Rosa's FloatVsDoubleBenchmark

Percentage Accurate: 69.4% → 99.5%

Time: 1.5min

Alternatives: 26

Speedup: 4.4×

• 47.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 69.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := 3 \cdot \left(x1 \cdot x1\right)\\ t_2 := x1 \cdot \left(x1 \cdot 3\right)\\ t_3 := \frac{\left(t\_2 + 2 \cdot x2\right) - x1}{t\_0}\\ t_4 := \frac{\mathsf{fma}\left(x1, x1 \cdot 3, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}\\ \mathbf{if}\;x1 + \left(\left(x1 + \left(\left(t\_0 \cdot \left(\left(t\_3 \cdot \left(x1 \cdot 2\right)\right) \cdot \left(t\_3 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(t\_3 \cdot 4 - 6\right)\right) + t\_2 \cdot t\_3\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 3 \cdot \frac{\left(t\_2 - 2 \cdot x2\right) - x1}{t\_0}\right) \leq \infty:\\ \;\;\;\;x1 + \mathsf{fma}\left(3, \frac{t\_1 - \mathsf{fma}\left(2, x2, x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}, x1 + \mathsf{fma}\left(\mathsf{fma}\left(x1, x1, 1\right), \mathsf{fma}\left(x1, x1 \cdot \mathsf{fma}\left(t\_4, 4, -6\right), \left(x1 \cdot \left(2 \cdot t\_4\right)\right) \cdot \left(t\_4 + -3\right)\right), \mathsf{fma}\left(t\_1, t\_4, {x1}^{3}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;{\left({\left(\mathsf{fma}\left(x2, -6, x1\right)\right)}^{3}\right)}^{0.3333333333333333}\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ (* x1 x1) 1.0))
        (t_1 (* 3.0 (* x1 x1)))
        (t_2 (* x1 (* x1 3.0)))
        (t_3 (/ (- (+ t_2 (* 2.0 x2)) x1) t_0))
        (t_4 (/ (- (fma x1 (* x1 3.0) (* 2.0 x2)) x1) (fma x1 x1 1.0))))
   (if (<=
        (+
         x1
         (+
          (+
           x1
           (+
            (+
             (*
              t_0
              (+
               (* (* t_3 (* x1 2.0)) (- t_3 3.0))
               (* (* x1 x1) (- (* t_3 4.0) 6.0))))
             (* t_2 t_3))
            (* x1 (* x1 x1))))
          (* 3.0 (/ (- (- t_2 (* 2.0 x2)) x1) t_0))))
        INFINITY)
     (+
      x1
      (fma
       3.0
       (/ (- t_1 (fma 2.0 x2 x1)) (fma x1 x1 1.0))
       (+
        x1
        (fma
         (fma x1 x1 1.0)
         (fma x1 (* x1 (fma t_4 4.0 -6.0)) (* (* x1 (* 2.0 t_4)) (+ t_4 -3.0)))
         (fma t_1 t_4 (pow x1 3.0))))))
     (pow (pow (fma x2 -6.0 x1) 3.0) 0.3333333333333333))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = 3.0 * (x1 * x1);
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = ((t_2 + (2.0 * x2)) - x1) / t_0;
	double t_4 = (fma(x1, (x1 * 3.0), (2.0 * x2)) - x1) / fma(x1, x1, 1.0);
	double tmp;
	if ((x1 + ((x1 + (((t_0 * (((t_3 * (x1 * 2.0)) * (t_3 - 3.0)) + ((x1 * x1) * ((t_3 * 4.0) - 6.0)))) + (t_2 * t_3)) + (x1 * (x1 * x1)))) + (3.0 * (((t_2 - (2.0 * x2)) - x1) / t_0)))) <= ((double) INFINITY)) {
		tmp = x1 + fma(3.0, ((t_1 - fma(2.0, x2, x1)) / fma(x1, x1, 1.0)), (x1 + fma(fma(x1, x1, 1.0), fma(x1, (x1 * fma(t_4, 4.0, -6.0)), ((x1 * (2.0 * t_4)) * (t_4 + -3.0))), fma(t_1, t_4, pow(x1, 3.0)))));
	} else {
		tmp = pow(pow(fma(x2, -6.0, x1), 3.0), 0.3333333333333333);
	}
	return tmp;
}

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * x1) + 1.0)
	t_1 = Float64(3.0 * Float64(x1 * x1))
	t_2 = Float64(x1 * Float64(x1 * 3.0))
	t_3 = Float64(Float64(Float64(t_2 + Float64(2.0 * x2)) - x1) / t_0)
	t_4 = Float64(Float64(fma(x1, Float64(x1 * 3.0), Float64(2.0 * x2)) - x1) / fma(x1, x1, 1.0))
	tmp = 0.0
	if (Float64(x1 + Float64(Float64(x1 + Float64(Float64(Float64(t_0 * Float64(Float64(Float64(t_3 * Float64(x1 * 2.0)) * Float64(t_3 - 3.0)) + Float64(Float64(x1 * x1) * Float64(Float64(t_3 * 4.0) - 6.0)))) + Float64(t_2 * t_3)) + Float64(x1 * Float64(x1 * x1)))) + Float64(3.0 * Float64(Float64(Float64(t_2 - Float64(2.0 * x2)) - x1) / t_0)))) <= Inf)
		tmp = Float64(x1 + fma(3.0, Float64(Float64(t_1 - fma(2.0, x2, x1)) / fma(x1, x1, 1.0)), Float64(x1 + fma(fma(x1, x1, 1.0), fma(x1, Float64(x1 * fma(t_4, 4.0, -6.0)), Float64(Float64(x1 * Float64(2.0 * t_4)) * Float64(t_4 + -3.0))), fma(t_1, t_4, (x1 ^ 3.0))))));
	else
		tmp = (fma(x2, -6.0, x1) ^ 3.0) ^ 0.3333333333333333;
	end
	return tmp
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$1 = N[(3.0 * N[(x1 * x1), $MachinePrecision]), $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$0), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(x1 * N[(x1 * 3.0), $MachinePrecision] + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x1 + N[(N[(x1 + N[(N[(N[(t$95$0 * N[(N[(N[(t$95$3 * N[(x1 * 2.0), $MachinePrecision]), $MachinePrecision] * N[(t$95$3 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$3 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$2 * t$95$3), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(N[(N[(t$95$2 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(x1 + N[(3.0 * N[(N[(t$95$1 - 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$4 * 4.0 + -6.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * N[(2.0 * t$95$4), $MachinePrecision]), $MachinePrecision] * N[(t$95$4 + -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$1 * t$95$4 + N[Power[x1, 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[Power[N[Power[N[(x2 * -6.0 + x1), $MachinePrecision], 3.0], $MachinePrecision], 0.3333333333333333], $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 99.6%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in x1 around 0 1.3%

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

   4. Taylor expanded in x1 around 0 4.9%

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

      1. *-commutative 4.9%

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

   6. Simplified 4.9%

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

      1. add-cbrt-cube 48.7%

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

      2. pow1/3 100.0%

         \[\leadsto \color{blue}{{\left(\left(\left(x1 + x2 \cdot -6\right) \cdot \left(x1 + x2 \cdot -6\right)\right) \cdot \left(x1 + x2 \cdot -6\right)\right)}^{0.3333333333333333}} \]

      3. pow3 100.0%

         \[\leadsto {\color{blue}{\left({\left(x1 + x2 \cdot -6\right)}^{3}\right)}}^{0.3333333333333333} \]

      4. +-commutative 100.0%

         \[\leadsto {\left({\color{blue}{\left(x2 \cdot -6 + x1\right)}}^{3}\right)}^{0.3333333333333333} \]

      5. fma-define 100.0%

         \[\leadsto {\left({\color{blue}{\left(\mathsf{fma}\left(x2, -6, x1\right)\right)}}^{3}\right)}^{0.3333333333333333} \]

   8. Applied egg-rr 100.0%

      \[\leadsto \color{blue}{{\left({\left(\mathsf{fma}\left(x2, -6, x1\right)\right)}^{3}\right)}^{0.3333333333333333}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 + \left(\left(x1 + \left(\left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot \left(x1 \cdot 2\right)\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right)\right) + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \leq \infty:\\ \;\;\;\;x1 + \mathsf{fma}\left(3, \frac{3 \cdot \left(x1 \cdot x1\right) - \mathsf{fma}\left(2, x2, x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}, x1 + \mathsf{fma}\left(\mathsf{fma}\left(x1, x1, 1\right), \mathsf{fma}\left(x1, x1 \cdot \mathsf{fma}\left(\frac{\mathsf{fma}\left(x1, x1 \cdot 3, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}, 4, -6\right), \left(x1 \cdot \left(2 \cdot \frac{\mathsf{fma}\left(x1, x1 \cdot 3, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}\right)\right) \cdot \left(\frac{\mathsf{fma}\left(x1, x1 \cdot 3, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)} + -3\right)\right), \mathsf{fma}\left(3 \cdot \left(x1 \cdot x1\right), \frac{\mathsf{fma}\left(x1, x1 \cdot 3, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}, {x1}^{3}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;{\left({\left(\mathsf{fma}\left(x2, -6, x1\right)\right)}^{3}\right)}^{0.3333333333333333}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 99.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot x1\right)\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := x1 \cdot x1 + 1\\ t_3 := 3 \cdot \frac{\left(t\_1 - 2 \cdot x2\right) - x1}{t\_2}\\ t_4 := \frac{\left(t\_1 + 2 \cdot x2\right) - x1}{t\_2}\\ t_5 := t\_4 \cdot \left(x1 \cdot 2\right)\\ t_6 := t\_1 \cdot t\_4\\ \mathbf{if}\;x1 + \left(\left(x1 + \left(\left(t\_2 \cdot \left(t\_5 \cdot \left(t\_4 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(t\_4 \cdot 4 - 6\right)\right) + t\_6\right) + t\_0\right)\right) + t\_3\right) \leq \infty:\\ \;\;\;\;x1 + \left(t\_3 + \left(x1 + \left(t\_0 + \left(t\_6 + t\_2 \cdot \left(t\_5 \cdot \left(\mathsf{fma}\left(3, {x1}^{2}, 2 \cdot x2 - x1\right) \cdot \frac{1}{\mathsf{fma}\left(x1, x1, 1\right)} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(2 \cdot x2 + 3 \cdot {x1}^{2}\right) - x1}{t\_2} - 6\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;{\left({\left(\mathsf{fma}\left(x2, -6, x1\right)\right)}^{3}\right)}^{0.3333333333333333}\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 x1)))
        (t_1 (* x1 (* x1 3.0)))
        (t_2 (+ (* x1 x1) 1.0))
        (t_3 (* 3.0 (/ (- (- t_1 (* 2.0 x2)) x1) t_2)))
        (t_4 (/ (- (+ t_1 (* 2.0 x2)) x1) t_2))
        (t_5 (* t_4 (* x1 2.0)))
        (t_6 (* t_1 t_4)))
   (if (<=
        (+
         x1
         (+
          (+
           x1
           (+
            (+
             (* t_2 (+ (* t_5 (- t_4 3.0)) (* (* x1 x1) (- (* t_4 4.0) 6.0))))
             t_6)
            t_0))
          t_3))
        INFINITY)
     (+
      x1
      (+
       t_3
       (+
        x1
        (+
         t_0
         (+
          t_6
          (*
           t_2
           (+
            (*
             t_5
             (-
              (*
               (fma 3.0 (pow x1 2.0) (- (* 2.0 x2) x1))
               (/ 1.0 (fma x1 x1 1.0)))
              3.0))
            (*
             (* x1 x1)
             (-
              (* 4.0 (/ (- (+ (* 2.0 x2) (* 3.0 (pow x1 2.0))) x1) t_2))
              6.0)))))))))
     (pow (pow (fma x2 -6.0 x1) 3.0) 0.3333333333333333))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * x1);
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = 3.0 * (((t_1 - (2.0 * x2)) - x1) / t_2);
	double t_4 = ((t_1 + (2.0 * x2)) - x1) / t_2;
	double t_5 = t_4 * (x1 * 2.0);
	double t_6 = t_1 * t_4;
	double tmp;
	if ((x1 + ((x1 + (((t_2 * ((t_5 * (t_4 - 3.0)) + ((x1 * x1) * ((t_4 * 4.0) - 6.0)))) + t_6) + t_0)) + t_3)) <= ((double) INFINITY)) {
		tmp = x1 + (t_3 + (x1 + (t_0 + (t_6 + (t_2 * ((t_5 * ((fma(3.0, pow(x1, 2.0), ((2.0 * x2) - x1)) * (1.0 / fma(x1, x1, 1.0))) - 3.0)) + ((x1 * x1) * ((4.0 * ((((2.0 * x2) + (3.0 * pow(x1, 2.0))) - x1) / t_2)) - 6.0))))))));
	} else {
		tmp = pow(pow(fma(x2, -6.0, x1), 3.0), 0.3333333333333333);
	}
	return tmp;
}

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * x1))
	t_1 = Float64(x1 * Float64(x1 * 3.0))
	t_2 = Float64(Float64(x1 * x1) + 1.0)
	t_3 = Float64(3.0 * Float64(Float64(Float64(t_1 - Float64(2.0 * x2)) - x1) / t_2))
	t_4 = Float64(Float64(Float64(t_1 + Float64(2.0 * x2)) - x1) / t_2)
	t_5 = Float64(t_4 * Float64(x1 * 2.0))
	t_6 = Float64(t_1 * t_4)
	tmp = 0.0
	if (Float64(x1 + Float64(Float64(x1 + Float64(Float64(Float64(t_2 * Float64(Float64(t_5 * Float64(t_4 - 3.0)) + Float64(Float64(x1 * x1) * Float64(Float64(t_4 * 4.0) - 6.0)))) + t_6) + t_0)) + t_3)) <= Inf)
		tmp = Float64(x1 + Float64(t_3 + Float64(x1 + Float64(t_0 + Float64(t_6 + Float64(t_2 * Float64(Float64(t_5 * Float64(Float64(fma(3.0, (x1 ^ 2.0), Float64(Float64(2.0 * x2) - x1)) * Float64(1.0 / fma(x1, x1, 1.0))) - 3.0)) + Float64(Float64(x1 * x1) * Float64(Float64(4.0 * Float64(Float64(Float64(Float64(2.0 * x2) + Float64(3.0 * (x1 ^ 2.0))) - x1) / t_2)) - 6.0)))))))));
	else
		tmp = (fma(x2, -6.0, x1) ^ 3.0) ^ 0.3333333333333333;
	end
	return tmp
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$3 = N[(3.0 * N[(N[(N[(t$95$1 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(t$95$1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]}, Block[{t$95$5 = N[(t$95$4 * N[(x1 * 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(t$95$1 * t$95$4), $MachinePrecision]}, If[LessEqual[N[(x1 + N[(N[(x1 + N[(N[(N[(t$95$2 * N[(N[(t$95$5 * N[(t$95$4 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$4 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$6), $MachinePrecision] + t$95$0), $MachinePrecision]), $MachinePrecision] + t$95$3), $MachinePrecision]), $MachinePrecision], Infinity], N[(x1 + N[(t$95$3 + N[(x1 + N[(t$95$0 + N[(t$95$6 + N[(t$95$2 * N[(N[(t$95$5 * N[(N[(N[(3.0 * N[Power[x1, 2.0], $MachinePrecision] + N[(N[(2.0 * x2), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision] * N[(1.0 / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(4.0 * N[(N[(N[(N[(2.0 * x2), $MachinePrecision] + N[(3.0 * N[Power[x1, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[Power[N[Power[N[(x2 * -6.0 + x1), $MachinePrecision], 3.0], $MachinePrecision], 0.3333333333333333], $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. Step-by-step derivation

      1. fma-define 99.4%

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

      2. div-inv 99.4%

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

      3. associate--l+ 99.4%

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

      4. associate-*r* 99.4%

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

      5. fma-define 99.4%

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

      6. pow2 99.4%

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

   4. Applied egg-rr 99.4%

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

   5. Taylor expanded in x1 around 0 99.5%

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

   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 0 1.3%

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

   4. Taylor expanded in x1 around 0 4.9%

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

      1. *-commutative 4.9%

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

   6. Simplified 4.9%

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

      1. add-cbrt-cube 48.7%

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

      2. pow1/3 100.0%

         \[\leadsto \color{blue}{{\left(\left(\left(x1 + x2 \cdot -6\right) \cdot \left(x1 + x2 \cdot -6\right)\right) \cdot \left(x1 + x2 \cdot -6\right)\right)}^{0.3333333333333333}} \]

      3. pow3 100.0%

         \[\leadsto {\color{blue}{\left({\left(x1 + x2 \cdot -6\right)}^{3}\right)}}^{0.3333333333333333} \]

      4. +-commutative 100.0%

         \[\leadsto {\left({\color{blue}{\left(x2 \cdot -6 + x1\right)}}^{3}\right)}^{0.3333333333333333} \]

      5. fma-define 100.0%

         \[\leadsto {\left({\color{blue}{\left(\mathsf{fma}\left(x2, -6, x1\right)\right)}}^{3}\right)}^{0.3333333333333333} \]

   8. Applied egg-rr 100.0%

      \[\leadsto \color{blue}{{\left({\left(\mathsf{fma}\left(x2, -6, x1\right)\right)}^{3}\right)}^{0.3333333333333333}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 + \left(\left(x1 + \left(\left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot \left(x1 \cdot 2\right)\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right)\right) + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \leq \infty:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot \left(x1 \cdot 2\right)\right) \cdot \left(\mathsf{fma}\left(3, {x1}^{2}, 2 \cdot x2 - x1\right) \cdot \frac{1}{\mathsf{fma}\left(x1, x1, 1\right)} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(2 \cdot x2 + 3 \cdot {x1}^{2}\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;{\left({\left(\mathsf{fma}\left(x2, -6, x1\right)\right)}^{3}\right)}^{0.3333333333333333}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 99.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot x1\right)\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := 3 \cdot {x1}^{2}\\ t_3 := x1 \cdot x1 + 1\\ t_4 := 3 \cdot \frac{\left(t\_1 - 2 \cdot x2\right) - x1}{t\_3}\\ t_5 := \frac{\left(t\_1 + 2 \cdot x2\right) - x1}{t\_3}\\ t_6 := t\_5 \cdot \left(x1 \cdot 2\right)\\ t_7 := t\_1 \cdot t\_5\\ \mathbf{if}\;x1 + \left(\left(x1 + \left(\left(t\_3 \cdot \left(t\_6 \cdot \left(t\_5 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(t\_5 \cdot 4 - 6\right)\right) + t\_7\right) + t\_0\right)\right) + t\_4\right) \leq \infty:\\ \;\;\;\;x1 + \left(t\_4 + \left(x1 + \left(t\_0 + \left(t\_7 + t\_3 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(2 \cdot x2 + t\_2\right) - x1}{t\_3} - 6\right) + t\_6 \cdot \left(\frac{\mathsf{fma}\left(2, x2, t\_2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)} - 3\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;{\left({\left(\mathsf{fma}\left(x2, -6, x1\right)\right)}^{3}\right)}^{0.3333333333333333}\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 x1)))
        (t_1 (* x1 (* x1 3.0)))
        (t_2 (* 3.0 (pow x1 2.0)))
        (t_3 (+ (* x1 x1) 1.0))
        (t_4 (* 3.0 (/ (- (- t_1 (* 2.0 x2)) x1) t_3)))
        (t_5 (/ (- (+ t_1 (* 2.0 x2)) x1) t_3))
        (t_6 (* t_5 (* x1 2.0)))
        (t_7 (* t_1 t_5)))
   (if (<=
        (+
         x1
         (+
          (+
           x1
           (+
            (+
             (* t_3 (+ (* t_6 (- t_5 3.0)) (* (* x1 x1) (- (* t_5 4.0) 6.0))))
             t_7)
            t_0))
          t_4))
        INFINITY)
     (+
      x1
      (+
       t_4
       (+
        x1
        (+
         t_0
         (+
          t_7
          (*
           t_3
           (+
            (* (* x1 x1) (- (* 4.0 (/ (- (+ (* 2.0 x2) t_2) x1) t_3)) 6.0))
            (* t_6 (- (/ (- (fma 2.0 x2 t_2) x1) (fma x1 x1 1.0)) 3.0)))))))))
     (pow (pow (fma x2 -6.0 x1) 3.0) 0.3333333333333333))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * x1);
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = 3.0 * pow(x1, 2.0);
	double t_3 = (x1 * x1) + 1.0;
	double t_4 = 3.0 * (((t_1 - (2.0 * x2)) - x1) / t_3);
	double t_5 = ((t_1 + (2.0 * x2)) - x1) / t_3;
	double t_6 = t_5 * (x1 * 2.0);
	double t_7 = t_1 * t_5;
	double tmp;
	if ((x1 + ((x1 + (((t_3 * ((t_6 * (t_5 - 3.0)) + ((x1 * x1) * ((t_5 * 4.0) - 6.0)))) + t_7) + t_0)) + t_4)) <= ((double) INFINITY)) {
		tmp = x1 + (t_4 + (x1 + (t_0 + (t_7 + (t_3 * (((x1 * x1) * ((4.0 * ((((2.0 * x2) + t_2) - x1) / t_3)) - 6.0)) + (t_6 * (((fma(2.0, x2, t_2) - x1) / fma(x1, x1, 1.0)) - 3.0))))))));
	} else {
		tmp = pow(pow(fma(x2, -6.0, x1), 3.0), 0.3333333333333333);
	}
	return tmp;
}

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * x1))
	t_1 = Float64(x1 * Float64(x1 * 3.0))
	t_2 = Float64(3.0 * (x1 ^ 2.0))
	t_3 = Float64(Float64(x1 * x1) + 1.0)
	t_4 = Float64(3.0 * Float64(Float64(Float64(t_1 - Float64(2.0 * x2)) - x1) / t_3))
	t_5 = Float64(Float64(Float64(t_1 + Float64(2.0 * x2)) - x1) / t_3)
	t_6 = Float64(t_5 * Float64(x1 * 2.0))
	t_7 = Float64(t_1 * t_5)
	tmp = 0.0
	if (Float64(x1 + Float64(Float64(x1 + Float64(Float64(Float64(t_3 * Float64(Float64(t_6 * Float64(t_5 - 3.0)) + Float64(Float64(x1 * x1) * Float64(Float64(t_5 * 4.0) - 6.0)))) + t_7) + t_0)) + t_4)) <= Inf)
		tmp = Float64(x1 + Float64(t_4 + Float64(x1 + Float64(t_0 + Float64(t_7 + Float64(t_3 * Float64(Float64(Float64(x1 * x1) * Float64(Float64(4.0 * Float64(Float64(Float64(Float64(2.0 * x2) + t_2) - x1) / t_3)) - 6.0)) + Float64(t_6 * Float64(Float64(Float64(fma(2.0, x2, t_2) - x1) / fma(x1, x1, 1.0)) - 3.0)))))))));
	else
		tmp = (fma(x2, -6.0, x1) ^ 3.0) ^ 0.3333333333333333;
	end
	return tmp
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(3.0 * N[Power[x1, 2.0], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$4 = N[(3.0 * N[(N[(N[(t$95$1 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(N[(t$95$1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$3), $MachinePrecision]}, Block[{t$95$6 = N[(t$95$5 * N[(x1 * 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(t$95$1 * t$95$5), $MachinePrecision]}, If[LessEqual[N[(x1 + N[(N[(x1 + N[(N[(N[(t$95$3 * N[(N[(t$95$6 * N[(t$95$5 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$5 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$7), $MachinePrecision] + t$95$0), $MachinePrecision]), $MachinePrecision] + t$95$4), $MachinePrecision]), $MachinePrecision], Infinity], N[(x1 + N[(t$95$4 + N[(x1 + N[(t$95$0 + N[(t$95$7 + N[(t$95$3 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(N[(4.0 * N[(N[(N[(N[(2.0 * x2), $MachinePrecision] + t$95$2), $MachinePrecision] - x1), $MachinePrecision] / t$95$3), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] + N[(t$95$6 * N[(N[(N[(N[(2.0 * x2 + t$95$2), $MachinePrecision] - x1), $MachinePrecision] / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[Power[N[Power[N[(x2 * -6.0 + x1), $MachinePrecision], 3.0], $MachinePrecision], 0.3333333333333333], $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. Step-by-step derivation

