Rosa's FloatVsDoubleBenchmark

Percentage Accurate: 70.2% → 99.4%

Time: 34.5s

Alternatives: 27

Speedup: 4.7×

• 47.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 70.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := x1 - \left(t\_0 - 2 \cdot x2\right)\\ t_2 := -1 - x1 \cdot x1\\ t_3 := x1 \cdot x1 + 1\\ t_4 := t\_0 + 2 \cdot x2\\ t_5 := \frac{x1 - t\_4}{t\_3}\\ t_6 := 3 + t\_5\\ t_7 := \frac{t\_4 - x1}{t\_3}\\ t_8 := t\_0 \cdot t\_7\\ t_9 := x1 \cdot \left(x1 \cdot x1\right)\\ \mathbf{if}\;x1 + \left(\left(x1 + \left(\left(t\_3 \cdot \left(t\_6 \cdot \left(\left(x1 \cdot 2\right) \cdot t\_5\right) - \left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot t\_5\right)\right) + t\_8\right) + t\_9\right)\right) + 3 \cdot \frac{t\_1}{t\_2}\right) \leq \infty:\\ \;\;\;\;x1 - \left(3 \cdot \frac{t\_1}{t\_3} - \left(x1 + \left(t\_9 + \left(t\_8 - t\_3 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{\left(2 \cdot x2 + 3 \cdot {x1}^{2}\right) - x1}{t\_2}\right) + \left(\left(x1 \cdot 2\right) \cdot t\_7\right) \cdot t\_6\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 + 6 \cdot {x1}^{4}\right) + 9\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (- x1 (- t_0 (* 2.0 x2))))
        (t_2 (- -1.0 (* x1 x1)))
        (t_3 (+ (* x1 x1) 1.0))
        (t_4 (+ t_0 (* 2.0 x2)))
        (t_5 (/ (- x1 t_4) t_3))
        (t_6 (+ 3.0 t_5))
        (t_7 (/ (- t_4 x1) t_3))
        (t_8 (* t_0 t_7))
        (t_9 (* x1 (* x1 x1))))
   (if (<=
        (+
         x1
         (+
          (+
           x1
           (+
            (+
             (*
              t_3
              (- (* t_6 (* (* x1 2.0) t_5)) (* (* x1 x1) (+ 6.0 (* 4.0 t_5)))))
             t_8)
            t_9))
          (* 3.0 (/ t_1 t_2))))
        INFINITY)
     (-
      x1
      (-
       (* 3.0 (/ t_1 t_3))
       (+
        x1
        (+
         t_9
         (-
          t_8
          (*
           t_3
           (+
            (*
             (* x1 x1)
             (+
              6.0
              (* 4.0 (/ (- (+ (* 2.0 x2) (* 3.0 (pow x1 2.0))) x1) t_2))))
            (* (* (* x1 2.0) t_7) t_6))))))))
     (+ x1 (+ (+ x1 (* 6.0 (pow x1 4.0))) 9.0)))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = x1 - (t_0 - (2.0 * x2));
	double t_2 = -1.0 - (x1 * x1);
	double t_3 = (x1 * x1) + 1.0;
	double t_4 = t_0 + (2.0 * x2);
	double t_5 = (x1 - t_4) / t_3;
	double t_6 = 3.0 + t_5;
	double t_7 = (t_4 - x1) / t_3;
	double t_8 = t_0 * t_7;
	double t_9 = x1 * (x1 * x1);
	double tmp;
	if ((x1 + ((x1 + (((t_3 * ((t_6 * ((x1 * 2.0) * t_5)) - ((x1 * x1) * (6.0 + (4.0 * t_5))))) + t_8) + t_9)) + (3.0 * (t_1 / t_2)))) <= ((double) INFINITY)) {
		tmp = x1 - ((3.0 * (t_1 / t_3)) - (x1 + (t_9 + (t_8 - (t_3 * (((x1 * x1) * (6.0 + (4.0 * ((((2.0 * x2) + (3.0 * pow(x1, 2.0))) - x1) / t_2)))) + (((x1 * 2.0) * t_7) * t_6)))))));
	} else {
		tmp = x1 + ((x1 + (6.0 * pow(x1, 4.0))) + 9.0);
	}
	return tmp;
}

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = x1 - (t_0 - (2.0 * x2));
	double t_2 = -1.0 - (x1 * x1);
	double t_3 = (x1 * x1) + 1.0;
	double t_4 = t_0 + (2.0 * x2);
	double t_5 = (x1 - t_4) / t_3;
	double t_6 = 3.0 + t_5;
	double t_7 = (t_4 - x1) / t_3;
	double t_8 = t_0 * t_7;
	double t_9 = x1 * (x1 * x1);
	double tmp;
	if ((x1 + ((x1 + (((t_3 * ((t_6 * ((x1 * 2.0) * t_5)) - ((x1 * x1) * (6.0 + (4.0 * t_5))))) + t_8) + t_9)) + (3.0 * (t_1 / t_2)))) <= Double.POSITIVE_INFINITY) {
		tmp = x1 - ((3.0 * (t_1 / t_3)) - (x1 + (t_9 + (t_8 - (t_3 * (((x1 * x1) * (6.0 + (4.0 * ((((2.0 * x2) + (3.0 * Math.pow(x1, 2.0))) - x1) / t_2)))) + (((x1 * 2.0) * t_7) * t_6)))))));
	} else {
		tmp = x1 + ((x1 + (6.0 * Math.pow(x1, 4.0))) + 9.0);
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = x1 - (t_0 - (2.0 * x2))
	t_2 = -1.0 - (x1 * x1)
	t_3 = (x1 * x1) + 1.0
	t_4 = t_0 + (2.0 * x2)
	t_5 = (x1 - t_4) / t_3
	t_6 = 3.0 + t_5
	t_7 = (t_4 - x1) / t_3
	t_8 = t_0 * t_7
	t_9 = x1 * (x1 * x1)
	tmp = 0
	if (x1 + ((x1 + (((t_3 * ((t_6 * ((x1 * 2.0) * t_5)) - ((x1 * x1) * (6.0 + (4.0 * t_5))))) + t_8) + t_9)) + (3.0 * (t_1 / t_2)))) <= math.inf:
		tmp = x1 - ((3.0 * (t_1 / t_3)) - (x1 + (t_9 + (t_8 - (t_3 * (((x1 * x1) * (6.0 + (4.0 * ((((2.0 * x2) + (3.0 * math.pow(x1, 2.0))) - x1) / t_2)))) + (((x1 * 2.0) * t_7) * t_6)))))))
	else:
		tmp = x1 + ((x1 + (6.0 * math.pow(x1, 4.0))) + 9.0)
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(x1 - Float64(t_0 - Float64(2.0 * x2)))
	t_2 = Float64(-1.0 - Float64(x1 * x1))
	t_3 = Float64(Float64(x1 * x1) + 1.0)
	t_4 = Float64(t_0 + Float64(2.0 * x2))
	t_5 = Float64(Float64(x1 - t_4) / t_3)
	t_6 = Float64(3.0 + t_5)
	t_7 = Float64(Float64(t_4 - x1) / t_3)
	t_8 = Float64(t_0 * t_7)
	t_9 = Float64(x1 * Float64(x1 * x1))
	tmp = 0.0
	if (Float64(x1 + Float64(Float64(x1 + Float64(Float64(Float64(t_3 * Float64(Float64(t_6 * Float64(Float64(x1 * 2.0) * t_5)) - Float64(Float64(x1 * x1) * Float64(6.0 + Float64(4.0 * t_5))))) + t_8) + t_9)) + Float64(3.0 * Float64(t_1 / t_2)))) <= Inf)
		tmp = Float64(x1 - Float64(Float64(3.0 * Float64(t_1 / t_3)) - Float64(x1 + Float64(t_9 + Float64(t_8 - Float64(t_3 * Float64(Float64(Float64(x1 * x1) * Float64(6.0 + Float64(4.0 * Float64(Float64(Float64(Float64(2.0 * x2) + Float64(3.0 * (x1 ^ 2.0))) - x1) / t_2)))) + Float64(Float64(Float64(x1 * 2.0) * t_7) * t_6))))))));
	else
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(6.0 * (x1 ^ 4.0))) + 9.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * 3.0);
	t_1 = x1 - (t_0 - (2.0 * x2));
	t_2 = -1.0 - (x1 * x1);
	t_3 = (x1 * x1) + 1.0;
	t_4 = t_0 + (2.0 * x2);
	t_5 = (x1 - t_4) / t_3;
	t_6 = 3.0 + t_5;
	t_7 = (t_4 - x1) / t_3;
	t_8 = t_0 * t_7;
	t_9 = x1 * (x1 * x1);
	tmp = 0.0;
	if ((x1 + ((x1 + (((t_3 * ((t_6 * ((x1 * 2.0) * t_5)) - ((x1 * x1) * (6.0 + (4.0 * t_5))))) + t_8) + t_9)) + (3.0 * (t_1 / t_2)))) <= Inf)
		tmp = x1 - ((3.0 * (t_1 / t_3)) - (x1 + (t_9 + (t_8 - (t_3 * (((x1 * x1) * (6.0 + (4.0 * ((((2.0 * x2) + (3.0 * (x1 ^ 2.0))) - x1) / t_2)))) + (((x1 * 2.0) * t_7) * t_6)))))));
	else
		tmp = x1 + ((x1 + (6.0 * (x1 ^ 4.0))) + 9.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 - N[(t$95$0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(x1 - t$95$4), $MachinePrecision] / t$95$3), $MachinePrecision]}, Block[{t$95$6 = N[(3.0 + t$95$5), $MachinePrecision]}, Block[{t$95$7 = N[(N[(t$95$4 - x1), $MachinePrecision] / t$95$3), $MachinePrecision]}, Block[{t$95$8 = N[(t$95$0 * t$95$7), $MachinePrecision]}, Block[{t$95$9 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x1 + N[(N[(x1 + N[(N[(N[(t$95$3 * N[(N[(t$95$6 * N[(N[(x1 * 2.0), $MachinePrecision] * t$95$5), $MachinePrecision]), $MachinePrecision] - N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 + N[(4.0 * t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$8), $MachinePrecision] + t$95$9), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(t$95$1 / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(x1 - N[(N[(3.0 * N[(t$95$1 / t$95$3), $MachinePrecision]), $MachinePrecision] - N[(x1 + N[(t$95$9 + N[(t$95$8 - N[(t$95$3 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 + 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]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$7), $MachinePrecision] * t$95$6), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x1 + N[(6.0 * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 9.0), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 99.3%

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

   3. Taylor expanded in x1 around 0 99.3%

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

   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 -inf 6.8%

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

   4. Taylor expanded in x1 around inf 6.8%

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

   5. Taylor expanded in x1 around inf 100.0%

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

4. Final simplification 99.5%

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

Alternative 2: 99.3% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = t_0 + (2.0 * x2);
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = (x1 - t_1) / t_2;
	double t_4 = x1 + (((t_2 * (((3.0 + t_3) * ((x1 * 2.0) * t_3)) - ((x1 * x1) * (6.0 + (4.0 * t_3))))) + (t_0 * ((t_1 - x1) / t_2))) + (x1 * (x1 * x1)));
	double tmp;
	if ((x1 + (t_4 + (3.0 * ((x1 - (t_0 - (2.0 * x2))) / (-1.0 - (x1 * x1)))))) <= Double.POSITIVE_INFINITY) {
		tmp = x1 + (t_4 + (3.0 * (((x1 * ((x1 * 3.0) + -1.0)) - (2.0 * x2)) / t_2)));
	} else {
		tmp = x1 + ((x1 + (6.0 * Math.pow(x1, 4.0))) + 9.0);
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = t_0 + (2.0 * x2)
	t_2 = (x1 * x1) + 1.0
	t_3 = (x1 - t_1) / t_2
	t_4 = x1 + (((t_2 * (((3.0 + t_3) * ((x1 * 2.0) * t_3)) - ((x1 * x1) * (6.0 + (4.0 * t_3))))) + (t_0 * ((t_1 - x1) / t_2))) + (x1 * (x1 * x1)))
	tmp = 0
	if (x1 + (t_4 + (3.0 * ((x1 - (t_0 - (2.0 * x2))) / (-1.0 - (x1 * x1)))))) <= math.inf:
		tmp = x1 + (t_4 + (3.0 * (((x1 * ((x1 * 3.0) + -1.0)) - (2.0 * x2)) / t_2)))
	else:
		tmp = x1 + ((x1 + (6.0 * math.pow(x1, 4.0))) + 9.0)
	return tmp

Julia

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

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * 3.0);
	t_1 = t_0 + (2.0 * x2);
	t_2 = (x1 * x1) + 1.0;
	t_3 = (x1 - t_1) / t_2;
	t_4 = x1 + (((t_2 * (((3.0 + t_3) * ((x1 * 2.0) * t_3)) - ((x1 * x1) * (6.0 + (4.0 * t_3))))) + (t_0 * ((t_1 - x1) / t_2))) + (x1 * (x1 * x1)));
	tmp = 0.0;
	if ((x1 + (t_4 + (3.0 * ((x1 - (t_0 - (2.0 * x2))) / (-1.0 - (x1 * x1)))))) <= Inf)
		tmp = x1 + (t_4 + (3.0 * (((x1 * ((x1 * 3.0) + -1.0)) - (2.0 * x2)) / t_2)));
	else
		tmp = x1 + ((x1 + (6.0 * (x1 ^ 4.0))) + 9.0);
	end
	tmp_2 = tmp;
end

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 99.3%

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

      1. expm1-log1p-u 83.0%

         \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(3 \cdot x1\right)\right)} \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      2. expm1-undefine 83.1%

         \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\color{blue}{\left(e^{\mathsf{log1p}\left(3 \cdot x1\right)} - 1\right)} \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      3. *-commutative 83.1%

         \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(e^{\mathsf{log1p}\left(\color{blue}{x1 \cdot 3}\right)} - 1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   4. Applied egg-rr 83.1%

      \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\color{blue}{\left(e^{\mathsf{log1p}\left(x1 \cdot 3\right)} - 1\right)} \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   5. Taylor expanded in x1 around 0 99.3%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in x1 around -inf 6.8%

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

   4. Taylor expanded in x1 around inf 6.8%

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

   5. Taylor expanded in x1 around inf 100.0%

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

4. Final simplification 99.5%

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

Alternative 3: 98.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := x1 + \left(\left(x1 + 6 \cdot {x1}^{4}\right) + 9\right)\\ t_2 := x1 \cdot \left(x1 \cdot 3\right)\\ t_3 := t\_2 + 2 \cdot x2\\ t_4 := \frac{t\_3 - x1}{t\_0}\\ t_5 := \frac{x1 - t\_3}{t\_0}\\ t_6 := x1 \cdot \left(x1 \cdot x1\right)\\ t_7 := 3 + t\_5\\ \mathbf{if}\;x1 \leq -7.1 \cdot 10^{+106}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x1 \leq -0.0085:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(t\_6 - \left(t\_2 \cdot t\_5 - \left(-1 - x1 \cdot x1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 - 4 \cdot \left(3 + \frac{-1 + \frac{2 \cdot x2 - 3}{x1}}{x1}\right)\right) + \left(\left(x1 \cdot 2\right) \cdot t\_4\right) \cdot t\_7\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 0.0155:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2 - x1 \cdot \left(x1 \cdot \left(x2 \cdot -2 - 3\right) - -1\right)\right) + \left(x1 + x2 \cdot \left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.2 \cdot 10^{+75}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(t\_0 \cdot \left(t\_7 \cdot \left(\left(x1 \cdot 2\right) \cdot t\_5\right) - \left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot t\_5\right)\right) + t\_2 \cdot t\_4\right) + t\_6\right)\right) + 3 \cdot \left(3 + \frac{-1}{x1}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ (* x1 x1) 1.0))
        (t_1 (+ x1 (+ (+ x1 (* 6.0 (pow x1 4.0))) 9.0)))
        (t_2 (* x1 (* x1 3.0)))
        (t_3 (+ t_2 (* 2.0 x2)))
        (t_4 (/ (- t_3 x1) t_0))
        (t_5 (/ (- x1 t_3) t_0))
        (t_6 (* x1 (* x1 x1)))
        (t_7 (+ 3.0 t_5)))
   (if (<= x1 -7.1e+106)
     t_1
     (if (<= x1 -0.0085)
       (+
        x1
        (+
         9.0
         (+
          x1
          (-
           t_6
           (-
            (* t_2 t_5)
            (*
             (- -1.0 (* x1 x1))
             (+
              (*
               (* x1 x1)
               (-
                6.0
                (* 4.0 (+ 3.0 (/ (+ -1.0 (/ (- (* 2.0 x2) 3.0) x1)) x1)))))
              (* (* (* x1 2.0) t_4) t_7))))))))
       (if (<= x1 0.0155)
         (+
          x1
          (+
           (* 3.0 (- (* x2 -2.0) (* x1 (- (* x1 (- (* x2 -2.0) 3.0)) -1.0))))
           (+ x1 (* x2 (+ (* x1 -12.0) (* 8.0 (* x1 x2)))))))
         (if (<= x1 1.2e+75)
           (+
            x1
            (+
             (+
              x1
              (+
               (+
                (*
                 t_0
                 (-
                  (* t_7 (* (* x1 2.0) t_5))
                  (* (* x1 x1) (+ 6.0 (* 4.0 t_5)))))
                (* t_2 t_4))
               t_6))
             (* 3.0 (+ 3.0 (/ -1.0 x1)))))
           t_1))))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = x1 + ((x1 + (6.0 * pow(x1, 4.0))) + 9.0);
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = t_2 + (2.0 * x2);
	double t_4 = (t_3 - x1) / t_0;
	double t_5 = (x1 - t_3) / t_0;
	double t_6 = x1 * (x1 * x1);
	double t_7 = 3.0 + t_5;
	double tmp;
	if (x1 <= -7.1e+106) {
		tmp = t_1;
	} else if (x1 <= -0.0085) {
		tmp = x1 + (9.0 + (x1 + (t_6 - ((t_2 * t_5) - ((-1.0 - (x1 * x1)) * (((x1 * x1) * (6.0 - (4.0 * (3.0 + ((-1.0 + (((2.0 * x2) - 3.0) / x1)) / x1))))) + (((x1 * 2.0) * t_4) * t_7)))))));
	} else if (x1 <= 0.0155) {
		tmp = x1 + ((3.0 * ((x2 * -2.0) - (x1 * ((x1 * ((x2 * -2.0) - 3.0)) - -1.0)))) + (x1 + (x2 * ((x1 * -12.0) + (8.0 * (x1 * x2))))));
	} else if (x1 <= 1.2e+75) {
		tmp = x1 + ((x1 + (((t_0 * ((t_7 * ((x1 * 2.0) * t_5)) - ((x1 * x1) * (6.0 + (4.0 * t_5))))) + (t_2 * t_4)) + t_6)) + (3.0 * (3.0 + (-1.0 / x1))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: tmp
    t_0 = (x1 * x1) + 1.0d0
    t_1 = x1 + ((x1 + (6.0d0 * (x1 ** 4.0d0))) + 9.0d0)
    t_2 = x1 * (x1 * 3.0d0)
    t_3 = t_2 + (2.0d0 * x2)
    t_4 = (t_3 - x1) / t_0
    t_5 = (x1 - t_3) / t_0
    t_6 = x1 * (x1 * x1)
    t_7 = 3.0d0 + t_5
    if (x1 <= (-7.1d+106)) then
        tmp = t_1
    else if (x1 <= (-0.0085d0)) then
        tmp = x1 + (9.0d0 + (x1 + (t_6 - ((t_2 * t_5) - (((-1.0d0) - (x1 * x1)) * (((x1 * x1) * (6.0d0 - (4.0d0 * (3.0d0 + (((-1.0d0) + (((2.0d0 * x2) - 3.0d0) / x1)) / x1))))) + (((x1 * 2.0d0) * t_4) * t_7)))))))
    else if (x1 <= 0.0155d0) then
        tmp = x1 + ((3.0d0 * ((x2 * (-2.0d0)) - (x1 * ((x1 * ((x2 * (-2.0d0)) - 3.0d0)) - (-1.0d0))))) + (x1 + (x2 * ((x1 * (-12.0d0)) + (8.0d0 * (x1 * x2))))))
    else if (x1 <= 1.2d+75) then
        tmp = x1 + ((x1 + (((t_0 * ((t_7 * ((x1 * 2.0d0) * t_5)) - ((x1 * x1) * (6.0d0 + (4.0d0 * t_5))))) + (t_2 * t_4)) + t_6)) + (3.0d0 * (3.0d0 + ((-1.0d0) / x1))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = x1 + ((x1 + (6.0 * Math.pow(x1, 4.0))) + 9.0);
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = t_2 + (2.0 * x2);
	double t_4 = (t_3 - x1) / t_0;
	double t_5 = (x1 - t_3) / t_0;
	double t_6 = x1 * (x1 * x1);
	double t_7 = 3.0 + t_5;
	double tmp;
	if (x1 <= -7.1e+106) {
		tmp = t_1;
	} else if (x1 <= -0.0085) {
		tmp = x1 + (9.0 + (x1 + (t_6 - ((t_2 * t_5) - ((-1.0 - (x1 * x1)) * (((x1 * x1) * (6.0 - (4.0 * (3.0 + ((-1.0 + (((2.0 * x2) - 3.0) / x1)) / x1))))) + (((x1 * 2.0) * t_4) * t_7)))))));
	} else if (x1 <= 0.0155) {
		tmp = x1 + ((3.0 * ((x2 * -2.0) - (x1 * ((x1 * ((x2 * -2.0) - 3.0)) - -1.0)))) + (x1 + (x2 * ((x1 * -12.0) + (8.0 * (x1 * x2))))));
	} else if (x1 <= 1.2e+75) {
		tmp = x1 + ((x1 + (((t_0 * ((t_7 * ((x1 * 2.0) * t_5)) - ((x1 * x1) * (6.0 + (4.0 * t_5))))) + (t_2 * t_4)) + t_6)) + (3.0 * (3.0 + (-1.0 / x1))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x1 * x1) + 1.0
	t_1 = x1 + ((x1 + (6.0 * math.pow(x1, 4.0))) + 9.0)
	t_2 = x1 * (x1 * 3.0)
	t_3 = t_2 + (2.0 * x2)
	t_4 = (t_3 - x1) / t_0
	t_5 = (x1 - t_3) / t_0
	t_6 = x1 * (x1 * x1)
	t_7 = 3.0 + t_5
	tmp = 0
	if x1 <= -7.1e+106:
		tmp = t_1
	elif x1 <= -0.0085:
		tmp = x1 + (9.0 + (x1 + (t_6 - ((t_2 * t_5) - ((-1.0 - (x1 * x1)) * (((x1 * x1) * (6.0 - (4.0 * (3.0 + ((-1.0 + (((2.0 * x2) - 3.0) / x1)) / x1))))) + (((x1 * 2.0) * t_4) * t_7)))))))
	elif x1 <= 0.0155:
		tmp = x1 + ((3.0 * ((x2 * -2.0) - (x1 * ((x1 * ((x2 * -2.0) - 3.0)) - -1.0)))) + (x1 + (x2 * ((x1 * -12.0) + (8.0 * (x1 * x2))))))
	elif x1 <= 1.2e+75:
		tmp = x1 + ((x1 + (((t_0 * ((t_7 * ((x1 * 2.0) * t_5)) - ((x1 * x1) * (6.0 + (4.0 * t_5))))) + (t_2 * t_4)) + t_6)) + (3.0 * (3.0 + (-1.0 / x1))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * x1) + 1.0)
	t_1 = Float64(x1 + Float64(Float64(x1 + Float64(6.0 * (x1 ^ 4.0))) + 9.0))
	t_2 = Float64(x1 * Float64(x1 * 3.0))
	t_3 = Float64(t_2 + Float64(2.0 * x2))
	t_4 = Float64(Float64(t_3 - x1) / t_0)
	t_5 = Float64(Float64(x1 - t_3) / t_0)
	t_6 = Float64(x1 * Float64(x1 * x1))
	t_7 = Float64(3.0 + t_5)
	tmp = 0.0
	if (x1 <= -7.1e+106)
		tmp = t_1;
	elseif (x1 <= -0.0085)
		tmp = Float64(x1 + Float64(9.0 + Float64(x1 + Float64(t_6 - Float64(Float64(t_2 * t_5) - Float64(Float64(-1.0 - Float64(x1 * x1)) * Float64(Float64(Float64(x1 * x1) * Float64(6.0 - Float64(4.0 * Float64(3.0 + Float64(Float64(-1.0 + Float64(Float64(Float64(2.0 * x2) - 3.0) / x1)) / x1))))) + Float64(Float64(Float64(x1 * 2.0) * t_4) * t_7))))))));
	elseif (x1 <= 0.0155)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(x2 * -2.0) - Float64(x1 * Float64(Float64(x1 * Float64(Float64(x2 * -2.0) - 3.0)) - -1.0)))) + Float64(x1 + Float64(x2 * Float64(Float64(x1 * -12.0) + Float64(8.0 * Float64(x1 * x2)))))));
	elseif (x1 <= 1.2e+75)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(Float64(Float64(t_0 * Float64(Float64(t_7 * Float64(Float64(x1 * 2.0) * t_5)) - Float64(Float64(x1 * x1) * Float64(6.0 + Float64(4.0 * t_5))))) + Float64(t_2 * t_4)) + t_6)) + Float64(3.0 * Float64(3.0 + Float64(-1.0 / x1)))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x1 * x1) + 1.0;
	t_1 = x1 + ((x1 + (6.0 * (x1 ^ 4.0))) + 9.0);
	t_2 = x1 * (x1 * 3.0);
	t_3 = t_2 + (2.0 * x2);
	t_4 = (t_3 - x1) / t_0;
	t_5 = (x1 - t_3) / t_0;
	t_6 = x1 * (x1 * x1);
	t_7 = 3.0 + t_5;
	tmp = 0.0;
	if (x1 <= -7.1e+106)
		tmp = t_1;
	elseif (x1 <= -0.0085)
		tmp = x1 + (9.0 + (x1 + (t_6 - ((t_2 * t_5) - ((-1.0 - (x1 * x1)) * (((x1 * x1) * (6.0 - (4.0 * (3.0 + ((-1.0 + (((2.0 * x2) - 3.0) / x1)) / x1))))) + (((x1 * 2.0) * t_4) * t_7)))))));
	elseif (x1 <= 0.0155)
		tmp = x1 + ((3.0 * ((x2 * -2.0) - (x1 * ((x1 * ((x2 * -2.0) - 3.0)) - -1.0)))) + (x1 + (x2 * ((x1 * -12.0) + (8.0 * (x1 * x2))))));
	elseif (x1 <= 1.2e+75)
		tmp = x1 + ((x1 + (((t_0 * ((t_7 * ((x1 * 2.0) * t_5)) - ((x1 * x1) * (6.0 + (4.0 * t_5))))) + (t_2 * t_4)) + t_6)) + (3.0 * (3.0 + (-1.0 / x1))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$1 = N[(x1 + N[(N[(x1 + N[(6.0 * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 9.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(t$95$3 - x1), $MachinePrecision] / t$95$0), $MachinePrecision]}, Block[{t$95$5 = N[(N[(x1 - t$95$3), $MachinePrecision] / t$95$0), $MachinePrecision]}, Block[{t$95$6 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(3.0 + t$95$5), $MachinePrecision]}, If[LessEqual[x1, -7.1e+106], t$95$1, If[LessEqual[x1, -0.0085], N[(x1 + N[(9.0 + N[(x1 + N[(t$95$6 - N[(N[(t$95$2 * t$95$5), $MachinePrecision] - N[(N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision] * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 - N[(4.0 * N[(3.0 + N[(N[(-1.0 + N[(N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision] / x1), $MachinePrecision]), $MachinePrecision] / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$4), $MachinePrecision] * t$95$7), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 0.0155], N[(x1 + N[(N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - N[(x1 * N[(N[(x1 * N[(N[(x2 * -2.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(x2 * N[(N[(x1 * -12.0), $MachinePrecision] + N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.2e+75], N[(x1 + N[(N[(x1 + N[(N[(N[(t$95$0 * N[(N[(t$95$7 * N[(N[(x1 * 2.0), $MachinePrecision] * t$95$5), $MachinePrecision]), $MachinePrecision] - N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 + N[(4.0 * t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$2 * t$95$4), $MachinePrecision]), $MachinePrecision] + t$95$6), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(3.0 + N[(-1.0 / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -7.1000000000000003e106 or 1.2e75 < x1

