Rosa's FloatVsDoubleBenchmark

Percentage Accurate: 70.5% → 99.4%

Time: 1.2min

Alternatives: 20

Speedup: 3.3×

• 47.1% 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: 70.5% 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

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 99.4%

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

   3. Simplified 99.7%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in x1 around inf 10.7%

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

   4. Taylor expanded in x1 around inf 100.0%

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

4. Final simplification 99.8%

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

Alternative 2: 99.2% accurate, 0.2× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 99.4%

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

   3. Taylor expanded in x2 around 0 99.4%

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

      1. associate--l+ 99.5%

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

      2. associate-*r/ 99.5%

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

      3. +-commutative 99.5%

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

      4. unpow2 99.5%

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

      5. fma-undefine 99.5%

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

      6. associate-*r/ 99.5%

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

      7. div-sub 99.5%

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

      8. +-commutative 99.5%

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

      9. unpow2 99.5%

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

      10. fma-undefine 99.5%

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

   5. Simplified 99.5%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in x1 around inf 10.7%

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

   4. Taylor expanded in x1 around inf 100.0%

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

4. Final simplification 99.6%

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

Alternative 3: 99.2% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 99.4%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in x1 around inf 10.7%

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

   4. Taylor expanded in x1 around inf 100.0%

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

4. Final simplification 99.6%

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

Alternative 4: 98.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := x1 + \left(\left(x1 + 6 \cdot {x1}^{4}\right) + 9\right)\\ t_2 := -1 - x1 \cdot x1\\ t_3 := x1 \cdot \left(x1 \cdot x1\right)\\ t_4 := x1 \cdot \left(x1 \cdot 3\right)\\ t_5 := \frac{\left(t\_4 + 2 \cdot x2\right) - x1}{t\_0}\\ t_6 := \left(\left(x1 \cdot 2\right) \cdot t\_5\right) \cdot \left(3 - t\_5\right)\\ t_7 := t\_4 \cdot t\_5\\ \mathbf{if}\;x1 \leq -5 \cdot 10^{+103}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x1 \leq -1.7:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(\left(\left(x1 \cdot x1\right) \cdot \left(6 - t\_5 \cdot 4\right) + t\_6\right) \cdot t\_2 + t\_7\right) + t\_3\right)\right) + 9\right)\\ \mathbf{elif}\;x1 \leq 1.8 \cdot 10^{-12}:\\ \;\;\;\;x1 - \left(\left(x1 \cdot \left(2 - x1 \cdot 9\right) + x2 \cdot \left(x1 \cdot \left(12 - x1 \cdot 6\right) - 8 \cdot \left(x1 \cdot x2\right)\right)\right) - x2 \cdot -6\right)\\ \mathbf{elif}\;x1 \leq 4 \cdot 10^{+82}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{x1 + \left(2 \cdot x2 - t\_4\right)}{t\_2} + \left(x1 + \left(t\_3 + \left(t\_7 - t\_0 \cdot \left(\left(4 \cdot \left(3 - 2 \cdot x2\right) + x1 \cdot \left(4 - x1 \cdot 6\right)\right) + t\_6\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ (* x1 x1) 1.0))
        (t_1 (+ x1 (+ (+ x1 (* 6.0 (pow x1 4.0))) 9.0)))
        (t_2 (- -1.0 (* x1 x1)))
        (t_3 (* x1 (* x1 x1)))
        (t_4 (* x1 (* x1 3.0)))
        (t_5 (/ (- (+ t_4 (* 2.0 x2)) x1) t_0))
        (t_6 (* (* (* x1 2.0) t_5) (- 3.0 t_5)))
        (t_7 (* t_4 t_5)))
   (if (<= x1 -5e+103)
     t_1
     (if (<= x1 -1.7)
       (+
        x1
        (+
         (+
          x1
          (+ (+ (* (+ (* (* x1 x1) (- 6.0 (* t_5 4.0))) t_6) t_2) t_7) t_3))
         9.0))
       (if (<= x1 1.8e-12)
         (-
          x1
          (-
           (+
            (* x1 (- 2.0 (* x1 9.0)))
            (* x2 (- (* x1 (- 12.0 (* x1 6.0))) (* 8.0 (* x1 x2)))))
           (* x2 -6.0)))
         (if (<= x1 4e+82)
           (+
            x1
            (+
             (* 3.0 (/ (+ x1 (- (* 2.0 x2) t_4)) t_2))
             (+
              x1
              (+
               t_3
               (-
                t_7
                (*
                 t_0
                 (+
                  (+ (* 4.0 (- 3.0 (* 2.0 x2))) (* x1 (- 4.0 (* x1 6.0))))
                  t_6)))))))
           t_1))))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = x1 + ((x1 + (6.0 * pow(x1, 4.0))) + 9.0);
	double t_2 = -1.0 - (x1 * x1);
	double t_3 = x1 * (x1 * x1);
	double t_4 = x1 * (x1 * 3.0);
	double t_5 = ((t_4 + (2.0 * x2)) - x1) / t_0;
	double t_6 = ((x1 * 2.0) * t_5) * (3.0 - t_5);
	double t_7 = t_4 * t_5;
	double tmp;
	if (x1 <= -5e+103) {
		tmp = t_1;
	} else if (x1 <= -1.7) {
		tmp = x1 + ((x1 + ((((((x1 * x1) * (6.0 - (t_5 * 4.0))) + t_6) * t_2) + t_7) + t_3)) + 9.0);
	} else if (x1 <= 1.8e-12) {
		tmp = x1 - (((x1 * (2.0 - (x1 * 9.0))) + (x2 * ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))) - (x2 * -6.0));
	} else if (x1 <= 4e+82) {
		tmp = x1 + ((3.0 * ((x1 + ((2.0 * x2) - t_4)) / t_2)) + (x1 + (t_3 + (t_7 - (t_0 * (((4.0 * (3.0 - (2.0 * x2))) + (x1 * (4.0 - (x1 * 6.0)))) + t_6))))));
	} else {
		tmp = 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) :: t_7
    real(8) :: tmp
    t_0 = (x1 * x1) + 1.0d0
    t_1 = x1 + ((x1 + (6.0d0 * (x1 ** 4.0d0))) + 9.0d0)
    t_2 = (-1.0d0) - (x1 * x1)
    t_3 = x1 * (x1 * x1)
    t_4 = x1 * (x1 * 3.0d0)
    t_5 = ((t_4 + (2.0d0 * x2)) - x1) / t_0
    t_6 = ((x1 * 2.0d0) * t_5) * (3.0d0 - t_5)
    t_7 = t_4 * t_5
    if (x1 <= (-5d+103)) then
        tmp = t_1
    else if (x1 <= (-1.7d0)) then
        tmp = x1 + ((x1 + ((((((x1 * x1) * (6.0d0 - (t_5 * 4.0d0))) + t_6) * t_2) + t_7) + t_3)) + 9.0d0)
    else if (x1 <= 1.8d-12) then
        tmp = x1 - (((x1 * (2.0d0 - (x1 * 9.0d0))) + (x2 * ((x1 * (12.0d0 - (x1 * 6.0d0))) - (8.0d0 * (x1 * x2))))) - (x2 * (-6.0d0)))
    else if (x1 <= 4d+82) then
        tmp = x1 + ((3.0d0 * ((x1 + ((2.0d0 * x2) - t_4)) / t_2)) + (x1 + (t_3 + (t_7 - (t_0 * (((4.0d0 * (3.0d0 - (2.0d0 * x2))) + (x1 * (4.0d0 - (x1 * 6.0d0)))) + t_6))))))
    else
        tmp = 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 = x1 + ((x1 + (6.0 * Math.pow(x1, 4.0))) + 9.0);
	double t_2 = -1.0 - (x1 * x1);
	double t_3 = x1 * (x1 * x1);
	double t_4 = x1 * (x1 * 3.0);
	double t_5 = ((t_4 + (2.0 * x2)) - x1) / t_0;
	double t_6 = ((x1 * 2.0) * t_5) * (3.0 - t_5);
	double t_7 = t_4 * t_5;
	double tmp;
	if (x1 <= -5e+103) {
		tmp = t_1;
	} else if (x1 <= -1.7) {
		tmp = x1 + ((x1 + ((((((x1 * x1) * (6.0 - (t_5 * 4.0))) + t_6) * t_2) + t_7) + t_3)) + 9.0);
	} else if (x1 <= 1.8e-12) {
		tmp = x1 - (((x1 * (2.0 - (x1 * 9.0))) + (x2 * ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))) - (x2 * -6.0));
	} else if (x1 <= 4e+82) {
		tmp = x1 + ((3.0 * ((x1 + ((2.0 * x2) - t_4)) / t_2)) + (x1 + (t_3 + (t_7 - (t_0 * (((4.0 * (3.0 - (2.0 * x2))) + (x1 * (4.0 - (x1 * 6.0)))) + t_6))))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x1 * x1) + 1.0
	t_1 = x1 + ((x1 + (6.0 * math.pow(x1, 4.0))) + 9.0)
	t_2 = -1.0 - (x1 * x1)
	t_3 = x1 * (x1 * x1)
	t_4 = x1 * (x1 * 3.0)
	t_5 = ((t_4 + (2.0 * x2)) - x1) / t_0
	t_6 = ((x1 * 2.0) * t_5) * (3.0 - t_5)
	t_7 = t_4 * t_5
	tmp = 0
	if x1 <= -5e+103:
		tmp = t_1
	elif x1 <= -1.7:
		tmp = x1 + ((x1 + ((((((x1 * x1) * (6.0 - (t_5 * 4.0))) + t_6) * t_2) + t_7) + t_3)) + 9.0)
	elif x1 <= 1.8e-12:
		tmp = x1 - (((x1 * (2.0 - (x1 * 9.0))) + (x2 * ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))) - (x2 * -6.0))
	elif x1 <= 4e+82:
		tmp = x1 + ((3.0 * ((x1 + ((2.0 * x2) - t_4)) / t_2)) + (x1 + (t_3 + (t_7 - (t_0 * (((4.0 * (3.0 - (2.0 * x2))) + (x1 * (4.0 - (x1 * 6.0)))) + t_6))))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * x1) + 1.0)
	t_1 = Float64(x1 + Float64(Float64(x1 + Float64(6.0 * (x1 ^ 4.0))) + 9.0))
	t_2 = Float64(-1.0 - Float64(x1 * x1))
	t_3 = Float64(x1 * Float64(x1 * x1))
	t_4 = Float64(x1 * Float64(x1 * 3.0))
	t_5 = Float64(Float64(Float64(t_4 + Float64(2.0 * x2)) - x1) / t_0)
	t_6 = Float64(Float64(Float64(x1 * 2.0) * t_5) * Float64(3.0 - t_5))
	t_7 = Float64(t_4 * t_5)
	tmp = 0.0
	if (x1 <= -5e+103)
		tmp = t_1;
	elseif (x1 <= -1.7)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(Float64(Float64(Float64(Float64(Float64(x1 * x1) * Float64(6.0 - Float64(t_5 * 4.0))) + t_6) * t_2) + t_7) + t_3)) + 9.0));
	elseif (x1 <= 1.8e-12)
		tmp = Float64(x1 - Float64(Float64(Float64(x1 * Float64(2.0 - Float64(x1 * 9.0))) + Float64(x2 * Float64(Float64(x1 * Float64(12.0 - Float64(x1 * 6.0))) - Float64(8.0 * Float64(x1 * x2))))) - Float64(x2 * -6.0)));
	elseif (x1 <= 4e+82)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(x1 + Float64(Float64(2.0 * x2) - t_4)) / t_2)) + Float64(x1 + Float64(t_3 + Float64(t_7 - Float64(t_0 * Float64(Float64(Float64(4.0 * Float64(3.0 - Float64(2.0 * x2))) + Float64(x1 * Float64(4.0 - Float64(x1 * 6.0)))) + t_6)))))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x1 * x1) + 1.0;
	t_1 = x1 + ((x1 + (6.0 * (x1 ^ 4.0))) + 9.0);
	t_2 = -1.0 - (x1 * x1);
	t_3 = x1 * (x1 * x1);
	t_4 = x1 * (x1 * 3.0);
	t_5 = ((t_4 + (2.0 * x2)) - x1) / t_0;
	t_6 = ((x1 * 2.0) * t_5) * (3.0 - t_5);
	t_7 = t_4 * t_5;
	tmp = 0.0;
	if (x1 <= -5e+103)
		tmp = t_1;
	elseif (x1 <= -1.7)
		tmp = x1 + ((x1 + ((((((x1 * x1) * (6.0 - (t_5 * 4.0))) + t_6) * t_2) + t_7) + t_3)) + 9.0);
	elseif (x1 <= 1.8e-12)
		tmp = x1 - (((x1 * (2.0 - (x1 * 9.0))) + (x2 * ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))) - (x2 * -6.0));
	elseif (x1 <= 4e+82)
		tmp = x1 + ((3.0 * ((x1 + ((2.0 * x2) - t_4)) / t_2)) + (x1 + (t_3 + (t_7 - (t_0 * (((4.0 * (3.0 - (2.0 * x2))) + (x1 * (4.0 - (x1 * 6.0)))) + t_6))))));
	else
		tmp = 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[(x1 + N[(N[(x1 + N[(6.0 * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 9.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(N[(t$95$4 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]}, Block[{t$95$6 = N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$5), $MachinePrecision] * N[(3.0 - t$95$5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(t$95$4 * t$95$5), $MachinePrecision]}, If[LessEqual[x1, -5e+103], t$95$1, If[LessEqual[x1, -1.7], N[(x1 + N[(N[(x1 + N[(N[(N[(N[(N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 - N[(t$95$5 * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$6), $MachinePrecision] * t$95$2), $MachinePrecision] + t$95$7), $MachinePrecision] + t$95$3), $MachinePrecision]), $MachinePrecision] + 9.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.8e-12], N[(x1 - N[(N[(N[(x1 * N[(2.0 - N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x2 * N[(N[(x1 * N[(12.0 - N[(x1 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 4e+82], N[(x1 + N[(N[(3.0 * N[(N[(x1 + N[(N[(2.0 * x2), $MachinePrecision] - t$95$4), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(t$95$3 + N[(t$95$7 - N[(t$95$0 * N[(N[(N[(4.0 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(4.0 - N[(x1 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$6), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -5e103 or 3.9999999999999999e82 < x1

   1. Initial program 13.8%

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

   3. Taylor expanded in x1 around inf 23.0%

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

   4. Taylor expanded in x1 around inf 100.0%

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

   if -5e103 < x1 < -1.69999999999999996

   1. Initial program 99.5%

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

   3. Taylor expanded in x1 around inf 99.5%

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

   if -1.69999999999999996 < x1 < 1.8e-12

   1. Initial program 99.4%

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

   3. Taylor expanded in x1 around 0 86.7%

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

   4. Taylor expanded in x1 around 0 86.7%

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

   5. Taylor expanded in x1 around 0 87.1%

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

   6. Taylor expanded in x2 around 0 99.2%

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

   if 1.8e-12 < x1 < 3.9999999999999999e82

   1. Initial program 98.9%

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

   3. Taylor expanded in x1 around -inf 99.0%

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

   4. Taylor expanded in x1 around 0 99.4%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5 \cdot 10^{+103}:\\ \;\;\;\;x1 + \left(\left(x1 + 6 \cdot {x1}^{4}\right) + 9\right)\\ \mathbf{elif}\;x1 \leq -1.7:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(\left(\left(x1 \cdot x1\right) \cdot \left(6 - \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4\right) + \left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(3 - \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right)\right) \cdot \left(-1 - x1 \cdot x1\right) + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 9\right)\\ \mathbf{elif}\;x1 \leq 1.8 \cdot 10^{-12}:\\ \;\;\;\;x1 - \left(\left(x1 \cdot \left(2 - x1 \cdot 9\right) + x2 \cdot \left(x1 \cdot \left(12 - x1 \cdot 6\right) - 8 \cdot \left(x1 \cdot x2\right)\right)\right) - x2 \cdot -6\right)\\ \mathbf{elif}\;x1 \leq 4 \cdot 10^{+82}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{x1 + \left(2 \cdot x2 - x1 \cdot \left(x1 \cdot 3\right)\right)}{-1 - x1 \cdot x1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - \left(x1 \cdot x1 + 1\right) \cdot \left(\left(4 \cdot \left(3 - 2 \cdot x2\right) + x1 \cdot \left(4 - x1 \cdot 6\right)\right) + \left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(3 - \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 + 6 \cdot {x1}^{4}\right) + 9\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 98.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 + \left(\left(x1 + 6 \cdot {x1}^{4}\right) + 9\right)\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := \frac{\left(t\_1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\\ t_3 := x1 + \left(\left(x1 + \left(\left(\left(\left(x1 \cdot x1\right) \cdot \left(6 - t\_2 \cdot 4\right) + \left(\left(x1 \cdot 2\right) \cdot t\_2\right) \cdot \left(3 - t\_2\right)\right) \cdot \left(-1 - x1 \cdot x1\right) + t\_1 \cdot t\_2\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 9\right)\\ \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x1 \leq -1.7:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x1 \leq 1.8 \cdot 10^{-12}:\\ \;\;\;\;x1 - \left(\left(x1 \cdot \left(2 - x1 \cdot 9\right) + x2 \cdot \left(x1 \cdot \left(12 - x1 \cdot 6\right) - 8 \cdot \left(x1 \cdot x2\right)\right)\right) - x2 \cdot -6\right)\\ \mathbf{elif}\;x1 \leq 10^{+81}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ x1 (+ (+ x1 (* 6.0 (pow x1 4.0))) 9.0)))
        (t_1 (* x1 (* x1 3.0)))
        (t_2 (/ (- (+ t_1 (* 2.0 x2)) x1) (+ (* x1 x1) 1.0)))
        (t_3
         (+
          x1
          (+
           (+
            x1
            (+
             (+
              (*
               (+
                (* (* x1 x1) (- 6.0 (* t_2 4.0)))
                (* (* (* x1 2.0) t_2) (- 3.0 t_2)))
               (- -1.0 (* x1 x1)))
              (* t_1 t_2))
             (* x1 (* x1 x1))))
           9.0))))
   (if (<= x1 -5.6e+102)
     t_0
     (if (<= x1 -1.7)
       t_3
       (if (<= x1 1.8e-12)
         (-
          x1
          (-
           (+
            (* x1 (- 2.0 (* x1 9.0)))
            (* x2 (- (* x1 (- 12.0 (* x1 6.0))) (* 8.0 (* x1 x2)))))
           (* x2 -6.0)))
         (if (<= x1 1e+81) t_3 t_0))))))