      1. fma-define 99.4%

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

      2. div-inv 99.4%

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

      3. associate--l+ 99.4%

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

      4. associate-*r* 99.4%

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

      5. fma-define 99.4%

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

      6. pow2 99.4%

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

   4. Applied egg-rr 99.4%

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

   5. Taylor expanded in x1 around 0 99.5%

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

      1. fma-define 99.5%

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

      2. un-div-inv 99.4%

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

      3. fma-undefine 99.4%

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

      4. pow2 99.4%

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

      5. associate-*l* 99.4%

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

      6. associate--l+ 99.4%

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

      7. div-sub 99.4%

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

      8. +-commutative 99.4%

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

      9. fma-define 99.4%

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

      10. associate-*l* 99.4%

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

      11. pow2 99.4%

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

      12. fma-define 99.4%

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

      13. fma-define 99.4%

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

   7. Applied egg-rr 99.4%

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

      1. div-sub 99.4%

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

   9. Simplified 99.4%

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

   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 0 1.3%

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

   4. Taylor expanded in x1 around 0 4.9%

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

      1. *-commutative 4.9%

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

   6. Simplified 4.9%

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

      1. add-cbrt-cube 48.7%

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

      2. pow1/3 100.0%

         \[\leadsto \color{blue}{{\left(\left(\left(x1 + x2 \cdot -6\right) \cdot \left(x1 + x2 \cdot -6\right)\right) \cdot \left(x1 + x2 \cdot -6\right)\right)}^{0.3333333333333333}} \]

      3. pow3 100.0%

         \[\leadsto {\color{blue}{\left({\left(x1 + x2 \cdot -6\right)}^{3}\right)}}^{0.3333333333333333} \]

      4. +-commutative 100.0%

         \[\leadsto {\left({\color{blue}{\left(x2 \cdot -6 + x1\right)}}^{3}\right)}^{0.3333333333333333} \]

      5. fma-define 100.0%

         \[\leadsto {\left({\color{blue}{\left(\mathsf{fma}\left(x2, -6, x1\right)\right)}}^{3}\right)}^{0.3333333333333333} \]

   8. Applied egg-rr 100.0%

      \[\leadsto \color{blue}{{\left({\left(\mathsf{fma}\left(x2, -6, x1\right)\right)}^{3}\right)}^{0.3333333333333333}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 + \left(\left(x1 + \left(\left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot \left(x1 \cdot 2\right)\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right)\right) + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \leq \infty:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(2 \cdot x2 + 3 \cdot {x1}^{2}\right) - x1}{x1 \cdot x1 + 1} - 6\right) + \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot \left(x1 \cdot 2\right)\right) \cdot \left(\frac{\mathsf{fma}\left(2, x2, 3 \cdot {x1}^{2}\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)} - 3\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;{\left({\left(\mathsf{fma}\left(x2, -6, x1\right)\right)}^{3}\right)}^{0.3333333333333333}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 99.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot x1\right)\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := x1 \cdot x1 + 1\\ t_3 := 3 \cdot \frac{\left(t\_1 - 2 \cdot x2\right) - x1}{t\_2}\\ t_4 := \frac{\left(t\_1 + 2 \cdot x2\right) - x1}{t\_2}\\ t_5 := t\_4 \cdot \left(x1 \cdot 2\right)\\ t_6 := \left(x1 \cdot x1\right) \cdot \left(t\_4 \cdot 4 - 6\right)\\ t_7 := t\_1 \cdot t\_4\\ \mathbf{if}\;x1 + \left(\left(x1 + \left(\left(t\_2 \cdot \left(t\_5 \cdot \left(t\_4 - 3\right) + t\_6\right) + t\_7\right) + t\_0\right)\right) + t\_3\right) \leq \infty:\\ \;\;\;\;x1 + \left(t\_3 + \left(x1 + \left(t\_0 + \left(t\_7 + t\_2 \cdot \left(t\_6 + t\_5 \cdot \left(\mathsf{fma}\left(3, {x1}^{2}, 2 \cdot x2 - x1\right) \cdot \frac{1}{\mathsf{fma}\left(x1, x1, 1\right)} - 3\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;{\left({\left(\mathsf{fma}\left(x2, -6, x1\right)\right)}^{3}\right)}^{0.3333333333333333}\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 x1)))
        (t_1 (* x1 (* x1 3.0)))
        (t_2 (+ (* x1 x1) 1.0))
        (t_3 (* 3.0 (/ (- (- t_1 (* 2.0 x2)) x1) t_2)))
        (t_4 (/ (- (+ t_1 (* 2.0 x2)) x1) t_2))
        (t_5 (* t_4 (* x1 2.0)))
        (t_6 (* (* x1 x1) (- (* t_4 4.0) 6.0)))
        (t_7 (* t_1 t_4)))
   (if (<=
        (+
         x1
         (+ (+ x1 (+ (+ (* t_2 (+ (* t_5 (- t_4 3.0)) t_6)) t_7) t_0)) t_3))
        INFINITY)
     (+
      x1
      (+
       t_3
       (+
        x1
        (+
         t_0
         (+
          t_7
          (*
           t_2
           (+
            t_6
            (*
             t_5
             (-
              (*
               (fma 3.0 (pow x1 2.0) (- (* 2.0 x2) x1))
               (/ 1.0 (fma x1 x1 1.0)))
              3.0)))))))))
     (pow (pow (fma x2 -6.0 x1) 3.0) 0.3333333333333333))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * x1);
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = 3.0 * (((t_1 - (2.0 * x2)) - x1) / t_2);
	double t_4 = ((t_1 + (2.0 * x2)) - x1) / t_2;
	double t_5 = t_4 * (x1 * 2.0);
	double t_6 = (x1 * x1) * ((t_4 * 4.0) - 6.0);
	double t_7 = t_1 * t_4;
	double tmp;
	if ((x1 + ((x1 + (((t_2 * ((t_5 * (t_4 - 3.0)) + t_6)) + t_7) + t_0)) + t_3)) <= ((double) INFINITY)) {
		tmp = x1 + (t_3 + (x1 + (t_0 + (t_7 + (t_2 * (t_6 + (t_5 * ((fma(3.0, pow(x1, 2.0), ((2.0 * x2) - x1)) * (1.0 / fma(x1, x1, 1.0))) - 3.0))))))));
	} else {
		tmp = pow(pow(fma(x2, -6.0, x1), 3.0), 0.3333333333333333);
	}
	return tmp;
}

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * x1))
	t_1 = Float64(x1 * Float64(x1 * 3.0))
	t_2 = Float64(Float64(x1 * x1) + 1.0)
	t_3 = Float64(3.0 * Float64(Float64(Float64(t_1 - Float64(2.0 * x2)) - x1) / t_2))
	t_4 = Float64(Float64(Float64(t_1 + Float64(2.0 * x2)) - x1) / t_2)
	t_5 = Float64(t_4 * Float64(x1 * 2.0))
	t_6 = Float64(Float64(x1 * x1) * Float64(Float64(t_4 * 4.0) - 6.0))
	t_7 = Float64(t_1 * t_4)
	tmp = 0.0
	if (Float64(x1 + Float64(Float64(x1 + Float64(Float64(Float64(t_2 * Float64(Float64(t_5 * Float64(t_4 - 3.0)) + t_6)) + t_7) + t_0)) + t_3)) <= Inf)
		tmp = Float64(x1 + Float64(t_3 + Float64(x1 + Float64(t_0 + Float64(t_7 + Float64(t_2 * Float64(t_6 + Float64(t_5 * Float64(Float64(fma(3.0, (x1 ^ 2.0), Float64(Float64(2.0 * x2) - x1)) * Float64(1.0 / fma(x1, x1, 1.0))) - 3.0)))))))));
	else
		tmp = (fma(x2, -6.0, x1) ^ 3.0) ^ 0.3333333333333333;
	end
	return tmp
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$3 = N[(3.0 * N[(N[(N[(t$95$1 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(t$95$1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]}, Block[{t$95$5 = N[(t$95$4 * N[(x1 * 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$4 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(t$95$1 * t$95$4), $MachinePrecision]}, If[LessEqual[N[(x1 + N[(N[(x1 + N[(N[(N[(t$95$2 * N[(N[(t$95$5 * N[(t$95$4 - 3.0), $MachinePrecision]), $MachinePrecision] + t$95$6), $MachinePrecision]), $MachinePrecision] + t$95$7), $MachinePrecision] + t$95$0), $MachinePrecision]), $MachinePrecision] + t$95$3), $MachinePrecision]), $MachinePrecision], Infinity], N[(x1 + N[(t$95$3 + N[(x1 + N[(t$95$0 + N[(t$95$7 + N[(t$95$2 * N[(t$95$6 + N[(t$95$5 * N[(N[(N[(3.0 * N[Power[x1, 2.0], $MachinePrecision] + N[(N[(2.0 * x2), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision] * N[(1.0 / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[Power[N[Power[N[(x2 * -6.0 + x1), $MachinePrecision], 3.0], $MachinePrecision], 0.3333333333333333], $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. Step-by-step derivation

      1. fma-define 99.4%

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

      2. div-inv 99.4%

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

      3. associate--l+ 99.4%

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

      4. associate-*r* 99.4%

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

      5. fma-define 99.4%

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

      6. pow2 99.4%

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

   4. Applied egg-rr 99.4%

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

   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 0 1.3%

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

   4. Taylor expanded in x1 around 0 4.9%

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

      1. *-commutative 4.9%

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

   6. Simplified 4.9%

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

      1. add-cbrt-cube 48.7%

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

      2. pow1/3 100.0%

         \[\leadsto \color{blue}{{\left(\left(\left(x1 + x2 \cdot -6\right) \cdot \left(x1 + x2 \cdot -6\right)\right) \cdot \left(x1 + x2 \cdot -6\right)\right)}^{0.3333333333333333}} \]

      3. pow3 100.0%

         \[\leadsto {\color{blue}{\left({\left(x1 + x2 \cdot -6\right)}^{3}\right)}}^{0.3333333333333333} \]

      4. +-commutative 100.0%

         \[\leadsto {\left({\color{blue}{\left(x2 \cdot -6 + x1\right)}}^{3}\right)}^{0.3333333333333333} \]

      5. fma-define 100.0%

         \[\leadsto {\left({\color{blue}{\left(\mathsf{fma}\left(x2, -6, x1\right)\right)}}^{3}\right)}^{0.3333333333333333} \]

   8. Applied egg-rr 100.0%

      \[\leadsto \color{blue}{{\left({\left(\mathsf{fma}\left(x2, -6, x1\right)\right)}^{3}\right)}^{0.3333333333333333}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 + \left(\left(x1 + \left(\left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot \left(x1 \cdot 2\right)\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right)\right) + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \leq \infty:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right) + \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot \left(x1 \cdot 2\right)\right) \cdot \left(\mathsf{fma}\left(3, {x1}^{2}, 2 \cdot x2 - x1\right) \cdot \frac{1}{\mathsf{fma}\left(x1, x1, 1\right)} - 3\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;{\left({\left(\mathsf{fma}\left(x2, -6, x1\right)\right)}^{3}\right)}^{0.3333333333333333}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 99.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot x1\right)\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := x1 \cdot x1 + 1\\ t_3 := 3 \cdot \frac{\left(t\_1 - 2 \cdot x2\right) - x1}{t\_2}\\ t_4 := \frac{\left(t\_1 + 2 \cdot x2\right) - x1}{t\_2}\\ t_5 := \left(t\_4 \cdot \left(x1 \cdot 2\right)\right) \cdot \left(t\_4 - 3\right)\\ t_6 := t\_1 \cdot t\_4\\ \mathbf{if}\;x1 + \left(\left(x1 + \left(\left(t\_2 \cdot \left(t\_5 + \left(x1 \cdot x1\right) \cdot \left(t\_4 \cdot 4 - 6\right)\right) + t\_6\right) + t\_0\right)\right) + t\_3\right) \leq \infty:\\ \;\;\;\;x1 + \left(t\_3 + \left(x1 + \left(t\_0 + \left(t\_6 + t\_2 \cdot \left(t\_5 + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\mathsf{fma}\left(3, {x1}^{2}, 2 \cdot x2 - x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)} - 6\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;{\left({\left(\mathsf{fma}\left(x2, -6, x1\right)\right)}^{3}\right)}^{0.3333333333333333}\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 x1)))
        (t_1 (* x1 (* x1 3.0)))
        (t_2 (+ (* x1 x1) 1.0))
        (t_3 (* 3.0 (/ (- (- t_1 (* 2.0 x2)) x1) t_2)))
        (t_4 (/ (- (+ t_1 (* 2.0 x2)) x1) t_2))
        (t_5 (* (* t_4 (* x1 2.0)) (- t_4 3.0)))
        (t_6 (* t_1 t_4)))
   (if (<=
        (+
         x1
         (+
          (+
           x1
           (+ (+ (* t_2 (+ t_5 (* (* x1 x1) (- (* t_4 4.0) 6.0)))) t_6) t_0))
          t_3))
        INFINITY)
     (+
      x1
      (+
       t_3
       (+
        x1
        (+
         t_0
         (+
          t_6
          (*
           t_2
           (+
            t_5
            (*
             (* x1 x1)
             (-
              (*
               4.0
               (/ (fma 3.0 (pow x1 2.0) (- (* 2.0 x2) x1)) (fma x1 x1 1.0)))
              6.0)))))))))
     (pow (pow (fma x2 -6.0 x1) 3.0) 0.3333333333333333))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * x1);
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = 3.0 * (((t_1 - (2.0 * x2)) - x1) / t_2);
	double t_4 = ((t_1 + (2.0 * x2)) - x1) / t_2;
	double t_5 = (t_4 * (x1 * 2.0)) * (t_4 - 3.0);
	double t_6 = t_1 * t_4;
	double tmp;
	if ((x1 + ((x1 + (((t_2 * (t_5 + ((x1 * x1) * ((t_4 * 4.0) - 6.0)))) + t_6) + t_0)) + t_3)) <= ((double) INFINITY)) {
		tmp = x1 + (t_3 + (x1 + (t_0 + (t_6 + (t_2 * (t_5 + ((x1 * x1) * ((4.0 * (fma(3.0, pow(x1, 2.0), ((2.0 * x2) - x1)) / fma(x1, x1, 1.0))) - 6.0))))))));
	} else {
		tmp = pow(pow(fma(x2, -6.0, x1), 3.0), 0.3333333333333333);
	}
	return tmp;
}

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * x1))
	t_1 = Float64(x1 * Float64(x1 * 3.0))
	t_2 = Float64(Float64(x1 * x1) + 1.0)
	t_3 = Float64(3.0 * Float64(Float64(Float64(t_1 - Float64(2.0 * x2)) - x1) / t_2))
	t_4 = Float64(Float64(Float64(t_1 + Float64(2.0 * x2)) - x1) / t_2)
	t_5 = Float64(Float64(t_4 * Float64(x1 * 2.0)) * Float64(t_4 - 3.0))
	t_6 = Float64(t_1 * t_4)
	tmp = 0.0
	if (Float64(x1 + Float64(Float64(x1 + Float64(Float64(Float64(t_2 * Float64(t_5 + Float64(Float64(x1 * x1) * Float64(Float64(t_4 * 4.0) - 6.0)))) + t_6) + t_0)) + t_3)) <= Inf)
		tmp = Float64(x1 + Float64(t_3 + Float64(x1 + Float64(t_0 + Float64(t_6 + Float64(t_2 * Float64(t_5 + Float64(Float64(x1 * x1) * Float64(Float64(4.0 * Float64(fma(3.0, (x1 ^ 2.0), Float64(Float64(2.0 * x2) - x1)) / fma(x1, x1, 1.0))) - 6.0)))))))));
	else
		tmp = (fma(x2, -6.0, x1) ^ 3.0) ^ 0.3333333333333333;
	end
	return tmp
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$3 = N[(3.0 * N[(N[(N[(t$95$1 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(t$95$1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]}, Block[{t$95$5 = N[(N[(t$95$4 * N[(x1 * 2.0), $MachinePrecision]), $MachinePrecision] * N[(t$95$4 - 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(t$95$1 * t$95$4), $MachinePrecision]}, If[LessEqual[N[(x1 + N[(N[(x1 + N[(N[(N[(t$95$2 * N[(t$95$5 + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$4 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$6), $MachinePrecision] + t$95$0), $MachinePrecision]), $MachinePrecision] + t$95$3), $MachinePrecision]), $MachinePrecision], Infinity], N[(x1 + N[(t$95$3 + N[(x1 + N[(t$95$0 + N[(t$95$6 + N[(t$95$2 * N[(t$95$5 + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(4.0 * N[(N[(3.0 * N[Power[x1, 2.0], $MachinePrecision] + N[(N[(2.0 * x2), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision] / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[Power[N[Power[N[(x2 * -6.0 + x1), $MachinePrecision], 3.0], $MachinePrecision], 0.3333333333333333], $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. Step-by-step derivation

      1. fma-define 99.4%

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

      2. *-un-lft-identity 99.4%

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

      3. associate--l+ 99.4%

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

      4. associate-*r* 99.4%

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

      5. fma-define 99.4%

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

      6. pow2 99.4%

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

   4. Applied egg-rr 99.4%

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

      1. *-lft-identity 99.4%

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

   6. Simplified 99.4%

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

   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 0 1.3%

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

   4. Taylor expanded in x1 around 0 4.9%

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

      1. *-commutative 4.9%

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

   6. Simplified 4.9%

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

      1. add-cbrt-cube 48.7%

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

      2. pow1/3 100.0%

         \[\leadsto \color{blue}{{\left(\left(\left(x1 + x2 \cdot -6\right) \cdot \left(x1 + x2 \cdot -6\right)\right) \cdot \left(x1 + x2 \cdot -6\right)\right)}^{0.3333333333333333}} \]

      3. pow3 100.0%

         \[\leadsto {\color{blue}{\left({\left(x1 + x2 \cdot -6\right)}^{3}\right)}}^{0.3333333333333333} \]

      4. +-commutative 100.0%

         \[\leadsto {\left({\color{blue}{\left(x2 \cdot -6 + x1\right)}}^{3}\right)}^{0.3333333333333333} \]

      5. fma-define 100.0%

         \[\leadsto {\left({\color{blue}{\left(\mathsf{fma}\left(x2, -6, x1\right)\right)}}^{3}\right)}^{0.3333333333333333} \]

   8. Applied egg-rr 100.0%

      \[\leadsto \color{blue}{{\left({\left(\mathsf{fma}\left(x2, -6, x1\right)\right)}^{3}\right)}^{0.3333333333333333}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 + \left(\left(x1 + \left(\left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot \left(x1 \cdot 2\right)\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right)\right) + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \leq \infty:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot \left(x1 \cdot 2\right)\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\mathsf{fma}\left(3, {x1}^{2}, 2 \cdot x2 - x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)} - 6\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;{\left({\left(\mathsf{fma}\left(x2, -6, x1\right)\right)}^{3}\right)}^{0.3333333333333333}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 99.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := \frac{\left(t\_1 + 2 \cdot x2\right) - x1}{t\_0}\\ t_3 := x1 + \left(\left(x1 + \left(\left(t\_0 \cdot \left(\left(t\_2 \cdot \left(x1 \cdot 2\right)\right) \cdot \left(t\_2 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(t\_2 \cdot 4 - 6\right)\right) + t\_1 \cdot t\_2\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 3 \cdot \frac{\left(t\_1 - 2 \cdot x2\right) - x1}{t\_0}\right)\\ \mathbf{if}\;t\_3 \leq \infty:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;{\left({\left(\mathsf{fma}\left(x2, -6, x1\right)\right)}^{3}\right)}^{0.3333333333333333}\\ \end{array} \end{array} \]

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
         (+
          x1
          (+
           (+
            x1
            (+
             (+
              (*
               t_0
               (+
                (* (* t_2 (* x1 2.0)) (- t_2 3.0))
                (* (* x1 x1) (- (* t_2 4.0) 6.0))))
              (* t_1 t_2))
             (* x1 (* x1 x1))))
           (* 3.0 (/ (- (- t_1 (* 2.0 x2)) x1) t_0))))))
   (if (<= t_3 INFINITY)
     t_3
     (pow (pow (fma x2 -6.0 x1) 3.0) 0.3333333333333333))))

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 = x1 + ((x1 + (((t_0 * (((t_2 * (x1 * 2.0)) * (t_2 - 3.0)) + ((x1 * x1) * ((t_2 * 4.0) - 6.0)))) + (t_1 * t_2)) + (x1 * (x1 * x1)))) + (3.0 * (((t_1 - (2.0 * x2)) - x1) / t_0)));
	double tmp;
	if (t_3 <= ((double) INFINITY)) {
		tmp = t_3;
	} else {
		tmp = pow(pow(fma(x2, -6.0, x1), 3.0), 0.3333333333333333);
	}
	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(x1 + Float64(Float64(x1 + Float64(Float64(Float64(t_0 * Float64(Float64(Float64(t_2 * Float64(x1 * 2.0)) * Float64(t_2 - 3.0)) + Float64(Float64(x1 * x1) * Float64(Float64(t_2 * 4.0) - 6.0)))) + Float64(t_1 * t_2)) + Float64(x1 * Float64(x1 * x1)))) + Float64(3.0 * Float64(Float64(Float64(t_1 - Float64(2.0 * x2)) - x1) / t_0))))
	tmp = 0.0
	if (t_3 <= Inf)
		tmp = t_3;
	else
		tmp = (fma(x2, -6.0, x1) ^ 3.0) ^ 0.3333333333333333;
	end
	return tmp
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(t$95$1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]}, Block[{t$95$3 = N[(x1 + N[(N[(x1 + N[(N[(N[(t$95$0 * N[(N[(N[(t$95$2 * N[(x1 * 2.0), $MachinePrecision]), $MachinePrecision] * N[(t$95$2 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$2 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$1 * t$95$2), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(N[(N[(t$95$1 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, Infinity], t$95$3, N[Power[N[Power[N[(x2 * -6.0 + x1), $MachinePrecision], 3.0], $MachinePrecision], 0.3333333333333333], $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 0 1.3%

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

   4. Taylor expanded in x1 around 0 4.9%

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

      1. *-commutative 4.9%

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

   6. Simplified 4.9%

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

      1. add-cbrt-cube 48.7%

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

      2. pow1/3 100.0%

         \[\leadsto \color{blue}{{\left(\left(\left(x1 + x2 \cdot -6\right) \cdot \left(x1 + x2 \cdot -6\right)\right) \cdot \left(x1 + x2 \cdot -6\right)\right)}^{0.3333333333333333}} \]

      3. pow3 100.0%

         \[\leadsto {\color{blue}{\left({\left(x1 + x2 \cdot -6\right)}^{3}\right)}}^{0.3333333333333333} \]

      4. +-commutative 100.0%

         \[\leadsto {\left({\color{blue}{\left(x2 \cdot -6 + x1\right)}}^{3}\right)}^{0.3333333333333333} \]

      5. fma-define 100.0%

         \[\leadsto {\left({\color{blue}{\left(\mathsf{fma}\left(x2, -6, x1\right)\right)}}^{3}\right)}^{0.3333333333333333} \]

   8. Applied egg-rr 100.0%

      \[\leadsto \color{blue}{{\left({\left(\mathsf{fma}\left(x2, -6, x1\right)\right)}^{3}\right)}^{0.3333333333333333}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 + \left(\left(x1 + \left(\left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot \left(x1 \cdot 2\right)\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right)\right) + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \leq \infty:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot \left(x1 \cdot 2\right)\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right)\right) + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right)\\ \mathbf{else}:\\ \;\;\;\;{\left({\left(\mathsf{fma}\left(x2, -6, x1\right)\right)}^{3}\right)}^{0.3333333333333333}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 95.4% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (+.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 0 1.3%