   1. Initial program 21.5%

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

   3. Taylor expanded in x1 around -inf 26.9%

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

   4. Taylor expanded in x1 around inf 24.7%

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

   5. Taylor expanded in x1 around inf 97.8%

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

   if -7.1000000000000003e106 < x1 < -0.0085000000000000006

   1. Initial program 99.0%

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

   3. Taylor expanded in x1 around -inf 99.2%

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

   4. Taylor expanded in x1 around inf 99.2%

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

   if -0.0085000000000000006 < x1 < 0.0155

   1. Initial program 99.3%

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

   3. Taylor expanded in x1 around 0 87.5%

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

   4. Taylor expanded in x1 around 0 87.6%

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

   5. Taylor expanded in x2 around 0 98.8%

      \[\leadsto x1 + \left(\left(\color{blue}{x2 \cdot \left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right)} + x1\right) + 3 \cdot \left(-2 \cdot x2 + x1 \cdot \left(x1 \cdot \left(3 - -2 \cdot x2\right) - 1\right)\right)\right) \]

   if 0.0155 < x1 < 1.2e75

   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 97.6%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -7.1 \cdot 10^{+106}:\\ \;\;\;\;x1 + \left(\left(x1 + 6 \cdot {x1}^{4}\right) + 9\right)\\ \mathbf{elif}\;x1 \leq -0.0085:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) - \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1} - \left(-1 - x1 \cdot x1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 - 4 \cdot \left(3 + \frac{-1 + \frac{2 \cdot x2 - 3}{x1}}{x1}\right)\right) + \left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(3 + \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 0.0155:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2 - x1 \cdot \left(x1 \cdot \left(x2 \cdot -2 - 3\right) - -1\right)\right) + \left(x1 + x2 \cdot \left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.2 \cdot 10^{+75}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(3 + \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right) - \left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right)\right) + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 3 \cdot \left(3 + \frac{-1}{x1}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 + 6 \cdot {x1}^{4}\right) + 9\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 96.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := t\_0 + 2 \cdot x2\\ t_2 := x1 \cdot x1 + 1\\ t_3 := \frac{x1 - t\_1}{t\_2}\\ \mathbf{if}\;x1 \leq -7.1 \cdot 10^{+106} \lor \neg \left(x1 \leq 1.65 \cdot 10^{+49}\right):\\ \;\;\;\;x1 + \left(\left(x1 + 6 \cdot {x1}^{4}\right) + 9\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(t\_2 \cdot \left(\left(3 + t\_3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot t\_3\right) - \left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot t\_3\right)\right) + t\_0 \cdot \frac{t\_1 - x1}{t\_2}\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 3 \cdot \left(x2 \cdot -2 - x1 \cdot \left(x1 \cdot \left(x2 \cdot -2 - 3\right) - -1\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (+ t_0 (* 2.0 x2)))
        (t_2 (+ (* x1 x1) 1.0))
        (t_3 (/ (- x1 t_1) t_2)))
   (if (or (<= x1 -7.1e+106) (not (<= x1 1.65e+49)))
     (+ x1 (+ (+ x1 (* 6.0 (pow x1 4.0))) 9.0))
     (+
      x1
      (+
       (+
        x1
        (+
         (+
          (*
           t_2
           (-
            (* (+ 3.0 t_3) (* (* x1 2.0) t_3))
            (* (* x1 x1) (+ 6.0 (* 4.0 t_3)))))
          (* t_0 (/ (- t_1 x1) t_2)))
         (* x1 (* x1 x1))))
       (* 3.0 (- (* x2 -2.0) (* x1 (- (* x1 (- (* x2 -2.0) 3.0)) -1.0)))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = t_0 + (2.0 * x2);
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = (x1 - t_1) / t_2;
	double tmp;
	if ((x1 <= -7.1e+106) || !(x1 <= 1.65e+49)) {
		tmp = x1 + ((x1 + (6.0 * pow(x1, 4.0))) + 9.0);
	} else {
		tmp = x1 + ((x1 + (((t_2 * (((3.0 + t_3) * ((x1 * 2.0) * t_3)) - ((x1 * x1) * (6.0 + (4.0 * t_3))))) + (t_0 * ((t_1 - x1) / t_2))) + (x1 * (x1 * x1)))) + (3.0 * ((x2 * -2.0) - (x1 * ((x1 * ((x2 * -2.0) - 3.0)) - -1.0)))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_0 = x1 * (x1 * 3.0d0)
    t_1 = t_0 + (2.0d0 * x2)
    t_2 = (x1 * x1) + 1.0d0
    t_3 = (x1 - t_1) / t_2
    if ((x1 <= (-7.1d+106)) .or. (.not. (x1 <= 1.65d+49))) then
        tmp = x1 + ((x1 + (6.0d0 * (x1 ** 4.0d0))) + 9.0d0)
    else
        tmp = x1 + ((x1 + (((t_2 * (((3.0d0 + t_3) * ((x1 * 2.0d0) * t_3)) - ((x1 * x1) * (6.0d0 + (4.0d0 * t_3))))) + (t_0 * ((t_1 - x1) / t_2))) + (x1 * (x1 * x1)))) + (3.0d0 * ((x2 * (-2.0d0)) - (x1 * ((x1 * ((x2 * (-2.0d0)) - 3.0d0)) - (-1.0d0))))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = t_0 + (2.0 * x2);
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = (x1 - t_1) / t_2;
	double tmp;
	if ((x1 <= -7.1e+106) || !(x1 <= 1.65e+49)) {
		tmp = x1 + ((x1 + (6.0 * Math.pow(x1, 4.0))) + 9.0);
	} else {
		tmp = x1 + ((x1 + (((t_2 * (((3.0 + t_3) * ((x1 * 2.0) * t_3)) - ((x1 * x1) * (6.0 + (4.0 * t_3))))) + (t_0 * ((t_1 - x1) / t_2))) + (x1 * (x1 * x1)))) + (3.0 * ((x2 * -2.0) - (x1 * ((x1 * ((x2 * -2.0) - 3.0)) - -1.0)))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = t_0 + (2.0 * x2)
	t_2 = (x1 * x1) + 1.0
	t_3 = (x1 - t_1) / t_2
	tmp = 0
	if (x1 <= -7.1e+106) or not (x1 <= 1.65e+49):
		tmp = x1 + ((x1 + (6.0 * math.pow(x1, 4.0))) + 9.0)
	else:
		tmp = x1 + ((x1 + (((t_2 * (((3.0 + t_3) * ((x1 * 2.0) * t_3)) - ((x1 * x1) * (6.0 + (4.0 * t_3))))) + (t_0 * ((t_1 - x1) / t_2))) + (x1 * (x1 * x1)))) + (3.0 * ((x2 * -2.0) - (x1 * ((x1 * ((x2 * -2.0) - 3.0)) - -1.0)))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(t_0 + Float64(2.0 * x2))
	t_2 = Float64(Float64(x1 * x1) + 1.0)
	t_3 = Float64(Float64(x1 - t_1) / t_2)
	tmp = 0.0
	if ((x1 <= -7.1e+106) || !(x1 <= 1.65e+49))
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(6.0 * (x1 ^ 4.0))) + 9.0));
	else
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(Float64(Float64(t_2 * Float64(Float64(Float64(3.0 + t_3) * Float64(Float64(x1 * 2.0) * t_3)) - Float64(Float64(x1 * x1) * Float64(6.0 + Float64(4.0 * t_3))))) + Float64(t_0 * Float64(Float64(t_1 - x1) / t_2))) + Float64(x1 * Float64(x1 * x1)))) + Float64(3.0 * Float64(Float64(x2 * -2.0) - Float64(x1 * Float64(Float64(x1 * Float64(Float64(x2 * -2.0) - 3.0)) - -1.0))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * 3.0);
	t_1 = t_0 + (2.0 * x2);
	t_2 = (x1 * x1) + 1.0;
	t_3 = (x1 - t_1) / t_2;
	tmp = 0.0;
	if ((x1 <= -7.1e+106) || ~((x1 <= 1.65e+49)))
		tmp = x1 + ((x1 + (6.0 * (x1 ^ 4.0))) + 9.0);
	else
		tmp = x1 + ((x1 + (((t_2 * (((3.0 + t_3) * ((x1 * 2.0) * t_3)) - ((x1 * x1) * (6.0 + (4.0 * t_3))))) + (t_0 * ((t_1 - x1) / t_2))) + (x1 * (x1 * x1)))) + (3.0 * ((x2 * -2.0) - (x1 * ((x1 * ((x2 * -2.0) - 3.0)) - -1.0)))));
	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[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x1 - t$95$1), $MachinePrecision] / t$95$2), $MachinePrecision]}, If[Or[LessEqual[x1, -7.1e+106], N[Not[LessEqual[x1, 1.65e+49]], $MachinePrecision]], N[(x1 + N[(N[(x1 + N[(6.0 * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 9.0), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x1 + N[(N[(N[(t$95$2 * N[(N[(N[(3.0 + t$95$3), $MachinePrecision] * N[(N[(x1 * 2.0), $MachinePrecision] * t$95$3), $MachinePrecision]), $MachinePrecision] - N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 + N[(4.0 * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$0 * N[(N[(t$95$1 - x1), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - N[(x1 * N[(N[(x1 * N[(N[(x2 * -2.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 2 regimes

2. if x1 < -7.1000000000000003e106 or 1.6499999999999999e49 < x1

   1. Initial program 26.1%

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

   3. Taylor expanded in x1 around -inf 30.3%

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

   4. Taylor expanded in x1 around inf 28.3%

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

   5. Taylor expanded in x1 around inf 97.0%

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

   if -7.1000000000000003e106 < x1 < 1.6499999999999999e49

   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 0 96.1%

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

4. Final simplification 96.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -7.1 \cdot 10^{+106} \lor \neg \left(x1 \leq 1.65 \cdot 10^{+49}\right):\\ \;\;\;\;x1 + \left(\left(x1 + 6 \cdot {x1}^{4}\right) + 9\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(3 + \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right) - \left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right)\right) + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 3 \cdot \left(x2 \cdot -2 - x1 \cdot \left(x1 \cdot \left(x2 \cdot -2 - 3\right) - -1\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 98.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := x1 + \left(\left(x1 + 6 \cdot {x1}^{4}\right) + 9\right)\\ t_2 := x1 \cdot \left(x1 \cdot 3\right)\\ t_3 := t\_2 + 2 \cdot x2\\ t_4 := \frac{t\_3 - x1}{t\_0}\\ t_5 := \frac{x1 - t\_3}{t\_0}\\ t_6 := x1 \cdot \left(x1 \cdot x1\right)\\ t_7 := 3 + t\_5\\ \mathbf{if}\;x1 \leq -7.1 \cdot 10^{+106}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x1 \leq -0.034:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(t\_6 - \left(t\_2 \cdot t\_5 - \left(-1 - x1 \cdot x1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 - 4 \cdot \left(3 + \frac{-1 + \frac{2 \cdot x2 - 3}{x1}}{x1}\right)\right) + \left(\left(x1 \cdot 2\right) \cdot t\_4\right) \cdot t\_7\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 0.05:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2 - x1 \cdot \left(x1 \cdot \left(x2 \cdot -2 - 3\right) - -1\right)\right) + \left(x1 + x2 \cdot \left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.2 \cdot 10^{+75}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(t\_0 \cdot \left(t\_7 \cdot \left(\left(x1 \cdot 2\right) \cdot t\_5\right) - \left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot t\_5\right)\right) + t\_2 \cdot t\_4\right) + t\_6\right)\right) + 9\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ (* x1 x1) 1.0))
        (t_1 (+ x1 (+ (+ x1 (* 6.0 (pow x1 4.0))) 9.0)))
        (t_2 (* x1 (* x1 3.0)))
        (t_3 (+ t_2 (* 2.0 x2)))
        (t_4 (/ (- t_3 x1) t_0))
        (t_5 (/ (- x1 t_3) t_0))
        (t_6 (* x1 (* x1 x1)))
        (t_7 (+ 3.0 t_5)))
   (if (<= x1 -7.1e+106)
     t_1
     (if (<= x1 -0.034)
       (+
        x1
        (+
         9.0
         (+
          x1
          (-
           t_6
           (-
            (* t_2 t_5)
            (*
             (- -1.0 (* x1 x1))
             (+
              (*
               (* x1 x1)
               (-
                6.0
                (* 4.0 (+ 3.0 (/ (+ -1.0 (/ (- (* 2.0 x2) 3.0) x1)) x1)))))
              (* (* (* x1 2.0) t_4) t_7))))))))
       (if (<= x1 0.05)
         (+
          x1
          (+
           (* 3.0 (- (* x2 -2.0) (* x1 (- (* x1 (- (* x2 -2.0) 3.0)) -1.0))))
           (+ x1 (* x2 (+ (* x1 -12.0) (* 8.0 (* x1 x2)))))))
         (if (<= x1 1.2e+75)
           (+
            x1
            (+
             (+
              x1
              (+
               (+
                (*
                 t_0
                 (-
                  (* t_7 (* (* x1 2.0) t_5))
                  (* (* x1 x1) (+ 6.0 (* 4.0 t_5)))))
                (* t_2 t_4))
               t_6))
             9.0))
           t_1))))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = x1 + ((x1 + (6.0 * pow(x1, 4.0))) + 9.0);
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = t_2 + (2.0 * x2);
	double t_4 = (t_3 - x1) / t_0;
	double t_5 = (x1 - t_3) / t_0;
	double t_6 = x1 * (x1 * x1);
	double t_7 = 3.0 + t_5;
	double tmp;
	if (x1 <= -7.1e+106) {
		tmp = t_1;
	} else if (x1 <= -0.034) {
		tmp = x1 + (9.0 + (x1 + (t_6 - ((t_2 * t_5) - ((-1.0 - (x1 * x1)) * (((x1 * x1) * (6.0 - (4.0 * (3.0 + ((-1.0 + (((2.0 * x2) - 3.0) / x1)) / x1))))) + (((x1 * 2.0) * t_4) * t_7)))))));
	} else if (x1 <= 0.05) {
		tmp = x1 + ((3.0 * ((x2 * -2.0) - (x1 * ((x1 * ((x2 * -2.0) - 3.0)) - -1.0)))) + (x1 + (x2 * ((x1 * -12.0) + (8.0 * (x1 * x2))))));
	} else if (x1 <= 1.2e+75) {
		tmp = x1 + ((x1 + (((t_0 * ((t_7 * ((x1 * 2.0) * t_5)) - ((x1 * x1) * (6.0 + (4.0 * t_5))))) + (t_2 * t_4)) + t_6)) + 9.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: tmp
    t_0 = (x1 * x1) + 1.0d0
    t_1 = x1 + ((x1 + (6.0d0 * (x1 ** 4.0d0))) + 9.0d0)
    t_2 = x1 * (x1 * 3.0d0)
    t_3 = t_2 + (2.0d0 * x2)
    t_4 = (t_3 - x1) / t_0
    t_5 = (x1 - t_3) / t_0
    t_6 = x1 * (x1 * x1)
    t_7 = 3.0d0 + t_5
    if (x1 <= (-7.1d+106)) then
        tmp = t_1
    else if (x1 <= (-0.034d0)) then
        tmp = x1 + (9.0d0 + (x1 + (t_6 - ((t_2 * t_5) - (((-1.0d0) - (x1 * x1)) * (((x1 * x1) * (6.0d0 - (4.0d0 * (3.0d0 + (((-1.0d0) + (((2.0d0 * x2) - 3.0d0) / x1)) / x1))))) + (((x1 * 2.0d0) * t_4) * t_7)))))))
    else if (x1 <= 0.05d0) then
        tmp = x1 + ((3.0d0 * ((x2 * (-2.0d0)) - (x1 * ((x1 * ((x2 * (-2.0d0)) - 3.0d0)) - (-1.0d0))))) + (x1 + (x2 * ((x1 * (-12.0d0)) + (8.0d0 * (x1 * x2))))))
    else if (x1 <= 1.2d+75) then
        tmp = x1 + ((x1 + (((t_0 * ((t_7 * ((x1 * 2.0d0) * t_5)) - ((x1 * x1) * (6.0d0 + (4.0d0 * t_5))))) + (t_2 * t_4)) + t_6)) + 9.0d0)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = x1 + ((x1 + (6.0 * Math.pow(x1, 4.0))) + 9.0);
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = t_2 + (2.0 * x2);
	double t_4 = (t_3 - x1) / t_0;
	double t_5 = (x1 - t_3) / t_0;
	double t_6 = x1 * (x1 * x1);
	double t_7 = 3.0 + t_5;
	double tmp;
	if (x1 <= -7.1e+106) {
		tmp = t_1;
	} else if (x1 <= -0.034) {
		tmp = x1 + (9.0 + (x1 + (t_6 - ((t_2 * t_5) - ((-1.0 - (x1 * x1)) * (((x1 * x1) * (6.0 - (4.0 * (3.0 + ((-1.0 + (((2.0 * x2) - 3.0) / x1)) / x1))))) + (((x1 * 2.0) * t_4) * t_7)))))));
	} else if (x1 <= 0.05) {
		tmp = x1 + ((3.0 * ((x2 * -2.0) - (x1 * ((x1 * ((x2 * -2.0) - 3.0)) - -1.0)))) + (x1 + (x2 * ((x1 * -12.0) + (8.0 * (x1 * x2))))));
	} else if (x1 <= 1.2e+75) {
		tmp = x1 + ((x1 + (((t_0 * ((t_7 * ((x1 * 2.0) * t_5)) - ((x1 * x1) * (6.0 + (4.0 * t_5))))) + (t_2 * t_4)) + t_6)) + 9.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x1 * x1) + 1.0
	t_1 = x1 + ((x1 + (6.0 * math.pow(x1, 4.0))) + 9.0)
	t_2 = x1 * (x1 * 3.0)
	t_3 = t_2 + (2.0 * x2)
	t_4 = (t_3 - x1) / t_0
	t_5 = (x1 - t_3) / t_0
	t_6 = x1 * (x1 * x1)
	t_7 = 3.0 + t_5
	tmp = 0
	if x1 <= -7.1e+106:
		tmp = t_1
	elif x1 <= -0.034:
		tmp = x1 + (9.0 + (x1 + (t_6 - ((t_2 * t_5) - ((-1.0 - (x1 * x1)) * (((x1 * x1) * (6.0 - (4.0 * (3.0 + ((-1.0 + (((2.0 * x2) - 3.0) / x1)) / x1))))) + (((x1 * 2.0) * t_4) * t_7)))))))
	elif x1 <= 0.05:
		tmp = x1 + ((3.0 * ((x2 * -2.0) - (x1 * ((x1 * ((x2 * -2.0) - 3.0)) - -1.0)))) + (x1 + (x2 * ((x1 * -12.0) + (8.0 * (x1 * x2))))))
	elif x1 <= 1.2e+75:
		tmp = x1 + ((x1 + (((t_0 * ((t_7 * ((x1 * 2.0) * t_5)) - ((x1 * x1) * (6.0 + (4.0 * t_5))))) + (t_2 * t_4)) + t_6)) + 9.0)
	else:
		tmp = t_1
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * x1) + 1.0)
	t_1 = Float64(x1 + Float64(Float64(x1 + Float64(6.0 * (x1 ^ 4.0))) + 9.0))
	t_2 = Float64(x1 * Float64(x1 * 3.0))
	t_3 = Float64(t_2 + Float64(2.0 * x2))
	t_4 = Float64(Float64(t_3 - x1) / t_0)
	t_5 = Float64(Float64(x1 - t_3) / t_0)
	t_6 = Float64(x1 * Float64(x1 * x1))
	t_7 = Float64(3.0 + t_5)
	tmp = 0.0
	if (x1 <= -7.1e+106)
		tmp = t_1;
	elseif (x1 <= -0.034)
		tmp = Float64(x1 + Float64(9.0 + Float64(x1 + Float64(t_6 - Float64(Float64(t_2 * t_5) - Float64(Float64(-1.0 - Float64(x1 * x1)) * Float64(Float64(Float64(x1 * x1) * Float64(6.0 - Float64(4.0 * Float64(3.0 + Float64(Float64(-1.0 + Float64(Float64(Float64(2.0 * x2) - 3.0) / x1)) / x1))))) + Float64(Float64(Float64(x1 * 2.0) * t_4) * t_7))))))));
	elseif (x1 <= 0.05)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(x2 * -2.0) - Float64(x1 * Float64(Float64(x1 * Float64(Float64(x2 * -2.0) - 3.0)) - -1.0)))) + Float64(x1 + Float64(x2 * Float64(Float64(x1 * -12.0) + Float64(8.0 * Float64(x1 * x2)))))));
	elseif (x1 <= 1.2e+75)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(Float64(Float64(t_0 * Float64(Float64(t_7 * Float64(Float64(x1 * 2.0) * t_5)) - Float64(Float64(x1 * x1) * Float64(6.0 + Float64(4.0 * t_5))))) + Float64(t_2 * t_4)) + t_6)) + 9.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x1 * x1) + 1.0;
	t_1 = x1 + ((x1 + (6.0 * (x1 ^ 4.0))) + 9.0);
	t_2 = x1 * (x1 * 3.0);
	t_3 = t_2 + (2.0 * x2);
	t_4 = (t_3 - x1) / t_0;
	t_5 = (x1 - t_3) / t_0;
	t_6 = x1 * (x1 * x1);
	t_7 = 3.0 + t_5;
	tmp = 0.0;
	if (x1 <= -7.1e+106)
		tmp = t_1;
	elseif (x1 <= -0.034)
		tmp = x1 + (9.0 + (x1 + (t_6 - ((t_2 * t_5) - ((-1.0 - (x1 * x1)) * (((x1 * x1) * (6.0 - (4.0 * (3.0 + ((-1.0 + (((2.0 * x2) - 3.0) / x1)) / x1))))) + (((x1 * 2.0) * t_4) * t_7)))))));
	elseif (x1 <= 0.05)
		tmp = x1 + ((3.0 * ((x2 * -2.0) - (x1 * ((x1 * ((x2 * -2.0) - 3.0)) - -1.0)))) + (x1 + (x2 * ((x1 * -12.0) + (8.0 * (x1 * x2))))));
	elseif (x1 <= 1.2e+75)
		tmp = x1 + ((x1 + (((t_0 * ((t_7 * ((x1 * 2.0) * t_5)) - ((x1 * x1) * (6.0 + (4.0 * t_5))))) + (t_2 * t_4)) + t_6)) + 9.0);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$1 = N[(x1 + N[(N[(x1 + N[(6.0 * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 9.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(t$95$3 - x1), $MachinePrecision] / t$95$0), $MachinePrecision]}, Block[{t$95$5 = N[(N[(x1 - t$95$3), $MachinePrecision] / t$95$0), $MachinePrecision]}, Block[{t$95$6 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(3.0 + t$95$5), $MachinePrecision]}, If[LessEqual[x1, -7.1e+106], t$95$1, If[LessEqual[x1, -0.034], N[(x1 + N[(9.0 + N[(x1 + N[(t$95$6 - N[(N[(t$95$2 * t$95$5), $MachinePrecision] - N[(N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision] * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 - N[(4.0 * N[(3.0 + N[(N[(-1.0 + N[(N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision] / x1), $MachinePrecision]), $MachinePrecision] / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$4), $MachinePrecision] * t$95$7), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 0.05], N[(x1 + N[(N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - N[(x1 * N[(N[(x1 * N[(N[(x2 * -2.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(x2 * N[(N[(x1 * -12.0), $MachinePrecision] + N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.2e+75], N[(x1 + N[(N[(x1 + N[(N[(N[(t$95$0 * N[(N[(t$95$7 * N[(N[(x1 * 2.0), $MachinePrecision] * t$95$5), $MachinePrecision]), $MachinePrecision] - N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 + N[(4.0 * t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$2 * t$95$4), $MachinePrecision]), $MachinePrecision] + t$95$6), $MachinePrecision]), $MachinePrecision] + 9.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -7.1000000000000003e106 or 1.2e75 < x1

   1. Initial program 21.5%

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

   3. Taylor expanded in x1 around -inf 26.9%

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

   4. Taylor expanded in x1 around inf 24.7%

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

   5. Taylor expanded in x1 around inf 97.8%

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

   if -7.1000000000000003e106 < x1 < -0.034000000000000002

   1. Initial program 99.0%

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

   3. Taylor expanded in x1 around -inf 99.2%

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

   4. Taylor expanded in x1 around inf 99.2%

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

   if -0.034000000000000002 < x1 < 0.050000000000000003

   1. Initial program 99.3%

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

   3. Taylor expanded in x1 around 0 87.5%

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

   4. Taylor expanded in x1 around 0 87.6%

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

   5. Taylor expanded in x2 around 0 98.8%

      \[\leadsto x1 + \left(\left(\color{blue}{x2 \cdot \left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right)} + x1\right) + 3 \cdot \left(-2 \cdot x2 + x1 \cdot \left(x1 \cdot \left(3 - -2 \cdot x2\right) - 1\right)\right)\right) \]

   if 0.050000000000000003 < x1 < 1.2e75

   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 97.2%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -7.1 \cdot 10^{+106}:\\ \;\;\;\;x1 + \left(\left(x1 + 6 \cdot {x1}^{4}\right) + 9\right)\\ \mathbf{elif}\;x1 \leq -0.034:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) - \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1} - \left(-1 - x1 \cdot x1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 - 4 \cdot \left(3 + \frac{-1 + \frac{2 \cdot x2 - 3}{x1}}{x1}\right)\right) + \left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(3 + \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 0.05:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2 - x1 \cdot \left(x1 \cdot \left(x2 \cdot -2 - 3\right) - -1\right)\right) + \left(x1 + x2 \cdot \left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.2 \cdot 10^{+75}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(3 + \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right) - \left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right)\right) + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 9\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 + 6 \cdot {x1}^{4}\right) + 9\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 98.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := x1 + \left(\left(x1 + 6 \cdot {x1}^{4}\right) + 9\right)\\ t_2 := x1 \cdot \left(x1 \cdot 3\right)\\ t_3 := t\_2 + 2 \cdot x2\\ t_4 := \frac{x1 - t\_3}{t\_0}\\ t_5 := x1 + \left(9 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) - \left(t\_2 \cdot t\_4 - \left(-1 - x1 \cdot x1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 - 4 \cdot \left(3 + \frac{-1 + \frac{2 \cdot x2 - 3}{x1}}{x1}\right)\right) + \left(\left(x1 \cdot 2\right) \cdot \frac{t\_3 - x1}{t\_0}\right) \cdot \left(3 + t\_4\right)\right)\right)\right)\right)\right)\\ \mathbf{if}\;x1 \leq -7.1 \cdot 10^{+106}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x1 \leq -0.017:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;x1 \leq 0.009:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2 - x1 \cdot \left(x1 \cdot \left(x2 \cdot -2 - 3\right) - -1\right)\right) + \left(x1 + x2 \cdot \left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.2 \cdot 10^{+75}:\\ \;\;\;\;t\_5\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ (* x1 x1) 1.0))
        (t_1 (+ x1 (+ (+ x1 (* 6.0 (pow x1 4.0))) 9.0)))
        (t_2 (* x1 (* x1 3.0)))
        (t_3 (+ t_2 (* 2.0 x2)))
        (t_4 (/ (- x1 t_3) t_0))
        (t_5
         (+
          x1
          (+
           9.0
           (+
            x1
            (-
             (* x1 (* x1 x1))
             (-
              (* t_2 t_4)
              (*
               (- -1.0 (* x1 x1))
               (+
                (*
                 (* x1 x1)
                 (-
                  6.0
                  (* 4.0 (+ 3.0 (/ (+ -1.0 (/ (- (* 2.0 x2) 3.0) x1)) x1)))))
                (* (* (* x1 2.0) (/ (- t_3 x1) t_0)) (+ 3.0 t_4)))))))))))
   (if (<= x1 -7.1e+106)
     t_1
     (if (<= x1 -0.017)
       t_5
       (if (<= x1 0.009)
         (+
          x1
          (+
           (* 3.0 (- (* x2 -2.0) (* x1 (- (* x1 (- (* x2 -2.0) 3.0)) -1.0))))
           (+ x1 (* x2 (+ (* x1 -12.0) (* 8.0 (* x1 x2)))))))
         (if (<= x1 1.2e+75) t_5 t_1))))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = x1 + ((x1 + (6.0 * pow(x1, 4.0))) + 9.0);
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = t_2 + (2.0 * x2);
	double t_4 = (x1 - t_3) / t_0;
	double t_5 = x1 + (9.0 + (x1 + ((x1 * (x1 * x1)) - ((t_2 * t_4) - ((-1.0 - (x1 * x1)) * (((x1 * x1) * (6.0 - (4.0 * (3.0 + ((-1.0 + (((2.0 * x2) - 3.0) / x1)) / x1))))) + (((x1 * 2.0) * ((t_3 - x1) / t_0)) * (3.0 + t_4))))))));
	double tmp;
	if (x1 <= -7.1e+106) {
		tmp = t_1;
	} else if (x1 <= -0.017) {
		tmp = t_5;
	} else if (x1 <= 0.009) {
		tmp = x1 + ((3.0 * ((x2 * -2.0) - (x1 * ((x1 * ((x2 * -2.0) - 3.0)) - -1.0)))) + (x1 + (x2 * ((x1 * -12.0) + (8.0 * (x1 * x2))))));
	} else if (x1 <= 1.2e+75) {
		tmp = t_5;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_0 = (x1 * x1) + 1.0d0
    t_1 = x1 + ((x1 + (6.0d0 * (x1 ** 4.0d0))) + 9.0d0)
    t_2 = x1 * (x1 * 3.0d0)
    t_3 = t_2 + (2.0d0 * x2)
    t_4 = (x1 - t_3) / t_0
    t_5 = x1 + (9.0d0 + (x1 + ((x1 * (x1 * x1)) - ((t_2 * t_4) - (((-1.0d0) - (x1 * x1)) * (((x1 * x1) * (6.0d0 - (4.0d0 * (3.0d0 + (((-1.0d0) + (((2.0d0 * x2) - 3.0d0) / x1)) / x1))))) + (((x1 * 2.0d0) * ((t_3 - x1) / t_0)) * (3.0d0 + t_4))))))))
    if (x1 <= (-7.1d+106)) then
        tmp = t_1
    else if (x1 <= (-0.017d0)) then
        tmp = t_5
    else if (x1 <= 0.009d0) then
        tmp = x1 + ((3.0d0 * ((x2 * (-2.0d0)) - (x1 * ((x1 * ((x2 * (-2.0d0)) - 3.0d0)) - (-1.0d0))))) + (x1 + (x2 * ((x1 * (-12.0d0)) + (8.0d0 * (x1 * x2))))))
    else if (x1 <= 1.2d+75) then
        tmp = t_5
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = x1 + ((x1 + (6.0 * Math.pow(x1, 4.0))) + 9.0);
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = t_2 + (2.0 * x2);
	double t_4 = (x1 - t_3) / t_0;
	double t_5 = x1 + (9.0 + (x1 + ((x1 * (x1 * x1)) - ((t_2 * t_4) - ((-1.0 - (x1 * x1)) * (((x1 * x1) * (6.0 - (4.0 * (3.0 + ((-1.0 + (((2.0 * x2) - 3.0) / x1)) / x1))))) + (((x1 * 2.0) * ((t_3 - x1) / t_0)) * (3.0 + t_4))))))));
	double tmp;
	if (x1 <= -7.1e+106) {
		tmp = t_1;
	} else if (x1 <= -0.017) {
		tmp = t_5;
	} else if (x1 <= 0.009) {
		tmp = x1 + ((3.0 * ((x2 * -2.0) - (x1 * ((x1 * ((x2 * -2.0) - 3.0)) - -1.0)))) + (x1 + (x2 * ((x1 * -12.0) + (8.0 * (x1 * x2))))));
	} else if (x1 <= 1.2e+75) {
		tmp = t_5;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x1 * x1) + 1.0
	t_1 = x1 + ((x1 + (6.0 * math.pow(x1, 4.0))) + 9.0)
	t_2 = x1 * (x1 * 3.0)
	t_3 = t_2 + (2.0 * x2)
	t_4 = (x1 - t_3) / t_0
	t_5 = x1 + (9.0 + (x1 + ((x1 * (x1 * x1)) - ((t_2 * t_4) - ((-1.0 - (x1 * x1)) * (((x1 * x1) * (6.0 - (4.0 * (3.0 + ((-1.0 + (((2.0 * x2) - 3.0) / x1)) / x1))))) + (((x1 * 2.0) * ((t_3 - x1) / t_0)) * (3.0 + t_4))))))))
	tmp = 0
	if x1 <= -7.1e+106:
		tmp = t_1
	elif x1 <= -0.017:
		tmp = t_5
	elif x1 <= 0.009:
		tmp = x1 + ((3.0 * ((x2 * -2.0) - (x1 * ((x1 * ((x2 * -2.0) - 3.0)) - -1.0)))) + (x1 + (x2 * ((x1 * -12.0) + (8.0 * (x1 * x2))))))
	elif x1 <= 1.2e+75:
		tmp = t_5
	else:
		tmp = t_1
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * x1) + 1.0)
	t_1 = Float64(x1 + Float64(Float64(x1 + Float64(6.0 * (x1 ^ 4.0))) + 9.0))
	t_2 = Float64(x1 * Float64(x1 * 3.0))
	t_3 = Float64(t_2 + Float64(2.0 * x2))
	t_4 = Float64(Float64(x1 - t_3) / t_0)
	t_5 = Float64(x1 + Float64(9.0 + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) - Float64(Float64(t_2 * t_4) - Float64(Float64(-1.0 - Float64(x1 * x1)) * Float64(Float64(Float64(x1 * x1) * Float64(6.0 - Float64(4.0 * Float64(3.0 + Float64(Float64(-1.0 + Float64(Float64(Float64(2.0 * x2) - 3.0) / x1)) / x1))))) + Float64(Float64(Float64(x1 * 2.0) * Float64(Float64(t_3 - x1) / t_0)) * Float64(3.0 + t_4)))))))))
	tmp = 0.0
	if (x1 <= -7.1e+106)
		tmp = t_1;
	elseif (x1 <= -0.017)
		tmp = t_5;
	elseif (x1 <= 0.009)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(x2 * -2.0) - Float64(x1 * Float64(Float64(x1 * Float64(Float64(x2 * -2.0) - 3.0)) - -1.0)))) + Float64(x1 + Float64(x2 * Float64(Float64(x1 * -12.0) + Float64(8.0 * Float64(x1 * x2)))))));
	elseif (x1 <= 1.2e+75)
		tmp = t_5;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x1 * x1) + 1.0;
	t_1 = x1 + ((x1 + (6.0 * (x1 ^ 4.0))) + 9.0);
	t_2 = x1 * (x1 * 3.0);
	t_3 = t_2 + (2.0 * x2);
	t_4 = (x1 - t_3) / t_0;
	t_5 = x1 + (9.0 + (x1 + ((x1 * (x1 * x1)) - ((t_2 * t_4) - ((-1.0 - (x1 * x1)) * (((x1 * x1) * (6.0 - (4.0 * (3.0 + ((-1.0 + (((2.0 * x2) - 3.0) / x1)) / x1))))) + (((x1 * 2.0) * ((t_3 - x1) / t_0)) * (3.0 + t_4))))))));
	tmp = 0.0;
	if (x1 <= -7.1e+106)
		tmp = t_1;
	elseif (x1 <= -0.017)
		tmp = t_5;
	elseif (x1 <= 0.009)
		tmp = x1 + ((3.0 * ((x2 * -2.0) - (x1 * ((x1 * ((x2 * -2.0) - 3.0)) - -1.0)))) + (x1 + (x2 * ((x1 * -12.0) + (8.0 * (x1 * x2))))));
	elseif (x1 <= 1.2e+75)
		tmp = t_5;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$1 = N[(x1 + N[(N[(x1 + N[(6.0 * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 9.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(x1 - t$95$3), $MachinePrecision] / t$95$0), $MachinePrecision]}, Block[{t$95$5 = N[(x1 + N[(9.0 + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] - N[(N[(t$95$2 * t$95$4), $MachinePrecision] - N[(N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision] * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 - N[(4.0 * N[(3.0 + N[(N[(-1.0 + N[(N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision] / x1), $MachinePrecision]), $MachinePrecision] / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(x1 * 2.0), $MachinePrecision] * N[(N[(t$95$3 - x1), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision] * N[(3.0 + t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -7.1e+106], t$95$1, If[LessEqual[x1, -0.017], t$95$5, If[LessEqual[x1, 0.009], N[(x1 + N[(N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - N[(x1 * N[(N[(x1 * N[(N[(x2 * -2.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(x2 * N[(N[(x1 * -12.0), $MachinePrecision] + N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.2e+75], t$95$5, t$95$1]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -7.1000000000000003e106 or 1.2e75 < x1

