Rosa's FloatVsDoubleBenchmark

Percentage Accurate: 69.9% → 99.4%

Time: 58.5s

Alternatives: 17

Speedup: 3.3×

• 47.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 69.9% 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

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 99.4%

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

   3. Simplified 99.4%

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

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

   1. Initial program 0.0%

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

   3. Simplified 17.9%

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

   5. Taylor expanded in x1 around inf 17.9%

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

   6. Taylor expanded in x1 around inf 17.9%

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

   7. Taylor expanded in x1 around 0 100.0%

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

      1. *-commutative 100.0%

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

   9. Simplified 100.0%

      \[\leadsto \left(\left(x1 + \color{blue}{x2 \cdot -6}\right) + x1 \cdot \left(9 \cdot x1 - 3\right)\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(x1 \cdot \left(6 \cdot x1 - 4\right) + x1\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.6%

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

Alternative 2: 99.4% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 99.4%

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

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

   1. Initial program 0.0%

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

   3. Simplified 17.9%

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

   5. Taylor expanded in x1 around inf 17.9%

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

   6. Taylor expanded in x1 around inf 17.9%

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

   7. Taylor expanded in x1 around 0 100.0%

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

      1. *-commutative 100.0%

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

   9. Simplified 100.0%

      \[\leadsto \left(\left(x1 + \color{blue}{x2 \cdot -6}\right) + x1 \cdot \left(9 \cdot x1 - 3\right)\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(x1 \cdot \left(6 \cdot x1 - 4\right) + x1\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.6%