C

double code(double x1, double x2) {
	double t_0 = x1 + ((x1 + (6.0 * pow(x1, 4.0))) + 9.0);
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = ((t_1 + (2.0 * x2)) - x1) / ((x1 * x1) + 1.0);
	double t_3 = x1 + ((x1 + ((((((x1 * x1) * (6.0 - (t_2 * 4.0))) + (((x1 * 2.0) * t_2) * (3.0 - t_2))) * (-1.0 - (x1 * x1))) + (t_1 * t_2)) + (x1 * (x1 * x1)))) + 9.0);
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = t_0;
	} else if (x1 <= -1.7) {
		tmp = t_3;
	} else if (x1 <= 1.8e-12) {
		tmp = x1 - (((x1 * (2.0 - (x1 * 9.0))) + (x2 * ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))) - (x2 * -6.0));
	} else if (x1 <= 1e+81) {
		tmp = t_3;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_0 = x1 + ((x1 + (6.0d0 * (x1 ** 4.0d0))) + 9.0d0)
    t_1 = x1 * (x1 * 3.0d0)
    t_2 = ((t_1 + (2.0d0 * x2)) - x1) / ((x1 * x1) + 1.0d0)
    t_3 = x1 + ((x1 + ((((((x1 * x1) * (6.0d0 - (t_2 * 4.0d0))) + (((x1 * 2.0d0) * t_2) * (3.0d0 - t_2))) * ((-1.0d0) - (x1 * x1))) + (t_1 * t_2)) + (x1 * (x1 * x1)))) + 9.0d0)
    if (x1 <= (-5.6d+102)) then
        tmp = t_0
    else if (x1 <= (-1.7d0)) then
        tmp = t_3
    else if (x1 <= 1.8d-12) then
        tmp = x1 - (((x1 * (2.0d0 - (x1 * 9.0d0))) + (x2 * ((x1 * (12.0d0 - (x1 * 6.0d0))) - (8.0d0 * (x1 * x2))))) - (x2 * (-6.0d0)))
    else if (x1 <= 1d+81) then
        tmp = t_3
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 + ((x1 + (6.0 * Math.pow(x1, 4.0))) + 9.0);
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = ((t_1 + (2.0 * x2)) - x1) / ((x1 * x1) + 1.0);
	double t_3 = x1 + ((x1 + ((((((x1 * x1) * (6.0 - (t_2 * 4.0))) + (((x1 * 2.0) * t_2) * (3.0 - t_2))) * (-1.0 - (x1 * x1))) + (t_1 * t_2)) + (x1 * (x1 * x1)))) + 9.0);
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = t_0;
	} else if (x1 <= -1.7) {
		tmp = t_3;
	} else if (x1 <= 1.8e-12) {
		tmp = x1 - (((x1 * (2.0 - (x1 * 9.0))) + (x2 * ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))) - (x2 * -6.0));
	} else if (x1 <= 1e+81) {
		tmp = t_3;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 + ((x1 + (6.0 * math.pow(x1, 4.0))) + 9.0)
	t_1 = x1 * (x1 * 3.0)
	t_2 = ((t_1 + (2.0 * x2)) - x1) / ((x1 * x1) + 1.0)
	t_3 = x1 + ((x1 + ((((((x1 * x1) * (6.0 - (t_2 * 4.0))) + (((x1 * 2.0) * t_2) * (3.0 - t_2))) * (-1.0 - (x1 * x1))) + (t_1 * t_2)) + (x1 * (x1 * x1)))) + 9.0)
	tmp = 0
	if x1 <= -5.6e+102:
		tmp = t_0
	elif x1 <= -1.7:
		tmp = t_3
	elif x1 <= 1.8e-12:
		tmp = x1 - (((x1 * (2.0 - (x1 * 9.0))) + (x2 * ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))) - (x2 * -6.0))
	elif x1 <= 1e+81:
		tmp = t_3
	else:
		tmp = t_0
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 + Float64(Float64(x1 + Float64(6.0 * (x1 ^ 4.0))) + 9.0))
	t_1 = Float64(x1 * Float64(x1 * 3.0))
	t_2 = Float64(Float64(Float64(t_1 + Float64(2.0 * x2)) - x1) / Float64(Float64(x1 * x1) + 1.0))
	t_3 = Float64(x1 + Float64(Float64(x1 + Float64(Float64(Float64(Float64(Float64(Float64(x1 * x1) * Float64(6.0 - Float64(t_2 * 4.0))) + Float64(Float64(Float64(x1 * 2.0) * t_2) * Float64(3.0 - t_2))) * Float64(-1.0 - Float64(x1 * x1))) + Float64(t_1 * t_2)) + Float64(x1 * Float64(x1 * x1)))) + 9.0))
	tmp = 0.0
	if (x1 <= -5.6e+102)
		tmp = t_0;
	elseif (x1 <= -1.7)
		tmp = t_3;
	elseif (x1 <= 1.8e-12)
		tmp = Float64(x1 - Float64(Float64(Float64(x1 * Float64(2.0 - Float64(x1 * 9.0))) + Float64(x2 * Float64(Float64(x1 * Float64(12.0 - Float64(x1 * 6.0))) - Float64(8.0 * Float64(x1 * x2))))) - Float64(x2 * -6.0)));
	elseif (x1 <= 1e+81)
		tmp = t_3;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 + ((x1 + (6.0 * (x1 ^ 4.0))) + 9.0);
	t_1 = x1 * (x1 * 3.0);
	t_2 = ((t_1 + (2.0 * x2)) - x1) / ((x1 * x1) + 1.0);
	t_3 = x1 + ((x1 + ((((((x1 * x1) * (6.0 - (t_2 * 4.0))) + (((x1 * 2.0) * t_2) * (3.0 - t_2))) * (-1.0 - (x1 * x1))) + (t_1 * t_2)) + (x1 * (x1 * x1)))) + 9.0);
	tmp = 0.0;
	if (x1 <= -5.6e+102)
		tmp = t_0;
	elseif (x1 <= -1.7)
		tmp = t_3;
	elseif (x1 <= 1.8e-12)
		tmp = x1 - (((x1 * (2.0 - (x1 * 9.0))) + (x2 * ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))) - (x2 * -6.0));
	elseif (x1 <= 1e+81)
		tmp = t_3;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 + N[(N[(x1 + N[(6.0 * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 9.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(t$95$1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x1 + N[(N[(x1 + N[(N[(N[(N[(N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 - N[(t$95$2 * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$2), $MachinePrecision] * N[(3.0 - t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$1 * t$95$2), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 9.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -5.6e+102], t$95$0, If[LessEqual[x1, -1.7], t$95$3, If[LessEqual[x1, 1.8e-12], N[(x1 - N[(N[(N[(x1 * N[(2.0 - N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x2 * N[(N[(x1 * N[(12.0 - N[(x1 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1e+81], t$95$3, t$95$0]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -5.60000000000000037e102 or 9.99999999999999921e80 < x1

   1. Initial program 13.8%

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

   3. Taylor expanded in x1 around inf 23.0%

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

   4. Taylor expanded in x1 around inf 100.0%

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

   if -5.60000000000000037e102 < x1 < -1.69999999999999996 or 1.8e-12 < x1 < 9.99999999999999921e80

   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. Add Preprocessing

   3. Taylor expanded in x1 around inf 99.2%

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

   if -1.69999999999999996 < x1 < 1.8e-12

   1. Initial program 99.4%

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

   3. Taylor expanded in x1 around 0 86.7%

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

   4. Taylor expanded in x1 around 0 86.7%

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

   5. Taylor expanded in x1 around 0 87.1%

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

   6. Taylor expanded in x2 around 0 99.2%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(\left(x1 + 6 \cdot {x1}^{4}\right) + 9\right)\\ \mathbf{elif}\;x1 \leq -1.7:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(\left(\left(x1 \cdot x1\right) \cdot \left(6 - \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4\right) + \left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(3 - \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right)\right) \cdot \left(-1 - x1 \cdot x1\right) + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 9\right)\\ \mathbf{elif}\;x1 \leq 1.8 \cdot 10^{-12}:\\ \;\;\;\;x1 - \left(\left(x1 \cdot \left(2 - x1 \cdot 9\right) + x2 \cdot \left(x1 \cdot \left(12 - x1 \cdot 6\right) - 8 \cdot \left(x1 \cdot x2\right)\right)\right) - x2 \cdot -6\right)\\ \mathbf{elif}\;x1 \leq 10^{+81}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(\left(\left(x1 \cdot x1\right) \cdot \left(6 - \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4\right) + \left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(3 - \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right)\right) \cdot \left(-1 - x1 \cdot x1\right) + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 9\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 + 6 \cdot {x1}^{4}\right) + 9\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 91.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 + \left(\left(x1 + 6 \cdot {x1}^{4}\right) + 9\right)\\ t_1 := x1 \cdot x1 + 1\\ t_2 := x1 \cdot \left(x1 \cdot 3\right)\\ t_3 := \frac{\left(t\_2 + 2 \cdot x2\right) - x1}{t\_1}\\ \mathbf{if}\;x1 \leq -1.1 \cdot 10^{+74}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x1 \leq -1.7:\\ \;\;\;\;x1 + \left(3 \cdot \frac{x1 + \left(2 \cdot x2 - t\_2\right)}{-1 - x1 \cdot x1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(t\_2 \cdot t\_3 + t\_1 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t\_3\right) \cdot \left(t\_3 - 3\right) + x2 \cdot 8\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 8.5 \cdot 10^{+34}:\\ \;\;\;\;x1 - \left(\left(x1 \cdot \left(2 - x1 \cdot 9\right) + x2 \cdot \left(x1 \cdot \left(12 - x1 \cdot 6\right) - 8 \cdot \left(x1 \cdot x2\right)\right)\right) - x2 \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ x1 (+ (+ x1 (* 6.0 (pow x1 4.0))) 9.0)))
        (t_1 (+ (* x1 x1) 1.0))
        (t_2 (* x1 (* x1 3.0)))
        (t_3 (/ (- (+ t_2 (* 2.0 x2)) x1) t_1)))
   (if (<= x1 -1.1e+74)
     t_0
     (if (<= x1 -1.7)
       (+
        x1
        (+
         (* 3.0 (/ (+ x1 (- (* 2.0 x2) t_2)) (- -1.0 (* x1 x1))))
         (+
          x1
          (+
           (* x1 (* x1 x1))
           (+
            (* t_2 t_3)
            (* t_1 (+ (* (* (* x1 2.0) t_3) (- t_3 3.0)) (* x2 8.0))))))))
       (if (<= x1 8.5e+34)
         (-
          x1
          (-
           (+
            (* x1 (- 2.0 (* x1 9.0)))
            (* x2 (- (* x1 (- 12.0 (* x1 6.0))) (* 8.0 (* x1 x2)))))
           (* x2 -6.0)))
         t_0)))))

C

double code(double x1, double x2) {
	double t_0 = x1 + ((x1 + (6.0 * pow(x1, 4.0))) + 9.0);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = ((t_2 + (2.0 * x2)) - x1) / t_1;
	double tmp;
	if (x1 <= -1.1e+74) {
		tmp = t_0;
	} else if (x1 <= -1.7) {
		tmp = x1 + ((3.0 * ((x1 + ((2.0 * x2) - t_2)) / (-1.0 - (x1 * x1)))) + (x1 + ((x1 * (x1 * x1)) + ((t_2 * t_3) + (t_1 * ((((x1 * 2.0) * t_3) * (t_3 - 3.0)) + (x2 * 8.0)))))));
	} else if (x1 <= 8.5e+34) {
		tmp = x1 - (((x1 * (2.0 - (x1 * 9.0))) + (x2 * ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))) - (x2 * -6.0));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_0 = x1 + ((x1 + (6.0d0 * (x1 ** 4.0d0))) + 9.0d0)
    t_1 = (x1 * x1) + 1.0d0
    t_2 = x1 * (x1 * 3.0d0)
    t_3 = ((t_2 + (2.0d0 * x2)) - x1) / t_1
    if (x1 <= (-1.1d+74)) then
        tmp = t_0
    else if (x1 <= (-1.7d0)) then
        tmp = x1 + ((3.0d0 * ((x1 + ((2.0d0 * x2) - t_2)) / ((-1.0d0) - (x1 * x1)))) + (x1 + ((x1 * (x1 * x1)) + ((t_2 * t_3) + (t_1 * ((((x1 * 2.0d0) * t_3) * (t_3 - 3.0d0)) + (x2 * 8.0d0)))))))
    else if (x1 <= 8.5d+34) then
        tmp = x1 - (((x1 * (2.0d0 - (x1 * 9.0d0))) + (x2 * ((x1 * (12.0d0 - (x1 * 6.0d0))) - (8.0d0 * (x1 * x2))))) - (x2 * (-6.0d0)))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 + ((x1 + (6.0 * Math.pow(x1, 4.0))) + 9.0);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = ((t_2 + (2.0 * x2)) - x1) / t_1;
	double tmp;
	if (x1 <= -1.1e+74) {
		tmp = t_0;
	} else if (x1 <= -1.7) {
		tmp = x1 + ((3.0 * ((x1 + ((2.0 * x2) - t_2)) / (-1.0 - (x1 * x1)))) + (x1 + ((x1 * (x1 * x1)) + ((t_2 * t_3) + (t_1 * ((((x1 * 2.0) * t_3) * (t_3 - 3.0)) + (x2 * 8.0)))))));
	} else if (x1 <= 8.5e+34) {
		tmp = x1 - (((x1 * (2.0 - (x1 * 9.0))) + (x2 * ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))) - (x2 * -6.0));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 + ((x1 + (6.0 * math.pow(x1, 4.0))) + 9.0)
	t_1 = (x1 * x1) + 1.0
	t_2 = x1 * (x1 * 3.0)
	t_3 = ((t_2 + (2.0 * x2)) - x1) / t_1
	tmp = 0
	if x1 <= -1.1e+74:
		tmp = t_0
	elif x1 <= -1.7:
		tmp = x1 + ((3.0 * ((x1 + ((2.0 * x2) - t_2)) / (-1.0 - (x1 * x1)))) + (x1 + ((x1 * (x1 * x1)) + ((t_2 * t_3) + (t_1 * ((((x1 * 2.0) * t_3) * (t_3 - 3.0)) + (x2 * 8.0)))))))
	elif x1 <= 8.5e+34:
		tmp = x1 - (((x1 * (2.0 - (x1 * 9.0))) + (x2 * ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))) - (x2 * -6.0))
	else:
		tmp = t_0
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 + Float64(Float64(x1 + Float64(6.0 * (x1 ^ 4.0))) + 9.0))
	t_1 = Float64(Float64(x1 * x1) + 1.0)
	t_2 = Float64(x1 * Float64(x1 * 3.0))
	t_3 = Float64(Float64(Float64(t_2 + Float64(2.0 * x2)) - x1) / t_1)
	tmp = 0.0
	if (x1 <= -1.1e+74)
		tmp = t_0;
	elseif (x1 <= -1.7)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(x1 + Float64(Float64(2.0 * x2) - t_2)) / Float64(-1.0 - Float64(x1 * x1)))) + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(t_2 * t_3) + Float64(t_1 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_3) * Float64(t_3 - 3.0)) + Float64(x2 * 8.0))))))));
	elseif (x1 <= 8.5e+34)
		tmp = Float64(x1 - Float64(Float64(Float64(x1 * Float64(2.0 - Float64(x1 * 9.0))) + Float64(x2 * Float64(Float64(x1 * Float64(12.0 - Float64(x1 * 6.0))) - Float64(8.0 * Float64(x1 * x2))))) - Float64(x2 * -6.0)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 + ((x1 + (6.0 * (x1 ^ 4.0))) + 9.0);
	t_1 = (x1 * x1) + 1.0;
	t_2 = x1 * (x1 * 3.0);
	t_3 = ((t_2 + (2.0 * x2)) - x1) / t_1;
	tmp = 0.0;
	if (x1 <= -1.1e+74)
		tmp = t_0;
	elseif (x1 <= -1.7)
		tmp = x1 + ((3.0 * ((x1 + ((2.0 * x2) - t_2)) / (-1.0 - (x1 * x1)))) + (x1 + ((x1 * (x1 * x1)) + ((t_2 * t_3) + (t_1 * ((((x1 * 2.0) * t_3) * (t_3 - 3.0)) + (x2 * 8.0)))))));
	elseif (x1 <= 8.5e+34)
		tmp = x1 - (((x1 * (2.0 - (x1 * 9.0))) + (x2 * ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))) - (x2 * -6.0));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 + N[(N[(x1 + N[(6.0 * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 9.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$2 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(t$95$2 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[x1, -1.1e+74], t$95$0, If[LessEqual[x1, -1.7], N[(x1 + N[(N[(3.0 * N[(N[(x1 + N[(N[(2.0 * x2), $MachinePrecision] - t$95$2), $MachinePrecision]), $MachinePrecision] / N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$2 * t$95$3), $MachinePrecision] + N[(t$95$1 * N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$3), $MachinePrecision] * N[(t$95$3 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(x2 * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 8.5e+34], N[(x1 - N[(N[(N[(x1 * N[(2.0 - N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x2 * N[(N[(x1 * N[(12.0 - N[(x1 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -1.1000000000000001e74 or 8.5000000000000003e34 < x1