   1. Initial program 21.5%

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

   3. Taylor expanded in x1 around -inf 26.9%

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

   4. Taylor expanded in x1 around inf 24.7%

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

   5. Taylor expanded in x1 around inf 97.8%

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

   if -7.1000000000000003e106 < x1 < -0.017000000000000001 or 0.00899999999999999932 < x1 < 1.2e75

   1. Initial program 99.1%

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

   3. Taylor expanded in x1 around -inf 98.2%

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

   4. Taylor expanded in x1 around inf 98.2%

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

   if -0.017000000000000001 < x1 < 0.00899999999999999932

   1. Initial program 99.3%

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

   3. Taylor expanded in x1 around 0 87.5%

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

   4. Taylor expanded in x1 around 0 87.6%

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

   5. Taylor expanded in x2 around 0 98.8%

      \[\leadsto x1 + \left(\left(\color{blue}{x2 \cdot \left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right)} + x1\right) + 3 \cdot \left(-2 \cdot x2 + x1 \cdot \left(x1 \cdot \left(3 - -2 \cdot x2\right) - 1\right)\right)\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -7.1 \cdot 10^{+106}:\\ \;\;\;\;x1 + \left(\left(x1 + 6 \cdot {x1}^{4}\right) + 9\right)\\ \mathbf{elif}\;x1 \leq -0.017:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) - \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1} - \left(-1 - x1 \cdot x1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 - 4 \cdot \left(3 + \frac{-1 + \frac{2 \cdot x2 - 3}{x1}}{x1}\right)\right) + \left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(3 + \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 0.009:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2 - x1 \cdot \left(x1 \cdot \left(x2 \cdot -2 - 3\right) - -1\right)\right) + \left(x1 + x2 \cdot \left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.2 \cdot 10^{+75}:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) - \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1} - \left(-1 - x1 \cdot x1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 - 4 \cdot \left(3 + \frac{-1 + \frac{2 \cdot x2 - 3}{x1}}{x1}\right)\right) + \left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(3 + \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 + 6 \cdot {x1}^{4}\right) + 9\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 96.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot x1\right)\\ t_1 := x1 \cdot x1 + 1\\ t_2 := x1 \cdot \left(x1 \cdot 3\right)\\ t_3 := x1 + \left(\left(x1 + 6 \cdot {x1}^{4}\right) + 9\right)\\ t_4 := x1 - \left(t\_2 - 2 \cdot x2\right)\\ t_5 := t\_2 + 2 \cdot x2\\ t_6 := \frac{x1 - t\_5}{t\_1}\\ t_7 := 3 + t\_6\\ \mathbf{if}\;x1 \leq -7.1 \cdot 10^{+106}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x1 \leq -0.032:\\ \;\;\;\;x1 + \left(3 \cdot \frac{t\_4}{-1 - x1 \cdot x1} - \left(\left(\left(t\_2 \cdot t\_6 + t\_1 \cdot \left(\left(4 \cdot \left(3 - 2 \cdot x2\right) + x1 \cdot \left(4 - x1 \cdot 6\right)\right) - t\_7 \cdot \left(\left(x1 \cdot 2\right) \cdot t\_6\right)\right)\right) - t\_0\right) - x1\right)\right)\\ \mathbf{elif}\;x1 \leq 7.7 \cdot 10^{+49}:\\ \;\;\;\;x1 - \left(3 \cdot \frac{t\_4}{t\_1} - \left(x1 + \left(t\_0 + \left(t\_2 \cdot \frac{t\_5 - x1}{t\_1} - t\_1 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot t\_6\right) + \left(\left(x1 \cdot 2\right) \cdot \left(2 \cdot x2 - x1\right)\right) \cdot t\_7\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 x1)))
        (t_1 (+ (* x1 x1) 1.0))
        (t_2 (* x1 (* x1 3.0)))
        (t_3 (+ x1 (+ (+ x1 (* 6.0 (pow x1 4.0))) 9.0)))
        (t_4 (- x1 (- t_2 (* 2.0 x2))))
        (t_5 (+ t_2 (* 2.0 x2)))
        (t_6 (/ (- x1 t_5) t_1))
        (t_7 (+ 3.0 t_6)))
   (if (<= x1 -7.1e+106)
     t_3
     (if (<= x1 -0.032)
       (+
        x1
        (-
         (* 3.0 (/ t_4 (- -1.0 (* x1 x1))))
         (-
          (-
           (+
            (* t_2 t_6)
            (*
             t_1
             (-
              (+ (* 4.0 (- 3.0 (* 2.0 x2))) (* x1 (- 4.0 (* x1 6.0))))
              (* t_7 (* (* x1 2.0) t_6)))))
           t_0)
          x1)))
       (if (<= x1 7.7e+49)
         (-
          x1
          (-
           (* 3.0 (/ t_4 t_1))
           (+
            x1
            (+
             t_0
             (-
              (* t_2 (/ (- t_5 x1) t_1))
              (*
               t_1
               (+
                (* (* x1 x1) (+ 6.0 (* 4.0 t_6)))
                (* (* (* x1 2.0) (- (* 2.0 x2) x1)) t_7))))))))
         t_3)))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * x1);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = x1 + ((x1 + (6.0 * pow(x1, 4.0))) + 9.0);
	double t_4 = x1 - (t_2 - (2.0 * x2));
	double t_5 = t_2 + (2.0 * x2);
	double t_6 = (x1 - t_5) / t_1;
	double t_7 = 3.0 + t_6;
	double tmp;
	if (x1 <= -7.1e+106) {
		tmp = t_3;
	} else if (x1 <= -0.032) {
		tmp = x1 + ((3.0 * (t_4 / (-1.0 - (x1 * x1)))) - ((((t_2 * t_6) + (t_1 * (((4.0 * (3.0 - (2.0 * x2))) + (x1 * (4.0 - (x1 * 6.0)))) - (t_7 * ((x1 * 2.0) * t_6))))) - t_0) - x1));
	} else if (x1 <= 7.7e+49) {
		tmp = x1 - ((3.0 * (t_4 / t_1)) - (x1 + (t_0 + ((t_2 * ((t_5 - x1) / t_1)) - (t_1 * (((x1 * x1) * (6.0 + (4.0 * t_6))) + (((x1 * 2.0) * ((2.0 * x2) - x1)) * t_7)))))));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: tmp
    t_0 = x1 * (x1 * x1)
    t_1 = (x1 * x1) + 1.0d0
    t_2 = x1 * (x1 * 3.0d0)
    t_3 = x1 + ((x1 + (6.0d0 * (x1 ** 4.0d0))) + 9.0d0)
    t_4 = x1 - (t_2 - (2.0d0 * x2))
    t_5 = t_2 + (2.0d0 * x2)
    t_6 = (x1 - t_5) / t_1
    t_7 = 3.0d0 + t_6
    if (x1 <= (-7.1d+106)) then
        tmp = t_3
    else if (x1 <= (-0.032d0)) then
        tmp = x1 + ((3.0d0 * (t_4 / ((-1.0d0) - (x1 * x1)))) - ((((t_2 * t_6) + (t_1 * (((4.0d0 * (3.0d0 - (2.0d0 * x2))) + (x1 * (4.0d0 - (x1 * 6.0d0)))) - (t_7 * ((x1 * 2.0d0) * t_6))))) - t_0) - x1))
    else if (x1 <= 7.7d+49) then
        tmp = x1 - ((3.0d0 * (t_4 / t_1)) - (x1 + (t_0 + ((t_2 * ((t_5 - x1) / t_1)) - (t_1 * (((x1 * x1) * (6.0d0 + (4.0d0 * t_6))) + (((x1 * 2.0d0) * ((2.0d0 * x2) - x1)) * t_7)))))))
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * x1);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = x1 + ((x1 + (6.0 * Math.pow(x1, 4.0))) + 9.0);
	double t_4 = x1 - (t_2 - (2.0 * x2));
	double t_5 = t_2 + (2.0 * x2);
	double t_6 = (x1 - t_5) / t_1;
	double t_7 = 3.0 + t_6;
	double tmp;
	if (x1 <= -7.1e+106) {
		tmp = t_3;
	} else if (x1 <= -0.032) {
		tmp = x1 + ((3.0 * (t_4 / (-1.0 - (x1 * x1)))) - ((((t_2 * t_6) + (t_1 * (((4.0 * (3.0 - (2.0 * x2))) + (x1 * (4.0 - (x1 * 6.0)))) - (t_7 * ((x1 * 2.0) * t_6))))) - t_0) - x1));
	} else if (x1 <= 7.7e+49) {
		tmp = x1 - ((3.0 * (t_4 / t_1)) - (x1 + (t_0 + ((t_2 * ((t_5 - x1) / t_1)) - (t_1 * (((x1 * x1) * (6.0 + (4.0 * t_6))) + (((x1 * 2.0) * ((2.0 * x2) - x1)) * t_7)))))));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * x1)
	t_1 = (x1 * x1) + 1.0
	t_2 = x1 * (x1 * 3.0)
	t_3 = x1 + ((x1 + (6.0 * math.pow(x1, 4.0))) + 9.0)
	t_4 = x1 - (t_2 - (2.0 * x2))
	t_5 = t_2 + (2.0 * x2)
	t_6 = (x1 - t_5) / t_1
	t_7 = 3.0 + t_6
	tmp = 0
	if x1 <= -7.1e+106:
		tmp = t_3
	elif x1 <= -0.032:
		tmp = x1 + ((3.0 * (t_4 / (-1.0 - (x1 * x1)))) - ((((t_2 * t_6) + (t_1 * (((4.0 * (3.0 - (2.0 * x2))) + (x1 * (4.0 - (x1 * 6.0)))) - (t_7 * ((x1 * 2.0) * t_6))))) - t_0) - x1))
	elif x1 <= 7.7e+49:
		tmp = x1 - ((3.0 * (t_4 / t_1)) - (x1 + (t_0 + ((t_2 * ((t_5 - x1) / t_1)) - (t_1 * (((x1 * x1) * (6.0 + (4.0 * t_6))) + (((x1 * 2.0) * ((2.0 * x2) - x1)) * t_7)))))))
	else:
		tmp = t_3
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * x1))
	t_1 = Float64(Float64(x1 * x1) + 1.0)
	t_2 = Float64(x1 * Float64(x1 * 3.0))
	t_3 = Float64(x1 + Float64(Float64(x1 + Float64(6.0 * (x1 ^ 4.0))) + 9.0))
	t_4 = Float64(x1 - Float64(t_2 - Float64(2.0 * x2)))
	t_5 = Float64(t_2 + Float64(2.0 * x2))
	t_6 = Float64(Float64(x1 - t_5) / t_1)
	t_7 = Float64(3.0 + t_6)
	tmp = 0.0
	if (x1 <= -7.1e+106)
		tmp = t_3;
	elseif (x1 <= -0.032)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(t_4 / Float64(-1.0 - Float64(x1 * x1)))) - Float64(Float64(Float64(Float64(t_2 * t_6) + Float64(t_1 * Float64(Float64(Float64(4.0 * Float64(3.0 - Float64(2.0 * x2))) + Float64(x1 * Float64(4.0 - Float64(x1 * 6.0)))) - Float64(t_7 * Float64(Float64(x1 * 2.0) * t_6))))) - t_0) - x1)));
	elseif (x1 <= 7.7e+49)
		tmp = Float64(x1 - Float64(Float64(3.0 * Float64(t_4 / t_1)) - Float64(x1 + Float64(t_0 + Float64(Float64(t_2 * Float64(Float64(t_5 - x1) / t_1)) - Float64(t_1 * Float64(Float64(Float64(x1 * x1) * Float64(6.0 + Float64(4.0 * t_6))) + Float64(Float64(Float64(x1 * 2.0) * Float64(Float64(2.0 * x2) - x1)) * t_7))))))));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * x1);
	t_1 = (x1 * x1) + 1.0;
	t_2 = x1 * (x1 * 3.0);
	t_3 = x1 + ((x1 + (6.0 * (x1 ^ 4.0))) + 9.0);
	t_4 = x1 - (t_2 - (2.0 * x2));
	t_5 = t_2 + (2.0 * x2);
	t_6 = (x1 - t_5) / t_1;
	t_7 = 3.0 + t_6;
	tmp = 0.0;
	if (x1 <= -7.1e+106)
		tmp = t_3;
	elseif (x1 <= -0.032)
		tmp = x1 + ((3.0 * (t_4 / (-1.0 - (x1 * x1)))) - ((((t_2 * t_6) + (t_1 * (((4.0 * (3.0 - (2.0 * x2))) + (x1 * (4.0 - (x1 * 6.0)))) - (t_7 * ((x1 * 2.0) * t_6))))) - t_0) - x1));
	elseif (x1 <= 7.7e+49)
		tmp = x1 - ((3.0 * (t_4 / t_1)) - (x1 + (t_0 + ((t_2 * ((t_5 - x1) / t_1)) - (t_1 * (((x1 * x1) * (6.0 + (4.0 * t_6))) + (((x1 * 2.0) * ((2.0 * x2) - x1)) * t_7)))))));
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$2 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x1 + N[(N[(x1 + N[(6.0 * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 9.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(x1 - N[(t$95$2 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(t$95$2 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(x1 - t$95$5), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$7 = N[(3.0 + t$95$6), $MachinePrecision]}, If[LessEqual[x1, -7.1e+106], t$95$3, If[LessEqual[x1, -0.032], N[(x1 + N[(N[(3.0 * N[(t$95$4 / N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(N[(t$95$2 * t$95$6), $MachinePrecision] + N[(t$95$1 * N[(N[(N[(4.0 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(4.0 - N[(x1 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t$95$7 * N[(N[(x1 * 2.0), $MachinePrecision] * t$95$6), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$0), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 7.7e+49], N[(x1 - N[(N[(3.0 * N[(t$95$4 / t$95$1), $MachinePrecision]), $MachinePrecision] - N[(x1 + N[(t$95$0 + N[(N[(t$95$2 * N[(N[(t$95$5 - x1), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] - N[(t$95$1 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 + N[(4.0 * t$95$6), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(x1 * 2.0), $MachinePrecision] * N[(N[(2.0 * x2), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision] * t$95$7), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -7.1000000000000003e106 or 7.7e49 < x1

   1. Initial program 26.1%

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

   3. Taylor expanded in x1 around -inf 30.3%

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

   4. Taylor expanded in x1 around inf 28.3%

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

   5. Taylor expanded in x1 around inf 97.0%

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

   if -7.1000000000000003e106 < x1 < -0.032000000000000001

   1. Initial program 99.0%

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

   3. Taylor expanded in x1 around -inf 99.2%

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

   4. Taylor expanded in x1 around 0 99.4%

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

   if -0.032000000000000001 < x1 < 7.7e49

   1. Initial program 99.3%

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

   3. Taylor expanded in x1 around 0 96.7%

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

4. Final simplification 97.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -7.1 \cdot 10^{+106}:\\ \;\;\;\;x1 + \left(\left(x1 + 6 \cdot {x1}^{4}\right) + 9\right)\\ \mathbf{elif}\;x1 \leq -0.032:\\ \;\;\;\;x1 + \left(3 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right)}{-1 - x1 \cdot x1} - \left(\left(\left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1} + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(4 \cdot \left(3 - 2 \cdot x2\right) + x1 \cdot \left(4 - x1 \cdot 6\right)\right) - \left(3 + \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right)\right)\right) - x1 \cdot \left(x1 \cdot x1\right)\right) - x1\right)\right)\\ \mathbf{elif}\;x1 \leq 7.7 \cdot 10^{+49}:\\ \;\;\;\;x1 - \left(3 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right)}{x1 \cdot x1 + 1} - \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right) + \left(\left(x1 \cdot 2\right) \cdot \left(2 \cdot x2 - x1\right)\right) \cdot \left(3 + \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 + 6 \cdot {x1}^{4}\right) + 9\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 96.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := x1 + \left(\left(x1 + 6 \cdot {x1}^{4}\right) + 9\right)\\ t_2 := x1 \cdot \left(x1 \cdot 3\right)\\ t_3 := t\_2 + 2 \cdot x2\\ t_4 := \frac{t\_3 - x1}{t\_0}\\ t_5 := \frac{x1 - t\_3}{t\_0}\\ t_6 := x1 \cdot \left(x1 \cdot x1\right)\\ t_7 := 3 + t\_5\\ \mathbf{if}\;x1 \leq -7.1 \cdot 10^{+106}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x1 \leq -0.021:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(t\_6 - \left(t\_2 \cdot t\_5 - \left(-1 - x1 \cdot x1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 - 4 \cdot \left(3 + \frac{-1 + \frac{2 \cdot x2 - 3}{x1}}{x1}\right)\right) + \left(\left(x1 \cdot 2\right) \cdot t\_4\right) \cdot t\_7\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 6.4 \cdot 10^{+49}:\\ \;\;\;\;x1 - \left(3 \cdot \frac{x1 - \left(t\_2 - 2 \cdot x2\right)}{t\_0} - \left(x1 + \left(t\_6 + \left(t\_2 \cdot t\_4 - t\_0 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot t\_5\right) + \left(\left(x1 \cdot 2\right) \cdot \left(2 \cdot x2 - x1\right)\right) \cdot t\_7\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ (* x1 x1) 1.0))
        (t_1 (+ x1 (+ (+ x1 (* 6.0 (pow x1 4.0))) 9.0)))
        (t_2 (* x1 (* x1 3.0)))
        (t_3 (+ t_2 (* 2.0 x2)))
        (t_4 (/ (- t_3 x1) t_0))
        (t_5 (/ (- x1 t_3) t_0))
        (t_6 (* x1 (* x1 x1)))
        (t_7 (+ 3.0 t_5)))
   (if (<= x1 -7.1e+106)
     t_1
     (if (<= x1 -0.021)
       (+
        x1
        (+
         9.0
         (+
          x1
          (-
           t_6
           (-
            (* t_2 t_5)
            (*
             (- -1.0 (* x1 x1))
             (+
              (*
               (* x1 x1)
               (-
                6.0
                (* 4.0 (+ 3.0 (/ (+ -1.0 (/ (- (* 2.0 x2) 3.0) x1)) x1)))))
              (* (* (* x1 2.0) t_4) t_7))))))))
       (if (<= x1 6.4e+49)
         (-
          x1
          (-
           (* 3.0 (/ (- x1 (- t_2 (* 2.0 x2))) t_0))
           (+
            x1
            (+
             t_6
             (-
              (* t_2 t_4)
              (*
               t_0
               (+
                (* (* x1 x1) (+ 6.0 (* 4.0 t_5)))
                (* (* (* x1 2.0) (- (* 2.0 x2) x1)) t_7))))))))
         t_1)))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = x1 + ((x1 + (6.0 * pow(x1, 4.0))) + 9.0);
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = t_2 + (2.0 * x2);
	double t_4 = (t_3 - x1) / t_0;
	double t_5 = (x1 - t_3) / t_0;
	double t_6 = x1 * (x1 * x1);
	double t_7 = 3.0 + t_5;
	double tmp;
	if (x1 <= -7.1e+106) {
		tmp = t_1;
	} else if (x1 <= -0.021) {
		tmp = x1 + (9.0 + (x1 + (t_6 - ((t_2 * t_5) - ((-1.0 - (x1 * x1)) * (((x1 * x1) * (6.0 - (4.0 * (3.0 + ((-1.0 + (((2.0 * x2) - 3.0) / x1)) / x1))))) + (((x1 * 2.0) * t_4) * t_7)))))));
	} else if (x1 <= 6.4e+49) {
		tmp = x1 - ((3.0 * ((x1 - (t_2 - (2.0 * x2))) / t_0)) - (x1 + (t_6 + ((t_2 * t_4) - (t_0 * (((x1 * x1) * (6.0 + (4.0 * t_5))) + (((x1 * 2.0) * ((2.0 * x2) - x1)) * t_7)))))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: tmp
    t_0 = (x1 * x1) + 1.0d0
    t_1 = x1 + ((x1 + (6.0d0 * (x1 ** 4.0d0))) + 9.0d0)
    t_2 = x1 * (x1 * 3.0d0)
    t_3 = t_2 + (2.0d0 * x2)
    t_4 = (t_3 - x1) / t_0
    t_5 = (x1 - t_3) / t_0
    t_6 = x1 * (x1 * x1)
    t_7 = 3.0d0 + t_5
    if (x1 <= (-7.1d+106)) then
        tmp = t_1
    else if (x1 <= (-0.021d0)) then
        tmp = x1 + (9.0d0 + (x1 + (t_6 - ((t_2 * t_5) - (((-1.0d0) - (x1 * x1)) * (((x1 * x1) * (6.0d0 - (4.0d0 * (3.0d0 + (((-1.0d0) + (((2.0d0 * x2) - 3.0d0) / x1)) / x1))))) + (((x1 * 2.0d0) * t_4) * t_7)))))))
    else if (x1 <= 6.4d+49) then
        tmp = x1 - ((3.0d0 * ((x1 - (t_2 - (2.0d0 * x2))) / t_0)) - (x1 + (t_6 + ((t_2 * t_4) - (t_0 * (((x1 * x1) * (6.0d0 + (4.0d0 * t_5))) + (((x1 * 2.0d0) * ((2.0d0 * x2) - x1)) * t_7)))))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = x1 + ((x1 + (6.0 * Math.pow(x1, 4.0))) + 9.0);
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = t_2 + (2.0 * x2);
	double t_4 = (t_3 - x1) / t_0;
	double t_5 = (x1 - t_3) / t_0;
	double t_6 = x1 * (x1 * x1);
	double t_7 = 3.0 + t_5;
	double tmp;
	if (x1 <= -7.1e+106) {
		tmp = t_1;
	} else if (x1 <= -0.021) {
		tmp = x1 + (9.0 + (x1 + (t_6 - ((t_2 * t_5) - ((-1.0 - (x1 * x1)) * (((x1 * x1) * (6.0 - (4.0 * (3.0 + ((-1.0 + (((2.0 * x2) - 3.0) / x1)) / x1))))) + (((x1 * 2.0) * t_4) * t_7)))))));
	} else if (x1 <= 6.4e+49) {
		tmp = x1 - ((3.0 * ((x1 - (t_2 - (2.0 * x2))) / t_0)) - (x1 + (t_6 + ((t_2 * t_4) - (t_0 * (((x1 * x1) * (6.0 + (4.0 * t_5))) + (((x1 * 2.0) * ((2.0 * x2) - x1)) * t_7)))))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x1 * x1) + 1.0
	t_1 = x1 + ((x1 + (6.0 * math.pow(x1, 4.0))) + 9.0)
	t_2 = x1 * (x1 * 3.0)
	t_3 = t_2 + (2.0 * x2)
	t_4 = (t_3 - x1) / t_0
	t_5 = (x1 - t_3) / t_0
	t_6 = x1 * (x1 * x1)
	t_7 = 3.0 + t_5
	tmp = 0
	if x1 <= -7.1e+106:
		tmp = t_1
	elif x1 <= -0.021:
		tmp = x1 + (9.0 + (x1 + (t_6 - ((t_2 * t_5) - ((-1.0 - (x1 * x1)) * (((x1 * x1) * (6.0 - (4.0 * (3.0 + ((-1.0 + (((2.0 * x2) - 3.0) / x1)) / x1))))) + (((x1 * 2.0) * t_4) * t_7)))))))
	elif x1 <= 6.4e+49:
		tmp = x1 - ((3.0 * ((x1 - (t_2 - (2.0 * x2))) / t_0)) - (x1 + (t_6 + ((t_2 * t_4) - (t_0 * (((x1 * x1) * (6.0 + (4.0 * t_5))) + (((x1 * 2.0) * ((2.0 * x2) - x1)) * t_7)))))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * x1) + 1.0)
	t_1 = Float64(x1 + Float64(Float64(x1 + Float64(6.0 * (x1 ^ 4.0))) + 9.0))
	t_2 = Float64(x1 * Float64(x1 * 3.0))
	t_3 = Float64(t_2 + Float64(2.0 * x2))
	t_4 = Float64(Float64(t_3 - x1) / t_0)
	t_5 = Float64(Float64(x1 - t_3) / t_0)
	t_6 = Float64(x1 * Float64(x1 * x1))
	t_7 = Float64(3.0 + t_5)
	tmp = 0.0
	if (x1 <= -7.1e+106)
		tmp = t_1;
	elseif (x1 <= -0.021)
		tmp = Float64(x1 + Float64(9.0 + Float64(x1 + Float64(t_6 - Float64(Float64(t_2 * t_5) - Float64(Float64(-1.0 - Float64(x1 * x1)) * Float64(Float64(Float64(x1 * x1) * Float64(6.0 - Float64(4.0 * Float64(3.0 + Float64(Float64(-1.0 + Float64(Float64(Float64(2.0 * x2) - 3.0) / x1)) / x1))))) + Float64(Float64(Float64(x1 * 2.0) * t_4) * t_7))))))));
	elseif (x1 <= 6.4e+49)
		tmp = Float64(x1 - Float64(Float64(3.0 * Float64(Float64(x1 - Float64(t_2 - Float64(2.0 * x2))) / t_0)) - Float64(x1 + Float64(t_6 + Float64(Float64(t_2 * t_4) - Float64(t_0 * Float64(Float64(Float64(x1 * x1) * Float64(6.0 + Float64(4.0 * t_5))) + Float64(Float64(Float64(x1 * 2.0) * Float64(Float64(2.0 * x2) - x1)) * t_7))))))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x1 * x1) + 1.0;
	t_1 = x1 + ((x1 + (6.0 * (x1 ^ 4.0))) + 9.0);
	t_2 = x1 * (x1 * 3.0);
	t_3 = t_2 + (2.0 * x2);
	t_4 = (t_3 - x1) / t_0;
	t_5 = (x1 - t_3) / t_0;
	t_6 = x1 * (x1 * x1);
	t_7 = 3.0 + t_5;
	tmp = 0.0;
	if (x1 <= -7.1e+106)
		tmp = t_1;
	elseif (x1 <= -0.021)
		tmp = x1 + (9.0 + (x1 + (t_6 - ((t_2 * t_5) - ((-1.0 - (x1 * x1)) * (((x1 * x1) * (6.0 - (4.0 * (3.0 + ((-1.0 + (((2.0 * x2) - 3.0) / x1)) / x1))))) + (((x1 * 2.0) * t_4) * t_7)))))));
	elseif (x1 <= 6.4e+49)
		tmp = x1 - ((3.0 * ((x1 - (t_2 - (2.0 * x2))) / t_0)) - (x1 + (t_6 + ((t_2 * t_4) - (t_0 * (((x1 * x1) * (6.0 + (4.0 * t_5))) + (((x1 * 2.0) * ((2.0 * x2) - x1)) * t_7)))))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$1 = N[(x1 + N[(N[(x1 + N[(6.0 * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 9.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(t$95$3 - x1), $MachinePrecision] / t$95$0), $MachinePrecision]}, Block[{t$95$5 = N[(N[(x1 - t$95$3), $MachinePrecision] / t$95$0), $MachinePrecision]}, Block[{t$95$6 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(3.0 + t$95$5), $MachinePrecision]}, If[LessEqual[x1, -7.1e+106], t$95$1, If[LessEqual[x1, -0.021], N[(x1 + N[(9.0 + N[(x1 + N[(t$95$6 - N[(N[(t$95$2 * t$95$5), $MachinePrecision] - N[(N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision] * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 - N[(4.0 * N[(3.0 + N[(N[(-1.0 + N[(N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision] / x1), $MachinePrecision]), $MachinePrecision] / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$4), $MachinePrecision] * t$95$7), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 6.4e+49], N[(x1 - N[(N[(3.0 * N[(N[(x1 - N[(t$95$2 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision] - N[(x1 + N[(t$95$6 + N[(N[(t$95$2 * t$95$4), $MachinePrecision] - N[(t$95$0 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 + N[(4.0 * t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(x1 * 2.0), $MachinePrecision] * N[(N[(2.0 * x2), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision] * t$95$7), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -7.1000000000000003e106 or 6.40000000000000028e49 < x1

