0%

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

      1. *-commutative 0.0%

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

      2. unpow2 0.0%

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

   7. Simplified 0.0%

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

   8. Taylor expanded in x1 around 0 65.4%

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

      1. unpow2 65.4%

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

   10. Simplified 65.4%

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

   if -5.60000000000000037e102 < x1 < -1.02e15 or 8.2e9 < x1 < 4.2000000000000003e69

   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 99.2%

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

      1. *-commutative 99.2%

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

   4. Simplified 99.2%

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

   5. Taylor expanded in x1 around inf 89.0%

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

   if -1.02e15 < x1 < -8.3999999999999998e-166

   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 79.7%

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

   3. Taylor expanded in x1 around 0 80.6%

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

   if -8.3999999999999998e-166 < x1 < 4.3999999999999998e-285

   1. Initial program 99.3%

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

   2. Taylor expanded in x1 around 0 78.3%

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

   3. Taylor expanded in x2 around 0 99.3%

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

      1. associate-*r* 99.3%

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

   5. Simplified 99.3%

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

   6. Taylor expanded in x1 around 0 99.7%

      \[\leadsto x1 + \color{blue}{\left(-6 \cdot x2 + x1 \cdot \left(-12 \cdot x2 - 2\right)\right)} \]
   7. Step-by-step derivation

      1. fma-def 99.9%

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

      2. *-commutative 99.9%

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

      3. fma-neg 99.9%

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

      4. metadata-eval 99.9%

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

   8. Simplified 99.9%

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

   9. Taylor expanded in x1 around 0 99.8%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(-12 \cdot x2 - 1\right)} \]

   if 4.3999999999999998e-285 < x1 < 8.2e9

   1. Initial program 97.8%

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

   2. Taylor expanded in x1 around 0 91.7%

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

   3. Taylor expanded in x2 around inf 91.7%

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

      1. associate-*r* 91.7%

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

      2. *-commutative 91.7%

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

      3. associate-*l* 91.7%

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

      4. unpow2 91.7%

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

   5. Simplified 91.7%

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

   if 4.2000000000000003e69 < x1

   1. Initial program 47.1%

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

   2. Taylor expanded in x1 around 0 47.1%

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

      1. *-commutative 47.1%

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

   4. Simplified 47.1%

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

   5. Taylor expanded in x1 around inf 47.1%

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

      1. *-commutative 47.1%

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

      2. unpow2 47.1%

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

   7. Simplified 47.1%

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

   8. Taylor expanded in x1 around inf 98.1%

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

      1. *-commutative 98.1%

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

      2. unpow2 98.1%

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

   10. Simplified 98.1%

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

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2\right) + \left(x1 + \left(x1 \cdot x1\right) \cdot \left(6 + x2 \cdot 6\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -1.02 \cdot 10^{+15}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2\right) + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right) + \left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \frac{-1}{x1}\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -8.4 \cdot 10^{-166}:\\ \;\;\;\;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 4.4 \cdot 10^{-285}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(x2 \cdot -12 + -1\right)\\ \mathbf{elif}\;x1 \leq 8200000000:\\ \;\;\;\;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(2 \cdot \left(x2 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 4.2 \cdot 10^{+69}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2\right) + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right) + \left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \frac{-1}{x1}\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\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 6\right) + \left(x1 \cdot x1\right) \cdot 9\right)\right)\right) + 3 \cdot \left(x2 \cdot -2\right)\right)\\ \end{array} \]

Alternative 7: 85.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := 3 \cdot \left(x2 \cdot -2\right)\\ t_2 := x1 \cdot \left(x1 \cdot x1\right)\\ t_3 := x1 \cdot x1 + 1\\ t_4 := \frac{\left(t_0 + 2 \cdot x2\right) - x1}{t_3}\\ t_5 := \left(x1 \cdot 2\right) \cdot t_4\\ t_6 := \left(x1 \cdot x1\right) \cdot \left(t_4 \cdot 4 - 6\right)\\ \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(t_1 + \left(x1 + \left(x1 \cdot x1\right) \cdot \left(6 + x2 \cdot 6\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -0.0022:\\ \;\;\;\;x1 + \left(t_1 + \left(x1 + \left(t_2 + \left(t_3 \cdot \left(t_5 \cdot \left(t_4 - 3\right) + t_6\right) + t_0 \cdot \left(x2 + x2\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -9.5 \cdot 10^{-166}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)\\ \mathbf{elif}\;x1 \leq 4.9 \cdot 10^{-285}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(x2 \cdot -12 + -1\right)\\ \mathbf{elif}\;x1 \leq 19.5:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t_0 - 2 \cdot x2\right) - x1}{t_3} + \left(x1 + 4 \cdot \left(x1 \cdot \left(2 \cdot \left(x2 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 4.2 \cdot 10^{+69}:\\ \;\;\;\;x1 + \left(t_1 + \left(x1 + \left(t_2 + \left(t_0 \cdot t_4 + t_3 \cdot \left(t_6 + t_5 \cdot \frac{-1}{x1}\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(t_2 + \left(t_3 \cdot \left(\left(x1 \cdot x1\right) \cdot 6\right) + \left(x1 \cdot x1\right) \cdot 9\right)\right)\right) + t_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (* 3.0 (* x2 -2.0)))
        (t_2 (* x1 (* x1 x1)))
        (t_3 (+ (* x1 x1) 1.0))
        (t_4 (/ (- (+ t_0 (* 2.0 x2)) x1) t_3))
        (t_5 (* (* x1 2.0) t_4))
        (t_6 (* (* x1 x1) (- (* t_4 4.0) 6.0))))
   (if (<= x1 -5.6e+102)
     (+ x1 (+ t_1 (+ x1 (* (* x1 x1) (+ 6.0 (* x2 6.0))))))
     (if (<= x1 -0.0022)
       (+
        x1
        (+
         t_1
         (+
          x1
          (+ t_2 (+ (* t_3 (+ (* t_5 (- t_4 3.0)) t_6)) (* t_0 (+ x2 x2)))))))
       (if (<= x1 -9.5e-166)
         (+
          x1
          (+ (* x2 -6.0) (* x1 (- (* 4.0 (* x2 (- (* 2.0 x2) 3.0))) 2.0))))
         (if (<= x1 4.9e-285)
           (+ (* x2 -6.0) (* x1 (+ (* x2 -12.0) -1.0)))
           (if (<= x1 19.5)
             (+
              x1
              (+
               (* 3.0 (/ (- (- t_0 (* 2.0 x2)) x1) t_3))
               (+ x1 (* 4.0 (* x1 (* 2.0 (* x2 x2)))))))
             (if (<= x1 4.2e+69)
               (+
                x1
                (+
                 t_1
                 (+
                  x1
                  (+
                   t_2
                   (+ (* t_0 t_4) (* t_3 (+ t_6 (* t_5 (/ -1.0 x1)))))))))
               (+
                x1
                (+
                 (+ x1 (+ t_2 (+ (* t_3 (* (* x1 x1) 6.0)) (* (* x1 x1) 9.0))))
                 t_1))))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = 3.0 * (x2 * -2.0);
	double t_2 = x1 * (x1 * x1);
	double t_3 = (x1 * x1) + 1.0;
	double t_4 = ((t_0 + (2.0 * x2)) - x1) / t_3;
	double t_5 = (x1 * 2.0) * t_4;
	double t_6 = (x1 * x1) * ((t_4 * 4.0) - 6.0);
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = x1 + (t_1 + (x1 + ((x1 * x1) * (6.0 + (x2 * 6.0)))));
	} else if (x1 <= -0.0022) {
		tmp = x1 + (t_1 + (x1 + (t_2 + ((t_3 * ((t_5 * (t_4 - 3.0)) + t_6)) + (t_0 * (x2 + x2))))));
	} else if (x1 <= -9.5e-166) {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)));
	} else if (x1 <= 4.9e-285) {
		tmp = (x2 * -6.0) + (x1 * ((x2 * -12.0) + -1.0));
	} else if (x1 <= 19.5) {
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_3)) + (x1 + (4.0 * (x1 * (2.0 * (x2 * x2))))));
	} else if (x1 <= 4.2e+69) {
		tmp = x1 + (t_1 + (x1 + (t_2 + ((t_0 * t_4) + (t_3 * (t_6 + (t_5 * (-1.0 / x1))))))));
	} else {
		tmp = x1 + ((x1 + (t_2 + ((t_3 * ((x1 * x1) * 6.0)) + ((x1 * x1) * 9.0)))) + t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: tmp
    t_0 = x1 * (x1 * 3.0d0)
    t_1 = 3.0d0 * (x2 * (-2.0d0))
    t_2 = x1 * (x1 * x1)
    t_3 = (x1 * x1) + 1.0d0
    t_4 = ((t_0 + (2.0d0 * x2)) - x1) / t_3
    t_5 = (x1 * 2.0d0) * t_4
    t_6 = (x1 * x1) * ((t_4 * 4.0d0) - 6.0d0)
    if (x1 <= (-5.6d+102)) then
        tmp = x1 + (t_1 + (x1 + ((x1 * x1) * (6.0d0 + (x2 * 6.0d0)))))
    else if (x1 <= (-0.0022d0)) then
        tmp = x1 + (t_1 + (x1 + (t_2 + ((t_3 * ((t_5 * (t_4 - 3.0d0)) + t_6)) + (t_0 * (x2 + x2))))))
    else if (x1 <= (-9.5d-166)) then
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * ((4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0))) - 2.0d0)))
    else if (x1 <= 4.9d-285) then
        tmp = (x2 * (-6.0d0)) + (x1 * ((x2 * (-12.0d0)) + (-1.0d0)))
    else if (x1 <= 19.5d0) then
        tmp = x1 + ((3.0d0 * (((t_0 - (2.0d0 * x2)) - x1) / t_3)) + (x1 + (4.0d0 * (x1 * (2.0d0 * (x2 * x2))))))
    else if (x1 <= 4.2d+69) then
        tmp = x1 + (t_1 + (x1 + (t_2 + ((t_0 * t_4) + (t_3 * (t_6 + (t_5 * ((-1.0d0) / x1))))))))
    else
        tmp = x1 + ((x1 + (t_2 + ((t_3 * ((x1 * x1) * 6.0d0)) + ((x1 * x1) * 9.0d0)))) + t_1)
    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 * (x2 * -2.0);
	double t_2 = x1 * (x1 * x1);
	double t_3 = (x1 * x1) + 1.0;
	double t_4 = ((t_0 + (2.0 * x2)) - x1) / t_3;
	double t_5 = (x1 * 2.0) * t_4;
	double t_6 = (x1 * x1) * ((t_4 * 4.0) - 6.0);
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = x1 + (t_1 + (x1 + ((x1 * x1) * (6.0 + (x2 * 6.0)))));
	} else if (x1 <= -0.0022) {
		tmp = x1 + (t_1 + (x1 + (t_2 + ((t_3 * ((t_5 * (t_4 - 3.0)) + t_6)) + (t_0 * (x2 + x2))))));
	} else if (x1 <= -9.5e-166) {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)));
	} else if (x1 <= 4.9e-285) {
		tmp = (x2 * -6.0) + (x1 * ((x2 * -12.0) + -1.0));
	} else if (x1 <= 19.5) {
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_3)) + (x1 + (4.0 * (x1 * (2.0 * (x2 * x2))))));
	} else if (x1 <= 4.2e+69) {
		tmp = x1 + (t_1 + (x1 + (t_2 + ((t_0 * t_4) + (t_3 * (t_6 + (t_5 * (-1.0 / x1))))))));
	} else {
		tmp = x1 + ((x1 + (t_2 + ((t_3 * ((x1 * x1) * 6.0)) + ((x1 * x1) * 9.0)))) + t_1);
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = 3.0 * (x2 * -2.0)
	t_2 = x1 * (x1 * x1)
	t_3 = (x1 * x1) + 1.0
	t_4 = ((t_0 + (2.0 * x2)) - x1) / t_3
	t_5 = (x1 * 2.0) * t_4
	t_6 = (x1 * x1) * ((t_4 * 4.0) - 6.0)
	tmp = 0
	if x1 <= -5.6e+102:
		tmp = x1 + (t_1 + (x1 + ((x1 * x1) * (6.0 + (x2 * 6.0)))))
	elif x1 <= -0.0022:
		tmp = x1 + (t_1 + (x1 + (t_2 + ((t_3 * ((t_5 * (t_4 - 3.0)) + t_6)) + (t_0 * (x2 + x2))))))
	elif x1 <= -9.5e-166:
		tmp = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)))
	elif x1 <= 4.9e-285:
		tmp = (x2 * -6.0) + (x1 * ((x2 * -12.0) + -1.0))
	elif x1 <= 19.5:
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_3)) + (x1 + (4.0 * (x1 * (2.0 * (x2 * x2))))))
	elif x1 <= 4.2e+69:
		tmp = x1 + (t_1 + (x1 + (t_2 + ((t_0 * t_4) + (t_3 * (t_6 + (t_5 * (-1.0 / x1))))))))
	else:
		tmp = x1 + ((x1 + (t_2 + ((t_3 * ((x1 * x1) * 6.0)) + ((x1 * x1) * 9.0)))) + t_1)
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(3.0 * Float64(x2 * -2.0))
	t_2 = Float64(x1 * Float64(x1 * x1))
	t_3 = Float64(Float64(x1 * x1) + 1.0)
	t_4 = Float64(Float64(Float64(t_0 + Float64(2.0 * x2)) - x1) / t_3)
	t_5 = Float64(Float64(x1 * 2.0) * t_4)
	t_6 = Float64(Float64(x1 * x1) * Float64(Float64(t_4 * 4.0) - 6.0))
	tmp = 0.0
	if (x1 <= -5.6e+102)
		tmp = Float64(x1 + Float64(t_1 + Float64(x1 + Float64(Float64(x1 * x1) * Float64(6.0 + Float64(x2 * 6.0))))));
	elseif (x1 <= -0.0022)
		tmp = Float64(x1 + Float64(t_1 + Float64(x1 + Float64(t_2 + Float64(Float64(t_3 * Float64(Float64(t_5 * Float64(t_4 - 3.0)) + t_6)) + Float64(t_0 * Float64(x2 + x2)))))));
	elseif (x1 <= -9.5e-166)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0))) - 2.0))));
	elseif (x1 <= 4.9e-285)
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(x2 * -12.0) + -1.0)));
	elseif (x1 <= 19.5)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_0 - Float64(2.0 * x2)) - x1) / t_3)) + Float64(x1 + Float64(4.0 * Float64(x1 * Float64(2.0 * Float64(x2 * x2)))))));
	elseif (x1 <= 4.2e+69)
		tmp = Float64(x1 + Float64(t_1 + Float64(x1 + Float64(t_2 + Float64(Float64(t_0 * t_4) + Float64(t_3 * Float64(t_6 + Float64(t_5 * Float64(-1.0 / x1)))))))));
	else
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(t_2 + Float64(Float64(t_3 * Float64(Float64(x1 * x1) * 6.0)) + Float64(Float64(x1 * x1) * 9.0)))) + t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * 3.0);
	t_1 = 3.0 * (x2 * -2.0);
	t_2 = x1 * (x1 * x1);
	t_3 = (x1 * x1) + 1.0;
	t_4 = ((t_0 + (2.0 * x2)) - x1) / t_3;
	t_5 = (x1 * 2.0) * t_4;
	t_6 = (x1 * x1) * ((t_4 * 4.0) - 6.0);
	tmp = 0.0;
	if (x1 <= -5.6e+102)
		tmp = x1 + (t_1 + (x1 + ((x1 * x1) * (6.0 + (x2 * 6.0)))));
	elseif (x1 <= -0.0022)
		tmp = x1 + (t_1 + (x1 + (t_2 + ((t_3 * ((t_5 * (t_4 - 3.0)) + t_6)) + (t_0 * (x2 + x2))))));
	elseif (x1 <= -9.5e-166)
		tmp = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)));
	elseif (x1 <= 4.9e-285)
		tmp = (x2 * -6.0) + (x1 * ((x2 * -12.0) + -1.0));
	elseif (x1 <= 19.5)
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_3)) + (x1 + (4.0 * (x1 * (2.0 * (x2 * x2))))));
	elseif (x1 <= 4.2e+69)
		tmp = x1 + (t_1 + (x1 + (t_2 + ((t_0 * t_4) + (t_3 * (t_6 + (t_5 * (-1.0 / x1))))))));
	else
		tmp = x1 + ((x1 + (t_2 + ((t_3 * ((x1 * x1) * 6.0)) + ((x1 * x1) * 9.0)))) + t_1);
	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 * N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$3), $MachinePrecision]}, Block[{t$95$5 = N[(N[(x1 * 2.0), $MachinePrecision] * t$95$4), $MachinePrecision]}, Block[{t$95$6 = N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$4 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -5.6e+102], N[(x1 + N[(t$95$1 + N[(x1 + N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 + N[(x2 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -0.0022], N[(x1 + N[(t$95$1 + N[(x1 + N[(t$95$2 + N[(N[(t$95$3 * N[(N[(t$95$5 * N[(t$95$4 - 3.0), $MachinePrecision]), $MachinePrecision] + t$95$6), $MachinePrecision]), $MachinePrecision] + N[(t$95$0 * N[(x2 + x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -9.5e-166], 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, 4.9e-285], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(x2 * -12.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 19.5], N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$3), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(4.0 * N[(x1 * N[(2.0 * N[(x2 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 4.2e+69], N[(x1 + N[(t$95$1 + N[(x1 + N[(t$95$2 + N[(N[(t$95$0 * t$95$4), $MachinePrecision] + N[(t$95$3 * N[(t$95$6 + N[(t$95$5 * N[(-1.0 / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x1 + N[(t$95$2 + N[(N[(t$95$3 * N[(N[(x1 * x1), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if x1 < -5.60000000000000037e102