   1. Initial program 26.4%

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

   3. Taylor expanded in x1 around inf 30.6%

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

   4. Taylor expanded in x1 around inf 96.3%

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

   if -1.1000000000000001e74 < x1 < -1.69999999999999996

   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. Add Preprocessing

   3. Taylor expanded in x1 around -inf 98.0%

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

   4. Taylor expanded in x2 around inf 67.7%

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

      1. *-commutative 67.7%

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

   6. Simplified 67.7%

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

   if -1.69999999999999996 < x1 < 8.5000000000000003e34

   1. Initial program 99.4%

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

   3. Taylor expanded in x1 around 0 84.9%

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

   4. Taylor expanded in x1 around 0 84.9%

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

   5. Taylor expanded in x1 around 0 85.2%

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

   6. Taylor expanded in x2 around 0 96.5%

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

4. Final simplification 95.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.1 \cdot 10^{+74}:\\ \;\;\;\;x1 + \left(\left(x1 + 6 \cdot {x1}^{4}\right) + 9\right)\\ \mathbf{elif}\;x1 \leq -1.7:\\ \;\;\;\;x1 + \left(3 \cdot \frac{x1 + \left(2 \cdot x2 - x1 \cdot \left(x1 \cdot 3\right)\right)}{-1 - x1 \cdot x1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + x2 \cdot 8\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 8.5 \cdot 10^{+34}:\\ \;\;\;\;x1 - \left(\left(x1 \cdot \left(2 - x1 \cdot 9\right) + x2 \cdot \left(x1 \cdot \left(12 - x1 \cdot 6\right) - 8 \cdot \left(x1 \cdot x2\right)\right)\right) - x2 \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 + 6 \cdot {x1}^{4}\right) + 9\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 93.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := \frac{\left(t\_1 + 2 \cdot x2\right) - x1}{t\_0}\\ t_3 := t\_2 \cdot 4\\ t_4 := x1 \cdot \left(x1 \cdot x1\right)\\ t_5 := x1 \cdot \left(2 - x1 \cdot 9\right)\\ t_6 := 3 - 2 \cdot x2\\ t_7 := 4 \cdot \left(x2 \cdot t\_6\right)\\ \mathbf{if}\;x1 \leq -5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - t\_5\right)\\ \mathbf{elif}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(9 + \left(x1 - x1 \cdot \left(x1 \cdot \left(6 + \left(2 \cdot \left(\left(2 \cdot x2 - 3\right) - x2 \cdot -2\right) + \left(\left(x1 \cdot \left(6 + \left(t\_7 + 2 \cdot \left(-1 - 2 \cdot \left(x2 \cdot \left(3 + x2 \cdot -2\right)\right)\right)\right)\right) - x2 \cdot 8\right) - x2 \cdot 6\right)\right)\right) + t\_7\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -4 \cdot 10^{-5}:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(t\_4 + \left(t\_0 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(t\_3 - 6\right) + \left(t\_2 - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(2 \cdot x2 - x1\right)\right)\right) + t\_1 \cdot \left(3 - \frac{1 + \frac{t\_6}{x1}}{x1}\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 9.2 \cdot 10^{+34}:\\ \;\;\;\;x1 - \left(\left(t\_5 + x2 \cdot \left(x1 \cdot \left(12 - x1 \cdot 6\right) - 8 \cdot \left(x1 \cdot x2\right)\right)\right) - x2 \cdot -6\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(t\_4 + \left(t\_1 \cdot t\_2 + \left(\left(x1 \cdot x1\right) \cdot \left(6 - t\_3\right) - x1 \cdot 2\right) \cdot \left(-1 - x1 \cdot x1\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(-1 + x1 \cdot \left(x1 + 3\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ (* x1 x1) 1.0))
        (t_1 (* x1 (* x1 3.0)))
        (t_2 (/ (- (+ t_1 (* 2.0 x2)) x1) t_0))
        (t_3 (* t_2 4.0))
        (t_4 (* x1 (* x1 x1)))
        (t_5 (* x1 (- 2.0 (* x1 9.0))))
        (t_6 (- 3.0 (* 2.0 x2)))
        (t_7 (* 4.0 (* x2 t_6))))
   (if (<= x1 -5e+153)
     (+ x1 (- (* x2 -6.0) t_5))
     (if (<= x1 -5.6e+102)
       (+
        x1
        (+
         9.0
         (-
          x1
          (*
           x1
           (+
            (*
             x1
             (+
              6.0
              (+
               (* 2.0 (- (- (* 2.0 x2) 3.0) (* x2 -2.0)))
               (-
                (-
                 (*
                  x1
                  (+
                   6.0
                   (+
                    t_7
                    (* 2.0 (- -1.0 (* 2.0 (* x2 (+ 3.0 (* x2 -2.0)))))))))
                 (* x2 8.0))
                (* x2 6.0)))))
            t_7)))))
       (if (<= x1 -4e-5)
         (+
          x1
          (+
           9.0
           (+
            x1
            (+
             t_4
             (+
              (*
               t_0
               (+
                (* (* x1 x1) (- t_3 6.0))
                (* (- t_2 3.0) (* (* x1 2.0) (- (* 2.0 x2) x1)))))
              (* t_1 (- 3.0 (/ (+ 1.0 (/ t_6 x1)) x1))))))))
         (if (<= x1 9.2e+34)
           (-
            x1
            (-
             (+ t_5 (* x2 (- (* x1 (- 12.0 (* x1 6.0))) (* 8.0 (* x1 x2)))))
             (* x2 -6.0)))
           (if (<= x1 5e+102)
             (+
              x1
              (+
               9.0
               (+
                x1
                (+
                 t_4
                 (+
                  (* t_1 t_2)
                  (*
                   (- (* (* x1 x1) (- 6.0 t_3)) (* x1 2.0))
                   (- -1.0 (* x1 x1))))))))
             (+ x1 (+ x1 (* 3.0 (* x1 (+ -1.0 (* x1 (+ x1 3.0))))))))))))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = ((t_1 + (2.0 * x2)) - x1) / t_0;
	double t_3 = t_2 * 4.0;
	double t_4 = x1 * (x1 * x1);
	double t_5 = x1 * (2.0 - (x1 * 9.0));
	double t_6 = 3.0 - (2.0 * x2);
	double t_7 = 4.0 * (x2 * t_6);
	double tmp;
	if (x1 <= -5e+153) {
		tmp = x1 + ((x2 * -6.0) - t_5);
	} else if (x1 <= -5.6e+102) {
		tmp = x1 + (9.0 + (x1 - (x1 * ((x1 * (6.0 + ((2.0 * (((2.0 * x2) - 3.0) - (x2 * -2.0))) + (((x1 * (6.0 + (t_7 + (2.0 * (-1.0 - (2.0 * (x2 * (3.0 + (x2 * -2.0))))))))) - (x2 * 8.0)) - (x2 * 6.0))))) + t_7))));
	} else if (x1 <= -4e-5) {
		tmp = x1 + (9.0 + (x1 + (t_4 + ((t_0 * (((x1 * x1) * (t_3 - 6.0)) + ((t_2 - 3.0) * ((x1 * 2.0) * ((2.0 * x2) - x1))))) + (t_1 * (3.0 - ((1.0 + (t_6 / x1)) / x1)))))));
	} else if (x1 <= 9.2e+34) {
		tmp = x1 - ((t_5 + (x2 * ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))) - (x2 * -6.0));
	} else if (x1 <= 5e+102) {
		tmp = x1 + (9.0 + (x1 + (t_4 + ((t_1 * t_2) + ((((x1 * x1) * (6.0 - t_3)) - (x1 * 2.0)) * (-1.0 - (x1 * x1)))))));
	} else {
		tmp = x1 + (x1 + (3.0 * (x1 * (-1.0 + (x1 * (x1 + 3.0))))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: tmp
    t_0 = (x1 * x1) + 1.0d0
    t_1 = x1 * (x1 * 3.0d0)
    t_2 = ((t_1 + (2.0d0 * x2)) - x1) / t_0
    t_3 = t_2 * 4.0d0
    t_4 = x1 * (x1 * x1)
    t_5 = x1 * (2.0d0 - (x1 * 9.0d0))
    t_6 = 3.0d0 - (2.0d0 * x2)
    t_7 = 4.0d0 * (x2 * t_6)
    if (x1 <= (-5d+153)) then
        tmp = x1 + ((x2 * (-6.0d0)) - t_5)
    else if (x1 <= (-5.6d+102)) then
        tmp = x1 + (9.0d0 + (x1 - (x1 * ((x1 * (6.0d0 + ((2.0d0 * (((2.0d0 * x2) - 3.0d0) - (x2 * (-2.0d0)))) + (((x1 * (6.0d0 + (t_7 + (2.0d0 * ((-1.0d0) - (2.0d0 * (x2 * (3.0d0 + (x2 * (-2.0d0)))))))))) - (x2 * 8.0d0)) - (x2 * 6.0d0))))) + t_7))))
    else if (x1 <= (-4d-5)) then
        tmp = x1 + (9.0d0 + (x1 + (t_4 + ((t_0 * (((x1 * x1) * (t_3 - 6.0d0)) + ((t_2 - 3.0d0) * ((x1 * 2.0d0) * ((2.0d0 * x2) - x1))))) + (t_1 * (3.0d0 - ((1.0d0 + (t_6 / x1)) / x1)))))))
    else if (x1 <= 9.2d+34) then
        tmp = x1 - ((t_5 + (x2 * ((x1 * (12.0d0 - (x1 * 6.0d0))) - (8.0d0 * (x1 * x2))))) - (x2 * (-6.0d0)))
    else if (x1 <= 5d+102) then
        tmp = x1 + (9.0d0 + (x1 + (t_4 + ((t_1 * t_2) + ((((x1 * x1) * (6.0d0 - t_3)) - (x1 * 2.0d0)) * ((-1.0d0) - (x1 * x1)))))))
    else
        tmp = x1 + (x1 + (3.0d0 * (x1 * ((-1.0d0) + (x1 * (x1 + 3.0d0))))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = ((t_1 + (2.0 * x2)) - x1) / t_0;
	double t_3 = t_2 * 4.0;
	double t_4 = x1 * (x1 * x1);
	double t_5 = x1 * (2.0 - (x1 * 9.0));
	double t_6 = 3.0 - (2.0 * x2);
	double t_7 = 4.0 * (x2 * t_6);
	double tmp;
	if (x1 <= -5e+153) {
		tmp = x1 + ((x2 * -6.0) - t_5);
	} else if (x1 <= -5.6e+102) {
		tmp = x1 + (9.0 + (x1 - (x1 * ((x1 * (6.0 + ((2.0 * (((2.0 * x2) - 3.0) - (x2 * -2.0))) + (((x1 * (6.0 + (t_7 + (2.0 * (-1.0 - (2.0 * (x2 * (3.0 + (x2 * -2.0))))))))) - (x2 * 8.0)) - (x2 * 6.0))))) + t_7))));
	} else if (x1 <= -4e-5) {
		tmp = x1 + (9.0 + (x1 + (t_4 + ((t_0 * (((x1 * x1) * (t_3 - 6.0)) + ((t_2 - 3.0) * ((x1 * 2.0) * ((2.0 * x2) - x1))))) + (t_1 * (3.0 - ((1.0 + (t_6 / x1)) / x1)))))));
	} else if (x1 <= 9.2e+34) {
		tmp = x1 - ((t_5 + (x2 * ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))) - (x2 * -6.0));
	} else if (x1 <= 5e+102) {
		tmp = x1 + (9.0 + (x1 + (t_4 + ((t_1 * t_2) + ((((x1 * x1) * (6.0 - t_3)) - (x1 * 2.0)) * (-1.0 - (x1 * x1)))))));
	} else {
		tmp = x1 + (x1 + (3.0 * (x1 * (-1.0 + (x1 * (x1 + 3.0))))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x1 * x1) + 1.0
	t_1 = x1 * (x1 * 3.0)
	t_2 = ((t_1 + (2.0 * x2)) - x1) / t_0
	t_3 = t_2 * 4.0
	t_4 = x1 * (x1 * x1)
	t_5 = x1 * (2.0 - (x1 * 9.0))
	t_6 = 3.0 - (2.0 * x2)
	t_7 = 4.0 * (x2 * t_6)
	tmp = 0
	if x1 <= -5e+153:
		tmp = x1 + ((x2 * -6.0) - t_5)
	elif x1 <= -5.6e+102:
		tmp = x1 + (9.0 + (x1 - (x1 * ((x1 * (6.0 + ((2.0 * (((2.0 * x2) - 3.0) - (x2 * -2.0))) + (((x1 * (6.0 + (t_7 + (2.0 * (-1.0 - (2.0 * (x2 * (3.0 + (x2 * -2.0))))))))) - (x2 * 8.0)) - (x2 * 6.0))))) + t_7))))
	elif x1 <= -4e-5:
		tmp = x1 + (9.0 + (x1 + (t_4 + ((t_0 * (((x1 * x1) * (t_3 - 6.0)) + ((t_2 - 3.0) * ((x1 * 2.0) * ((2.0 * x2) - x1))))) + (t_1 * (3.0 - ((1.0 + (t_6 / x1)) / x1)))))))
	elif x1 <= 9.2e+34:
		tmp = x1 - ((t_5 + (x2 * ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))) - (x2 * -6.0))
	elif x1 <= 5e+102:
		tmp = x1 + (9.0 + (x1 + (t_4 + ((t_1 * t_2) + ((((x1 * x1) * (6.0 - t_3)) - (x1 * 2.0)) * (-1.0 - (x1 * x1)))))))
	else:
		tmp = x1 + (x1 + (3.0 * (x1 * (-1.0 + (x1 * (x1 + 3.0))))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * x1) + 1.0)
	t_1 = Float64(x1 * Float64(x1 * 3.0))
	t_2 = Float64(Float64(Float64(t_1 + Float64(2.0 * x2)) - x1) / t_0)
	t_3 = Float64(t_2 * 4.0)
	t_4 = Float64(x1 * Float64(x1 * x1))
	t_5 = Float64(x1 * Float64(2.0 - Float64(x1 * 9.0)))
	t_6 = Float64(3.0 - Float64(2.0 * x2))
	t_7 = Float64(4.0 * Float64(x2 * t_6))
	tmp = 0.0
	if (x1 <= -5e+153)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) - t_5));
	elseif (x1 <= -5.6e+102)
		tmp = Float64(x1 + Float64(9.0 + Float64(x1 - Float64(x1 * Float64(Float64(x1 * Float64(6.0 + Float64(Float64(2.0 * Float64(Float64(Float64(2.0 * x2) - 3.0) - Float64(x2 * -2.0))) + Float64(Float64(Float64(x1 * Float64(6.0 + Float64(t_7 + Float64(2.0 * Float64(-1.0 - Float64(2.0 * Float64(x2 * Float64(3.0 + Float64(x2 * -2.0))))))))) - Float64(x2 * 8.0)) - Float64(x2 * 6.0))))) + t_7)))));
	elseif (x1 <= -4e-5)
		tmp = Float64(x1 + Float64(9.0 + Float64(x1 + Float64(t_4 + Float64(Float64(t_0 * Float64(Float64(Float64(x1 * x1) * Float64(t_3 - 6.0)) + Float64(Float64(t_2 - 3.0) * Float64(Float64(x1 * 2.0) * Float64(Float64(2.0 * x2) - x1))))) + Float64(t_1 * Float64(3.0 - Float64(Float64(1.0 + Float64(t_6 / x1)) / x1))))))));
	elseif (x1 <= 9.2e+34)
		tmp = Float64(x1 - Float64(Float64(t_5 + Float64(x2 * Float64(Float64(x1 * Float64(12.0 - Float64(x1 * 6.0))) - Float64(8.0 * Float64(x1 * x2))))) - Float64(x2 * -6.0)));
	elseif (x1 <= 5e+102)
		tmp = Float64(x1 + Float64(9.0 + Float64(x1 + Float64(t_4 + Float64(Float64(t_1 * t_2) + Float64(Float64(Float64(Float64(x1 * x1) * Float64(6.0 - t_3)) - Float64(x1 * 2.0)) * Float64(-1.0 - Float64(x1 * x1))))))));
	else
		tmp = Float64(x1 + Float64(x1 + Float64(3.0 * Float64(x1 * Float64(-1.0 + Float64(x1 * Float64(x1 + 3.0)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x1 * x1) + 1.0;
	t_1 = x1 * (x1 * 3.0);
	t_2 = ((t_1 + (2.0 * x2)) - x1) / t_0;
	t_3 = t_2 * 4.0;
	t_4 = x1 * (x1 * x1);
	t_5 = x1 * (2.0 - (x1 * 9.0));
	t_6 = 3.0 - (2.0 * x2);
	t_7 = 4.0 * (x2 * t_6);
	tmp = 0.0;
	if (x1 <= -5e+153)
		tmp = x1 + ((x2 * -6.0) - t_5);
	elseif (x1 <= -5.6e+102)
		tmp = x1 + (9.0 + (x1 - (x1 * ((x1 * (6.0 + ((2.0 * (((2.0 * x2) - 3.0) - (x2 * -2.0))) + (((x1 * (6.0 + (t_7 + (2.0 * (-1.0 - (2.0 * (x2 * (3.0 + (x2 * -2.0))))))))) - (x2 * 8.0)) - (x2 * 6.0))))) + t_7))));
	elseif (x1 <= -4e-5)
		tmp = x1 + (9.0 + (x1 + (t_4 + ((t_0 * (((x1 * x1) * (t_3 - 6.0)) + ((t_2 - 3.0) * ((x1 * 2.0) * ((2.0 * x2) - x1))))) + (t_1 * (3.0 - ((1.0 + (t_6 / x1)) / x1)))))));
	elseif (x1 <= 9.2e+34)
		tmp = x1 - ((t_5 + (x2 * ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))) - (x2 * -6.0));
	elseif (x1 <= 5e+102)
		tmp = x1 + (9.0 + (x1 + (t_4 + ((t_1 * t_2) + ((((x1 * x1) * (6.0 - t_3)) - (x1 * 2.0)) * (-1.0 - (x1 * x1)))))));
	else
		tmp = x1 + (x1 + (3.0 * (x1 * (-1.0 + (x1 * (x1 + 3.0))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(t$95$1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 * 4.0), $MachinePrecision]}, Block[{t$95$4 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(x1 * N[(2.0 - N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(4.0 * N[(x2 * t$95$6), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -5e+153], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] - t$95$5), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -5.6e+102], N[(x1 + N[(9.0 + N[(x1 - N[(x1 * N[(N[(x1 * N[(6.0 + N[(N[(2.0 * N[(N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision] - N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(x1 * N[(6.0 + N[(t$95$7 + N[(2.0 * N[(-1.0 - N[(2.0 * N[(x2 * N[(3.0 + N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x2 * 8.0), $MachinePrecision]), $MachinePrecision] - N[(x2 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$7), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -4e-5], N[(x1 + N[(9.0 + N[(x1 + N[(t$95$4 + N[(N[(t$95$0 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(t$95$3 - 6.0), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$2 - 3.0), $MachinePrecision] * N[(N[(x1 * 2.0), $MachinePrecision] * N[(N[(2.0 * x2), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$1 * N[(3.0 - N[(N[(1.0 + N[(t$95$6 / x1), $MachinePrecision]), $MachinePrecision] / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 9.2e+34], N[(x1 - N[(N[(t$95$5 + N[(x2 * N[(N[(x1 * N[(12.0 - N[(x1 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 5e+102], N[(x1 + N[(9.0 + N[(x1 + N[(t$95$4 + N[(N[(t$95$1 * t$95$2), $MachinePrecision] + N[(N[(N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 - t$95$3), $MachinePrecision]), $MachinePrecision] - N[(x1 * 2.0), $MachinePrecision]), $MachinePrecision] * N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(x1 + N[(3.0 * N[(x1 * N[(-1.0 + N[(x1 * N[(x1 + 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if x1 < -5.00000000000000018e153