   1. Initial program 26.1%

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

   3. Taylor expanded in x1 around -inf 30.3%

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

   4. Taylor expanded in x1 around inf 28.3%

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

   5. Taylor expanded in x1 around inf 97.0%

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

   if -7.1000000000000003e106 < x1 < -0.0210000000000000013

   1. Initial program 99.0%

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

   3. Taylor expanded in x1 around -inf 99.2%

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

   4. Taylor expanded in x1 around inf 99.2%

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

   if -0.0210000000000000013 < x1 < 6.40000000000000028e49

   1. Initial program 99.3%

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

   3. Taylor expanded in x1 around 0 96.7%

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

4. Final simplification 97.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -7.1 \cdot 10^{+106}:\\ \;\;\;\;x1 + \left(\left(x1 + 6 \cdot {x1}^{4}\right) + 9\right)\\ \mathbf{elif}\;x1 \leq -0.021:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) - \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1} - \left(-1 - x1 \cdot x1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 - 4 \cdot \left(3 + \frac{-1 + \frac{2 \cdot x2 - 3}{x1}}{x1}\right)\right) + \left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(3 + \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 6.4 \cdot 10^{+49}:\\ \;\;\;\;x1 - \left(3 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right)}{x1 \cdot x1 + 1} - \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right) + \left(\left(x1 \cdot 2\right) \cdot \left(2 \cdot x2 - x1\right)\right) \cdot \left(3 + \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 + 6 \cdot {x1}^{4}\right) + 9\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 94.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := t\_1 + 2 \cdot x2\\ t_3 := x1 \cdot x1 + 1\\ t_4 := \frac{x1 - t\_2}{t\_3}\\ t_5 := x1 + \left(9 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) - \left(t\_1 \cdot t\_4 - \left(-1 - x1 \cdot x1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 - 4 \cdot \left(3 + \frac{-1 + \frac{2 \cdot x2 - 3}{x1}}{x1}\right)\right) + \left(\left(x1 \cdot 2\right) \cdot \frac{t\_2 - x1}{t\_3}\right) \cdot \left(3 + t\_4\right)\right)\right)\right)\right)\right)\\ \mathbf{if}\;x1 \leq -2.2 \cdot 10^{+140}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x1 \leq -0.016:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;x1 \leq 0.001:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2 - x1 \cdot \left(x1 \cdot \left(x2 \cdot -2 - 3\right) - -1\right)\right) + \left(x1 + x2 \cdot \left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+152}:\\ \;\;\;\;t\_5\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ x1 (+ x1 (* 3.0 (* x1 (+ (* x1 3.0) -1.0))))))
        (t_1 (* x1 (* x1 3.0)))
        (t_2 (+ t_1 (* 2.0 x2)))
        (t_3 (+ (* x1 x1) 1.0))
        (t_4 (/ (- x1 t_2) t_3))
        (t_5
         (+
          x1
          (+
           9.0
           (+
            x1
            (-
             (* x1 (* x1 x1))
             (-
              (* t_1 t_4)
              (*
               (- -1.0 (* x1 x1))
               (+
                (*
                 (* x1 x1)
                 (-
                  6.0
                  (* 4.0 (+ 3.0 (/ (+ -1.0 (/ (- (* 2.0 x2) 3.0) x1)) x1)))))
                (* (* (* x1 2.0) (/ (- t_2 x1) t_3)) (+ 3.0 t_4)))))))))))
   (if (<= x1 -2.2e+140)
     t_0
     (if (<= x1 -0.016)
       t_5
       (if (<= x1 0.001)
         (+
          x1
          (+
           (* 3.0 (- (* x2 -2.0) (* x1 (- (* x1 (- (* x2 -2.0) 3.0)) -1.0))))
           (+ x1 (* x2 (+ (* x1 -12.0) (* 8.0 (* x1 x2)))))))
         (if (<= x1 5e+152) t_5 t_0))))))

C

double code(double x1, double x2) {
	double t_0 = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = t_1 + (2.0 * x2);
	double t_3 = (x1 * x1) + 1.0;
	double t_4 = (x1 - t_2) / t_3;
	double t_5 = x1 + (9.0 + (x1 + ((x1 * (x1 * x1)) - ((t_1 * t_4) - ((-1.0 - (x1 * x1)) * (((x1 * x1) * (6.0 - (4.0 * (3.0 + ((-1.0 + (((2.0 * x2) - 3.0) / x1)) / x1))))) + (((x1 * 2.0) * ((t_2 - x1) / t_3)) * (3.0 + t_4))))))));
	double tmp;
	if (x1 <= -2.2e+140) {
		tmp = t_0;
	} else if (x1 <= -0.016) {
		tmp = t_5;
	} else if (x1 <= 0.001) {
		tmp = x1 + ((3.0 * ((x2 * -2.0) - (x1 * ((x1 * ((x2 * -2.0) - 3.0)) - -1.0)))) + (x1 + (x2 * ((x1 * -12.0) + (8.0 * (x1 * x2))))));
	} else if (x1 <= 5e+152) {
		tmp = t_5;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_0 = x1 + (x1 + (3.0d0 * (x1 * ((x1 * 3.0d0) + (-1.0d0)))))
    t_1 = x1 * (x1 * 3.0d0)
    t_2 = t_1 + (2.0d0 * x2)
    t_3 = (x1 * x1) + 1.0d0
    t_4 = (x1 - t_2) / t_3
    t_5 = x1 + (9.0d0 + (x1 + ((x1 * (x1 * x1)) - ((t_1 * t_4) - (((-1.0d0) - (x1 * x1)) * (((x1 * x1) * (6.0d0 - (4.0d0 * (3.0d0 + (((-1.0d0) + (((2.0d0 * x2) - 3.0d0) / x1)) / x1))))) + (((x1 * 2.0d0) * ((t_2 - x1) / t_3)) * (3.0d0 + t_4))))))))
    if (x1 <= (-2.2d+140)) then
        tmp = t_0
    else if (x1 <= (-0.016d0)) then
        tmp = t_5
    else if (x1 <= 0.001d0) then
        tmp = x1 + ((3.0d0 * ((x2 * (-2.0d0)) - (x1 * ((x1 * ((x2 * (-2.0d0)) - 3.0d0)) - (-1.0d0))))) + (x1 + (x2 * ((x1 * (-12.0d0)) + (8.0d0 * (x1 * x2))))))
    else if (x1 <= 5d+152) then
        tmp = t_5
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = t_1 + (2.0 * x2);
	double t_3 = (x1 * x1) + 1.0;
	double t_4 = (x1 - t_2) / t_3;
	double t_5 = x1 + (9.0 + (x1 + ((x1 * (x1 * x1)) - ((t_1 * t_4) - ((-1.0 - (x1 * x1)) * (((x1 * x1) * (6.0 - (4.0 * (3.0 + ((-1.0 + (((2.0 * x2) - 3.0) / x1)) / x1))))) + (((x1 * 2.0) * ((t_2 - x1) / t_3)) * (3.0 + t_4))))))));
	double tmp;
	if (x1 <= -2.2e+140) {
		tmp = t_0;
	} else if (x1 <= -0.016) {
		tmp = t_5;
	} else if (x1 <= 0.001) {
		tmp = x1 + ((3.0 * ((x2 * -2.0) - (x1 * ((x1 * ((x2 * -2.0) - 3.0)) - -1.0)))) + (x1 + (x2 * ((x1 * -12.0) + (8.0 * (x1 * x2))))));
	} else if (x1 <= 5e+152) {
		tmp = t_5;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))))
	t_1 = x1 * (x1 * 3.0)
	t_2 = t_1 + (2.0 * x2)
	t_3 = (x1 * x1) + 1.0
	t_4 = (x1 - t_2) / t_3
	t_5 = x1 + (9.0 + (x1 + ((x1 * (x1 * x1)) - ((t_1 * t_4) - ((-1.0 - (x1 * x1)) * (((x1 * x1) * (6.0 - (4.0 * (3.0 + ((-1.0 + (((2.0 * x2) - 3.0) / x1)) / x1))))) + (((x1 * 2.0) * ((t_2 - x1) / t_3)) * (3.0 + t_4))))))))
	tmp = 0
	if x1 <= -2.2e+140:
		tmp = t_0
	elif x1 <= -0.016:
		tmp = t_5
	elif x1 <= 0.001:
		tmp = x1 + ((3.0 * ((x2 * -2.0) - (x1 * ((x1 * ((x2 * -2.0) - 3.0)) - -1.0)))) + (x1 + (x2 * ((x1 * -12.0) + (8.0 * (x1 * x2))))))
	elif x1 <= 5e+152:
		tmp = t_5
	else:
		tmp = t_0
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 + Float64(x1 + Float64(3.0 * Float64(x1 * Float64(Float64(x1 * 3.0) + -1.0)))))
	t_1 = Float64(x1 * Float64(x1 * 3.0))
	t_2 = Float64(t_1 + Float64(2.0 * x2))
	t_3 = Float64(Float64(x1 * x1) + 1.0)
	t_4 = Float64(Float64(x1 - t_2) / t_3)
	t_5 = Float64(x1 + Float64(9.0 + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) - Float64(Float64(t_1 * t_4) - Float64(Float64(-1.0 - Float64(x1 * x1)) * Float64(Float64(Float64(x1 * x1) * Float64(6.0 - Float64(4.0 * Float64(3.0 + Float64(Float64(-1.0 + Float64(Float64(Float64(2.0 * x2) - 3.0) / x1)) / x1))))) + Float64(Float64(Float64(x1 * 2.0) * Float64(Float64(t_2 - x1) / t_3)) * Float64(3.0 + t_4)))))))))
	tmp = 0.0
	if (x1 <= -2.2e+140)
		tmp = t_0;
	elseif (x1 <= -0.016)
		tmp = t_5;
	elseif (x1 <= 0.001)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(x2 * -2.0) - Float64(x1 * Float64(Float64(x1 * Float64(Float64(x2 * -2.0) - 3.0)) - -1.0)))) + Float64(x1 + Float64(x2 * Float64(Float64(x1 * -12.0) + Float64(8.0 * Float64(x1 * x2)))))));
	elseif (x1 <= 5e+152)
		tmp = t_5;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	t_1 = x1 * (x1 * 3.0);
	t_2 = t_1 + (2.0 * x2);
	t_3 = (x1 * x1) + 1.0;
	t_4 = (x1 - t_2) / t_3;
	t_5 = x1 + (9.0 + (x1 + ((x1 * (x1 * x1)) - ((t_1 * t_4) - ((-1.0 - (x1 * x1)) * (((x1 * x1) * (6.0 - (4.0 * (3.0 + ((-1.0 + (((2.0 * x2) - 3.0) / x1)) / x1))))) + (((x1 * 2.0) * ((t_2 - x1) / t_3)) * (3.0 + t_4))))))));
	tmp = 0.0;
	if (x1 <= -2.2e+140)
		tmp = t_0;
	elseif (x1 <= -0.016)
		tmp = t_5;
	elseif (x1 <= 0.001)
		tmp = x1 + ((3.0 * ((x2 * -2.0) - (x1 * ((x1 * ((x2 * -2.0) - 3.0)) - -1.0)))) + (x1 + (x2 * ((x1 * -12.0) + (8.0 * (x1 * x2))))));
	elseif (x1 <= 5e+152)
		tmp = t_5;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 + N[(x1 + N[(3.0 * N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$4 = N[(N[(x1 - t$95$2), $MachinePrecision] / t$95$3), $MachinePrecision]}, Block[{t$95$5 = N[(x1 + N[(9.0 + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] - N[(N[(t$95$1 * t$95$4), $MachinePrecision] - N[(N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision] * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 - N[(4.0 * N[(3.0 + N[(N[(-1.0 + N[(N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision] / x1), $MachinePrecision]), $MachinePrecision] / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(x1 * 2.0), $MachinePrecision] * N[(N[(t$95$2 - x1), $MachinePrecision] / t$95$3), $MachinePrecision]), $MachinePrecision] * N[(3.0 + t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -2.2e+140], t$95$0, If[LessEqual[x1, -0.016], t$95$5, If[LessEqual[x1, 0.001], N[(x1 + N[(N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - N[(x1 * N[(N[(x1 * N[(N[(x2 * -2.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(x2 * N[(N[(x1 * -12.0), $MachinePrecision] + N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 5e+152], t$95$5, t$95$0]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -2.1999999999999998e140 or 5e152 < x1

   1. Initial program 0.0%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   2. 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 69.1%

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

   5. Taylor expanded in x2 around 0 100.0%

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

   if -2.1999999999999998e140 < x1 < -0.016 or 1e-3 < x1 < 5e152

   1. Initial program 92.4%

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

   3. Taylor expanded in x1 around -inf 91.8%

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

   4. Taylor expanded in x1 around inf 91.8%

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

   if -0.016 < x1 < 1e-3

   1. Initial program 99.3%

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

   3. Taylor expanded in x1 around 0 87.5%

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

   4. Taylor expanded in x1 around 0 87.6%

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

   5. Taylor expanded in x2 around 0 98.8%

      \[\leadsto x1 + \left(\left(\color{blue}{x2 \cdot \left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right)} + x1\right) + 3 \cdot \left(-2 \cdot x2 + x1 \cdot \left(x1 \cdot \left(3 - -2 \cdot x2\right) - 1\right)\right)\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 97.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -2.2 \cdot 10^{+140}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -0.016:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) - \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1} - \left(-1 - x1 \cdot x1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 - 4 \cdot \left(3 + \frac{-1 + \frac{2 \cdot x2 - 3}{x1}}{x1}\right)\right) + \left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(3 + \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 0.001:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2 - x1 \cdot \left(x1 \cdot \left(x2 \cdot -2 - 3\right) - -1\right)\right) + \left(x1 + x2 \cdot \left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+152}:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) - \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1} - \left(-1 - x1 \cdot x1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 - 4 \cdot \left(3 + \frac{-1 + \frac{2 \cdot x2 - 3}{x1}}{x1}\right)\right) + \left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(3 + \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 94.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ t_2 := x1 \cdot \left(x1 \cdot 3\right)\\ t_3 := t\_2 + 2 \cdot x2\\ t_4 := \frac{x1 - t\_3}{t\_0}\\ t_5 := x1 + \left(x2 \cdot -6 - \left(\left(\left(t\_2 \cdot t\_4 + t\_0 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{t\_3 - x1}{t\_0}\right) \cdot \frac{\left(1 + \frac{3}{x1}\right) - \frac{2 \cdot x2}{x1}}{x1} + \left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot t\_4\right)\right)\right) - x1 \cdot \left(x1 \cdot x1\right)\right) - x1\right)\right)\\ \mathbf{if}\;x1 \leq -3.2 \cdot 10^{+140}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x1 \leq -0.75:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;x1 \leq 0.33:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2 - x1 \cdot \left(x1 \cdot \left(x2 \cdot -2 - 3\right) - -1\right)\right) + \left(x1 + x2 \cdot \left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+153}:\\ \;\;\;\;t\_5\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ (* x1 x1) 1.0))
        (t_1 (+ x1 (+ x1 (* 3.0 (* x1 (+ (* x1 3.0) -1.0))))))
        (t_2 (* x1 (* x1 3.0)))
        (t_3 (+ t_2 (* 2.0 x2)))
        (t_4 (/ (- x1 t_3) t_0))
        (t_5
         (+
          x1
          (-
           (* x2 -6.0)
           (-
            (-
             (+
              (* t_2 t_4)
              (*
               t_0
               (+
                (*
                 (* (* x1 2.0) (/ (- t_3 x1) t_0))
                 (/ (- (+ 1.0 (/ 3.0 x1)) (/ (* 2.0 x2) x1)) x1))
                (* (* x1 x1) (+ 6.0 (* 4.0 t_4))))))
             (* x1 (* x1 x1)))
            x1)))))
   (if (<= x1 -3.2e+140)
     t_1
     (if (<= x1 -0.75)
       t_5
       (if (<= x1 0.33)
         (+
          x1
          (+
           (* 3.0 (- (* x2 -2.0) (* x1 (- (* x1 (- (* x2 -2.0) 3.0)) -1.0))))
           (+ x1 (* x2 (+ (* x1 -12.0) (* 8.0 (* x1 x2)))))))
         (if (<= x1 5e+153) t_5 t_1))))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = t_2 + (2.0 * x2);
	double t_4 = (x1 - t_3) / t_0;
	double t_5 = x1 + ((x2 * -6.0) - ((((t_2 * t_4) + (t_0 * ((((x1 * 2.0) * ((t_3 - x1) / t_0)) * (((1.0 + (3.0 / x1)) - ((2.0 * x2) / x1)) / x1)) + ((x1 * x1) * (6.0 + (4.0 * t_4)))))) - (x1 * (x1 * x1))) - x1));
	double tmp;
	if (x1 <= -3.2e+140) {
		tmp = t_1;
	} else if (x1 <= -0.75) {
		tmp = t_5;
	} else if (x1 <= 0.33) {
		tmp = x1 + ((3.0 * ((x2 * -2.0) - (x1 * ((x1 * ((x2 * -2.0) - 3.0)) - -1.0)))) + (x1 + (x2 * ((x1 * -12.0) + (8.0 * (x1 * x2))))));
	} else if (x1 <= 5e+153) {
		tmp = t_5;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_0 = (x1 * x1) + 1.0d0
    t_1 = x1 + (x1 + (3.0d0 * (x1 * ((x1 * 3.0d0) + (-1.0d0)))))
    t_2 = x1 * (x1 * 3.0d0)
    t_3 = t_2 + (2.0d0 * x2)
    t_4 = (x1 - t_3) / t_0
    t_5 = x1 + ((x2 * (-6.0d0)) - ((((t_2 * t_4) + (t_0 * ((((x1 * 2.0d0) * ((t_3 - x1) / t_0)) * (((1.0d0 + (3.0d0 / x1)) - ((2.0d0 * x2) / x1)) / x1)) + ((x1 * x1) * (6.0d0 + (4.0d0 * t_4)))))) - (x1 * (x1 * x1))) - x1))
    if (x1 <= (-3.2d+140)) then
        tmp = t_1
    else if (x1 <= (-0.75d0)) then
        tmp = t_5
    else if (x1 <= 0.33d0) then
        tmp = x1 + ((3.0d0 * ((x2 * (-2.0d0)) - (x1 * ((x1 * ((x2 * (-2.0d0)) - 3.0d0)) - (-1.0d0))))) + (x1 + (x2 * ((x1 * (-12.0d0)) + (8.0d0 * (x1 * x2))))))
    else if (x1 <= 5d+153) then
        tmp = t_5
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = t_2 + (2.0 * x2);
	double t_4 = (x1 - t_3) / t_0;
	double t_5 = x1 + ((x2 * -6.0) - ((((t_2 * t_4) + (t_0 * ((((x1 * 2.0) * ((t_3 - x1) / t_0)) * (((1.0 + (3.0 / x1)) - ((2.0 * x2) / x1)) / x1)) + ((x1 * x1) * (6.0 + (4.0 * t_4)))))) - (x1 * (x1 * x1))) - x1));
	double tmp;
	if (x1 <= -3.2e+140) {
		tmp = t_1;
	} else if (x1 <= -0.75) {
		tmp = t_5;
	} else if (x1 <= 0.33) {
		tmp = x1 + ((3.0 * ((x2 * -2.0) - (x1 * ((x1 * ((x2 * -2.0) - 3.0)) - -1.0)))) + (x1 + (x2 * ((x1 * -12.0) + (8.0 * (x1 * x2))))));
	} else if (x1 <= 5e+153) {
		tmp = t_5;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x1 * x1) + 1.0
	t_1 = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))))
	t_2 = x1 * (x1 * 3.0)
	t_3 = t_2 + (2.0 * x2)
	t_4 = (x1 - t_3) / t_0
	t_5 = x1 + ((x2 * -6.0) - ((((t_2 * t_4) + (t_0 * ((((x1 * 2.0) * ((t_3 - x1) / t_0)) * (((1.0 + (3.0 / x1)) - ((2.0 * x2) / x1)) / x1)) + ((x1 * x1) * (6.0 + (4.0 * t_4)))))) - (x1 * (x1 * x1))) - x1))
	tmp = 0
	if x1 <= -3.2e+140:
		tmp = t_1
	elif x1 <= -0.75:
		tmp = t_5
	elif x1 <= 0.33:
		tmp = x1 + ((3.0 * ((x2 * -2.0) - (x1 * ((x1 * ((x2 * -2.0) - 3.0)) - -1.0)))) + (x1 + (x2 * ((x1 * -12.0) + (8.0 * (x1 * x2))))))
	elif x1 <= 5e+153:
		tmp = t_5
	else:
		tmp = t_1
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * x1) + 1.0)
	t_1 = Float64(x1 + Float64(x1 + Float64(3.0 * Float64(x1 * Float64(Float64(x1 * 3.0) + -1.0)))))
	t_2 = Float64(x1 * Float64(x1 * 3.0))
	t_3 = Float64(t_2 + Float64(2.0 * x2))
	t_4 = Float64(Float64(x1 - t_3) / t_0)
	t_5 = Float64(x1 + Float64(Float64(x2 * -6.0) - Float64(Float64(Float64(Float64(t_2 * t_4) + Float64(t_0 * Float64(Float64(Float64(Float64(x1 * 2.0) * Float64(Float64(t_3 - x1) / t_0)) * Float64(Float64(Float64(1.0 + Float64(3.0 / x1)) - Float64(Float64(2.0 * x2) / x1)) / x1)) + Float64(Float64(x1 * x1) * Float64(6.0 + Float64(4.0 * t_4)))))) - Float64(x1 * Float64(x1 * x1))) - x1)))
	tmp = 0.0
	if (x1 <= -3.2e+140)
		tmp = t_1;
	elseif (x1 <= -0.75)
		tmp = t_5;
	elseif (x1 <= 0.33)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(x2 * -2.0) - Float64(x1 * Float64(Float64(x1 * Float64(Float64(x2 * -2.0) - 3.0)) - -1.0)))) + Float64(x1 + Float64(x2 * Float64(Float64(x1 * -12.0) + Float64(8.0 * Float64(x1 * x2)))))));
	elseif (x1 <= 5e+153)
		tmp = t_5;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x1 * x1) + 1.0;
	t_1 = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	t_2 = x1 * (x1 * 3.0);
	t_3 = t_2 + (2.0 * x2);
	t_4 = (x1 - t_3) / t_0;
	t_5 = x1 + ((x2 * -6.0) - ((((t_2 * t_4) + (t_0 * ((((x1 * 2.0) * ((t_3 - x1) / t_0)) * (((1.0 + (3.0 / x1)) - ((2.0 * x2) / x1)) / x1)) + ((x1 * x1) * (6.0 + (4.0 * t_4)))))) - (x1 * (x1 * x1))) - x1));
	tmp = 0.0;
	if (x1 <= -3.2e+140)
		tmp = t_1;
	elseif (x1 <= -0.75)
		tmp = t_5;
	elseif (x1 <= 0.33)
		tmp = x1 + ((3.0 * ((x2 * -2.0) - (x1 * ((x1 * ((x2 * -2.0) - 3.0)) - -1.0)))) + (x1 + (x2 * ((x1 * -12.0) + (8.0 * (x1 * x2))))));
	elseif (x1 <= 5e+153)
		tmp = t_5;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$1 = N[(x1 + N[(x1 + N[(3.0 * N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(x1 - t$95$3), $MachinePrecision] / t$95$0), $MachinePrecision]}, Block[{t$95$5 = N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] - N[(N[(N[(N[(t$95$2 * t$95$4), $MachinePrecision] + N[(t$95$0 * N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * N[(N[(t$95$3 - x1), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision] * N[(N[(N[(1.0 + N[(3.0 / x1), $MachinePrecision]), $MachinePrecision] - N[(N[(2.0 * x2), $MachinePrecision] / x1), $MachinePrecision]), $MachinePrecision] / x1), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 + N[(4.0 * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -3.2e+140], t$95$1, If[LessEqual[x1, -0.75], t$95$5, If[LessEqual[x1, 0.33], N[(x1 + N[(N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - N[(x1 * N[(N[(x1 * N[(N[(x2 * -2.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(x2 * N[(N[(x1 * -12.0), $MachinePrecision] + N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 5e+153], t$95$5, t$95$1]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -3.20000000000000011e140 or 5.00000000000000018e153 < x1

   1. Initial program 0.0%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   2. 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 69.1%

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

   5. Taylor expanded in x2 around 0 100.0%

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

   if -3.20000000000000011e140 < x1 < -0.75 or 0.330000000000000016 < x1 < 5.00000000000000018e153