   1. Initial program 2.2%

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

   2. Taylor expanded in x1 around 0 2.2%

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

      1. *-commutative 2.2%

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

   4. Simplified 2.2%

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

   5. Taylor expanded in x1 around inf 0.0%

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

      1. *-commutative 0.0%

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

      2. unpow2 0.0%

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

   7. Simplified 0.0%

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

   8. Taylor expanded in x1 around 0 65.4%

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

      1. unpow2 65.4%

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

   10. Simplified 65.4%

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

   if -5.60000000000000037e102 < x1 < -0.00220000000000000013

   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 98.8%

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

      1. *-commutative 98.8%

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

   4. Simplified 98.8%

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

   5. Taylor expanded in x1 around 0 88.4%

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

      1. count-2 88.4%

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

   7. Simplified 88.4%

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

   if -0.00220000000000000013 < x1 < -9.50000000000000046e-166

   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 86.6%

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

   3. Taylor expanded in x1 around 0 87.2%

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

   if -9.50000000000000046e-166 < x1 < 4.89999999999999975e-285

   1. Initial program 99.3%

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

   2. Taylor expanded in x1 around 0 78.3%

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

   3. Taylor expanded in x2 around 0 99.3%

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

      1. associate-*r* 99.3%

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

   5. Simplified 99.3%

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

   6. Taylor expanded in x1 around 0 99.7%

      \[\leadsto x1 + \color{blue}{\left(-6 \cdot x2 + x1 \cdot \left(-12 \cdot x2 - 2\right)\right)} \]
   7. Step-by-step derivation

      1. fma-def 99.9%

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

      2. *-commutative 99.9%

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

      3. fma-neg 99.9%

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

      4. metadata-eval 99.9%

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

   8. Simplified 99.9%

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

   9. Taylor expanded in x1 around 0 99.8%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(-12 \cdot x2 - 1\right)} \]

   if 4.89999999999999975e-285 < x1 < 19.5

   1. Initial program 97.8%

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

   2. Taylor expanded in x1 around 0 91.7%

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

   3. Taylor expanded in x2 around inf 91.7%

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

      1. associate-*r* 91.7%

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

      2. *-commutative 91.7%

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

      3. associate-*l* 91.7%

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

      4. unpow2 91.7%

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

   5. Simplified 91.7%

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

   if 19.5 < x1 < 4.2000000000000003e69

   1. Initial program 99.1%

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

   2. Taylor expanded in x1 around 0 99.1%

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

      1. *-commutative 99.1%

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

   4. Simplified 99.1%

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

   5. Taylor expanded in x1 around inf 88.7%

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

   if 4.2000000000000003e69 < x1

   1. Initial program 47.1%

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

   2. Taylor expanded in x1 around 0 47.1%

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

      1. *-commutative 47.1%

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

   4. Simplified 47.1%

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

   5. Taylor expanded in x1 around inf 47.1%

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

      1. *-commutative 47.1%

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

      2. unpow2 47.1%

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

   7. Simplified 47.1%

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

   8. Taylor expanded in x1 around inf 98.1%

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

      1. *-commutative 98.1%

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

      2. unpow2 98.1%

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

   10. Simplified 98.1%

       \[\leadsto x1 + \left(\left(\left(\left(\left(\left(x1 \cdot x1\right) \cdot 6\right) \cdot \left(x1 \cdot x1 + 1\right) + \color{blue}{\left(x1 \cdot x1\right) \cdot 9}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \left(x2 \cdot -2\right)\right) \]
3. Recombined 7 regimes into one program.

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2\right) + \left(x1 + \left(x1 \cdot x1\right) \cdot \left(6 + x2 \cdot 6\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -0.0022:\\ \;\;\;\;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) + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(x2 + x2\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -9.5 \cdot 10^{-166}:\\ \;\;\;\;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 4.9 \cdot 10^{-285}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(x2 \cdot -12 + -1\right)\\ \mathbf{elif}\;x1 \leq 19.5:\\ \;\;\;\;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(2 \cdot \left(x2 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 4.2 \cdot 10^{+69}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2\right) + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right) + \left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \frac{-1}{x1}\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\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 6\right) + \left(x1 \cdot x1\right) \cdot 9\right)\right)\right) + 3 \cdot \left(x2 \cdot -2\right)\right)\\ \end{array} \]

Alternative 8: 81.7% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 3 \cdot \left(x2 \cdot -2\right)\\ t_1 := x1 \cdot x1 + 1\\ t_2 := x1 + \left(\left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(t_1 \cdot \left(\left(x1 \cdot x1\right) \cdot 6\right) + \left(x1 \cdot x1\right) \cdot 9\right)\right)\right) + t_0\right)\\ \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(t_0 + \left(x1 + \left(x1 \cdot x1\right) \cdot \left(6 + x2 \cdot 6\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -2.6 \cdot 10^{+34}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x1 \leq -8.5 \cdot 10^{-166}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)\\ \mathbf{elif}\;x1 \leq 4.9 \cdot 10^{-285}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(x2 \cdot -12 + -1\right)\\ \mathbf{elif}\;x1 \leq 650000:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{t_1} + \left(x1 + 4 \cdot \left(x1 \cdot \left(2 \cdot \left(x2 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* 3.0 (* x2 -2.0)))
        (t_1 (+ (* x1 x1) 1.0))
        (t_2
         (+
          x1
          (+
           (+
            x1
            (+
             (* x1 (* x1 x1))
             (+ (* t_1 (* (* x1 x1) 6.0)) (* (* x1 x1) 9.0))))
           t_0))))
   (if (<= x1 -5.6e+102)
     (+ x1 (+ t_0 (+ x1 (* (* x1 x1) (+ 6.0 (* x2 6.0))))))
     (if (<= x1 -2.6e+34)
       t_2
       (if (<= x1 -8.5e-166)
         (+
          x1
          (+ (* x2 -6.0) (* x1 (- (* 4.0 (* x2 (- (* 2.0 x2) 3.0))) 2.0))))
         (if (<= x1 4.9e-285)
           (+ (* x2 -6.0) (* x1 (+ (* x2 -12.0) -1.0)))
           (if (<= x1 650000.0)
             (+
              x1
              (+
               (* 3.0 (/ (- (- (* x1 (* x1 3.0)) (* 2.0 x2)) x1) t_1))
               (+ x1 (* 4.0 (* x1 (* 2.0 (* x2 x2)))))))
             t_2)))))))

C

double code(double x1, double x2) {
	double t_0 = 3.0 * (x2 * -2.0);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = x1 + ((x1 + ((x1 * (x1 * x1)) + ((t_1 * ((x1 * x1) * 6.0)) + ((x1 * x1) * 9.0)))) + t_0);
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = x1 + (t_0 + (x1 + ((x1 * x1) * (6.0 + (x2 * 6.0)))));
	} else if (x1 <= -2.6e+34) {
		tmp = t_2;
	} else if (x1 <= -8.5e-166) {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)));
	} else if (x1 <= 4.9e-285) {
		tmp = (x2 * -6.0) + (x1 * ((x2 * -12.0) + -1.0));
	} else if (x1 <= 650000.0) {
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / t_1)) + (x1 + (4.0 * (x1 * (2.0 * (x2 * x2))))));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = 3.0d0 * (x2 * (-2.0d0))
    t_1 = (x1 * x1) + 1.0d0
    t_2 = x1 + ((x1 + ((x1 * (x1 * x1)) + ((t_1 * ((x1 * x1) * 6.0d0)) + ((x1 * x1) * 9.0d0)))) + t_0)
    if (x1 <= (-5.6d+102)) then
        tmp = x1 + (t_0 + (x1 + ((x1 * x1) * (6.0d0 + (x2 * 6.0d0)))))
    else if (x1 <= (-2.6d+34)) then
        tmp = t_2
    else if (x1 <= (-8.5d-166)) then
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * ((4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0))) - 2.0d0)))
    else if (x1 <= 4.9d-285) then
        tmp = (x2 * (-6.0d0)) + (x1 * ((x2 * (-12.0d0)) + (-1.0d0)))
    else if (x1 <= 650000.0d0) then
        tmp = x1 + ((3.0d0 * ((((x1 * (x1 * 3.0d0)) - (2.0d0 * x2)) - x1) / t_1)) + (x1 + (4.0d0 * (x1 * (2.0d0 * (x2 * x2))))))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = 3.0 * (x2 * -2.0);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = x1 + ((x1 + ((x1 * (x1 * x1)) + ((t_1 * ((x1 * x1) * 6.0)) + ((x1 * x1) * 9.0)))) + t_0);
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = x1 + (t_0 + (x1 + ((x1 * x1) * (6.0 + (x2 * 6.0)))));
	} else if (x1 <= -2.6e+34) {
		tmp = t_2;
	} else if (x1 <= -8.5e-166) {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)));
	} else if (x1 <= 4.9e-285) {
		tmp = (x2 * -6.0) + (x1 * ((x2 * -12.0) + -1.0));
	} else if (x1 <= 650000.0) {
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / t_1)) + (x1 + (4.0 * (x1 * (2.0 * (x2 * x2))))));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = 3.0 * (x2 * -2.0)
	t_1 = (x1 * x1) + 1.0
	t_2 = x1 + ((x1 + ((x1 * (x1 * x1)) + ((t_1 * ((x1 * x1) * 6.0)) + ((x1 * x1) * 9.0)))) + t_0)
	tmp = 0
	if x1 <= -5.6e+102:
		tmp = x1 + (t_0 + (x1 + ((x1 * x1) * (6.0 + (x2 * 6.0)))))
	elif x1 <= -2.6e+34:
		tmp = t_2
	elif x1 <= -8.5e-166:
		tmp = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)))
	elif x1 <= 4.9e-285:
		tmp = (x2 * -6.0) + (x1 * ((x2 * -12.0) + -1.0))
	elif x1 <= 650000.0:
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / t_1)) + (x1 + (4.0 * (x1 * (2.0 * (x2 * x2))))))
	else:
		tmp = t_2
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(3.0 * Float64(x2 * -2.0))
	t_1 = Float64(Float64(x1 * x1) + 1.0)
	t_2 = Float64(x1 + Float64(Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(t_1 * Float64(Float64(x1 * x1) * 6.0)) + Float64(Float64(x1 * x1) * 9.0)))) + t_0))
	tmp = 0.0
	if (x1 <= -5.6e+102)
		tmp = Float64(x1 + Float64(t_0 + Float64(x1 + Float64(Float64(x1 * x1) * Float64(6.0 + Float64(x2 * 6.0))))));
	elseif (x1 <= -2.6e+34)
		tmp = t_2;
	elseif (x1 <= -8.5e-166)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0))) - 2.0))));
	elseif (x1 <= 4.9e-285)
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(x2 * -12.0) + -1.0)));
	elseif (x1 <= 650000.0)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(Float64(x1 * Float64(x1 * 3.0)) - Float64(2.0 * x2)) - x1) / t_1)) + Float64(x1 + Float64(4.0 * Float64(x1 * Float64(2.0 * Float64(x2 * x2)))))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = 3.0 * (x2 * -2.0);
	t_1 = (x1 * x1) + 1.0;
	t_2 = x1 + ((x1 + ((x1 * (x1 * x1)) + ((t_1 * ((x1 * x1) * 6.0)) + ((x1 * x1) * 9.0)))) + t_0);
	tmp = 0.0;
	if (x1 <= -5.6e+102)
		tmp = x1 + (t_0 + (x1 + ((x1 * x1) * (6.0 + (x2 * 6.0)))));
	elseif (x1 <= -2.6e+34)
		tmp = t_2;
	elseif (x1 <= -8.5e-166)
		tmp = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)));
	elseif (x1 <= 4.9e-285)
		tmp = (x2 * -6.0) + (x1 * ((x2 * -12.0) + -1.0));
	elseif (x1 <= 650000.0)
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / t_1)) + (x1 + (4.0 * (x1 * (2.0 * (x2 * x2))))));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(3.0 * N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$2 = N[(x1 + N[(N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$1 * N[(N[(x1 * x1), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -5.6e+102], N[(x1 + N[(t$95$0 + N[(x1 + N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 + N[(x2 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -2.6e+34], t$95$2, If[LessEqual[x1, -8.5e-166], 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, 4.9e-285], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(x2 * -12.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 650000.0], 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] / t$95$1), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(4.0 * N[(x1 * N[(2.0 * N[(x2 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x1 < -5.60000000000000037e102