   1. Initial program 0.0%

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

   3. Taylor expanded in x1 around 0 0.0%

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

   4. Taylor expanded in x1 around 0 0.0%

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

   5. Taylor expanded in x1 around 0 73.3%

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

   6. Taylor expanded in x2 around 0 100.0%

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

      1. *-commutative 100.0%

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

   8. Simplified 100.0%

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

   if -5.00000000000000018e153 < x1 < -5.60000000000000037e102

   1. Initial program 0.0%

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

   3. Taylor expanded in x1 around 0 0.0%

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

      1. +-commutative 0.0%

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

      2. mul-1-neg 0.0%

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

      3. sub-neg 0.0%

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

   5. Simplified 0.0%

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

   6. Taylor expanded in x1 around inf 0.0%

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

   7. Taylor expanded in x1 around 0 100.0%

      \[\leadsto x1 + \left(\left(\color{blue}{x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(\left(2 \cdot \left(-2 \cdot x2 + -1 \cdot \left(2 \cdot x2 - 3\right)\right) + \left(6 \cdot x2 + \left(8 \cdot x2 + x1 \cdot \left(\left(2 \cdot \left(1 + 2 \cdot \left(x2 \cdot \left(3 + -2 \cdot x2\right)\right)\right) + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) - 6\right)\right)\right)\right) - 6\right)\right)} + x1\right) + 9\right) \]

   if -5.60000000000000037e102 < x1 < -4.00000000000000033e-5

   1. Initial program 99.5%

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

   3. Taylor expanded in x1 around 0 65.7%

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

      1. +-commutative 65.7%

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

      2. mul-1-neg 65.7%

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

      3. sub-neg 65.7%

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

   5. Simplified 65.7%

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

   6. Taylor expanded in x1 around inf 65.3%

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

   7. Taylor expanded in x1 around -inf 65.7%

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

   if -4.00000000000000033e-5 < x1 < 9.1999999999999993e34

   1. Initial program 99.4%

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

   3. Taylor expanded in x1 around 0 85.2%

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

   4. Taylor expanded in x1 around 0 85.2%

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

   5. Taylor expanded in x1 around 0 85.5%

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

   6. Taylor expanded in x2 around 0 97.0%

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

   if 9.1999999999999993e34 < x1 < 5e102

   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. Add Preprocessing

   3. Taylor expanded in x1 around 0 63.3%

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

      1. +-commutative 63.3%

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

      2. mul-1-neg 63.3%

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

      3. sub-neg 63.3%

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

   5. Simplified 63.3%

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

   6. Taylor expanded in x1 around inf 63.3%

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

   7. Taylor expanded in x1 around inf 99.1%

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

      1. *-commutative 99.1%

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

   9. Simplified 99.1%

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

   if 5e102 < x1

   1. Initial program 21.3%

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

   3. Taylor expanded in x1 around 0 5.0%

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

   4. Taylor expanded in x1 around 0 85.1%

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

   5. Taylor expanded in x2 around 0 100.0%

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

4. Final simplification 95.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 - x1 \cdot 9\right)\right)\\ \mathbf{elif}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(9 + \left(x1 - x1 \cdot \left(x1 \cdot \left(6 + \left(2 \cdot \left(\left(2 \cdot x2 - 3\right) - x2 \cdot -2\right) + \left(\left(x1 \cdot \left(6 + \left(4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right) + 2 \cdot \left(-1 - 2 \cdot \left(x2 \cdot \left(3 + x2 \cdot -2\right)\right)\right)\right)\right) - x2 \cdot 8\right) - x2 \cdot 6\right)\right)\right) + 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -4 \cdot 10^{-5}:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right) + \left(\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(2 \cdot x2 - x1\right)\right)\right) + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(3 - \frac{1 + \frac{3 - 2 \cdot x2}{x1}}{x1}\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 9.2 \cdot 10^{+34}:\\ \;\;\;\;x1 - \left(\left(x1 \cdot \left(2 - x1 \cdot 9\right) + x2 \cdot \left(x1 \cdot \left(12 - x1 \cdot 6\right) - 8 \cdot \left(x1 \cdot x2\right)\right)\right) - x2 \cdot -6\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(9 + \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(\left(x1 \cdot x1\right) \cdot \left(6 - \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4\right) - x1 \cdot 2\right) \cdot \left(-1 - x1 \cdot x1\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(-1 + x1 \cdot \left(x1 + 3\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 92.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := \frac{\left(t\_0 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\\ t_2 := x1 \cdot \left(2 - x1 \cdot 9\right)\\ t_3 := 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\\ t_4 := x1 + \left(9 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(t\_0 \cdot t\_1 + \left(\left(x1 \cdot x1\right) \cdot \left(6 - t\_1 \cdot 4\right) - x1 \cdot 2\right) \cdot \left(-1 - x1 \cdot x1\right)\right)\right)\right)\right)\\ \mathbf{if}\;x1 \leq -4.5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - t\_2\right)\\ \mathbf{elif}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(9 + \left(x1 - x1 \cdot \left(x1 \cdot \left(6 + \left(2 \cdot \left(\left(2 \cdot x2 - 3\right) - x2 \cdot -2\right) + \left(\left(x1 \cdot \left(6 + \left(t\_3 + 2 \cdot \left(-1 - 2 \cdot \left(x2 \cdot \left(3 + x2 \cdot -2\right)\right)\right)\right)\right) - x2 \cdot 8\right) - x2 \cdot 6\right)\right)\right) + t\_3\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -1.25 \cdot 10^{+31}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;x1 \leq 8.5 \cdot 10^{+34}:\\ \;\;\;\;x1 - \left(\left(t\_2 + x2 \cdot \left(x1 \cdot \left(12 - x1 \cdot 6\right) - 8 \cdot \left(x1 \cdot x2\right)\right)\right) - x2 \cdot -6\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+102}:\\ \;\;\;\;t\_4\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(-1 + x1 \cdot \left(x1 + 3\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (/ (- (+ t_0 (* 2.0 x2)) x1) (+ (* x1 x1) 1.0)))
        (t_2 (* x1 (- 2.0 (* x1 9.0))))
        (t_3 (* 4.0 (* x2 (- 3.0 (* 2.0 x2)))))
        (t_4
         (+
          x1
          (+
           9.0
           (+
            x1
            (+
             (* x1 (* x1 x1))
             (+
              (* t_0 t_1)
              (*
               (- (* (* x1 x1) (- 6.0 (* t_1 4.0))) (* x1 2.0))
               (- -1.0 (* x1 x1))))))))))
   (if (<= x1 -4.5e+153)
     (+ x1 (- (* x2 -6.0) t_2))
     (if (<= x1 -5.6e+102)
       (+
        x1
        (+
         9.0
         (-
          x1
          (*
           x1
           (+
            (*
             x1
             (+
              6.0
              (+
               (* 2.0 (- (- (* 2.0 x2) 3.0) (* x2 -2.0)))
               (-
                (-
                 (*
                  x1
                  (+
                   6.0
                   (+
                    t_3
                    (* 2.0 (- -1.0 (* 2.0 (* x2 (+ 3.0 (* x2 -2.0)))))))))
                 (* x2 8.0))
                (* x2 6.0)))))
            t_3)))))
       (if (<= x1 -1.25e+31)
         t_4
         (if (<= x1 8.5e+34)
           (-
            x1
            (-
             (+ t_2 (* x2 (- (* x1 (- 12.0 (* x1 6.0))) (* 8.0 (* x1 x2)))))
             (* x2 -6.0)))
           (if (<= x1 5e+102)
             t_4
             (+ x1 (+ x1 (* 3.0 (* x1 (+ -1.0 (* x1 (+ x1 3.0))))))))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = ((t_0 + (2.0 * x2)) - x1) / ((x1 * x1) + 1.0);
	double t_2 = x1 * (2.0 - (x1 * 9.0));
	double t_3 = 4.0 * (x2 * (3.0 - (2.0 * x2)));
	double t_4 = x1 + (9.0 + (x1 + ((x1 * (x1 * x1)) + ((t_0 * t_1) + ((((x1 * x1) * (6.0 - (t_1 * 4.0))) - (x1 * 2.0)) * (-1.0 - (x1 * x1)))))));
	double tmp;
	if (x1 <= -4.5e+153) {
		tmp = x1 + ((x2 * -6.0) - t_2);
	} else if (x1 <= -5.6e+102) {
		tmp = x1 + (9.0 + (x1 - (x1 * ((x1 * (6.0 + ((2.0 * (((2.0 * x2) - 3.0) - (x2 * -2.0))) + (((x1 * (6.0 + (t_3 + (2.0 * (-1.0 - (2.0 * (x2 * (3.0 + (x2 * -2.0))))))))) - (x2 * 8.0)) - (x2 * 6.0))))) + t_3))));
	} else if (x1 <= -1.25e+31) {
		tmp = t_4;
	} else if (x1 <= 8.5e+34) {
		tmp = x1 - ((t_2 + (x2 * ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))) - (x2 * -6.0));
	} else if (x1 <= 5e+102) {
		tmp = t_4;
	} else {
		tmp = x1 + (x1 + (3.0 * (x1 * (-1.0 + (x1 * (x1 + 3.0))))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_0 = x1 * (x1 * 3.0d0)
    t_1 = ((t_0 + (2.0d0 * x2)) - x1) / ((x1 * x1) + 1.0d0)
    t_2 = x1 * (2.0d0 - (x1 * 9.0d0))
    t_3 = 4.0d0 * (x2 * (3.0d0 - (2.0d0 * x2)))
    t_4 = x1 + (9.0d0 + (x1 + ((x1 * (x1 * x1)) + ((t_0 * t_1) + ((((x1 * x1) * (6.0d0 - (t_1 * 4.0d0))) - (x1 * 2.0d0)) * ((-1.0d0) - (x1 * x1)))))))
    if (x1 <= (-4.5d+153)) then
        tmp = x1 + ((x2 * (-6.0d0)) - t_2)
    else if (x1 <= (-5.6d+102)) then
        tmp = x1 + (9.0d0 + (x1 - (x1 * ((x1 * (6.0d0 + ((2.0d0 * (((2.0d0 * x2) - 3.0d0) - (x2 * (-2.0d0)))) + (((x1 * (6.0d0 + (t_3 + (2.0d0 * ((-1.0d0) - (2.0d0 * (x2 * (3.0d0 + (x2 * (-2.0d0)))))))))) - (x2 * 8.0d0)) - (x2 * 6.0d0))))) + t_3))))
    else if (x1 <= (-1.25d+31)) then
        tmp = t_4
    else if (x1 <= 8.5d+34) then
        tmp = x1 - ((t_2 + (x2 * ((x1 * (12.0d0 - (x1 * 6.0d0))) - (8.0d0 * (x1 * x2))))) - (x2 * (-6.0d0)))
    else if (x1 <= 5d+102) then
        tmp = t_4
    else
        tmp = x1 + (x1 + (3.0d0 * (x1 * ((-1.0d0) + (x1 * (x1 + 3.0d0))))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = ((t_0 + (2.0 * x2)) - x1) / ((x1 * x1) + 1.0);
	double t_2 = x1 * (2.0 - (x1 * 9.0));
	double t_3 = 4.0 * (x2 * (3.0 - (2.0 * x2)));
	double t_4 = x1 + (9.0 + (x1 + ((x1 * (x1 * x1)) + ((t_0 * t_1) + ((((x1 * x1) * (6.0 - (t_1 * 4.0))) - (x1 * 2.0)) * (-1.0 - (x1 * x1)))))));
	double tmp;
	if (x1 <= -4.5e+153) {
		tmp = x1 + ((x2 * -6.0) - t_2);
	} else if (x1 <= -5.6e+102) {
		tmp = x1 + (9.0 + (x1 - (x1 * ((x1 * (6.0 + ((2.0 * (((2.0 * x2) - 3.0) - (x2 * -2.0))) + (((x1 * (6.0 + (t_3 + (2.0 * (-1.0 - (2.0 * (x2 * (3.0 + (x2 * -2.0))))))))) - (x2 * 8.0)) - (x2 * 6.0))))) + t_3))));
	} else if (x1 <= -1.25e+31) {
		tmp = t_4;
	} else if (x1 <= 8.5e+34) {
		tmp = x1 - ((t_2 + (x2 * ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))) - (x2 * -6.0));
	} else if (x1 <= 5e+102) {
		tmp = t_4;
	} else {
		tmp = x1 + (x1 + (3.0 * (x1 * (-1.0 + (x1 * (x1 + 3.0))))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = ((t_0 + (2.0 * x2)) - x1) / ((x1 * x1) + 1.0)
	t_2 = x1 * (2.0 - (x1 * 9.0))
	t_3 = 4.0 * (x2 * (3.0 - (2.0 * x2)))
	t_4 = x1 + (9.0 + (x1 + ((x1 * (x1 * x1)) + ((t_0 * t_1) + ((((x1 * x1) * (6.0 - (t_1 * 4.0))) - (x1 * 2.0)) * (-1.0 - (x1 * x1)))))))
	tmp = 0
	if x1 <= -4.5e+153:
		tmp = x1 + ((x2 * -6.0) - t_2)
	elif x1 <= -5.6e+102:
		tmp = x1 + (9.0 + (x1 - (x1 * ((x1 * (6.0 + ((2.0 * (((2.0 * x2) - 3.0) - (x2 * -2.0))) + (((x1 * (6.0 + (t_3 + (2.0 * (-1.0 - (2.0 * (x2 * (3.0 + (x2 * -2.0))))))))) - (x2 * 8.0)) - (x2 * 6.0))))) + t_3))))
	elif x1 <= -1.25e+31:
		tmp = t_4
	elif x1 <= 8.5e+34:
		tmp = x1 - ((t_2 + (x2 * ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))) - (x2 * -6.0))
	elif x1 <= 5e+102:
		tmp = t_4
	else:
		tmp = x1 + (x1 + (3.0 * (x1 * (-1.0 + (x1 * (x1 + 3.0))))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(Float64(Float64(t_0 + Float64(2.0 * x2)) - x1) / Float64(Float64(x1 * x1) + 1.0))
	t_2 = Float64(x1 * Float64(2.0 - Float64(x1 * 9.0)))
	t_3 = Float64(4.0 * Float64(x2 * Float64(3.0 - Float64(2.0 * x2))))
	t_4 = Float64(x1 + Float64(9.0 + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(t_0 * t_1) + Float64(Float64(Float64(Float64(x1 * x1) * Float64(6.0 - Float64(t_1 * 4.0))) - Float64(x1 * 2.0)) * Float64(-1.0 - Float64(x1 * x1))))))))
	tmp = 0.0
	if (x1 <= -4.5e+153)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) - t_2));
	elseif (x1 <= -5.6e+102)
		tmp = Float64(x1 + Float64(9.0 + Float64(x1 - Float64(x1 * Float64(Float64(x1 * Float64(6.0 + Float64(Float64(2.0 * Float64(Float64(Float64(2.0 * x2) - 3.0) - Float64(x2 * -2.0))) + Float64(Float64(Float64(x1 * Float64(6.0 + Float64(t_3 + Float64(2.0 * Float64(-1.0 - Float64(2.0 * Float64(x2 * Float64(3.0 + Float64(x2 * -2.0))))))))) - Float64(x2 * 8.0)) - Float64(x2 * 6.0))))) + t_3)))));
	elseif (x1 <= -1.25e+31)
		tmp = t_4;
	elseif (x1 <= 8.5e+34)
		tmp = Float64(x1 - Float64(Float64(t_2 + Float64(x2 * Float64(Float64(x1 * Float64(12.0 - Float64(x1 * 6.0))) - Float64(8.0 * Float64(x1 * x2))))) - Float64(x2 * -6.0)));
	elseif (x1 <= 5e+102)
		tmp = t_4;
	else
		tmp = Float64(x1 + Float64(x1 + Float64(3.0 * Float64(x1 * Float64(-1.0 + Float64(x1 * Float64(x1 + 3.0)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * 3.0);
	t_1 = ((t_0 + (2.0 * x2)) - x1) / ((x1 * x1) + 1.0);
	t_2 = x1 * (2.0 - (x1 * 9.0));
	t_3 = 4.0 * (x2 * (3.0 - (2.0 * x2)));
	t_4 = x1 + (9.0 + (x1 + ((x1 * (x1 * x1)) + ((t_0 * t_1) + ((((x1 * x1) * (6.0 - (t_1 * 4.0))) - (x1 * 2.0)) * (-1.0 - (x1 * x1)))))));
	tmp = 0.0;
	if (x1 <= -4.5e+153)
		tmp = x1 + ((x2 * -6.0) - t_2);
	elseif (x1 <= -5.6e+102)
		tmp = x1 + (9.0 + (x1 - (x1 * ((x1 * (6.0 + ((2.0 * (((2.0 * x2) - 3.0) - (x2 * -2.0))) + (((x1 * (6.0 + (t_3 + (2.0 * (-1.0 - (2.0 * (x2 * (3.0 + (x2 * -2.0))))))))) - (x2 * 8.0)) - (x2 * 6.0))))) + t_3))));
	elseif (x1 <= -1.25e+31)
		tmp = t_4;
	elseif (x1 <= 8.5e+34)
		tmp = x1 - ((t_2 + (x2 * ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))) - (x2 * -6.0));
	elseif (x1 <= 5e+102)
		tmp = t_4;
	else
		tmp = x1 + (x1 + (3.0 * (x1 * (-1.0 + (x1 * (x1 + 3.0))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(N[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x1 * N[(2.0 - N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(4.0 * N[(x2 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(x1 + N[(9.0 + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$0 * t$95$1), $MachinePrecision] + N[(N[(N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 - N[(t$95$1 * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x1 * 2.0), $MachinePrecision]), $MachinePrecision] * N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -4.5e+153], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] - t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -5.6e+102], N[(x1 + N[(9.0 + N[(x1 - N[(x1 * N[(N[(x1 * N[(6.0 + N[(N[(2.0 * N[(N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision] - N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(x1 * N[(6.0 + N[(t$95$3 + N[(2.0 * N[(-1.0 - N[(2.0 * N[(x2 * N[(3.0 + N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x2 * 8.0), $MachinePrecision]), $MachinePrecision] - N[(x2 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -1.25e+31], t$95$4, If[LessEqual[x1, 8.5e+34], N[(x1 - N[(N[(t$95$2 + N[(x2 * N[(N[(x1 * N[(12.0 - N[(x1 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 5e+102], t$95$4, N[(x1 + N[(x1 + N[(3.0 * N[(x1 * N[(-1.0 + N[(x1 * N[(x1 + 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x1 < -4.5000000000000001e153