   1. Initial program 92.1%

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

   3. Taylor expanded in x1 around 0 91.5%

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

      1. *-commutative 91.5%

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

   5. Simplified 91.5%

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

   6. Taylor expanded in x1 around inf 91.5%

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

      1. associate-*r/ 91.5%

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

      2. associate-*r/ 91.5%

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

      3. metadata-eval 91.5%

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

   8. Simplified 91.5%

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

   9. Taylor expanded in x2 around 0 91.5%

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

       1. *-commutative 91.5%

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

   11. Simplified 91.5%

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

   if -0.75 < x1 < 0.330000000000000016

   1. Initial program 99.3%

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

   3. Taylor expanded in x1 around 0 86.0%

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

   4. Taylor expanded in x1 around 0 86.0%

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

   5. Taylor expanded in x2 around 0 97.0%

      \[\leadsto x1 + \left(\left(\color{blue}{x2 \cdot \left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right)} + x1\right) + 3 \cdot \left(-2 \cdot x2 + x1 \cdot \left(x1 \cdot \left(3 - -2 \cdot x2\right) - 1\right)\right)\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 96.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -3.2 \cdot 10^{+140}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -0.75:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - \left(\left(\left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1} + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \frac{\left(1 + \frac{3}{x1}\right) - \frac{2 \cdot x2}{x1}}{x1} + \left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right)\right)\right) - x1 \cdot \left(x1 \cdot x1\right)\right) - x1\right)\right)\\ \mathbf{elif}\;x1 \leq 0.33:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2 - x1 \cdot \left(x1 \cdot \left(x2 \cdot -2 - 3\right) - -1\right)\right) + \left(x1 + x2 \cdot \left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - \left(\left(\left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1} + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \frac{\left(1 + \frac{3}{x1}\right) - \frac{2 \cdot x2}{x1}}{x1} + \left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right)\right)\right) - x1 \cdot \left(x1 \cdot x1\right)\right) - x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 94.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := 3 \cdot \left(x2 \cdot -2\right)\\ t_2 := 3 + \frac{-1 + \frac{2 \cdot x2 - 3}{x1}}{x1}\\ t_3 := x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ t_4 := x1 \cdot \left(x1 \cdot 3\right)\\ t_5 := t\_4 + 2 \cdot x2\\ t_6 := \frac{t\_5 - x1}{t\_0}\\ t_7 := \frac{2 \cdot x2}{x1}\\ t_8 := t\_4 \cdot \frac{x1 - t\_5}{t\_0}\\ t_9 := x1 \cdot \left(x1 \cdot x1\right)\\ \mathbf{if}\;x1 \leq -2.2 \cdot 10^{+140}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x1 \leq -0.7:\\ \;\;\;\;x1 + \left(t\_1 - \left(\left(\left(t\_8 + t\_0 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t\_6\right) \cdot \frac{\left(1 + \frac{3}{x1}\right) - t\_7}{x1} + \left(x1 \cdot x1\right) \cdot \left(6 - 4 \cdot t\_2\right)\right)\right) - t\_9\right) - x1\right)\right)\\ \mathbf{elif}\;x1 \leq 1.26:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2 - x1 \cdot \left(x1 \cdot \left(x2 \cdot -2 - 3\right) - -1\right)\right) + \left(x1 + x2 \cdot \left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+152}:\\ \;\;\;\;x1 + \left(t\_1 + \left(x1 + \left(t\_9 - \left(t\_8 - t\_0 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(t\_6 \cdot 4 - 6\right) + \frac{t\_7 + \left(-1 - \frac{3}{x1}\right)}{x1} \cdot \left(\left(x1 \cdot 2\right) \cdot t\_2\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ (* x1 x1) 1.0))
        (t_1 (* 3.0 (* x2 -2.0)))
        (t_2 (+ 3.0 (/ (+ -1.0 (/ (- (* 2.0 x2) 3.0) x1)) x1)))
        (t_3 (+ x1 (+ x1 (* 3.0 (* x1 (+ (* x1 3.0) -1.0))))))
        (t_4 (* x1 (* x1 3.0)))
        (t_5 (+ t_4 (* 2.0 x2)))
        (t_6 (/ (- t_5 x1) t_0))
        (t_7 (/ (* 2.0 x2) x1))
        (t_8 (* t_4 (/ (- x1 t_5) t_0)))
        (t_9 (* x1 (* x1 x1))))
   (if (<= x1 -2.2e+140)
     t_3
     (if (<= x1 -0.7)
       (+
        x1
        (-
         t_1
         (-
          (-
           (+
            t_8
            (*
             t_0
             (+
              (* (* (* x1 2.0) t_6) (/ (- (+ 1.0 (/ 3.0 x1)) t_7) x1))
              (* (* x1 x1) (- 6.0 (* 4.0 t_2))))))
           t_9)
          x1)))
       (if (<= x1 1.26)
         (+
          x1
          (+
           (* 3.0 (- (* x2 -2.0) (* x1 (- (* x1 (- (* x2 -2.0) 3.0)) -1.0))))
           (+ x1 (* x2 (+ (* x1 -12.0) (* 8.0 (* x1 x2)))))))
         (if (<= x1 5e+152)
           (+
            x1
            (+
             t_1
             (+
              x1
              (-
               t_9
               (-
                t_8
                (*
                 t_0
                 (+
                  (* (* x1 x1) (- (* t_6 4.0) 6.0))
                  (*
                   (/ (+ t_7 (- -1.0 (/ 3.0 x1))) x1)
                   (* (* x1 2.0) t_2)))))))))
           t_3))))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = 3.0 * (x2 * -2.0);
	double t_2 = 3.0 + ((-1.0 + (((2.0 * x2) - 3.0) / x1)) / x1);
	double t_3 = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	double t_4 = x1 * (x1 * 3.0);
	double t_5 = t_4 + (2.0 * x2);
	double t_6 = (t_5 - x1) / t_0;
	double t_7 = (2.0 * x2) / x1;
	double t_8 = t_4 * ((x1 - t_5) / t_0);
	double t_9 = x1 * (x1 * x1);
	double tmp;
	if (x1 <= -2.2e+140) {
		tmp = t_3;
	} else if (x1 <= -0.7) {
		tmp = x1 + (t_1 - (((t_8 + (t_0 * ((((x1 * 2.0) * t_6) * (((1.0 + (3.0 / x1)) - t_7) / x1)) + ((x1 * x1) * (6.0 - (4.0 * t_2)))))) - t_9) - x1));
	} else if (x1 <= 1.26) {
		tmp = x1 + ((3.0 * ((x2 * -2.0) - (x1 * ((x1 * ((x2 * -2.0) - 3.0)) - -1.0)))) + (x1 + (x2 * ((x1 * -12.0) + (8.0 * (x1 * x2))))));
	} else if (x1 <= 5e+152) {
		tmp = x1 + (t_1 + (x1 + (t_9 - (t_8 - (t_0 * (((x1 * x1) * ((t_6 * 4.0) - 6.0)) + (((t_7 + (-1.0 - (3.0 / x1))) / x1) * ((x1 * 2.0) * t_2))))))));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: t_8
    real(8) :: t_9
    real(8) :: tmp
    t_0 = (x1 * x1) + 1.0d0
    t_1 = 3.0d0 * (x2 * (-2.0d0))
    t_2 = 3.0d0 + (((-1.0d0) + (((2.0d0 * x2) - 3.0d0) / x1)) / x1)
    t_3 = x1 + (x1 + (3.0d0 * (x1 * ((x1 * 3.0d0) + (-1.0d0)))))
    t_4 = x1 * (x1 * 3.0d0)
    t_5 = t_4 + (2.0d0 * x2)
    t_6 = (t_5 - x1) / t_0
    t_7 = (2.0d0 * x2) / x1
    t_8 = t_4 * ((x1 - t_5) / t_0)
    t_9 = x1 * (x1 * x1)
    if (x1 <= (-2.2d+140)) then
        tmp = t_3
    else if (x1 <= (-0.7d0)) then
        tmp = x1 + (t_1 - (((t_8 + (t_0 * ((((x1 * 2.0d0) * t_6) * (((1.0d0 + (3.0d0 / x1)) - t_7) / x1)) + ((x1 * x1) * (6.0d0 - (4.0d0 * t_2)))))) - t_9) - x1))
    else if (x1 <= 1.26d0) then
        tmp = x1 + ((3.0d0 * ((x2 * (-2.0d0)) - (x1 * ((x1 * ((x2 * (-2.0d0)) - 3.0d0)) - (-1.0d0))))) + (x1 + (x2 * ((x1 * (-12.0d0)) + (8.0d0 * (x1 * x2))))))
    else if (x1 <= 5d+152) then
        tmp = x1 + (t_1 + (x1 + (t_9 - (t_8 - (t_0 * (((x1 * x1) * ((t_6 * 4.0d0) - 6.0d0)) + (((t_7 + ((-1.0d0) - (3.0d0 / x1))) / x1) * ((x1 * 2.0d0) * t_2))))))))
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = 3.0 * (x2 * -2.0);
	double t_2 = 3.0 + ((-1.0 + (((2.0 * x2) - 3.0) / x1)) / x1);
	double t_3 = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	double t_4 = x1 * (x1 * 3.0);
	double t_5 = t_4 + (2.0 * x2);
	double t_6 = (t_5 - x1) / t_0;
	double t_7 = (2.0 * x2) / x1;
	double t_8 = t_4 * ((x1 - t_5) / t_0);
	double t_9 = x1 * (x1 * x1);
	double tmp;
	if (x1 <= -2.2e+140) {
		tmp = t_3;
	} else if (x1 <= -0.7) {
		tmp = x1 + (t_1 - (((t_8 + (t_0 * ((((x1 * 2.0) * t_6) * (((1.0 + (3.0 / x1)) - t_7) / x1)) + ((x1 * x1) * (6.0 - (4.0 * t_2)))))) - t_9) - x1));
	} else if (x1 <= 1.26) {
		tmp = x1 + ((3.0 * ((x2 * -2.0) - (x1 * ((x1 * ((x2 * -2.0) - 3.0)) - -1.0)))) + (x1 + (x2 * ((x1 * -12.0) + (8.0 * (x1 * x2))))));
	} else if (x1 <= 5e+152) {
		tmp = x1 + (t_1 + (x1 + (t_9 - (t_8 - (t_0 * (((x1 * x1) * ((t_6 * 4.0) - 6.0)) + (((t_7 + (-1.0 - (3.0 / x1))) / x1) * ((x1 * 2.0) * t_2))))))));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x1 * x1) + 1.0
	t_1 = 3.0 * (x2 * -2.0)
	t_2 = 3.0 + ((-1.0 + (((2.0 * x2) - 3.0) / x1)) / x1)
	t_3 = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))))
	t_4 = x1 * (x1 * 3.0)
	t_5 = t_4 + (2.0 * x2)
	t_6 = (t_5 - x1) / t_0
	t_7 = (2.0 * x2) / x1
	t_8 = t_4 * ((x1 - t_5) / t_0)
	t_9 = x1 * (x1 * x1)
	tmp = 0
	if x1 <= -2.2e+140:
		tmp = t_3
	elif x1 <= -0.7:
		tmp = x1 + (t_1 - (((t_8 + (t_0 * ((((x1 * 2.0) * t_6) * (((1.0 + (3.0 / x1)) - t_7) / x1)) + ((x1 * x1) * (6.0 - (4.0 * t_2)))))) - t_9) - x1))
	elif x1 <= 1.26:
		tmp = x1 + ((3.0 * ((x2 * -2.0) - (x1 * ((x1 * ((x2 * -2.0) - 3.0)) - -1.0)))) + (x1 + (x2 * ((x1 * -12.0) + (8.0 * (x1 * x2))))))
	elif x1 <= 5e+152:
		tmp = x1 + (t_1 + (x1 + (t_9 - (t_8 - (t_0 * (((x1 * x1) * ((t_6 * 4.0) - 6.0)) + (((t_7 + (-1.0 - (3.0 / x1))) / x1) * ((x1 * 2.0) * t_2))))))))
	else:
		tmp = t_3
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * x1) + 1.0)
	t_1 = Float64(3.0 * Float64(x2 * -2.0))
	t_2 = Float64(3.0 + Float64(Float64(-1.0 + Float64(Float64(Float64(2.0 * x2) - 3.0) / x1)) / x1))
	t_3 = Float64(x1 + Float64(x1 + Float64(3.0 * Float64(x1 * Float64(Float64(x1 * 3.0) + -1.0)))))
	t_4 = Float64(x1 * Float64(x1 * 3.0))
	t_5 = Float64(t_4 + Float64(2.0 * x2))
	t_6 = Float64(Float64(t_5 - x1) / t_0)
	t_7 = Float64(Float64(2.0 * x2) / x1)
	t_8 = Float64(t_4 * Float64(Float64(x1 - t_5) / t_0))
	t_9 = Float64(x1 * Float64(x1 * x1))
	tmp = 0.0
	if (x1 <= -2.2e+140)
		tmp = t_3;
	elseif (x1 <= -0.7)
		tmp = Float64(x1 + Float64(t_1 - Float64(Float64(Float64(t_8 + Float64(t_0 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_6) * Float64(Float64(Float64(1.0 + Float64(3.0 / x1)) - t_7) / x1)) + Float64(Float64(x1 * x1) * Float64(6.0 - Float64(4.0 * t_2)))))) - t_9) - x1)));
	elseif (x1 <= 1.26)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(x2 * -2.0) - Float64(x1 * Float64(Float64(x1 * Float64(Float64(x2 * -2.0) - 3.0)) - -1.0)))) + Float64(x1 + Float64(x2 * Float64(Float64(x1 * -12.0) + Float64(8.0 * Float64(x1 * x2)))))));
	elseif (x1 <= 5e+152)
		tmp = Float64(x1 + Float64(t_1 + Float64(x1 + Float64(t_9 - Float64(t_8 - Float64(t_0 * Float64(Float64(Float64(x1 * x1) * Float64(Float64(t_6 * 4.0) - 6.0)) + Float64(Float64(Float64(t_7 + Float64(-1.0 - Float64(3.0 / x1))) / x1) * Float64(Float64(x1 * 2.0) * t_2)))))))));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x1 * x1) + 1.0;
	t_1 = 3.0 * (x2 * -2.0);
	t_2 = 3.0 + ((-1.0 + (((2.0 * x2) - 3.0) / x1)) / x1);
	t_3 = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	t_4 = x1 * (x1 * 3.0);
	t_5 = t_4 + (2.0 * x2);
	t_6 = (t_5 - x1) / t_0;
	t_7 = (2.0 * x2) / x1;
	t_8 = t_4 * ((x1 - t_5) / t_0);
	t_9 = x1 * (x1 * x1);
	tmp = 0.0;
	if (x1 <= -2.2e+140)
		tmp = t_3;
	elseif (x1 <= -0.7)
		tmp = x1 + (t_1 - (((t_8 + (t_0 * ((((x1 * 2.0) * t_6) * (((1.0 + (3.0 / x1)) - t_7) / x1)) + ((x1 * x1) * (6.0 - (4.0 * t_2)))))) - t_9) - x1));
	elseif (x1 <= 1.26)
		tmp = x1 + ((3.0 * ((x2 * -2.0) - (x1 * ((x1 * ((x2 * -2.0) - 3.0)) - -1.0)))) + (x1 + (x2 * ((x1 * -12.0) + (8.0 * (x1 * x2))))));
	elseif (x1 <= 5e+152)
		tmp = x1 + (t_1 + (x1 + (t_9 - (t_8 - (t_0 * (((x1 * x1) * ((t_6 * 4.0) - 6.0)) + (((t_7 + (-1.0 - (3.0 / x1))) / x1) * ((x1 * 2.0) * t_2))))))));
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$1 = N[(3.0 * N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(3.0 + N[(N[(-1.0 + N[(N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision] / x1), $MachinePrecision]), $MachinePrecision] / x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x1 + N[(x1 + N[(3.0 * N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(t$95$4 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(t$95$5 - x1), $MachinePrecision] / t$95$0), $MachinePrecision]}, Block[{t$95$7 = N[(N[(2.0 * x2), $MachinePrecision] / x1), $MachinePrecision]}, Block[{t$95$8 = N[(t$95$4 * N[(N[(x1 - t$95$5), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$9 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -2.2e+140], t$95$3, If[LessEqual[x1, -0.7], N[(x1 + N[(t$95$1 - N[(N[(N[(t$95$8 + N[(t$95$0 * N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$6), $MachinePrecision] * N[(N[(N[(1.0 + N[(3.0 / x1), $MachinePrecision]), $MachinePrecision] - t$95$7), $MachinePrecision] / x1), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 - N[(4.0 * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$9), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.26], N[(x1 + N[(N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - N[(x1 * N[(N[(x1 * N[(N[(x2 * -2.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(x2 * N[(N[(x1 * -12.0), $MachinePrecision] + N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 5e+152], N[(x1 + N[(t$95$1 + N[(x1 + N[(t$95$9 - N[(t$95$8 - N[(t$95$0 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$6 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(t$95$7 + N[(-1.0 - N[(3.0 / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x1), $MachinePrecision] * N[(N[(x1 * 2.0), $MachinePrecision] * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -2.1999999999999998e140 or 5e152 < x1

   1. Initial program 0.0%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   2. 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 69.1%

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

   5. Taylor expanded in x2 around 0 100.0%

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

   if -2.1999999999999998e140 < x1 < -0.69999999999999996

   1. Initial program 85.0%

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

   3. Taylor expanded in x1 around 0 85.0%

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

      1. *-commutative 85.0%

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

   5. Simplified 85.0%

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

   6. Taylor expanded in x1 around inf 85.0%

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

      1. associate-*r/ 85.0%

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

      2. associate-*r/ 85.0%

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

      3. metadata-eval 85.0%

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

   8. Simplified 85.0%

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

   9. Taylor expanded in x1 around -inf 85.1%

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

   if -0.69999999999999996 < x1 < 1.26000000000000001

   1. Initial program 99.3%

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

   3. Taylor expanded in x1 around 0 86.0%

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

   4. Taylor expanded in x1 around 0 86.0%

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

   5. Taylor expanded in x2 around 0 97.0%

      \[\leadsto x1 + \left(\left(\color{blue}{x2 \cdot \left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right)} + x1\right) + 3 \cdot \left(-2 \cdot x2 + x1 \cdot \left(x1 \cdot \left(3 - -2 \cdot x2\right) - 1\right)\right)\right) \]

   if 1.26000000000000001 < x1 < 5e152

   1. Initial program 99.5%

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

   3. Taylor expanded in x1 around 0 98.2%

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

      1. *-commutative 98.2%

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

   5. Simplified 98.2%

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

   6. Taylor expanded in x1 around inf 98.2%

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

      1. associate-*r/ 98.2%

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

      2. associate-*r/ 98.2%

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

      3. metadata-eval 98.2%

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

   8. Simplified 98.2%

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

   9. Taylor expanded in x1 around -inf 98.2%

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

4. Final simplification 96.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -2.2 \cdot 10^{+140}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -0.7:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2\right) - \left(\left(\left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1} + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \frac{\left(1 + \frac{3}{x1}\right) - \frac{2 \cdot x2}{x1}}{x1} + \left(x1 \cdot x1\right) \cdot \left(6 - 4 \cdot \left(3 + \frac{-1 + \frac{2 \cdot x2 - 3}{x1}}{x1}\right)\right)\right)\right) - x1 \cdot \left(x1 \cdot x1\right)\right) - x1\right)\right)\\ \mathbf{elif}\;x1 \leq 1.26:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2 - x1 \cdot \left(x1 \cdot \left(x2 \cdot -2 - 3\right) - -1\right)\right) + \left(x1 + x2 \cdot \left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+152}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2\right) + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) - \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1} - \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right) + \frac{\frac{2 \cdot x2}{x1} + \left(-1 - \frac{3}{x1}\right)}{x1} \cdot \left(\left(x1 \cdot 2\right) \cdot \left(3 + \frac{-1 + \frac{2 \cdot x2 - 3}{x1}}{x1}\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 94.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := x1 \cdot \left(x1 \cdot x1\right)\\ t_2 := x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ t_3 := x1 \cdot \left(x1 \cdot 3\right)\\ t_4 := t\_3 + 2 \cdot x2\\ t_5 := \frac{t\_4 - x1}{t\_0}\\ t_6 := \frac{x1 - t\_4}{t\_0}\\ t_7 := t\_3 \cdot t\_6\\ t_8 := \frac{2 \cdot x2}{x1}\\ \mathbf{if}\;x1 \leq -2.2 \cdot 10^{+140}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x1 \leq -0.72:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - \left(\left(\left(t\_7 + t\_0 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t\_5\right) \cdot \frac{\left(1 + \frac{3}{x1}\right) - t\_8}{x1} + \left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot t\_6\right)\right)\right) - t\_1\right) - x1\right)\right)\\ \mathbf{elif}\;x1 \leq 1.26:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2 - x1 \cdot \left(x1 \cdot \left(x2 \cdot -2 - 3\right) - -1\right)\right) + \left(x1 + x2 \cdot \left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+152}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2\right) + \left(x1 + \left(t\_1 - \left(t\_7 - t\_0 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(t\_5 \cdot 4 - 6\right) + \frac{t\_8 + \left(-1 - \frac{3}{x1}\right)}{x1} \cdot \left(\left(x1 \cdot 2\right) \cdot \left(3 + \frac{-1 + \frac{2 \cdot x2 - 3}{x1}}{x1}\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ (* x1 x1) 1.0))
        (t_1 (* x1 (* x1 x1)))
        (t_2 (+ x1 (+ x1 (* 3.0 (* x1 (+ (* x1 3.0) -1.0))))))
        (t_3 (* x1 (* x1 3.0)))
        (t_4 (+ t_3 (* 2.0 x2)))
        (t_5 (/ (- t_4 x1) t_0))
        (t_6 (/ (- x1 t_4) t_0))
        (t_7 (* t_3 t_6))
        (t_8 (/ (* 2.0 x2) x1)))
   (if (<= x1 -2.2e+140)
     t_2
     (if (<= x1 -0.72)
       (+
        x1
        (-
         (* x2 -6.0)
         (-
          (-
           (+
            t_7
            (*
             t_0
             (+
              (* (* (* x1 2.0) t_5) (/ (- (+ 1.0 (/ 3.0 x1)) t_8) x1))
              (* (* x1 x1) (+ 6.0 (* 4.0 t_6))))))
           t_1)
          x1)))
       (if (<= x1 1.26)
         (+
          x1
          (+
           (* 3.0 (- (* x2 -2.0) (* x1 (- (* x1 (- (* x2 -2.0) 3.0)) -1.0))))
           (+ x1 (* x2 (+ (* x1 -12.0) (* 8.0 (* x1 x2)))))))
         (if (<= x1 5e+152)
           (+
            x1
            (+
             (* 3.0 (* x2 -2.0))
             (+
              x1
              (-
               t_1
               (-
                t_7
                (*
                 t_0
                 (+
                  (* (* x1 x1) (- (* t_5 4.0) 6.0))
                  (*
                   (/ (+ t_8 (- -1.0 (/ 3.0 x1))) x1)
                   (*
                    (* x1 2.0)
                    (+ 3.0 (/ (+ -1.0 (/ (- (* 2.0 x2) 3.0) x1)) x1)))))))))))
           t_2))))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = x1 * (x1 * x1);
	double t_2 = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	double t_3 = x1 * (x1 * 3.0);
	double t_4 = t_3 + (2.0 * x2);
	double t_5 = (t_4 - x1) / t_0;
	double t_6 = (x1 - t_4) / t_0;
	double t_7 = t_3 * t_6;
	double t_8 = (2.0 * x2) / x1;
	double tmp;
	if (x1 <= -2.2e+140) {
		tmp = t_2;
	} else if (x1 <= -0.72) {
		tmp = x1 + ((x2 * -6.0) - (((t_7 + (t_0 * ((((x1 * 2.0) * t_5) * (((1.0 + (3.0 / x1)) - t_8) / x1)) + ((x1 * x1) * (6.0 + (4.0 * t_6)))))) - t_1) - x1));
	} else if (x1 <= 1.26) {
		tmp = x1 + ((3.0 * ((x2 * -2.0) - (x1 * ((x1 * ((x2 * -2.0) - 3.0)) - -1.0)))) + (x1 + (x2 * ((x1 * -12.0) + (8.0 * (x1 * x2))))));
	} else if (x1 <= 5e+152) {
		tmp = x1 + ((3.0 * (x2 * -2.0)) + (x1 + (t_1 - (t_7 - (t_0 * (((x1 * x1) * ((t_5 * 4.0) - 6.0)) + (((t_8 + (-1.0 - (3.0 / x1))) / x1) * ((x1 * 2.0) * (3.0 + ((-1.0 + (((2.0 * x2) - 3.0) / x1)) / x1))))))))));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: t_8
    real(8) :: tmp
    t_0 = (x1 * x1) + 1.0d0
    t_1 = x1 * (x1 * x1)
    t_2 = x1 + (x1 + (3.0d0 * (x1 * ((x1 * 3.0d0) + (-1.0d0)))))
    t_3 = x1 * (x1 * 3.0d0)
    t_4 = t_3 + (2.0d0 * x2)
    t_5 = (t_4 - x1) / t_0
    t_6 = (x1 - t_4) / t_0
    t_7 = t_3 * t_6
    t_8 = (2.0d0 * x2) / x1
    if (x1 <= (-2.2d+140)) then
        tmp = t_2
    else if (x1 <= (-0.72d0)) then
        tmp = x1 + ((x2 * (-6.0d0)) - (((t_7 + (t_0 * ((((x1 * 2.0d0) * t_5) * (((1.0d0 + (3.0d0 / x1)) - t_8) / x1)) + ((x1 * x1) * (6.0d0 + (4.0d0 * t_6)))))) - t_1) - x1))
    else if (x1 <= 1.26d0) then
        tmp = x1 + ((3.0d0 * ((x2 * (-2.0d0)) - (x1 * ((x1 * ((x2 * (-2.0d0)) - 3.0d0)) - (-1.0d0))))) + (x1 + (x2 * ((x1 * (-12.0d0)) + (8.0d0 * (x1 * x2))))))
    else if (x1 <= 5d+152) then
        tmp = x1 + ((3.0d0 * (x2 * (-2.0d0))) + (x1 + (t_1 - (t_7 - (t_0 * (((x1 * x1) * ((t_5 * 4.0d0) - 6.0d0)) + (((t_8 + ((-1.0d0) - (3.0d0 / x1))) / x1) * ((x1 * 2.0d0) * (3.0d0 + (((-1.0d0) + (((2.0d0 * x2) - 3.0d0) / x1)) / x1))))))))))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = x1 * (x1 * x1);
	double t_2 = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	double t_3 = x1 * (x1 * 3.0);
	double t_4 = t_3 + (2.0 * x2);
	double t_5 = (t_4 - x1) / t_0;
	double t_6 = (x1 - t_4) / t_0;
	double t_7 = t_3 * t_6;
	double t_8 = (2.0 * x2) / x1;
	double tmp;
	if (x1 <= -2.2e+140) {
		tmp = t_2;
	} else if (x1 <= -0.72) {
		tmp = x1 + ((x2 * -6.0) - (((t_7 + (t_0 * ((((x1 * 2.0) * t_5) * (((1.0 + (3.0 / x1)) - t_8) / x1)) + ((x1 * x1) * (6.0 + (4.0 * t_6)))))) - t_1) - x1));
	} else if (x1 <= 1.26) {
		tmp = x1 + ((3.0 * ((x2 * -2.0) - (x1 * ((x1 * ((x2 * -2.0) - 3.0)) - -1.0)))) + (x1 + (x2 * ((x1 * -12.0) + (8.0 * (x1 * x2))))));
	} else if (x1 <= 5e+152) {
		tmp = x1 + ((3.0 * (x2 * -2.0)) + (x1 + (t_1 - (t_7 - (t_0 * (((x1 * x1) * ((t_5 * 4.0) - 6.0)) + (((t_8 + (-1.0 - (3.0 / x1))) / x1) * ((x1 * 2.0) * (3.0 + ((-1.0 + (((2.0 * x2) - 3.0) / x1)) / x1))))))))));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x1 * x1) + 1.0
	t_1 = x1 * (x1 * x1)
	t_2 = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))))
	t_3 = x1 * (x1 * 3.0)
	t_4 = t_3 + (2.0 * x2)
	t_5 = (t_4 - x1) / t_0
	t_6 = (x1 - t_4) / t_0
	t_7 = t_3 * t_6
	t_8 = (2.0 * x2) / x1
	tmp = 0
	if x1 <= -2.2e+140:
		tmp = t_2
	elif x1 <= -0.72:
		tmp = x1 + ((x2 * -6.0) - (((t_7 + (t_0 * ((((x1 * 2.0) * t_5) * (((1.0 + (3.0 / x1)) - t_8) / x1)) + ((x1 * x1) * (6.0 + (4.0 * t_6)))))) - t_1) - x1))
	elif x1 <= 1.26:
		tmp = x1 + ((3.0 * ((x2 * -2.0) - (x1 * ((x1 * ((x2 * -2.0) - 3.0)) - -1.0)))) + (x1 + (x2 * ((x1 * -12.0) + (8.0 * (x1 * x2))))))
	elif x1 <= 5e+152:
		tmp = x1 + ((3.0 * (x2 * -2.0)) + (x1 + (t_1 - (t_7 - (t_0 * (((x1 * x1) * ((t_5 * 4.0) - 6.0)) + (((t_8 + (-1.0 - (3.0 / x1))) / x1) * ((x1 * 2.0) * (3.0 + ((-1.0 + (((2.0 * x2) - 3.0) / x1)) / x1))))))))))
	else:
		tmp = t_2
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * x1) + 1.0)
	t_1 = Float64(x1 * Float64(x1 * x1))
	t_2 = Float64(x1 + Float64(x1 + Float64(3.0 * Float64(x1 * Float64(Float64(x1 * 3.0) + -1.0)))))
	t_3 = Float64(x1 * Float64(x1 * 3.0))
	t_4 = Float64(t_3 + Float64(2.0 * x2))
	t_5 = Float64(Float64(t_4 - x1) / t_0)
	t_6 = Float64(Float64(x1 - t_4) / t_0)
	t_7 = Float64(t_3 * t_6)
	t_8 = Float64(Float64(2.0 * x2) / x1)
	tmp = 0.0
	if (x1 <= -2.2e+140)
		tmp = t_2;
	elseif (x1 <= -0.72)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) - Float64(Float64(Float64(t_7 + Float64(t_0 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_5) * Float64(Float64(Float64(1.0 + Float64(3.0 / x1)) - t_8) / x1)) + Float64(Float64(x1 * x1) * Float64(6.0 + Float64(4.0 * t_6)))))) - t_1) - x1)));
	elseif (x1 <= 1.26)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(x2 * -2.0) - Float64(x1 * Float64(Float64(x1 * Float64(Float64(x2 * -2.0) - 3.0)) - -1.0)))) + Float64(x1 + Float64(x2 * Float64(Float64(x1 * -12.0) + Float64(8.0 * Float64(x1 * x2)))))));
	elseif (x1 <= 5e+152)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(x2 * -2.0)) + Float64(x1 + Float64(t_1 - Float64(t_7 - Float64(t_0 * Float64(Float64(Float64(x1 * x1) * Float64(Float64(t_5 * 4.0) - 6.0)) + Float64(Float64(Float64(t_8 + Float64(-1.0 - Float64(3.0 / x1))) / x1) * Float64(Float64(x1 * 2.0) * Float64(3.0 + Float64(Float64(-1.0 + Float64(Float64(Float64(2.0 * x2) - 3.0) / x1)) / x1)))))))))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x1 * x1) + 1.0;
	t_1 = x1 * (x1 * x1);
	t_2 = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	t_3 = x1 * (x1 * 3.0);
	t_4 = t_3 + (2.0 * x2);
	t_5 = (t_4 - x1) / t_0;
	t_6 = (x1 - t_4) / t_0;
	t_7 = t_3 * t_6;
	t_8 = (2.0 * x2) / x1;
	tmp = 0.0;
	if (x1 <= -2.2e+140)
		tmp = t_2;
	elseif (x1 <= -0.72)
		tmp = x1 + ((x2 * -6.0) - (((t_7 + (t_0 * ((((x1 * 2.0) * t_5) * (((1.0 + (3.0 / x1)) - t_8) / x1)) + ((x1 * x1) * (6.0 + (4.0 * t_6)))))) - t_1) - x1));
	elseif (x1 <= 1.26)
		tmp = x1 + ((3.0 * ((x2 * -2.0) - (x1 * ((x1 * ((x2 * -2.0) - 3.0)) - -1.0)))) + (x1 + (x2 * ((x1 * -12.0) + (8.0 * (x1 * x2))))));
	elseif (x1 <= 5e+152)
		tmp = x1 + ((3.0 * (x2 * -2.0)) + (x1 + (t_1 - (t_7 - (t_0 * (((x1 * x1) * ((t_5 * 4.0) - 6.0)) + (((t_8 + (-1.0 - (3.0 / x1))) / x1) * ((x1 * 2.0) * (3.0 + ((-1.0 + (((2.0 * x2) - 3.0) / x1)) / x1))))))))));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x1 + N[(x1 + N[(3.0 * N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$3 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(t$95$4 - x1), $MachinePrecision] / t$95$0), $MachinePrecision]}, Block[{t$95$6 = N[(N[(x1 - t$95$4), $MachinePrecision] / t$95$0), $MachinePrecision]}, Block[{t$95$7 = N[(t$95$3 * t$95$6), $MachinePrecision]}, Block[{t$95$8 = N[(N[(2.0 * x2), $MachinePrecision] / x1), $MachinePrecision]}, If[LessEqual[x1, -2.2e+140], t$95$2, If[LessEqual[x1, -0.72], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] - N[(N[(N[(t$95$7 + N[(t$95$0 * N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$5), $MachinePrecision] * N[(N[(N[(1.0 + N[(3.0 / x1), $MachinePrecision]), $MachinePrecision] - t$95$8), $MachinePrecision] / x1), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 + N[(4.0 * t$95$6), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.26], N[(x1 + N[(N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - N[(x1 * N[(N[(x1 * N[(N[(x2 * -2.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(x2 * N[(N[(x1 * -12.0), $MachinePrecision] + N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 5e+152], N[(x1 + N[(N[(3.0 * N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(t$95$1 - N[(t$95$7 - N[(t$95$0 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$5 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(t$95$8 + N[(-1.0 - N[(3.0 / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x1), $MachinePrecision] * N[(N[(x1 * 2.0), $MachinePrecision] * N[(3.0 + N[(N[(-1.0 + N[(N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision] / x1), $MachinePrecision]), $MachinePrecision] / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -2.1999999999999998e140 or 5e152 < x1

   1. Initial program 0.0%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   2. 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 69.1%