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

   4. Taylor expanded in x1 around 0 39.7%

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

   5. Taylor expanded in x1 around 0 54.3%

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

      1. associate-*r* 54.3%

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

      2. cancel-sign-sub-inv 54.3%

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

      3. metadata-eval 54.3%

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

      4. *-commutative 54.3%

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

      5. *-commutative 54.3%

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

   7. Simplified 54.3%

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

   8. Taylor expanded in x2 around 0 90.5%

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

4. Final simplification 96.7%

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

Alternative 8: 97.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(2 \cdot x2 - 3\right)\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := x1 \cdot x1 + 1\\ t_3 := \frac{\left(t\_1 + 2 \cdot x2\right) - x1}{t\_2}\\ \mathbf{if}\;x1 \leq -4.5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 - 2\right)\right)\\ \mathbf{elif}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t\_1 - 2 \cdot x2\right) - x1}{t\_2} + \left(x1 + x1 \cdot \left(t\_0 + x1 \cdot \left(\left(x2 \cdot 8 + x1 \cdot \left(\left(t\_0 + 6 \cdot \left(3 + x2 \cdot -2\right)\right) - 3\right)\right) - 3\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 7 \cdot 10^{+83}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(t\_2 \cdot \left(\left(t\_3 \cdot \left(x1 \cdot 2\right)\right) \cdot \left(t\_3 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(t\_3 \cdot 4 - 6\right)\right) + 3 \cdot t\_1\right)\right)\right) + 3 \cdot \left(x2 \cdot -2 - x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot -3\right) + x2 \cdot \left(x1 \cdot 6 + \frac{x1 \cdot \left(x1 \cdot 3 + 9\right)}{x2}\right)\right) - 2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* 6.0 (- (* 2.0 x2) 3.0)))
        (t_1 (* x1 (* x1 3.0)))
        (t_2 (+ (* x1 x1) 1.0))
        (t_3 (/ (- (+ t_1 (* 2.0 x2)) x1) t_2)))
   (if (<= x1 -4.5e+153)
     (+ x1 (+ (* x2 -6.0) (* x1 (- (* x1 9.0) 2.0))))
     (if (<= x1 -5.6e+102)
       (+
        x1
        (+
         (* 3.0 (/ (- (- t_1 (* 2.0 x2)) x1) t_2))
         (+
          x1
          (*
           x1
           (+
            t_0
            (*
             x1
             (-
              (+ (* x2 8.0) (* x1 (- (+ t_0 (* 6.0 (+ 3.0 (* x2 -2.0)))) 3.0)))
              3.0)))))))
       (if (<= x1 7e+83)
         (+
          x1
          (+
           (+
            x1
            (+
             (* x1 (* x1 x1))
             (+
              (*
               t_2
               (+
                (* (* t_3 (* x1 2.0)) (- t_3 3.0))
                (* (* x1 x1) (- (* t_3 4.0) 6.0))))
              (* 3.0 t_1))))
           (* 3.0 (- (* x2 -2.0) x1))))
         (+
          x1
          (+
           (* x2 -6.0)
           (*
            x1
            (-
             (+
              (* 4.0 (* x2 -3.0))
              (* x2 (+ (* x1 6.0) (/ (* x1 (+ (* x1 3.0) 9.0)) x2))))
             2.0)))))))))

C

double code(double x1, double x2) {
	double t_0 = 6.0 * ((2.0 * x2) - 3.0);
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = ((t_1 + (2.0 * x2)) - x1) / t_2;
	double tmp;
	if (x1 <= -4.5e+153) {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) - 2.0)));
	} else if (x1 <= -5.6e+102) {
		tmp = x1 + ((3.0 * (((t_1 - (2.0 * x2)) - x1) / t_2)) + (x1 + (x1 * (t_0 + (x1 * (((x2 * 8.0) + (x1 * ((t_0 + (6.0 * (3.0 + (x2 * -2.0)))) - 3.0))) - 3.0))))));
	} else if (x1 <= 7e+83) {
		tmp = x1 + ((x1 + ((x1 * (x1 * x1)) + ((t_2 * (((t_3 * (x1 * 2.0)) * (t_3 - 3.0)) + ((x1 * x1) * ((t_3 * 4.0) - 6.0)))) + (3.0 * t_1)))) + (3.0 * ((x2 * -2.0) - x1)));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * (((4.0 * (x2 * -3.0)) + (x2 * ((x1 * 6.0) + ((x1 * ((x1 * 3.0) + 9.0)) / x2)))) - 2.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_0 = 6.0d0 * ((2.0d0 * x2) - 3.0d0)
    t_1 = x1 * (x1 * 3.0d0)
    t_2 = (x1 * x1) + 1.0d0
    t_3 = ((t_1 + (2.0d0 * x2)) - x1) / t_2
    if (x1 <= (-4.5d+153)) then
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * ((x1 * 9.0d0) - 2.0d0)))
    else if (x1 <= (-5.6d+102)) then
        tmp = x1 + ((3.0d0 * (((t_1 - (2.0d0 * x2)) - x1) / t_2)) + (x1 + (x1 * (t_0 + (x1 * (((x2 * 8.0d0) + (x1 * ((t_0 + (6.0d0 * (3.0d0 + (x2 * (-2.0d0))))) - 3.0d0))) - 3.0d0))))))
    else if (x1 <= 7d+83) then
        tmp = x1 + ((x1 + ((x1 * (x1 * x1)) + ((t_2 * (((t_3 * (x1 * 2.0d0)) * (t_3 - 3.0d0)) + ((x1 * x1) * ((t_3 * 4.0d0) - 6.0d0)))) + (3.0d0 * t_1)))) + (3.0d0 * ((x2 * (-2.0d0)) - x1)))
    else
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * (((4.0d0 * (x2 * (-3.0d0))) + (x2 * ((x1 * 6.0d0) + ((x1 * ((x1 * 3.0d0) + 9.0d0)) / x2)))) - 2.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = 6.0 * ((2.0 * x2) - 3.0);
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = ((t_1 + (2.0 * x2)) - x1) / t_2;
	double tmp;
	if (x1 <= -4.5e+153) {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) - 2.0)));
	} else if (x1 <= -5.6e+102) {
		tmp = x1 + ((3.0 * (((t_1 - (2.0 * x2)) - x1) / t_2)) + (x1 + (x1 * (t_0 + (x1 * (((x2 * 8.0) + (x1 * ((t_0 + (6.0 * (3.0 + (x2 * -2.0)))) - 3.0))) - 3.0))))));
	} else if (x1 <= 7e+83) {
		tmp = x1 + ((x1 + ((x1 * (x1 * x1)) + ((t_2 * (((t_3 * (x1 * 2.0)) * (t_3 - 3.0)) + ((x1 * x1) * ((t_3 * 4.0) - 6.0)))) + (3.0 * t_1)))) + (3.0 * ((x2 * -2.0) - x1)));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * (((4.0 * (x2 * -3.0)) + (x2 * ((x1 * 6.0) + ((x1 * ((x1 * 3.0) + 9.0)) / x2)))) - 2.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = 6.0 * ((2.0 * x2) - 3.0)
	t_1 = x1 * (x1 * 3.0)
	t_2 = (x1 * x1) + 1.0
	t_3 = ((t_1 + (2.0 * x2)) - x1) / t_2
	tmp = 0
	if x1 <= -4.5e+153:
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) - 2.0)))
	elif x1 <= -5.6e+102:
		tmp = x1 + ((3.0 * (((t_1 - (2.0 * x2)) - x1) / t_2)) + (x1 + (x1 * (t_0 + (x1 * (((x2 * 8.0) + (x1 * ((t_0 + (6.0 * (3.0 + (x2 * -2.0)))) - 3.0))) - 3.0))))))
	elif x1 <= 7e+83:
		tmp = x1 + ((x1 + ((x1 * (x1 * x1)) + ((t_2 * (((t_3 * (x1 * 2.0)) * (t_3 - 3.0)) + ((x1 * x1) * ((t_3 * 4.0) - 6.0)))) + (3.0 * t_1)))) + (3.0 * ((x2 * -2.0) - x1)))
	else:
		tmp = x1 + ((x2 * -6.0) + (x1 * (((4.0 * (x2 * -3.0)) + (x2 * ((x1 * 6.0) + ((x1 * ((x1 * 3.0) + 9.0)) / x2)))) - 2.0)))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(6.0 * Float64(Float64(2.0 * x2) - 3.0))
	t_1 = Float64(x1 * Float64(x1 * 3.0))
	t_2 = Float64(Float64(x1 * x1) + 1.0)
	t_3 = Float64(Float64(Float64(t_1 + Float64(2.0 * x2)) - x1) / t_2)
	tmp = 0.0
	if (x1 <= -4.5e+153)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(x1 * 9.0) - 2.0))));
	elseif (x1 <= -5.6e+102)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_1 - Float64(2.0 * x2)) - x1) / t_2)) + Float64(x1 + Float64(x1 * Float64(t_0 + Float64(x1 * Float64(Float64(Float64(x2 * 8.0) + Float64(x1 * Float64(Float64(t_0 + Float64(6.0 * Float64(3.0 + Float64(x2 * -2.0)))) - 3.0))) - 3.0)))))));
	elseif (x1 <= 7e+83)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(t_2 * Float64(Float64(Float64(t_3 * Float64(x1 * 2.0)) * Float64(t_3 - 3.0)) + Float64(Float64(x1 * x1) * Float64(Float64(t_3 * 4.0) - 6.0)))) + Float64(3.0 * t_1)))) + Float64(3.0 * Float64(Float64(x2 * -2.0) - x1))));
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(Float64(4.0 * Float64(x2 * -3.0)) + Float64(x2 * Float64(Float64(x1 * 6.0) + Float64(Float64(x1 * Float64(Float64(x1 * 3.0) + 9.0)) / x2)))) - 2.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = 6.0 * ((2.0 * x2) - 3.0);
	t_1 = x1 * (x1 * 3.0);
	t_2 = (x1 * x1) + 1.0;
	t_3 = ((t_1 + (2.0 * x2)) - x1) / t_2;
	tmp = 0.0;
	if (x1 <= -4.5e+153)
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) - 2.0)));
	elseif (x1 <= -5.6e+102)
		tmp = x1 + ((3.0 * (((t_1 - (2.0 * x2)) - x1) / t_2)) + (x1 + (x1 * (t_0 + (x1 * (((x2 * 8.0) + (x1 * ((t_0 + (6.0 * (3.0 + (x2 * -2.0)))) - 3.0))) - 3.0))))));
	elseif (x1 <= 7e+83)
		tmp = x1 + ((x1 + ((x1 * (x1 * x1)) + ((t_2 * (((t_3 * (x1 * 2.0)) * (t_3 - 3.0)) + ((x1 * x1) * ((t_3 * 4.0) - 6.0)))) + (3.0 * t_1)))) + (3.0 * ((x2 * -2.0) - x1)));
	else
		tmp = x1 + ((x2 * -6.0) + (x1 * (((4.0 * (x2 * -3.0)) + (x2 * ((x1 * 6.0) + ((x1 * ((x1 * 3.0) + 9.0)) / x2)))) - 2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(6.0 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(t$95$1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]}, If[LessEqual[x1, -4.5e+153], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -5.6e+102], N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$1 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(x1 * N[(t$95$0 + N[(x1 * N[(N[(N[(x2 * 8.0), $MachinePrecision] + N[(x1 * N[(N[(t$95$0 + N[(6.0 * N[(3.0 + N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 7e+83], N[(x1 + N[(N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$2 * N[(N[(N[(t$95$3 * N[(x1 * 2.0), $MachinePrecision]), $MachinePrecision] * N[(t$95$3 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$3 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(N[(4.0 * N[(x2 * -3.0), $MachinePrecision]), $MachinePrecision] + N[(x2 * N[(N[(x1 * 6.0), $MachinePrecision] + N[(N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + 9.0), $MachinePrecision]), $MachinePrecision] / x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $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%

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

   5. Taylor expanded in x1 around 0 65.6%

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

      1. associate-*r* 65.6%

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

      2. cancel-sign-sub-inv 65.6%

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

      3. metadata-eval 65.6%

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

      4. *-commutative 65.6%

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

      5. *-commutative 65.6%

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

   7. Simplified 65.6%

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

   8. Taylor expanded in x2 around 0 100.0%

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

   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 inf 0.0%

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

   4. Taylor expanded in x1 around inf 0.0%

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

   5. Taylor expanded in x1 around 0 87.5%

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

   if -5.60000000000000037e102 < x1 < 6.99999999999999954e83

   1. Initial program 98.8%

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

   3. Taylor expanded in x1 around inf 96.8%

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

   4. Taylor expanded in x1 around 0 98.7%

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

      1. mul-1-neg 98.7%

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

      2. unsub-neg 98.7%

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

      3. *-commutative 98.7%

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

   6. Simplified 98.7%

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

   if 6.99999999999999954e83 < 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 83.4%

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

   5. Taylor expanded in x2 around inf 100.0%

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

   6. Taylor expanded in x2 around 0 100.0%

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

      1. *-commutative 100.0%

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

   8. Simplified 100.0%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4.5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 - 2\right)\right)\\ \mathbf{elif}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + x1 \cdot \left(6 \cdot \left(2 \cdot x2 - 3\right) + x1 \cdot \left(\left(x2 \cdot 8 + x1 \cdot \left(\left(6 \cdot \left(2 \cdot x2 - 3\right) + 6 \cdot \left(3 + x2 \cdot -2\right)\right) - 3\right)\right) - 3\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 7 \cdot 10^{+83}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot \left(x1 \cdot 2\right)\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right)\right) + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right)\right)\right)\right) + 3 \cdot \left(x2 \cdot -2 - x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot -3\right) + x2 \cdot \left(x1 \cdot 6 + \frac{x1 \cdot \left(x1 \cdot 3 + 9\right)}{x2}\right)\right) - 2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 95.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(2 \cdot x2 - 3\right)\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := x1 \cdot x1 + 1\\ t_3 := \frac{\left(t\_1 + 2 \cdot x2\right) - x1}{t\_2}\\ t_4 := 3 \cdot \frac{\left(t\_1 - 2 \cdot x2\right) - x1}{t\_2}\\ \mathbf{if}\;x1 \leq -4.4 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 - 2\right)\right)\\ \mathbf{elif}\;x1 \leq -4.4 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(t\_4 + \left(x1 + x1 \cdot \left(t\_0 + x1 \cdot \left(\left(x2 \cdot 8 + x1 \cdot \left(\left(t\_0 + 6 \cdot \left(3 + x2 \cdot -2\right)\right) - 3\right)\right) - 3\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 7 \cdot 10^{+83}:\\ \;\;\;\;x1 + \left(t\_4 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot t\_1 + t\_2 \cdot \left(\left(t\_3 \cdot \left(x1 \cdot 2\right)\right) \cdot \left(t\_3 - 3\right) + \left(x1 \cdot x1\right) \cdot 6\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot -3\right) + x2 \cdot \left(x1 \cdot 6 + \frac{x1 \cdot \left(x1 \cdot 3 + 9\right)}{x2}\right)\right) - 2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* 6.0 (- (* 2.0 x2) 3.0)))
        (t_1 (* x1 (* x1 3.0)))
        (t_2 (+ (* x1 x1) 1.0))
        (t_3 (/ (- (+ t_1 (* 2.0 x2)) x1) t_2))
        (t_4 (* 3.0 (/ (- (- t_1 (* 2.0 x2)) x1) t_2))))
   (if (<= x1 -4.4e+153)
     (+ x1 (+ (* x2 -6.0) (* x1 (- (* x1 9.0) 2.0))))
     (if (<= x1 -4.4e+102)
       (+
        x1
        (+
         t_4
         (+
          x1
          (*
           x1
           (+
            t_0
            (*
             x1
             (-
              (+ (* x2 8.0) (* x1 (- (+ t_0 (* 6.0 (+ 3.0 (* x2 -2.0)))) 3.0)))
              3.0)))))))
       (if (<= x1 7e+83)
         (+
          x1
          (+
           t_4
           (+
            x1
            (+
             (* x1 (* x1 x1))
             (+
              (* 3.0 t_1)
              (*
               t_2
               (+ (* (* t_3 (* x1 2.0)) (- t_3 3.0)) (* (* x1 x1) 6.0))))))))
         (+
          x1
          (+
           (* x2 -6.0)
           (*
            x1
            (-
             (+
              (* 4.0 (* x2 -3.0))
              (* x2 (+ (* x1 6.0) (/ (* x1 (+ (* x1 3.0) 9.0)) x2))))
             2.0)))))))))

C

double code(double x1, double x2) {
	double t_0 = 6.0 * ((2.0 * x2) - 3.0);
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = ((t_1 + (2.0 * x2)) - x1) / t_2;
	double t_4 = 3.0 * (((t_1 - (2.0 * x2)) - x1) / t_2);
	double tmp;
	if (x1 <= -4.4e+153) {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) - 2.0)));
	} else if (x1 <= -4.4e+102) {
		tmp = x1 + (t_4 + (x1 + (x1 * (t_0 + (x1 * (((x2 * 8.0) + (x1 * ((t_0 + (6.0 * (3.0 + (x2 * -2.0)))) - 3.0))) - 3.0))))));
	} else if (x1 <= 7e+83) {
		tmp = x1 + (t_4 + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_1) + (t_2 * (((t_3 * (x1 * 2.0)) * (t_3 - 3.0)) + ((x1 * x1) * 6.0)))))));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * (((4.0 * (x2 * -3.0)) + (x2 * ((x1 * 6.0) + ((x1 * ((x1 * 3.0) + 9.0)) / x2)))) - 2.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_0 = 6.0d0 * ((2.0d0 * x2) - 3.0d0)
    t_1 = x1 * (x1 * 3.0d0)
    t_2 = (x1 * x1) + 1.0d0
    t_3 = ((t_1 + (2.0d0 * x2)) - x1) / t_2
    t_4 = 3.0d0 * (((t_1 - (2.0d0 * x2)) - x1) / t_2)
    if (x1 <= (-4.4d+153)) then
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * ((x1 * 9.0d0) - 2.0d0)))
    else if (x1 <= (-4.4d+102)) then
        tmp = x1 + (t_4 + (x1 + (x1 * (t_0 + (x1 * (((x2 * 8.0d0) + (x1 * ((t_0 + (6.0d0 * (3.0d0 + (x2 * (-2.0d0))))) - 3.0d0))) - 3.0d0))))))
    else if (x1 <= 7d+83) then
        tmp = x1 + (t_4 + (x1 + ((x1 * (x1 * x1)) + ((3.0d0 * t_1) + (t_2 * (((t_3 * (x1 * 2.0d0)) * (t_3 - 3.0d0)) + ((x1 * x1) * 6.0d0)))))))
    else
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * (((4.0d0 * (x2 * (-3.0d0))) + (x2 * ((x1 * 6.0d0) + ((x1 * ((x1 * 3.0d0) + 9.0d0)) / x2)))) - 2.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = 6.0 * ((2.0 * x2) - 3.0);
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = ((t_1 + (2.0 * x2)) - x1) / t_2;
	double t_4 = 3.0 * (((t_1 - (2.0 * x2)) - x1) / t_2);
	double tmp;
	if (x1 <= -4.4e+153) {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) - 2.0)));
	} else if (x1 <= -4.4e+102) {
		tmp = x1 + (t_4 + (x1 + (x1 * (t_0 + (x1 * (((x2 * 8.0) + (x1 * ((t_0 + (6.0 * (3.0 + (x2 * -2.0)))) - 3.0))) - 3.0))))));
	} else if (x1 <= 7e+83) {
		tmp = x1 + (t_4 + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_1) + (t_2 * (((t_3 * (x1 * 2.0)) * (t_3 - 3.0)) + ((x1 * x1) * 6.0)))))));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * (((4.0 * (x2 * -3.0)) + (x2 * ((x1 * 6.0) + ((x1 * ((x1 * 3.0) + 9.0)) / x2)))) - 2.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = 6.0 * ((2.0 * x2) - 3.0)
	t_1 = x1 * (x1 * 3.0)
	t_2 = (x1 * x1) + 1.0
	t_3 = ((t_1 + (2.0 * x2)) - x1) / t_2
	t_4 = 3.0 * (((t_1 - (2.0 * x2)) - x1) / t_2)
	tmp = 0
	if x1 <= -4.4e+153:
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) - 2.0)))
	elif x1 <= -4.4e+102:
		tmp = x1 + (t_4 + (x1 + (x1 * (t_0 + (x1 * (((x2 * 8.0) + (x1 * ((t_0 + (6.0 * (3.0 + (x2 * -2.0)))) - 3.0))) - 3.0))))))
	elif x1 <= 7e+83:
		tmp = x1 + (t_4 + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_1) + (t_2 * (((t_3 * (x1 * 2.0)) * (t_3 - 3.0)) + ((x1 * x1) * 6.0)))))))
	else:
		tmp = x1 + ((x2 * -6.0) + (x1 * (((4.0 * (x2 * -3.0)) + (x2 * ((x1 * 6.0) + ((x1 * ((x1 * 3.0) + 9.0)) / x2)))) - 2.0)))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(6.0 * Float64(Float64(2.0 * x2) - 3.0))
	t_1 = Float64(x1 * Float64(x1 * 3.0))
	t_2 = Float64(Float64(x1 * x1) + 1.0)
	t_3 = Float64(Float64(Float64(t_1 + Float64(2.0 * x2)) - x1) / t_2)
	t_4 = Float64(3.0 * Float64(Float64(Float64(t_1 - Float64(2.0 * x2)) - x1) / t_2))
	tmp = 0.0
	if (x1 <= -4.4e+153)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(x1 * 9.0) - 2.0))));
	elseif (x1 <= -4.4e+102)
		tmp = Float64(x1 + Float64(t_4 + Float64(x1 + Float64(x1 * Float64(t_0 + Float64(x1 * Float64(Float64(Float64(x2 * 8.0) + Float64(x1 * Float64(Float64(t_0 + Float64(6.0 * Float64(3.0 + Float64(x2 * -2.0)))) - 3.0))) - 3.0)))))));
	elseif (x1 <= 7e+83)
		tmp = Float64(x1 + Float64(t_4 + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(3.0 * t_1) + Float64(t_2 * Float64(Float64(Float64(t_3 * Float64(x1 * 2.0)) * Float64(t_3 - 3.0)) + Float64(Float64(x1 * x1) * 6.0))))))));
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(Float64(4.0 * Float64(x2 * -3.0)) + Float64(x2 * Float64(Float64(x1 * 6.0) + Float64(Float64(x1 * Float64(Float64(x1 * 3.0) + 9.0)) / x2)))) - 2.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = 6.0 * ((2.0 * x2) - 3.0);
	t_1 = x1 * (x1 * 3.0);
	t_2 = (x1 * x1) + 1.0;
	t_3 = ((t_1 + (2.0 * x2)) - x1) / t_2;
	t_4 = 3.0 * (((t_1 - (2.0 * x2)) - x1) / t_2);
	tmp = 0.0;
	if (x1 <= -4.4e+153)
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) - 2.0)));
	elseif (x1 <= -4.4e+102)
		tmp = x1 + (t_4 + (x1 + (x1 * (t_0 + (x1 * (((x2 * 8.0) + (x1 * ((t_0 + (6.0 * (3.0 + (x2 * -2.0)))) - 3.0))) - 3.0))))));
	elseif (x1 <= 7e+83)
		tmp = x1 + (t_4 + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_1) + (t_2 * (((t_3 * (x1 * 2.0)) * (t_3 - 3.0)) + ((x1 * x1) * 6.0)))))));
	else
		tmp = x1 + ((x2 * -6.0) + (x1 * (((4.0 * (x2 * -3.0)) + (x2 * ((x1 * 6.0) + ((x1 * ((x1 * 3.0) + 9.0)) / x2)))) - 2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(6.0 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(t$95$1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(3.0 * N[(N[(N[(t$95$1 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -4.4e+153], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -4.4e+102], N[(x1 + N[(t$95$4 + N[(x1 + N[(x1 * N[(t$95$0 + N[(x1 * N[(N[(N[(x2 * 8.0), $MachinePrecision] + N[(x1 * N[(N[(t$95$0 + N[(6.0 * N[(3.0 + N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 7e+83], N[(x1 + N[(t$95$4 + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(3.0 * t$95$1), $MachinePrecision] + N[(t$95$2 * N[(N[(N[(t$95$3 * N[(x1 * 2.0), $MachinePrecision]), $MachinePrecision] * N[(t$95$3 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(N[(4.0 * N[(x2 * -3.0), $MachinePrecision]), $MachinePrecision] + N[(x2 * N[(N[(x1 * 6.0), $MachinePrecision] + N[(N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + 9.0), $MachinePrecision]), $MachinePrecision] / x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -4.3999999999999999e153