   1. Initial program 0.0%

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

   3. Taylor expanded in x1 around 0 0.0%

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

   4. Taylor expanded in x1 around 0 0.0%

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

   5. Taylor expanded in x1 around 0 73.3%

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

   6. Taylor expanded in x2 around 0 100.0%

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

      1. *-commutative 100.0%

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

   8. Simplified 100.0%

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

   if -4.5000000000000001e153 < x1 < -5.60000000000000037e102

   1. Initial program 0.0%

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

   3. Taylor expanded in x1 around 0 0.0%

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

      1. +-commutative 0.0%

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

      2. mul-1-neg 0.0%

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

      3. sub-neg 0.0%

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

   5. Simplified 0.0%

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

   6. Taylor expanded in x1 around inf 0.0%

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

   7. Taylor expanded in x1 around 0 100.0%

      \[\leadsto x1 + \left(\left(\color{blue}{x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(\left(2 \cdot \left(-2 \cdot x2 + -1 \cdot \left(2 \cdot x2 - 3\right)\right) + \left(6 \cdot x2 + \left(8 \cdot x2 + x1 \cdot \left(\left(2 \cdot \left(1 + 2 \cdot \left(x2 \cdot \left(3 + -2 \cdot x2\right)\right)\right) + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) - 6\right)\right)\right)\right) - 6\right)\right)} + x1\right) + 9\right) \]

   if -5.60000000000000037e102 < x1 < -1.25000000000000007e31 or 8.5000000000000003e34 < x1 < 5e102

   1. Initial program 99.5%

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

   3. Taylor expanded in x1 around 0 73.8%

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

      1. +-commutative 73.8%

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

      2. mul-1-neg 73.8%

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

      3. sub-neg 73.8%

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

   5. Simplified 73.8%

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

   6. Taylor expanded in x1 around inf 73.8%

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

   7. Taylor expanded in x1 around inf 80.4%

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

      1. *-commutative 80.4%

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

   9. Simplified 80.4%

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

   if -1.25000000000000007e31 < x1 < 8.5000000000000003e34

   1. Initial program 99.4%

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

   3. Taylor expanded in x1 around 0 82.8%

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

   4. Taylor expanded in x1 around 0 82.8%

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

   5. Taylor expanded in x1 around 0 83.1%

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

   6. Taylor expanded in x2 around 0 94.1%

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

   if 5e102 < x1

   1. Initial program 21.3%

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

   3. Taylor expanded in x1 around 0 5.0%

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

   4. Taylor expanded in x1 around 0 85.1%

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

   5. Taylor expanded in x2 around 0 100.0%

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

4. Final simplification 94.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4.5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 - x1 \cdot 9\right)\right)\\ \mathbf{elif}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(9 + \left(x1 - x1 \cdot \left(x1 \cdot \left(6 + \left(2 \cdot \left(\left(2 \cdot x2 - 3\right) - x2 \cdot -2\right) + \left(\left(x1 \cdot \left(6 + \left(4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right) + 2 \cdot \left(-1 - 2 \cdot \left(x2 \cdot \left(3 + x2 \cdot -2\right)\right)\right)\right)\right) - x2 \cdot 8\right) - x2 \cdot 6\right)\right)\right) + 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -1.25 \cdot 10^{+31}:\\ \;\;\;\;x1 + \left(9 + \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(\left(x1 \cdot x1\right) \cdot \left(6 - \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4\right) - x1 \cdot 2\right) \cdot \left(-1 - x1 \cdot x1\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 8.5 \cdot 10^{+34}:\\ \;\;\;\;x1 - \left(\left(x1 \cdot \left(2 - x1 \cdot 9\right) + x2 \cdot \left(x1 \cdot \left(12 - x1 \cdot 6\right) - 8 \cdot \left(x1 \cdot x2\right)\right)\right) - x2 \cdot -6\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(9 + \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(\left(x1 \cdot x1\right) \cdot \left(6 - \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4\right) - x1 \cdot 2\right) \cdot \left(-1 - x1 \cdot x1\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(-1 + x1 \cdot \left(x1 + 3\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 85.2% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\\ t_1 := x1 \cdot \left(2 - x1 \cdot 9\right)\\ \mathbf{if}\;x1 \leq -4.5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - t\_1\right)\\ \mathbf{elif}\;x1 \leq -2.4 \cdot 10^{+83}:\\ \;\;\;\;x1 + \left(9 + \left(x1 - x1 \cdot \left(x1 \cdot \left(6 + \left(2 \cdot \left(\left(2 \cdot x2 - 3\right) - x2 \cdot -2\right) + \left(\left(x1 \cdot \left(6 + \left(t\_0 + 2 \cdot \left(-1 - 2 \cdot \left(x2 \cdot \left(3 + x2 \cdot -2\right)\right)\right)\right)\right) - x2 \cdot 8\right) - x2 \cdot 6\right)\right)\right) + t\_0\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 6 \cdot 10^{+82}:\\ \;\;\;\;x1 - \left(\left(t\_1 + x2 \cdot \left(x1 \cdot \left(12 - x1 \cdot 6\right) - 8 \cdot \left(x1 \cdot x2\right)\right)\right) - x2 \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(-1 + x1 \cdot \left(x1 + 3\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* 4.0 (* x2 (- 3.0 (* 2.0 x2)))))
        (t_1 (* x1 (- 2.0 (* x1 9.0)))))
   (if (<= x1 -4.5e+153)
     (+ x1 (- (* x2 -6.0) t_1))
     (if (<= x1 -2.4e+83)
       (+
        x1
        (+
         9.0
         (-
          x1
          (*
           x1
           (+
            (*
             x1
             (+
              6.0
              (+
               (* 2.0 (- (- (* 2.0 x2) 3.0) (* x2 -2.0)))
               (-
                (-
                 (*
                  x1
                  (+
                   6.0
                   (+
                    t_0
                    (* 2.0 (- -1.0 (* 2.0 (* x2 (+ 3.0 (* x2 -2.0)))))))))
                 (* x2 8.0))
                (* x2 6.0)))))
            t_0)))))
       (if (<= x1 6e+82)
         (-
          x1
          (-
           (+ t_1 (* x2 (- (* x1 (- 12.0 (* x1 6.0))) (* 8.0 (* x1 x2)))))
           (* x2 -6.0)))
         (+ x1 (+ x1 (* 3.0 (* x1 (+ -1.0 (* x1 (+ x1 3.0))))))))))))

C

double code(double x1, double x2) {
	double t_0 = 4.0 * (x2 * (3.0 - (2.0 * x2)));
	double t_1 = x1 * (2.0 - (x1 * 9.0));
	double tmp;
	if (x1 <= -4.5e+153) {
		tmp = x1 + ((x2 * -6.0) - t_1);
	} else if (x1 <= -2.4e+83) {
		tmp = x1 + (9.0 + (x1 - (x1 * ((x1 * (6.0 + ((2.0 * (((2.0 * x2) - 3.0) - (x2 * -2.0))) + (((x1 * (6.0 + (t_0 + (2.0 * (-1.0 - (2.0 * (x2 * (3.0 + (x2 * -2.0))))))))) - (x2 * 8.0)) - (x2 * 6.0))))) + t_0))));
	} else if (x1 <= 6e+82) {
		tmp = x1 - ((t_1 + (x2 * ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))) - (x2 * -6.0));
	} else {
		tmp = x1 + (x1 + (3.0 * (x1 * (-1.0 + (x1 * (x1 + 3.0))))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = 4.0d0 * (x2 * (3.0d0 - (2.0d0 * x2)))
    t_1 = x1 * (2.0d0 - (x1 * 9.0d0))
    if (x1 <= (-4.5d+153)) then
        tmp = x1 + ((x2 * (-6.0d0)) - t_1)
    else if (x1 <= (-2.4d+83)) then
        tmp = x1 + (9.0d0 + (x1 - (x1 * ((x1 * (6.0d0 + ((2.0d0 * (((2.0d0 * x2) - 3.0d0) - (x2 * (-2.0d0)))) + (((x1 * (6.0d0 + (t_0 + (2.0d0 * ((-1.0d0) - (2.0d0 * (x2 * (3.0d0 + (x2 * (-2.0d0)))))))))) - (x2 * 8.0d0)) - (x2 * 6.0d0))))) + t_0))))
    else if (x1 <= 6d+82) then
        tmp = x1 - ((t_1 + (x2 * ((x1 * (12.0d0 - (x1 * 6.0d0))) - (8.0d0 * (x1 * x2))))) - (x2 * (-6.0d0)))
    else
        tmp = x1 + (x1 + (3.0d0 * (x1 * ((-1.0d0) + (x1 * (x1 + 3.0d0))))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = 4.0 * (x2 * (3.0 - (2.0 * x2)));
	double t_1 = x1 * (2.0 - (x1 * 9.0));
	double tmp;
	if (x1 <= -4.5e+153) {
		tmp = x1 + ((x2 * -6.0) - t_1);
	} else if (x1 <= -2.4e+83) {
		tmp = x1 + (9.0 + (x1 - (x1 * ((x1 * (6.0 + ((2.0 * (((2.0 * x2) - 3.0) - (x2 * -2.0))) + (((x1 * (6.0 + (t_0 + (2.0 * (-1.0 - (2.0 * (x2 * (3.0 + (x2 * -2.0))))))))) - (x2 * 8.0)) - (x2 * 6.0))))) + t_0))));
	} else if (x1 <= 6e+82) {
		tmp = x1 - ((t_1 + (x2 * ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))) - (x2 * -6.0));
	} else {
		tmp = x1 + (x1 + (3.0 * (x1 * (-1.0 + (x1 * (x1 + 3.0))))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = 4.0 * (x2 * (3.0 - (2.0 * x2)))
	t_1 = x1 * (2.0 - (x1 * 9.0))
	tmp = 0
	if x1 <= -4.5e+153:
		tmp = x1 + ((x2 * -6.0) - t_1)
	elif x1 <= -2.4e+83:
		tmp = x1 + (9.0 + (x1 - (x1 * ((x1 * (6.0 + ((2.0 * (((2.0 * x2) - 3.0) - (x2 * -2.0))) + (((x1 * (6.0 + (t_0 + (2.0 * (-1.0 - (2.0 * (x2 * (3.0 + (x2 * -2.0))))))))) - (x2 * 8.0)) - (x2 * 6.0))))) + t_0))))
	elif x1 <= 6e+82:
		tmp = x1 - ((t_1 + (x2 * ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))) - (x2 * -6.0))
	else:
		tmp = x1 + (x1 + (3.0 * (x1 * (-1.0 + (x1 * (x1 + 3.0))))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(4.0 * Float64(x2 * Float64(3.0 - Float64(2.0 * x2))))
	t_1 = Float64(x1 * Float64(2.0 - Float64(x1 * 9.0)))
	tmp = 0.0
	if (x1 <= -4.5e+153)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) - t_1));
	elseif (x1 <= -2.4e+83)
		tmp = Float64(x1 + Float64(9.0 + Float64(x1 - Float64(x1 * Float64(Float64(x1 * Float64(6.0 + Float64(Float64(2.0 * Float64(Float64(Float64(2.0 * x2) - 3.0) - Float64(x2 * -2.0))) + Float64(Float64(Float64(x1 * Float64(6.0 + Float64(t_0 + Float64(2.0 * Float64(-1.0 - Float64(2.0 * Float64(x2 * Float64(3.0 + Float64(x2 * -2.0))))))))) - Float64(x2 * 8.0)) - Float64(x2 * 6.0))))) + t_0)))));
	elseif (x1 <= 6e+82)
		tmp = Float64(x1 - Float64(Float64(t_1 + Float64(x2 * Float64(Float64(x1 * Float64(12.0 - Float64(x1 * 6.0))) - Float64(8.0 * Float64(x1 * x2))))) - Float64(x2 * -6.0)));
	else
		tmp = Float64(x1 + Float64(x1 + Float64(3.0 * Float64(x1 * Float64(-1.0 + Float64(x1 * Float64(x1 + 3.0)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = 4.0 * (x2 * (3.0 - (2.0 * x2)));
	t_1 = x1 * (2.0 - (x1 * 9.0));
	tmp = 0.0;
	if (x1 <= -4.5e+153)
		tmp = x1 + ((x2 * -6.0) - t_1);
	elseif (x1 <= -2.4e+83)
		tmp = x1 + (9.0 + (x1 - (x1 * ((x1 * (6.0 + ((2.0 * (((2.0 * x2) - 3.0) - (x2 * -2.0))) + (((x1 * (6.0 + (t_0 + (2.0 * (-1.0 - (2.0 * (x2 * (3.0 + (x2 * -2.0))))))))) - (x2 * 8.0)) - (x2 * 6.0))))) + t_0))));
	elseif (x1 <= 6e+82)
		tmp = x1 - ((t_1 + (x2 * ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))) - (x2 * -6.0));
	else
		tmp = x1 + (x1 + (3.0 * (x1 * (-1.0 + (x1 * (x1 + 3.0))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(4.0 * N[(x2 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(2.0 - N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -4.5e+153], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -2.4e+83], N[(x1 + N[(9.0 + N[(x1 - N[(x1 * N[(N[(x1 * N[(6.0 + N[(N[(2.0 * N[(N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision] - N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(x1 * N[(6.0 + N[(t$95$0 + N[(2.0 * N[(-1.0 - N[(2.0 * N[(x2 * N[(3.0 + N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x2 * 8.0), $MachinePrecision]), $MachinePrecision] - N[(x2 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 6e+82], N[(x1 - N[(N[(t$95$1 + N[(x2 * N[(N[(x1 * N[(12.0 - N[(x1 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(x1 + N[(3.0 * N[(x1 * N[(-1.0 + N[(x1 * N[(x1 + 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -4.5000000000000001e153