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

   5. Taylor expanded in x2 around 0 100.0%

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

   if -2.1999999999999998e140 < x1 < -0.71999999999999997

   1. Initial program 85.0%

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

   3. Taylor expanded in x1 around 0 85.0%

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

      1. *-commutative 85.0%

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

   5. Simplified 85.0%

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

   6. Taylor expanded in x1 around inf 85.0%

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

      1. associate-*r/ 85.0%

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

      2. associate-*r/ 85.0%

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

      3. metadata-eval 85.0%

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

   8. Simplified 85.0%

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

   9. Taylor expanded in x2 around 0 85.0%

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

       1. *-commutative 85.0%

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

   11. Simplified 85.0%

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

   if -0.71999999999999997 < x1 < 1.26000000000000001

   1. Initial program 99.3%

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

   3. Taylor expanded in x1 around 0 86.0%

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

   4. Taylor expanded in x1 around 0 86.0%

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

   5. Taylor expanded in x2 around 0 97.0%

      \[\leadsto x1 + \left(\left(\color{blue}{x2 \cdot \left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right)} + x1\right) + 3 \cdot \left(-2 \cdot x2 + x1 \cdot \left(x1 \cdot \left(3 - -2 \cdot x2\right) - 1\right)\right)\right) \]

   if 1.26000000000000001 < x1 < 5e152

   1. Initial program 99.5%

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

   3. Taylor expanded in x1 around 0 98.2%

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

      1. *-commutative 98.2%

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

   5. Simplified 98.2%

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

   6. Taylor expanded in x1 around inf 98.2%

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

      1. associate-*r/ 98.2%

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

      2. associate-*r/ 98.2%

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

      3. metadata-eval 98.2%

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

   8. Simplified 98.2%

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

   9. Taylor expanded in x1 around -inf 98.2%

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

4. Final simplification 96.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -2.2 \cdot 10^{+140}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -0.72:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - \left(\left(\left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1} + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \frac{\left(1 + \frac{3}{x1}\right) - \frac{2 \cdot x2}{x1}}{x1} + \left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right)\right)\right) - x1 \cdot \left(x1 \cdot x1\right)\right) - x1\right)\right)\\ \mathbf{elif}\;x1 \leq 1.26:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2 - x1 \cdot \left(x1 \cdot \left(x2 \cdot -2 - 3\right) - -1\right)\right) + \left(x1 + x2 \cdot \left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+152}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2\right) + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) - \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1} - \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right) + \frac{\frac{2 \cdot x2}{x1} + \left(-1 - \frac{3}{x1}\right)}{x1} \cdot \left(\left(x1 \cdot 2\right) \cdot \left(3 + \frac{-1 + \frac{2 \cdot x2 - 3}{x1}}{x1}\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 92.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := t\_0 + 2 \cdot x2\\ t_2 := x1 \cdot x1 + 1\\ t_3 := \frac{x1 - t\_1}{t\_2}\\ t_4 := x1 + \left(3 \cdot \left(x2 \cdot -2\right) + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(t\_0 \cdot \left(2 \cdot x2\right) - t\_2 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot t\_3\right) + \left(\left(x1 \cdot 2\right) \cdot \frac{t\_1 - x1}{t\_2}\right) \cdot \left(3 + t\_3\right)\right)\right)\right)\right)\right)\\ \mathbf{if}\;x1 \leq -2.2 \cdot 10^{+140}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -0.021:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;x1 \leq 0.0185:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2 - x1 \cdot \left(x1 \cdot \left(x2 \cdot -2 - 3\right) - -1\right)\right) + \left(x1 + x2 \cdot \left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 8 \cdot 10^{+144}:\\ \;\;\;\;t\_4\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot 9\right) - 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (+ t_0 (* 2.0 x2)))
        (t_2 (+ (* x1 x1) 1.0))
        (t_3 (/ (- x1 t_1) t_2))
        (t_4
         (+
          x1
          (+
           (* 3.0 (* x2 -2.0))
           (+
            x1
            (+
             (* x1 (* x1 x1))
             (-
              (* t_0 (* 2.0 x2))
              (*
               t_2
               (+
                (* (* x1 x1) (+ 6.0 (* 4.0 t_3)))
                (* (* (* x1 2.0) (/ (- t_1 x1) t_2)) (+ 3.0 t_3)))))))))))
   (if (<= x1 -2.2e+140)
     (+ x1 (+ x1 (* 3.0 (* x1 (+ (* x1 3.0) -1.0)))))
     (if (<= x1 -0.021)
       t_4
       (if (<= x1 0.0185)
         (+
          x1
          (+
           (* 3.0 (- (* x2 -2.0) (* x1 (- (* x1 (- (* x2 -2.0) 3.0)) -1.0))))
           (+ x1 (* x2 (+ (* x1 -12.0) (* 8.0 (* x1 x2)))))))
         (if (<= x1 8e+144)
           t_4
           (+
            x1
            (*
             x1
             (- (+ (* 4.0 (* x2 (- (* 2.0 x2) 3.0))) (* x1 9.0)) 2.0)))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = t_0 + (2.0 * x2);
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = (x1 - t_1) / t_2;
	double t_4 = x1 + ((3.0 * (x2 * -2.0)) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * (2.0 * x2)) - (t_2 * (((x1 * x1) * (6.0 + (4.0 * t_3))) + (((x1 * 2.0) * ((t_1 - x1) / t_2)) * (3.0 + t_3))))))));
	double tmp;
	if (x1 <= -2.2e+140) {
		tmp = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	} else if (x1 <= -0.021) {
		tmp = t_4;
	} else if (x1 <= 0.0185) {
		tmp = x1 + ((3.0 * ((x2 * -2.0) - (x1 * ((x1 * ((x2 * -2.0) - 3.0)) - -1.0)))) + (x1 + (x2 * ((x1 * -12.0) + (8.0 * (x1 * x2))))));
	} else if (x1 <= 8e+144) {
		tmp = t_4;
	} else {
		tmp = x1 + (x1 * (((4.0 * (x2 * ((2.0 * x2) - 3.0))) + (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) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_0 = x1 * (x1 * 3.0d0)
    t_1 = t_0 + (2.0d0 * x2)
    t_2 = (x1 * x1) + 1.0d0
    t_3 = (x1 - t_1) / t_2
    t_4 = x1 + ((3.0d0 * (x2 * (-2.0d0))) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * (2.0d0 * x2)) - (t_2 * (((x1 * x1) * (6.0d0 + (4.0d0 * t_3))) + (((x1 * 2.0d0) * ((t_1 - x1) / t_2)) * (3.0d0 + t_3))))))))
    if (x1 <= (-2.2d+140)) then
        tmp = x1 + (x1 + (3.0d0 * (x1 * ((x1 * 3.0d0) + (-1.0d0)))))
    else if (x1 <= (-0.021d0)) then
        tmp = t_4
    else if (x1 <= 0.0185d0) then
        tmp = x1 + ((3.0d0 * ((x2 * (-2.0d0)) - (x1 * ((x1 * ((x2 * (-2.0d0)) - 3.0d0)) - (-1.0d0))))) + (x1 + (x2 * ((x1 * (-12.0d0)) + (8.0d0 * (x1 * x2))))))
    else if (x1 <= 8d+144) then
        tmp = t_4
    else
        tmp = x1 + (x1 * (((4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0))) + (x1 * 9.0d0)) - 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 = t_0 + (2.0 * x2);
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = (x1 - t_1) / t_2;
	double t_4 = x1 + ((3.0 * (x2 * -2.0)) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * (2.0 * x2)) - (t_2 * (((x1 * x1) * (6.0 + (4.0 * t_3))) + (((x1 * 2.0) * ((t_1 - x1) / t_2)) * (3.0 + t_3))))))));
	double tmp;
	if (x1 <= -2.2e+140) {
		tmp = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	} else if (x1 <= -0.021) {
		tmp = t_4;
	} else if (x1 <= 0.0185) {
		tmp = x1 + ((3.0 * ((x2 * -2.0) - (x1 * ((x1 * ((x2 * -2.0) - 3.0)) - -1.0)))) + (x1 + (x2 * ((x1 * -12.0) + (8.0 * (x1 * x2))))));
	} else if (x1 <= 8e+144) {
		tmp = t_4;
	} else {
		tmp = x1 + (x1 * (((4.0 * (x2 * ((2.0 * x2) - 3.0))) + (x1 * 9.0)) - 2.0));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = t_0 + (2.0 * x2)
	t_2 = (x1 * x1) + 1.0
	t_3 = (x1 - t_1) / t_2
	t_4 = x1 + ((3.0 * (x2 * -2.0)) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * (2.0 * x2)) - (t_2 * (((x1 * x1) * (6.0 + (4.0 * t_3))) + (((x1 * 2.0) * ((t_1 - x1) / t_2)) * (3.0 + t_3))))))))
	tmp = 0
	if x1 <= -2.2e+140:
		tmp = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))))
	elif x1 <= -0.021:
		tmp = t_4
	elif x1 <= 0.0185:
		tmp = x1 + ((3.0 * ((x2 * -2.0) - (x1 * ((x1 * ((x2 * -2.0) - 3.0)) - -1.0)))) + (x1 + (x2 * ((x1 * -12.0) + (8.0 * (x1 * x2))))))
	elif x1 <= 8e+144:
		tmp = t_4
	else:
		tmp = x1 + (x1 * (((4.0 * (x2 * ((2.0 * x2) - 3.0))) + (x1 * 9.0)) - 2.0))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(t_0 + Float64(2.0 * x2))
	t_2 = Float64(Float64(x1 * x1) + 1.0)
	t_3 = Float64(Float64(x1 - t_1) / t_2)
	t_4 = Float64(x1 + Float64(Float64(3.0 * Float64(x2 * -2.0)) + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(t_0 * Float64(2.0 * x2)) - Float64(t_2 * Float64(Float64(Float64(x1 * x1) * Float64(6.0 + Float64(4.0 * t_3))) + Float64(Float64(Float64(x1 * 2.0) * Float64(Float64(t_1 - x1) / t_2)) * Float64(3.0 + t_3)))))))))
	tmp = 0.0
	if (x1 <= -2.2e+140)
		tmp = Float64(x1 + Float64(x1 + Float64(3.0 * Float64(x1 * Float64(Float64(x1 * 3.0) + -1.0)))));
	elseif (x1 <= -0.021)
		tmp = t_4;
	elseif (x1 <= 0.0185)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(x2 * -2.0) - Float64(x1 * Float64(Float64(x1 * Float64(Float64(x2 * -2.0) - 3.0)) - -1.0)))) + Float64(x1 + Float64(x2 * Float64(Float64(x1 * -12.0) + Float64(8.0 * Float64(x1 * x2)))))));
	elseif (x1 <= 8e+144)
		tmp = t_4;
	else
		tmp = Float64(x1 + Float64(x1 * Float64(Float64(Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0))) + Float64(x1 * 9.0)) - 2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * 3.0);
	t_1 = t_0 + (2.0 * x2);
	t_2 = (x1 * x1) + 1.0;
	t_3 = (x1 - t_1) / t_2;
	t_4 = x1 + ((3.0 * (x2 * -2.0)) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * (2.0 * x2)) - (t_2 * (((x1 * x1) * (6.0 + (4.0 * t_3))) + (((x1 * 2.0) * ((t_1 - x1) / t_2)) * (3.0 + t_3))))))));
	tmp = 0.0;
	if (x1 <= -2.2e+140)
		tmp = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	elseif (x1 <= -0.021)
		tmp = t_4;
	elseif (x1 <= 0.0185)
		tmp = x1 + ((3.0 * ((x2 * -2.0) - (x1 * ((x1 * ((x2 * -2.0) - 3.0)) - -1.0)))) + (x1 + (x2 * ((x1 * -12.0) + (8.0 * (x1 * x2))))));
	elseif (x1 <= 8e+144)
		tmp = t_4;
	else
		tmp = x1 + (x1 * (((4.0 * (x2 * ((2.0 * x2) - 3.0))) + (x1 * 9.0)) - 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[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x1 - t$95$1), $MachinePrecision] / t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(x1 + N[(N[(3.0 * N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$0 * N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - N[(t$95$2 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 + N[(4.0 * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(x1 * 2.0), $MachinePrecision] * N[(N[(t$95$1 - x1), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision] * N[(3.0 + t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -2.2e+140], N[(x1 + N[(x1 + N[(3.0 * N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -0.021], t$95$4, If[LessEqual[x1, 0.0185], N[(x1 + N[(N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - N[(x1 * N[(N[(x1 * N[(N[(x2 * -2.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(x2 * N[(N[(x1 * -12.0), $MachinePrecision] + N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 8e+144], t$95$4, N[(x1 + N[(x1 * N[(N[(N[(4.0 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -2.1999999999999998e140

   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 64.1%

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

   5. Taylor expanded in x2 around 0 100.0%

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

   if -2.1999999999999998e140 < x1 < -0.0210000000000000013 or 0.0184999999999999991 < x1 < 8.00000000000000019e144

   1. Initial program 92.3%

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

   3. Taylor expanded in x1 around 0 91.7%

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

      1. *-commutative 91.7%

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

   5. Simplified 91.7%

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

   6. Taylor expanded in x1 around 0 81.7%

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

   if -0.0210000000000000013 < x1 < 0.0184999999999999991

   1. Initial program 99.3%

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

   3. Taylor expanded in x1 around 0 87.5%

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

   4. Taylor expanded in x1 around 0 87.6%

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

   5. Taylor expanded in x2 around 0 98.8%

      \[\leadsto x1 + \left(\left(\color{blue}{x2 \cdot \left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right)} + x1\right) + 3 \cdot \left(-2 \cdot x2 + x1 \cdot \left(x1 \cdot \left(3 - -2 \cdot x2\right) - 1\right)\right)\right) \]

   if 8.00000000000000019e144 < x1

   1. Initial program 3.3%

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

   3. Taylor expanded in x1 around 0 3.3%

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

   4. Taylor expanded in x1 around 0 73.3%

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

   5. Taylor expanded in x2 around 0 100.0%

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

   6. Taylor expanded in x1 around 0 100.0%

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

4. Final simplification 94.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -2.2 \cdot 10^{+140}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -0.021:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2\right) + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(2 \cdot x2\right) - \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right) + \left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(3 + \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 0.0185:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2 - x1 \cdot \left(x1 \cdot \left(x2 \cdot -2 - 3\right) - -1\right)\right) + \left(x1 + x2 \cdot \left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 8 \cdot 10^{+144}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2\right) + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(2 \cdot x2\right) - \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right) + \left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(3 + \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot 9\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 90.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot x1\right)\\ t_1 := 3 \cdot \left(x2 \cdot -2\right)\\ t_2 := x1 \cdot x1 + 1\\ t_3 := x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ t_4 := -1 - x1 \cdot x1\\ t_5 := x1 \cdot \left(x1 \cdot 3\right)\\ t_6 := t\_5 + 2 \cdot x2\\ t_7 := \frac{x1 - t\_6}{t\_2}\\ t_8 := \left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot t\_7\right)\\ \mathbf{if}\;x1 \leq -2.2 \cdot 10^{+140}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x1 \leq -3.2 \cdot 10^{+21}:\\ \;\;\;\;x1 + \left(t\_1 + \left(x1 + \left(t\_0 + \left(t\_5 \cdot \frac{t\_6 - x1}{t\_2} + t\_4 \cdot \left(t\_8 - -6\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 3 \cdot 10^{+33}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{x1 - \left(t\_5 - 2 \cdot x2\right)}{t\_4} + \left(x1 + x2 \cdot \left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(t\_1 + \left(x1 + \left(t\_0 - \left(t\_5 \cdot t\_7 - t\_2 \cdot \left(\left(x1 \cdot \left(x1 \cdot 2\right)\right) \cdot \left(3 + t\_7\right) - t\_8\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 x1)))
        (t_1 (* 3.0 (* x2 -2.0)))
        (t_2 (+ (* x1 x1) 1.0))
        (t_3 (+ x1 (+ x1 (* 3.0 (* x1 (+ (* x1 3.0) -1.0))))))
        (t_4 (- -1.0 (* x1 x1)))
        (t_5 (* x1 (* x1 3.0)))
        (t_6 (+ t_5 (* 2.0 x2)))
        (t_7 (/ (- x1 t_6) t_2))
        (t_8 (* (* x1 x1) (+ 6.0 (* 4.0 t_7)))))
   (if (<= x1 -2.2e+140)
     t_3
     (if (<= x1 -3.2e+21)
       (+
        x1
        (+
         t_1
         (+ x1 (+ t_0 (+ (* t_5 (/ (- t_6 x1) t_2)) (* t_4 (- t_8 -6.0)))))))
       (if (<= x1 3e+33)
         (+
          x1
          (+
           (* 3.0 (/ (- x1 (- t_5 (* 2.0 x2))) t_4))
           (+ x1 (* x2 (+ (* x1 -12.0) (* 8.0 (* x1 x2)))))))
         (if (<= x1 5e+153)
           (+
            x1
            (+
             t_1
             (+
              x1
              (-
               t_0
               (-
                (* t_5 t_7)
                (* t_2 (- (* (* x1 (* x1 2.0)) (+ 3.0 t_7)) t_8)))))))
           t_3))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * x1);
	double t_1 = 3.0 * (x2 * -2.0);
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	double t_4 = -1.0 - (x1 * x1);
	double t_5 = x1 * (x1 * 3.0);
	double t_6 = t_5 + (2.0 * x2);
	double t_7 = (x1 - t_6) / t_2;
	double t_8 = (x1 * x1) * (6.0 + (4.0 * t_7));
	double tmp;
	if (x1 <= -2.2e+140) {
		tmp = t_3;
	} else if (x1 <= -3.2e+21) {
		tmp = x1 + (t_1 + (x1 + (t_0 + ((t_5 * ((t_6 - x1) / t_2)) + (t_4 * (t_8 - -6.0))))));
	} else if (x1 <= 3e+33) {
		tmp = x1 + ((3.0 * ((x1 - (t_5 - (2.0 * x2))) / t_4)) + (x1 + (x2 * ((x1 * -12.0) + (8.0 * (x1 * x2))))));
	} else if (x1 <= 5e+153) {
		tmp = x1 + (t_1 + (x1 + (t_0 - ((t_5 * t_7) - (t_2 * (((x1 * (x1 * 2.0)) * (3.0 + t_7)) - t_8))))));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: t_8
    real(8) :: tmp
    t_0 = x1 * (x1 * x1)
    t_1 = 3.0d0 * (x2 * (-2.0d0))
    t_2 = (x1 * x1) + 1.0d0
    t_3 = x1 + (x1 + (3.0d0 * (x1 * ((x1 * 3.0d0) + (-1.0d0)))))
    t_4 = (-1.0d0) - (x1 * x1)
    t_5 = x1 * (x1 * 3.0d0)
    t_6 = t_5 + (2.0d0 * x2)
    t_7 = (x1 - t_6) / t_2
    t_8 = (x1 * x1) * (6.0d0 + (4.0d0 * t_7))
    if (x1 <= (-2.2d+140)) then
        tmp = t_3
    else if (x1 <= (-3.2d+21)) then
        tmp = x1 + (t_1 + (x1 + (t_0 + ((t_5 * ((t_6 - x1) / t_2)) + (t_4 * (t_8 - (-6.0d0)))))))
    else if (x1 <= 3d+33) then
        tmp = x1 + ((3.0d0 * ((x1 - (t_5 - (2.0d0 * x2))) / t_4)) + (x1 + (x2 * ((x1 * (-12.0d0)) + (8.0d0 * (x1 * x2))))))
    else if (x1 <= 5d+153) then
        tmp = x1 + (t_1 + (x1 + (t_0 - ((t_5 * t_7) - (t_2 * (((x1 * (x1 * 2.0d0)) * (3.0d0 + t_7)) - t_8))))))
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * x1);
	double t_1 = 3.0 * (x2 * -2.0);
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	double t_4 = -1.0 - (x1 * x1);
	double t_5 = x1 * (x1 * 3.0);
	double t_6 = t_5 + (2.0 * x2);
	double t_7 = (x1 - t_6) / t_2;
	double t_8 = (x1 * x1) * (6.0 + (4.0 * t_7));
	double tmp;
	if (x1 <= -2.2e+140) {
		tmp = t_3;
	} else if (x1 <= -3.2e+21) {
		tmp = x1 + (t_1 + (x1 + (t_0 + ((t_5 * ((t_6 - x1) / t_2)) + (t_4 * (t_8 - -6.0))))));
	} else if (x1 <= 3e+33) {
		tmp = x1 + ((3.0 * ((x1 - (t_5 - (2.0 * x2))) / t_4)) + (x1 + (x2 * ((x1 * -12.0) + (8.0 * (x1 * x2))))));
	} else if (x1 <= 5e+153) {
		tmp = x1 + (t_1 + (x1 + (t_0 - ((t_5 * t_7) - (t_2 * (((x1 * (x1 * 2.0)) * (3.0 + t_7)) - t_8))))));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * x1)
	t_1 = 3.0 * (x2 * -2.0)
	t_2 = (x1 * x1) + 1.0
	t_3 = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))))
	t_4 = -1.0 - (x1 * x1)
	t_5 = x1 * (x1 * 3.0)
	t_6 = t_5 + (2.0 * x2)
	t_7 = (x1 - t_6) / t_2
	t_8 = (x1 * x1) * (6.0 + (4.0 * t_7))
	tmp = 0
	if x1 <= -2.2e+140:
		tmp = t_3
	elif x1 <= -3.2e+21:
		tmp = x1 + (t_1 + (x1 + (t_0 + ((t_5 * ((t_6 - x1) / t_2)) + (t_4 * (t_8 - -6.0))))))
	elif x1 <= 3e+33:
		tmp = x1 + ((3.0 * ((x1 - (t_5 - (2.0 * x2))) / t_4)) + (x1 + (x2 * ((x1 * -12.0) + (8.0 * (x1 * x2))))))
	elif x1 <= 5e+153:
		tmp = x1 + (t_1 + (x1 + (t_0 - ((t_5 * t_7) - (t_2 * (((x1 * (x1 * 2.0)) * (3.0 + t_7)) - t_8))))))
	else:
		tmp = t_3
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * x1))
	t_1 = Float64(3.0 * Float64(x2 * -2.0))
	t_2 = Float64(Float64(x1 * x1) + 1.0)
	t_3 = Float64(x1 + Float64(x1 + Float64(3.0 * Float64(x1 * Float64(Float64(x1 * 3.0) + -1.0)))))
	t_4 = Float64(-1.0 - Float64(x1 * x1))
	t_5 = Float64(x1 * Float64(x1 * 3.0))
	t_6 = Float64(t_5 + Float64(2.0 * x2))
	t_7 = Float64(Float64(x1 - t_6) / t_2)
	t_8 = Float64(Float64(x1 * x1) * Float64(6.0 + Float64(4.0 * t_7)))
	tmp = 0.0
	if (x1 <= -2.2e+140)
		tmp = t_3;
	elseif (x1 <= -3.2e+21)
		tmp = Float64(x1 + Float64(t_1 + Float64(x1 + Float64(t_0 + Float64(Float64(t_5 * Float64(Float64(t_6 - x1) / t_2)) + Float64(t_4 * Float64(t_8 - -6.0)))))));
	elseif (x1 <= 3e+33)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(x1 - Float64(t_5 - Float64(2.0 * x2))) / t_4)) + Float64(x1 + Float64(x2 * Float64(Float64(x1 * -12.0) + Float64(8.0 * Float64(x1 * x2)))))));
	elseif (x1 <= 5e+153)
		tmp = Float64(x1 + Float64(t_1 + Float64(x1 + Float64(t_0 - Float64(Float64(t_5 * t_7) - Float64(t_2 * Float64(Float64(Float64(x1 * Float64(x1 * 2.0)) * Float64(3.0 + t_7)) - t_8)))))));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * x1);
	t_1 = 3.0 * (x2 * -2.0);
	t_2 = (x1 * x1) + 1.0;
	t_3 = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	t_4 = -1.0 - (x1 * x1);
	t_5 = x1 * (x1 * 3.0);
	t_6 = t_5 + (2.0 * x2);
	t_7 = (x1 - t_6) / t_2;
	t_8 = (x1 * x1) * (6.0 + (4.0 * t_7));
	tmp = 0.0;
	if (x1 <= -2.2e+140)
		tmp = t_3;
	elseif (x1 <= -3.2e+21)
		tmp = x1 + (t_1 + (x1 + (t_0 + ((t_5 * ((t_6 - x1) / t_2)) + (t_4 * (t_8 - -6.0))))));
	elseif (x1 <= 3e+33)
		tmp = x1 + ((3.0 * ((x1 - (t_5 - (2.0 * x2))) / t_4)) + (x1 + (x2 * ((x1 * -12.0) + (8.0 * (x1 * x2))))));
	elseif (x1 <= 5e+153)
		tmp = x1 + (t_1 + (x1 + (t_0 - ((t_5 * t_7) - (t_2 * (((x1 * (x1 * 2.0)) * (3.0 + t_7)) - t_8))))));
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(3.0 * N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$3 = N[(x1 + N[(x1 + N[(3.0 * N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(t$95$5 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(N[(x1 - t$95$6), $MachinePrecision] / t$95$2), $MachinePrecision]}, Block[{t$95$8 = N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 + N[(4.0 * t$95$7), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -2.2e+140], t$95$3, If[LessEqual[x1, -3.2e+21], N[(x1 + N[(t$95$1 + N[(x1 + N[(t$95$0 + N[(N[(t$95$5 * N[(N[(t$95$6 - x1), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision] + N[(t$95$4 * N[(t$95$8 - -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 3e+33], N[(x1 + N[(N[(3.0 * N[(N[(x1 - N[(t$95$5 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$4), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(x2 * N[(N[(x1 * -12.0), $MachinePrecision] + N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 5e+153], N[(x1 + N[(t$95$1 + N[(x1 + N[(t$95$0 - N[(N[(t$95$5 * t$95$7), $MachinePrecision] - N[(t$95$2 * N[(N[(N[(x1 * N[(x1 * 2.0), $MachinePrecision]), $MachinePrecision] * N[(3.0 + t$95$7), $MachinePrecision]), $MachinePrecision] - t$95$8), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -2.1999999999999998e140 or 5.00000000000000018e153 < x1

   1. Initial program 0.0%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   2. 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 69.1%

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

   5. Taylor expanded in x2 around 0 100.0%

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

   if -2.1999999999999998e140 < x1 < -3.2e21

   1. Initial program 82.5%

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

   3. Taylor expanded in x1 around 0 82.5%

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

      1. *-commutative 82.5%

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

   5. Simplified 82.5%

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

   6. Taylor expanded in x1 around inf 82.5%

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

      1. associate-*r/ 82.5%

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

      2. associate-*r/ 82.5%

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

      3. metadata-eval 82.5%

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

   8. Simplified 82.5%

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

   9. Taylor expanded in x1 around inf 76.2%

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

   if -3.2e21 < x1 < 2.99999999999999984e33

   1. Initial program 99.3%

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

   3. Taylor expanded in x1 around 0 83.7%

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

   4. Taylor expanded in x2 around 0 93.7%

      \[\leadsto x1 + \left(\left(\color{blue}{x2 \cdot \left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   if 2.99999999999999984e33 < x1 < 5.00000000000000018e153

   1. Initial program 99.6%

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

   3. Taylor expanded in x1 around 0 99.6%

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

      1. *-commutative 99.6%

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

   5. Simplified 99.6%

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

   6. Taylor expanded in x1 around 0 89.4%

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

   7. Taylor expanded in x1 around inf 96.1%

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

   9. Simplified 96.1%

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

4. Final simplification 93.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -2.2 \cdot 10^{+140}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -3.2 \cdot 10^{+21}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2\right) + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(-1 - x1 \cdot x1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right) - -6\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 3 \cdot 10^{+33}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right)}{-1 - x1 \cdot x1} + \left(x1 + x2 \cdot \left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2\right) + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) - \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1} - \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot \left(x1 \cdot 2\right)\right) \cdot \left(3 + \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right) - \left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 90.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot x1\right)\\ t_1 := 3 \cdot \left(x2 \cdot -2\right)\\ t_2 := x1 \cdot x1 + 1\\ t_3 := x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ t_4 := -1 - x1 \cdot x1\\ t_5 := x1 \cdot \left(x1 \cdot 3\right)\\ t_6 := t\_5 + 2 \cdot x2\\ t_7 := \frac{t\_6 - x1}{t\_2}\\ t_8 := t\_5 \cdot t\_7\\ t_9 := \frac{x1 - t\_6}{t\_2}\\ \mathbf{if}\;x1 \leq -2.2 \cdot 10^{+140}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x1 \leq -3.2 \cdot 10^{+21}:\\ \;\;\;\;x1 + \left(t\_1 + \left(x1 + \left(t\_0 + \left(t\_8 + t\_4 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot t\_9\right) - -6\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 3 \cdot 10^{+33}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{x1 - \left(t\_5 - 2 \cdot x2\right)}{t\_4} + \left(x1 + x2 \cdot \left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(t\_1 + \left(x1 + \left(t\_0 + \left(t\_8 + t\_2 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(t\_7 \cdot 4 - 6\right) + \frac{1}{x1} \cdot \left(\left(x1 \cdot 2\right) \cdot t\_9\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 x1)))
        (t_1 (* 3.0 (* x2 -2.0)))
        (t_2 (+ (* x1 x1) 1.0))
        (t_3 (+ x1 (+ x1 (* 3.0 (* x1 (+ (* x1 3.0) -1.0))))))
        (t_4 (- -1.0 (* x1 x1)))
        (t_5 (* x1 (* x1 3.0)))
        (t_6 (+ t_5 (* 2.0 x2)))
        (t_7 (/ (- t_6 x1) t_2))
        (t_8 (* t_5 t_7))
        (t_9 (/ (- x1 t_6) t_2)))
   (if (<= x1 -2.2e+140)
     t_3
     (if (<= x1 -3.2e+21)
       (+
        x1
        (+
         t_1
         (+
          x1
          (+ t_0 (+ t_8 (* t_4 (- (* (* x1 x1) (+ 6.0 (* 4.0 t_9))) -6.0)))))))
       (if (<= x1 3e+33)
         (+
          x1
          (+
           (* 3.0 (/ (- x1 (- t_5 (* 2.0 x2))) t_4))
           (+ x1 (* x2 (+ (* x1 -12.0) (* 8.0 (* x1 x2)))))))
         (if (<= x1 5e+153)
           (+
            x1
            (+
             t_1
             (+
              x1
              (+
               t_0
               (+
                t_8
                (*
                 t_2
                 (+
                  (* (* x1 x1) (- (* t_7 4.0) 6.0))
                  (* (/ 1.0 x1) (* (* x1 2.0) t_9)))))))))
           t_3))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * x1);
	double t_1 = 3.0 * (x2 * -2.0);
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	double t_4 = -1.0 - (x1 * x1);
	double t_5 = x1 * (x1 * 3.0);
	double t_6 = t_5 + (2.0 * x2);
	double t_7 = (t_6 - x1) / t_2;
	double t_8 = t_5 * t_7;
	double t_9 = (x1 - t_6) / t_2;
	double tmp;
	if (x1 <= -2.2e+140) {
		tmp = t_3;
	} else if (x1 <= -3.2e+21) {
		tmp = x1 + (t_1 + (x1 + (t_0 + (t_8 + (t_4 * (((x1 * x1) * (6.0 + (4.0 * t_9))) - -6.0))))));
	} else if (x1 <= 3e+33) {
		tmp = x1 + ((3.0 * ((x1 - (t_5 - (2.0 * x2))) / t_4)) + (x1 + (x2 * ((x1 * -12.0) + (8.0 * (x1 * x2))))));
	} else if (x1 <= 5e+153) {
		tmp = x1 + (t_1 + (x1 + (t_0 + (t_8 + (t_2 * (((x1 * x1) * ((t_7 * 4.0) - 6.0)) + ((1.0 / x1) * ((x1 * 2.0) * t_9))))))));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: t_8
    real(8) :: t_9
    real(8) :: tmp
    t_0 = x1 * (x1 * x1)
    t_1 = 3.0d0 * (x2 * (-2.0d0))
    t_2 = (x1 * x1) + 1.0d0
    t_3 = x1 + (x1 + (3.0d0 * (x1 * ((x1 * 3.0d0) + (-1.0d0)))))
    t_4 = (-1.0d0) - (x1 * x1)
    t_5 = x1 * (x1 * 3.0d0)
    t_6 = t_5 + (2.0d0 * x2)
    t_7 = (t_6 - x1) / t_2
    t_8 = t_5 * t_7
    t_9 = (x1 - t_6) / t_2
    if (x1 <= (-2.2d+140)) then
        tmp = t_3
    else if (x1 <= (-3.2d+21)) then
        tmp = x1 + (t_1 + (x1 + (t_0 + (t_8 + (t_4 * (((x1 * x1) * (6.0d0 + (4.0d0 * t_9))) - (-6.0d0)))))))
    else if (x1 <= 3d+33) then
        tmp = x1 + ((3.0d0 * ((x1 - (t_5 - (2.0d0 * x2))) / t_4)) + (x1 + (x2 * ((x1 * (-12.0d0)) + (8.0d0 * (x1 * x2))))))
    else if (x1 <= 5d+153) then
        tmp = x1 + (t_1 + (x1 + (t_0 + (t_8 + (t_2 * (((x1 * x1) * ((t_7 * 4.0d0) - 6.0d0)) + ((1.0d0 / x1) * ((x1 * 2.0d0) * t_9))))))))
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * x1);
	double t_1 = 3.0 * (x2 * -2.0);
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	double t_4 = -1.0 - (x1 * x1);
	double t_5 = x1 * (x1 * 3.0);
	double t_6 = t_5 + (2.0 * x2);
	double t_7 = (t_6 - x1) / t_2;
	double t_8 = t_5 * t_7;
	double t_9 = (x1 - t_6) / t_2;
	double tmp;
	if (x1 <= -2.2e+140) {
		tmp = t_3;
	} else if (x1 <= -3.2e+21) {
		tmp = x1 + (t_1 + (x1 + (t_0 + (t_8 + (t_4 * (((x1 * x1) * (6.0 + (4.0 * t_9))) - -6.0))))));
	} else if (x1 <= 3e+33) {
		tmp = x1 + ((3.0 * ((x1 - (t_5 - (2.0 * x2))) / t_4)) + (x1 + (x2 * ((x1 * -12.0) + (8.0 * (x1 * x2))))));
	} else if (x1 <= 5e+153) {
		tmp = x1 + (t_1 + (x1 + (t_0 + (t_8 + (t_2 * (((x1 * x1) * ((t_7 * 4.0) - 6.0)) + ((1.0 / x1) * ((x1 * 2.0) * t_9))))))));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * x1)
	t_1 = 3.0 * (x2 * -2.0)
	t_2 = (x1 * x1) + 1.0
	t_3 = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))))
	t_4 = -1.0 - (x1 * x1)
	t_5 = x1 * (x1 * 3.0)
	t_6 = t_5 + (2.0 * x2)
	t_7 = (t_6 - x1) / t_2
	t_8 = t_5 * t_7
	t_9 = (x1 - t_6) / t_2
	tmp = 0
	if x1 <= -2.2e+140:
		tmp = t_3
	elif x1 <= -3.2e+21:
		tmp = x1 + (t_1 + (x1 + (t_0 + (t_8 + (t_4 * (((x1 * x1) * (6.0 + (4.0 * t_9))) - -6.0))))))
	elif x1 <= 3e+33:
		tmp = x1 + ((3.0 * ((x1 - (t_5 - (2.0 * x2))) / t_4)) + (x1 + (x2 * ((x1 * -12.0) + (8.0 * (x1 * x2))))))
	elif x1 <= 5e+153:
		tmp = x1 + (t_1 + (x1 + (t_0 + (t_8 + (t_2 * (((x1 * x1) * ((t_7 * 4.0) - 6.0)) + ((1.0 / x1) * ((x1 * 2.0) * t_9))))))))
	else:
		tmp = t_3
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * x1))
	t_1 = Float64(3.0 * Float64(x2 * -2.0))
	t_2 = Float64(Float64(x1 * x1) + 1.0)
	t_3 = Float64(x1 + Float64(x1 + Float64(3.0 * Float64(x1 * Float64(Float64(x1 * 3.0) + -1.0)))))
	t_4 = Float64(-1.0 - Float64(x1 * x1))
	t_5 = Float64(x1 * Float64(x1 * 3.0))
	t_6 = Float64(t_5 + Float64(2.0 * x2))
	t_7 = Float64(Float64(t_6 - x1) / t_2)
	t_8 = Float64(t_5 * t_7)
	t_9 = Float64(Float64(x1 - t_6) / t_2)
	tmp = 0.0
	if (x1 <= -2.2e+140)
		tmp = t_3;
	elseif (x1 <= -3.2e+21)
		tmp = Float64(x1 + Float64(t_1 + Float64(x1 + Float64(t_0 + Float64(t_8 + Float64(t_4 * Float64(Float64(Float64(x1 * x1) * Float64(6.0 + Float64(4.0 * t_9))) - -6.0)))))));
	elseif (x1 <= 3e+33)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(x1 - Float64(t_5 - Float64(2.0 * x2))) / t_4)) + Float64(x1 + Float64(x2 * Float64(Float64(x1 * -12.0) + Float64(8.0 * Float64(x1 * x2)))))));
	elseif (x1 <= 5e+153)
		tmp = Float64(x1 + Float64(t_1 + Float64(x1 + Float64(t_0 + Float64(t_8 + Float64(t_2 * Float64(Float64(Float64(x1 * x1) * Float64(Float64(t_7 * 4.0) - 6.0)) + Float64(Float64(1.0 / x1) * Float64(Float64(x1 * 2.0) * t_9)))))))));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * x1);
	t_1 = 3.0 * (x2 * -2.0);
	t_2 = (x1 * x1) + 1.0;
	t_3 = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	t_4 = -1.0 - (x1 * x1);
	t_5 = x1 * (x1 * 3.0);
	t_6 = t_5 + (2.0 * x2);
	t_7 = (t_6 - x1) / t_2;
	t_8 = t_5 * t_7;
	t_9 = (x1 - t_6) / t_2;
	tmp = 0.0;
	if (x1 <= -2.2e+140)
		tmp = t_3;
	elseif (x1 <= -3.2e+21)
		tmp = x1 + (t_1 + (x1 + (t_0 + (t_8 + (t_4 * (((x1 * x1) * (6.0 + (4.0 * t_9))) - -6.0))))));
	elseif (x1 <= 3e+33)
		tmp = x1 + ((3.0 * ((x1 - (t_5 - (2.0 * x2))) / t_4)) + (x1 + (x2 * ((x1 * -12.0) + (8.0 * (x1 * x2))))));
	elseif (x1 <= 5e+153)
		tmp = x1 + (t_1 + (x1 + (t_0 + (t_8 + (t_2 * (((x1 * x1) * ((t_7 * 4.0) - 6.0)) + ((1.0 / x1) * ((x1 * 2.0) * t_9))))))));
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(3.0 * N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$3 = N[(x1 + N[(x1 + N[(3.0 * N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(t$95$5 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(N[(t$95$6 - x1), $MachinePrecision] / t$95$2), $MachinePrecision]}, Block[{t$95$8 = N[(t$95$5 * t$95$7), $MachinePrecision]}, Block[{t$95$9 = N[(N[(x1 - t$95$6), $MachinePrecision] / t$95$2), $MachinePrecision]}, If[LessEqual[x1, -2.2e+140], t$95$3, If[LessEqual[x1, -3.2e+21], N[(x1 + N[(t$95$1 + N[(x1 + N[(t$95$0 + N[(t$95$8 + N[(t$95$4 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 + N[(4.0 * t$95$9), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 3e+33], N[(x1 + N[(N[(3.0 * N[(N[(x1 - N[(t$95$5 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$4), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(x2 * N[(N[(x1 * -12.0), $MachinePrecision] + N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 5e+153], N[(x1 + N[(t$95$1 + N[(x1 + N[(t$95$0 + N[(t$95$8 + N[(t$95$2 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$7 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] + N[(N[(1.0 / x1), $MachinePrecision] * N[(N[(x1 * 2.0), $MachinePrecision] * t$95$9), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -2.1999999999999998e140 or 5.00000000000000018e153 < x1