   1. Initial program 2.2%

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

   2. Taylor expanded in x1 around 0 2.2%

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

      1. *-commutative 2.2%

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

   4. Simplified 2.2%

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

   5. Taylor expanded in x1 around inf 0.0%

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

      1. *-commutative 0.0%

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

      2. unpow2 0.0%

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

   7. Simplified 0.0%

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

   8. Taylor expanded in x1 around 0 65.4%

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

      1. unpow2 65.4%

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

   10. Simplified 65.4%

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

   if -5.60000000000000037e102 < x1 < -2.59999999999999997e34 or 6.5e5 < x1

   1. Initial program 65.9%

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

   2. Taylor expanded in x1 around 0 65.9%

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

      1. *-commutative 65.9%

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

   4. Simplified 65.9%

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

   5. Taylor expanded in x1 around inf 56.3%

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

      1. *-commutative 56.3%

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

      2. unpow2 56.3%

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

   7. Simplified 56.3%

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

   8. Taylor expanded in x1 around inf 88.7%

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

      1. *-commutative 88.7%

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

      2. unpow2 88.7%

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

   10. Simplified 88.7%

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

   if -2.59999999999999997e34 < x1 < -8.5e-166

   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 76.6%

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

   3. Taylor expanded in x1 around 0 77.6%

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

   if -8.5e-166 < x1 < 4.89999999999999975e-285

   1. Initial program 99.3%

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

   2. Taylor expanded in x1 around 0 78.3%

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

   3. Taylor expanded in x2 around 0 99.3%

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

      1. associate-*r* 99.3%

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

   5. Simplified 99.3%

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

   6. Taylor expanded in x1 around 0 99.7%

      \[\leadsto x1 + \color{blue}{\left(-6 \cdot x2 + x1 \cdot \left(-12 \cdot x2 - 2\right)\right)} \]
   7. Step-by-step derivation

      1. fma-def 99.9%

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

      2. *-commutative 99.9%

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

      3. fma-neg 99.9%

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

      4. metadata-eval 99.9%

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

   8. Simplified 99.9%

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

   9. Taylor expanded in x1 around 0 99.8%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(-12 \cdot x2 - 1\right)} \]

   if 4.89999999999999975e-285 < x1 < 6.5e5

   1. Initial program 97.8%

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

   2. Taylor expanded in x1 around 0 91.7%

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

   3. Taylor expanded in x2 around inf 91.7%

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

      1. associate-*r* 91.7%

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

      2. *-commutative 91.7%

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

      3. associate-*l* 91.7%

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

      4. unpow2 91.7%

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

   5. Simplified 91.7%

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

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2\right) + \left(x1 + \left(x1 \cdot x1\right) \cdot \left(6 + x2 \cdot 6\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -2.6 \cdot 10^{+34}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot 6\right) + \left(x1 \cdot x1\right) \cdot 9\right)\right)\right) + 3 \cdot \left(x2 \cdot -2\right)\right)\\ \mathbf{elif}\;x1 \leq -8.5 \cdot 10^{-166}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)\\ \mathbf{elif}\;x1 \leq 4.9 \cdot 10^{-285}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(x2 \cdot -12 + -1\right)\\ \mathbf{elif}\;x1 \leq 650000:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + 4 \cdot \left(x1 \cdot \left(2 \cdot \left(x2 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot 6\right) + \left(x1 \cdot x1\right) \cdot 9\right)\right)\right) + 3 \cdot \left(x2 \cdot -2\right)\right)\\ \end{array} \]

Alternative 9: 82.7% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 3 \cdot \left(x2 \cdot -2\right)\\ t_1 := x1 \cdot \left(x1 \cdot x1\right)\\ t_2 := x1 \cdot x1 + 1\\ t_3 := t_2 \cdot \left(\left(x1 \cdot x1\right) \cdot 6\right)\\ \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(t_0 + \left(x1 + \left(x1 \cdot x1\right) \cdot \left(6 + x2 \cdot 6\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -23000000000000:\\ \;\;\;\;x1 + \left(t_0 + \left(x1 + \left(t_1 + \left(t_3 + x2 \cdot \left(x1 \cdot \left(x1 \cdot 6\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -8.4 \cdot 10^{-166}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)\\ \mathbf{elif}\;x1 \leq 4.9 \cdot 10^{-285}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(x2 \cdot -12 + -1\right)\\ \mathbf{elif}\;x1 \leq 96000000:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{t_2} + \left(x1 + 4 \cdot \left(x1 \cdot \left(2 \cdot \left(x2 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(t_1 + \left(t_3 + \left(x1 \cdot x1\right) \cdot 9\right)\right)\right) + t_0\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* 3.0 (* x2 -2.0)))
        (t_1 (* x1 (* x1 x1)))
        (t_2 (+ (* x1 x1) 1.0))
        (t_3 (* t_2 (* (* x1 x1) 6.0))))
   (if (<= x1 -5.6e+102)
     (+ x1 (+ t_0 (+ x1 (* (* x1 x1) (+ 6.0 (* x2 6.0))))))
     (if (<= x1 -23000000000000.0)
       (+ x1 (+ t_0 (+ x1 (+ t_1 (+ t_3 (* x2 (* x1 (* x1 6.0))))))))
       (if (<= x1 -8.4e-166)
         (+
          x1
          (+ (* x2 -6.0) (* x1 (- (* 4.0 (* x2 (- (* 2.0 x2) 3.0))) 2.0))))
         (if (<= x1 4.9e-285)
           (+ (* x2 -6.0) (* x1 (+ (* x2 -12.0) -1.0)))
           (if (<= x1 96000000.0)
             (+
              x1
              (+
               (* 3.0 (/ (- (- (* x1 (* x1 3.0)) (* 2.0 x2)) x1) t_2))
               (+ x1 (* 4.0 (* x1 (* 2.0 (* x2 x2)))))))
             (+ x1 (+ (+ x1 (+ t_1 (+ t_3 (* (* x1 x1) 9.0)))) t_0)))))))))

C

double code(double x1, double x2) {
	double t_0 = 3.0 * (x2 * -2.0);
	double t_1 = x1 * (x1 * x1);
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = t_2 * ((x1 * x1) * 6.0);
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = x1 + (t_0 + (x1 + ((x1 * x1) * (6.0 + (x2 * 6.0)))));
	} else if (x1 <= -23000000000000.0) {
		tmp = x1 + (t_0 + (x1 + (t_1 + (t_3 + (x2 * (x1 * (x1 * 6.0)))))));
	} else if (x1 <= -8.4e-166) {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)));
	} else if (x1 <= 4.9e-285) {
		tmp = (x2 * -6.0) + (x1 * ((x2 * -12.0) + -1.0));
	} else if (x1 <= 96000000.0) {
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / t_2)) + (x1 + (4.0 * (x1 * (2.0 * (x2 * x2))))));
	} else {
		tmp = x1 + ((x1 + (t_1 + (t_3 + ((x1 * x1) * 9.0)))) + t_0);
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_0 = 3.0d0 * (x2 * (-2.0d0))
    t_1 = x1 * (x1 * x1)
    t_2 = (x1 * x1) + 1.0d0
    t_3 = t_2 * ((x1 * x1) * 6.0d0)
    if (x1 <= (-5.6d+102)) then
        tmp = x1 + (t_0 + (x1 + ((x1 * x1) * (6.0d0 + (x2 * 6.0d0)))))
    else if (x1 <= (-23000000000000.0d0)) then
        tmp = x1 + (t_0 + (x1 + (t_1 + (t_3 + (x2 * (x1 * (x1 * 6.0d0)))))))
    else if (x1 <= (-8.4d-166)) then
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * ((4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0))) - 2.0d0)))
    else if (x1 <= 4.9d-285) then
        tmp = (x2 * (-6.0d0)) + (x1 * ((x2 * (-12.0d0)) + (-1.0d0)))
    else if (x1 <= 96000000.0d0) then
        tmp = x1 + ((3.0d0 * ((((x1 * (x1 * 3.0d0)) - (2.0d0 * x2)) - x1) / t_2)) + (x1 + (4.0d0 * (x1 * (2.0d0 * (x2 * x2))))))
    else
        tmp = x1 + ((x1 + (t_1 + (t_3 + ((x1 * x1) * 9.0d0)))) + t_0)
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = 3.0 * (x2 * -2.0);
	double t_1 = x1 * (x1 * x1);
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = t_2 * ((x1 * x1) * 6.0);
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = x1 + (t_0 + (x1 + ((x1 * x1) * (6.0 + (x2 * 6.0)))));
	} else if (x1 <= -23000000000000.0) {
		tmp = x1 + (t_0 + (x1 + (t_1 + (t_3 + (x2 * (x1 * (x1 * 6.0)))))));
	} else if (x1 <= -8.4e-166) {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)));
	} else if (x1 <= 4.9e-285) {
		tmp = (x2 * -6.0) + (x1 * ((x2 * -12.0) + -1.0));
	} else if (x1 <= 96000000.0) {
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / t_2)) + (x1 + (4.0 * (x1 * (2.0 * (x2 * x2))))));
	} else {
		tmp = x1 + ((x1 + (t_1 + (t_3 + ((x1 * x1) * 9.0)))) + t_0);
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = 3.0 * (x2 * -2.0)
	t_1 = x1 * (x1 * x1)
	t_2 = (x1 * x1) + 1.0
	t_3 = t_2 * ((x1 * x1) * 6.0)
	tmp = 0
	if x1 <= -5.6e+102:
		tmp = x1 + (t_0 + (x1 + ((x1 * x1) * (6.0 + (x2 * 6.0)))))
	elif x1 <= -23000000000000.0:
		tmp = x1 + (t_0 + (x1 + (t_1 + (t_3 + (x2 * (x1 * (x1 * 6.0)))))))
	elif x1 <= -8.4e-166:
		tmp = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)))
	elif x1 <= 4.9e-285:
		tmp = (x2 * -6.0) + (x1 * ((x2 * -12.0) + -1.0))
	elif x1 <= 96000000.0:
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / t_2)) + (x1 + (4.0 * (x1 * (2.0 * (x2 * x2))))))
	else:
		tmp = x1 + ((x1 + (t_1 + (t_3 + ((x1 * x1) * 9.0)))) + t_0)
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(3.0 * Float64(x2 * -2.0))
	t_1 = Float64(x1 * Float64(x1 * x1))
	t_2 = Float64(Float64(x1 * x1) + 1.0)
	t_3 = Float64(t_2 * Float64(Float64(x1 * x1) * 6.0))
	tmp = 0.0
	if (x1 <= -5.6e+102)
		tmp = Float64(x1 + Float64(t_0 + Float64(x1 + Float64(Float64(x1 * x1) * Float64(6.0 + Float64(x2 * 6.0))))));
	elseif (x1 <= -23000000000000.0)
		tmp = Float64(x1 + Float64(t_0 + Float64(x1 + Float64(t_1 + Float64(t_3 + Float64(x2 * Float64(x1 * Float64(x1 * 6.0))))))));
	elseif (x1 <= -8.4e-166)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0))) - 2.0))));
	elseif (x1 <= 4.9e-285)
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(x2 * -12.0) + -1.0)));
	elseif (x1 <= 96000000.0)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(Float64(x1 * Float64(x1 * 3.0)) - Float64(2.0 * x2)) - x1) / t_2)) + Float64(x1 + Float64(4.0 * Float64(x1 * Float64(2.0 * Float64(x2 * x2)))))));
	else
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(t_1 + Float64(t_3 + Float64(Float64(x1 * x1) * 9.0)))) + t_0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = 3.0 * (x2 * -2.0);
	t_1 = x1 * (x1 * x1);
	t_2 = (x1 * x1) + 1.0;
	t_3 = t_2 * ((x1 * x1) * 6.0);
	tmp = 0.0;
	if (x1 <= -5.6e+102)
		tmp = x1 + (t_0 + (x1 + ((x1 * x1) * (6.0 + (x2 * 6.0)))));
	elseif (x1 <= -23000000000000.0)
		tmp = x1 + (t_0 + (x1 + (t_1 + (t_3 + (x2 * (x1 * (x1 * 6.0)))))));
	elseif (x1 <= -8.4e-166)
		tmp = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)));
	elseif (x1 <= 4.9e-285)
		tmp = (x2 * -6.0) + (x1 * ((x2 * -12.0) + -1.0));
	elseif (x1 <= 96000000.0)
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / t_2)) + (x1 + (4.0 * (x1 * (2.0 * (x2 * x2))))));
	else
		tmp = x1 + ((x1 + (t_1 + (t_3 + ((x1 * x1) * 9.0)))) + t_0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(3.0 * N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 * N[(N[(x1 * x1), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -5.6e+102], N[(x1 + N[(t$95$0 + N[(x1 + N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 + N[(x2 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -23000000000000.0], N[(x1 + N[(t$95$0 + N[(x1 + N[(t$95$1 + N[(t$95$3 + N[(x2 * N[(x1 * N[(x1 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -8.4e-166], 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, 4.9e-285], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(x2 * -12.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 96000000.0], 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] / t$95$2), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(4.0 * N[(x1 * N[(2.0 * N[(x2 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x1 + N[(t$95$1 + N[(t$95$3 + N[(N[(x1 * x1), $MachinePrecision] * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$0), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if x1 < -5.60000000000000037e102