   1. Initial program 0.0%

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

   3. Taylor expanded in x1 around 0 0.0%

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

   4. Taylor expanded in x1 around 0 0.0%

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

   5. Taylor expanded in x1 around 0 73.3%

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

   6. Taylor expanded in x2 around 0 100.0%

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

      1. *-commutative 100.0%

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

   8. Simplified 100.0%

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

   if -4.5000000000000001e153 < x1 < -2.39999999999999991e83

   1. Initial program 38.5%

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

   3. Taylor expanded in x1 around 0 30.8%

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

      1. +-commutative 30.8%

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

      2. mul-1-neg 30.8%

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

      3. sub-neg 30.8%

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

   5. Simplified 30.8%

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

   6. Taylor expanded in x1 around inf 30.8%

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

   7. Taylor expanded in x1 around 0 64.3%

      \[\leadsto x1 + \left(\left(\color{blue}{x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(\left(2 \cdot \left(-2 \cdot x2 + -1 \cdot \left(2 \cdot x2 - 3\right)\right) + \left(6 \cdot x2 + \left(8 \cdot x2 + x1 \cdot \left(\left(2 \cdot \left(1 + 2 \cdot \left(x2 \cdot \left(3 + -2 \cdot x2\right)\right)\right) + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) - 6\right)\right)\right)\right) - 6\right)\right)} + x1\right) + 9\right) \]

   if -2.39999999999999991e83 < x1 < 5.99999999999999978e82

   1. Initial program 99.4%

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

   3. Taylor expanded in x1 around 0 76.5%

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

   4. Taylor expanded in x1 around 0 74.7%

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

   5. Taylor expanded in x1 around 0 75.7%

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

   6. Taylor expanded in x2 around 0 86.7%

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

   if 5.99999999999999978e82 < x1

   1. Initial program 24.5%

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

   3. Taylor expanded in x1 around 0 5.0%

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

   4. Taylor expanded in x1 around 0 81.9%

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

   5. Taylor expanded in x2 around 0 96.2%

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

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4.5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 - x1 \cdot 9\right)\right)\\ \mathbf{elif}\;x1 \leq -2.4 \cdot 10^{+83}:\\ \;\;\;\;x1 + \left(9 + \left(x1 - x1 \cdot \left(x1 \cdot \left(6 + \left(2 \cdot \left(\left(2 \cdot x2 - 3\right) - x2 \cdot -2\right) + \left(\left(x1 \cdot \left(6 + \left(4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right) + 2 \cdot \left(-1 - 2 \cdot \left(x2 \cdot \left(3 + x2 \cdot -2\right)\right)\right)\right)\right) - x2 \cdot 8\right) - x2 \cdot 6\right)\right)\right) + 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 6 \cdot 10^{+82}:\\ \;\;\;\;x1 - \left(\left(x1 \cdot \left(2 - x1 \cdot 9\right) + x2 \cdot \left(x1 \cdot \left(12 - x1 \cdot 6\right) - 8 \cdot \left(x1 \cdot x2\right)\right)\right) - x2 \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(-1 + x1 \cdot \left(x1 + 3\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 77.9% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 - x1 \cdot 9\right)\right)\\ t_1 := 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\\ \mathbf{if}\;x1 \leq -2.6 \cdot 10^{+83}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x1 \leq -1.9 \cdot 10^{-209}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(t\_1 - 2\right)\right)\\ \mathbf{elif}\;x1 \leq 1.55 \cdot 10^{-234}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x1 \leq 6 \cdot 10^{+82}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(\left(t\_1 - 3 \cdot \left(x1 \cdot \left(x2 \cdot -2 - 3\right)\right)\right) - 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(-1 + x1 \cdot \left(x1 + 3\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ x1 (- (* x2 -6.0) (* x1 (- 2.0 (* x1 9.0))))))
        (t_1 (* 4.0 (* x2 (- (* 2.0 x2) 3.0)))))
   (if (<= x1 -2.6e+83)
     t_0
     (if (<= x1 -1.9e-209)
       (+ x1 (+ (* x2 -6.0) (* x1 (- t_1 2.0))))
       (if (<= x1 1.55e-234)
         t_0
         (if (<= x1 6e+82)
           (+
            x1
            (+
             (* x2 -6.0)
             (* x1 (- (- t_1 (* 3.0 (* x1 (- (* x2 -2.0) 3.0)))) 2.0))))
           (+ x1 (+ x1 (* 3.0 (* x1 (+ -1.0 (* x1 (+ x1 3.0)))))))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 + ((x2 * -6.0) - (x1 * (2.0 - (x1 * 9.0))));
	double t_1 = 4.0 * (x2 * ((2.0 * x2) - 3.0));
	double tmp;
	if (x1 <= -2.6e+83) {
		tmp = t_0;
	} else if (x1 <= -1.9e-209) {
		tmp = x1 + ((x2 * -6.0) + (x1 * (t_1 - 2.0)));
	} else if (x1 <= 1.55e-234) {
		tmp = t_0;
	} else if (x1 <= 6e+82) {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((t_1 - (3.0 * (x1 * ((x2 * -2.0) - 3.0)))) - 2.0)));
	} else {
		tmp = x1 + (x1 + (3.0 * (x1 * (-1.0 + (x1 * (x1 + 3.0))))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x1 + ((x2 * (-6.0d0)) - (x1 * (2.0d0 - (x1 * 9.0d0))))
    t_1 = 4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0))
    if (x1 <= (-2.6d+83)) then
        tmp = t_0
    else if (x1 <= (-1.9d-209)) then
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * (t_1 - 2.0d0)))
    else if (x1 <= 1.55d-234) then
        tmp = t_0
    else if (x1 <= 6d+82) then
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * ((t_1 - (3.0d0 * (x1 * ((x2 * (-2.0d0)) - 3.0d0)))) - 2.0d0)))
    else
        tmp = x1 + (x1 + (3.0d0 * (x1 * ((-1.0d0) + (x1 * (x1 + 3.0d0))))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 + ((x2 * -6.0) - (x1 * (2.0 - (x1 * 9.0))));
	double t_1 = 4.0 * (x2 * ((2.0 * x2) - 3.0));
	double tmp;
	if (x1 <= -2.6e+83) {
		tmp = t_0;
	} else if (x1 <= -1.9e-209) {
		tmp = x1 + ((x2 * -6.0) + (x1 * (t_1 - 2.0)));
	} else if (x1 <= 1.55e-234) {
		tmp = t_0;
	} else if (x1 <= 6e+82) {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((t_1 - (3.0 * (x1 * ((x2 * -2.0) - 3.0)))) - 2.0)));
	} else {
		tmp = x1 + (x1 + (3.0 * (x1 * (-1.0 + (x1 * (x1 + 3.0))))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 + ((x2 * -6.0) - (x1 * (2.0 - (x1 * 9.0))))
	t_1 = 4.0 * (x2 * ((2.0 * x2) - 3.0))
	tmp = 0
	if x1 <= -2.6e+83:
		tmp = t_0
	elif x1 <= -1.9e-209:
		tmp = x1 + ((x2 * -6.0) + (x1 * (t_1 - 2.0)))
	elif x1 <= 1.55e-234:
		tmp = t_0
	elif x1 <= 6e+82:
		tmp = x1 + ((x2 * -6.0) + (x1 * ((t_1 - (3.0 * (x1 * ((x2 * -2.0) - 3.0)))) - 2.0)))
	else:
		tmp = x1 + (x1 + (3.0 * (x1 * (-1.0 + (x1 * (x1 + 3.0))))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 + Float64(Float64(x2 * -6.0) - Float64(x1 * Float64(2.0 - Float64(x1 * 9.0)))))
	t_1 = Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0)))
	tmp = 0.0
	if (x1 <= -2.6e+83)
		tmp = t_0;
	elseif (x1 <= -1.9e-209)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(t_1 - 2.0))));
	elseif (x1 <= 1.55e-234)
		tmp = t_0;
	elseif (x1 <= 6e+82)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(t_1 - Float64(3.0 * Float64(x1 * Float64(Float64(x2 * -2.0) - 3.0)))) - 2.0))));
	else
		tmp = Float64(x1 + Float64(x1 + Float64(3.0 * Float64(x1 * Float64(-1.0 + Float64(x1 * Float64(x1 + 3.0)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 + ((x2 * -6.0) - (x1 * (2.0 - (x1 * 9.0))));
	t_1 = 4.0 * (x2 * ((2.0 * x2) - 3.0));
	tmp = 0.0;
	if (x1 <= -2.6e+83)
		tmp = t_0;
	elseif (x1 <= -1.9e-209)
		tmp = x1 + ((x2 * -6.0) + (x1 * (t_1 - 2.0)));
	elseif (x1 <= 1.55e-234)
		tmp = t_0;
	elseif (x1 <= 6e+82)
		tmp = x1 + ((x2 * -6.0) + (x1 * ((t_1 - (3.0 * (x1 * ((x2 * -2.0) - 3.0)))) - 2.0)));
	else
		tmp = x1 + (x1 + (3.0 * (x1 * (-1.0 + (x1 * (x1 + 3.0))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] - N[(x1 * N[(2.0 - N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(4.0 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -2.6e+83], t$95$0, If[LessEqual[x1, -1.9e-209], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(t$95$1 - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.55e-234], t$95$0, If[LessEqual[x1, 6e+82], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(t$95$1 - N[(3.0 * N[(x1 * N[(N[(x2 * -2.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(x1 + N[(3.0 * N[(x1 * N[(-1.0 + N[(x1 * N[(x1 + 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -2.6000000000000001e83 or -1.8999999999999999e-209 < x1 < 1.5500000000000001e-234

   1. Initial program 47.9%

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

   3. Taylor expanded in x1 around 0 32.0%

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

   4. Taylor expanded in x1 around 0 31.9%

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

   5. Taylor expanded in x1 around 0 64.5%

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

   6. Taylor expanded in x2 around 0 83.7%

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

      1. *-commutative 83.7%

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

   8. Simplified 83.7%

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

   if -2.6000000000000001e83 < x1 < -1.8999999999999999e-209

   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. Add Preprocessing

   3. Taylor expanded in x1 around 0 75.1%

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

   4. Taylor expanded in x1 around 0 70.8%

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

   5. Taylor expanded in x1 around 0 75.8%

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

   if 1.5500000000000001e-234 < x1 < 5.99999999999999978e82

   1. Initial program 99.4%

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

   3. Taylor expanded in x1 around 0 77.6%

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

   4. Taylor expanded in x1 around 0 77.7%

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

   5. Taylor expanded in x1 around 0 77.8%

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

   if 5.99999999999999978e82 < x1

   1. Initial program 24.5%

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

   3. Taylor expanded in x1 around 0 5.0%

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

   4. Taylor expanded in x1 around 0 81.9%

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

   5. Taylor expanded in x2 around 0 96.2%

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

4. Final simplification 82.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -2.6 \cdot 10^{+83}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 - x1 \cdot 9\right)\right)\\ \mathbf{elif}\;x1 \leq -1.9 \cdot 10^{-209}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)\\ \mathbf{elif}\;x1 \leq 1.55 \cdot 10^{-234}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 - x1 \cdot 9\right)\right)\\ \mathbf{elif}\;x1 \leq 6 \cdot 10^{+82}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 3 \cdot \left(x1 \cdot \left(x2 \cdot -2 - 3\right)\right)\right) - 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(-1 + x1 \cdot \left(x1 + 3\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 77.6% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 - x1 \cdot 9\right)\right)\\ \mathbf{if}\;x1 \leq -2.6 \cdot 10^{+83}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x1 \leq -4.2 \cdot 10^{-209}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)\\ \mathbf{elif}\;x1 \leq 2.5 \cdot 10^{-233}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x1 \leq 6 \cdot 10^{+82}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 + \left(4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right) - x2 \cdot \left(x1 \cdot 6\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(-1 + x1 \cdot \left(x1 + 3\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ x1 (- (* x2 -6.0) (* x1 (- 2.0 (* x1 9.0)))))))
   (if (<= x1 -2.6e+83)
     t_0
     (if (<= x1 -4.2e-209)
       (+ x1 (+ (* x2 -6.0) (* x1 (- (* 4.0 (* x2 (- (* 2.0 x2) 3.0))) 2.0))))
       (if (<= x1 2.5e-233)
         t_0
         (if (<= x1 6e+82)
           (+
            x1
            (-
             (* x2 -6.0)
             (*
              x1
              (+
               2.0
               (- (* 4.0 (* x2 (- 3.0 (* 2.0 x2)))) (* x2 (* x1 6.0)))))))
           (+ x1 (+ x1 (* 3.0 (* x1 (+ -1.0 (* x1 (+ x1 3.0)))))))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 + ((x2 * -6.0) - (x1 * (2.0 - (x1 * 9.0))));
	double tmp;
	if (x1 <= -2.6e+83) {
		tmp = t_0;
	} else if (x1 <= -4.2e-209) {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)));
	} else if (x1 <= 2.5e-233) {
		tmp = t_0;
	} else if (x1 <= 6e+82) {
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((4.0 * (x2 * (3.0 - (2.0 * x2)))) - (x2 * (x1 * 6.0))))));
	} else {
		tmp = x1 + (x1 + (3.0 * (x1 * (-1.0 + (x1 * (x1 + 3.0))))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x1 + ((x2 * (-6.0d0)) - (x1 * (2.0d0 - (x1 * 9.0d0))))
    if (x1 <= (-2.6d+83)) then
        tmp = t_0
    else if (x1 <= (-4.2d-209)) then
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * ((4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0))) - 2.0d0)))
    else if (x1 <= 2.5d-233) then
        tmp = t_0
    else if (x1 <= 6d+82) then
        tmp = x1 + ((x2 * (-6.0d0)) - (x1 * (2.0d0 + ((4.0d0 * (x2 * (3.0d0 - (2.0d0 * x2)))) - (x2 * (x1 * 6.0d0))))))
    else
        tmp = x1 + (x1 + (3.0d0 * (x1 * ((-1.0d0) + (x1 * (x1 + 3.0d0))))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 + ((x2 * -6.0) - (x1 * (2.0 - (x1 * 9.0))));
	double tmp;
	if (x1 <= -2.6e+83) {
		tmp = t_0;
	} else if (x1 <= -4.2e-209) {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)));
	} else if (x1 <= 2.5e-233) {
		tmp = t_0;
	} else if (x1 <= 6e+82) {
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((4.0 * (x2 * (3.0 - (2.0 * x2)))) - (x2 * (x1 * 6.0))))));
	} else {
		tmp = x1 + (x1 + (3.0 * (x1 * (-1.0 + (x1 * (x1 + 3.0))))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 + ((x2 * -6.0) - (x1 * (2.0 - (x1 * 9.0))))
	tmp = 0
	if x1 <= -2.6e+83:
		tmp = t_0
	elif x1 <= -4.2e-209:
		tmp = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)))
	elif x1 <= 2.5e-233:
		tmp = t_0
	elif x1 <= 6e+82:
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((4.0 * (x2 * (3.0 - (2.0 * x2)))) - (x2 * (x1 * 6.0))))))
	else:
		tmp = x1 + (x1 + (3.0 * (x1 * (-1.0 + (x1 * (x1 + 3.0))))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 + Float64(Float64(x2 * -6.0) - Float64(x1 * Float64(2.0 - Float64(x1 * 9.0)))))
	tmp = 0.0
	if (x1 <= -2.6e+83)
		tmp = t_0;
	elseif (x1 <= -4.2e-209)
		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 <= 2.5e-233)
		tmp = t_0;
	elseif (x1 <= 6e+82)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) - Float64(x1 * Float64(2.0 + Float64(Float64(4.0 * Float64(x2 * Float64(3.0 - Float64(2.0 * x2)))) - Float64(x2 * Float64(x1 * 6.0)))))));
	else
		tmp = Float64(x1 + Float64(x1 + Float64(3.0 * Float64(x1 * Float64(-1.0 + Float64(x1 * Float64(x1 + 3.0)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 + ((x2 * -6.0) - (x1 * (2.0 - (x1 * 9.0))));
	tmp = 0.0;
	if (x1 <= -2.6e+83)
		tmp = t_0;
	elseif (x1 <= -4.2e-209)
		tmp = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)));
	elseif (x1 <= 2.5e-233)
		tmp = t_0;
	elseif (x1 <= 6e+82)
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((4.0 * (x2 * (3.0 - (2.0 * x2)))) - (x2 * (x1 * 6.0))))));
	else
		tmp = x1 + (x1 + (3.0 * (x1 * (-1.0 + (x1 * (x1 + 3.0))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] - N[(x1 * N[(2.0 - N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -2.6e+83], t$95$0, If[LessEqual[x1, -4.2e-209], 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, 2.5e-233], t$95$0, If[LessEqual[x1, 6e+82], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] - N[(x1 * N[(2.0 + N[(N[(4.0 * N[(x2 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x2 * N[(x1 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(x1 + N[(3.0 * N[(x1 * N[(-1.0 + N[(x1 * N[(x1 + 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -2.6000000000000001e83 or -4.19999999999999991e-209 < x1 < 2.50000000000000006e-233