   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%

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

   5. Taylor expanded in x1 around 0 65.6%

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

      1. associate-*r* 65.6%

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

      2. cancel-sign-sub-inv 65.6%

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

      3. metadata-eval 65.6%

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

      4. *-commutative 65.6%

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

      5. *-commutative 65.6%

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

   7. Simplified 65.6%

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

   8. Taylor expanded in x2 around 0 100.0%

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

   if -4.3999999999999999e153 < x1 < -4.40000000000000015e102

   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 0.0%

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

   4. Taylor expanded in x1 around inf 0.0%

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

   5. Taylor expanded in x1 around 0 87.5%

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

   if -4.40000000000000015e102 < x1 < 6.99999999999999954e83

   1. Initial program 98.8%

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

   3. Taylor expanded in x1 around inf 96.8%

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

   4. Taylor expanded in x1 around inf 97.1%

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

   if 6.99999999999999954e83 < 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 83.4%

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

   5. Taylor expanded in x2 around inf 100.0%

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

   6. Taylor expanded in x2 around 0 100.0%

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

      1. *-commutative 100.0%

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

   8. Simplified 100.0%

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

4. Final simplification 97.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4.4 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 - 2\right)\right)\\ \mathbf{elif}\;x1 \leq -4.4 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + x1 \cdot \left(6 \cdot \left(2 \cdot x2 - 3\right) + x1 \cdot \left(\left(x2 \cdot 8 + x1 \cdot \left(\left(6 \cdot \left(2 \cdot x2 - 3\right) + 6 \cdot \left(3 + x2 \cdot -2\right)\right) - 3\right)\right) - 3\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 7 \cdot 10^{+83}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot \left(x1 \cdot 2\right)\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot 6\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot -3\right) + x2 \cdot \left(x1 \cdot 6 + \frac{x1 \cdot \left(x1 \cdot 3 + 9\right)}{x2}\right)\right) - 2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 94.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(2 \cdot x2 - 3\right)\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := x1 \cdot x1 + 1\\ t_3 := \frac{\left(t\_1 + 2 \cdot x2\right) - x1}{t\_2}\\ \mathbf{if}\;x1 \leq -4.4 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 - 2\right)\right)\\ \mathbf{elif}\;x1 \leq -4.3 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t\_1 - 2 \cdot x2\right) - x1}{t\_2} + \left(x1 + x1 \cdot \left(t\_0 + x1 \cdot \left(\left(x2 \cdot 8 + x1 \cdot \left(\left(t\_0 + 6 \cdot \left(3 + x2 \cdot -2\right)\right) - 3\right)\right) - 3\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 7 \cdot 10^{+83}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot t\_1 + t\_2 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(t\_3 \cdot 4 - 6\right) + \left(t\_3 - 3\right) \cdot \left(\left(2 \cdot x2 - x1\right) \cdot \left(x1 \cdot 2\right)\right)\right)\right)\right)\right) + \left(x2 \cdot -6 + x1 \cdot -3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot -3\right) + x2 \cdot \left(x1 \cdot 6 + \frac{x1 \cdot \left(x1 \cdot 3 + 9\right)}{x2}\right)\right) - 2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* 6.0 (- (* 2.0 x2) 3.0)))
        (t_1 (* x1 (* x1 3.0)))
        (t_2 (+ (* x1 x1) 1.0))
        (t_3 (/ (- (+ t_1 (* 2.0 x2)) x1) t_2)))
   (if (<= x1 -4.4e+153)
     (+ x1 (+ (* x2 -6.0) (* x1 (- (* x1 9.0) 2.0))))
     (if (<= x1 -4.3e+102)
       (+
        x1
        (+
         (* 3.0 (/ (- (- t_1 (* 2.0 x2)) x1) t_2))
         (+
          x1
          (*
           x1
           (+
            t_0
            (*
             x1
             (-
              (+ (* x2 8.0) (* x1 (- (+ t_0 (* 6.0 (+ 3.0 (* x2 -2.0)))) 3.0)))
              3.0)))))))
       (if (<= x1 7e+83)
         (+
          x1
          (+
           (+
            x1
            (+
             (* x1 (* x1 x1))
             (+
              (* 3.0 t_1)
              (*
               t_2
               (+
                (* (* x1 x1) (- (* t_3 4.0) 6.0))
                (* (- t_3 3.0) (* (- (* 2.0 x2) x1) (* x1 2.0))))))))
           (+ (* x2 -6.0) (* x1 -3.0))))
         (+
          x1
          (+
           (* x2 -6.0)
           (*
            x1
            (-
             (+
              (* 4.0 (* x2 -3.0))
              (* x2 (+ (* x1 6.0) (/ (* x1 (+ (* x1 3.0) 9.0)) x2))))
             2.0)))))))))

C

double code(double x1, double x2) {
	double t_0 = 6.0 * ((2.0 * x2) - 3.0);
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = ((t_1 + (2.0 * x2)) - x1) / t_2;
	double tmp;
	if (x1 <= -4.4e+153) {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) - 2.0)));
	} else if (x1 <= -4.3e+102) {
		tmp = x1 + ((3.0 * (((t_1 - (2.0 * x2)) - x1) / t_2)) + (x1 + (x1 * (t_0 + (x1 * (((x2 * 8.0) + (x1 * ((t_0 + (6.0 * (3.0 + (x2 * -2.0)))) - 3.0))) - 3.0))))));
	} else if (x1 <= 7e+83) {
		tmp = x1 + ((x1 + ((x1 * (x1 * x1)) + ((3.0 * t_1) + (t_2 * (((x1 * x1) * ((t_3 * 4.0) - 6.0)) + ((t_3 - 3.0) * (((2.0 * x2) - x1) * (x1 * 2.0)))))))) + ((x2 * -6.0) + (x1 * -3.0)));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * (((4.0 * (x2 * -3.0)) + (x2 * ((x1 * 6.0) + ((x1 * ((x1 * 3.0) + 9.0)) / x2)))) - 2.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_0 = 6.0d0 * ((2.0d0 * x2) - 3.0d0)
    t_1 = x1 * (x1 * 3.0d0)
    t_2 = (x1 * x1) + 1.0d0
    t_3 = ((t_1 + (2.0d0 * x2)) - x1) / t_2
    if (x1 <= (-4.4d+153)) then
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * ((x1 * 9.0d0) - 2.0d0)))
    else if (x1 <= (-4.3d+102)) then
        tmp = x1 + ((3.0d0 * (((t_1 - (2.0d0 * x2)) - x1) / t_2)) + (x1 + (x1 * (t_0 + (x1 * (((x2 * 8.0d0) + (x1 * ((t_0 + (6.0d0 * (3.0d0 + (x2 * (-2.0d0))))) - 3.0d0))) - 3.0d0))))))
    else if (x1 <= 7d+83) then
        tmp = x1 + ((x1 + ((x1 * (x1 * x1)) + ((3.0d0 * t_1) + (t_2 * (((x1 * x1) * ((t_3 * 4.0d0) - 6.0d0)) + ((t_3 - 3.0d0) * (((2.0d0 * x2) - x1) * (x1 * 2.0d0)))))))) + ((x2 * (-6.0d0)) + (x1 * (-3.0d0))))
    else
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * (((4.0d0 * (x2 * (-3.0d0))) + (x2 * ((x1 * 6.0d0) + ((x1 * ((x1 * 3.0d0) + 9.0d0)) / x2)))) - 2.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = 6.0 * ((2.0 * x2) - 3.0);
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = ((t_1 + (2.0 * x2)) - x1) / t_2;
	double tmp;
	if (x1 <= -4.4e+153) {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) - 2.0)));
	} else if (x1 <= -4.3e+102) {
		tmp = x1 + ((3.0 * (((t_1 - (2.0 * x2)) - x1) / t_2)) + (x1 + (x1 * (t_0 + (x1 * (((x2 * 8.0) + (x1 * ((t_0 + (6.0 * (3.0 + (x2 * -2.0)))) - 3.0))) - 3.0))))));
	} else if (x1 <= 7e+83) {
		tmp = x1 + ((x1 + ((x1 * (x1 * x1)) + ((3.0 * t_1) + (t_2 * (((x1 * x1) * ((t_3 * 4.0) - 6.0)) + ((t_3 - 3.0) * (((2.0 * x2) - x1) * (x1 * 2.0)))))))) + ((x2 * -6.0) + (x1 * -3.0)));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * (((4.0 * (x2 * -3.0)) + (x2 * ((x1 * 6.0) + ((x1 * ((x1 * 3.0) + 9.0)) / x2)))) - 2.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = 6.0 * ((2.0 * x2) - 3.0)
	t_1 = x1 * (x1 * 3.0)
	t_2 = (x1 * x1) + 1.0
	t_3 = ((t_1 + (2.0 * x2)) - x1) / t_2
	tmp = 0
	if x1 <= -4.4e+153:
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) - 2.0)))
	elif x1 <= -4.3e+102:
		tmp = x1 + ((3.0 * (((t_1 - (2.0 * x2)) - x1) / t_2)) + (x1 + (x1 * (t_0 + (x1 * (((x2 * 8.0) + (x1 * ((t_0 + (6.0 * (3.0 + (x2 * -2.0)))) - 3.0))) - 3.0))))))
	elif x1 <= 7e+83:
		tmp = x1 + ((x1 + ((x1 * (x1 * x1)) + ((3.0 * t_1) + (t_2 * (((x1 * x1) * ((t_3 * 4.0) - 6.0)) + ((t_3 - 3.0) * (((2.0 * x2) - x1) * (x1 * 2.0)))))))) + ((x2 * -6.0) + (x1 * -3.0)))
	else:
		tmp = x1 + ((x2 * -6.0) + (x1 * (((4.0 * (x2 * -3.0)) + (x2 * ((x1 * 6.0) + ((x1 * ((x1 * 3.0) + 9.0)) / x2)))) - 2.0)))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(6.0 * Float64(Float64(2.0 * x2) - 3.0))
	t_1 = Float64(x1 * Float64(x1 * 3.0))
	t_2 = Float64(Float64(x1 * x1) + 1.0)
	t_3 = Float64(Float64(Float64(t_1 + Float64(2.0 * x2)) - x1) / t_2)
	tmp = 0.0
	if (x1 <= -4.4e+153)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(x1 * 9.0) - 2.0))));
	elseif (x1 <= -4.3e+102)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_1 - Float64(2.0 * x2)) - x1) / t_2)) + Float64(x1 + Float64(x1 * Float64(t_0 + Float64(x1 * Float64(Float64(Float64(x2 * 8.0) + Float64(x1 * Float64(Float64(t_0 + Float64(6.0 * Float64(3.0 + Float64(x2 * -2.0)))) - 3.0))) - 3.0)))))));
	elseif (x1 <= 7e+83)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(3.0 * t_1) + Float64(t_2 * Float64(Float64(Float64(x1 * x1) * Float64(Float64(t_3 * 4.0) - 6.0)) + Float64(Float64(t_3 - 3.0) * Float64(Float64(Float64(2.0 * x2) - x1) * Float64(x1 * 2.0)))))))) + Float64(Float64(x2 * -6.0) + Float64(x1 * -3.0))));
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(Float64(4.0 * Float64(x2 * -3.0)) + Float64(x2 * Float64(Float64(x1 * 6.0) + Float64(Float64(x1 * Float64(Float64(x1 * 3.0) + 9.0)) / x2)))) - 2.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = 6.0 * ((2.0 * x2) - 3.0);
	t_1 = x1 * (x1 * 3.0);
	t_2 = (x1 * x1) + 1.0;
	t_3 = ((t_1 + (2.0 * x2)) - x1) / t_2;
	tmp = 0.0;
	if (x1 <= -4.4e+153)
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) - 2.0)));
	elseif (x1 <= -4.3e+102)
		tmp = x1 + ((3.0 * (((t_1 - (2.0 * x2)) - x1) / t_2)) + (x1 + (x1 * (t_0 + (x1 * (((x2 * 8.0) + (x1 * ((t_0 + (6.0 * (3.0 + (x2 * -2.0)))) - 3.0))) - 3.0))))));
	elseif (x1 <= 7e+83)
		tmp = x1 + ((x1 + ((x1 * (x1 * x1)) + ((3.0 * t_1) + (t_2 * (((x1 * x1) * ((t_3 * 4.0) - 6.0)) + ((t_3 - 3.0) * (((2.0 * x2) - x1) * (x1 * 2.0)))))))) + ((x2 * -6.0) + (x1 * -3.0)));
	else
		tmp = x1 + ((x2 * -6.0) + (x1 * (((4.0 * (x2 * -3.0)) + (x2 * ((x1 * 6.0) + ((x1 * ((x1 * 3.0) + 9.0)) / x2)))) - 2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(6.0 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(t$95$1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]}, If[LessEqual[x1, -4.4e+153], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -4.3e+102], N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$1 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(x1 * N[(t$95$0 + N[(x1 * N[(N[(N[(x2 * 8.0), $MachinePrecision] + N[(x1 * N[(N[(t$95$0 + N[(6.0 * N[(3.0 + N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 7e+83], N[(x1 + N[(N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(3.0 * t$95$1), $MachinePrecision] + N[(t$95$2 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$3 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$3 - 3.0), $MachinePrecision] * N[(N[(N[(2.0 * x2), $MachinePrecision] - x1), $MachinePrecision] * N[(x1 * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(N[(4.0 * N[(x2 * -3.0), $MachinePrecision]), $MachinePrecision] + N[(x2 * N[(N[(x1 * 6.0), $MachinePrecision] + N[(N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + 9.0), $MachinePrecision]), $MachinePrecision] / x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -4.3999999999999999e153

   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%

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

   5. Taylor expanded in x1 around 0 65.6%

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

      1. associate-*r* 65.6%

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

      2. cancel-sign-sub-inv 65.6%

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

      3. metadata-eval 65.6%

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

      4. *-commutative 65.6%

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

      5. *-commutative 65.6%

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

   7. Simplified 65.6%

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

   8. Taylor expanded in x2 around 0 100.0%

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

   if -4.3999999999999999e153 < x1 < -4.3000000000000001e102

   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 0.0%

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

   4. Taylor expanded in x1 around inf 0.0%

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

   5. Taylor expanded in x1 around 0 87.5%

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

   if -4.3000000000000001e102 < x1 < 6.99999999999999954e83

   1. Initial program 98.8%

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

   3. Taylor expanded in x1 around inf 96.8%

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

   4. Taylor expanded in x1 around 0 94.9%

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

      1. +-commutative 94.9%

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

      2. mul-1-neg 94.9%

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

      3. sub-neg 94.9%

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

   6. Simplified 94.9%

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

   7. Taylor expanded in x1 around 0 95.5%

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

   if 6.99999999999999954e83 < 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 83.4%

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

   5. Taylor expanded in x2 around inf 100.0%

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

   6. Taylor expanded in x2 around 0 100.0%

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

      1. *-commutative 100.0%

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

   8. Simplified 100.0%

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

4. Final simplification 96.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4.4 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 - 2\right)\right)\\ \mathbf{elif}\;x1 \leq -4.3 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + x1 \cdot \left(6 \cdot \left(2 \cdot x2 - 3\right) + x1 \cdot \left(\left(x2 \cdot 8 + x1 \cdot \left(\left(6 \cdot \left(2 \cdot x2 - 3\right) + 6 \cdot \left(3 + x2 \cdot -2\right)\right) - 3\right)\right) - 3\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 7 \cdot 10^{+83}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right) + \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) \cdot \left(\left(2 \cdot x2 - x1\right) \cdot \left(x1 \cdot 2\right)\right)\right)\right)\right)\right) + \left(x2 \cdot -6 + x1 \cdot -3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot -3\right) + x2 \cdot \left(x1 \cdot 6 + \frac{x1 \cdot \left(x1 \cdot 3 + 9\right)}{x2}\right)\right) - 2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 92.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := x1 \cdot \left(x1 \cdot 9 - 2\right)\\ t_2 := x1 \cdot x1 + 1\\ t_3 := 3 \cdot \frac{\left(t\_0 - 2 \cdot x2\right) - x1}{t\_2}\\ t_4 := 2 \cdot x2 - 3\\ t_5 := 6 \cdot t\_4\\ \mathbf{if}\;x1 \leq -4.4 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + t\_1\right)\\ \mathbf{elif}\;x1 \leq -1.1 \cdot 10^{+18}:\\ \;\;\;\;x1 + \left(t\_3 + \left(x1 + x1 \cdot \left(t\_5 + x1 \cdot \left(\left(x2 \cdot 8 + x1 \cdot \left(\left(6 \cdot \left(3 + x2 \cdot -2\right) + \left(t\_5 + x1 \cdot \left(\left(x2 \cdot 8 + 4 \cdot \left(3 - 2 \cdot x2\right)\right) - 6\right)\right)\right) - 3\right)\right) - 3\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 2.3:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + \left(t\_1 + x2 \cdot \left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(x1 \cdot 6 - 12\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 7 \cdot 10^{+83}:\\ \;\;\;\;x1 + \left(t\_3 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot t\_0 + t\_2 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(\frac{\left(t\_0 + 2 \cdot x2\right) - x1}{t\_2} \cdot 4 - 6\right) + 4 \cdot \left(x1 \cdot \left(x2 \cdot t\_4\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot -3\right) + x2 \cdot \left(x1 \cdot 6 + \frac{x1 \cdot \left(x1 \cdot 3 + 9\right)}{x2}\right)\right) - 2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (* x1 (- (* x1 9.0) 2.0)))
        (t_2 (+ (* x1 x1) 1.0))
        (t_3 (* 3.0 (/ (- (- t_0 (* 2.0 x2)) x1) t_2)))
        (t_4 (- (* 2.0 x2) 3.0))
        (t_5 (* 6.0 t_4)))
   (if (<= x1 -4.4e+153)
     (+ x1 (+ (* x2 -6.0) t_1))
     (if (<= x1 -1.1e+18)
       (+
        x1
        (+
         t_3
         (+
          x1
          (*
           x1
           (+
            t_5
            (*
             x1
             (-
              (+
               (* x2 8.0)
               (*
                x1
                (-
                 (+
                  (* 6.0 (+ 3.0 (* x2 -2.0)))
                  (+
                   t_5
                   (* x1 (- (+ (* x2 8.0) (* 4.0 (- 3.0 (* 2.0 x2)))) 6.0))))
                 3.0)))
              3.0)))))))
       (if (<= x1 2.3)
         (+
          x1
          (+
           (* x2 -6.0)
           (+ t_1 (* x2 (+ (* 8.0 (* x1 x2)) (* x1 (- (* x1 6.0) 12.0)))))))
         (if (<= x1 7e+83)
           (+
            x1
            (+
             t_3
             (+
              x1
              (+
               (* x1 (* x1 x1))
               (+
                (* 3.0 t_0)
                (*
                 t_2
                 (+
                  (*
                   (* x1 x1)
                   (- (* (/ (- (+ t_0 (* 2.0 x2)) x1) t_2) 4.0) 6.0))
                  (* 4.0 (* x1 (* x2 t_4))))))))))
           (+
            x1
            (+
             (* x2 -6.0)
             (*
              x1
              (-
               (+
                (* 4.0 (* x2 -3.0))
                (* x2 (+ (* x1 6.0) (/ (* x1 (+ (* x1 3.0) 9.0)) x2))))
               2.0))))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = x1 * ((x1 * 9.0) - 2.0);
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = 3.0 * (((t_0 - (2.0 * x2)) - x1) / t_2);
	double t_4 = (2.0 * x2) - 3.0;
	double t_5 = 6.0 * t_4;
	double tmp;
	if (x1 <= -4.4e+153) {
		tmp = x1 + ((x2 * -6.0) + t_1);
	} else if (x1 <= -1.1e+18) {
		tmp = x1 + (t_3 + (x1 + (x1 * (t_5 + (x1 * (((x2 * 8.0) + (x1 * (((6.0 * (3.0 + (x2 * -2.0))) + (t_5 + (x1 * (((x2 * 8.0) + (4.0 * (3.0 - (2.0 * x2)))) - 6.0)))) - 3.0))) - 3.0))))));
	} else if (x1 <= 2.3) {
		tmp = x1 + ((x2 * -6.0) + (t_1 + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 6.0) - 12.0))))));
	} else if (x1 <= 7e+83) {
		tmp = x1 + (t_3 + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_0) + (t_2 * (((x1 * x1) * (((((t_0 + (2.0 * x2)) - x1) / t_2) * 4.0) - 6.0)) + (4.0 * (x1 * (x2 * t_4)))))))));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * (((4.0 * (x2 * -3.0)) + (x2 * ((x1 * 6.0) + ((x1 * ((x1 * 3.0) + 9.0)) / x2)))) - 2.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_0 = x1 * (x1 * 3.0d0)
    t_1 = x1 * ((x1 * 9.0d0) - 2.0d0)
    t_2 = (x1 * x1) + 1.0d0
    t_3 = 3.0d0 * (((t_0 - (2.0d0 * x2)) - x1) / t_2)
    t_4 = (2.0d0 * x2) - 3.0d0
    t_5 = 6.0d0 * t_4
    if (x1 <= (-4.4d+153)) then
        tmp = x1 + ((x2 * (-6.0d0)) + t_1)
    else if (x1 <= (-1.1d+18)) then
        tmp = x1 + (t_3 + (x1 + (x1 * (t_5 + (x1 * (((x2 * 8.0d0) + (x1 * (((6.0d0 * (3.0d0 + (x2 * (-2.0d0)))) + (t_5 + (x1 * (((x2 * 8.0d0) + (4.0d0 * (3.0d0 - (2.0d0 * x2)))) - 6.0d0)))) - 3.0d0))) - 3.0d0))))))
    else if (x1 <= 2.3d0) then
        tmp = x1 + ((x2 * (-6.0d0)) + (t_1 + (x2 * ((8.0d0 * (x1 * x2)) + (x1 * ((x1 * 6.0d0) - 12.0d0))))))
    else if (x1 <= 7d+83) then
        tmp = x1 + (t_3 + (x1 + ((x1 * (x1 * x1)) + ((3.0d0 * t_0) + (t_2 * (((x1 * x1) * (((((t_0 + (2.0d0 * x2)) - x1) / t_2) * 4.0d0) - 6.0d0)) + (4.0d0 * (x1 * (x2 * t_4)))))))))
    else
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * (((4.0d0 * (x2 * (-3.0d0))) + (x2 * ((x1 * 6.0d0) + ((x1 * ((x1 * 3.0d0) + 9.0d0)) / x2)))) - 2.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = x1 * ((x1 * 9.0) - 2.0);
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = 3.0 * (((t_0 - (2.0 * x2)) - x1) / t_2);
	double t_4 = (2.0 * x2) - 3.0;
	double t_5 = 6.0 * t_4;
	double tmp;
	if (x1 <= -4.4e+153) {
		tmp = x1 + ((x2 * -6.0) + t_1);
	} else if (x1 <= -1.1e+18) {
		tmp = x1 + (t_3 + (x1 + (x1 * (t_5 + (x1 * (((x2 * 8.0) + (x1 * (((6.0 * (3.0 + (x2 * -2.0))) + (t_5 + (x1 * (((x2 * 8.0) + (4.0 * (3.0 - (2.0 * x2)))) - 6.0)))) - 3.0))) - 3.0))))));
	} else if (x1 <= 2.3) {
		tmp = x1 + ((x2 * -6.0) + (t_1 + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 6.0) - 12.0))))));
	} else if (x1 <= 7e+83) {
		tmp = x1 + (t_3 + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_0) + (t_2 * (((x1 * x1) * (((((t_0 + (2.0 * x2)) - x1) / t_2) * 4.0) - 6.0)) + (4.0 * (x1 * (x2 * t_4)))))))));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * (((4.0 * (x2 * -3.0)) + (x2 * ((x1 * 6.0) + ((x1 * ((x1 * 3.0) + 9.0)) / x2)))) - 2.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = x1 * ((x1 * 9.0) - 2.0)
	t_2 = (x1 * x1) + 1.0
	t_3 = 3.0 * (((t_0 - (2.0 * x2)) - x1) / t_2)
	t_4 = (2.0 * x2) - 3.0
	t_5 = 6.0 * t_4
	tmp = 0
	if x1 <= -4.4e+153:
		tmp = x1 + ((x2 * -6.0) + t_1)
	elif x1 <= -1.1e+18:
		tmp = x1 + (t_3 + (x1 + (x1 * (t_5 + (x1 * (((x2 * 8.0) + (x1 * (((6.0 * (3.0 + (x2 * -2.0))) + (t_5 + (x1 * (((x2 * 8.0) + (4.0 * (3.0 - (2.0 * x2)))) - 6.0)))) - 3.0))) - 3.0))))))
	elif x1 <= 2.3:
		tmp = x1 + ((x2 * -6.0) + (t_1 + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 6.0) - 12.0))))))
	elif x1 <= 7e+83:
		tmp = x1 + (t_3 + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_0) + (t_2 * (((x1 * x1) * (((((t_0 + (2.0 * x2)) - x1) / t_2) * 4.0) - 6.0)) + (4.0 * (x1 * (x2 * t_4)))))))))
	else:
		tmp = x1 + ((x2 * -6.0) + (x1 * (((4.0 * (x2 * -3.0)) + (x2 * ((x1 * 6.0) + ((x1 * ((x1 * 3.0) + 9.0)) / x2)))) - 2.0)))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(x1 * Float64(Float64(x1 * 9.0) - 2.0))
	t_2 = Float64(Float64(x1 * x1) + 1.0)
	t_3 = Float64(3.0 * Float64(Float64(Float64(t_0 - Float64(2.0 * x2)) - x1) / t_2))
	t_4 = Float64(Float64(2.0 * x2) - 3.0)
	t_5 = Float64(6.0 * t_4)
	tmp = 0.0
	if (x1 <= -4.4e+153)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + t_1));
	elseif (x1 <= -1.1e+18)
		tmp = Float64(x1 + Float64(t_3 + Float64(x1 + Float64(x1 * Float64(t_5 + Float64(x1 * Float64(Float64(Float64(x2 * 8.0) + Float64(x1 * Float64(Float64(Float64(6.0 * Float64(3.0 + Float64(x2 * -2.0))) + Float64(t_5 + Float64(x1 * Float64(Float64(Float64(x2 * 8.0) + Float64(4.0 * Float64(3.0 - Float64(2.0 * x2)))) - 6.0)))) - 3.0))) - 3.0)))))));
	elseif (x1 <= 2.3)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(t_1 + Float64(x2 * Float64(Float64(8.0 * Float64(x1 * x2)) + Float64(x1 * Float64(Float64(x1 * 6.0) - 12.0)))))));
	elseif (x1 <= 7e+83)
		tmp = Float64(x1 + Float64(t_3 + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(3.0 * t_0) + Float64(t_2 * Float64(Float64(Float64(x1 * x1) * Float64(Float64(Float64(Float64(Float64(t_0 + Float64(2.0 * x2)) - x1) / t_2) * 4.0) - 6.0)) + Float64(4.0 * Float64(x1 * Float64(x2 * t_4))))))))));
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(Float64(4.0 * Float64(x2 * -3.0)) + Float64(x2 * Float64(Float64(x1 * 6.0) + Float64(Float64(x1 * Float64(Float64(x1 * 3.0) + 9.0)) / x2)))) - 2.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * 3.0);
	t_1 = x1 * ((x1 * 9.0) - 2.0);
	t_2 = (x1 * x1) + 1.0;
	t_3 = 3.0 * (((t_0 - (2.0 * x2)) - x1) / t_2);
	t_4 = (2.0 * x2) - 3.0;
	t_5 = 6.0 * t_4;
	tmp = 0.0;
	if (x1 <= -4.4e+153)
		tmp = x1 + ((x2 * -6.0) + t_1);
	elseif (x1 <= -1.1e+18)
		tmp = x1 + (t_3 + (x1 + (x1 * (t_5 + (x1 * (((x2 * 8.0) + (x1 * (((6.0 * (3.0 + (x2 * -2.0))) + (t_5 + (x1 * (((x2 * 8.0) + (4.0 * (3.0 - (2.0 * x2)))) - 6.0)))) - 3.0))) - 3.0))))));
	elseif (x1 <= 2.3)
		tmp = x1 + ((x2 * -6.0) + (t_1 + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 6.0) - 12.0))))));
	elseif (x1 <= 7e+83)
		tmp = x1 + (t_3 + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_0) + (t_2 * (((x1 * x1) * (((((t_0 + (2.0 * x2)) - x1) / t_2) * 4.0) - 6.0)) + (4.0 * (x1 * (x2 * t_4)))))))));
	else
		tmp = x1 + ((x2 * -6.0) + (x1 * (((4.0 * (x2 * -3.0)) + (x2 * ((x1 * 6.0) + ((x1 * ((x1 * 3.0) + 9.0)) / x2)))) - 2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$3 = N[(3.0 * N[(N[(N[(t$95$0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]}, Block[{t$95$5 = N[(6.0 * t$95$4), $MachinePrecision]}, If[LessEqual[x1, -4.4e+153], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -1.1e+18], N[(x1 + N[(t$95$3 + N[(x1 + N[(x1 * N[(t$95$5 + N[(x1 * N[(N[(N[(x2 * 8.0), $MachinePrecision] + N[(x1 * N[(N[(N[(6.0 * N[(3.0 + N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$5 + N[(x1 * N[(N[(N[(x2 * 8.0), $MachinePrecision] + N[(4.0 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 2.3], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(t$95$1 + N[(x2 * N[(N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(N[(x1 * 6.0), $MachinePrecision] - 12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 7e+83], N[(x1 + N[(t$95$3 + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(3.0 * t$95$0), $MachinePrecision] + N[(t$95$2 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(N[(N[(N[(N[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision] * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] + N[(4.0 * N[(x1 * N[(x2 * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(N[(4.0 * N[(x2 * -3.0), $MachinePrecision]), $MachinePrecision] + N[(x2 * N[(N[(x1 * 6.0), $MachinePrecision] + N[(N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + 9.0), $MachinePrecision]), $MachinePrecision] / x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x1 < -4.3999999999999999e153