   1. Initial program 2.2%

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

   2. Taylor expanded in x1 around 0 2.2%

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

      1. *-commutative 2.2%

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

   4. Simplified 2.2%

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

   5. Taylor expanded in x1 around inf 0.0%

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

      1. *-commutative 0.0%

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

      2. unpow2 0.0%

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

   7. Simplified 0.0%

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

   8. Taylor expanded in x1 around 0 65.4%

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

      1. unpow2 65.4%

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

   10. Simplified 65.4%

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

   if -5.60000000000000037e102 < x1 < -2.3e13

   1. Initial program 99.3%

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

   2. Taylor expanded in x1 around 0 99.3%

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

      1. *-commutative 99.3%

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

   4. Simplified 99.3%

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

   5. Taylor expanded in x1 around inf 79.8%

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

      1. *-commutative 79.8%

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

      2. unpow2 79.8%

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

   7. Simplified 79.8%

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

   8. Taylor expanded in x1 around 0 88.7%

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

      1. *-commutative 88.7%

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

      2. *-commutative 88.7%

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

      3. associate-*l* 88.7%

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

      4. unpow2 88.7%

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

      5. associate-*l* 88.7%

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

   10. Simplified 88.7%

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

   if -2.3e13 < x1 < -8.3999999999999998e-166

   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 79.7%

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

   3. Taylor expanded in x1 around 0 80.6%

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

   if -8.3999999999999998e-166 < x1 < 4.89999999999999975e-285

   1. Initial program 99.3%

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

   2. Taylor expanded in x1 around 0 78.3%

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

   3. Taylor expanded in x2 around 0 99.3%

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

      1. associate-*r* 99.3%

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

   5. Simplified 99.3%

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

   6. Taylor expanded in x1 around 0 99.7%

      \[\leadsto x1 + \color{blue}{\left(-6 \cdot x2 + x1 \cdot \left(-12 \cdot x2 - 2\right)\right)} \]
   7. Step-by-step derivation

      1. fma-def 99.9%

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

      2. *-commutative 99.9%

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

      3. fma-neg 99.9%

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

      4. metadata-eval 99.9%

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

   8. Simplified 99.9%

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

   9. Taylor expanded in x1 around 0 99.8%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(-12 \cdot x2 - 1\right)} \]

   if 4.89999999999999975e-285 < x1 < 9.6e7

   1. Initial program 97.8%

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

   2. Taylor expanded in x1 around 0 91.7%

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

   3. Taylor expanded in x2 around inf 91.7%

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

      1. associate-*r* 91.7%

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

      2. *-commutative 91.7%

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

      3. associate-*l* 91.7%

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

      4. unpow2 91.7%

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

   5. Simplified 91.7%

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

   if 9.6e7 < x1

   1. Initial program 58.0%

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

   2. Taylor expanded in x1 around 0 58.0%

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

      1. *-commutative 58.0%

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

   4. Simplified 58.0%

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

   5. Taylor expanded in x1 around inf 49.0%

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

      1. *-commutative 49.0%

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

      2. unpow2 49.0%

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

   7. Simplified 49.0%

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

   8. Taylor expanded in x1 around inf 89.2%

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

      1. *-commutative 89.2%

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

      2. unpow2 89.2%

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

   10. Simplified 89.2%

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

4. Final simplification 85.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2\right) + \left(x1 + \left(x1 \cdot x1\right) \cdot \left(6 + x2 \cdot 6\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -23000000000000:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2\right) + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot 6\right) + x2 \cdot \left(x1 \cdot \left(x1 \cdot 6\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -8.4 \cdot 10^{-166}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)\\ \mathbf{elif}\;x1 \leq 4.9 \cdot 10^{-285}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(x2 \cdot -12 + -1\right)\\ \mathbf{elif}\;x1 \leq 96000000:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + 4 \cdot \left(x1 \cdot \left(2 \cdot \left(x2 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot 6\right) + \left(x1 \cdot x1\right) \cdot 9\right)\right)\right) + 3 \cdot \left(x2 \cdot -2\right)\right)\\ \end{array} \]

Alternative 10: 69.8% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -1.15 \cdot 10^{+53}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2\right) + \left(x1 + \left(x1 \cdot x1\right) \cdot \left(6 + x2 \cdot 6\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -1.05 \cdot 10^{-165}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)\\ \mathbf{elif}\;x1 \leq 4.9 \cdot 10^{-285}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(x2 \cdot -12 + -1\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + 4 \cdot \left(x1 \cdot \left(2 \cdot \left(x2 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - x2 \cdot -6}\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -1.15e+53)
   (+ x1 (+ (* 3.0 (* x2 -2.0)) (+ x1 (* (* x1 x1) (+ 6.0 (* x2 6.0))))))
   (if (<= x1 -1.05e-165)
     (+ x1 (+ (* x2 -6.0) (* x1 (- (* 4.0 (* x2 (- (* 2.0 x2) 3.0))) 2.0))))
     (if (<= x1 4.9e-285)
       (+ (* x2 -6.0) (* x1 (+ (* x2 -12.0) -1.0)))
       (if (<= x1 1.35e+154)
         (+
          x1
          (+
           (*
            3.0
            (/ (- (- (* x1 (* x1 3.0)) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0)))
           (+ x1 (* 4.0 (* x1 (* 2.0 (* x2 x2)))))))
         (/ (- (* x1 x1) (* (* x2 x2) 36.0)) (- x1 (* x2 -6.0))))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -1.15e+53) {
		tmp = x1 + ((3.0 * (x2 * -2.0)) + (x1 + ((x1 * x1) * (6.0 + (x2 * 6.0)))));
	} else if (x1 <= -1.05e-165) {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)));
	} else if (x1 <= 4.9e-285) {
		tmp = (x2 * -6.0) + (x1 * ((x2 * -12.0) + -1.0));
	} else if (x1 <= 1.35e+154) {
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / ((x1 * x1) + 1.0))) + (x1 + (4.0 * (x1 * (2.0 * (x2 * x2))))));
	} 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) :: tmp
    if (x1 <= (-1.15d+53)) then
        tmp = x1 + ((3.0d0 * (x2 * (-2.0d0))) + (x1 + ((x1 * x1) * (6.0d0 + (x2 * 6.0d0)))))
    else if (x1 <= (-1.05d-165)) then
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * ((4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0))) - 2.0d0)))
    else if (x1 <= 4.9d-285) then
        tmp = (x2 * (-6.0d0)) + (x1 * ((x2 * (-12.0d0)) + (-1.0d0)))
    else if (x1 <= 1.35d+154) then
        tmp = x1 + ((3.0d0 * ((((x1 * (x1 * 3.0d0)) - (2.0d0 * x2)) - x1) / ((x1 * x1) + 1.0d0))) + (x1 + (4.0d0 * (x1 * (2.0d0 * (x2 * x2))))))
    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 tmp;
	if (x1 <= -1.15e+53) {
		tmp = x1 + ((3.0 * (x2 * -2.0)) + (x1 + ((x1 * x1) * (6.0 + (x2 * 6.0)))));
	} else if (x1 <= -1.05e-165) {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)));
	} else if (x1 <= 4.9e-285) {
		tmp = (x2 * -6.0) + (x1 * ((x2 * -12.0) + -1.0));
	} else if (x1 <= 1.35e+154) {
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / ((x1 * x1) + 1.0))) + (x1 + (4.0 * (x1 * (2.0 * (x2 * x2))))));
	} else {
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -1.15e+53:
		tmp = x1 + ((3.0 * (x2 * -2.0)) + (x1 + ((x1 * x1) * (6.0 + (x2 * 6.0)))))
	elif x1 <= -1.05e-165:
		tmp = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)))
	elif x1 <= 4.9e-285:
		tmp = (x2 * -6.0) + (x1 * ((x2 * -12.0) + -1.0))
	elif x1 <= 1.35e+154:
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / ((x1 * x1) + 1.0))) + (x1 + (4.0 * (x1 * (2.0 * (x2 * x2))))))
	else:
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -1.15e+53)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(x2 * -2.0)) + Float64(x1 + Float64(Float64(x1 * x1) * Float64(6.0 + Float64(x2 * 6.0))))));
	elseif (x1 <= -1.05e-165)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0))) - 2.0))));
	elseif (x1 <= 4.9e-285)
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(x2 * -12.0) + -1.0)));
	elseif (x1 <= 1.35e+154)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(Float64(x1 * Float64(x1 * 3.0)) - Float64(2.0 * x2)) - x1) / Float64(Float64(x1 * x1) + 1.0))) + Float64(x1 + Float64(4.0 * Float64(x1 * Float64(2.0 * Float64(x2 * x2)))))));
	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)
	tmp = 0.0;
	if (x1 <= -1.15e+53)
		tmp = x1 + ((3.0 * (x2 * -2.0)) + (x1 + ((x1 * x1) * (6.0 + (x2 * 6.0)))));
	elseif (x1 <= -1.05e-165)
		tmp = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)));
	elseif (x1 <= 4.9e-285)
		tmp = (x2 * -6.0) + (x1 * ((x2 * -12.0) + -1.0));
	elseif (x1 <= 1.35e+154)
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / ((x1 * x1) + 1.0))) + (x1 + (4.0 * (x1 * (2.0 * (x2 * x2))))));
	else
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -1.15e+53], N[(x1 + N[(N[(3.0 * N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 + N[(x2 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -1.05e-165], 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, 4.9e-285], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(x2 * -12.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.35e+154], N[(x1 + N[(N[(3.0 * N[(N[(N[(N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision] - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(4.0 * N[(x1 * N[(2.0 * N[(x2 * x2), $MachinePrecision]), $MachinePrecision]), $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 < -1.1500000000000001e53

   1. Initial program 19.5%

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

   2. Taylor expanded in x1 around 0 19.5%

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

      1. *-commutative 19.5%

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

   4. Simplified 19.5%

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

   5. Taylor expanded in x1 around inf 17.8%

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

      1. *-commutative 17.8%

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

      2. unpow2 17.8%

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

   7. Simplified 17.8%

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

   8. Taylor expanded in x1 around 0 54.5%

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

      1. unpow2 54.5%

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

   10. Simplified 54.5%

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

   if -1.1500000000000001e53 < x1 < -1.04999999999999997e-165

   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 70.6%

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

   3. Taylor expanded in x1 around 0 71.6%

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

   if -1.04999999999999997e-165 < x1 < 4.89999999999999975e-285

   1. Initial program 99.3%

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

   2. Taylor expanded in x1 around 0 78.3%

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

   3. Taylor expanded in x2 around 0 99.3%

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

      1. associate-*r* 99.3%

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

   5. Simplified 99.3%

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

   6. Taylor expanded in x1 around 0 99.7%

      \[\leadsto x1 + \color{blue}{\left(-6 \cdot x2 + x1 \cdot \left(-12 \cdot x2 - 2\right)\right)} \]
   7. Step-by-step derivation

      1. fma-def 99.9%

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

      2. *-commutative 99.9%

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

      3. fma-neg 99.9%

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

      4. metadata-eval 99.9%

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

   8. Simplified 99.9%

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

   9. Taylor expanded in x1 around 0 99.8%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(-12 \cdot x2 - 1\right)} \]

   if 4.89999999999999975e-285 < x1 < 1.35000000000000003e154

   1. Initial program 97.5%

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

   2. Taylor expanded in x1 around 0 67.9%

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

   3. Taylor expanded in x2 around inf 67.9%

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

      1. associate-*r* 67.9%

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

      2. *-commutative 67.9%

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

      3. associate-*l* 67.9%

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

      4. unpow2 67.9%

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

   5. Simplified 67.9%

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

   if 1.35000000000000003e154 < 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 6.8%

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

      1. *-commutative 6.8%

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

   5. Simplified 6.8%

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

      1. flip-+ 74.1%

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

   7. Applied egg-rr 74.1%

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

      1. swap-sqr 74.1%

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

      2. metadata-eval 74.1%

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

      3. *-commutative 74.1%

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

   9. Simplified 74.1%

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

4. Final simplification 69.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.15 \cdot 10^{+53}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2\right) + \left(x1 + \left(x1 \cdot x1\right) \cdot \left(6 + x2 \cdot 6\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -1.05 \cdot 10^{-165}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)\\ \mathbf{elif}\;x1 \leq 4.9 \cdot 10^{-285}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(x2 \cdot -12 + -1\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + 4 \cdot \left(x1 \cdot \left(2 \cdot \left(x2 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - x2 \cdot -6}\\ \end{array} \]

Alternative 11: 62.2% accurate, 4.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x2 \cdot -12 + -1\right)\\ t_1 := x1 + \left(x2 \cdot -6 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)\\ \mathbf{if}\;x1 \leq -5.5 \cdot 10^{+66}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x1 \leq -8.4 \cdot 10^{-166}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x1 \leq 4.9 \cdot 10^{-285}:\\ \;\;\;\;x2 \cdot -6 + t_0\\ \mathbf{elif}\;x1 \leq 6.2 \cdot 10^{+147}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - x2 \cdot -6}\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (+ (* x2 -12.0) -1.0)))
        (t_1
         (+
          x1
          (+ (* x2 -6.0) (* x1 (- (* 4.0 (* x2 (- (* 2.0 x2) 3.0))) 2.0))))))
   (if (<= x1 -5.5e+66)
     t_0
     (if (<= x1 -8.4e-166)
       t_1
       (if (<= x1 4.9e-285)
         (+ (* x2 -6.0) t_0)
         (if (<= x1 6.2e+147)
           t_1
           (/ (- (* x1 x1) (* (* x2 x2) 36.0)) (- x1 (* x2 -6.0)))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * ((x2 * -12.0) + -1.0);
	double t_1 = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)));
	double tmp;
	if (x1 <= -5.5e+66) {
		tmp = t_0;
	} else if (x1 <= -8.4e-166) {
		tmp = t_1;
	} else if (x1 <= 4.9e-285) {
		tmp = (x2 * -6.0) + t_0;
	} else if (x1 <= 6.2e+147) {
		tmp = 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 = x1 * ((x2 * (-12.0d0)) + (-1.0d0))
    t_1 = x1 + ((x2 * (-6.0d0)) + (x1 * ((4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0))) - 2.0d0)))
    if (x1 <= (-5.5d+66)) then
        tmp = t_0
    else if (x1 <= (-8.4d-166)) then
        tmp = t_1
    else if (x1 <= 4.9d-285) then
        tmp = (x2 * (-6.0d0)) + t_0
    else if (x1 <= 6.2d+147) then
        tmp = 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 = x1 * ((x2 * -12.0) + -1.0);
	double t_1 = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)));
	double tmp;
	if (x1 <= -5.5e+66) {
		tmp = t_0;
	} else if (x1 <= -8.4e-166) {
		tmp = t_1;
	} else if (x1 <= 4.9e-285) {
		tmp = (x2 * -6.0) + t_0;
	} else if (x1 <= 6.2e+147) {
		tmp = t_1;
	} else {
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * ((x2 * -12.0) + -1.0)
	t_1 = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)))
	tmp = 0
	if x1 <= -5.5e+66:
		tmp = t_0
	elif x1 <= -8.4e-166:
		tmp = t_1
	elif x1 <= 4.9e-285:
		tmp = (x2 * -6.0) + t_0
	elif x1 <= 6.2e+147:
		tmp = t_1
	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 * -12.0) + -1.0))
	t_1 = 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 <= -5.5e+66)
		tmp = t_0;
	elseif (x1 <= -8.4e-166)
		tmp = t_1;
	elseif (x1 <= 4.9e-285)
		tmp = Float64(Float64(x2 * -6.0) + t_0);
	elseif (x1 <= 6.2e+147)
		tmp = 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 = x1 * ((x2 * -12.0) + -1.0);
	t_1 = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)));
	tmp = 0.0;
	if (x1 <= -5.5e+66)
		tmp = t_0;
	elseif (x1 <= -8.4e-166)
		tmp = t_1;
	elseif (x1 <= 4.9e-285)
		tmp = (x2 * -6.0) + t_0;
	elseif (x1 <= 6.2e+147)
		tmp = 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[(x1 * N[(N[(x2 * -12.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = 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, -5.5e+66], t$95$0, If[LessEqual[x1, -8.4e-166], t$95$1, If[LessEqual[x1, 4.9e-285], N[(N[(x2 * -6.0), $MachinePrecision] + t$95$0), $MachinePrecision], If[LessEqual[x1, 6.2e+147], t$95$1, 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 < -5.5e66