   1. Initial program 0.0%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   2. 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 69.1%

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

   5. Taylor expanded in x2 around 0 100.0%

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

   if -2.1999999999999998e140 < x1 < -3.2e21

   1. Initial program 82.5%

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

   3. Taylor expanded in x1 around 0 82.5%

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

      1. *-commutative 82.5%

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

   5. Simplified 82.5%

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

   6. Taylor expanded in x1 around inf 82.5%

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

      1. associate-*r/ 82.5%

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

      2. associate-*r/ 82.5%

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

      3. metadata-eval 82.5%

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

   8. Simplified 82.5%

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

   9. Taylor expanded in x1 around inf 76.2%

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

   if -3.2e21 < x1 < 2.99999999999999984e33

   1. Initial program 99.3%

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

   3. Taylor expanded in x1 around 0 83.7%

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

   4. Taylor expanded in x2 around 0 93.7%

      \[\leadsto x1 + \left(\left(\color{blue}{x2 \cdot \left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   if 2.99999999999999984e33 < x1 < 5.00000000000000018e153

   1. Initial program 99.6%

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

   3. Taylor expanded in x1 around 0 99.6%

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

      1. *-commutative 99.6%

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

   5. Simplified 99.6%

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

   6. Taylor expanded in x1 around inf 96.0%

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

4. Final simplification 93.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -2.2 \cdot 10^{+140}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -3.2 \cdot 10^{+21}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2\right) + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(-1 - x1 \cdot x1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right) - -6\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 3 \cdot 10^{+33}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right)}{-1 - x1 \cdot x1} + \left(x1 + x2 \cdot \left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2\right) + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right) + \frac{1}{x1} \cdot \left(\left(x1 \cdot 2\right) \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 90.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := t\_1 + 2 \cdot x2\\ t_3 := x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ t_4 := -1 - x1 \cdot x1\\ t_5 := x1 + \left(3 \cdot \left(x2 \cdot -2\right) + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(t\_1 \cdot \frac{t\_2 - x1}{t\_0} + t\_4 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{x1 - t\_2}{t\_0}\right) - -6\right)\right)\right)\right)\right)\\ \mathbf{if}\;x1 \leq -2.2 \cdot 10^{+140}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x1 \leq -3.2 \cdot 10^{+21}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;x1 \leq 3 \cdot 10^{+33}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{x1 - \left(t\_1 - 2 \cdot x2\right)}{t\_4} + \left(x1 + x2 \cdot \left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+152}:\\ \;\;\;\;t\_5\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ (* x1 x1) 1.0))
        (t_1 (* x1 (* x1 3.0)))
        (t_2 (+ t_1 (* 2.0 x2)))
        (t_3 (+ x1 (+ x1 (* 3.0 (* x1 (+ (* x1 3.0) -1.0))))))
        (t_4 (- -1.0 (* x1 x1)))
        (t_5
         (+
          x1
          (+
           (* 3.0 (* x2 -2.0))
           (+
            x1
            (+
             (* x1 (* x1 x1))
             (+
              (* t_1 (/ (- t_2 x1) t_0))
              (*
               t_4
               (-
                (* (* x1 x1) (+ 6.0 (* 4.0 (/ (- x1 t_2) t_0))))
                -6.0)))))))))
   (if (<= x1 -2.2e+140)
     t_3
     (if (<= x1 -3.2e+21)
       t_5
       (if (<= x1 3e+33)
         (+
          x1
          (+
           (* 3.0 (/ (- x1 (- t_1 (* 2.0 x2))) t_4))
           (+ x1 (* x2 (+ (* x1 -12.0) (* 8.0 (* x1 x2)))))))
         (if (<= x1 5e+152) t_5 t_3))))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = t_1 + (2.0 * x2);
	double t_3 = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	double t_4 = -1.0 - (x1 * x1);
	double t_5 = x1 + ((3.0 * (x2 * -2.0)) + (x1 + ((x1 * (x1 * x1)) + ((t_1 * ((t_2 - x1) / t_0)) + (t_4 * (((x1 * x1) * (6.0 + (4.0 * ((x1 - t_2) / t_0)))) - -6.0))))));
	double tmp;
	if (x1 <= -2.2e+140) {
		tmp = t_3;
	} else if (x1 <= -3.2e+21) {
		tmp = t_5;
	} else if (x1 <= 3e+33) {
		tmp = x1 + ((3.0 * ((x1 - (t_1 - (2.0 * x2))) / t_4)) + (x1 + (x2 * ((x1 * -12.0) + (8.0 * (x1 * x2))))));
	} else if (x1 <= 5e+152) {
		tmp = t_5;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_0 = (x1 * x1) + 1.0d0
    t_1 = x1 * (x1 * 3.0d0)
    t_2 = t_1 + (2.0d0 * x2)
    t_3 = x1 + (x1 + (3.0d0 * (x1 * ((x1 * 3.0d0) + (-1.0d0)))))
    t_4 = (-1.0d0) - (x1 * x1)
    t_5 = x1 + ((3.0d0 * (x2 * (-2.0d0))) + (x1 + ((x1 * (x1 * x1)) + ((t_1 * ((t_2 - x1) / t_0)) + (t_4 * (((x1 * x1) * (6.0d0 + (4.0d0 * ((x1 - t_2) / t_0)))) - (-6.0d0)))))))
    if (x1 <= (-2.2d+140)) then
        tmp = t_3
    else if (x1 <= (-3.2d+21)) then
        tmp = t_5
    else if (x1 <= 3d+33) then
        tmp = x1 + ((3.0d0 * ((x1 - (t_1 - (2.0d0 * x2))) / t_4)) + (x1 + (x2 * ((x1 * (-12.0d0)) + (8.0d0 * (x1 * x2))))))
    else if (x1 <= 5d+152) then
        tmp = t_5
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = t_1 + (2.0 * x2);
	double t_3 = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	double t_4 = -1.0 - (x1 * x1);
	double t_5 = x1 + ((3.0 * (x2 * -2.0)) + (x1 + ((x1 * (x1 * x1)) + ((t_1 * ((t_2 - x1) / t_0)) + (t_4 * (((x1 * x1) * (6.0 + (4.0 * ((x1 - t_2) / t_0)))) - -6.0))))));
	double tmp;
	if (x1 <= -2.2e+140) {
		tmp = t_3;
	} else if (x1 <= -3.2e+21) {
		tmp = t_5;
	} else if (x1 <= 3e+33) {
		tmp = x1 + ((3.0 * ((x1 - (t_1 - (2.0 * x2))) / t_4)) + (x1 + (x2 * ((x1 * -12.0) + (8.0 * (x1 * x2))))));
	} else if (x1 <= 5e+152) {
		tmp = t_5;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x1 * x1) + 1.0
	t_1 = x1 * (x1 * 3.0)
	t_2 = t_1 + (2.0 * x2)
	t_3 = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))))
	t_4 = -1.0 - (x1 * x1)
	t_5 = x1 + ((3.0 * (x2 * -2.0)) + (x1 + ((x1 * (x1 * x1)) + ((t_1 * ((t_2 - x1) / t_0)) + (t_4 * (((x1 * x1) * (6.0 + (4.0 * ((x1 - t_2) / t_0)))) - -6.0))))))
	tmp = 0
	if x1 <= -2.2e+140:
		tmp = t_3
	elif x1 <= -3.2e+21:
		tmp = t_5
	elif x1 <= 3e+33:
		tmp = x1 + ((3.0 * ((x1 - (t_1 - (2.0 * x2))) / t_4)) + (x1 + (x2 * ((x1 * -12.0) + (8.0 * (x1 * x2))))))
	elif x1 <= 5e+152:
		tmp = t_5
	else:
		tmp = t_3
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * x1) + 1.0)
	t_1 = Float64(x1 * Float64(x1 * 3.0))
	t_2 = Float64(t_1 + Float64(2.0 * x2))
	t_3 = Float64(x1 + Float64(x1 + Float64(3.0 * Float64(x1 * Float64(Float64(x1 * 3.0) + -1.0)))))
	t_4 = Float64(-1.0 - Float64(x1 * x1))
	t_5 = Float64(x1 + Float64(Float64(3.0 * Float64(x2 * -2.0)) + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(t_1 * Float64(Float64(t_2 - x1) / t_0)) + Float64(t_4 * Float64(Float64(Float64(x1 * x1) * Float64(6.0 + Float64(4.0 * Float64(Float64(x1 - t_2) / t_0)))) - -6.0)))))))
	tmp = 0.0
	if (x1 <= -2.2e+140)
		tmp = t_3;
	elseif (x1 <= -3.2e+21)
		tmp = t_5;
	elseif (x1 <= 3e+33)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(x1 - Float64(t_1 - Float64(2.0 * x2))) / t_4)) + Float64(x1 + Float64(x2 * Float64(Float64(x1 * -12.0) + Float64(8.0 * Float64(x1 * x2)))))));
	elseif (x1 <= 5e+152)
		tmp = t_5;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x1 * x1) + 1.0;
	t_1 = x1 * (x1 * 3.0);
	t_2 = t_1 + (2.0 * x2);
	t_3 = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	t_4 = -1.0 - (x1 * x1);
	t_5 = x1 + ((3.0 * (x2 * -2.0)) + (x1 + ((x1 * (x1 * x1)) + ((t_1 * ((t_2 - x1) / t_0)) + (t_4 * (((x1 * x1) * (6.0 + (4.0 * ((x1 - t_2) / t_0)))) - -6.0))))));
	tmp = 0.0;
	if (x1 <= -2.2e+140)
		tmp = t_3;
	elseif (x1 <= -3.2e+21)
		tmp = t_5;
	elseif (x1 <= 3e+33)
		tmp = x1 + ((3.0 * ((x1 - (t_1 - (2.0 * x2))) / t_4)) + (x1 + (x2 * ((x1 * -12.0) + (8.0 * (x1 * x2))))));
	elseif (x1 <= 5e+152)
		tmp = t_5;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x1 + N[(x1 + N[(3.0 * N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(x1 + N[(N[(3.0 * N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$1 * N[(N[(t$95$2 - x1), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision] + N[(t$95$4 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 + N[(4.0 * N[(N[(x1 - t$95$2), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -2.2e+140], t$95$3, If[LessEqual[x1, -3.2e+21], t$95$5, If[LessEqual[x1, 3e+33], N[(x1 + N[(N[(3.0 * N[(N[(x1 - N[(t$95$1 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$4), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(x2 * N[(N[(x1 * -12.0), $MachinePrecision] + N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 5e+152], t$95$5, t$95$3]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -2.1999999999999998e140 or 5e152 < x1

   1. Initial program 0.0%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   2. 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 69.1%

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

   5. Taylor expanded in x2 around 0 100.0%

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

   if -2.1999999999999998e140 < x1 < -3.2e21 or 2.99999999999999984e33 < x1 < 5e152

   1. Initial program 90.8%

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

   3. Taylor expanded in x1 around 0 90.8%

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

      1. *-commutative 90.8%

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

   5. Simplified 90.8%

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

   6. Taylor expanded in x1 around inf 90.8%

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

      1. associate-*r/ 90.8%

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

      2. associate-*r/ 90.8%

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

      3. metadata-eval 90.8%

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

   8. Simplified 90.8%

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

   9. Taylor expanded in x1 around inf 85.7%

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

   if -3.2e21 < x1 < 2.99999999999999984e33

   1. Initial program 99.3%

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

   3. Taylor expanded in x1 around 0 83.7%

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

   4. Taylor expanded in x2 around 0 93.7%

      \[\leadsto x1 + \left(\left(\color{blue}{x2 \cdot \left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 93.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -2.2 \cdot 10^{+140}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -3.2 \cdot 10^{+21}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2\right) + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(-1 - x1 \cdot x1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right) - -6\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 3 \cdot 10^{+33}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right)}{-1 - x1 \cdot x1} + \left(x1 + x2 \cdot \left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+152}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2\right) + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(-1 - x1 \cdot x1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right) - -6\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 82.1% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -4.4 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 4 \cdot 10^{-112}:\\ \;\;\;\;x1 + \left(\left(x1 + x2 \cdot \left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right)\right) + 3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(-1 + x2 \cdot \left(x1 \cdot 2 + 3 \cdot \frac{x1}{x2}\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 + \left(x1 \cdot \left(3 \cdot \left(x2 \cdot -2 - 3\right) - x1 \cdot 3\right) + 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -4.4e+153)
   (+ x1 (+ x1 (* 3.0 (* x1 (+ (* x1 3.0) -1.0)))))
   (if (<= x1 4e-112)
     (+
      x1
      (+
       (+ x1 (* x2 (+ (* x1 -12.0) (* 8.0 (* x1 x2)))))
       (*
        3.0
        (+
         (* x2 -2.0)
         (* x1 (+ -1.0 (* x2 (+ (* x1 2.0) (* 3.0 (/ x1 x2))))))))))
     (+
      x1
      (-
       (* x2 -6.0)
       (*
        x1
        (+
         2.0
         (+
          (* x1 (- (* 3.0 (- (* x2 -2.0) 3.0)) (* x1 3.0)))
          (* 4.0 (* x2 (- 3.0 (* 2.0 x2))))))))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -4.4e+153) {
		tmp = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	} else if (x1 <= 4e-112) {
		tmp = x1 + ((x1 + (x2 * ((x1 * -12.0) + (8.0 * (x1 * x2))))) + (3.0 * ((x2 * -2.0) + (x1 * (-1.0 + (x2 * ((x1 * 2.0) + (3.0 * (x1 / x2)))))))));
	} else {
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - (x1 * 3.0))) + (4.0 * (x2 * (3.0 - (2.0 * x2))))))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x1 <= (-4.4d+153)) then
        tmp = x1 + (x1 + (3.0d0 * (x1 * ((x1 * 3.0d0) + (-1.0d0)))))
    else if (x1 <= 4d-112) then
        tmp = x1 + ((x1 + (x2 * ((x1 * (-12.0d0)) + (8.0d0 * (x1 * x2))))) + (3.0d0 * ((x2 * (-2.0d0)) + (x1 * ((-1.0d0) + (x2 * ((x1 * 2.0d0) + (3.0d0 * (x1 / x2)))))))))
    else
        tmp = x1 + ((x2 * (-6.0d0)) - (x1 * (2.0d0 + ((x1 * ((3.0d0 * ((x2 * (-2.0d0)) - 3.0d0)) - (x1 * 3.0d0))) + (4.0d0 * (x2 * (3.0d0 - (2.0d0 * x2))))))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= -4.4e+153) {
		tmp = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	} else if (x1 <= 4e-112) {
		tmp = x1 + ((x1 + (x2 * ((x1 * -12.0) + (8.0 * (x1 * x2))))) + (3.0 * ((x2 * -2.0) + (x1 * (-1.0 + (x2 * ((x1 * 2.0) + (3.0 * (x1 / x2)))))))));
	} else {
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - (x1 * 3.0))) + (4.0 * (x2 * (3.0 - (2.0 * x2))))))));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -4.4e+153:
		tmp = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))))
	elif x1 <= 4e-112:
		tmp = x1 + ((x1 + (x2 * ((x1 * -12.0) + (8.0 * (x1 * x2))))) + (3.0 * ((x2 * -2.0) + (x1 * (-1.0 + (x2 * ((x1 * 2.0) + (3.0 * (x1 / x2)))))))))
	else:
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - (x1 * 3.0))) + (4.0 * (x2 * (3.0 - (2.0 * x2))))))))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -4.4e+153)
		tmp = Float64(x1 + Float64(x1 + Float64(3.0 * Float64(x1 * Float64(Float64(x1 * 3.0) + -1.0)))));
	elseif (x1 <= 4e-112)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(x2 * Float64(Float64(x1 * -12.0) + Float64(8.0 * Float64(x1 * x2))))) + Float64(3.0 * Float64(Float64(x2 * -2.0) + Float64(x1 * Float64(-1.0 + Float64(x2 * Float64(Float64(x1 * 2.0) + Float64(3.0 * Float64(x1 / x2))))))))));
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) - Float64(x1 * Float64(2.0 + Float64(Float64(x1 * Float64(Float64(3.0 * Float64(Float64(x2 * -2.0) - 3.0)) - Float64(x1 * 3.0))) + Float64(4.0 * Float64(x2 * Float64(3.0 - Float64(2.0 * x2)))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -4.4e+153)
		tmp = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	elseif (x1 <= 4e-112)
		tmp = x1 + ((x1 + (x2 * ((x1 * -12.0) + (8.0 * (x1 * x2))))) + (3.0 * ((x2 * -2.0) + (x1 * (-1.0 + (x2 * ((x1 * 2.0) + (3.0 * (x1 / x2)))))))));
	else
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - (x1 * 3.0))) + (4.0 * (x2 * (3.0 - (2.0 * x2))))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -4.4e+153], N[(x1 + N[(x1 + N[(3.0 * N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 4e-112], N[(x1 + N[(N[(x1 + N[(x2 * N[(N[(x1 * -12.0), $MachinePrecision] + N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] + N[(x1 * N[(-1.0 + N[(x2 * N[(N[(x1 * 2.0), $MachinePrecision] + N[(3.0 * N[(x1 / x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] - N[(x1 * N[(2.0 + N[(N[(x1 * N[(N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision] - N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(4.0 * N[(x2 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 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 64.1%

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

   5. Taylor expanded in x2 around 0 100.0%

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

   if -4.3999999999999999e153 < x1 < 3.9999999999999998e-112

   1. Initial program 95.6%

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

   3. Taylor expanded in x1 around 0 68.4%

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

   4. Taylor expanded in x1 around 0 66.8%

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

   5. Taylor expanded in x2 around 0 76.6%

      \[\leadsto x1 + \left(\left(\color{blue}{x2 \cdot \left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right)} + x1\right) + 3 \cdot \left(-2 \cdot x2 + x1 \cdot \left(x1 \cdot \left(3 - -2 \cdot x2\right) - 1\right)\right)\right) \]

   6. Taylor expanded in x2 around inf 79.4%

      \[\leadsto x1 + \left(\left(x2 \cdot \left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) + x1\right) + 3 \cdot \left(-2 \cdot x2 + x1 \cdot \left(\color{blue}{x2 \cdot \left(2 \cdot x1 + 3 \cdot \frac{x1}{x2}\right)} - 1\right)\right)\right) \]

   if 3.9999999999999998e-112 < x1

   1. Initial program 64.6%

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

   3. Taylor expanded in x1 around 0 37.7%

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

   4. Taylor expanded in x1 around 0 80.0%

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

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4.4 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 4 \cdot 10^{-112}:\\ \;\;\;\;x1 + \left(\left(x1 + x2 \cdot \left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right)\right) + 3 \cdot \left(x2 \cdot -2 + x1 \cdot \left(-1 + x2 \cdot \left(x1 \cdot 2 + 3 \cdot \frac{x1}{x2}\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 + \left(x1 \cdot \left(3 \cdot \left(x2 \cdot -2 - 3\right) - x1 \cdot 3\right) + 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 81.2% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -4.5 \cdot 10^{+142}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.1 \cdot 10^{-111}:\\ \;\;\;\;x1 + \left(\left(x1 + x2 \cdot \left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right)\right) + \left(x2 \cdot -6 + x1 \cdot -3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 + \left(x1 \cdot \left(3 \cdot \left(x2 \cdot -2 - 3\right) - x1 \cdot 3\right) + 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -4.5e+142)
   (+ x1 (+ x1 (* 3.0 (* x1 (+ (* x1 3.0) -1.0)))))
   (if (<= x1 1.1e-111)
     (+
      x1
      (+
       (+ x1 (* x2 (+ (* x1 -12.0) (* 8.0 (* x1 x2)))))
       (+ (* x2 -6.0) (* x1 -3.0))))
     (+
      x1
      (-
       (* x2 -6.0)
       (*
        x1
        (+
         2.0
         (+
          (* x1 (- (* 3.0 (- (* x2 -2.0) 3.0)) (* x1 3.0)))
          (* 4.0 (* x2 (- 3.0 (* 2.0 x2))))))))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -4.5e+142) {
		tmp = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	} else if (x1 <= 1.1e-111) {
		tmp = x1 + ((x1 + (x2 * ((x1 * -12.0) + (8.0 * (x1 * x2))))) + ((x2 * -6.0) + (x1 * -3.0)));
	} else {
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - (x1 * 3.0))) + (4.0 * (x2 * (3.0 - (2.0 * x2))))))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x1 <= (-4.5d+142)) then
        tmp = x1 + (x1 + (3.0d0 * (x1 * ((x1 * 3.0d0) + (-1.0d0)))))
    else if (x1 <= 1.1d-111) then
        tmp = x1 + ((x1 + (x2 * ((x1 * (-12.0d0)) + (8.0d0 * (x1 * x2))))) + ((x2 * (-6.0d0)) + (x1 * (-3.0d0))))
    else
        tmp = x1 + ((x2 * (-6.0d0)) - (x1 * (2.0d0 + ((x1 * ((3.0d0 * ((x2 * (-2.0d0)) - 3.0d0)) - (x1 * 3.0d0))) + (4.0d0 * (x2 * (3.0d0 - (2.0d0 * x2))))))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= -4.5e+142) {
		tmp = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	} else if (x1 <= 1.1e-111) {
		tmp = x1 + ((x1 + (x2 * ((x1 * -12.0) + (8.0 * (x1 * x2))))) + ((x2 * -6.0) + (x1 * -3.0)));
	} else {
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - (x1 * 3.0))) + (4.0 * (x2 * (3.0 - (2.0 * x2))))))));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -4.5e+142:
		tmp = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))))
	elif x1 <= 1.1e-111:
		tmp = x1 + ((x1 + (x2 * ((x1 * -12.0) + (8.0 * (x1 * x2))))) + ((x2 * -6.0) + (x1 * -3.0)))
	else:
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - (x1 * 3.0))) + (4.0 * (x2 * (3.0 - (2.0 * x2))))))))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -4.5e+142)
		tmp = Float64(x1 + Float64(x1 + Float64(3.0 * Float64(x1 * Float64(Float64(x1 * 3.0) + -1.0)))));
	elseif (x1 <= 1.1e-111)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(x2 * Float64(Float64(x1 * -12.0) + Float64(8.0 * Float64(x1 * x2))))) + Float64(Float64(x2 * -6.0) + Float64(x1 * -3.0))));
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) - Float64(x1 * Float64(2.0 + Float64(Float64(x1 * Float64(Float64(3.0 * Float64(Float64(x2 * -2.0) - 3.0)) - Float64(x1 * 3.0))) + Float64(4.0 * Float64(x2 * Float64(3.0 - Float64(2.0 * x2)))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -4.5e+142)
		tmp = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	elseif (x1 <= 1.1e-111)
		tmp = x1 + ((x1 + (x2 * ((x1 * -12.0) + (8.0 * (x1 * x2))))) + ((x2 * -6.0) + (x1 * -3.0)));
	else
		tmp = x1 + ((x2 * -6.0) - (x1 * (2.0 + ((x1 * ((3.0 * ((x2 * -2.0) - 3.0)) - (x1 * 3.0))) + (4.0 * (x2 * (3.0 - (2.0 * x2))))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -4.5e+142], N[(x1 + N[(x1 + N[(3.0 * N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.1e-111], N[(x1 + N[(N[(x1 + N[(x2 * N[(N[(x1 * -12.0), $MachinePrecision] + N[(8.0 * N[(x1 * x2), $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[(2.0 + N[(N[(x1 * N[(N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision] - N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(4.0 * N[(x2 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -4.4999999999999999e142

   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 64.1%

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

   5. Taylor expanded in x2 around 0 100.0%

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

   if -4.4999999999999999e142 < x1 < 1.1e-111

   1. Initial program 95.6%

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

   3. Taylor expanded in x1 around 0 68.4%

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

   4. Taylor expanded in x1 around 0 66.8%

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

   5. Taylor expanded in x2 around 0 76.6%

      \[\leadsto x1 + \left(\left(\color{blue}{x2 \cdot \left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right)} + x1\right) + 3 \cdot \left(-2 \cdot x2 + x1 \cdot \left(x1 \cdot \left(3 - -2 \cdot x2\right) - 1\right)\right)\right) \]

   6. Taylor expanded in x1 around 0 78.3%

      \[\leadsto x1 + \left(\left(x2 \cdot \left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) + x1\right) + \color{blue}{\left(-6 \cdot x2 + -3 \cdot x1\right)}\right) \]

   if 1.1e-111 < x1

   1. Initial program 64.6%

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

   3. Taylor expanded in x1 around 0 37.7%

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

   4. Taylor expanded in x1 around 0 80.0%

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

4. Final simplification 82.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4.5 \cdot 10^{+142}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.1 \cdot 10^{-111}:\\ \;\;\;\;x1 + \left(\left(x1 + x2 \cdot \left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right)\right) + \left(x2 \cdot -6 + x1 \cdot -3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 - x1 \cdot \left(2 + \left(x1 \cdot \left(3 \cdot \left(x2 \cdot -2 - 3\right) - x1 \cdot 3\right) + 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 64.2% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 - x1 \cdot \left(2 + 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\\ t_1 := x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ \mathbf{if}\;x1 \leq -5.2 \cdot 10^{+140}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x1 \leq -1.3 \cdot 10^{-74}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x1 \leq 3.8 \cdot 10^{-140}:\\ \;\;\;\;x1 + x2 \cdot -6\\ \mathbf{elif}\;x1 \leq 4.4 \cdot 10^{+153}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (- x1 (* x1 (+ 2.0 (* 4.0 (* x2 (- 3.0 (* 2.0 x2))))))))
        (t_1 (+ x1 (+ x1 (* 3.0 (* x1 (+ (* x1 3.0) -1.0)))))))
   (if (<= x1 -5.2e+140)
     t_1
     (if (<= x1 -1.3e-74)
       t_0
       (if (<= x1 3.8e-140)
         (+ x1 (* x2 -6.0))
         (if (<= x1 4.4e+153) t_0 t_1))))))