   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%

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

   5. Taylor expanded in x1 around 0 65.6%

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

      1. associate-*r* 65.6%

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

      2. cancel-sign-sub-inv 65.6%

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

      3. metadata-eval 65.6%

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

      4. *-commutative 65.6%

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

      5. *-commutative 65.6%

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

   7. Simplified 65.6%

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

   8. Taylor expanded in x2 around 0 100.0%

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

   if -4.3999999999999999e153 < x1 < -1.1e18

   1. Initial program 66.3%

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

   3. Taylor expanded in x1 around inf 66.3%

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

   4. Taylor expanded in x1 around inf 57.9%

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

   5. Taylor expanded in x1 around 0 78.9%

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

   if -1.1e18 < x1 < 2.2999999999999998

   1. Initial program 98.7%

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

   3. Taylor expanded in x1 around 0 89.7%

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

   4. Taylor expanded in x1 around 0 89.3%

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

   5. Taylor expanded in x1 around 0 89.4%

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

      1. associate-*r* 89.4%

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

      2. cancel-sign-sub-inv 89.4%

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

      3. metadata-eval 89.4%

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

      4. *-commutative 89.4%

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

      5. *-commutative 89.4%

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

   7. Simplified 89.4%

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

   8. Taylor expanded in x2 around 0 97.3%

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

   if 2.2999999999999998 < x1 < 6.99999999999999954e83

   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 90.4%

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

   4. Taylor expanded in x1 around 0 81.3%

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

      1. +-commutative 81.3%

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

      2. mul-1-neg 81.3%

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

      3. sub-neg 81.3%

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

   6. Simplified 81.3%

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

   7. Taylor expanded in x1 around 0 75.5%

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

   if 6.99999999999999954e83 < 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 83.4%

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

   5. Taylor expanded in x2 around inf 100.0%

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

   6. Taylor expanded in x2 around 0 100.0%

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

      1. *-commutative 100.0%

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

   8. Simplified 100.0%

      \[\leadsto x1 + \left(-6 \cdot x2 + x1 \cdot \left(\left(4 \cdot \color{blue}{\left(x2 \cdot -3\right)} + x2 \cdot \left(6 \cdot x1 + \frac{x1 \cdot \left(9 + 3 \cdot x1\right)}{x2}\right)\right) - 2\right)\right) \]
3. Recombined 5 regimes into one program.

4. Final simplification 95.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4.4 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 - 2\right)\right)\\ \mathbf{elif}\;x1 \leq -1.1 \cdot 10^{+18}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + x1 \cdot \left(6 \cdot \left(2 \cdot x2 - 3\right) + x1 \cdot \left(\left(x2 \cdot 8 + x1 \cdot \left(\left(6 \cdot \left(3 + x2 \cdot -2\right) + \left(6 \cdot \left(2 \cdot x2 - 3\right) + x1 \cdot \left(\left(x2 \cdot 8 + 4 \cdot \left(3 - 2 \cdot x2\right)\right) - 6\right)\right)\right) - 3\right)\right) - 3\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 2.3:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + \left(x1 \cdot \left(x1 \cdot 9 - 2\right) + x2 \cdot \left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(x1 \cdot 6 - 12\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 7 \cdot 10^{+83}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right) + 4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot -3\right) + x2 \cdot \left(x1 \cdot 6 + \frac{x1 \cdot \left(x1 \cdot 3 + 9\right)}{x2}\right)\right) - 2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 94.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(2 \cdot x2 - 3\right)\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := x1 \cdot x1 + 1\\ t_3 := 3 \cdot \frac{\left(t\_1 - 2 \cdot x2\right) - x1}{t\_2}\\ \mathbf{if}\;x1 \leq -4.4 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 - 2\right)\right)\\ \mathbf{elif}\;x1 \leq -4.5 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(t\_3 + \left(x1 + x1 \cdot \left(t\_0 + x1 \cdot \left(\left(x2 \cdot 8 + x1 \cdot \left(\left(t\_0 + 6 \cdot \left(3 + x2 \cdot -2\right)\right) - 3\right)\right) - 3\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 7 \cdot 10^{+83}:\\ \;\;\;\;x1 + \left(t\_3 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot t\_1 + t\_2 \cdot \left(\left(x1 \cdot x1\right) \cdot 6 + \left(\frac{\left(t\_1 + 2 \cdot x2\right) - x1}{t\_2} - 3\right) \cdot \left(\left(2 \cdot x2 - x1\right) \cdot \left(x1 \cdot 2\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot -3\right) + x2 \cdot \left(x1 \cdot 6 + \frac{x1 \cdot \left(x1 \cdot 3 + 9\right)}{x2}\right)\right) - 2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* 6.0 (- (* 2.0 x2) 3.0)))
        (t_1 (* x1 (* x1 3.0)))
        (t_2 (+ (* x1 x1) 1.0))
        (t_3 (* 3.0 (/ (- (- t_1 (* 2.0 x2)) x1) t_2))))
   (if (<= x1 -4.4e+153)
     (+ x1 (+ (* x2 -6.0) (* x1 (- (* x1 9.0) 2.0))))
     (if (<= x1 -4.5e+102)
       (+
        x1
        (+
         t_3
         (+
          x1
          (*
           x1
           (+
            t_0
            (*
             x1
             (-
              (+ (* x2 8.0) (* x1 (- (+ t_0 (* 6.0 (+ 3.0 (* x2 -2.0)))) 3.0)))
              3.0)))))))
       (if (<= x1 7e+83)
         (+
          x1
          (+
           t_3
           (+
            x1
            (+
             (* x1 (* x1 x1))
             (+
              (* 3.0 t_1)
              (*
               t_2
               (+
                (* (* x1 x1) 6.0)
                (*
                 (- (/ (- (+ t_1 (* 2.0 x2)) x1) t_2) 3.0)
                 (* (- (* 2.0 x2) x1) (* x1 2.0))))))))))
         (+
          x1
          (+
           (* x2 -6.0)
           (*
            x1
            (-
             (+
              (* 4.0 (* x2 -3.0))
              (* x2 (+ (* x1 6.0) (/ (* x1 (+ (* x1 3.0) 9.0)) x2))))
             2.0)))))))))

C

double code(double x1, double x2) {
	double t_0 = 6.0 * ((2.0 * x2) - 3.0);
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = 3.0 * (((t_1 - (2.0 * x2)) - x1) / t_2);
	double tmp;
	if (x1 <= -4.4e+153) {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) - 2.0)));
	} else if (x1 <= -4.5e+102) {
		tmp = x1 + (t_3 + (x1 + (x1 * (t_0 + (x1 * (((x2 * 8.0) + (x1 * ((t_0 + (6.0 * (3.0 + (x2 * -2.0)))) - 3.0))) - 3.0))))));
	} else if (x1 <= 7e+83) {
		tmp = x1 + (t_3 + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_1) + (t_2 * (((x1 * x1) * 6.0) + (((((t_1 + (2.0 * x2)) - x1) / t_2) - 3.0) * (((2.0 * x2) - x1) * (x1 * 2.0)))))))));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * (((4.0 * (x2 * -3.0)) + (x2 * ((x1 * 6.0) + ((x1 * ((x1 * 3.0) + 9.0)) / x2)))) - 2.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_0 = 6.0d0 * ((2.0d0 * x2) - 3.0d0)
    t_1 = x1 * (x1 * 3.0d0)
    t_2 = (x1 * x1) + 1.0d0
    t_3 = 3.0d0 * (((t_1 - (2.0d0 * x2)) - x1) / t_2)
    if (x1 <= (-4.4d+153)) then
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * ((x1 * 9.0d0) - 2.0d0)))
    else if (x1 <= (-4.5d+102)) then
        tmp = x1 + (t_3 + (x1 + (x1 * (t_0 + (x1 * (((x2 * 8.0d0) + (x1 * ((t_0 + (6.0d0 * (3.0d0 + (x2 * (-2.0d0))))) - 3.0d0))) - 3.0d0))))))
    else if (x1 <= 7d+83) then
        tmp = x1 + (t_3 + (x1 + ((x1 * (x1 * x1)) + ((3.0d0 * t_1) + (t_2 * (((x1 * x1) * 6.0d0) + (((((t_1 + (2.0d0 * x2)) - x1) / t_2) - 3.0d0) * (((2.0d0 * x2) - x1) * (x1 * 2.0d0)))))))))
    else
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * (((4.0d0 * (x2 * (-3.0d0))) + (x2 * ((x1 * 6.0d0) + ((x1 * ((x1 * 3.0d0) + 9.0d0)) / x2)))) - 2.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = 6.0 * ((2.0 * x2) - 3.0);
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = 3.0 * (((t_1 - (2.0 * x2)) - x1) / t_2);
	double tmp;
	if (x1 <= -4.4e+153) {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) - 2.0)));
	} else if (x1 <= -4.5e+102) {
		tmp = x1 + (t_3 + (x1 + (x1 * (t_0 + (x1 * (((x2 * 8.0) + (x1 * ((t_0 + (6.0 * (3.0 + (x2 * -2.0)))) - 3.0))) - 3.0))))));
	} else if (x1 <= 7e+83) {
		tmp = x1 + (t_3 + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_1) + (t_2 * (((x1 * x1) * 6.0) + (((((t_1 + (2.0 * x2)) - x1) / t_2) - 3.0) * (((2.0 * x2) - x1) * (x1 * 2.0)))))))));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * (((4.0 * (x2 * -3.0)) + (x2 * ((x1 * 6.0) + ((x1 * ((x1 * 3.0) + 9.0)) / x2)))) - 2.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = 6.0 * ((2.0 * x2) - 3.0)
	t_1 = x1 * (x1 * 3.0)
	t_2 = (x1 * x1) + 1.0
	t_3 = 3.0 * (((t_1 - (2.0 * x2)) - x1) / t_2)
	tmp = 0
	if x1 <= -4.4e+153:
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) - 2.0)))
	elif x1 <= -4.5e+102:
		tmp = x1 + (t_3 + (x1 + (x1 * (t_0 + (x1 * (((x2 * 8.0) + (x1 * ((t_0 + (6.0 * (3.0 + (x2 * -2.0)))) - 3.0))) - 3.0))))))
	elif x1 <= 7e+83:
		tmp = x1 + (t_3 + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_1) + (t_2 * (((x1 * x1) * 6.0) + (((((t_1 + (2.0 * x2)) - x1) / t_2) - 3.0) * (((2.0 * x2) - x1) * (x1 * 2.0)))))))))
	else:
		tmp = x1 + ((x2 * -6.0) + (x1 * (((4.0 * (x2 * -3.0)) + (x2 * ((x1 * 6.0) + ((x1 * ((x1 * 3.0) + 9.0)) / x2)))) - 2.0)))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(6.0 * Float64(Float64(2.0 * x2) - 3.0))
	t_1 = Float64(x1 * Float64(x1 * 3.0))
	t_2 = Float64(Float64(x1 * x1) + 1.0)
	t_3 = Float64(3.0 * Float64(Float64(Float64(t_1 - Float64(2.0 * x2)) - x1) / t_2))
	tmp = 0.0
	if (x1 <= -4.4e+153)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(x1 * 9.0) - 2.0))));
	elseif (x1 <= -4.5e+102)
		tmp = Float64(x1 + Float64(t_3 + Float64(x1 + Float64(x1 * Float64(t_0 + Float64(x1 * Float64(Float64(Float64(x2 * 8.0) + Float64(x1 * Float64(Float64(t_0 + Float64(6.0 * Float64(3.0 + Float64(x2 * -2.0)))) - 3.0))) - 3.0)))))));
	elseif (x1 <= 7e+83)
		tmp = Float64(x1 + Float64(t_3 + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(3.0 * t_1) + Float64(t_2 * Float64(Float64(Float64(x1 * x1) * 6.0) + Float64(Float64(Float64(Float64(Float64(t_1 + Float64(2.0 * x2)) - x1) / t_2) - 3.0) * Float64(Float64(Float64(2.0 * x2) - x1) * Float64(x1 * 2.0))))))))));
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(Float64(4.0 * Float64(x2 * -3.0)) + Float64(x2 * Float64(Float64(x1 * 6.0) + Float64(Float64(x1 * Float64(Float64(x1 * 3.0) + 9.0)) / x2)))) - 2.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = 6.0 * ((2.0 * x2) - 3.0);
	t_1 = x1 * (x1 * 3.0);
	t_2 = (x1 * x1) + 1.0;
	t_3 = 3.0 * (((t_1 - (2.0 * x2)) - x1) / t_2);
	tmp = 0.0;
	if (x1 <= -4.4e+153)
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) - 2.0)));
	elseif (x1 <= -4.5e+102)
		tmp = x1 + (t_3 + (x1 + (x1 * (t_0 + (x1 * (((x2 * 8.0) + (x1 * ((t_0 + (6.0 * (3.0 + (x2 * -2.0)))) - 3.0))) - 3.0))))));
	elseif (x1 <= 7e+83)
		tmp = x1 + (t_3 + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_1) + (t_2 * (((x1 * x1) * 6.0) + (((((t_1 + (2.0 * x2)) - x1) / t_2) - 3.0) * (((2.0 * x2) - x1) * (x1 * 2.0)))))))));
	else
		tmp = x1 + ((x2 * -6.0) + (x1 * (((4.0 * (x2 * -3.0)) + (x2 * ((x1 * 6.0) + ((x1 * ((x1 * 3.0) + 9.0)) / x2)))) - 2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(6.0 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$3 = N[(3.0 * N[(N[(N[(t$95$1 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -4.4e+153], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -4.5e+102], N[(x1 + N[(t$95$3 + N[(x1 + N[(x1 * N[(t$95$0 + N[(x1 * N[(N[(N[(x2 * 8.0), $MachinePrecision] + N[(x1 * N[(N[(t$95$0 + N[(6.0 * N[(3.0 + N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 7e+83], N[(x1 + N[(t$95$3 + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(3.0 * t$95$1), $MachinePrecision] + N[(t$95$2 * N[(N[(N[(x1 * x1), $MachinePrecision] * 6.0), $MachinePrecision] + N[(N[(N[(N[(N[(t$95$1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision] - 3.0), $MachinePrecision] * N[(N[(N[(2.0 * x2), $MachinePrecision] - x1), $MachinePrecision] * N[(x1 * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(N[(4.0 * N[(x2 * -3.0), $MachinePrecision]), $MachinePrecision] + N[(x2 * N[(N[(x1 * 6.0), $MachinePrecision] + N[(N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + 9.0), $MachinePrecision]), $MachinePrecision] / x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -4.3999999999999999e153

   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%

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

   5. Taylor expanded in x1 around 0 65.6%

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

      1. associate-*r* 65.6%

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

      2. cancel-sign-sub-inv 65.6%

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

      3. metadata-eval 65.6%

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

      4. *-commutative 65.6%

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

      5. *-commutative 65.6%

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

   7. Simplified 65.6%

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

   8. Taylor expanded in x2 around 0 100.0%

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

   if -4.3999999999999999e153 < x1 < -4.50000000000000021e102

   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 0.0%

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

   4. Taylor expanded in x1 around inf 0.0%

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

   5. Taylor expanded in x1 around 0 87.5%

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

   if -4.50000000000000021e102 < x1 < 6.99999999999999954e83

   1. Initial program 98.8%

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

   3. Taylor expanded in x1 around inf 96.8%

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

   4. Taylor expanded in x1 around 0 94.9%

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

      1. +-commutative 94.9%

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

      2. mul-1-neg 94.9%

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

      3. sub-neg 94.9%

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

   6. Simplified 94.9%

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

   7. Taylor expanded in x1 around inf 95.4%

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

   if 6.99999999999999954e83 < 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 83.4%