   1. Initial program 13.4%

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

   2. Taylor expanded in x1 around 0 2.0%

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

   3. Taylor expanded in x2 around 0 7.8%

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

      1. associate-*r* 7.8%

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

   5. Simplified 7.8%

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

   6. Taylor expanded in x1 around 0 22.1%

      \[\leadsto x1 + \color{blue}{\left(-6 \cdot x2 + x1 \cdot \left(-12 \cdot x2 - 2\right)\right)} \]
   7. Step-by-step derivation

      1. fma-def 22.1%

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

      2. *-commutative 22.1%

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

      3. fma-neg 22.1%

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

      4. metadata-eval 22.1%

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

   8. Simplified 22.1%

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

   9. Taylor expanded in x1 around inf 22.1%

      \[\leadsto \color{blue}{x1 \cdot \left(-12 \cdot x2 - 1\right)} \]

   if -5.5e66 < x1 < -8.3999999999999998e-166 or 4.89999999999999975e-285 < x1 < 6.2000000000000001e147

   1. Initial program 98.0%

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

   2. Taylor expanded in x1 around 0 68.6%

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

   3. Taylor expanded in x1 around 0 68.5%

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

   if -8.3999999999999998e-166 < x1 < 4.89999999999999975e-285

   1. Initial program 99.3%

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

   2. Taylor expanded in x1 around 0 78.3%

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

   3. Taylor expanded in x2 around 0 99.3%

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

      1. associate-*r* 99.3%

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

   5. Simplified 99.3%

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

   6. Taylor expanded in x1 around 0 99.7%

      \[\leadsto x1 + \color{blue}{\left(-6 \cdot x2 + x1 \cdot \left(-12 \cdot x2 - 2\right)\right)} \]
   7. Step-by-step derivation

      1. fma-def 99.9%

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

      2. *-commutative 99.9%

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

      3. fma-neg 99.9%

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

      4. metadata-eval 99.9%

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

   8. Simplified 99.9%

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

   9. Taylor expanded in x1 around 0 99.8%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(-12 \cdot x2 - 1\right)} \]

   if 6.2000000000000001e147 < x1

   1. Initial program 12.9%

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

   2. Taylor expanded in x1 around 0 0.6%

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

   3. Taylor expanded in x1 around 0 6.5%

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

      1. *-commutative 6.5%

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

   5. Simplified 6.5%

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

      1. flip-+ 65.1%

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

   7. Applied egg-rr 65.1%

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

      1. swap-sqr 65.1%

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

      2. metadata-eval 65.1%

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

      3. *-commutative 65.1%

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

   9. Simplified 65.1%

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

4. Final simplification 62.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.5 \cdot 10^{+66}:\\ \;\;\;\;x1 \cdot \left(x2 \cdot -12 + -1\right)\\ \mathbf{elif}\;x1 \leq -8.4 \cdot 10^{-166}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)\\ \mathbf{elif}\;x1 \leq 4.9 \cdot 10^{-285}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(x2 \cdot -12 + -1\right)\\ \mathbf{elif}\;x1 \leq 6.2 \cdot 10^{+147}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - x2 \cdot -6}\\ \end{array} \]

Alternative 12: 69.4% accurate, 4.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 + \left(x2 \cdot -6 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)\\ \mathbf{if}\;x1 \leq -1.22 \cdot 10^{+53}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2\right) + \left(x1 + \left(x1 \cdot x1\right) \cdot \left(6 + x2 \cdot 6\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -8.4 \cdot 10^{-166}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x1 \leq 4.9 \cdot 10^{-285}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(x2 \cdot -12 + -1\right)\\ \mathbf{elif}\;x1 \leq 7.6 \cdot 10^{+147}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - x2 \cdot -6}\\ \end{array} \end{array} \]

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 -1.22e+53)
     (+ x1 (+ (* 3.0 (* x2 -2.0)) (+ x1 (* (* x1 x1) (+ 6.0 (* x2 6.0))))))
     (if (<= x1 -8.4e-166)
       t_0
       (if (<= x1 4.9e-285)
         (+ (* x2 -6.0) (* x1 (+ (* x2 -12.0) -1.0)))
         (if (<= x1 7.6e+147)
           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 <= -1.22e+53) {
		tmp = x1 + ((3.0 * (x2 * -2.0)) + (x1 + ((x1 * x1) * (6.0 + (x2 * 6.0)))));
	} else if (x1 <= -8.4e-166) {
		tmp = t_0;
	} else if (x1 <= 4.9e-285) {
		tmp = (x2 * -6.0) + (x1 * ((x2 * -12.0) + -1.0));
	} else if (x1 <= 7.6e+147) {
		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 <= (-1.22d+53)) then
        tmp = x1 + ((3.0d0 * (x2 * (-2.0d0))) + (x1 + ((x1 * x1) * (6.0d0 + (x2 * 6.0d0)))))
    else if (x1 <= (-8.4d-166)) then
        tmp = t_0
    else if (x1 <= 4.9d-285) then
        tmp = (x2 * (-6.0d0)) + (x1 * ((x2 * (-12.0d0)) + (-1.0d0)))
    else if (x1 <= 7.6d+147) 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 <= -1.22e+53) {
		tmp = x1 + ((3.0 * (x2 * -2.0)) + (x1 + ((x1 * x1) * (6.0 + (x2 * 6.0)))));
	} else if (x1 <= -8.4e-166) {
		tmp = t_0;
	} else if (x1 <= 4.9e-285) {
		tmp = (x2 * -6.0) + (x1 * ((x2 * -12.0) + -1.0));
	} else if (x1 <= 7.6e+147) {
		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 <= -1.22e+53:
		tmp = x1 + ((3.0 * (x2 * -2.0)) + (x1 + ((x1 * x1) * (6.0 + (x2 * 6.0)))))
	elif x1 <= -8.4e-166:
		tmp = t_0
	elif x1 <= 4.9e-285:
		tmp = (x2 * -6.0) + (x1 * ((x2 * -12.0) + -1.0))
	elif x1 <= 7.6e+147:
		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 <= -1.22e+53)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(x2 * -2.0)) + Float64(x1 + Float64(Float64(x1 * x1) * Float64(6.0 + Float64(x2 * 6.0))))));
	elseif (x1 <= -8.4e-166)
		tmp = t_0;
	elseif (x1 <= 4.9e-285)
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(x2 * -12.0) + -1.0)));
	elseif (x1 <= 7.6e+147)
		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 <= -1.22e+53)
		tmp = x1 + ((3.0 * (x2 * -2.0)) + (x1 + ((x1 * x1) * (6.0 + (x2 * 6.0)))));
	elseif (x1 <= -8.4e-166)
		tmp = t_0;
	elseif (x1 <= 4.9e-285)
		tmp = (x2 * -6.0) + (x1 * ((x2 * -12.0) + -1.0));
	elseif (x1 <= 7.6e+147)
		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, -1.22e+53], N[(x1 + N[(N[(3.0 * N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 + N[(x2 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -8.4e-166], t$95$0, If[LessEqual[x1, 4.9e-285], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(x2 * -12.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 7.6e+147], 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 < -1.21999999999999999e53

   1. Initial program 19.5%

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

   2. Taylor expanded in x1 around 0 19.5%

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

      1. *-commutative 19.5%

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

   4. Simplified 19.5%

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

   5. Taylor expanded in x1 around inf 17.8%

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

      1. *-commutative 17.8%

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

      2. unpow2 17.8%

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

   7. Simplified 17.8%

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

   8. Taylor expanded in x1 around 0 54.5%

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

      1. unpow2 54.5%

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

   10. Simplified 54.5%

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

   if -1.21999999999999999e53 < x1 < -8.3999999999999998e-166 or 4.89999999999999975e-285 < x1 < 7.59999999999999941e147

   1. Initial program 98.0%

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

   2. Taylor expanded in x1 around 0 70.5%

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

   3. Taylor expanded in x1 around 0 70.3%

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

   if -8.3999999999999998e-166 < x1 < 4.89999999999999975e-285

   1. Initial program 99.3%

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

   2. Taylor expanded in x1 around 0 78.3%

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

   3. Taylor expanded in x2 around 0 99.3%

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

      1. associate-*r* 99.3%

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

   5. Simplified 99.3%

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

   6. Taylor expanded in x1 around 0 99.7%

      \[\leadsto x1 + \color{blue}{\left(-6 \cdot x2 + x1 \cdot \left(-12 \cdot x2 - 2\right)\right)} \]
   7. Step-by-step derivation

      1. fma-def 99.9%

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

      2. *-commutative 99.9%

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

      3. fma-neg 99.9%

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

      4. metadata-eval 99.9%

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

   8. Simplified 99.9%

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

   9. Taylor expanded in x1 around 0 99.8%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(-12 \cdot x2 - 1\right)} \]

   if 7.59999999999999941e147 < x1

   1. Initial program 12.9%

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

   2. Taylor expanded in x1 around 0 0.6%

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

   3. Taylor expanded in x1 around 0 6.5%

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

      1. *-commutative 6.5%

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

   5. Simplified 6.5%

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

      1. flip-+ 65.1%

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

   7. Applied egg-rr 65.1%

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

      1. swap-sqr 65.1%

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

      2. metadata-eval 65.1%

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

      3. *-commutative 65.1%

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

   9. Simplified 65.1%

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

4. Final simplification 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.22 \cdot 10^{+53}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2\right) + \left(x1 + \left(x1 \cdot x1\right) \cdot \left(6 + x2 \cdot 6\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -8.4 \cdot 10^{-166}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)\\ \mathbf{elif}\;x1 \leq 4.9 \cdot 10^{-285}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(x2 \cdot -12 + -1\right)\\ \mathbf{elif}\;x1 \leq 7.6 \cdot 10^{+147}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - x2 \cdot -6}\\ \end{array} \]

Alternative 13: 55.6% accurate, 5.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x2 \cdot -12 + -1\right)\\ \mathbf{if}\;x1 \leq -1.2 \cdot 10^{+52}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x1 \leq -4.4 \cdot 10^{-27}:\\ \;\;\;\;x1 \cdot \left(x2 \cdot \left(x2 \cdot 8\right)\right)\\ \mathbf{elif}\;x1 \leq 8 \cdot 10^{-28}:\\ \;\;\;\;x2 \cdot -6 + t_0\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + x1 \cdot \left(1 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - x2 \cdot -6}\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (+ (* x2 -12.0) -1.0))))
   (if (<= x1 -1.2e+52)
     t_0
     (if (<= x1 -4.4e-27)
       (* x1 (* x2 (* x2 8.0)))
       (if (<= x1 8e-28)
         (+ (* x2 -6.0) t_0)
         (if (<= x1 1.35e+154)
           (+ x1 (* x1 (+ 1.0 (* 4.0 (* x2 (- (* 2.0 x2) 3.0))))))
           (/ (- (* x1 x1) (* (* x2 x2) 36.0)) (- x1 (* x2 -6.0)))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * ((x2 * -12.0) + -1.0);
	double tmp;
	if (x1 <= -1.2e+52) {
		tmp = t_0;
	} else if (x1 <= -4.4e-27) {
		tmp = x1 * (x2 * (x2 * 8.0));
	} else if (x1 <= 8e-28) {
		tmp = (x2 * -6.0) + t_0;
	} else if (x1 <= 1.35e+154) {
		tmp = x1 + (x1 * (1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0)))));
	} 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 * (-12.0d0)) + (-1.0d0))
    if (x1 <= (-1.2d+52)) then
        tmp = t_0
    else if (x1 <= (-4.4d-27)) then
        tmp = x1 * (x2 * (x2 * 8.0d0))
    else if (x1 <= 8d-28) then
        tmp = (x2 * (-6.0d0)) + t_0
    else if (x1 <= 1.35d+154) then
        tmp = x1 + (x1 * (1.0d0 + (4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0)))))
    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 * -12.0) + -1.0);
	double tmp;
	if (x1 <= -1.2e+52) {
		tmp = t_0;
	} else if (x1 <= -4.4e-27) {
		tmp = x1 * (x2 * (x2 * 8.0));
	} else if (x1 <= 8e-28) {
		tmp = (x2 * -6.0) + t_0;
	} else if (x1 <= 1.35e+154) {
		tmp = x1 + (x1 * (1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0)))));
	} else {
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * ((x2 * -12.0) + -1.0)
	tmp = 0
	if x1 <= -1.2e+52:
		tmp = t_0
	elif x1 <= -4.4e-27:
		tmp = x1 * (x2 * (x2 * 8.0))
	elif x1 <= 8e-28:
		tmp = (x2 * -6.0) + t_0
	elif x1 <= 1.35e+154:
		tmp = x1 + (x1 * (1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0)))))
	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 * -12.0) + -1.0))
	tmp = 0.0
	if (x1 <= -1.2e+52)
		tmp = t_0;
	elseif (x1 <= -4.4e-27)
		tmp = Float64(x1 * Float64(x2 * Float64(x2 * 8.0)));
	elseif (x1 <= 8e-28)
		tmp = Float64(Float64(x2 * -6.0) + t_0);
	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 = 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 * -12.0) + -1.0);
	tmp = 0.0;
	if (x1 <= -1.2e+52)
		tmp = t_0;
	elseif (x1 <= -4.4e-27)
		tmp = x1 * (x2 * (x2 * 8.0));
	elseif (x1 <= 8e-28)
		tmp = (x2 * -6.0) + t_0;
	elseif (x1 <= 1.35e+154)
		tmp = x1 + (x1 * (1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0)))));
	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 * -12.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -1.2e+52], t$95$0, If[LessEqual[x1, -4.4e-27], N[(x1 * N[(x2 * N[(x2 * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 8e-28], N[(N[(x2 * -6.0), $MachinePrecision] + t$95$0), $MachinePrecision], 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], 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 < -1.2e52