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

Alternative 3: 97.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := \left(\left(x1 + x2 \cdot -6\right) + x1 \cdot \left(x1 \cdot 9 - 3\right)\right) + t\_0 \cdot \left(x1 + x1 \cdot \left(x1 \cdot 6 - 4\right)\right)\\ t_2 := \frac{2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)}{t\_0}\\ t_3 := t\_0 \cdot \left(x1 + x1 \cdot \left(2 \cdot \left(t\_2 \cdot \left(-3 + t\_2\right)\right) + x1 \cdot \left(-6 + 4 \cdot t\_2\right)\right)\right)\\ \mathbf{if}\;x1 \leq -1 \cdot 10^{+154}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x1 \leq -7.9 \cdot 10^{-25}:\\ \;\;\;\;\left(x2 \cdot -6 + \left(3 \cdot \left(2 \cdot x2\right) + -9\right)\right) + t\_3\\ \mathbf{elif}\;x1 \leq 6 \cdot 10^{-8}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{t\_0} + \left(x1 + 4 \cdot \left(\left(x1 \cdot x2\right) \cdot \left(2 \cdot x2 + -3\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+81}:\\ \;\;\;\;t\_3 + \left(\left(x1 + \left(9 - \frac{3}{x1}\right)\right) + x1 \cdot \left(\left(x1 \cdot 9 + 3 \cdot \frac{2 \cdot x2 - 3}{x1}\right) - 3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ (* x1 x1) 1.0))
        (t_1
         (+
          (+ (+ x1 (* x2 -6.0)) (* x1 (- (* x1 9.0) 3.0)))
          (* t_0 (+ x1 (* x1 (- (* x1 6.0) 4.0))))))
        (t_2 (/ (+ (* 2.0 x2) (* x1 (+ (* x1 3.0) -1.0))) t_0))
        (t_3
         (*
          t_0
          (+
           x1
           (*
            x1
            (+ (* 2.0 (* t_2 (+ -3.0 t_2))) (* x1 (+ -6.0 (* 4.0 t_2)))))))))
   (if (<= x1 -1e+154)
     t_1
     (if (<= x1 -7.9e-25)
       (+ (+ (* x2 -6.0) (+ (* 3.0 (* 2.0 x2)) -9.0)) t_3)
       (if (<= x1 6e-8)
         (+
          x1
          (+
           (* 3.0 (/ (- (- (* x1 (* x1 3.0)) (* 2.0 x2)) x1) t_0))
           (+ x1 (* 4.0 (* (* x1 x2) (+ (* 2.0 x2) -3.0))))))
         (if (<= x1 5e+81)
           (+
            t_3
            (+
             (+ x1 (- 9.0 (/ 3.0 x1)))
             (* x1 (- (+ (* x1 9.0) (* 3.0 (/ (- (* 2.0 x2) 3.0) x1))) 3.0))))
           t_1))))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = ((x1 + (x2 * -6.0)) + (x1 * ((x1 * 9.0) - 3.0))) + (t_0 * (x1 + (x1 * ((x1 * 6.0) - 4.0))));
	double t_2 = ((2.0 * x2) + (x1 * ((x1 * 3.0) + -1.0))) / t_0;
	double t_3 = t_0 * (x1 + (x1 * ((2.0 * (t_2 * (-3.0 + t_2))) + (x1 * (-6.0 + (4.0 * t_2))))));
	double tmp;
	if (x1 <= -1e+154) {
		tmp = t_1;
	} else if (x1 <= -7.9e-25) {
		tmp = ((x2 * -6.0) + ((3.0 * (2.0 * x2)) + -9.0)) + t_3;
	} else if (x1 <= 6e-8) {
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / t_0)) + (x1 + (4.0 * ((x1 * x2) * ((2.0 * x2) + -3.0)))));
	} else if (x1 <= 5e+81) {
		tmp = t_3 + ((x1 + (9.0 - (3.0 / x1))) + (x1 * (((x1 * 9.0) + (3.0 * (((2.0 * x2) - 3.0) / x1))) - 3.0)));
	} 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) :: tmp
    t_0 = (x1 * x1) + 1.0d0
    t_1 = ((x1 + (x2 * (-6.0d0))) + (x1 * ((x1 * 9.0d0) - 3.0d0))) + (t_0 * (x1 + (x1 * ((x1 * 6.0d0) - 4.0d0))))
    t_2 = ((2.0d0 * x2) + (x1 * ((x1 * 3.0d0) + (-1.0d0)))) / t_0
    t_3 = t_0 * (x1 + (x1 * ((2.0d0 * (t_2 * ((-3.0d0) + t_2))) + (x1 * ((-6.0d0) + (4.0d0 * t_2))))))
    if (x1 <= (-1d+154)) then
        tmp = t_1
    else if (x1 <= (-7.9d-25)) then
        tmp = ((x2 * (-6.0d0)) + ((3.0d0 * (2.0d0 * x2)) + (-9.0d0))) + t_3
    else if (x1 <= 6d-8) then
        tmp = x1 + ((3.0d0 * ((((x1 * (x1 * 3.0d0)) - (2.0d0 * x2)) - x1) / t_0)) + (x1 + (4.0d0 * ((x1 * x2) * ((2.0d0 * x2) + (-3.0d0))))))
    else if (x1 <= 5d+81) then
        tmp = t_3 + ((x1 + (9.0d0 - (3.0d0 / x1))) + (x1 * (((x1 * 9.0d0) + (3.0d0 * (((2.0d0 * x2) - 3.0d0) / x1))) - 3.0d0)))
    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 + (x2 * -6.0)) + (x1 * ((x1 * 9.0) - 3.0))) + (t_0 * (x1 + (x1 * ((x1 * 6.0) - 4.0))));
	double t_2 = ((2.0 * x2) + (x1 * ((x1 * 3.0) + -1.0))) / t_0;
	double t_3 = t_0 * (x1 + (x1 * ((2.0 * (t_2 * (-3.0 + t_2))) + (x1 * (-6.0 + (4.0 * t_2))))));
	double tmp;
	if (x1 <= -1e+154) {
		tmp = t_1;
	} else if (x1 <= -7.9e-25) {
		tmp = ((x2 * -6.0) + ((3.0 * (2.0 * x2)) + -9.0)) + t_3;
	} else if (x1 <= 6e-8) {