   1. Initial program 47.9%

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

   3. Taylor expanded in x1 around 0 32.0%

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

   4. Taylor expanded in x1 around 0 31.9%

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

   5. Taylor expanded in x1 around 0 64.5%

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

   6. Taylor expanded in x2 around 0 83.7%

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

      1. *-commutative 83.7%

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

   8. Simplified 83.7%

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

   if -2.6000000000000001e83 < x1 < -4.19999999999999991e-209

   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. Add Preprocessing

   3. Taylor expanded in x1 around 0 75.1%

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

   4. Taylor expanded in x1 around 0 70.8%

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

   5. Taylor expanded in x1 around 0 75.8%

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

   if 2.50000000000000006e-233 < x1 < 5.99999999999999978e82

   1. Initial program 99.4%

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

   3. Taylor expanded in x1 around 0 77.6%

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

   4. Taylor expanded in x1 around 0 77.7%

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

   5. Taylor expanded in x1 around 0 77.8%

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

   6. Taylor expanded in x2 around inf 77.3%

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

      1. associate-*r* 77.3%

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

      2. *-commutative 77.3%

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

   8. Simplified 77.3%

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

   if 5.99999999999999978e82 < x1

   1. Initial program 24.5%

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

   3. Taylor expanded in x1 around 0 5.0%

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

   4. Taylor expanded in x1 around 0 81.9%

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

   5. Taylor expanded in x2 around 0 96.2%

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

4. Final simplification 82.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -2.6 \cdot 10^{+83}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 - x1 \cdot 9\right)\right)\\ \mathbf{elif}\;x1 \leq -4.2 \cdot 10^{-209}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)\\ \mathbf{elif}\;x1 \leq 2.5 \cdot 10^{-233}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 - x1 \cdot 9\right)\right)\\ \mathbf{elif}\;x1 \leq 6 \cdot 10^{+82}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 + \left(4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right) - x2 \cdot \left(x1 \cdot 6\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(-1 + x1 \cdot \left(x1 + 3\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 78.0% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 + \left(x2 \cdot -6 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)\\ t_1 := x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 - x1 \cdot 9\right)\right)\\ \mathbf{if}\;x1 \leq -2.6 \cdot 10^{+83}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x1 \leq -1 \cdot 10^{-209}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x1 \leq 8 \cdot 10^{-231}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x1 \leq 6 \cdot 10^{+82}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(-1 + x1 \cdot \left(x1 + 3\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0
         (+
          x1
          (+ (* x2 -6.0) (* x1 (- (* 4.0 (* x2 (- (* 2.0 x2) 3.0))) 2.0)))))
        (t_1 (+ x1 (- (* x2 -6.0) (* x1 (- 2.0 (* x1 9.0)))))))
   (if (<= x1 -2.6e+83)
     t_1
     (if (<= x1 -1e-209)
       t_0
       (if (<= x1 8e-231)
         t_1
         (if (<= x1 6e+82)
           t_0
           (+ x1 (+ x1 (* 3.0 (* x1 (+ -1.0 (* x1 (+ x1 3.0)))))))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)));
	double t_1 = x1 + ((x2 * -6.0) - (x1 * (2.0 - (x1 * 9.0))));
	double tmp;
	if (x1 <= -2.6e+83) {
		tmp = t_1;
	} else if (x1 <= -1e-209) {
		tmp = t_0;
	} else if (x1 <= 8e-231) {
		tmp = t_1;
	} else if (x1 <= 6e+82) {
		tmp = t_0;
	} else {
		tmp = x1 + (x1 + (3.0 * (x1 * (-1.0 + (x1 * (x1 + 3.0))))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x1 + ((x2 * (-6.0d0)) + (x1 * ((4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0))) - 2.0d0)))
    t_1 = x1 + ((x2 * (-6.0d0)) - (x1 * (2.0d0 - (x1 * 9.0d0))))
    if (x1 <= (-2.6d+83)) then
        tmp = t_1
    else if (x1 <= (-1d-209)) then
        tmp = t_0
    else if (x1 <= 8d-231) then
        tmp = t_1
    else if (x1 <= 6d+82) then
        tmp = t_0
    else
        tmp = x1 + (x1 + (3.0d0 * (x1 * ((-1.0d0) + (x1 * (x1 + 3.0d0))))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)));
	double t_1 = x1 + ((x2 * -6.0) - (x1 * (2.0 - (x1 * 9.0))));
	double tmp;
	if (x1 <= -2.6e+83) {
		tmp = t_1;
	} else if (x1 <= -1e-209) {
		tmp = t_0;
	} else if (x1 <= 8e-231) {
		tmp = t_1;
	} else if (x1 <= 6e+82) {
		tmp = t_0;
	} else {
		tmp = x1 + (x1 + (3.0 * (x1 * (-1.0 + (x1 * (x1 + 3.0))))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)))
	t_1 = x1 + ((x2 * -6.0) - (x1 * (2.0 - (x1 * 9.0))))
	tmp = 0
	if x1 <= -2.6e+83:
		tmp = t_1
	elif x1 <= -1e-209:
		tmp = t_0
	elif x1 <= 8e-231:
		tmp = t_1
	elif x1 <= 6e+82:
		tmp = t_0
	else:
		tmp = x1 + (x1 + (3.0 * (x1 * (-1.0 + (x1 * (x1 + 3.0))))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0))) - 2.0))))
	t_1 = Float64(x1 + Float64(Float64(x2 * -6.0) - Float64(x1 * Float64(2.0 - Float64(x1 * 9.0)))))
	tmp = 0.0
	if (x1 <= -2.6e+83)
		tmp = t_1;
	elseif (x1 <= -1e-209)
		tmp = t_0;
	elseif (x1 <= 8e-231)
		tmp = t_1;
	elseif (x1 <= 6e+82)
		tmp = t_0;
	else
		tmp = Float64(x1 + Float64(x1 + Float64(3.0 * Float64(x1 * Float64(-1.0 + Float64(x1 * Float64(x1 + 3.0)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)));
	t_1 = x1 + ((x2 * -6.0) - (x1 * (2.0 - (x1 * 9.0))));
	tmp = 0.0;
	if (x1 <= -2.6e+83)
		tmp = t_1;
	elseif (x1 <= -1e-209)
		tmp = t_0;
	elseif (x1 <= 8e-231)
		tmp = t_1;
	elseif (x1 <= 6e+82)
		tmp = t_0;
	else
		tmp = x1 + (x1 + (3.0 * (x1 * (-1.0 + (x1 * (x1 + 3.0))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(4.0 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] - N[(x1 * N[(2.0 - N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -2.6e+83], t$95$1, If[LessEqual[x1, -1e-209], t$95$0, If[LessEqual[x1, 8e-231], t$95$1, If[LessEqual[x1, 6e+82], t$95$0, N[(x1 + N[(x1 + N[(3.0 * N[(x1 * N[(-1.0 + N[(x1 * N[(x1 + 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -2.6000000000000001e83 or -1e-209 < x1 < 7.9999999999999999e-231

   1. Initial program 47.9%

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

   3. Taylor expanded in x1 around 0 32.0%

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

   4. Taylor expanded in x1 around 0 31.9%

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

   5. Taylor expanded in x1 around 0 64.5%

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

   6. Taylor expanded in x2 around 0 83.7%

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

      1. *-commutative 83.7%

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

   8. Simplified 83.7%

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

   if -2.6000000000000001e83 < x1 < -1e-209 or 7.9999999999999999e-231 < x1 < 5.99999999999999978e82

   1. Initial program 99.3%

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

   3. Taylor expanded in x1 around 0 76.3%

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

   4. Taylor expanded in x1 around 0 74.1%

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

   5. Taylor expanded in x1 around 0 76.5%

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

   if 5.99999999999999978e82 < x1

   1. Initial program 24.5%

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

   3. Taylor expanded in x1 around 0 5.0%

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

   4. Taylor expanded in x1 around 0 81.9%

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

   5. Taylor expanded in x2 around 0 96.2%

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

4. Final simplification 82.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -2.6 \cdot 10^{+83}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 - x1 \cdot 9\right)\right)\\ \mathbf{elif}\;x1 \leq -1 \cdot 10^{-209}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)\\ \mathbf{elif}\;x1 \leq 8 \cdot 10^{-231}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 - x1 \cdot 9\right)\right)\\ \mathbf{elif}\;x1 \leq 6 \cdot 10^{+82}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(-1 + x1 \cdot \left(x1 + 3\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 83.2% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(2 - x1 \cdot 9\right)\\ \mathbf{if}\;x1 \leq -1.8 \cdot 10^{+152}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - t\_0\right)\\ \mathbf{elif}\;x1 \leq 6 \cdot 10^{+82}:\\ \;\;\;\;x1 - \left(\left(t\_0 + x2 \cdot \left(x1 \cdot \left(12 - x1 \cdot 6\right) - 8 \cdot \left(x1 \cdot x2\right)\right)\right) - x2 \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(-1 + x1 \cdot \left(x1 + 3\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (- 2.0 (* x1 9.0)))))
   (if (<= x1 -1.8e+152)
     (+ x1 (- (* x2 -6.0) t_0))
     (if (<= x1 6e+82)
       (-
        x1
        (-
         (+ t_0 (* x2 (- (* x1 (- 12.0 (* x1 6.0))) (* 8.0 (* x1 x2)))))
         (* x2 -6.0)))
       (+ x1 (+ x1 (* 3.0 (* x1 (+ -1.0 (* x1 (+ x1 3.0)))))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (2.0 - (x1 * 9.0));
	double tmp;
	if (x1 <= -1.8e+152) {
		tmp = x1 + ((x2 * -6.0) - t_0);
	} else if (x1 <= 6e+82) {
		tmp = x1 - ((t_0 + (x2 * ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))) - (x2 * -6.0));
	} else {
		tmp = x1 + (x1 + (3.0 * (x1 * (-1.0 + (x1 * (x1 + 3.0))))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x1 * (2.0d0 - (x1 * 9.0d0))
    if (x1 <= (-1.8d+152)) then
        tmp = x1 + ((x2 * (-6.0d0)) - t_0)
    else if (x1 <= 6d+82) then
        tmp = x1 - ((t_0 + (x2 * ((x1 * (12.0d0 - (x1 * 6.0d0))) - (8.0d0 * (x1 * x2))))) - (x2 * (-6.0d0)))
    else
        tmp = x1 + (x1 + (3.0d0 * (x1 * ((-1.0d0) + (x1 * (x1 + 3.0d0))))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (2.0 - (x1 * 9.0));
	double tmp;
	if (x1 <= -1.8e+152) {
		tmp = x1 + ((x2 * -6.0) - t_0);
	} else if (x1 <= 6e+82) {
		tmp = x1 - ((t_0 + (x2 * ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))) - (x2 * -6.0));
	} else {
		tmp = x1 + (x1 + (3.0 * (x1 * (-1.0 + (x1 * (x1 + 3.0))))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (2.0 - (x1 * 9.0))
	tmp = 0
	if x1 <= -1.8e+152:
		tmp = x1 + ((x2 * -6.0) - t_0)
	elif x1 <= 6e+82:
		tmp = x1 - ((t_0 + (x2 * ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))) - (x2 * -6.0))
	else:
		tmp = x1 + (x1 + (3.0 * (x1 * (-1.0 + (x1 * (x1 + 3.0))))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(2.0 - Float64(x1 * 9.0)))
	tmp = 0.0
	if (x1 <= -1.8e+152)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) - t_0));
	elseif (x1 <= 6e+82)
		tmp = Float64(x1 - Float64(Float64(t_0 + Float64(x2 * Float64(Float64(x1 * Float64(12.0 - Float64(x1 * 6.0))) - Float64(8.0 * Float64(x1 * x2))))) - Float64(x2 * -6.0)));
	else
		tmp = Float64(x1 + Float64(x1 + Float64(3.0 * Float64(x1 * Float64(-1.0 + Float64(x1 * Float64(x1 + 3.0)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (2.0 - (x1 * 9.0));
	tmp = 0.0;
	if (x1 <= -1.8e+152)
		tmp = x1 + ((x2 * -6.0) - t_0);
	elseif (x1 <= 6e+82)
		tmp = x1 - ((t_0 + (x2 * ((x1 * (12.0 - (x1 * 6.0))) - (8.0 * (x1 * x2))))) - (x2 * -6.0));
	else
		tmp = x1 + (x1 + (3.0 * (x1 * (-1.0 + (x1 * (x1 + 3.0))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(2.0 - N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -1.8e+152], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] - t$95$0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 6e+82], N[(x1 - N[(N[(t$95$0 + N[(x2 * N[(N[(x1 * N[(12.0 - N[(x1 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(x1 + N[(3.0 * N[(x1 * N[(-1.0 + N[(x1 * N[(x1 + 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -1.7999999999999999e152