   1. Initial program 19.5%

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

   2. Taylor expanded in x1 around 0 1.9%

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

   3. Taylor expanded in x2 around 0 7.2%

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

      1. associate-*r* 7.2%

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

   5. Simplified 7.2%

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

   6. Taylor expanded in x1 around 0 20.8%

      \[\leadsto x1 + \color{blue}{\left(-6 \cdot x2 + x1 \cdot \left(-12 \cdot x2 - 2\right)\right)} \]
   7. Step-by-step derivation

      1. fma-def 20.8%

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

      2. *-commutative 20.8%

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

      3. fma-neg 20.8%

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

      4. metadata-eval 20.8%

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

   8. Simplified 20.8%

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

   9. Taylor expanded in x1 around inf 20.8%

      \[\leadsto \color{blue}{x1 \cdot \left(-12 \cdot x2 - 1\right)} \]

   if -1.2e52 < x1 < -4.39999999999999974e-27

   1. Initial program 99.3%

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

   2. Taylor expanded in x1 around 0 45.4%

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

   3. Taylor expanded in x2 around inf 45.4%

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

   4. Taylor expanded in x2 around inf 45.6%

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

      1. *-commutative 45.6%

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

      2. unpow2 45.6%

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

      3. associate-*l* 45.6%

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

      4. associate-*l* 45.6%

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

   6. Simplified 45.6%

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

   if -4.39999999999999974e-27 < x1 < 7.99999999999999977e-28

   1. Initial program 99.3%

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

   2. Taylor expanded in x1 around 0 87.4%

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

   3. Taylor expanded in x2 around 0 76.3%

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

      1. associate-*r* 76.3%

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

   5. Simplified 76.3%

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

   6. Taylor expanded in x1 around 0 76.8%

      \[\leadsto x1 + \color{blue}{\left(-6 \cdot x2 + x1 \cdot \left(-12 \cdot x2 - 2\right)\right)} \]
   7. Step-by-step derivation

      1. fma-def 76.9%

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

      2. *-commutative 76.9%

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

      3. fma-neg 76.9%

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

      4. metadata-eval 76.9%

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

   8. Simplified 76.9%

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

   9. Taylor expanded in x1 around 0 76.8%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(-12 \cdot x2 - 1\right)} \]

   if 7.99999999999999977e-28 < x1 < 1.35000000000000003e154

   1. Initial program 95.1%

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

   2. Taylor expanded in x1 around 0 36.4%

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

   3. Taylor expanded in x1 around inf 36.5%

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

   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 6.8%

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

      1. *-commutative 6.8%

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

   5. Simplified 6.8%

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

      1. flip-+ 74.1%

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

   7. Applied egg-rr 74.1%

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

      1. swap-sqr 74.1%

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

      2. metadata-eval 74.1%

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

      3. *-commutative 74.1%

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

   9. Simplified 74.1%

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

4. Final simplification 55.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.2 \cdot 10^{+52}:\\ \;\;\;\;x1 \cdot \left(x2 \cdot -12 + -1\right)\\ \mathbf{elif}\;x1 \leq -4.4 \cdot 10^{-27}:\\ \;\;\;\;x1 \cdot \left(x2 \cdot \left(x2 \cdot 8\right)\right)\\ \mathbf{elif}\;x1 \leq 8 \cdot 10^{-28}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(x2 \cdot -12 + -1\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + x1 \cdot \left(1 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - x2 \cdot -6}\\ \end{array} \]

Alternative 14: 41.1% accurate, 6.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x2 \cdot \left(x2 \cdot 8\right)\right)\\ t_1 := x1 + x2 \cdot -6\\ \mathbf{if}\;x2 \leq -1.36 \cdot 10^{+216}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x2 \leq -1.35 \cdot 10^{+126}:\\ \;\;\;\;x2 \cdot -6\\ \mathbf{elif}\;x2 \leq -2 \cdot 10^{+57}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x2 \leq -1.92 \cdot 10^{-190}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x2 \leq 3 \cdot 10^{-243}:\\ \;\;\;\;-x1\\ \mathbf{elif}\;x2 \leq 2.4 \cdot 10^{+118}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x2 (* x2 8.0)))) (t_1 (+ x1 (* x2 -6.0))))
   (if (<= x2 -1.36e+216)
     t_0
     (if (<= x2 -1.35e+126)
       (* x2 -6.0)
       (if (<= x2 -2e+57)
         t_0
         (if (<= x2 -1.92e-190)
           t_1
           (if (<= x2 3e-243) (- x1) (if (<= x2 2.4e+118) t_1 t_0))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x2 * (x2 * 8.0));
	double t_1 = x1 + (x2 * -6.0);
	double tmp;
	if (x2 <= -1.36e+216) {
		tmp = t_0;
	} else if (x2 <= -1.35e+126) {
		tmp = x2 * -6.0;
	} else if (x2 <= -2e+57) {
		tmp = t_0;
	} else if (x2 <= -1.92e-190) {
		tmp = t_1;
	} else if (x2 <= 3e-243) {
		tmp = -x1;
	} else if (x2 <= 2.4e+118) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x1 * (x2 * (x2 * 8.0d0))
    t_1 = x1 + (x2 * (-6.0d0))
    if (x2 <= (-1.36d+216)) then
        tmp = t_0
    else if (x2 <= (-1.35d+126)) then
        tmp = x2 * (-6.0d0)
    else if (x2 <= (-2d+57)) then
        tmp = t_0
    else if (x2 <= (-1.92d-190)) then
        tmp = t_1
    else if (x2 <= 3d-243) then
        tmp = -x1
    else if (x2 <= 2.4d+118) then
        tmp = t_1
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x2 * (x2 * 8.0));
	double t_1 = x1 + (x2 * -6.0);
	double tmp;
	if (x2 <= -1.36e+216) {
		tmp = t_0;
	} else if (x2 <= -1.35e+126) {
		tmp = x2 * -6.0;
	} else if (x2 <= -2e+57) {
		tmp = t_0;
	} else if (x2 <= -1.92e-190) {
		tmp = t_1;
	} else if (x2 <= 3e-243) {
		tmp = -x1;
	} else if (x2 <= 2.4e+118) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x2 * (x2 * 8.0))
	t_1 = x1 + (x2 * -6.0)
	tmp = 0
	if x2 <= -1.36e+216:
		tmp = t_0
	elif x2 <= -1.35e+126:
		tmp = x2 * -6.0
	elif x2 <= -2e+57:
		tmp = t_0
	elif x2 <= -1.92e-190:
		tmp = t_1
	elif x2 <= 3e-243:
		tmp = -x1
	elif x2 <= 2.4e+118:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x2 * Float64(x2 * 8.0)))
	t_1 = Float64(x1 + Float64(x2 * -6.0))
	tmp = 0.0
	if (x2 <= -1.36e+216)
		tmp = t_0;
	elseif (x2 <= -1.35e+126)
		tmp = Float64(x2 * -6.0);
	elseif (x2 <= -2e+57)
		tmp = t_0;
	elseif (x2 <= -1.92e-190)
		tmp = t_1;
	elseif (x2 <= 3e-243)
		tmp = Float64(-x1);
	elseif (x2 <= 2.4e+118)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x2 * (x2 * 8.0));
	t_1 = x1 + (x2 * -6.0);
	tmp = 0.0;
	if (x2 <= -1.36e+216)
		tmp = t_0;
	elseif (x2 <= -1.35e+126)
		tmp = x2 * -6.0;
	elseif (x2 <= -2e+57)
		tmp = t_0;
	elseif (x2 <= -1.92e-190)
		tmp = t_1;
	elseif (x2 <= 3e-243)
		tmp = -x1;
	elseif (x2 <= 2.4e+118)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x2 * N[(x2 * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x2, -1.36e+216], t$95$0, If[LessEqual[x2, -1.35e+126], N[(x2 * -6.0), $MachinePrecision], If[LessEqual[x2, -2e+57], t$95$0, If[LessEqual[x2, -1.92e-190], t$95$1, If[LessEqual[x2, 3e-243], (-x1), If[LessEqual[x2, 2.4e+118], t$95$1, t$95$0]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x2 < -1.36000000000000007e216 or -1.35000000000000001e126 < x2 < -2.0000000000000001e57 or 2.4e118 < x2

   1. Initial program 64.0%

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

   2. Taylor expanded in x1 around 0 52.0%

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

   3. Taylor expanded in x2 around inf 62.4%

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

   4. Taylor expanded in x2 around inf 62.4%

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

      1. *-commutative 62.4%

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

      2. unpow2 62.4%

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

      3. associate-*l* 62.4%

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

      4. associate-*l* 62.4%

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

   6. Simplified 62.4%

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

   if -1.36000000000000007e216 < x2 < -1.35000000000000001e126

   1. Initial program 55.5%

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

   2. Taylor expanded in x1 around 0 13.0%

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

   3. Taylor expanded in x1 around 0 42.2%

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

      1. *-commutative 42.2%

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

   5. Simplified 42.2%

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

   6. Taylor expanded in x1 around 0 42.2%

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

   if -2.0000000000000001e57 < x2 < -1.9199999999999999e-190 or 3.0000000000000001e-243 < x2 < 2.4e118

   1. Initial program 79.3%

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

   2. Taylor expanded in x1 around 0 51.6%

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

   3. Taylor expanded in x1 around 0 37.6%

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

      1. *-commutative 37.6%

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

   5. Simplified 37.6%

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

   if -1.9199999999999999e-190 < x2 < 3.0000000000000001e-243

   1. Initial program 64.2%

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

   2. Taylor expanded in x1 around 0 44.7%

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

   3. Taylor expanded in x2 around 0 44.7%

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

      1. associate-*r* 44.7%

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

   5. Simplified 44.7%

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

   6. Taylor expanded in x1 around 0 47.1%

      \[\leadsto x1 + \color{blue}{\left(-6 \cdot x2 + x1 \cdot \left(-12 \cdot x2 - 2\right)\right)} \]
   7. Step-by-step derivation

      1. fma-def 47.1%

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

      2. *-commutative 47.1%

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

      3. fma-neg 47.1%

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

      4. metadata-eval 47.1%

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

   8. Simplified 47.1%

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

   9. Taylor expanded in x2 around 0 40.5%

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

       1. distribute-rgt1-in 40.5%

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

       2. metadata-eval 40.5%

          \[\leadsto \color{blue}{-1} \cdot x1 \]

       3. neg-mul-1 40.5%

          \[\leadsto \color{blue}{-x1} \]

   11. Simplified 40.5%

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

4. Final simplification 45.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq -1.36 \cdot 10^{+216}:\\ \;\;\;\;x1 \cdot \left(x2 \cdot \left(x2 \cdot 8\right)\right)\\ \mathbf{elif}\;x2 \leq -1.35 \cdot 10^{+126}:\\ \;\;\;\;x2 \cdot -6\\ \mathbf{elif}\;x2 \leq -2 \cdot 10^{+57}:\\ \;\;\;\;x1 \cdot \left(x2 \cdot \left(x2 \cdot 8\right)\right)\\ \mathbf{elif}\;x2 \leq -1.92 \cdot 10^{-190}:\\ \;\;\;\;x1 + x2 \cdot -6\\ \mathbf{elif}\;x2 \leq 3 \cdot 10^{-243}:\\ \;\;\;\;-x1\\ \mathbf{elif}\;x2 \leq 2.4 \cdot 10^{+118}:\\ \;\;\;\;x1 + x2 \cdot -6\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot \left(x2 \cdot \left(x2 \cdot 8\right)\right)\\ \end{array} \]

Alternative 15: 51.7% accurate, 6.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x2 \leq -7.8 \cdot 10^{+183} \lor \neg \left(x2 \leq -3.6 \cdot 10^{+125}\right) \land \left(x2 \leq -1 \cdot 10^{+57} \lor \neg \left(x2 \leq 9.5 \cdot 10^{+111}\right)\right):\\ \;\;\;\;x1 + 8 \cdot \left(x2 \cdot \left(x1 \cdot x2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(x2 \cdot -12 + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x2 -7.8e+183)
         (and (not (<= x2 -3.6e+125))
              (or (<= x2 -1e+57) (not (<= x2 9.5e+111)))))
   (+ x1 (* 8.0 (* x2 (* x1 x2))))
   (+ (* x2 -6.0) (* x1 (+ (* x2 -12.0) -1.0)))))

C

double code(double x1, double x2) {
	double tmp;
	if ((x2 <= -7.8e+183) || (!(x2 <= -3.6e+125) && ((x2 <= -1e+57) || !(x2 <= 9.5e+111)))) {
		tmp = x1 + (8.0 * (x2 * (x1 * x2)));
	} else {
		tmp = (x2 * -6.0) + (x1 * ((x2 * -12.0) + -1.0));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if ((x2 <= (-7.8d+183)) .or. (.not. (x2 <= (-3.6d+125))) .and. (x2 <= (-1d+57)) .or. (.not. (x2 <= 9.5d+111))) then
        tmp = x1 + (8.0d0 * (x2 * (x1 * x2)))
    else
        tmp = (x2 * (-6.0d0)) + (x1 * ((x2 * (-12.0d0)) + (-1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x2 <= -7.8e+183) || (!(x2 <= -3.6e+125) && ((x2 <= -1e+57) || !(x2 <= 9.5e+111)))) {
		tmp = x1 + (8.0 * (x2 * (x1 * x2)));
	} else {
		tmp = (x2 * -6.0) + (x1 * ((x2 * -12.0) + -1.0));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x2 <= -7.8e+183) or (not (x2 <= -3.6e+125) and ((x2 <= -1e+57) or not (x2 <= 9.5e+111))):
		tmp = x1 + (8.0 * (x2 * (x1 * x2)))
	else:
		tmp = (x2 * -6.0) + (x1 * ((x2 * -12.0) + -1.0))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x2 <= -7.8e+183) || (!(x2 <= -3.6e+125) && ((x2 <= -1e+57) || !(x2 <= 9.5e+111))))
		tmp = Float64(x1 + Float64(8.0 * Float64(x2 * Float64(x1 * x2))));
	else
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(x2 * -12.0) + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x2 <= -7.8e+183) || (~((x2 <= -3.6e+125)) && ((x2 <= -1e+57) || ~((x2 <= 9.5e+111)))))
		tmp = x1 + (8.0 * (x2 * (x1 * x2)));
	else
		tmp = (x2 * -6.0) + (x1 * ((x2 * -12.0) + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x2, -7.8e+183], And[N[Not[LessEqual[x2, -3.6e+125]], $MachinePrecision], Or[LessEqual[x2, -1e+57], N[Not[LessEqual[x2, 9.5e+111]], $MachinePrecision]]]], N[(x1 + N[(8.0 * N[(x2 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(x2 * -12.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x2 < -7.7999999999999998e183 or -3.6000000000000003e125 < x2 < -1.00000000000000005e57 or 9.50000000000000019e111 < x2