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / t_0)) + (x1 + (4.0 * ((x1 * x2) * ((2.0 * x2) + -3.0)))));
	} else if (x1 <= 5e+81) {
		tmp = t_3 + ((x1 + (9.0 - (3.0 / x1))) + (x1 * (((x1 * 9.0) + (3.0 * (((2.0 * x2) - 3.0) / x1))) - 3.0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x1 * x1) + 1.0
	t_1 = ((x1 + (x2 * -6.0)) + (x1 * ((x1 * 9.0) - 3.0))) + (t_0 * (x1 + (x1 * ((x1 * 6.0) - 4.0))))
	t_2 = ((2.0 * x2) + (x1 * ((x1 * 3.0) + -1.0))) / t_0
	t_3 = t_0 * (x1 + (x1 * ((2.0 * (t_2 * (-3.0 + t_2))) + (x1 * (-6.0 + (4.0 * t_2))))))
	tmp = 0
	if x1 <= -1e+154:
		tmp = t_1
	elif x1 <= -7.9e-25:
		tmp = ((x2 * -6.0) + ((3.0 * (2.0 * x2)) + -9.0)) + t_3
	elif x1 <= 6e-8:
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / t_0)) + (x1 + (4.0 * ((x1 * x2) * ((2.0 * x2) + -3.0)))))
	elif x1 <= 5e+81:
		tmp = t_3 + ((x1 + (9.0 - (3.0 / x1))) + (x1 * (((x1 * 9.0) + (3.0 * (((2.0 * x2) - 3.0) / x1))) - 3.0)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * x1) + 1.0)
	t_1 = Float64(Float64(Float64(x1 + Float64(x2 * -6.0)) + Float64(x1 * Float64(Float64(x1 * 9.0) - 3.0))) + Float64(t_0 * Float64(x1 + Float64(x1 * Float64(Float64(x1 * 6.0) - 4.0)))))
	t_2 = Float64(Float64(Float64(2.0 * x2) + Float64(x1 * Float64(Float64(x1 * 3.0) + -1.0))) / t_0)
	t_3 = Float64(t_0 * Float64(x1 + Float64(x1 * Float64(Float64(2.0 * Float64(t_2 * Float64(-3.0 + t_2))) + Float64(x1 * Float64(-6.0 + Float64(4.0 * t_2)))))))
	tmp = 0.0
	if (x1 <= -1e+154)
		tmp = t_1;
	elseif (x1 <= -7.9e-25)
		tmp = Float64(Float64(Float64(x2 * -6.0) + Float64(Float64(3.0 * Float64(2.0 * x2)) + -9.0)) + t_3);
	elseif (x1 <= 6e-8)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(Float64(x1 * Float64(x1 * 3.0)) - Float64(2.0 * x2)) - x1) / t_0)) + Float64(x1 + Float64(4.0 * Float64(Float64(x1 * x2) * Float64(Float64(2.0 * x2) + -3.0))))));
	elseif (x1 <= 5e+81)
		tmp = Float64(t_3 + Float64(Float64(x1 + Float64(9.0 - Float64(3.0 / x1))) + Float64(x1 * Float64(Float64(Float64(x1 * 9.0) + Float64(3.0 * Float64(Float64(Float64(2.0 * x2) - 3.0) / x1))) - 3.0))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x1 * x1) + 1.0;
	t_1 = ((x1 + (x2 * -6.0)) + (x1 * ((x1 * 9.0) - 3.0))) + (t_0 * (x1 + (x1 * ((x1 * 6.0) - 4.0))));
	t_2 = ((2.0 * x2) + (x1 * ((x1 * 3.0) + -1.0))) / t_0;
	t_3 = t_0 * (x1 + (x1 * ((2.0 * (t_2 * (-3.0 + t_2))) + (x1 * (-6.0 + (4.0 * t_2))))));
	tmp = 0.0;
	if (x1 <= -1e+154)
		tmp = t_1;
	elseif (x1 <= -7.9e-25)
		tmp = ((x2 * -6.0) + ((3.0 * (2.0 * x2)) + -9.0)) + t_3;
	elseif (x1 <= 6e-8)
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / t_0)) + (x1 + (4.0 * ((x1 * x2) * ((2.0 * x2) + -3.0)))));
	elseif (x1 <= 5e+81)
		tmp = t_3 + ((x1 + (9.0 - (3.0 / x1))) + (x1 * (((x1 * 9.0) + (3.0 * (((2.0 * x2) - 3.0) / x1))) - 3.0)));
	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[(N[(N[(x1 + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$0 * N[(x1 + N[(x1 * N[(N[(x1 * 6.0), $MachinePrecision] - 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(2.0 * x2), $MachinePrecision] + N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$0), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$0 * N[(x1 + N[(x1 * N[(N[(2.0 * N[(t$95$2 * N[(-3.0 + t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(-6.0 + N[(4.0 * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -1e+154], t$95$1, If[LessEqual[x1, -7.9e-25], N[(N[(N[(x2 * -6.0), $MachinePrecision] + N[(N[(3.0 * N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] + -9.0), $MachinePrecision]), $MachinePrecision] + t$95$3), $MachinePrecision], If[LessEqual[x1, 6e-8], N[(x1 + N[(N[(3.0 * N[(N[(N[(N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision] - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(4.0 * N[(N[(x1 * x2), $MachinePrecision] * N[(N[(2.0 * x2), $MachinePrecision] + -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 5e+81], N[(t$95$3 + N[(N[(x1 + N[(9.0 - N[(3.0 / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(N[(N[(x1 * 9.0), $MachinePrecision] + N[(3.0 * N[(N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision] / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -1.00000000000000004e154 or 4.9999999999999998e81 < x1