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

   5. Taylor expanded in x2 around inf 100.0%

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

   6. Taylor expanded in x2 around 0 100.0%

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

      1. *-commutative 100.0%

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

   8. Simplified 100.0%

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

4. Final simplification 96.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4.4 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 - 2\right)\right)\\ \mathbf{elif}\;x1 \leq -4.5 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + x1 \cdot \left(6 \cdot \left(2 \cdot x2 - 3\right) + x1 \cdot \left(\left(x2 \cdot 8 + x1 \cdot \left(\left(6 \cdot \left(2 \cdot x2 - 3\right) + 6 \cdot \left(3 + x2 \cdot -2\right)\right) - 3\right)\right) - 3\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 7 \cdot 10^{+83}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot 6 + \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) \cdot \left(\left(2 \cdot x2 - x1\right) \cdot \left(x1 \cdot 2\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot -3\right) + x2 \cdot \left(x1 \cdot 6 + \frac{x1 \cdot \left(x1 \cdot 3 + 9\right)}{x2}\right)\right) - 2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 90.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := x1 \cdot \left(x1 \cdot 9 - 2\right)\\ t_2 := x1 \cdot x1 + 1\\ t_3 := 3 \cdot \frac{\left(t\_0 - 2 \cdot x2\right) - x1}{t\_2}\\ t_4 := 2 \cdot x2 - 3\\ t_5 := 6 \cdot t\_4\\ \mathbf{if}\;x1 \leq -4.4 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + t\_1\right)\\ \mathbf{elif}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(t\_3 + \left(x1 + x1 \cdot \left(t\_5 + x1 \cdot \left(\left(x2 \cdot 8 + x1 \cdot \left(\left(t\_5 + 6 \cdot \left(3 + x2 \cdot -2\right)\right) - 3\right)\right) - 3\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -9.5 \cdot 10^{+17}:\\ \;\;\;\;x1 + \left(t\_3 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot t\_0 + t\_2 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(\frac{\left(t\_0 + 2 \cdot x2\right) - x1}{t\_2} \cdot 4 - 6\right) + x1 \cdot 2\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 5.6 \cdot 10^{+27}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + \left(t\_1 + x2 \cdot \left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(x1 \cdot 6 - 12\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(\left(x2 \cdot \left(x1 \cdot 6 + \frac{x1 \cdot \left(x1 \cdot 3 + 9\right)}{x2}\right) + 4 \cdot \left(x2 \cdot t\_4\right)\right) - 2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (* x1 (- (* x1 9.0) 2.0)))
        (t_2 (+ (* x1 x1) 1.0))
        (t_3 (* 3.0 (/ (- (- t_0 (* 2.0 x2)) x1) t_2)))
        (t_4 (- (* 2.0 x2) 3.0))
        (t_5 (* 6.0 t_4)))
   (if (<= x1 -4.4e+153)
     (+ x1 (+ (* x2 -6.0) t_1))
     (if (<= x1 -5.6e+102)
       (+
        x1
        (+
         t_3
         (+
          x1
          (*
           x1
           (+
            t_5
            (*
             x1
             (-
              (+ (* x2 8.0) (* x1 (- (+ t_5 (* 6.0 (+ 3.0 (* x2 -2.0)))) 3.0)))
              3.0)))))))
       (if (<= x1 -9.5e+17)
         (+
          x1
          (+
           t_3
           (+
            x1
            (+
             (* x1 (* x1 x1))
             (+
              (* 3.0 t_0)
              (*
               t_2
               (+
                (* (* x1 x1) (- (* (/ (- (+ t_0 (* 2.0 x2)) x1) t_2) 4.0) 6.0))
                (* x1 2.0))))))))
         (if (<= x1 5.6e+27)
           (+
            x1
            (+
             (* x2 -6.0)
             (+ t_1 (* x2 (+ (* 8.0 (* x1 x2)) (* x1 (- (* x1 6.0) 12.0)))))))
           (+
            x1
            (+
             (* x2 -6.0)
             (*
              x1
              (-
               (+
                (* x2 (+ (* x1 6.0) (/ (* x1 (+ (* x1 3.0) 9.0)) x2)))
                (* 4.0 (* x2 t_4)))
               2.0))))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = x1 * ((x1 * 9.0) - 2.0);
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = 3.0 * (((t_0 - (2.0 * x2)) - x1) / t_2);
	double t_4 = (2.0 * x2) - 3.0;
	double t_5 = 6.0 * t_4;
	double tmp;
	if (x1 <= -4.4e+153) {
		tmp = x1 + ((x2 * -6.0) + t_1);
	} else if (x1 <= -5.6e+102) {
		tmp = x1 + (t_3 + (x1 + (x1 * (t_5 + (x1 * (((x2 * 8.0) + (x1 * ((t_5 + (6.0 * (3.0 + (x2 * -2.0)))) - 3.0))) - 3.0))))));
	} else if (x1 <= -9.5e+17) {
		tmp = x1 + (t_3 + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_0) + (t_2 * (((x1 * x1) * (((((t_0 + (2.0 * x2)) - x1) / t_2) * 4.0) - 6.0)) + (x1 * 2.0)))))));
	} else if (x1 <= 5.6e+27) {
		tmp = x1 + ((x2 * -6.0) + (t_1 + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 6.0) - 12.0))))));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * (((x2 * ((x1 * 6.0) + ((x1 * ((x1 * 3.0) + 9.0)) / x2))) + (4.0 * (x2 * t_4))) - 2.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_0 = x1 * (x1 * 3.0d0)
    t_1 = x1 * ((x1 * 9.0d0) - 2.0d0)
    t_2 = (x1 * x1) + 1.0d0
    t_3 = 3.0d0 * (((t_0 - (2.0d0 * x2)) - x1) / t_2)
    t_4 = (2.0d0 * x2) - 3.0d0
    t_5 = 6.0d0 * t_4
    if (x1 <= (-4.4d+153)) then
        tmp = x1 + ((x2 * (-6.0d0)) + t_1)
    else if (x1 <= (-5.6d+102)) then
        tmp = x1 + (t_3 + (x1 + (x1 * (t_5 + (x1 * (((x2 * 8.0d0) + (x1 * ((t_5 + (6.0d0 * (3.0d0 + (x2 * (-2.0d0))))) - 3.0d0))) - 3.0d0))))))
    else if (x1 <= (-9.5d+17)) then
        tmp = x1 + (t_3 + (x1 + ((x1 * (x1 * x1)) + ((3.0d0 * t_0) + (t_2 * (((x1 * x1) * (((((t_0 + (2.0d0 * x2)) - x1) / t_2) * 4.0d0) - 6.0d0)) + (x1 * 2.0d0)))))))
    else if (x1 <= 5.6d+27) then
        tmp = x1 + ((x2 * (-6.0d0)) + (t_1 + (x2 * ((8.0d0 * (x1 * x2)) + (x1 * ((x1 * 6.0d0) - 12.0d0))))))
    else
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * (((x2 * ((x1 * 6.0d0) + ((x1 * ((x1 * 3.0d0) + 9.0d0)) / x2))) + (4.0d0 * (x2 * t_4))) - 2.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = x1 * ((x1 * 9.0) - 2.0);
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = 3.0 * (((t_0 - (2.0 * x2)) - x1) / t_2);
	double t_4 = (2.0 * x2) - 3.0;
	double t_5 = 6.0 * t_4;
	double tmp;
	if (x1 <= -4.4e+153) {
		tmp = x1 + ((x2 * -6.0) + t_1);
	} else if (x1 <= -5.6e+102) {
		tmp = x1 + (t_3 + (x1 + (x1 * (t_5 + (x1 * (((x2 * 8.0) + (x1 * ((t_5 + (6.0 * (3.0 + (x2 * -2.0)))) - 3.0))) - 3.0))))));
	} else if (x1 <= -9.5e+17) {
		tmp = x1 + (t_3 + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_0) + (t_2 * (((x1 * x1) * (((((t_0 + (2.0 * x2)) - x1) / t_2) * 4.0) - 6.0)) + (x1 * 2.0)))))));
	} else if (x1 <= 5.6e+27) {
		tmp = x1 + ((x2 * -6.0) + (t_1 + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 6.0) - 12.0))))));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * (((x2 * ((x1 * 6.0) + ((x1 * ((x1 * 3.0) + 9.0)) / x2))) + (4.0 * (x2 * t_4))) - 2.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = x1 * ((x1 * 9.0) - 2.0)
	t_2 = (x1 * x1) + 1.0
	t_3 = 3.0 * (((t_0 - (2.0 * x2)) - x1) / t_2)
	t_4 = (2.0 * x2) - 3.0
	t_5 = 6.0 * t_4
	tmp = 0
	if x1 <= -4.4e+153:
		tmp = x1 + ((x2 * -6.0) + t_1)
	elif x1 <= -5.6e+102:
		tmp = x1 + (t_3 + (x1 + (x1 * (t_5 + (x1 * (((x2 * 8.0) + (x1 * ((t_5 + (6.0 * (3.0 + (x2 * -2.0)))) - 3.0))) - 3.0))))))
	elif x1 <= -9.5e+17:
		tmp = x1 + (t_3 + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_0) + (t_2 * (((x1 * x1) * (((((t_0 + (2.0 * x2)) - x1) / t_2) * 4.0) - 6.0)) + (x1 * 2.0)))))))
	elif x1 <= 5.6e+27:
		tmp = x1 + ((x2 * -6.0) + (t_1 + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 6.0) - 12.0))))))
	else:
		tmp = x1 + ((x2 * -6.0) + (x1 * (((x2 * ((x1 * 6.0) + ((x1 * ((x1 * 3.0) + 9.0)) / x2))) + (4.0 * (x2 * t_4))) - 2.0)))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(x1 * Float64(Float64(x1 * 9.0) - 2.0))
	t_2 = Float64(Float64(x1 * x1) + 1.0)
	t_3 = Float64(3.0 * Float64(Float64(Float64(t_0 - Float64(2.0 * x2)) - x1) / t_2))
	t_4 = Float64(Float64(2.0 * x2) - 3.0)
	t_5 = Float64(6.0 * t_4)
	tmp = 0.0
	if (x1 <= -4.4e+153)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + t_1));
	elseif (x1 <= -5.6e+102)
		tmp = Float64(x1 + Float64(t_3 + Float64(x1 + Float64(x1 * Float64(t_5 + Float64(x1 * Float64(Float64(Float64(x2 * 8.0) + Float64(x1 * Float64(Float64(t_5 + Float64(6.0 * Float64(3.0 + Float64(x2 * -2.0)))) - 3.0))) - 3.0)))))));
	elseif (x1 <= -9.5e+17)
		tmp = Float64(x1 + Float64(t_3 + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(3.0 * t_0) + Float64(t_2 * Float64(Float64(Float64(x1 * x1) * Float64(Float64(Float64(Float64(Float64(t_0 + Float64(2.0 * x2)) - x1) / t_2) * 4.0) - 6.0)) + Float64(x1 * 2.0))))))));
	elseif (x1 <= 5.6e+27)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(t_1 + Float64(x2 * Float64(Float64(8.0 * Float64(x1 * x2)) + Float64(x1 * Float64(Float64(x1 * 6.0) - 12.0)))))));
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(Float64(x2 * Float64(Float64(x1 * 6.0) + Float64(Float64(x1 * Float64(Float64(x1 * 3.0) + 9.0)) / x2))) + Float64(4.0 * Float64(x2 * t_4))) - 2.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * 3.0);
	t_1 = x1 * ((x1 * 9.0) - 2.0);
	t_2 = (x1 * x1) + 1.0;
	t_3 = 3.0 * (((t_0 - (2.0 * x2)) - x1) / t_2);
	t_4 = (2.0 * x2) - 3.0;
	t_5 = 6.0 * t_4;
	tmp = 0.0;
	if (x1 <= -4.4e+153)
		tmp = x1 + ((x2 * -6.0) + t_1);
	elseif (x1 <= -5.6e+102)
		tmp = x1 + (t_3 + (x1 + (x1 * (t_5 + (x1 * (((x2 * 8.0) + (x1 * ((t_5 + (6.0 * (3.0 + (x2 * -2.0)))) - 3.0))) - 3.0))))));
	elseif (x1 <= -9.5e+17)
		tmp = x1 + (t_3 + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_0) + (t_2 * (((x1 * x1) * (((((t_0 + (2.0 * x2)) - x1) / t_2) * 4.0) - 6.0)) + (x1 * 2.0)))))));
	elseif (x1 <= 5.6e+27)
		tmp = x1 + ((x2 * -6.0) + (t_1 + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 6.0) - 12.0))))));
	else
		tmp = x1 + ((x2 * -6.0) + (x1 * (((x2 * ((x1 * 6.0) + ((x1 * ((x1 * 3.0) + 9.0)) / x2))) + (4.0 * (x2 * t_4))) - 2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$3 = N[(3.0 * N[(N[(N[(t$95$0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]}, Block[{t$95$5 = N[(6.0 * t$95$4), $MachinePrecision]}, If[LessEqual[x1, -4.4e+153], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -5.6e+102], N[(x1 + N[(t$95$3 + N[(x1 + N[(x1 * N[(t$95$5 + N[(x1 * N[(N[(N[(x2 * 8.0), $MachinePrecision] + N[(x1 * N[(N[(t$95$5 + N[(6.0 * N[(3.0 + N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -9.5e+17], N[(x1 + N[(t$95$3 + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(3.0 * t$95$0), $MachinePrecision] + N[(t$95$2 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(N[(N[(N[(N[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision] * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] + N[(x1 * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 5.6e+27], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(t$95$1 + N[(x2 * N[(N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(N[(x1 * 6.0), $MachinePrecision] - 12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(N[(x2 * N[(N[(x1 * 6.0), $MachinePrecision] + N[(N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + 9.0), $MachinePrecision]), $MachinePrecision] / x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(4.0 * N[(x2 * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x1 < -4.3999999999999999e153

   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%

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

   5. Taylor expanded in x1 around 0 65.6%

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

      1. associate-*r* 65.6%

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

      2. cancel-sign-sub-inv 65.6%

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

      3. metadata-eval 65.6%

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

      4. *-commutative 65.6%

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

      5. *-commutative 65.6%

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

   7. Simplified 65.6%

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

   8. Taylor expanded in x2 around 0 100.0%

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

   if -4.3999999999999999e153 < 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 inf 0.0%

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

   4. Taylor expanded in x1 around inf 0.0%

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

   5. Taylor expanded in x1 around 0 87.5%

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

   if -5.60000000000000037e102 < x1 < -9.5e17

   1. Initial program 99.4%

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

   3. Taylor expanded in x1 around inf 99.4%

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

   4. Taylor expanded in x1 around 0 99.5%

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

      1. +-commutative 99.5%

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

      2. mul-1-neg 99.5%

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

      3. sub-neg 99.5%

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

   6. Simplified 99.5%

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

   7. Taylor expanded in x1 around inf 86.9%

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

      1. *-commutative 86.9%

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

   9. Simplified 86.9%

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

   if -9.5e17 < x1 < 5.5999999999999999e27

   1. Initial program 98.7%

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

   3. Taylor expanded in x1 around 0 88.2%

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

   4. Taylor expanded in x1 around 0 87.2%

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

   5. Taylor expanded in x1 around 0 87.3%

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

      1. associate-*r* 87.3%

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

      2. cancel-sign-sub-inv 87.3%

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

      3. metadata-eval 87.3%

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

      4. *-commutative 87.3%

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

      5. *-commutative 87.3%

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

   7. Simplified 87.3%

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

   8. Taylor expanded in x2 around 0 95.6%

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

   if 5.5999999999999999e27 < x1

   1. Initial program 32.6%

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

   3. Taylor expanded in x1 around 0 10.1%

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

   4. Taylor expanded in x1 around 0 77.4%

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

   5. Taylor expanded in x2 around inf 91.6%

      \[\leadsto x1 + \left(-6 \cdot x2 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + \color{blue}{x2 \cdot \left(6 \cdot x1 + \frac{x1 \cdot \left(9 + 3 \cdot x1\right)}{x2}\right)}\right) - 2\right)\right) \]
3. Recombined 5 regimes into one program.

4. Final simplification 94.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4.4 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 - 2\right)\right)\\ \mathbf{elif}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + x1 \cdot \left(6 \cdot \left(2 \cdot x2 - 3\right) + x1 \cdot \left(\left(x2 \cdot 8 + x1 \cdot \left(\left(6 \cdot \left(2 \cdot x2 - 3\right) + 6 \cdot \left(3 + x2 \cdot -2\right)\right) - 3\right)\right) - 3\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -9.5 \cdot 10^{+17}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right) + x1 \cdot 2\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 5.6 \cdot 10^{+27}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + \left(x1 \cdot \left(x1 \cdot 9 - 2\right) + x2 \cdot \left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(x1 \cdot 6 - 12\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(\left(x2 \cdot \left(x1 \cdot 6 + \frac{x1 \cdot \left(x1 \cdot 3 + 9\right)}{x2}\right) + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) - 2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 88.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 2 \cdot x2 - 3\\ t_1 := 6 \cdot t\_0\\ t_2 := x1 \cdot \left(x1 \cdot 9 - 2\right)\\ \mathbf{if}\;x1 \leq -4.4 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + t\_2\right)\\ \mathbf{elif}\;x1 \leq -9.5 \cdot 10^{+17}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + x1 \cdot \left(t\_1 + x1 \cdot \left(\left(x2 \cdot 8 + x1 \cdot \left(\left(6 \cdot \left(3 + x2 \cdot -2\right) + \left(t\_1 + x1 \cdot \left(\left(x2 \cdot 8 + 4 \cdot \left(3 - 2 \cdot x2\right)\right) - 6\right)\right)\right) - 3\right)\right) - 3\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.55 \cdot 10^{+29}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + \left(t\_2 + x2 \cdot \left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(x1 \cdot 6 - 12\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(\left(x2 \cdot \left(x1 \cdot 6 + \frac{x1 \cdot \left(x1 \cdot 3 + 9\right)}{x2}\right) + 4 \cdot \left(x2 \cdot t\_0\right)\right) - 2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (- (* 2.0 x2) 3.0))
        (t_1 (* 6.0 t_0))
        (t_2 (* x1 (- (* x1 9.0) 2.0))))
   (if (<= x1 -4.4e+153)
     (+ x1 (+ (* x2 -6.0) t_2))
     (if (<= x1 -9.5e+17)
       (+
        x1
        (+
         (* 3.0 (/ (- (- (* x1 (* x1 3.0)) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0)))
         (+
          x1
          (*
           x1
           (+
            t_1
            (*
             x1
             (-
              (+
               (* x2 8.0)
               (*
                x1
                (-
                 (+
                  (* 6.0 (+ 3.0 (* x2 -2.0)))
                  (+
                   t_1
                   (* x1 (- (+ (* x2 8.0) (* 4.0 (- 3.0 (* 2.0 x2)))) 6.0))))
                 3.0)))
              3.0)))))))
       (if (<= x1 1.55e+29)
         (+
          x1
          (+
           (* x2 -6.0)
           (+ t_2 (* x2 (+ (* 8.0 (* x1 x2)) (* x1 (- (* x1 6.0) 12.0)))))))
         (+
          x1
          (+
           (* x2 -6.0)
           (*
            x1
            (-
             (+
              (* x2 (+ (* x1 6.0) (/ (* x1 (+ (* x1 3.0) 9.0)) x2)))
              (* 4.0 (* x2 t_0)))
             2.0)))))))))

C

double code(double x1, double x2) {
	double t_0 = (2.0 * x2) - 3.0;
	double t_1 = 6.0 * t_0;
	double t_2 = x1 * ((x1 * 9.0) - 2.0);
	double tmp;
	if (x1 <= -4.4e+153) {
		tmp = x1 + ((x2 * -6.0) + t_2);
	} else if (x1 <= -9.5e+17) {
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / ((x1 * x1) + 1.0))) + (x1 + (x1 * (t_1 + (x1 * (((x2 * 8.0) + (x1 * (((6.0 * (3.0 + (x2 * -2.0))) + (t_1 + (x1 * (((x2 * 8.0) + (4.0 * (3.0 - (2.0 * x2)))) - 6.0)))) - 3.0))) - 3.0))))));
	} else if (x1 <= 1.55e+29) {
		tmp = x1 + ((x2 * -6.0) + (t_2 + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 6.0) - 12.0))))));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * (((x2 * ((x1 * 6.0) + ((x1 * ((x1 * 3.0) + 9.0)) / x2))) + (4.0 * (x2 * t_0))) - 2.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = (2.0d0 * x2) - 3.0d0
    t_1 = 6.0d0 * t_0
    t_2 = x1 * ((x1 * 9.0d0) - 2.0d0)
    if (x1 <= (-4.4d+153)) then
        tmp = x1 + ((x2 * (-6.0d0)) + t_2)
    else if (x1 <= (-9.5d+17)) then
        tmp = x1 + ((3.0d0 * ((((x1 * (x1 * 3.0d0)) - (2.0d0 * x2)) - x1) / ((x1 * x1) + 1.0d0))) + (x1 + (x1 * (t_1 + (x1 * (((x2 * 8.0d0) + (x1 * (((6.0d0 * (3.0d0 + (x2 * (-2.0d0)))) + (t_1 + (x1 * (((x2 * 8.0d0) + (4.0d0 * (3.0d0 - (2.0d0 * x2)))) - 6.0d0)))) - 3.0d0))) - 3.0d0))))))
    else if (x1 <= 1.55d+29) then
        tmp = x1 + ((x2 * (-6.0d0)) + (t_2 + (x2 * ((8.0d0 * (x1 * x2)) + (x1 * ((x1 * 6.0d0) - 12.0d0))))))
    else
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * (((x2 * ((x1 * 6.0d0) + ((x1 * ((x1 * 3.0d0) + 9.0d0)) / x2))) + (4.0d0 * (x2 * t_0))) - 2.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (2.0 * x2) - 3.0;
	double t_1 = 6.0 * t_0;
	double t_2 = x1 * ((x1 * 9.0) - 2.0);
	double tmp;
	if (x1 <= -4.4e+153) {
		tmp = x1 + ((x2 * -6.0) + t_2);
	} else if (x1 <= -9.5e+17) {
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / ((x1 * x1) + 1.0))) + (x1 + (x1 * (t_1 + (x1 * (((x2 * 8.0) + (x1 * (((6.0 * (3.0 + (x2 * -2.0))) + (t_1 + (x1 * (((x2 * 8.0) + (4.0 * (3.0 - (2.0 * x2)))) - 6.0)))) - 3.0))) - 3.0))))));
	} else if (x1 <= 1.55e+29) {
		tmp = x1 + ((x2 * -6.0) + (t_2 + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 6.0) - 12.0))))));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * (((x2 * ((x1 * 6.0) + ((x1 * ((x1 * 3.0) + 9.0)) / x2))) + (4.0 * (x2 * t_0))) - 2.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (2.0 * x2) - 3.0
	t_1 = 6.0 * t_0
	t_2 = x1 * ((x1 * 9.0) - 2.0)
	tmp = 0
	if x1 <= -4.4e+153:
		tmp = x1 + ((x2 * -6.0) + t_2)
	elif x1 <= -9.5e+17:
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / ((x1 * x1) + 1.0))) + (x1 + (x1 * (t_1 + (x1 * (((x2 * 8.0) + (x1 * (((6.0 * (3.0 + (x2 * -2.0))) + (t_1 + (x1 * (((x2 * 8.0) + (4.0 * (3.0 - (2.0 * x2)))) - 6.0)))) - 3.0))) - 3.0))))))
	elif x1 <= 1.55e+29:
		tmp = x1 + ((x2 * -6.0) + (t_2 + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 6.0) - 12.0))))))
	else:
		tmp = x1 + ((x2 * -6.0) + (x1 * (((x2 * ((x1 * 6.0) + ((x1 * ((x1 * 3.0) + 9.0)) / x2))) + (4.0 * (x2 * t_0))) - 2.0)))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(2.0 * x2) - 3.0)
	t_1 = Float64(6.0 * t_0)
	t_2 = Float64(x1 * Float64(Float64(x1 * 9.0) - 2.0))
	tmp = 0.0
	if (x1 <= -4.4e+153)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + t_2));
	elseif (x1 <= -9.5e+17)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(Float64(x1 * Float64(x1 * 3.0)) - Float64(2.0 * x2)) - x1) / Float64(Float64(x1 * x1) + 1.0))) + Float64(x1 + Float64(x1 * Float64(t_1 + Float64(x1 * Float64(Float64(Float64(x2 * 8.0) + Float64(x1 * Float64(Float64(Float64(6.0 * Float64(3.0 + Float64(x2 * -2.0))) + Float64(t_1 + Float64(x1 * Float64(Float64(Float64(x2 * 8.0) + Float64(4.0 * Float64(3.0 - Float64(2.0 * x2)))) - 6.0)))) - 3.0))) - 3.0)))))));
	elseif (x1 <= 1.55e+29)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(t_2 + Float64(x2 * Float64(Float64(8.0 * Float64(x1 * x2)) + Float64(x1 * Float64(Float64(x1 * 6.0) - 12.0)))))));
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(Float64(x2 * Float64(Float64(x1 * 6.0) + Float64(Float64(x1 * Float64(Float64(x1 * 3.0) + 9.0)) / x2))) + Float64(4.0 * Float64(x2 * t_0))) - 2.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (2.0 * x2) - 3.0;
	t_1 = 6.0 * t_0;
	t_2 = x1 * ((x1 * 9.0) - 2.0);
	tmp = 0.0;
	if (x1 <= -4.4e+153)
		tmp = x1 + ((x2 * -6.0) + t_2);
	elseif (x1 <= -9.5e+17)
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / ((x1 * x1) + 1.0))) + (x1 + (x1 * (t_1 + (x1 * (((x2 * 8.0) + (x1 * (((6.0 * (3.0 + (x2 * -2.0))) + (t_1 + (x1 * (((x2 * 8.0) + (4.0 * (3.0 - (2.0 * x2)))) - 6.0)))) - 3.0))) - 3.0))))));
	elseif (x1 <= 1.55e+29)
		tmp = x1 + ((x2 * -6.0) + (t_2 + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 6.0) - 12.0))))));
	else
		tmp = x1 + ((x2 * -6.0) + (x1 * (((x2 * ((x1 * 6.0) + ((x1 * ((x1 * 3.0) + 9.0)) / x2))) + (4.0 * (x2 * t_0))) - 2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]}, Block[{t$95$1 = N[(6.0 * t$95$0), $MachinePrecision]}, Block[{t$95$2 = N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -4.4e+153], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -9.5e+17], N[(x1 + N[(N[(3.0 * N[(N[(N[(N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision] - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(x1 * N[(t$95$1 + N[(x1 * N[(N[(N[(x2 * 8.0), $MachinePrecision] + N[(x1 * N[(N[(N[(6.0 * N[(3.0 + N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$1 + N[(x1 * N[(N[(N[(x2 * 8.0), $MachinePrecision] + N[(4.0 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.55e+29], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(t$95$2 + N[(x2 * N[(N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(N[(x1 * 6.0), $MachinePrecision] - 12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(N[(x2 * N[(N[(x1 * 6.0), $MachinePrecision] + N[(N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + 9.0), $MachinePrecision]), $MachinePrecision] / x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(4.0 * N[(x2 * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -4.3999999999999999e153