   1. Initial program 62.9%

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

   2. Taylor expanded in x1 around 0 48.1%

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

   3. Taylor expanded in x2 around inf 57.3%

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

      1. pow1 57.3%

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

      2. unpow2 57.3%

         \[\leadsto x1 + 8 \cdot {\left(x1 \cdot \color{blue}{\left(x2 \cdot x2\right)}\right)}^{1} \]

   5. Applied egg-rr 57.3%

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

      1. unpow1 57.3%

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

      2. *-commutative 57.3%

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

      3. associate-*l* 63.8%

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

   7. Simplified 63.8%

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

   if -7.7999999999999998e183 < x2 < -3.6000000000000003e125 or -1.00000000000000005e57 < x2 < 9.50000000000000019e111

   1. Initial program 74.8%

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

   2. Taylor expanded in x1 around 0 47.8%

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

   3. Taylor expanded in x2 around 0 49.0%

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

      1. associate-*r* 49.0%

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

   5. Simplified 49.0%

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

   6. Taylor expanded in x1 around 0 50.4%

      \[\leadsto x1 + \color{blue}{\left(-6 \cdot x2 + x1 \cdot \left(-12 \cdot x2 - 2\right)\right)} \]
   7. Step-by-step derivation

      1. fma-def 50.5%

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

      2. *-commutative 50.5%

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

      3. fma-neg 50.5%

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

      4. metadata-eval 50.5%

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

   8. Simplified 50.5%

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

   9. Taylor expanded in x1 around 0 50.4%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(-12 \cdot x2 - 1\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 55.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq -7.8 \cdot 10^{+183} \lor \neg \left(x2 \leq -3.6 \cdot 10^{+125}\right) \land \left(x2 \leq -1 \cdot 10^{+57} \lor \neg \left(x2 \leq 9.5 \cdot 10^{+111}\right)\right):\\ \;\;\;\;x1 + 8 \cdot \left(x2 \cdot \left(x1 \cdot x2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(x2 \cdot -12 + -1\right)\\ \end{array} \]

Alternative 16: 43.8% accurate, 8.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -1.22 \cdot 10^{+53}:\\ \;\;\;\;x1 \cdot \left(x2 \cdot -12 + -1\right)\\ \mathbf{elif}\;x1 \leq -2.1 \cdot 10^{-126} \lor \neg \left(x1 \leq 3.5 \cdot 10^{-158}\right):\\ \;\;\;\;x1 + 8 \cdot \left(x2 \cdot \left(x1 \cdot x2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -1.22e+53)
   (* x1 (+ (* x2 -12.0) -1.0))
   (if (or (<= x1 -2.1e-126) (not (<= x1 3.5e-158)))
     (+ x1 (* 8.0 (* x2 (* x1 x2))))
     (* x2 -6.0))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -1.22e+53) {
		tmp = x1 * ((x2 * -12.0) + -1.0);
	} else if ((x1 <= -2.1e-126) || !(x1 <= 3.5e-158)) {
		tmp = x1 + (8.0 * (x2 * (x1 * x2)));
	} else {
		tmp = x2 * -6.0;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x1 <= (-1.22d+53)) then
        tmp = x1 * ((x2 * (-12.0d0)) + (-1.0d0))
    else if ((x1 <= (-2.1d-126)) .or. (.not. (x1 <= 3.5d-158))) then
        tmp = x1 + (8.0d0 * (x2 * (x1 * x2)))
    else
        tmp = x2 * (-6.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= -1.22e+53) {
		tmp = x1 * ((x2 * -12.0) + -1.0);
	} else if ((x1 <= -2.1e-126) || !(x1 <= 3.5e-158)) {
		tmp = x1 + (8.0 * (x2 * (x1 * x2)));
	} else {
		tmp = x2 * -6.0;
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -1.22e+53:
		tmp = x1 * ((x2 * -12.0) + -1.0)
	elif (x1 <= -2.1e-126) or not (x1 <= 3.5e-158):
		tmp = x1 + (8.0 * (x2 * (x1 * x2)))
	else:
		tmp = x2 * -6.0
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -1.22e+53)
		tmp = Float64(x1 * Float64(Float64(x2 * -12.0) + -1.0));
	elseif ((x1 <= -2.1e-126) || !(x1 <= 3.5e-158))
		tmp = Float64(x1 + Float64(8.0 * Float64(x2 * Float64(x1 * x2))));
	else
		tmp = Float64(x2 * -6.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -1.22e+53)
		tmp = x1 * ((x2 * -12.0) + -1.0);
	elseif ((x1 <= -2.1e-126) || ~((x1 <= 3.5e-158)))
		tmp = x1 + (8.0 * (x2 * (x1 * x2)));
	else
		tmp = x2 * -6.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -1.22e+53], N[(x1 * N[(N[(x2 * -12.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x1, -2.1e-126], N[Not[LessEqual[x1, 3.5e-158]], $MachinePrecision]], N[(x1 + N[(8.0 * N[(x2 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x2 * -6.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -1.21999999999999999e53

   1. Initial program 19.5%

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

   2. Taylor expanded in x1 around 0 1.9%

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

   3. Taylor expanded in x2 around 0 7.2%

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

      1. associate-*r* 7.2%

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

   5. Simplified 7.2%

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

   6. Taylor expanded in x1 around 0 20.8%

      \[\leadsto x1 + \color{blue}{\left(-6 \cdot x2 + x1 \cdot \left(-12 \cdot x2 - 2\right)\right)} \]
   7. Step-by-step derivation

      1. fma-def 20.8%

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

      2. *-commutative 20.8%

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

      3. fma-neg 20.8%

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

      4. metadata-eval 20.8%

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

   8. Simplified 20.8%

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

   9. Taylor expanded in x1 around inf 20.8%

      \[\leadsto \color{blue}{x1 \cdot \left(-12 \cdot x2 - 1\right)} \]

   if -1.21999999999999999e53 < x1 < -2.0999999999999999e-126 or 3.50000000000000012e-158 < x1

   1. Initial program 78.8%

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

   2. Taylor expanded in x1 around 0 49.8%

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

   3. Taylor expanded in x2 around inf 40.0%

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

      1. pow1 40.0%

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

      2. unpow2 40.0%

         \[\leadsto x1 + 8 \cdot {\left(x1 \cdot \color{blue}{\left(x2 \cdot x2\right)}\right)}^{1} \]

   5. Applied egg-rr 40.0%

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

      1. unpow1 40.0%

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

      2. *-commutative 40.0%

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

      3. associate-*l* 43.8%

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

   7. Simplified 43.8%

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

   if -2.0999999999999999e-126 < x1 < 3.50000000000000012e-158

   1. Initial program 99.3%

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

   2. Taylor expanded in x1 around 0 86.4%

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

   3. Taylor expanded in x1 around 0 71.4%

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

      1. *-commutative 71.4%

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

   5. Simplified 71.4%

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

   6. Taylor expanded in x1 around 0 71.7%

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

4. Final simplification 45.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.22 \cdot 10^{+53}:\\ \;\;\;\;x1 \cdot \left(x2 \cdot -12 + -1\right)\\ \mathbf{elif}\;x1 \leq -2.1 \cdot 10^{-126} \lor \neg \left(x1 \leq 3.5 \cdot 10^{-158}\right):\\ \;\;\;\;x1 + 8 \cdot \left(x2 \cdot \left(x1 \cdot x2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6\\ \end{array} \]

Alternative 17: 42.9% accurate, 8.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -1.05 \cdot 10^{+53}:\\ \;\;\;\;x1 \cdot \left(x2 \cdot -12 + -1\right)\\ \mathbf{elif}\;x1 \leq -4.3 \cdot 10^{-109}:\\ \;\;\;\;x1 \cdot \left(x2 \cdot \left(x2 \cdot 8\right)\right)\\ \mathbf{elif}\;x1 \leq 5.7 \cdot 10^{-158}:\\ \;\;\;\;x2 \cdot -6\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot \left(1 + \left(x2 \cdot x2\right) \cdot 8\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -1.05e+53)
   (* x1 (+ (* x2 -12.0) -1.0))
   (if (<= x1 -4.3e-109)
     (* x1 (* x2 (* x2 8.0)))
     (if (<= x1 5.7e-158) (* x2 -6.0) (* x1 (+ 1.0 (* (* x2 x2) 8.0)))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -1.05e+53) {
		tmp = x1 * ((x2 * -12.0) + -1.0);
	} else if (x1 <= -4.3e-109) {
		tmp = x1 * (x2 * (x2 * 8.0));
	} else if (x1 <= 5.7e-158) {
		tmp = x2 * -6.0;
	} else {
		tmp = x1 * (1.0 + ((x2 * x2) * 8.0));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x1 <= (-1.05d+53)) then
        tmp = x1 * ((x2 * (-12.0d0)) + (-1.0d0))
    else if (x1 <= (-4.3d-109)) then
        tmp = x1 * (x2 * (x2 * 8.0d0))
    else if (x1 <= 5.7d-158) then
        tmp = x2 * (-6.0d0)
    else
        tmp = x1 * (1.0d0 + ((x2 * x2) * 8.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= -1.05e+53) {
		tmp = x1 * ((x2 * -12.0) + -1.0);
	} else if (x1 <= -4.3e-109) {
		tmp = x1 * (x2 * (x2 * 8.0));
	} else if (x1 <= 5.7e-158) {
		tmp = x2 * -6.0;
	} else {
		tmp = x1 * (1.0 + ((x2 * x2) * 8.0));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -1.05e+53:
		tmp = x1 * ((x2 * -12.0) + -1.0)
	elif x1 <= -4.3e-109:
		tmp = x1 * (x2 * (x2 * 8.0))
	elif x1 <= 5.7e-158:
		tmp = x2 * -6.0
	else:
		tmp = x1 * (1.0 + ((x2 * x2) * 8.0))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -1.05e+53)
		tmp = Float64(x1 * Float64(Float64(x2 * -12.0) + -1.0));
	elseif (x1 <= -4.3e-109)
		tmp = Float64(x1 * Float64(x2 * Float64(x2 * 8.0)));
	elseif (x1 <= 5.7e-158)
		tmp = Float64(x2 * -6.0);
	else
		tmp = Float64(x1 * Float64(1.0 + Float64(Float64(x2 * x2) * 8.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -1.05e+53)
		tmp = x1 * ((x2 * -12.0) + -1.0);
	elseif (x1 <= -4.3e-109)
		tmp = x1 * (x2 * (x2 * 8.0));
	elseif (x1 <= 5.7e-158)
		tmp = x2 * -6.0;
	else
		tmp = x1 * (1.0 + ((x2 * x2) * 8.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -1.05e+53], N[(x1 * N[(N[(x2 * -12.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -4.3e-109], N[(x1 * N[(x2 * N[(x2 * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 5.7e-158], N[(x2 * -6.0), $MachinePrecision], N[(x1 * N[(1.0 + N[(N[(x2 * x2), $MachinePrecision] * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -1.0500000000000001e53

   1. Initial program 19.5%

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

   2. Taylor expanded in x1 around 0 1.9%

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

   3. Taylor expanded in x2 around 0 7.2%

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

      1. associate-*r* 7.2%

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

   5. Simplified 7.2%

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

   6. Taylor expanded in x1 around 0 20.8%

      \[\leadsto x1 + \color{blue}{\left(-6 \cdot x2 + x1 \cdot \left(-12 \cdot x2 - 2\right)\right)} \]
   7. Step-by-step derivation

      1. fma-def 20.8%

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

      2. *-commutative 20.8%

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

      3. fma-neg 20.8%

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

      4. metadata-eval 20.8%

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

   8. Simplified 20.8%

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

   9. Taylor expanded in x1 around inf 20.8%

      \[\leadsto \color{blue}{x1 \cdot \left(-12 \cdot x2 - 1\right)} \]

   if -1.0500000000000001e53 < x1 < -4.2999999999999997e-109

   1. Initial program 99.3%

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

   2. Taylor expanded in x1 around 0 68.5%

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

   3. Taylor expanded in x2 around inf 39.8%

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

   4. Taylor expanded in x2 around inf 40.0%

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

      1. *-commutative 40.0%

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

      2. unpow2 40.0%

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

      3. associate-*l* 40.0%

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

      4. associate-*l* 40.0%

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

   6. Simplified 40.0%

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

   if -4.2999999999999997e-109 < x1 < 5.69999999999999982e-158

   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 84.3%

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

   3. Taylor expanded in x1 around 0 68.7%

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

      1. *-commutative 68.7%

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

   5. Simplified 68.7%

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

   6. Taylor expanded in x1 around 0 69.1%

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

   if 5.69999999999999982e-158 < x1

   1. Initial program 71.2%

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

   2. Taylor expanded in x1 around 0 43.5%

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

   3. Taylor expanded in x2 around inf 41.4%

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

   4. Taylor expanded in x1 around 0 41.4%

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

      1. unpow2 41.4%

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

   6. Simplified 41.4%

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

4. Final simplification 43.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.05 \cdot 10^{+53}:\\ \;\;\;\;x1 \cdot \left(x2 \cdot -12 + -1\right)\\ \mathbf{elif}\;x1 \leq -4.3 \cdot 10^{-109}:\\ \;\;\;\;x1 \cdot \left(x2 \cdot \left(x2 \cdot 8\right)\right)\\ \mathbf{elif}\;x1 \leq 5.7 \cdot 10^{-158}:\\ \;\;\;\;x2 \cdot -6\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot \left(1 + \left(x2 \cdot x2\right) \cdot 8\right)\\ \end{array} \]