   1. Initial program 0.0%

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

   3. Taylor expanded in x1 around 0 0.0%

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

   4. Taylor expanded in x1 around 0 0.0%

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

   5. Taylor expanded in x1 around 0 69.3%

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

   6. Taylor expanded in x2 around 0 94.8%

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

      1. *-commutative 94.8%

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

   8. Simplified 94.8%

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

   if -1.7999999999999999e152 < x1 < 5.99999999999999978e82

   1. Initial program 96.0%

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

   3. Taylor expanded in x1 around 0 71.7%

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

   4. Taylor expanded in x1 around 0 70.1%

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

   5. Taylor expanded in x1 around 0 71.9%

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

   6. Taylor expanded in x2 around 0 82.2%

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

   if 5.99999999999999978e82 < x1

   1. Initial program 24.5%

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

   3. Taylor expanded in x1 around 0 5.0%

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

   4. Taylor expanded in x1 around 0 81.9%

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

   5. Taylor expanded in x2 around 0 96.2%

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

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.8 \cdot 10^{+152}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 - x1 \cdot 9\right)\right)\\ \mathbf{elif}\;x1 \leq 6 \cdot 10^{+82}:\\ \;\;\;\;x1 - \left(\left(x1 \cdot \left(2 - x1 \cdot 9\right) + x2 \cdot \left(x1 \cdot \left(12 - x1 \cdot 6\right) - 8 \cdot \left(x1 \cdot x2\right)\right)\right) - x2 \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(-1 + x1 \cdot \left(x1 + 3\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 42.7% accurate, 4.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -2.35 \cdot 10^{+83}:\\ \;\;\;\;9 + \left(x1 \cdot 2 + \left(x1 \cdot x2\right) \cdot -12\right)\\ \mathbf{elif}\;x1 \leq -2.9 \cdot 10^{-71} \lor \neg \left(x1 \leq 9.6 \cdot 10^{-111}\right):\\ \;\;\;\;x1 \cdot \left(2 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x2 \cdot -6\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -2.35e+83)
   (+ 9.0 (+ (* x1 2.0) (* (* x1 x2) -12.0)))
   (if (or (<= x1 -2.9e-71) (not (<= x1 9.6e-111)))
     (* x1 (+ 2.0 (* 4.0 (* x2 (- (* 2.0 x2) 3.0)))))
     (+ x1 (* x2 -6.0)))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -2.35e+83) {
		tmp = 9.0 + ((x1 * 2.0) + ((x1 * x2) * -12.0));
	} else if ((x1 <= -2.9e-71) || !(x1 <= 9.6e-111)) {
		tmp = x1 * (2.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0))));
	} else {
		tmp = x1 + (x2 * -6.0);
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x1 <= (-2.35d+83)) then
        tmp = 9.0d0 + ((x1 * 2.0d0) + ((x1 * x2) * (-12.0d0)))
    else if ((x1 <= (-2.9d-71)) .or. (.not. (x1 <= 9.6d-111))) then
        tmp = x1 * (2.0d0 + (4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0))))
    else
        tmp = x1 + (x2 * (-6.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= -2.35e+83) {
		tmp = 9.0 + ((x1 * 2.0) + ((x1 * x2) * -12.0));
	} else if ((x1 <= -2.9e-71) || !(x1 <= 9.6e-111)) {
		tmp = x1 * (2.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0))));
	} else {
		tmp = x1 + (x2 * -6.0);
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -2.35e+83:
		tmp = 9.0 + ((x1 * 2.0) + ((x1 * x2) * -12.0))
	elif (x1 <= -2.9e-71) or not (x1 <= 9.6e-111):
		tmp = x1 * (2.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0))))
	else:
		tmp = x1 + (x2 * -6.0)
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -2.35e+83)
		tmp = Float64(9.0 + Float64(Float64(x1 * 2.0) + Float64(Float64(x1 * x2) * -12.0)));
	elseif ((x1 <= -2.9e-71) || !(x1 <= 9.6e-111))
		tmp = Float64(x1 * Float64(2.0 + Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0)))));
	else
		tmp = Float64(x1 + Float64(x2 * -6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -2.35e+83)
		tmp = 9.0 + ((x1 * 2.0) + ((x1 * x2) * -12.0));
	elseif ((x1 <= -2.9e-71) || ~((x1 <= 9.6e-111)))
		tmp = x1 * (2.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0))));
	else
		tmp = x1 + (x2 * -6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -2.35e+83], N[(9.0 + N[(N[(x1 * 2.0), $MachinePrecision] + N[(N[(x1 * x2), $MachinePrecision] * -12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x1, -2.9e-71], N[Not[LessEqual[x1, 9.6e-111]], $MachinePrecision]], N[(x1 * N[(2.0 + N[(4.0 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -2.3499999999999999e83

   1. Initial program 11.6%

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

   3. Taylor expanded in x1 around 0 0.1%

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

   4. Taylor expanded in x1 around inf 0.1%

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

   5. Taylor expanded in x2 around 0 12.3%

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

   if -2.3499999999999999e83 < x1 < -2.8999999999999999e-71 or 9.6000000000000003e-111 < x1

   1. Initial program 68.5%

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

   3. Taylor expanded in x1 around 0 40.9%

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

   4. Taylor expanded in x1 around inf 43.8%

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

   5. Taylor expanded in x1 around inf 43.2%

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

   if -2.8999999999999999e-71 < x1 < 9.6000000000000003e-111

   1. Initial program 99.4%

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

   3. Taylor expanded in x1 around 0 84.4%

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

   4. Taylor expanded in x1 around 0 84.4%

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

   5. Taylor expanded in x1 around 0 61.2%

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

      1. *-commutative 61.2%

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

   7. Simplified 61.2%

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

4. Final simplification 44.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -2.35 \cdot 10^{+83}:\\ \;\;\;\;9 + \left(x1 \cdot 2 + \left(x1 \cdot x2\right) \cdot -12\right)\\ \mathbf{elif}\;x1 \leq -2.9 \cdot 10^{-71} \lor \neg \left(x1 \leq 9.6 \cdot 10^{-111}\right):\\ \;\;\;\;x1 \cdot \left(2 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x2 \cdot -6\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 68.8% accurate, 4.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x2 \leq -4.2 \cdot 10^{+165} \lor \neg \left(x2 \leq 2.6 \cdot 10^{+84}\right):\\ \;\;\;\;x1 + \left(9 + \left(x1 + x2 \cdot \left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot -12\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 - x1 \cdot 9\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x2 -4.2e+165) (not (<= x2 2.6e+84)))
   (+ x1 (+ 9.0 (+ x1 (* x2 (+ (* 8.0 (* x1 x2)) (* x1 -12.0))))))
   (+ x1 (- (* x2 -6.0) (* x1 (- 2.0 (* x1 9.0)))))))

C

double code(double x1, double x2) {
	double tmp;
	if ((x2 <= -4.2e+165) || !(x2 <= 2.6e+84)) {
		tmp = x1 + (9.0 + (x1 + (x2 * ((8.0 * (x1 * x2)) + (x1 * -12.0)))));
	} else {
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 - (x1 * 9.0))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if ((x2 <= (-4.2d+165)) .or. (.not. (x2 <= 2.6d+84))) then
        tmp = x1 + (9.0d0 + (x1 + (x2 * ((8.0d0 * (x1 * x2)) + (x1 * (-12.0d0))))))
    else
        tmp = x1 + ((x2 * (-6.0d0)) - (x1 * (2.0d0 - (x1 * 9.0d0))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x2 <= -4.2e+165) || !(x2 <= 2.6e+84)) {
		tmp = x1 + (9.0 + (x1 + (x2 * ((8.0 * (x1 * x2)) + (x1 * -12.0)))));
	} else {
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 - (x1 * 9.0))));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x2 <= -4.2e+165) or not (x2 <= 2.6e+84):
		tmp = x1 + (9.0 + (x1 + (x2 * ((8.0 * (x1 * x2)) + (x1 * -12.0)))))
	else:
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 - (x1 * 9.0))))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x2 <= -4.2e+165) || !(x2 <= 2.6e+84))
		tmp = Float64(x1 + Float64(9.0 + Float64(x1 + Float64(x2 * Float64(Float64(8.0 * Float64(x1 * x2)) + Float64(x1 * -12.0))))));
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) - Float64(x1 * Float64(2.0 - Float64(x1 * 9.0)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x2 <= -4.2e+165) || ~((x2 <= 2.6e+84)))
		tmp = x1 + (9.0 + (x1 + (x2 * ((8.0 * (x1 * x2)) + (x1 * -12.0)))));
	else
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 - (x1 * 9.0))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x2, -4.2e+165], N[Not[LessEqual[x2, 2.6e+84]], $MachinePrecision]], N[(x1 + N[(9.0 + N[(x1 + N[(x2 * N[(N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision] + N[(x1 * -12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] - N[(x1 * N[(2.0 - N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x2 < -4.2000000000000001e165 or 2.6000000000000001e84 < x2

   1. Initial program 72.5%

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

   3. Taylor expanded in x1 around 0 47.1%

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

   4. Taylor expanded in x1 around inf 65.4%

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

   5. Taylor expanded in x2 around 0 75.0%

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

   if -4.2000000000000001e165 < x2 < 2.6000000000000001e84

   1. Initial program 69.3%

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

   3. Taylor expanded in x1 around 0 51.3%

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

   4. Taylor expanded in x1 around 0 67.9%

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

   5. Taylor expanded in x1 around 0 75.7%

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

   6. Taylor expanded in x2 around 0 75.5%

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

      1. *-commutative 75.5%

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

   8. Simplified 75.5%

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

4. Final simplification 75.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq -4.2 \cdot 10^{+165} \lor \neg \left(x2 \leq 2.6 \cdot 10^{+84}\right):\\ \;\;\;\;x1 + \left(9 + \left(x1 + x2 \cdot \left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot -12\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 - x1 \cdot 9\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 66.3% accurate, 5.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x2 \leq -3.2 \cdot 10^{+166} \lor \neg \left(x2 \leq 2.6 \cdot 10^{+84}\right):\\ \;\;\;\;x1 \cdot \left(2 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 - x1 \cdot 9\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x2 -3.2e+166) (not (<= x2 2.6e+84)))
   (* x1 (+ 2.0 (* 4.0 (* x2 (- (* 2.0 x2) 3.0)))))
   (+ x1 (- (* x2 -6.0) (* x1 (- 2.0 (* x1 9.0)))))))

C

double code(double x1, double x2) {
	double tmp;
	if ((x2 <= -3.2e+166) || !(x2 <= 2.6e+84)) {
		tmp = x1 * (2.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0))));
	} else {
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 - (x1 * 9.0))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if ((x2 <= (-3.2d+166)) .or. (.not. (x2 <= 2.6d+84))) then
        tmp = x1 * (2.0d0 + (4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0))))
    else
        tmp = x1 + ((x2 * (-6.0d0)) - (x1 * (2.0d0 - (x1 * 9.0d0))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x2 <= -3.2e+166) || !(x2 <= 2.6e+84)) {
		tmp = x1 * (2.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0))));
	} else {
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 - (x1 * 9.0))));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x2 <= -3.2e+166) or not (x2 <= 2.6e+84):
		tmp = x1 * (2.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0))))
	else:
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 - (x1 * 9.0))))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x2 <= -3.2e+166) || !(x2 <= 2.6e+84))
		tmp = Float64(x1 * Float64(2.0 + Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0)))));
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) - Float64(x1 * Float64(2.0 - Float64(x1 * 9.0)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x2 <= -3.2e+166) || ~((x2 <= 2.6e+84)))
		tmp = x1 * (2.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0))));
	else
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 - (x1 * 9.0))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x2, -3.2e+166], N[Not[LessEqual[x2, 2.6e+84]], $MachinePrecision]], N[(x1 * N[(2.0 + N[(4.0 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] - N[(x1 * N[(2.0 - N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x2 < -3.19999999999999968e166 or 2.6000000000000001e84 < x2

   1. Initial program 72.5%

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

   3. Taylor expanded in x1 around 0 47.1%

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

   4. Taylor expanded in x1 around inf 65.4%

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

   5. Taylor expanded in x1 around inf 65.4%

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

   if -3.19999999999999968e166 < x2 < 2.6000000000000001e84

   1. Initial program 69.3%

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

   3. Taylor expanded in x1 around 0 51.3%

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

   4. Taylor expanded in x1 around 0 67.9%

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

   5. Taylor expanded in x1 around 0 75.7%

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

   6. Taylor expanded in x2 around 0 75.5%

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

      1. *-commutative 75.5%

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

   8. Simplified 75.5%

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

4. Final simplification 72.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq -3.2 \cdot 10^{+166} \lor \neg \left(x2 \leq 2.6 \cdot 10^{+84}\right):\\ \;\;\;\;x1 \cdot \left(2 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 - x1 \cdot 9\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 31.9% accurate, 6.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -1.9 \cdot 10^{-44} \lor \neg \left(x1 \leq 0.62\right):\\ \;\;\;\;9 + \left(x1 \cdot 2 + \left(x1 \cdot x2\right) \cdot -12\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x2 \cdot -6\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x1 -1.9e-44) (not (<= x1 0.62)))
   (+ 9.0 (+ (* x1 2.0) (* (* x1 x2) -12.0)))
   (+ x1 (* x2 -6.0))))

C

double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -1.9e-44) || !(x1 <= 0.62)) {
		tmp = 9.0 + ((x1 * 2.0) + ((x1 * x2) * -12.0));
	} else {
		tmp = x1 + (x2 * -6.0);
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if ((x1 <= (-1.9d-44)) .or. (.not. (x1 <= 0.62d0))) then
        tmp = 9.0d0 + ((x1 * 2.0d0) + ((x1 * x2) * (-12.0d0)))
    else
        tmp = x1 + (x2 * (-6.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -1.9e-44) || !(x1 <= 0.62)) {
		tmp = 9.0 + ((x1 * 2.0) + ((x1 * x2) * -12.0));
	} else {
		tmp = x1 + (x2 * -6.0);
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x1 <= -1.9e-44) or not (x1 <= 0.62):
		tmp = 9.0 + ((x1 * 2.0) + ((x1 * x2) * -12.0))
	else:
		tmp = x1 + (x2 * -6.0)
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x1 <= -1.9e-44) || !(x1 <= 0.62))
		tmp = Float64(9.0 + Float64(Float64(x1 * 2.0) + Float64(Float64(x1 * x2) * -12.0)));
	else
		tmp = Float64(x1 + Float64(x2 * -6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x1 <= -1.9e-44) || ~((x1 <= 0.62)))
		tmp = 9.0 + ((x1 * 2.0) + ((x1 * x2) * -12.0));
	else
		tmp = x1 + (x2 * -6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x1, -1.9e-44], N[Not[LessEqual[x1, 0.62]], $MachinePrecision]], N[(9.0 + N[(N[(x1 * 2.0), $MachinePrecision] + N[(N[(x1 * x2), $MachinePrecision] * -12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x1 < -1.9e-44 or 0.619999999999999996 < x1

   1. Initial program 42.9%

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

   3. Taylor expanded in x1 around 0 15.8%

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

   4. Taylor expanded in x1 around inf 25.5%

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

   5. Taylor expanded in x2 around 0 13.5%

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

   if -1.9e-44 < x1 < 0.619999999999999996

   1. Initial program 99.5%

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

   3. Taylor expanded in x1 around 0 86.4%

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

   4. Taylor expanded in x1 around 0 86.4%

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

   5. Taylor expanded in x1 around 0 50.1%

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

      1. *-commutative 50.1%

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

   7. Simplified 50.1%

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

4. Final simplification 31.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.9 \cdot 10^{-44} \lor \neg \left(x1 \leq 0.62\right):\\ \;\;\;\;9 + \left(x1 \cdot 2 + \left(x1 \cdot x2\right) \cdot -12\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x2 \cdot -6\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 26.1% accurate, 25.4× speedup

Math

\[\begin{array}{l} \\ x1 + x2 \cdot -6 \end{array} \]

FPCore

(FPCore (x1 x2) :precision binary64 (+ x1 (* x2 -6.0)))

C

double code(double x1, double x2) {
	return x1 + (x2 * -6.0);
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    code = x1 + (x2 * (-6.0d0))
end function

Java

public static double code(double x1, double x2) {
	return x1 + (x2 * -6.0);
}

Python

def code(x1, x2):
	return x1 + (x2 * -6.0)

Julia

function code(x1, x2)
	return Float64(x1 + Float64(x2 * -6.0))
end

MATLAB

function tmp = code(x1, x2)
	tmp = x1 + (x2 * -6.0);
end

Wolfram

code[x1_, x2_] := N[(x1 + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 70.3%

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

3. Taylor expanded in x1 around 0 50.0%

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

4. Taylor expanded in x1 around 0 63.6%

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

5. Taylor expanded in x1 around 0 26.0%

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

   1. *-commutative 26.0%

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

7. Simplified 26.0%

   \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]
8. Add Preprocessing

Alternative 19: 3.4% accurate, 25.4× speedup

Math

\[\begin{array}{l} \\ x1 \cdot 2 + 9 \end{array} \]

FPCore

(FPCore (x1 x2) :precision binary64 (+ (* x1 2.0) 9.0))

C

double code(double x1, double x2) {
	return (x1 * 2.0) + 9.0;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    code = (x1 * 2.0d0) + 9.0d0
end function

Java

public static double code(double x1, double x2) {
	return (x1 * 2.0) + 9.0;
}

Python

def code(x1, x2):
	return (x1 * 2.0) + 9.0

Julia

function code(x1, x2)
	return Float64(Float64(x1 * 2.0) + 9.0)
end

MATLAB

function tmp = code(x1, x2)
	tmp = (x1 * 2.0) + 9.0;
end

Wolfram

code[x1_, x2_] := N[(N[(x1 * 2.0), $MachinePrecision] + 9.0), $MachinePrecision]

Derivation

1. Initial program 70.3%

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

3. Taylor expanded in x1 around 0 50.0%

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

4. Taylor expanded in x1 around inf 25.4%

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

5. Taylor expanded in x2 around 0 3.6%

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

   1. *-commutative 3.6%

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

7. Simplified 3.6%

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

8. Final simplification 3.6%

   \[\leadsto x1 \cdot 2 + 9 \]
9. Add Preprocessing

Alternative 20: 3.5% accurate, 127.0× speedup

Math

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

FPCore

(FPCore (x1 x2) :precision binary64 9.0)

C

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

Fortran

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

Java

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

Python

def code(x1, x2):
	return 9.0

Julia

function code(x1, x2)
	return 9.0
end

MATLAB

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

Wolfram

code[x1_, x2_] := 9.0

Derivation

1. Initial program 70.3%

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

3. Taylor expanded in x1 around 0 50.0%

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

4. Taylor expanded in x1 around inf 25.4%

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

5. Taylor expanded in x1 around 0 3.5%

   \[\leadsto \color{blue}{9} \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024096 
(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))))))