   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%

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

   5. Taylor expanded in x1 around 0 65.6%

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

      1. associate-*r* 65.6%

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

      2. cancel-sign-sub-inv 65.6%

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

      3. metadata-eval 65.6%

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

      4. *-commutative 65.6%

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

      5. *-commutative 65.6%

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

   7. Simplified 65.6%

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

   8. Taylor expanded in x2 around 0 100.0%

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

   if -4.3999999999999999e153 < x1 < -9.5e17

   1. Initial program 66.3%

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

   3. Taylor expanded in x1 around inf 66.3%

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

   4. Taylor expanded in x1 around inf 57.9%

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

   5. Taylor expanded in x1 around 0 78.9%

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

   if -9.5e17 < x1 < 1.5499999999999999e29

   1. Initial program 98.7%

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

   3. Taylor expanded in x1 around 0 88.2%

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

   4. Taylor expanded in x1 around 0 87.2%

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

   5. Taylor expanded in x1 around 0 87.3%

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

      1. associate-*r* 87.3%

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

      2. cancel-sign-sub-inv 87.3%

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

      3. metadata-eval 87.3%

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

      4. *-commutative 87.3%

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

      5. *-commutative 87.3%

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

   7. Simplified 87.3%

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

   8. Taylor expanded in x2 around 0 95.6%

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

   if 1.5499999999999999e29 < x1

   1. Initial program 32.6%

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

   3. Taylor expanded in x1 around 0 10.1%

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

   4. Taylor expanded in x1 around 0 77.4%

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

   5. Taylor expanded in x2 around inf 91.6%

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

4. Final simplification 93.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4.4 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 - 2\right)\right)\\ \mathbf{elif}\;x1 \leq -9.5 \cdot 10^{+17}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + x1 \cdot \left(6 \cdot \left(2 \cdot x2 - 3\right) + x1 \cdot \left(\left(x2 \cdot 8 + x1 \cdot \left(\left(6 \cdot \left(3 + x2 \cdot -2\right) + \left(6 \cdot \left(2 \cdot x2 - 3\right) + x1 \cdot \left(\left(x2 \cdot 8 + 4 \cdot \left(3 - 2 \cdot x2\right)\right) - 6\right)\right)\right) - 3\right)\right) - 3\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.55 \cdot 10^{+29}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + \left(x1 \cdot \left(x1 \cdot 9 - 2\right) + x2 \cdot \left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(x1 \cdot 6 - 12\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(\left(x2 \cdot \left(x1 \cdot 6 + \frac{x1 \cdot \left(x1 \cdot 3 + 9\right)}{x2}\right) + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) - 2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 86.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 2 \cdot x2 - 3\\ t_1 := 6 \cdot t\_0\\ t_2 := x1 \cdot \left(x1 \cdot 9 - 2\right)\\ \mathbf{if}\;x1 \leq -4.4 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + t\_2\right)\\ \mathbf{elif}\;x1 \leq -4.5 \cdot 10^{+79}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + x1 \cdot \left(t\_1 + x1 \cdot \left(\left(x2 \cdot 8 + x1 \cdot \left(\left(t\_1 + 6 \cdot \left(3 + x2 \cdot -2\right)\right) - 3\right)\right) - 3\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.9 \cdot 10^{+27}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + \left(t\_2 + x2 \cdot \left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(x1 \cdot 6 - 12\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(\left(x2 \cdot \left(x1 \cdot 6 + \frac{x1 \cdot \left(x1 \cdot 3 + 9\right)}{x2}\right) + 4 \cdot \left(x2 \cdot t\_0\right)\right) - 2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (- (* 2.0 x2) 3.0))
        (t_1 (* 6.0 t_0))
        (t_2 (* x1 (- (* x1 9.0) 2.0))))
   (if (<= x1 -4.4e+153)
     (+ x1 (+ (* x2 -6.0) t_2))
     (if (<= x1 -4.5e+79)
       (+
        x1
        (+
         (* 3.0 (/ (- (- (* x1 (* x1 3.0)) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0)))
         (+
          x1
          (*
           x1
           (+
            t_1
            (*
             x1
             (-
              (+ (* x2 8.0) (* x1 (- (+ t_1 (* 6.0 (+ 3.0 (* x2 -2.0)))) 3.0)))
              3.0)))))))
       (if (<= x1 1.9e+27)
         (+
          x1
          (+
           (* x2 -6.0)
           (+ t_2 (* x2 (+ (* 8.0 (* x1 x2)) (* x1 (- (* x1 6.0) 12.0)))))))
         (+
          x1
          (+
           (* x2 -6.0)
           (*
            x1
            (-
             (+
              (* x2 (+ (* x1 6.0) (/ (* x1 (+ (* x1 3.0) 9.0)) x2)))
              (* 4.0 (* x2 t_0)))
             2.0)))))))))

C

double code(double x1, double x2) {
	double t_0 = (2.0 * x2) - 3.0;
	double t_1 = 6.0 * t_0;
	double t_2 = x1 * ((x1 * 9.0) - 2.0);
	double tmp;
	if (x1 <= -4.4e+153) {
		tmp = x1 + ((x2 * -6.0) + t_2);
	} else if (x1 <= -4.5e+79) {
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / ((x1 * x1) + 1.0))) + (x1 + (x1 * (t_1 + (x1 * (((x2 * 8.0) + (x1 * ((t_1 + (6.0 * (3.0 + (x2 * -2.0)))) - 3.0))) - 3.0))))));
	} else if (x1 <= 1.9e+27) {
		tmp = x1 + ((x2 * -6.0) + (t_2 + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 6.0) - 12.0))))));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * (((x2 * ((x1 * 6.0) + ((x1 * ((x1 * 3.0) + 9.0)) / x2))) + (4.0 * (x2 * t_0))) - 2.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = (2.0d0 * x2) - 3.0d0
    t_1 = 6.0d0 * t_0
    t_2 = x1 * ((x1 * 9.0d0) - 2.0d0)
    if (x1 <= (-4.4d+153)) then
        tmp = x1 + ((x2 * (-6.0d0)) + t_2)
    else if (x1 <= (-4.5d+79)) then
        tmp = x1 + ((3.0d0 * ((((x1 * (x1 * 3.0d0)) - (2.0d0 * x2)) - x1) / ((x1 * x1) + 1.0d0))) + (x1 + (x1 * (t_1 + (x1 * (((x2 * 8.0d0) + (x1 * ((t_1 + (6.0d0 * (3.0d0 + (x2 * (-2.0d0))))) - 3.0d0))) - 3.0d0))))))
    else if (x1 <= 1.9d+27) then
        tmp = x1 + ((x2 * (-6.0d0)) + (t_2 + (x2 * ((8.0d0 * (x1 * x2)) + (x1 * ((x1 * 6.0d0) - 12.0d0))))))
    else
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * (((x2 * ((x1 * 6.0d0) + ((x1 * ((x1 * 3.0d0) + 9.0d0)) / x2))) + (4.0d0 * (x2 * t_0))) - 2.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (2.0 * x2) - 3.0;
	double t_1 = 6.0 * t_0;
	double t_2 = x1 * ((x1 * 9.0) - 2.0);
	double tmp;
	if (x1 <= -4.4e+153) {
		tmp = x1 + ((x2 * -6.0) + t_2);
	} else if (x1 <= -4.5e+79) {
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / ((x1 * x1) + 1.0))) + (x1 + (x1 * (t_1 + (x1 * (((x2 * 8.0) + (x1 * ((t_1 + (6.0 * (3.0 + (x2 * -2.0)))) - 3.0))) - 3.0))))));
	} else if (x1 <= 1.9e+27) {
		tmp = x1 + ((x2 * -6.0) + (t_2 + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 6.0) - 12.0))))));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * (((x2 * ((x1 * 6.0) + ((x1 * ((x1 * 3.0) + 9.0)) / x2))) + (4.0 * (x2 * t_0))) - 2.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (2.0 * x2) - 3.0
	t_1 = 6.0 * t_0
	t_2 = x1 * ((x1 * 9.0) - 2.0)
	tmp = 0
	if x1 <= -4.4e+153:
		tmp = x1 + ((x2 * -6.0) + t_2)
	elif x1 <= -4.5e+79:
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / ((x1 * x1) + 1.0))) + (x1 + (x1 * (t_1 + (x1 * (((x2 * 8.0) + (x1 * ((t_1 + (6.0 * (3.0 + (x2 * -2.0)))) - 3.0))) - 3.0))))))
	elif x1 <= 1.9e+27:
		tmp = x1 + ((x2 * -6.0) + (t_2 + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 6.0) - 12.0))))))
	else:
		tmp = x1 + ((x2 * -6.0) + (x1 * (((x2 * ((x1 * 6.0) + ((x1 * ((x1 * 3.0) + 9.0)) / x2))) + (4.0 * (x2 * t_0))) - 2.0)))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(2.0 * x2) - 3.0)
	t_1 = Float64(6.0 * t_0)
	t_2 = Float64(x1 * Float64(Float64(x1 * 9.0) - 2.0))
	tmp = 0.0
	if (x1 <= -4.4e+153)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + t_2));
	elseif (x1 <= -4.5e+79)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(Float64(x1 * Float64(x1 * 3.0)) - Float64(2.0 * x2)) - x1) / Float64(Float64(x1 * x1) + 1.0))) + Float64(x1 + Float64(x1 * Float64(t_1 + Float64(x1 * Float64(Float64(Float64(x2 * 8.0) + Float64(x1 * Float64(Float64(t_1 + Float64(6.0 * Float64(3.0 + Float64(x2 * -2.0)))) - 3.0))) - 3.0)))))));
	elseif (x1 <= 1.9e+27)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(t_2 + Float64(x2 * Float64(Float64(8.0 * Float64(x1 * x2)) + Float64(x1 * Float64(Float64(x1 * 6.0) - 12.0)))))));
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(Float64(x2 * Float64(Float64(x1 * 6.0) + Float64(Float64(x1 * Float64(Float64(x1 * 3.0) + 9.0)) / x2))) + Float64(4.0 * Float64(x2 * t_0))) - 2.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (2.0 * x2) - 3.0;
	t_1 = 6.0 * t_0;
	t_2 = x1 * ((x1 * 9.0) - 2.0);
	tmp = 0.0;
	if (x1 <= -4.4e+153)
		tmp = x1 + ((x2 * -6.0) + t_2);
	elseif (x1 <= -4.5e+79)
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / ((x1 * x1) + 1.0))) + (x1 + (x1 * (t_1 + (x1 * (((x2 * 8.0) + (x1 * ((t_1 + (6.0 * (3.0 + (x2 * -2.0)))) - 3.0))) - 3.0))))));
	elseif (x1 <= 1.9e+27)
		tmp = x1 + ((x2 * -6.0) + (t_2 + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 6.0) - 12.0))))));
	else
		tmp = x1 + ((x2 * -6.0) + (x1 * (((x2 * ((x1 * 6.0) + ((x1 * ((x1 * 3.0) + 9.0)) / x2))) + (4.0 * (x2 * t_0))) - 2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]}, Block[{t$95$1 = N[(6.0 * t$95$0), $MachinePrecision]}, Block[{t$95$2 = N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -4.4e+153], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -4.5e+79], N[(x1 + N[(N[(3.0 * N[(N[(N[(N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision] - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(x1 * N[(t$95$1 + N[(x1 * N[(N[(N[(x2 * 8.0), $MachinePrecision] + N[(x1 * N[(N[(t$95$1 + N[(6.0 * N[(3.0 + N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.9e+27], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(t$95$2 + N[(x2 * N[(N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(N[(x1 * 6.0), $MachinePrecision] - 12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(N[(x2 * N[(N[(x1 * 6.0), $MachinePrecision] + N[(N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + 9.0), $MachinePrecision]), $MachinePrecision] / x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(4.0 * N[(x2 * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -4.3999999999999999e153

   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%

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

   5. Taylor expanded in x1 around 0 65.6%

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

      1. associate-*r* 65.6%

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

      2. cancel-sign-sub-inv 65.6%

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

      3. metadata-eval 65.6%

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

      4. *-commutative 65.6%

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

      5. *-commutative 65.6%

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

   7. Simplified 65.6%

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

   8. Taylor expanded in x2 around 0 100.0%

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

   if -4.3999999999999999e153 < x1 < -4.49999999999999994e79

   1. Initial program 33.3%

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

   3. Taylor expanded in x1 around inf 33.3%

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

   4. Taylor expanded in x1 around inf 33.3%

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

   5. Taylor expanded in x1 around 0 68.7%

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

   if -4.49999999999999994e79 < x1 < 1.90000000000000011e27

   1. Initial program 98.7%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   2. 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 81.2%

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

   5. Taylor expanded in x1 around 0 81.6%

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

      1. associate-*r* 81.6%

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

      2. cancel-sign-sub-inv 81.6%

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

      3. metadata-eval 81.6%

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

      4. *-commutative 81.6%

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

      5. *-commutative 81.6%

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

   7. Simplified 81.6%

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

   8. Taylor expanded in x2 around 0 89.9%

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

   if 1.90000000000000011e27 < x1

   1. Initial program 32.6%

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

   3. Taylor expanded in x1 around 0 10.1%

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

   4. Taylor expanded in x1 around 0 77.4%

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

   5. Taylor expanded in x2 around inf 91.6%

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

4. Final simplification 90.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4.4 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 - 2\right)\right)\\ \mathbf{elif}\;x1 \leq -4.5 \cdot 10^{+79}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + x1 \cdot \left(6 \cdot \left(2 \cdot x2 - 3\right) + x1 \cdot \left(\left(x2 \cdot 8 + x1 \cdot \left(\left(6 \cdot \left(2 \cdot x2 - 3\right) + 6 \cdot \left(3 + x2 \cdot -2\right)\right) - 3\right)\right) - 3\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.9 \cdot 10^{+27}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + \left(x1 \cdot \left(x1 \cdot 9 - 2\right) + x2 \cdot \left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(x1 \cdot 6 - 12\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(\left(x2 \cdot \left(x1 \cdot 6 + \frac{x1 \cdot \left(x1 \cdot 3 + 9\right)}{x2}\right) + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) - 2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 82.6% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 9 - 2\right)\\ \mathbf{if}\;x1 \leq -6.6 \cdot 10^{+93}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + t\_0\right)\\ \mathbf{elif}\;x1 \leq 7 \cdot 10^{+28}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + \left(t\_0 + x2 \cdot \left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(x1 \cdot 6 - 12\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(\left(x2 \cdot \left(x1 \cdot 6 + \frac{x1 \cdot \left(x1 \cdot 3 + 9\right)}{x2}\right) + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) - 2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (- (* x1 9.0) 2.0))))
   (if (<= x1 -6.6e+93)
     (+ x1 (+ (* x2 -6.0) t_0))
     (if (<= x1 7e+28)
       (+
        x1
        (+
         (* x2 -6.0)
         (+ t_0 (* x2 (+ (* 8.0 (* x1 x2)) (* x1 (- (* x1 6.0) 12.0)))))))
       (+
        x1
        (+
         (* x2 -6.0)
         (*
          x1
          (-
           (+
            (* x2 (+ (* x1 6.0) (/ (* x1 (+ (* x1 3.0) 9.0)) x2)))
            (* 4.0 (* x2 (- (* 2.0 x2) 3.0))))
           2.0))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * ((x1 * 9.0) - 2.0);
	double tmp;
	if (x1 <= -6.6e+93) {
		tmp = x1 + ((x2 * -6.0) + t_0);
	} else if (x1 <= 7e+28) {
		tmp = x1 + ((x2 * -6.0) + (t_0 + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 6.0) - 12.0))))));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * (((x2 * ((x1 * 6.0) + ((x1 * ((x1 * 3.0) + 9.0)) / x2))) + (4.0 * (x2 * ((2.0 * x2) - 3.0)))) - 2.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x1 * ((x1 * 9.0d0) - 2.0d0)
    if (x1 <= (-6.6d+93)) then
        tmp = x1 + ((x2 * (-6.0d0)) + t_0)
    else if (x1 <= 7d+28) then
        tmp = x1 + ((x2 * (-6.0d0)) + (t_0 + (x2 * ((8.0d0 * (x1 * x2)) + (x1 * ((x1 * 6.0d0) - 12.0d0))))))
    else
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * (((x2 * ((x1 * 6.0d0) + ((x1 * ((x1 * 3.0d0) + 9.0d0)) / x2))) + (4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0)))) - 2.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * ((x1 * 9.0) - 2.0);
	double tmp;
	if (x1 <= -6.6e+93) {
		tmp = x1 + ((x2 * -6.0) + t_0);
	} else if (x1 <= 7e+28) {
		tmp = x1 + ((x2 * -6.0) + (t_0 + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 6.0) - 12.0))))));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * (((x2 * ((x1 * 6.0) + ((x1 * ((x1 * 3.0) + 9.0)) / x2))) + (4.0 * (x2 * ((2.0 * x2) - 3.0)))) - 2.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * ((x1 * 9.0) - 2.0)
	tmp = 0
	if x1 <= -6.6e+93:
		tmp = x1 + ((x2 * -6.0) + t_0)
	elif x1 <= 7e+28:
		tmp = x1 + ((x2 * -6.0) + (t_0 + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 6.0) - 12.0))))))
	else:
		tmp = x1 + ((x2 * -6.0) + (x1 * (((x2 * ((x1 * 6.0) + ((x1 * ((x1 * 3.0) + 9.0)) / x2))) + (4.0 * (x2 * ((2.0 * x2) - 3.0)))) - 2.0)))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(Float64(x1 * 9.0) - 2.0))
	tmp = 0.0
	if (x1 <= -6.6e+93)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + t_0));
	elseif (x1 <= 7e+28)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(t_0 + Float64(x2 * Float64(Float64(8.0 * Float64(x1 * x2)) + Float64(x1 * Float64(Float64(x1 * 6.0) - 12.0)))))));
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(Float64(x2 * Float64(Float64(x1 * 6.0) + Float64(Float64(x1 * Float64(Float64(x1 * 3.0) + 9.0)) / x2))) + Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0)))) - 2.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * ((x1 * 9.0) - 2.0);
	tmp = 0.0;
	if (x1 <= -6.6e+93)
		tmp = x1 + ((x2 * -6.0) + t_0);
	elseif (x1 <= 7e+28)
		tmp = x1 + ((x2 * -6.0) + (t_0 + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 6.0) - 12.0))))));
	else
		tmp = x1 + ((x2 * -6.0) + (x1 * (((x2 * ((x1 * 6.0) + ((x1 * ((x1 * 3.0) + 9.0)) / x2))) + (4.0 * (x2 * ((2.0 * x2) - 3.0)))) - 2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -6.6e+93], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + t$95$0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 7e+28], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(t$95$0 + N[(x2 * N[(N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(N[(x1 * 6.0), $MachinePrecision] - 12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(N[(x2 * N[(N[(x1 * 6.0), $MachinePrecision] + N[(N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + 9.0), $MachinePrecision]), $MachinePrecision] / x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(4.0 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -6.60000000000000017e93

   1. Initial program 4.8%

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

   3. Taylor expanded in x1 around 0 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 0 0.0%

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

   5. Taylor expanded in x1 around 0 50.8%

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

      1. associate-*r* 50.8%

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

      2. cancel-sign-sub-inv 50.8%

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

      3. metadata-eval 50.8%

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

      4. *-commutative 50.8%

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

      5. *-commutative 50.8%

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

   7. Simplified 50.8%

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

   8. Taylor expanded in x2 around 0 77.8%

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

   if -6.60000000000000017e93 < x1 < 6.9999999999999999e28

   1. Initial program 98.7%

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

   3. Taylor expanded in x1 around 0 81.7%

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

   4. Taylor expanded in x1 around 0 80.2%

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

   5. Taylor expanded in x1 around 0 80.6%

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

      1. associate-*r* 80.6%

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

      2. cancel-sign-sub-inv 80.6%

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

      3. metadata-eval 80.6%

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

      4. *-commutative 80.6%

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

      5. *-commutative 80.6%

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

   7. Simplified 80.6%

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

   8. Taylor expanded in x2 around 0 88.9%

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

   if 6.9999999999999999e28 < x1

   1. Initial program 32.6%

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

   3. Taylor expanded in x1 around 0 10.1%

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

   4. Taylor expanded in x1 around 0 77.4%

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

   5. Taylor expanded in x2 around inf 91.6%

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

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -6.6 \cdot 10^{+93}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 - 2\right)\right)\\ \mathbf{elif}\;x1 \leq 7 \cdot 10^{+28}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + \left(x1 \cdot \left(x1 \cdot 9 - 2\right) + x2 \cdot \left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(x1 \cdot 6 - 12\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(\left(x2 \cdot \left(x1 \cdot 6 + \frac{x1 \cdot \left(x1 \cdot 3 + 9\right)}{x2}\right) + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) - 2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 82.7% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 9 - 2\right)\\ \mathbf{if}\;x1 \leq -7.2 \cdot 10^{+93}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + t\_0\right)\\ \mathbf{elif}\;x1 \leq 1.4 \cdot 10^{+41}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + \left(t\_0 + x2 \cdot \left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(x1 \cdot 6 - 12\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot -3\right) + x2 \cdot \left(x1 \cdot 6 + \frac{x1 \cdot \left(x1 \cdot 3 + 9\right)}{x2}\right)\right) - 2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (- (* x1 9.0) 2.0))))
   (if (<= x1 -7.2e+93)
     (+ x1 (+ (* x2 -6.0) t_0))
     (if (<= x1 1.4e+41)
       (+
        x1
        (+
         (* x2 -6.0)
         (+ t_0 (* x2 (+ (* 8.0 (* x1 x2)) (* x1 (- (* x1 6.0) 12.0)))))))
       (+
        x1
        (+
         (* x2 -6.0)
         (*
          x1
          (-
           (+
            (* 4.0 (* x2 -3.0))
            (* x2 (+ (* x1 6.0) (/ (* x1 (+ (* x1 3.0) 9.0)) x2))))
           2.0))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * ((x1 * 9.0) - 2.0);
	double tmp;
	if (x1 <= -7.2e+93) {
		tmp = x1 + ((x2 * -6.0) + t_0);
	} else if (x1 <= 1.4e+41) {
		tmp = x1 + ((x2 * -6.0) + (t_0 + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 6.0) - 12.0))))));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * (((4.0 * (x2 * -3.0)) + (x2 * ((x1 * 6.0) + ((x1 * ((x1 * 3.0) + 9.0)) / x2)))) - 2.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x1 * ((x1 * 9.0d0) - 2.0d0)
    if (x1 <= (-7.2d+93)) then
        tmp = x1 + ((x2 * (-6.0d0)) + t_0)
    else if (x1 <= 1.4d+41) then
        tmp = x1 + ((x2 * (-6.0d0)) + (t_0 + (x2 * ((8.0d0 * (x1 * x2)) + (x1 * ((x1 * 6.0d0) - 12.0d0))))))
    else
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * (((4.0d0 * (x2 * (-3.0d0))) + (x2 * ((x1 * 6.0d0) + ((x1 * ((x1 * 3.0d0) + 9.0d0)) / x2)))) - 2.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * ((x1 * 9.0) - 2.0);
	double tmp;
	if (x1 <= -7.2e+93) {
		tmp = x1 + ((x2 * -6.0) + t_0);
	} else if (x1 <= 1.4e+41) {
		tmp = x1 + ((x2 * -6.0) + (t_0 + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 6.0) - 12.0))))));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * (((4.0 * (x2 * -3.0)) + (x2 * ((x1 * 6.0) + ((x1 * ((x1 * 3.0) + 9.0)) / x2)))) - 2.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * ((x1 * 9.0) - 2.0)
	tmp = 0
	if x1 <= -7.2e+93:
		tmp = x1 + ((x2 * -6.0) + t_0)
	elif x1 <= 1.4e+41:
		tmp = x1 + ((x2 * -6.0) + (t_0 + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 6.0) - 12.0))))))
	else:
		tmp = x1 + ((x2 * -6.0) + (x1 * (((4.0 * (x2 * -3.0)) + (x2 * ((x1 * 6.0) + ((x1 * ((x1 * 3.0) + 9.0)) / x2)))) - 2.0)))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(Float64(x1 * 9.0) - 2.0))
	tmp = 0.0
	if (x1 <= -7.2e+93)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + t_0));
	elseif (x1 <= 1.4e+41)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(t_0 + Float64(x2 * Float64(Float64(8.0 * Float64(x1 * x2)) + Float64(x1 * Float64(Float64(x1 * 6.0) - 12.0)))))));
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(Float64(4.0 * Float64(x2 * -3.0)) + Float64(x2 * Float64(Float64(x1 * 6.0) + Float64(Float64(x1 * Float64(Float64(x1 * 3.0) + 9.0)) / x2)))) - 2.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * ((x1 * 9.0) - 2.0);
	tmp = 0.0;
	if (x1 <= -7.2e+93)
		tmp = x1 + ((x2 * -6.0) + t_0);
	elseif (x1 <= 1.4e+41)
		tmp = x1 + ((x2 * -6.0) + (t_0 + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 6.0) - 12.0))))));
	else
		tmp = x1 + ((x2 * -6.0) + (x1 * (((4.0 * (x2 * -3.0)) + (x2 * ((x1 * 6.0) + ((x1 * ((x1 * 3.0) + 9.0)) / x2)))) - 2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -7.2e+93], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + t$95$0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.4e+41], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(t$95$0 + N[(x2 * N[(N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(N[(x1 * 6.0), $MachinePrecision] - 12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(N[(4.0 * N[(x2 * -3.0), $MachinePrecision]), $MachinePrecision] + N[(x2 * N[(N[(x1 * 6.0), $MachinePrecision] + N[(N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + 9.0), $MachinePrecision]), $MachinePrecision] / x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -7.1999999999999998e93