   1. Initial program 17.9%

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

   3. Simplified 17.9%

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

   5. Taylor expanded in x1 around inf 17.9%

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

   6. Taylor expanded in x1 around inf 17.9%

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

   7. Taylor expanded in x1 around 0 100.0%

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

      1. *-commutative 100.0%

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

   9. Simplified 100.0%

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

   if -1.00000000000000004e154 < x1 < -7.8999999999999997e-25

   1. Initial program 58.4%

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

   3. Simplified 96.6%

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

   5. Taylor expanded in x1 around inf 99.6%

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

   6. Taylor expanded in x1 around 0 99.6%

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

      1. *-commutative 99.6%

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

      2. sub-neg 99.6%

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

      3. metadata-eval 99.6%

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

      4. distribute-lft-in 99.6%

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

      5. *-commutative 99.6%

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

      6. metadata-eval 99.6%

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

   8. Simplified 99.6%

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

   if -7.8999999999999997e-25 < x1 < 5.99999999999999946e-8

   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 88.2%

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

      1. associate-*r* 99.4%

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

      2. *-commutative 99.4%

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

      3. sub-neg 99.4%

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

      4. metadata-eval 99.4%

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

   5. Simplified 99.4%

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

   if 5.99999999999999946e-8 < x1 < 4.9999999999999998e81

   1. Initial program 99.4%

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

   3. Simplified 93.5%

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

   5. Taylor expanded in x1 around inf 98.2%

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

   6. Taylor expanded in x1 around inf 98.2%

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

      1. associate-*r/ 98.2%

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

      2. metadata-eval 98.2%

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

   8. Simplified 98.2%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1 \cdot 10^{+154}:\\ \;\;\;\;\left(\left(x1 + x2 \cdot -6\right) + x1 \cdot \left(x1 \cdot 9 - 3\right)\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(x1 + x1 \cdot \left(x1 \cdot 6 - 4\right)\right)\\ \mathbf{elif}\;x1 \leq -7.9 \cdot 10^{-25}:\\ \;\;\;\;\left(x2 \cdot -6 + \left(3 \cdot \left(2 \cdot x2\right) + -9\right)\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(x1 + x1 \cdot \left(2 \cdot \left(\frac{2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)}{x1 \cdot x1 + 1} \cdot \left(-3 + \frac{2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)}{x1 \cdot x1 + 1}\right)\right) + x1 \cdot \left(-6 + 4 \cdot \frac{2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)}{x1 \cdot x1 + 1}\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 6 \cdot 10^{-8}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + 4 \cdot \left(\left(x1 \cdot x2\right) \cdot \left(2 \cdot x2 + -3\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+81}:\\ \;\;\;\;\left(x1 \cdot x1 + 1\right) \cdot \left(x1 + x1 \cdot \left(2 \cdot \left(\frac{2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)}{x1 \cdot x1 + 1} \cdot \left(-3 + \frac{2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)}{x1 \cdot x1 + 1}\right)\right) + x1 \cdot \left(-6 + 4 \cdot \frac{2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)}{x1 \cdot x1 + 1}\right)\right)\right) + \left(\left(x1 + \left(9 - \frac{3}{x1}\right)\right) + x1 \cdot \left(\left(x1 \cdot 9 + 3 \cdot \frac{2 \cdot x2 - 3}{x1}\right) - 3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x1 + x2 \cdot -6\right) + x1 \cdot \left(x1 \cdot 9 - 3\right)\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(x1 + x1 \cdot \left(x1 \cdot 6 - 4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 97.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := x1 + x2 \cdot -6\\ t_2 := \left(t\_1 + x1 \cdot \left(x1 \cdot 9 - 3\right)\right) + t\_0 \cdot \left(x1 + x1 \cdot \left(x1 \cdot 6 - 4\right)\right)\\ t_3 := \frac{2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)}{t\_0}\\ t_4 := t\_0 \cdot \left(x1 + x1 \cdot \left(2 \cdot \left(t\_3 \cdot \left(-3 + t\_3\right)\right) + x1 \cdot \left(-6 + 4 \cdot t\_3\right)\right)\right)\\ \mathbf{if}\;x1 \leq -1 \cdot 10^{+154}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x1 \leq -7.9 \cdot 10^{-25}:\\ \;\;\;\;\left(x2 \cdot -6 + \left(3 \cdot \left(2 \cdot x2\right) + -9\right)\right) + t\_4\\ \mathbf{elif}\;x1 \leq 6 \cdot 10^{-8}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{t\_0} + \left(x1 + 4 \cdot \left(\left(x1 \cdot x2\right) \cdot \left(2 \cdot x2 + -3\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+79}:\\ \;\;\;\;t\_4 + \left(t\_1 + x1 \cdot \left(\left(x1 \cdot 9 + 3 \cdot \frac{2 \cdot x2 - 3}{x1}\right) - 3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ (* x1 x1) 1.0))
        (t_1 (+ x1 (* x2 -6.0)))
        (t_2
         (+
          (+ t_1 (* x1 (- (* x1 9.0) 3.0)))
          (* t_0 (+ x1 (* x1 (- (* x1 6.0) 4.0))))))
        (t_3 (/ (+ (* 2.0 x2) (* x1 (+ (* x1 3.0) -1.0))) t_0))
        (t_4
         (*
          t_0
          (+
           x1
           (*
            x1
            (+ (* 2.0 (* t_3 (+ -3.0 t_3))) (* x1 (+ -6.0 (* 4.0 t_3)))))))))
   (if (<= x1 -1e+154)
     t_2
     (if (<= x1 -7.9e-25)
       (+ (+ (* x2 -6.0) (+ (* 3.0 (* 2.0 x2)) -9.0)) t_4)
       (if (<= x1 6e-8)
         (+
          x1
          (+
           (* 3.0 (/ (- (- (* x1 (* x1 3.0)) (* 2.0 x2)) x1) t_0))