Alternative 18: 42.5% accurate, 9.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -1.22 \cdot 10^{+53}:\\ \;\;\;\;x1 \cdot \left(x2 \cdot -12 + -1\right)\\ \mathbf{elif}\;x1 \leq -5.5 \cdot 10^{-109} \lor \neg \left(x1 \leq 5.7 \cdot 10^{-158}\right):\\ \;\;\;\;x1 \cdot \left(x2 \cdot \left(x2 \cdot 8\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -1.22e+53)
   (* x1 (+ (* x2 -12.0) -1.0))
   (if (or (<= x1 -5.5e-109) (not (<= x1 5.7e-158)))
     (* x1 (* x2 (* x2 8.0)))
     (* x2 -6.0))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -1.22e+53) {
		tmp = x1 * ((x2 * -12.0) + -1.0);
	} else if ((x1 <= -5.5e-109) || !(x1 <= 5.7e-158)) {
		tmp = x1 * (x2 * (x2 * 8.0));
	} else {
		tmp = x2 * -6.0;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x1 <= (-1.22d+53)) then
        tmp = x1 * ((x2 * (-12.0d0)) + (-1.0d0))
    else if ((x1 <= (-5.5d-109)) .or. (.not. (x1 <= 5.7d-158))) then
        tmp = x1 * (x2 * (x2 * 8.0d0))
    else
        tmp = x2 * (-6.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= -1.22e+53) {
		tmp = x1 * ((x2 * -12.0) + -1.0);
	} else if ((x1 <= -5.5e-109) || !(x1 <= 5.7e-158)) {
		tmp = x1 * (x2 * (x2 * 8.0));
	} else {
		tmp = x2 * -6.0;
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -1.22e+53:
		tmp = x1 * ((x2 * -12.0) + -1.0)
	elif (x1 <= -5.5e-109) or not (x1 <= 5.7e-158):
		tmp = x1 * (x2 * (x2 * 8.0))
	else:
		tmp = x2 * -6.0
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -1.22e+53)
		tmp = Float64(x1 * Float64(Float64(x2 * -12.0) + -1.0));
	elseif ((x1 <= -5.5e-109) || !(x1 <= 5.7e-158))
		tmp = Float64(x1 * Float64(x2 * Float64(x2 * 8.0)));
	else
		tmp = Float64(x2 * -6.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -1.22e+53)
		tmp = x1 * ((x2 * -12.0) + -1.0);
	elseif ((x1 <= -5.5e-109) || ~((x1 <= 5.7e-158)))
		tmp = x1 * (x2 * (x2 * 8.0));
	else
		tmp = x2 * -6.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -1.22e+53], N[(x1 * N[(N[(x2 * -12.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x1, -5.5e-109], N[Not[LessEqual[x1, 5.7e-158]], $MachinePrecision]], N[(x1 * N[(x2 * N[(x2 * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x2 * -6.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -1.21999999999999999e53

   1. Initial program 19.5%

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

   2. Taylor expanded in x1 around 0 1.9%

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

   3. Taylor expanded in x2 around 0 7.2%

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

      1. associate-*r* 7.2%

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

   5. Simplified 7.2%

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

   6. Taylor expanded in x1 around 0 20.8%

      \[\leadsto x1 + \color{blue}{\left(-6 \cdot x2 + x1 \cdot \left(-12 \cdot x2 - 2\right)\right)} \]
   7. Step-by-step derivation

      1. fma-def 20.8%

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

      2. *-commutative 20.8%

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

      3. fma-neg 20.8%

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

      4. metadata-eval 20.8%

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

   8. Simplified 20.8%

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

   9. Taylor expanded in x1 around inf 20.8%

      \[\leadsto \color{blue}{x1 \cdot \left(-12 \cdot x2 - 1\right)} \]

   if -1.21999999999999999e53 < x1 < -5.5000000000000003e-109 or 5.69999999999999982e-158 < x1

   1. Initial program 78.2%

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

   2. Taylor expanded in x1 around 0 49.7%

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

   3. Taylor expanded in x2 around inf 41.0%

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

   4. Taylor expanded in x2 around inf 40.3%

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

      1. *-commutative 40.3%

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

      2. unpow2 40.3%

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

      3. associate-*l* 40.3%

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

      4. associate-*l* 40.3%

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

   6. Simplified 40.3%

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

   if -5.5000000000000003e-109 < x1 < 5.69999999999999982e-158

   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 84.3%

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

   3. Taylor expanded in x1 around 0 68.7%

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

      1. *-commutative 68.7%

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

   5. Simplified 68.7%

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

   6. Taylor expanded in x1 around 0 69.1%

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

4. Final simplification 43.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.22 \cdot 10^{+53}:\\ \;\;\;\;x1 \cdot \left(x2 \cdot -12 + -1\right)\\ \mathbf{elif}\;x1 \leq -5.5 \cdot 10^{-109} \lor \neg \left(x1 \leq 5.7 \cdot 10^{-158}\right):\\ \;\;\;\;x1 \cdot \left(x2 \cdot \left(x2 \cdot 8\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6\\ \end{array} \]

Alternative 19: 32.0% accurate, 13.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x2 \leq -2.8 \cdot 10^{-190}:\\ \;\;\;\;x2 \cdot -6\\ \mathbf{elif}\;x2 \leq 3 \cdot 10^{-243}:\\ \;\;\;\;-x1\\ \mathbf{else}:\\ \;\;\;\;x1 + x2 \cdot -6\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x2 -2.8e-190)
   (* x2 -6.0)
   (if (<= x2 3e-243) (- x1) (+ x1 (* x2 -6.0)))))

C

double code(double x1, double x2) {
	double tmp;
	if (x2 <= -2.8e-190) {
		tmp = x2 * -6.0;
	} else if (x2 <= 3e-243) {
		tmp = -x1;
	} else {
		tmp = x1 + (x2 * -6.0);
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x2 <= (-2.8d-190)) then
        tmp = x2 * (-6.0d0)
    else if (x2 <= 3d-243) then
        tmp = -x1
    else
        tmp = x1 + (x2 * (-6.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x2 <= -2.8e-190) {
		tmp = x2 * -6.0;
	} else if (x2 <= 3e-243) {
		tmp = -x1;
	} else {
		tmp = x1 + (x2 * -6.0);
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x2 <= -2.8e-190:
		tmp = x2 * -6.0
	elif x2 <= 3e-243:
		tmp = -x1
	else:
		tmp = x1 + (x2 * -6.0)
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x2 <= -2.8e-190)
		tmp = Float64(x2 * -6.0);
	elseif (x2 <= 3e-243)
		tmp = Float64(-x1);
	else
		tmp = Float64(x1 + Float64(x2 * -6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x2 <= -2.8e-190)
		tmp = x2 * -6.0;
	elseif (x2 <= 3e-243)
		tmp = -x1;
	else
		tmp = x1 + (x2 * -6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x2, -2.8e-190], N[(x2 * -6.0), $MachinePrecision], If[LessEqual[x2, 3e-243], (-x1), N[(x1 + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x2 < -2.80000000000000005e-190

   1. Initial program 66.4%

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

   2. Taylor expanded in x1 around 0 40.8%

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

   3. Taylor expanded in x1 around 0 27.8%

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

      1. *-commutative 27.8%

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

   5. Simplified 27.8%

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

   6. Taylor expanded in x1 around 0 27.8%

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

   if -2.80000000000000005e-190 < x2 < 3.0000000000000001e-243

   1. Initial program 64.2%

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

   2. Taylor expanded in x1 around 0 44.7%

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

   3. Taylor expanded in x2 around 0 44.7%

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

      1. associate-*r* 44.7%

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

   5. Simplified 44.7%

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

   6. Taylor expanded in x1 around 0 47.1%

      \[\leadsto x1 + \color{blue}{\left(-6 \cdot x2 + x1 \cdot \left(-12 \cdot x2 - 2\right)\right)} \]
   7. Step-by-step derivation

      1. fma-def 47.1%

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

      2. *-commutative 47.1%

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

      3. fma-neg 47.1%

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

      4. metadata-eval 47.1%

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

   8. Simplified 47.1%

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

   9. Taylor expanded in x2 around 0 40.5%

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

       1. distribute-rgt1-in 40.5%

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

       2. metadata-eval 40.5%

          \[\leadsto \color{blue}{-1} \cdot x1 \]

       3. neg-mul-1 40.5%

          \[\leadsto \color{blue}{-x1} \]

   11. Simplified 40.5%

       \[\leadsto \color{blue}{-x1} \]

   if 3.0000000000000001e-243 < x2

   1. Initial program 77.0%

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

   2. Taylor expanded in x1 around 0 55.7%

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

   3. Taylor expanded in x1 around 0 25.9%

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

      1. *-commutative 25.9%

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

   5. Simplified 25.9%

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

4. Final simplification 29.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq -2.8 \cdot 10^{-190}:\\ \;\;\;\;x2 \cdot -6\\ \mathbf{elif}\;x2 \leq 3 \cdot 10^{-243}:\\ \;\;\;\;-x1\\ \mathbf{else}:\\ \;\;\;\;x1 + x2 \cdot -6\\ \end{array} \]

Alternative 20: 31.7% accurate, 17.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x2 \leq -2.8 \cdot 10^{-190}:\\ \;\;\;\;x2 \cdot -6\\ \mathbf{elif}\;x2 \leq 3 \cdot 10^{-243}:\\ \;\;\;\;-x1\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x2 -2.8e-190) (* x2 -6.0) (if (<= x2 3e-243) (- x1) (* x2 -6.0))))

C

double code(double x1, double x2) {
	double tmp;
	if (x2 <= -2.8e-190) {
		tmp = x2 * -6.0;
	} else if (x2 <= 3e-243) {
		tmp = -x1;
	} else {
		tmp = x2 * -6.0;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x2 <= (-2.8d-190)) then
        tmp = x2 * (-6.0d0)
    else if (x2 <= 3d-243) then
        tmp = -x1
    else
        tmp = x2 * (-6.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x2 <= -2.8e-190) {
		tmp = x2 * -6.0;
	} else if (x2 <= 3e-243) {
		tmp = -x1;
	} else {
		tmp = x2 * -6.0;
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x2 <= -2.8e-190:
		tmp = x2 * -6.0
	elif x2 <= 3e-243:
		tmp = -x1
	else:
		tmp = x2 * -6.0
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x2 <= -2.8e-190)
		tmp = Float64(x2 * -6.0);
	elseif (x2 <= 3e-243)
		tmp = Float64(-x1);
	else
		tmp = Float64(x2 * -6.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x2 <= -2.8e-190)
		tmp = x2 * -6.0;
	elseif (x2 <= 3e-243)
		tmp = -x1;
	else
		tmp = x2 * -6.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x2, -2.8e-190], N[(x2 * -6.0), $MachinePrecision], If[LessEqual[x2, 3e-243], (-x1), N[(x2 * -6.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x2 < -2.80000000000000005e-190 or 3.0000000000000001e-243 < x2

   1. Initial program 71.8%

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

   2. Taylor expanded in x1 around 0 48.5%

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

   3. Taylor expanded in x1 around 0 26.8%

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

      1. *-commutative 26.8%

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

   5. Simplified 26.8%

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

   6. Taylor expanded in x1 around 0 26.7%

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

   if -2.80000000000000005e-190 < x2 < 3.0000000000000001e-243

   1. Initial program 64.2%

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

   2. Taylor expanded in x1 around 0 44.7%

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

   3. Taylor expanded in x2 around 0 44.7%

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

      1. associate-*r* 44.7%

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

   5. Simplified 44.7%

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

   6. Taylor expanded in x1 around 0 47.1%

      \[\leadsto x1 + \color{blue}{\left(-6 \cdot x2 + x1 \cdot \left(-12 \cdot x2 - 2\right)\right)} \]
   7. Step-by-step derivation

      1. fma-def 47.1%

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

      2. *-commutative 47.1%

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

      3. fma-neg 47.1%

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

      4. metadata-eval 47.1%

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

   8. Simplified 47.1%

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

   9. Taylor expanded in x2 around 0 40.5%

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

       1. distribute-rgt1-in 40.5%

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

       2. metadata-eval 40.5%

          \[\leadsto \color{blue}{-1} \cdot x1 \]

       3. neg-mul-1 40.5%

          \[\leadsto \color{blue}{-x1} \]

   11. Simplified 40.5%

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

4. Final simplification 28.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq -2.8 \cdot 10^{-190}:\\ \;\;\;\;x2 \cdot -6\\ \mathbf{elif}\;x2 \leq 3 \cdot 10^{-243}:\\ \;\;\;\;-x1\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6\\ \end{array} \]

Alternative 21: 13.6% accurate, 63.5× speedup

Math

\[\begin{array}{l} \\ -x1 \end{array} \]

FPCore

(FPCore (x1 x2) :precision binary64 (- x1))

C

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

Fortran

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

Java

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

Python

def code(x1, x2):
	return -x1

Julia

function code(x1, x2)
	return Float64(-x1)
end

MATLAB

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

Wolfram

code[x1_, x2_] := (-x1)

Derivation

1. Initial program 70.6%

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

2. Taylor expanded in x1 around 0 47.9%

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

3. Taylor expanded in x2 around 0 36.1%

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

   1. associate-*r* 36.1%

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

5. Simplified 36.1%

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

6. Taylor expanded in x1 around 0 41.8%

   \[\leadsto x1 + \color{blue}{\left(-6 \cdot x2 + x1 \cdot \left(-12 \cdot x2 - 2\right)\right)} \]
7. Step-by-step derivation

   1. fma-def 41.8%

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

   2. *-commutative 41.8%

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

   3. fma-neg 41.8%

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

   4. metadata-eval 41.8%

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

8. Simplified 41.8%

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

9. Taylor expanded in x2 around 0 13.0%

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

    1. distribute-rgt1-in 13.0%

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

    2. metadata-eval 13.0%

       \[\leadsto \color{blue}{-1} \cdot x1 \]

    3. neg-mul-1 13.0%

       \[\leadsto \color{blue}{-x1} \]

11. Simplified 13.0%

    \[\leadsto \color{blue}{-x1} \]

12. Final simplification 13.0%

    \[\leadsto -x1 \]

Alternative 22: 3.3% accurate, 127.0× speedup

Math

\[\begin{array}{l} \\ x1 \end{array} \]

FPCore

(FPCore (x1 x2) :precision binary64 x1)

C

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

Fortran

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

Java

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

Python

def code(x1, x2):
	return x1

Julia

function code(x1, x2)
	return x1
end

MATLAB

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

Wolfram

code[x1_, x2_] := x1

Derivation

1. Initial program 70.6%

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

2. Taylor expanded in x1 around 0 47.9%

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

3. Taylor expanded in x1 around 0 23.7%

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

   1. *-commutative 23.7%

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

5. Simplified 23.7%

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

6. Taylor expanded in x1 around inf 3.3%

   \[\leadsto \color{blue}{x1} \]

7. Final simplification 3.3%

   \[\leadsto x1 \]

Reproduce

herbie shell --seed 2023297 
(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))))))