   1. Initial program 4.8%

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

   3. Taylor expanded in x1 around 0 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 0 0.0%

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

   5. Taylor expanded in x1 around 0 50.8%

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

      1. associate-*r* 50.8%

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

      2. cancel-sign-sub-inv 50.8%

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

      3. metadata-eval 50.8%

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

      4. *-commutative 50.8%

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

      5. *-commutative 50.8%

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

   7. Simplified 50.8%

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

   8. Taylor expanded in x2 around 0 77.8%

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

   if -7.1999999999999998e93 < x1 < 1.4e41

   1. Initial program 98.8%

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

   3. Taylor expanded in x1 around 0 81.0%

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

   4. Taylor expanded in x1 around 0 79.6%

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

   5. Taylor expanded in x1 around 0 80.0%

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

      1. associate-*r* 80.0%

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

      2. cancel-sign-sub-inv 80.0%

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

      3. metadata-eval 80.0%

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

      4. *-commutative 80.0%

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

      5. *-commutative 80.0%

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

   7. Simplified 80.0%

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

   8. Taylor expanded in x2 around 0 88.0%

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

   if 1.4e41 < x1

   1. Initial program 27.4%

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

   3. Taylor expanded in x1 around 0 6.8%

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

   4. Taylor expanded in x1 around 0 79.2%

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

   5. Taylor expanded in x2 around inf 94.5%

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

   6. Taylor expanded in x2 around 0 94.5%

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

      1. *-commutative 94.5%

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

   8. Simplified 94.5%

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

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -7.2 \cdot 10^{+93}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 - 2\right)\right)\\ \mathbf{elif}\;x1 \leq 1.4 \cdot 10^{+41}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + \left(x1 \cdot \left(x1 \cdot 9 - 2\right) + x2 \cdot \left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(x1 \cdot 6 - 12\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot -3\right) + x2 \cdot \left(x1 \cdot 6 + \frac{x1 \cdot \left(x1 \cdot 3 + 9\right)}{x2}\right)\right) - 2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 76.7% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -1.85 \cdot 10^{+121}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 - 2\right)\right)\\ \mathbf{elif}\;x1 \leq 3.9 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x2 \cdot \left(x1 \cdot \left(6 + \frac{9}{x2}\right)\right)\right) - 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot \left(x1 \cdot 3 + 9\right) - 2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -1.85e+121)
   (+ x1 (+ (* x2 -6.0) (* x1 (- (* x1 9.0) 2.0))))
   (if (<= x1 3.9e+102)
     (+
      x1
      (+
       (* x2 -6.0)
       (*
        x1
        (-
         (+ (* 4.0 (* x2 (- (* 2.0 x2) 3.0))) (* x2 (* x1 (+ 6.0 (/ 9.0 x2)))))
         2.0))))
     (+ x1 (+ (* x2 -6.0) (* x1 (- (* x1 (+ (* x1 3.0) 9.0)) 2.0)))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -1.85e+121) {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) - 2.0)));
	} else if (x1 <= 3.9e+102) {
		tmp = x1 + ((x2 * -6.0) + (x1 * (((4.0 * (x2 * ((2.0 * x2) - 3.0))) + (x2 * (x1 * (6.0 + (9.0 / x2))))) - 2.0)));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * ((x1 * 3.0) + 9.0)) - 2.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x1 <= (-1.85d+121)) then
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * ((x1 * 9.0d0) - 2.0d0)))
    else if (x1 <= 3.9d+102) then
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * (((4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0))) + (x2 * (x1 * (6.0d0 + (9.0d0 / x2))))) - 2.0d0)))
    else
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * ((x1 * ((x1 * 3.0d0) + 9.0d0)) - 2.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= -1.85e+121) {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) - 2.0)));
	} else if (x1 <= 3.9e+102) {
		tmp = x1 + ((x2 * -6.0) + (x1 * (((4.0 * (x2 * ((2.0 * x2) - 3.0))) + (x2 * (x1 * (6.0 + (9.0 / x2))))) - 2.0)));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * ((x1 * 3.0) + 9.0)) - 2.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -1.85e+121:
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) - 2.0)))
	elif x1 <= 3.9e+102:
		tmp = x1 + ((x2 * -6.0) + (x1 * (((4.0 * (x2 * ((2.0 * x2) - 3.0))) + (x2 * (x1 * (6.0 + (9.0 / x2))))) - 2.0)))
	else:
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * ((x1 * 3.0) + 9.0)) - 2.0)))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -1.85e+121)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(x1 * 9.0) - 2.0))));
	elseif (x1 <= 3.9e+102)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0))) + Float64(x2 * Float64(x1 * Float64(6.0 + Float64(9.0 / x2))))) - 2.0))));
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(x1 * Float64(Float64(x1 * 3.0) + 9.0)) - 2.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -1.85e+121)
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) - 2.0)));
	elseif (x1 <= 3.9e+102)
		tmp = x1 + ((x2 * -6.0) + (x1 * (((4.0 * (x2 * ((2.0 * x2) - 3.0))) + (x2 * (x1 * (6.0 + (9.0 / x2))))) - 2.0)));
	else
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * ((x1 * 3.0) + 9.0)) - 2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -1.85e+121], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 3.9e+102], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(N[(4.0 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x2 * N[(x1 * N[(6.0 + N[(9.0 / x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + 9.0), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -1.85000000000000006e121

   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%

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

   5. Taylor expanded in x1 around 0 55.9%

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

      1. associate-*r* 55.9%

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

      2. cancel-sign-sub-inv 55.9%

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

      3. metadata-eval 55.9%

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

      4. *-commutative 55.9%

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

      5. *-commutative 55.9%

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

   7. Simplified 55.9%

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

   8. Taylor expanded in x2 around 0 85.4%

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

   if -1.85000000000000006e121 < x1 < 3.8999999999999998e102

   1. Initial program 97.7%

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

   3. Taylor expanded in x1 around 0 77.2%

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

   4. Taylor expanded in x1 around 0 75.9%

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

   5. Taylor expanded in x2 around inf 77.5%

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

   6. Taylor expanded in x1 around 0 76.2%

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

      1. associate-*r* 76.8%

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

      2. *-commutative 76.8%

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

      3. associate-*l* 78.4%

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

      4. +-commutative 78.4%

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

      5. associate-*r/ 78.4%

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

      6. metadata-eval 78.4%

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

   8. Simplified 78.4%

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

   if 3.8999999999999998e102 < x1

   1. Initial program 15.9%

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

   3. Taylor expanded in x1 around 0 2.9%

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

   4. Taylor expanded in x1 around 0 86.4%

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

   5. Taylor expanded in x2 around 0 100.0%

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

      1. *-commutative 100.0%

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

   7. Simplified 100.0%

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

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.85 \cdot 10^{+121}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 - 2\right)\right)\\ \mathbf{elif}\;x1 \leq 3.9 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x2 \cdot \left(x1 \cdot \left(6 + \frac{9}{x2}\right)\right)\right) - 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot \left(x1 \cdot 3 + 9\right) - 2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 82.3% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 9 - 2\right)\\ \mathbf{if}\;x1 \leq -7.2 \cdot 10^{+93}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + t\_0\right)\\ \mathbf{elif}\;x1 \leq 2.9 \cdot 10^{+84}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + \left(t\_0 + x2 \cdot \left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(x1 \cdot 6 - 12\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot \left(x1 \cdot 3 + 9\right) - 2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (- (* x1 9.0) 2.0))))
   (if (<= x1 -7.2e+93)
     (+ x1 (+ (* x2 -6.0) t_0))
     (if (<= x1 2.9e+84)
       (+
        x1
        (+
         (* x2 -6.0)
         (+ t_0 (* x2 (+ (* 8.0 (* x1 x2)) (* x1 (- (* x1 6.0) 12.0)))))))
       (+ x1 (+ (* x2 -6.0) (* x1 (- (* x1 (+ (* x1 3.0) 9.0)) 2.0))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * ((x1 * 9.0) - 2.0);
	double tmp;
	if (x1 <= -7.2e+93) {
		tmp = x1 + ((x2 * -6.0) + t_0);
	} else if (x1 <= 2.9e+84) {
		tmp = x1 + ((x2 * -6.0) + (t_0 + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 6.0) - 12.0))))));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * ((x1 * 3.0) + 9.0)) - 2.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x1 * ((x1 * 9.0d0) - 2.0d0)
    if (x1 <= (-7.2d+93)) then
        tmp = x1 + ((x2 * (-6.0d0)) + t_0)
    else if (x1 <= 2.9d+84) then
        tmp = x1 + ((x2 * (-6.0d0)) + (t_0 + (x2 * ((8.0d0 * (x1 * x2)) + (x1 * ((x1 * 6.0d0) - 12.0d0))))))
    else
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * ((x1 * ((x1 * 3.0d0) + 9.0d0)) - 2.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * ((x1 * 9.0) - 2.0);
	double tmp;
	if (x1 <= -7.2e+93) {
		tmp = x1 + ((x2 * -6.0) + t_0);
	} else if (x1 <= 2.9e+84) {
		tmp = x1 + ((x2 * -6.0) + (t_0 + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 6.0) - 12.0))))));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * ((x1 * 3.0) + 9.0)) - 2.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * ((x1 * 9.0) - 2.0)
	tmp = 0
	if x1 <= -7.2e+93:
		tmp = x1 + ((x2 * -6.0) + t_0)
	elif x1 <= 2.9e+84:
		tmp = x1 + ((x2 * -6.0) + (t_0 + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 6.0) - 12.0))))))
	else:
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * ((x1 * 3.0) + 9.0)) - 2.0)))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(Float64(x1 * 9.0) - 2.0))
	tmp = 0.0
	if (x1 <= -7.2e+93)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + t_0));
	elseif (x1 <= 2.9e+84)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(t_0 + Float64(x2 * Float64(Float64(8.0 * Float64(x1 * x2)) + Float64(x1 * Float64(Float64(x1 * 6.0) - 12.0)))))));
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(x1 * Float64(Float64(x1 * 3.0) + 9.0)) - 2.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * ((x1 * 9.0) - 2.0);
	tmp = 0.0;
	if (x1 <= -7.2e+93)
		tmp = x1 + ((x2 * -6.0) + t_0);
	elseif (x1 <= 2.9e+84)
		tmp = x1 + ((x2 * -6.0) + (t_0 + (x2 * ((8.0 * (x1 * x2)) + (x1 * ((x1 * 6.0) - 12.0))))));
	else
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * ((x1 * 3.0) + 9.0)) - 2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -7.2e+93], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + t$95$0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 2.9e+84], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(t$95$0 + N[(x2 * N[(N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(N[(x1 * 6.0), $MachinePrecision] - 12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + 9.0), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -7.1999999999999998e93

   1. Initial program 4.8%

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

   3. Taylor expanded in x1 around 0 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 0 0.0%

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

   5. Taylor expanded in x1 around 0 50.8%

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

      1. associate-*r* 50.8%

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

      2. cancel-sign-sub-inv 50.8%

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

      3. metadata-eval 50.8%

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

      4. *-commutative 50.8%

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

      5. *-commutative 50.8%

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

   7. Simplified 50.8%

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

   8. Taylor expanded in x2 around 0 77.8%

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

   if -7.1999999999999998e93 < x1 < 2.89999999999999989e84

   1. Initial program 98.8%

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

   3. Taylor expanded in x1 around 0 79.9%

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

   4. Taylor expanded in x1 around 0 78.5%

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

   5. Taylor expanded in x1 around 0 78.8%

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

      1. associate-*r* 78.8%

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

      2. cancel-sign-sub-inv 78.8%

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

      3. metadata-eval 78.8%

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

      4. *-commutative 78.8%

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

      5. *-commutative 78.8%

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

   7. Simplified 78.8%

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

   8. Taylor expanded in x2 around 0 86.6%

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

   if 2.89999999999999989e84 < x1

   1. Initial program 19.6%

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

   3. Taylor expanded in x1 around 0 2.9%

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

   4. Taylor expanded in x1 around 0 83.0%

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

   5. Taylor expanded in x2 around 0 96.1%

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

      1. *-commutative 96.1%

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

   7. Simplified 96.1%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -7.2 \cdot 10^{+93}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 - 2\right)\right)\\ \mathbf{elif}\;x1 \leq 2.9 \cdot 10^{+84}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + \left(x1 \cdot \left(x1 \cdot 9 - 2\right) + x2 \cdot \left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(x1 \cdot 6 - 12\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot \left(x1 \cdot 3 + 9\right) - 2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 75.5% accurate, 4.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -9 \cdot 10^{+86}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 - 2\right)\right)\\ \mathbf{elif}\;x1 \leq 1.22 \cdot 10^{+85}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot \left(x1 \cdot 3 + 9\right) - 2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -9e+86)
   (+ x1 (+ (* x2 -6.0) (* x1 (- (* x1 9.0) 2.0))))
   (if (<= x1 1.22e+85)
     (+ x1 (+ (* x2 -6.0) (* x1 (- (* 4.0 (* x2 (- (* 2.0 x2) 3.0))) 2.0))))
     (+ x1 (+ (* x2 -6.0) (* x1 (- (* x1 (+ (* x1 3.0) 9.0)) 2.0)))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -9e+86) {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) - 2.0)));
	} else if (x1 <= 1.22e+85) {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * ((x1 * 3.0) + 9.0)) - 2.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x1 <= (-9d+86)) then
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * ((x1 * 9.0d0) - 2.0d0)))
    else if (x1 <= 1.22d+85) then
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * ((4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0))) - 2.0d0)))
    else
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * ((x1 * ((x1 * 3.0d0) + 9.0d0)) - 2.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= -9e+86) {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) - 2.0)));
	} else if (x1 <= 1.22e+85) {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * ((x1 * 3.0) + 9.0)) - 2.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -9e+86:
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) - 2.0)))
	elif x1 <= 1.22e+85:
		tmp = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)))
	else:
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * ((x1 * 3.0) + 9.0)) - 2.0)))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -9e+86)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(x1 * 9.0) - 2.0))));
	elseif (x1 <= 1.22e+85)
		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))));
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(x1 * Float64(Float64(x1 * 3.0) + 9.0)) - 2.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -9e+86)
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) - 2.0)));
	elseif (x1 <= 1.22e+85)
		tmp = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)));
	else
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * ((x1 * 3.0) + 9.0)) - 2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -9e+86], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.22e+85], 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], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + 9.0), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -8.99999999999999986e86

   1. Initial program 9.1%

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

   3. Taylor expanded in x1 around 0 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 0 0.0%

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

   5. Taylor expanded in x1 around 0 48.7%

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

      1. associate-*r* 48.7%

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

      2. cancel-sign-sub-inv 48.7%

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

      3. metadata-eval 48.7%

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

      4. *-commutative 48.7%

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

      5. *-commutative 48.7%

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

   7. Simplified 48.7%

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

   8. Taylor expanded in x2 around 0 74.5%

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

   if -8.99999999999999986e86 < x1 < 1.22e85

   1. Initial program 98.8%

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

   3. Taylor expanded in x1 around 0 80.8%

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

   4. Taylor expanded in x1 around 0 80.6%

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

   if 1.22e85 < x1

   1. Initial program 19.6%

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

   3. Taylor expanded in x1 around 0 2.9%

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

   4. Taylor expanded in x1 around 0 83.0%

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

   5. Taylor expanded in x2 around 0 96.1%

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

      1. *-commutative 96.1%

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

   7. Simplified 96.1%

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

4. Final simplification 82.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -9 \cdot 10^{+86}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 - 2\right)\right)\\ \mathbf{elif}\;x1 \leq 1.22 \cdot 10^{+85}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot \left(x1 \cdot 3 + 9\right) - 2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 67.5% accurate, 5.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x2 \leq -1.42 \cdot 10^{+203} \lor \neg \left(x2 \leq 1.35 \cdot 10^{+130}\right):\\ \;\;\;\;x1 + x1 \cdot \left(1 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 - 2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x2 -1.42e+203) (not (<= x2 1.35e+130)))
   (+ x1 (* x1 (+ 1.0 (* 4.0 (* x2 (- (* 2.0 x2) 3.0))))))
   (+ x1 (+ (* x2 -6.0) (* x1 (- (* x1 9.0) 2.0))))))

C

double code(double x1, double x2) {
	double tmp;
	if ((x2 <= -1.42e+203) || !(x2 <= 1.35e+130)) {
		tmp = x1 + (x1 * (1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0)))));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) - 2.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if ((x2 <= (-1.42d+203)) .or. (.not. (x2 <= 1.35d+130))) then
        tmp = x1 + (x1 * (1.0d0 + (4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0)))))
    else
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * ((x1 * 9.0d0) - 2.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x2 <= -1.42e+203) || !(x2 <= 1.35e+130)) {
		tmp = x1 + (x1 * (1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0)))));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) - 2.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x2 <= -1.42e+203) or not (x2 <= 1.35e+130):
		tmp = x1 + (x1 * (1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0)))))
	else:
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) - 2.0)))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x2 <= -1.42e+203) || !(x2 <= 1.35e+130))
		tmp = Float64(x1 + Float64(x1 * Float64(1.0 + Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0))))));
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(x1 * 9.0) - 2.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x2 <= -1.42e+203) || ~((x2 <= 1.35e+130)))
		tmp = x1 + (x1 * (1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0)))));
	else
		tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) - 2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x2, -1.42e+203], N[Not[LessEqual[x2, 1.35e+130]], $MachinePrecision]], N[(x1 + N[(x1 * N[(1.0 + N[(4.0 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x2 < -1.41999999999999999e203 or 1.3499999999999999e130 < x2

   1. Initial program 62.8%

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

   3. Taylor expanded in x1 around 0 49.7%

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

   4. Taylor expanded in x1 around inf 70.7%

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

   if -1.41999999999999999e203 < x2 < 1.3499999999999999e130

   1. Initial program 71.1%

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

   3. Taylor expanded in x1 around 0 54.0%

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

   4. Taylor expanded in x1 around 0 69.2%

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

   5. Taylor expanded in x1 around 0 72.4%

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

      1. associate-*r* 72.4%

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

      2. cancel-sign-sub-inv 72.4%

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

      3. metadata-eval 72.4%

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

      4. *-commutative 72.4%

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

      5. *-commutative 72.4%

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

   7. Simplified 72.4%

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

   8. Taylor expanded in x2 around 0 76.6%

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

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq -1.42 \cdot 10^{+203} \lor \neg \left(x2 \leq 1.35 \cdot 10^{+130}\right):\\ \;\;\;\;x1 + x1 \cdot \left(1 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 - 2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 62.9% accurate, 9.8× speedup

Math

\[\begin{array}{l} \\ x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 - 2\right)\right) \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (+ x1 (+ (* x2 -6.0) (* x1 (- (* x1 9.0) 2.0)))))

C

double code(double x1, double x2) {
	return x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) - 2.0)));
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    code = x1 + ((x2 * (-6.0d0)) + (x1 * ((x1 * 9.0d0) - 2.0d0)))
end function

Java

public static double code(double x1, double x2) {
	return x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) - 2.0)));
}

Python

def code(x1, x2):
	return x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) - 2.0)))

Julia

function code(x1, x2)
	return Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(x1 * 9.0) - 2.0))))
end

MATLAB

function tmp = code(x1, x2)
	tmp = x1 + ((x2 * -6.0) + (x1 * ((x1 * 9.0) - 2.0)));
end

Wolfram

code[x1_, x2_] := N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 69.1%

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

3. Taylor expanded in x1 around 0 53.0%

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

4. Taylor expanded in x1 around 0 66.4%

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

5. Taylor expanded in x1 around 0 68.5%

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

   1. associate-*r* 68.5%

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

   2. cancel-sign-sub-inv 68.5%

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

   3. metadata-eval 68.5%

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

   4. *-commutative 68.5%

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

   5. *-commutative 68.5%

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

7. Simplified 68.5%

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

8. Taylor expanded in x2 around 0 67.9%

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

9. Final simplification 67.9%

   \[\leadsto x1 + \left(x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 - 2\right)\right) \]
10. Add Preprocessing

Alternative 23: 31.1% accurate, 18.1× speedup

Math

\[\begin{array}{l} \\ x2 \cdot \left(\frac{x1}{x2} - 6\right) \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 69.1%

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

3. Taylor expanded in x1 around 0 53.0%

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

4. Taylor expanded in x1 around 0 28.6%

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

   1. *-commutative 28.6%

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

6. Simplified 28.6%

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

7. Taylor expanded in x2 around inf 32.6%

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

8. Final simplification 32.6%

   \[\leadsto x2 \cdot \left(\frac{x1}{x2} - 6\right) \]
9. Add Preprocessing

Alternative 24: 25.9% 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 69.1%

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

3. Taylor expanded in x1 around 0 53.0%

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

4. Taylor expanded in x1 around 0 28.6%

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

   1. *-commutative 28.6%

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

6. Simplified 28.6%

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

7. Final simplification 28.6%

   \[\leadsto x1 + x2 \cdot -6 \]
8. Add Preprocessing

Alternative 25: 25.7% accurate, 42.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 69.1%

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

3. Taylor expanded in x1 around 0 53.0%

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

4. Taylor expanded in x1 around 0 28.6%

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

   1. *-commutative 28.6%

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

6. Simplified 28.6%

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

7. Taylor expanded in x1 around 0 28.4%

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

8. Final simplification 28.4%

   \[\leadsto x2 \cdot -6 \]
9. Add Preprocessing

Alternative 26: 3.3% accurate, 127.0× speedup

Math

\[\begin{array}{l} \\ x1 \end{array} \]

FPCore

(FPCore (x1 x2) :precision binary64 x1)

C

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

Fortran

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

Java

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

Python

def code(x1, x2):
	return x1

Julia

function code(x1, x2)
	return x1
end

MATLAB

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

Wolfram

code[x1_, x2_] := x1

Derivation

1. Initial program 69.1%

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

3. Taylor expanded in x1 around 0 53.0%

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

4. Taylor expanded in x1 around 0 28.6%

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

   1. *-commutative 28.6%

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

6. Simplified 28.6%

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

7. Taylor expanded in x1 around inf 3.4%

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

8. Final simplification 3.4%

   \[\leadsto x1 \]
9. Add Preprocessing

Reproduce

herbie shell --seed 2024059 
(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))))))