           (+ x1 (* 4.0 (* (* x1 x2) (+ (* 2.0 x2) -3.0))))))
         (if (<= x1 5e+79)
           (+
            t_4
            (+
             t_1
             (* x1 (- (+ (* x1 9.0) (* 3.0 (/ (- (* 2.0 x2) 3.0) x1))) 3.0))))
           t_2))))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = x1 + (x2 * -6.0);
	double t_2 = (t_1 + (x1 * ((x1 * 9.0) - 3.0))) + (t_0 * (x1 + (x1 * ((x1 * 6.0) - 4.0))));
	double t_3 = ((2.0 * x2) + (x1 * ((x1 * 3.0) + -1.0))) / t_0;
	double t_4 = t_0 * (x1 + (x1 * ((2.0 * (t_3 * (-3.0 + t_3))) + (x1 * (-6.0 + (4.0 * t_3))))));
	double tmp;
	if (x1 <= -1e+154) {
		tmp = t_2;
	} else if (x1 <= -7.9e-25) {
		tmp = ((x2 * -6.0) + ((3.0 * (2.0 * x2)) + -9.0)) + t_4;
	} else if (x1 <= 6e-8) {
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / t_0)) + (x1 + (4.0 * ((x1 * x2) * ((2.0 * x2) + -3.0)))));
	} else if (x1 <= 5e+79) {
		tmp = t_4 + (t_1 + (x1 * (((x1 * 9.0) + (3.0 * (((2.0 * x2) - 3.0) / x1))) - 3.0)));
	} 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) :: tmp
    t_0 = (x1 * x1) + 1.0d0
    t_1 = x1 + (x2 * (-6.0d0))
    t_2 = (t_1 + (x1 * ((x1 * 9.0d0) - 3.0d0))) + (t_0 * (x1 + (x1 * ((x1 * 6.0d0) - 4.0d0))))
    t_3 = ((2.0d0 * x2) + (x1 * ((x1 * 3.0d0) + (-1.0d0)))) / t_0
    t_4 = t_0 * (x1 + (x1 * ((2.0d0 * (t_3 * ((-3.0d0) + t_3))) + (x1 * ((-6.0d0) + (4.0d0 * t_3))))))
    if (x1 <= (-1d+154)) then
        tmp = t_2
    else if (x1 <= (-7.9d-25)) then
        tmp = ((x2 * (-6.0d0)) + ((3.0d0 * (2.0d0 * x2)) + (-9.0d0))) + t_4
    else if (x1 <= 6d-8) then
        tmp = x1 + ((3.0d0 * ((((x1 * (x1 * 3.0d0)) - (2.0d0 * x2)) - x1) / t_0)) + (x1 + (4.0d0 * ((x1 * x2) * ((2.0d0 * x2) + (-3.0d0))))))
    else if (x1 <= 5d+79) then
        tmp = t_4 + (t_1 + (x1 * (((x1 * 9.0d0) + (3.0d0 * (((2.0d0 * x2) - 3.0d0) / x1))) - 3.0d0)))
    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 + (x2 * -6.0);
	double t_2 = (t_1 + (x1 * ((x1 * 9.0) - 3.0))) + (t_0 * (x1 + (x1 * ((x1 * 6.0) - 4.0))));
	double t_3 = ((2.0 * x2) + (x1 * ((x1 * 3.0) + -1.0))) / t_0;
	double t_4 = t_0 * (x1 + (x1 * ((2.0 * (t_3 * (-3.0 + t_3))) + (x1 * (-6.0 + (4.0 * t_3))))));
	double tmp;
	if (x1 <= -1e+154) {
		tmp = t_2;
	} else if (x1 <= -7.9e-25) {
		tmp = ((x2 * -6.0) + ((3.0 * (2.0 * x2)) + -9.0)) + t_4;
	} else if (x1 <= 6e-8) {
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / t_0)) + (x1 + (4.0 * ((x1 * x2) * ((2.0 * x2) + -3.0)))));
	} else if (x1 <= 5e+79) {
		tmp = t_4 + (t_1 + (x1 * (((x1 * 9.0) + (3.0 * (((2.0 * x2) - 3.0) / x1))) - 3.0)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x1 * x1) + 1.0
	t_1 = x1 + (x2 * -6.0)
	t_2 = (t_1 + (x1 * ((x1 * 9.0) - 3.0))) + (t_0 * (x1 + (x1 * ((x1 * 6.0) - 4.0))))
	t_3 = ((2.0 * x2) + (x1 * ((x1 * 3.0) + -1.0))) / t_0
	t_4 = t_0 * (x1 + (x1 * ((2.0 * (t_3 * (-3.0 + t_3))) + (x1 * (-6.0 + (4.0 * t_3))))))
	tmp = 0
	if x1 <= -1e+154:
		tmp = t_2
	elif x1 <= -7.9e-25:
		tmp = ((x2 * -6.0) + ((3.0 * (2.0 * x2)) + -9.0)) + t_4
	elif x1 <= 6e-8:
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / t_0)) + (x1 + (4.0 * ((x1 * x2) * ((2.0 * x2) + -3.0)))))
	elif x1 <= 5e+79:
		tmp = t_4 + (t_1 + (x1 * (((x1 * 9.0) + (3.0 * (((2.0 * x2) - 3.0) / x1))) - 3.0)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * x1) + 1.0)
	t_1 = Float64(x1 + Float64(x2 * -6.0))
	t_2 = Float64(Float64(t_1 + Float64(x1 * Float64(Float64(x1 * 9.0) - 3.0))) + Float64(t_0 * Float64(x1 + Float64(x1 * Float64(Float64(x1 * 6.0) - 4.0)))))
	t_3 = Float64(Float64(Float64(2.0 * x2) + Float64(x1 * Float64(Float64(x1 * 3.0) + -1.0))) / t_0)
	t_4 = Float64(t_0 * Float64(x1 + Float64(x1 * Float64(Float64(2.0 * Float64(t_3 * Float64(-3.0 + t_3))) + Float64(x1 * Float64(-6.0 + Float64(4.0 * t_3)))))))
	tmp = 0.0
	if (x1 <= -1e+154)
		tmp = t_2;
	elseif (x1 <= -7.9e-25)
		tmp = Float64(Float64(Float64(x2 * -6.0) + Float64(Float64(3.0 * Float64(2.0 * x2)) + -9.0)) + t_4);
	elseif (x1 <= 6e-8)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(Float64(x1 * Float64(x1 * 3.0)) - Float64(2.0 * x2)) - x1) / t_0)) + Float64(x1 + Float64(4.0 * Float64(Float64(x1 * x2) * Float64(Float64(2.0 * x2) + -3.0))))));
	elseif (x1 <= 5e+79)
		tmp = Float64(t_4 + Float64(t_1 + Float64(x1 * Float64(Float64(Float64(x1 * 9.0) + Float64(3.0 * Float64(Float64(Float64(2.0 * x2) - 3.0) / x1))) - 3.0))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x1 * x1) + 1.0;
	t_1 = x1 + (x2 * -6.0);
	t_2 = (t_1 + (x1 * ((x1 * 9.0) - 3.0))) + (t_0 * (x1 + (x1 * ((x1 * 6.0) - 4.0))));
	t_3 = ((2.0 * x2) + (x1 * ((x1 * 3.0) + -1.0))) / t_0;
	t_4 = t_0 * (x1 + (x1 * ((2.0 * (t_3 * (-3.0 + t_3))) + (x1 * (-6.0 + (4.0 * t_3))))));
	tmp = 0.0;
	if (x1 <= -1e+154)
		tmp = t_2;
	elseif (x1 <= -7.9e-25)
		tmp = ((x2 * -6.0) + ((3.0 * (2.0 * x2)) + -9.0)) + t_4;
	elseif (x1 <= 6e-8)
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / t_0)) + (x1 + (4.0 * ((x1 * x2) * ((2.0 * x2) + -3.0)))));
	elseif (x1 <= 5e+79)
		tmp = t_4 + (t_1 + (x1 * (((x1 * 9.0) + (3.0 * (((2.0 * x2) - 3.0) / x1))) - 3.0)));
	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[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t$95$1 + N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$0 * N[(x1 + N[(x1 * N[(N[(x1 * 6.0), $MachinePrecision] - 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(2.0 * x2), $MachinePrecision] + N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$0), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$0 * N[(x1 + N[(x1 * N[(N[(2.0 * N[(t$95$3 * N[(-3.0 + t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(-6.0 + N[(4.0 * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -1e+154], t$95$2, If[LessEqual[x1, -7.9e-25], N[(N[(N[(x2 * -6.0), $MachinePrecision] + N[(N[(3.0 * N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] + -9.0), $MachinePrecision]), $MachinePrecision] + t$95$4), $MachinePrecision], If[LessEqual[x1, 6e-8], N[(x1 + N[(N[(3.0 * N[(N[(N[(N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision] - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(4.0 * N[(N[(x1 * x2), $MachinePrecision] * N[(N[(2.0 * x2), $MachinePrecision] + -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 5e+79], N[(t$95$4 + N[(t$95$1 + N[(x1 * N[(N[(N[(x1 * 9.0), $MachinePrecision] + N[(3.0 * N[(N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision] / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -1.00000000000000004e154 or 5e79 < x1