C

double code(double x1, double x2) {
	double t_0 = x1 - (x1 * (2.0 + (4.0 * (x2 * (3.0 - (2.0 * x2))))));
	double t_1 = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	double tmp;
	if (x1 <= -5.2e+140) {
		tmp = t_1;
	} else if (x1 <= -1.3e-74) {
		tmp = t_0;
	} else if (x1 <= 3.8e-140) {
		tmp = x1 + (x2 * -6.0);
	} else if (x1 <= 4.4e+153) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x1 - (x1 * (2.0d0 + (4.0d0 * (x2 * (3.0d0 - (2.0d0 * x2))))))
    t_1 = x1 + (x1 + (3.0d0 * (x1 * ((x1 * 3.0d0) + (-1.0d0)))))
    if (x1 <= (-5.2d+140)) then
        tmp = t_1
    else if (x1 <= (-1.3d-74)) then
        tmp = t_0
    else if (x1 <= 3.8d-140) then
        tmp = x1 + (x2 * (-6.0d0))
    else if (x1 <= 4.4d+153) then
        tmp = t_0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 - (x1 * (2.0 + (4.0 * (x2 * (3.0 - (2.0 * x2))))));
	double t_1 = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	double tmp;
	if (x1 <= -5.2e+140) {
		tmp = t_1;
	} else if (x1 <= -1.3e-74) {
		tmp = t_0;
	} else if (x1 <= 3.8e-140) {
		tmp = x1 + (x2 * -6.0);
	} else if (x1 <= 4.4e+153) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 - (x1 * (2.0 + (4.0 * (x2 * (3.0 - (2.0 * x2))))))
	t_1 = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))))
	tmp = 0
	if x1 <= -5.2e+140:
		tmp = t_1
	elif x1 <= -1.3e-74:
		tmp = t_0
	elif x1 <= 3.8e-140:
		tmp = x1 + (x2 * -6.0)
	elif x1 <= 4.4e+153:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 - Float64(x1 * Float64(2.0 + Float64(4.0 * Float64(x2 * Float64(3.0 - Float64(2.0 * x2)))))))
	t_1 = Float64(x1 + Float64(x1 + Float64(3.0 * Float64(x1 * Float64(Float64(x1 * 3.0) + -1.0)))))
	tmp = 0.0
	if (x1 <= -5.2e+140)
		tmp = t_1;
	elseif (x1 <= -1.3e-74)
		tmp = t_0;
	elseif (x1 <= 3.8e-140)
		tmp = Float64(x1 + Float64(x2 * -6.0));
	elseif (x1 <= 4.4e+153)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 - (x1 * (2.0 + (4.0 * (x2 * (3.0 - (2.0 * x2))))));
	t_1 = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	tmp = 0.0;
	if (x1 <= -5.2e+140)
		tmp = t_1;
	elseif (x1 <= -1.3e-74)
		tmp = t_0;
	elseif (x1 <= 3.8e-140)
		tmp = x1 + (x2 * -6.0);
	elseif (x1 <= 4.4e+153)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 - N[(x1 * N[(2.0 + N[(4.0 * N[(x2 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 + N[(x1 + N[(3.0 * N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -5.2e+140], t$95$1, If[LessEqual[x1, -1.3e-74], t$95$0, If[LessEqual[x1, 3.8e-140], N[(x1 + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 4.4e+153], t$95$0, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -5.2000000000000002e140 or 4.3999999999999999e153 < x1

   1. Initial program 0.0%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   2. 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 69.1%

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

   5. Taylor expanded in x2 around 0 100.0%

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

   if -5.2000000000000002e140 < x1 < -1.3e-74 or 3.79999999999999998e-140 < x1 < 4.3999999999999999e153

   1. Initial program 94.7%

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

   3. Taylor expanded in x1 around 0 51.4%

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

   4. Taylor expanded in x1 around 0 46.3%

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

   5. Taylor expanded in x2 around 0 42.7%

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

   6. Taylor expanded in x1 around 0 40.9%

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

   if -1.3e-74 < x1 < 3.79999999999999998e-140

   1. Initial program 99.4%

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

   3. Taylor expanded in x1 around 0 85.0%

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

   4. Taylor expanded in x1 around 0 85.0%

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

   5. Taylor expanded in x1 around 0 64.1%

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

      1. *-commutative 64.1%

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

   7. Simplified 64.1%

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

4. Final simplification 63.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.2 \cdot 10^{+140}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -1.3 \cdot 10^{-74}:\\ \;\;\;\;x1 - x1 \cdot \left(2 + 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 3.8 \cdot 10^{-140}:\\ \;\;\;\;x1 + x2 \cdot -6\\ \mathbf{elif}\;x1 \leq 4.4 \cdot 10^{+153}:\\ \;\;\;\;x1 - x1 \cdot \left(2 + 4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 57.8% accurate, 3.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 - x1 \cdot \left(-1 - x2 \cdot \left(x2 \cdot 8 - 12\right)\right)\\ t_1 := x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ \mathbf{if}\;x1 \leq -2.2 \cdot 10^{+140}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x1 \leq -3 \cdot 10^{-19}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x1 \leq 3.9 \cdot 10^{-63}:\\ \;\;\;\;x1 + x2 \cdot -6\\ \mathbf{elif}\;x1 \leq 4.4 \cdot 10^{+153}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (- x1 (* x1 (- -1.0 (* x2 (- (* x2 8.0) 12.0))))))
        (t_1 (+ x1 (+ x1 (* 3.0 (* x1 (+ (* x1 3.0) -1.0)))))))
   (if (<= x1 -2.2e+140)
     t_1
     (if (<= x1 -3e-19)
       t_0
       (if (<= x1 3.9e-63)
         (+ x1 (* x2 -6.0))
         (if (<= x1 4.4e+153) t_0 t_1))))))

C

double code(double x1, double x2) {
	double t_0 = x1 - (x1 * (-1.0 - (x2 * ((x2 * 8.0) - 12.0))));
	double t_1 = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	double tmp;
	if (x1 <= -2.2e+140) {
		tmp = t_1;
	} else if (x1 <= -3e-19) {
		tmp = t_0;
	} else if (x1 <= 3.9e-63) {
		tmp = x1 + (x2 * -6.0);
	} else if (x1 <= 4.4e+153) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x1 - (x1 * ((-1.0d0) - (x2 * ((x2 * 8.0d0) - 12.0d0))))
    t_1 = x1 + (x1 + (3.0d0 * (x1 * ((x1 * 3.0d0) + (-1.0d0)))))
    if (x1 <= (-2.2d+140)) then
        tmp = t_1
    else if (x1 <= (-3d-19)) then
        tmp = t_0
    else if (x1 <= 3.9d-63) then
        tmp = x1 + (x2 * (-6.0d0))
    else if (x1 <= 4.4d+153) then
        tmp = t_0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 - (x1 * (-1.0 - (x2 * ((x2 * 8.0) - 12.0))));
	double t_1 = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	double tmp;
	if (x1 <= -2.2e+140) {
		tmp = t_1;
	} else if (x1 <= -3e-19) {
		tmp = t_0;
	} else if (x1 <= 3.9e-63) {
		tmp = x1 + (x2 * -6.0);
	} else if (x1 <= 4.4e+153) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 - (x1 * (-1.0 - (x2 * ((x2 * 8.0) - 12.0))))
	t_1 = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))))
	tmp = 0
	if x1 <= -2.2e+140:
		tmp = t_1
	elif x1 <= -3e-19:
		tmp = t_0
	elif x1 <= 3.9e-63:
		tmp = x1 + (x2 * -6.0)
	elif x1 <= 4.4e+153:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 - Float64(x1 * Float64(-1.0 - Float64(x2 * Float64(Float64(x2 * 8.0) - 12.0)))))
	t_1 = Float64(x1 + Float64(x1 + Float64(3.0 * Float64(x1 * Float64(Float64(x1 * 3.0) + -1.0)))))
	tmp = 0.0
	if (x1 <= -2.2e+140)
		tmp = t_1;
	elseif (x1 <= -3e-19)
		tmp = t_0;
	elseif (x1 <= 3.9e-63)
		tmp = Float64(x1 + Float64(x2 * -6.0));
	elseif (x1 <= 4.4e+153)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 - (x1 * (-1.0 - (x2 * ((x2 * 8.0) - 12.0))));
	t_1 = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	tmp = 0.0;
	if (x1 <= -2.2e+140)
		tmp = t_1;
	elseif (x1 <= -3e-19)
		tmp = t_0;
	elseif (x1 <= 3.9e-63)
		tmp = x1 + (x2 * -6.0);
	elseif (x1 <= 4.4e+153)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 - N[(x1 * N[(-1.0 - N[(x2 * N[(N[(x2 * 8.0), $MachinePrecision] - 12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 + N[(x1 + N[(3.0 * N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -2.2e+140], t$95$1, If[LessEqual[x1, -3e-19], t$95$0, If[LessEqual[x1, 3.9e-63], N[(x1 + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 4.4e+153], t$95$0, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -2.1999999999999998e140 or 4.3999999999999999e153 < x1

   1. Initial program 0.0%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   2. 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 69.1%

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

   5. Taylor expanded in x2 around 0 100.0%

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

   if -2.1999999999999998e140 < x1 < -2.99999999999999993e-19 or 3.90000000000000022e-63 < x1 < 4.3999999999999999e153

   1. Initial program 93.4%

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

   3. Taylor expanded in x1 around 0 40.3%

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

   4. Taylor expanded in x1 around inf 30.9%

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

   5. Taylor expanded in x2 around 0 30.9%

      \[\leadsto x1 + x1 \cdot \left(1 + \color{blue}{x2 \cdot \left(8 \cdot x2 - 12\right)}\right) \]

   if -2.99999999999999993e-19 < x1 < 3.90000000000000022e-63

   1. Initial program 99.4%

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

   3. Taylor expanded in x1 around 0 86.5%

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

   4. Taylor expanded in x1 around 0 86.5%

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

   5. Taylor expanded in x1 around 0 57.7%

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

      1. *-commutative 57.7%

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

   7. Simplified 57.7%

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

4. Final simplification 59.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -2.2 \cdot 10^{+140}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -3 \cdot 10^{-19}:\\ \;\;\;\;x1 - x1 \cdot \left(-1 - x2 \cdot \left(x2 \cdot 8 - 12\right)\right)\\ \mathbf{elif}\;x1 \leq 3.9 \cdot 10^{-63}:\\ \;\;\;\;x1 + x2 \cdot -6\\ \mathbf{elif}\;x1 \leq 4.4 \cdot 10^{+153}:\\ \;\;\;\;x1 - x1 \cdot \left(-1 - x2 \cdot \left(x2 \cdot 8 - 12\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 79.8% accurate, 3.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -3.1 \cdot 10^{+141}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.1 \cdot 10^{-48}:\\ \;\;\;\;x1 + \left(\left(x1 + x2 \cdot \left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right)\right) + \left(x2 \cdot -6 + x1 \cdot -3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot 9\right) - 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -3.1e+141)
   (+ x1 (+ x1 (* 3.0 (* x1 (+ (* x1 3.0) -1.0)))))
   (if (<= x1 1.1e-48)
     (+
      x1
      (+
       (+ x1 (* x2 (+ (* x1 -12.0) (* 8.0 (* x1 x2)))))
       (+ (* x2 -6.0) (* x1 -3.0))))
     (+ x1 (* x1 (- (+ (* 4.0 (* x2 (- (* 2.0 x2) 3.0))) (* x1 9.0)) 2.0))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -3.1e+141) {
		tmp = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	} else if (x1 <= 1.1e-48) {
		tmp = x1 + ((x1 + (x2 * ((x1 * -12.0) + (8.0 * (x1 * x2))))) + ((x2 * -6.0) + (x1 * -3.0)));
	} else {
		tmp = x1 + (x1 * (((4.0 * (x2 * ((2.0 * x2) - 3.0))) + (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 (x1 <= (-3.1d+141)) then
        tmp = x1 + (x1 + (3.0d0 * (x1 * ((x1 * 3.0d0) + (-1.0d0)))))
    else if (x1 <= 1.1d-48) then
        tmp = x1 + ((x1 + (x2 * ((x1 * (-12.0d0)) + (8.0d0 * (x1 * x2))))) + ((x2 * (-6.0d0)) + (x1 * (-3.0d0))))
    else
        tmp = x1 + (x1 * (((4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0))) + (x1 * 9.0d0)) - 2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= -3.1e+141) {
		tmp = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	} else if (x1 <= 1.1e-48) {
		tmp = x1 + ((x1 + (x2 * ((x1 * -12.0) + (8.0 * (x1 * x2))))) + ((x2 * -6.0) + (x1 * -3.0)));
	} else {
		tmp = x1 + (x1 * (((4.0 * (x2 * ((2.0 * x2) - 3.0))) + (x1 * 9.0)) - 2.0));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -3.1e+141:
		tmp = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))))
	elif x1 <= 1.1e-48:
		tmp = x1 + ((x1 + (x2 * ((x1 * -12.0) + (8.0 * (x1 * x2))))) + ((x2 * -6.0) + (x1 * -3.0)))
	else:
		tmp = x1 + (x1 * (((4.0 * (x2 * ((2.0 * x2) - 3.0))) + (x1 * 9.0)) - 2.0))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -3.1e+141)
		tmp = Float64(x1 + Float64(x1 + Float64(3.0 * Float64(x1 * Float64(Float64(x1 * 3.0) + -1.0)))));
	elseif (x1 <= 1.1e-48)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(x2 * Float64(Float64(x1 * -12.0) + Float64(8.0 * Float64(x1 * x2))))) + Float64(Float64(x2 * -6.0) + Float64(x1 * -3.0))));
	else
		tmp = Float64(x1 + Float64(x1 * Float64(Float64(Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0))) + Float64(x1 * 9.0)) - 2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -3.1e+141)
		tmp = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	elseif (x1 <= 1.1e-48)
		tmp = x1 + ((x1 + (x2 * ((x1 * -12.0) + (8.0 * (x1 * x2))))) + ((x2 * -6.0) + (x1 * -3.0)));
	else
		tmp = x1 + (x1 * (((4.0 * (x2 * ((2.0 * x2) - 3.0))) + (x1 * 9.0)) - 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -3.1e+141], N[(x1 + N[(x1 + N[(3.0 * N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.1e-48], N[(x1 + N[(N[(x1 + N[(x2 * N[(N[(x1 * -12.0), $MachinePrecision] + N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(x1 * N[(N[(N[(4.0 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -3.10000000000000004e141

   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 64.1%

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

   5. Taylor expanded in x2 around 0 100.0%

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

   if -3.10000000000000004e141 < x1 < 1.10000000000000006e-48

   1. Initial program 95.9%

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

   3. Taylor expanded in x1 around 0 70.7%

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

   4. Taylor expanded in x1 around 0 69.3%

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

   5. Taylor expanded in x2 around 0 78.3%

      \[\leadsto x1 + \left(\left(\color{blue}{x2 \cdot \left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right)} + x1\right) + 3 \cdot \left(-2 \cdot x2 + x1 \cdot \left(x1 \cdot \left(3 - -2 \cdot x2\right) - 1\right)\right)\right) \]

   6. Taylor expanded in x1 around 0 79.9%

      \[\leadsto x1 + \left(\left(x2 \cdot \left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) + x1\right) + \color{blue}{\left(-6 \cdot x2 + -3 \cdot x1\right)}\right) \]

   if 1.10000000000000006e-48 < x1

   1. Initial program 59.3%

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

   3. Taylor expanded in x1 around 0 28.3%

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

   4. Taylor expanded in x1 around 0 53.8%

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

   5. Taylor expanded in x2 around 0 69.0%

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

   6. Taylor expanded in x1 around 0 69.2%

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

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -3.1 \cdot 10^{+141}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.1 \cdot 10^{-48}:\\ \;\;\;\;x1 + \left(\left(x1 + x2 \cdot \left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right)\right) + \left(x2 \cdot -6 + x1 \cdot -3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot 9\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 73.9% accurate, 4.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -9.5 \cdot 10^{+144}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.1 \cdot 10^{-48}:\\ \;\;\;\;x1 - \left(x1 \cdot \left(2 - x2 \cdot \left(x2 \cdot 8 - 12\right)\right) - x2 \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot 9\right) - 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -9.5e+144)
   (+ x1 (+ x1 (* 3.0 (* x1 (+ (* x1 3.0) -1.0)))))
   (if (<= x1 1.1e-48)
     (- x1 (- (* x1 (- 2.0 (* x2 (- (* x2 8.0) 12.0)))) (* x2 -6.0)))
     (+ x1 (* x1 (- (+ (* 4.0 (* x2 (- (* 2.0 x2) 3.0))) (* x1 9.0)) 2.0))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -9.5e+144) {
		tmp = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	} else if (x1 <= 1.1e-48) {
		tmp = x1 - ((x1 * (2.0 - (x2 * ((x2 * 8.0) - 12.0)))) - (x2 * -6.0));
	} else {
		tmp = x1 + (x1 * (((4.0 * (x2 * ((2.0 * x2) - 3.0))) + (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 (x1 <= (-9.5d+144)) then
        tmp = x1 + (x1 + (3.0d0 * (x1 * ((x1 * 3.0d0) + (-1.0d0)))))
    else if (x1 <= 1.1d-48) then
        tmp = x1 - ((x1 * (2.0d0 - (x2 * ((x2 * 8.0d0) - 12.0d0)))) - (x2 * (-6.0d0)))
    else
        tmp = x1 + (x1 * (((4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0))) + (x1 * 9.0d0)) - 2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= -9.5e+144) {
		tmp = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	} else if (x1 <= 1.1e-48) {
		tmp = x1 - ((x1 * (2.0 - (x2 * ((x2 * 8.0) - 12.0)))) - (x2 * -6.0));
	} else {
		tmp = x1 + (x1 * (((4.0 * (x2 * ((2.0 * x2) - 3.0))) + (x1 * 9.0)) - 2.0));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -9.5e+144:
		tmp = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))))
	elif x1 <= 1.1e-48:
		tmp = x1 - ((x1 * (2.0 - (x2 * ((x2 * 8.0) - 12.0)))) - (x2 * -6.0))
	else:
		tmp = x1 + (x1 * (((4.0 * (x2 * ((2.0 * x2) - 3.0))) + (x1 * 9.0)) - 2.0))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -9.5e+144)
		tmp = Float64(x1 + Float64(x1 + Float64(3.0 * Float64(x1 * Float64(Float64(x1 * 3.0) + -1.0)))));
	elseif (x1 <= 1.1e-48)
		tmp = Float64(x1 - Float64(Float64(x1 * Float64(2.0 - Float64(x2 * Float64(Float64(x2 * 8.0) - 12.0)))) - Float64(x2 * -6.0)));
	else
		tmp = Float64(x1 + Float64(x1 * Float64(Float64(Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0))) + Float64(x1 * 9.0)) - 2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -9.5e+144)
		tmp = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	elseif (x1 <= 1.1e-48)
		tmp = x1 - ((x1 * (2.0 - (x2 * ((x2 * 8.0) - 12.0)))) - (x2 * -6.0));
	else
		tmp = x1 + (x1 * (((4.0 * (x2 * ((2.0 * x2) - 3.0))) + (x1 * 9.0)) - 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -9.5e+144], N[(x1 + N[(x1 + N[(3.0 * N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.1e-48], N[(x1 - N[(N[(x1 * N[(2.0 - N[(x2 * N[(N[(x2 * 8.0), $MachinePrecision] - 12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(x1 * N[(N[(N[(4.0 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -9.50000000000000031e144

   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 64.1%

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

   5. Taylor expanded in x2 around 0 100.0%

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

   if -9.50000000000000031e144 < x1 < 1.10000000000000006e-48

   1. Initial program 95.9%

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

   3. Taylor expanded in x1 around 0 70.7%

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

   4. Taylor expanded in x1 around 0 69.3%

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

   5. Taylor expanded in x2 around 0 78.3%

      \[\leadsto x1 + \left(\left(\color{blue}{x2 \cdot \left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right)} + x1\right) + 3 \cdot \left(-2 \cdot x2 + x1 \cdot \left(x1 \cdot \left(3 - -2 \cdot x2\right) - 1\right)\right)\right) \]

   6. Taylor expanded in x1 around 0 71.1%

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

   if 1.10000000000000006e-48 < x1

   1. Initial program 59.3%

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

   3. Taylor expanded in x1 around 0 28.3%

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

   4. Taylor expanded in x1 around 0 53.8%

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

   5. Taylor expanded in x2 around 0 69.0%

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

   6. Taylor expanded in x1 around 0 69.2%

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

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -9.5 \cdot 10^{+144}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.1 \cdot 10^{-48}:\\ \;\;\;\;x1 - \left(x1 \cdot \left(2 - x2 \cdot \left(x2 \cdot 8 - 12\right)\right) - x2 \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot 9\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 73.6% accurate, 4.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -3.8 \cdot 10^{+140} \lor \neg \left(x1 \leq 4.4 \cdot 10^{+153}\right):\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 - \left(x1 \cdot \left(2 - x2 \cdot \left(x2 \cdot 8 - 12\right)\right) - x2 \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x1 -3.8e+140) (not (<= x1 4.4e+153)))
   (+ x1 (+ x1 (* 3.0 (* x1 (+ (* x1 3.0) -1.0)))))
   (- x1 (- (* x1 (- 2.0 (* x2 (- (* x2 8.0) 12.0)))) (* x2 -6.0)))))

C

double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -3.8e+140) || !(x1 <= 4.4e+153)) {
		tmp = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	} else {
		tmp = x1 - ((x1 * (2.0 - (x2 * ((x2 * 8.0) - 12.0)))) - (x2 * -6.0));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if ((x1 <= (-3.8d+140)) .or. (.not. (x1 <= 4.4d+153))) then
        tmp = x1 + (x1 + (3.0d0 * (x1 * ((x1 * 3.0d0) + (-1.0d0)))))
    else
        tmp = x1 - ((x1 * (2.0d0 - (x2 * ((x2 * 8.0d0) - 12.0d0)))) - (x2 * (-6.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -3.8e+140) || !(x1 <= 4.4e+153)) {
		tmp = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	} else {
		tmp = x1 - ((x1 * (2.0 - (x2 * ((x2 * 8.0) - 12.0)))) - (x2 * -6.0));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x1 <= -3.8e+140) or not (x1 <= 4.4e+153):
		tmp = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))))
	else:
		tmp = x1 - ((x1 * (2.0 - (x2 * ((x2 * 8.0) - 12.0)))) - (x2 * -6.0))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x1 <= -3.8e+140) || !(x1 <= 4.4e+153))
		tmp = Float64(x1 + Float64(x1 + Float64(3.0 * Float64(x1 * Float64(Float64(x1 * 3.0) + -1.0)))));
	else
		tmp = Float64(x1 - Float64(Float64(x1 * Float64(2.0 - Float64(x2 * Float64(Float64(x2 * 8.0) - 12.0)))) - Float64(x2 * -6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x1 <= -3.8e+140) || ~((x1 <= 4.4e+153)))
		tmp = x1 + (x1 + (3.0 * (x1 * ((x1 * 3.0) + -1.0))));
	else
		tmp = x1 - ((x1 * (2.0 - (x2 * ((x2 * 8.0) - 12.0)))) - (x2 * -6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x1, -3.8e+140], N[Not[LessEqual[x1, 4.4e+153]], $MachinePrecision]], N[(x1 + N[(x1 + N[(3.0 * N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 - N[(N[(x1 * N[(2.0 - N[(x2 * N[(N[(x2 * 8.0), $MachinePrecision] - 12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x1 < -3.8000000000000001e140 or 4.3999999999999999e153 < x1

   1. Initial program 0.0%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   2. 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 69.1%

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

   5. Taylor expanded in x2 around 0 100.0%

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

   if -3.8000000000000001e140 < x1 < 4.3999999999999999e153

   1. Initial program 96.6%

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

   3. Taylor expanded in x1 around 0 65.4%

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

   4. Taylor expanded in x1 around 0 62.4%

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

   5. Taylor expanded in x2 around 0 69.3%

      \[\leadsto x1 + \left(\left(\color{blue}{x2 \cdot \left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right)} + x1\right) + 3 \cdot \left(-2 \cdot x2 + x1 \cdot \left(x1 \cdot \left(3 - -2 \cdot x2\right) - 1\right)\right)\right) \]

   6. Taylor expanded in x1 around 0 65.0%

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

4. Final simplification 74.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -3.8 \cdot 10^{+140} \lor \neg \left(x1 \leq 4.4 \cdot 10^{+153}\right):\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3 + -1\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 - \left(x1 \cdot \left(2 - x2 \cdot \left(x2 \cdot 8 - 12\right)\right) - x2 \cdot -6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 37.3% accurate, 5.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x2 \leq -5.5 \cdot 10^{+88} \lor \neg \left(x2 \leq 4.2 \cdot 10^{+136}\right):\\ \;\;\;\;x1 - x1 \cdot \left(-1 - x2 \cdot \left(x2 \cdot 8 - 12\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x2 \cdot -6\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x2 -5.5e+88) (not (<= x2 4.2e+136)))
   (- x1 (* x1 (- -1.0 (* x2 (- (* x2 8.0) 12.0)))))
   (+ x1 (* x2 -6.0))))

C

double code(double x1, double x2) {
	double tmp;
	if ((x2 <= -5.5e+88) || !(x2 <= 4.2e+136)) {
		tmp = x1 - (x1 * (-1.0 - (x2 * ((x2 * 8.0) - 12.0))));
	} else {
		tmp = x1 + (x2 * -6.0);
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if ((x2 <= (-5.5d+88)) .or. (.not. (x2 <= 4.2d+136))) then
        tmp = x1 - (x1 * ((-1.0d0) - (x2 * ((x2 * 8.0d0) - 12.0d0))))
    else
        tmp = x1 + (x2 * (-6.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x2 <= -5.5e+88) || !(x2 <= 4.2e+136)) {
		tmp = x1 - (x1 * (-1.0 - (x2 * ((x2 * 8.0) - 12.0))));
	} else {
		tmp = x1 + (x2 * -6.0);
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x2 <= -5.5e+88) or not (x2 <= 4.2e+136):
		tmp = x1 - (x1 * (-1.0 - (x2 * ((x2 * 8.0) - 12.0))))
	else:
		tmp = x1 + (x2 * -6.0)
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x2 <= -5.5e+88) || !(x2 <= 4.2e+136))
		tmp = Float64(x1 - Float64(x1 * Float64(-1.0 - Float64(x2 * Float64(Float64(x2 * 8.0) - 12.0)))));
	else
		tmp = Float64(x1 + Float64(x2 * -6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x2 <= -5.5e+88) || ~((x2 <= 4.2e+136)))
		tmp = x1 - (x1 * (-1.0 - (x2 * ((x2 * 8.0) - 12.0))));
	else
		tmp = x1 + (x2 * -6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x2, -5.5e+88], N[Not[LessEqual[x2, 4.2e+136]], $MachinePrecision]], N[(x1 - N[(x1 * N[(-1.0 - N[(x2 * N[(N[(x2 * 8.0), $MachinePrecision] - 12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x2 < -5.5e88 or 4.1999999999999998e136 < x2

   1. Initial program 76.0%

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

   3. Taylor expanded in x1 around 0 51.1%

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

   4. Taylor expanded in x1 around inf 64.6%

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

   5. Taylor expanded in x2 around 0 64.6%

      \[\leadsto x1 + x1 \cdot \left(1 + \color{blue}{x2 \cdot \left(8 \cdot x2 - 12\right)}\right) \]

   if -5.5e88 < x2 < 4.1999999999999998e136

   1. Initial program 69.2%

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

   3. Taylor expanded in x1 around 0 46.9%

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

   4. Taylor expanded in x1 around 0 70.4%

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

   5. Taylor expanded in x1 around 0 30.6%

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

      1. *-commutative 30.6%

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

   7. Simplified 30.6%

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

4. Final simplification 39.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq -5.5 \cdot 10^{+88} \lor \neg \left(x2 \leq 4.2 \cdot 10^{+136}\right):\\ \;\;\;\;x1 - x1 \cdot \left(-1 - x2 \cdot \left(x2 \cdot 8 - 12\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x2 \cdot -6\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 32.1% accurate, 6.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -9.2 \cdot 10^{+33} \lor \neg \left(x1 \leq 6 \cdot 10^{+57}\right):\\ \;\;\;\;x1 + x1 \cdot \left(1 + x2 \cdot -12\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x2 \cdot -6\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x1 -9.2e+33) (not (<= x1 6e+57)))
   (+ x1 (* x1 (+ 1.0 (* x2 -12.0))))
   (+ x1 (* x2 -6.0))))

C

double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -9.2e+33) || !(x1 <= 6e+57)) {
		tmp = x1 + (x1 * (1.0 + (x2 * -12.0)));
	} else {
		tmp = x1 + (x2 * -6.0);
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if ((x1 <= (-9.2d+33)) .or. (.not. (x1 <= 6d+57))) then
        tmp = x1 + (x1 * (1.0d0 + (x2 * (-12.0d0))))
    else
        tmp = x1 + (x2 * (-6.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -9.2e+33) || !(x1 <= 6e+57)) {
		tmp = x1 + (x1 * (1.0 + (x2 * -12.0)));
	} else {
		tmp = x1 + (x2 * -6.0);
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x1 <= -9.2e+33) or not (x1 <= 6e+57):
		tmp = x1 + (x1 * (1.0 + (x2 * -12.0)))
	else:
		tmp = x1 + (x2 * -6.0)
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x1 <= -9.2e+33) || !(x1 <= 6e+57))
		tmp = Float64(x1 + Float64(x1 * Float64(1.0 + Float64(x2 * -12.0))));
	else
		tmp = Float64(x1 + Float64(x2 * -6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x1 <= -9.2e+33) || ~((x1 <= 6e+57)))
		tmp = x1 + (x1 * (1.0 + (x2 * -12.0)));
	else
		tmp = x1 + (x2 * -6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x1, -9.2e+33], N[Not[LessEqual[x1, 6e+57]], $MachinePrecision]], N[(x1 + N[(x1 * N[(1.0 + N[(x2 * -12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x1 < -9.20000000000000042e33 or 5.9999999999999999e57 < x1

   1. Initial program 37.9%

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

   3. Taylor expanded in x1 around 0 10.9%

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

   4. Taylor expanded in x1 around inf 22.9%

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

   5. Taylor expanded in x2 around 0 12.9%

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

      1. *-commutative 12.9%

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

   7. Simplified 12.9%

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

   if -9.20000000000000042e33 < x1 < 5.9999999999999999e57

   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 0 79.8%

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

   4. Taylor expanded in x1 around 0 78.5%

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

   5. Taylor expanded in x1 around 0 44.3%

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

      1. *-commutative 44.3%

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

   7. Simplified 44.3%

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

4. Final simplification 29.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -9.2 \cdot 10^{+33} \lor \neg \left(x1 \leq 6 \cdot 10^{+57}\right):\\ \;\;\;\;x1 + x1 \cdot \left(1 + x2 \cdot -12\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x2 \cdot -6\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 26.3% 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 71.0%

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

3. Taylor expanded in x1 around 0 48.0%

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

4. Taylor expanded in x1 around 0 64.2%

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

5. Taylor expanded in x1 around 0 25.2%

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

   1. *-commutative 25.2%

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

7. Simplified 25.2%

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

Alternative 27: 3.3% accurate, 42.3× speedup

Math

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

FPCore

(FPCore (x1 x2) :precision binary64 (+ x1 x1))

C

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

Fortran

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

Java

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

Python

def code(x1, x2):
	return x1 + x1

Julia

function code(x1, x2)
	return Float64(x1 + x1)
end

MATLAB

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

Wolfram

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

Derivation

1. Initial program 71.0%

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

3. Taylor expanded in x1 around 0 48.0%

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

4. Taylor expanded in x1 around inf 21.9%

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

5. Taylor expanded in x2 around 0 3.4%

   \[\leadsto x1 + \color{blue}{x1} \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024129 
(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))))))