   1. Initial program 17.9%

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

   3. Simplified 17.9%

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

   5. Taylor expanded in x1 around inf 17.9%

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

   6. Taylor expanded in x1 around inf 17.9%

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

   7. Taylor expanded in x1 around 0 100.0%

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

      1. *-commutative 100.0%

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

   9. Simplified 100.0%

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

   if -1.00000000000000004e154 < x1 < -7.8999999999999997e-25

   1. Initial program 58.4%

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

   3. Simplified 96.6%

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

   5. Taylor expanded in x1 around inf 99.6%

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

   6. Taylor expanded in x1 around 0 99.6%

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

      1. *-commutative 99.6%

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

      2. sub-neg 99.6%

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

      3. metadata-eval 99.6%

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

      4. distribute-lft-in 99.6%

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

      5. *-commutative 99.6%

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

      6. metadata-eval 99.6%

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

   8. Simplified 99.6%

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

   if -7.8999999999999997e-25 < x1 < 5.99999999999999946e-8

   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 88.2%

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

      1. associate-*r* 99.4%

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

      2. *-commutative 99.4%

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

      3. sub-neg 99.4%

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

      4. metadata-eval 99.4%

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

   5. Simplified 99.4%

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

   if 5.99999999999999946e-8 < x1 < 5e79

   1. Initial program 99.4%

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

   3. Simplified 93.5%

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

   5. Taylor expanded in x1 around inf 98.2%

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

   6. Taylor expanded in x1 around 0 91.5%

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

      1. *-commutative 45.5%

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

   8. Simplified 91.5%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1 \cdot 10^{+154}:\\ \;\;\;\;\left(\left(x1 + x2 \cdot -6\right) + x1 \cdot \left(x1 \cdot 9 - 3\right)\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(x1 + x1 \cdot \left(x1 \cdot 6 - 4\right)\right)\\ \mathbf{elif}\;x1 \leq -7.9 \cdot 10^{-25}:\\ \;\;\;\;\left(x2 \cdot -6 + \left(3 \cdot \left(2 \cdot x2\right) + -9\right)\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(x1 + x1 \cdot \left(2 \cdot \left(\frac{2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)}{x1 \cdot x1 + 1} \cdot \left(-3 + \frac{2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)}{x1 \cdot x1 + 1}\right)\right) + x1 \cdot \left(-6 + 4 \cdot \frac{2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)}{x1 \cdot x1 + 1}\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 6 \cdot 10^{-8}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + 4 \cdot \left(\left(x1 \cdot x2\right) \cdot \left(2 \cdot x2 + -3\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+79}:\\ \;\;\;\;\left(x1 \cdot x1 + 1\right) \cdot \left(x1 + x1 \cdot \left(2 \cdot \left(\frac{2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)}{x1 \cdot x1 + 1} \cdot \left(-3 + \frac{2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)}{x1 \cdot x1 + 1}\right)\right) + x1 \cdot \left(-6 + 4 \cdot \frac{2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)}{x1 \cdot x1 + 1}\right)\right)\right) + \left(\left(x1 + x2 \cdot -6\right) + x1 \cdot \left(\left(x1 \cdot 9 + 3 \cdot \frac{2 \cdot x2 - 3}{x1}\right) - 3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x1 + x2 \cdot -6\right) + x1 \cdot \left(x1 \cdot 9 - 3\right)\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(x1 + x1 \cdot \left(x1 \cdot 6 - 4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 97.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := \left(\left(x1 + x2 \cdot -6\right) + x1 \cdot \left(x1 \cdot 9 - 3\right)\right) + t\_0 \cdot \left(x1 + x1 \cdot \left(x1 \cdot 6 - 4\right)\right)\\ t_2 := \frac{2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)}{t\_0}\\ t_3 := \left(x2 \cdot -6 + \left(3 \cdot \left(2 \cdot x2\right) + -9\right)\right) + t\_0 \cdot \left(x1 + x1 \cdot \left(2 \cdot \left(t\_2 \cdot \left(-3 + t\_2\right)\right) + x1 \cdot \left(-6 + 4 \cdot t\_2\right)\right)\right)\\ \mathbf{if}\;x1 \leq -1 \cdot 10^{+154}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x1 \leq -7.9 \cdot 10^{-25}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x1 \leq 6 \cdot 10^{-8}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{t\_0} + \left(x1 + 4 \cdot \left(\left(x1 \cdot x2\right) \cdot \left(2 \cdot x2 + -3\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 3 \cdot 10^{+83}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ (* x1 x1) 1.0))
        (t_1
         (+
          (+ (+ x1 (* x2 -6.0)) (* x1 (- (* x1 9.0) 3.0)))
          (* t_0 (+ x1 (* x1 (- (* x1 6.0) 4.0))))))
        (t_2 (/ (+ (* 2.0 x2) (* x1 (+ (* x1 3.0) -1.0))) t_0))
        (t_3
         (+
          (+ (* x2 -6.0) (+ (* 3.0 (* 2.0 x2)) -9.0))
          (*
           t_0
           (+
            x1
            (*
             x1
             (+ (* 2.0 (* t_2 (+ -3.0 t_2))) (* x1 (+ -6.0 (* 4.0 t_2))))))))))
   (if (<= x1 -1e+154)
     t_1
     (if (<= x1 -7.9e-25)
       t_3
       (if (<= x1 6e-8)
         (+
          x1
          (+
           (* 3.0 (/ (- (- (* x1 (* x1 3.0)) (* 2.0 x2)) x1) t_0))
           (+ x1 (* 4.0 (* (* x1 x2) (+ (* 2.0 x2) -3.0))))))
         (if (<= x1 3e+83) t_3 t_1))))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = ((x1 + (x2 * -6.0)) + (x1 * ((x1 * 9.0) - 3.0))) + (t_0 * (x1 + (x1 * ((x1 * 6.0) - 4.0))));
	double t_2 = ((2.0 * x2) + (x1 * ((x1 * 3.0) + -1.0))) / t_0;
	double t_3 = ((x2 * -6.0) + ((3.0 * (2.0 * x2)) + -9.0)) + (t_0 * (x1 + (x1 * ((2.0 * (t_2 * (-3.0 + t_2))) + (x1 * (-6.0 + (4.0 * t_2)))))));
	double tmp;
	if (x1 <= -1e+154) {
		tmp = t_1;
	} else if (x1 <= -7.9e-25) {
		tmp = t_3;
	} else if (x1 <= 6e-8) {
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / t_0)) + (x1 + (4.0 * ((x1 * x2) * ((2.0 * x2) + -3.0)))));
	} else if (x1 <= 3e+83) {
		tmp = t_3;
	} 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) :: tmp
    t_0 = (x1 * x1) + 1.0d0
    t_1 = ((x1 + (x2 * (-6.0d0))) + (x1 * ((x1 * 9.0d0) - 3.0d0))) + (t_0 * (x1 + (x1 * ((x1 * 6.0d0) - 4.0d0))))
    t_2 = ((2.0d0 * x2) + (x1 * ((x1 * 3.0d0) + (-1.0d0)))) / t_0
    t_3 = ((x2 * (-6.0d0)) + ((3.0d0 * (2.0d0 * x2)) + (-9.0d0))) + (t_0 * (x1 + (x1 * ((2.0d0 * (t_2 * ((-3.0d0) + t_2))) + (x1 * ((-6.0d0) + (4.0d0 * t_2)))))))
    if (x1 <= (-1d+154)) then
        tmp = t_1
    else if (x1 <= (-7.9d-25)) then
        tmp = t_3
    else if (x1 <= 6d-8) then
        tmp = x1 + ((3.0d0 * ((((x1 * (x1 * 3.0d0)) - (2.0d0 * x2)) - x1) / t_0)) + (x1 + (4.0d0 * ((x1 * x2) * ((2.0d0 * x2) + (-3.0d0))))))
    else if (x1 <= 3d+83) then
        tmp = t_3
    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 + (x2 * -6.0)) + (x1 * ((x1 * 9.0) - 3.0))) + (t_0 * (x1 + (x1 * ((x1 * 6.0) - 4.0))));
	double t_2 = ((2.0 * x2) + (x1 * ((x1 * 3.0) + -1.0))) / t_0;
	double t_3 = ((x2 * -6.0) + ((3.0 * (2.0 * x2)) + -9.0)) + (t_0 * (x1 + (x1 * ((2.0 * (t_2 * (-3.0 + t_2))) + (x1 * (-6.0 + (4.0 * t_2)))))));
	double tmp;
	if (x1 <= -1e+154) {
		tmp = t_1;
	} else if (x1 <= -7.9e-25) {
		tmp = t_3;
	} else if (x1 <= 6e-8) {
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / t_0)) + (x1 + (4.0 * ((x1 * x2) * ((2.0 * x2) + -3.0)))));
	} else if (x1 <= 3e+83) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x1 * x1) + 1.0
	t_1 = ((x1 + (x2 * -6.0)) + (x1 * ((x1 * 9.0) - 3.0))) + (t_0 * (x1 + (x1 * ((x1 * 6.0) - 4.0))))
	t_2 = ((2.0 * x2) + (x1 * ((x1 * 3.0) + -1.0))) / t_0
	t_3 = ((x2 * -6.0) + ((3.0 * (2.0 * x2)) + -9.0)) + (t_0 * (x1 + (x1 * ((2.0 * (t_2 * (-3.0 + t_2))) + (x1 * (-6.0 + (4.0 * t_2)))))))
	tmp = 0
	if x1 <= -1e+154:
		tmp = t_1
	elif x1 <= -7.9e-25:
		tmp = t_3
	elif x1 <= 6e-8:
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / t_0)) + (x1 + (4.0 * ((x1 * x2) * ((2.0 * x2) + -3.0)))))
	elif x1 <= 3e+83:
		tmp = t_3
	else:
		tmp = t_1
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * x1) + 1.0)
	t_1 = Float64(Float64(Float64(x1 + Float64(x2 * -6.0)) + Float64(x1 * Float64(Float64(x1 * 9.0) - 3.0))) + Float64(t_0 * Float64(x1 + Float64(x1 * Float64(Float64(x1 * 6.0) - 4.0)))))
	t_2 = Float64(Float64(Float64(2.0 * x2) + Float64(x1 * Float64(Float64(x1 * 3.0) + -1.0))) / t_0)
	t_3 = Float64(Float64(Float64(x2 * -6.0) + Float64(Float64(3.0 * Float64(2.0 * x2)) + -9.0)) + Float64(t_0 * Float64(x1 + Float64(x1 * Float64(Float64(2.0 * Float64(t_2 * Float64(-3.0 + t_2))) + Float64(x1 * Float64(-6.0 + Float64(4.0 * t_2))))))))
	tmp = 0.0
	if (x1 <= -1e+154)
		tmp = t_1;
	elseif (x1 <= -7.9e-25)
		tmp = t_3;
	elseif (x1 <= 6e-8)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(Float64(x1 * Float64(x1 * 3.0)) - Float64(2.0 * x2)) - x1) / t_0)) + Float64(x1 + Float64(4.0 * Float64(Float64(x1 * x2) * Float64(Float64(2.0 * x2) + -3.0))))));
	elseif (x1 <= 3e+83)
		tmp = t_3;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x1 * x1) + 1.0;
	t_1 = ((x1 + (x2 * -6.0)) + (x1 * ((x1 * 9.0) - 3.0))) + (t_0 * (x1 + (x1 * ((x1 * 6.0) - 4.0))));
	t_2 = ((2.0 * x2) + (x1 * ((x1 * 3.0) + -1.0))) / t_0;
	t_3 = ((x2 * -6.0) + ((3.0 * (2.0 * x2)) + -9.0)) + (t_0 * (x1 + (x1 * ((2.0 * (t_2 * (-3.0 + t_2))) + (x1 * (-6.0 + (4.0 * t_2)))))));
	tmp = 0.0;
	if (x1 <= -1e+154)
		tmp = t_1;
	elseif (x1 <= -7.9e-25)
		tmp = t_3;
	elseif (x1 <= 6e-8)
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / t_0)) + (x1 + (4.0 * ((x1 * x2) * ((2.0 * x2) + -3.0)))));
	elseif (x1 <= 3e+83)
		tmp = t_3;
	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[(N[(N[(x1 + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$0 * N[(x1 + N[(x1 * N[(N[(x1 * 6.0), $MachinePrecision] - 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(2.0 * x2), $MachinePrecision] + N[(x1 * N[(N[(x1 * 3.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$0), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(x2 * -6.0), $MachinePrecision] + N[(N[(3.0 * N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] + -9.0), $MachinePrecision]), $MachinePrecision] + N[(t$95$0 * N[(x1 + N[(x1 * N[(N[(2.0 * N[(t$95$2 * N[(-3.0 + t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(-6.0 + N[(4.0 * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -1e+154], t$95$1, If[LessEqual[x1, -7.9e-25], t$95$3, If[LessEqual[x1, 6e-8], N[(x1 + N[(N[(3.0 * N[(N[(N[(N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision] - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(4.0 * N[(N[(x1 * x2), $MachinePrecision] * N[(N[(2.0 * x2), $MachinePrecision] + -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 3e+83], t$95$3, t$95$1]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -1.00000000000000004e154 or 3e83 < x1

   1. Initial program 17.9%

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

   3. Simplified 17.9%

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

   5. Taylor expanded in x1 around inf 17.9%

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

   6. Taylor expanded in x1 around inf 17.9%

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

   7. Taylor expanded in x1 around 0 100.0%

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

      1. *-commutative 100.0%

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

   9. Simplified 100.0%

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

   if -1.00000000000000004e154 < x1 < -7.8999999999999997e-25 or 5.99999999999999946e-8 < x1 < 3e83

   1. Initial program 72.0%

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

   3. Simplified 95.6%

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

   5. Taylor expanded in x1 around inf 99.1%

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

   6. Taylor expanded in x1 around 0 96.4%

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

      1. *-commutative 96.4%

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

      2. sub-neg 96.4%

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

      3. metadata-eval 96.4%

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

      4. distribute-lft-in 96.4%

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

      5. *-commutative 96.4%

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

      6. metadata-eval 96.4%

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

   8. Simplified 96.4%

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

   if -7.8999999999999997e-25 < x1 < 5.99999999999999946e-8

   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 88.2%

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

      1. associate-*r* 99.4%

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

      2. *-commutative 99.4%

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

      3. sub-neg 99.4%

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

      4. metadata-eval 99.4%

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

   5. Simplified 99.4%

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

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1 \cdot 10^{+154}:\\ \;\;\;\;\left(\left(x1 + x2 \cdot -6\right) + x1 \cdot \left(x1 \cdot 9 - 3\right)\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(x1 + x1 \cdot \left(x1 \cdot 6 - 4\right)\right)\\ \mathbf{elif}\;x1 \leq -7.9 \cdot 10^{-25}:\\ \;\;\;\;\left(x2 \cdot -6 + \left(3 \cdot \left(2 \cdot x2\right) + -9\right)\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(x1 + x1 \cdot \left(2 \cdot \left(\frac{2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)}{x1 \cdot x1 + 1} \cdot \left(-3 + \frac{2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)}{x1 \cdot x1 + 1}\right)\right) + x1 \cdot \left(-6 + 4 \cdot \frac{2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)}{x1 \cdot x1 + 1}\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 6 \cdot 10^{-8}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + 4 \cdot \left(\left(x1 \cdot x2\right) \cdot \left(2 \cdot x2 + -3\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 3 \cdot 10^{+83}:\\ \;\;\;\;\left(x2 \cdot -6 + \left(3 \cdot \left(2 \cdot x2\right) + -9\right)\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(x1 + x1 \cdot \left(2 \cdot \left(\frac{2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)}{x1 \cdot x1 + 1} \cdot \left(-3 + \frac{2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)}{x1 \cdot x1 + 1}\right)\right) + x1 \cdot \left(-6 + 4 \cdot \frac{2 \cdot x2 + x1 \cdot \left(x1 \cdot 3 + -1\right)}{x1 \cdot x1 + 1}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x1 + x2 \cdot -6\right) + x1 \cdot \left(x1 \cdot 9 - 3\right)\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(x1 + x1 \cdot \left(x1 \cdot 6 - 4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 93.8% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := t\_0 \cdot \left(x1 + x1 \cdot \left(x1 \cdot 6 - 4\right)\right)\\ t_2 := x1 \cdot \left(x1 \cdot 9 - 3\right)\\ \mathbf{if}\;x1 \leq -40000:\\ \;\;\;\;\left(\left(x1 + x2 \cdot -6\right) + t\_2\right) + t\_1\\ \mathbf{elif}\;x1 \leq 400000:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{t\_0} + \left(x1 + 4 \cdot \left(\left(x1 \cdot x2\right) \cdot \left(2 \cdot x2 + -3\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 + \left(t\_2 + \left(x1 + \left(x2 \cdot -6 + x1 \cdot -3\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ (* x1 x1) 1.0))
        (t_1 (* t_0 (+ x1 (* x1 (- (* x1 6.0) 4.0)))))
        (t_2 (* x1 (- (* x1 9.0) 3.0))))
   (if (<= x1 -40000.0)
     (+ (+ (+ x1 (* x2 -6.0)) t_2) t_1)
     (if (<= x1 400000.0)
       (+
        x1
        (+
         (* 3.0 (/ (- (- (* x1 (* x1 3.0)) (* 2.0 x2)) x1) t_0))
         (+ x1 (* 4.0 (* (* x1 x2) (+ (* 2.0 x2) -3.0))))))
       (+ t_1 (+ t_2 (+ x1 (+ (* x2 -6.0) (* x1 -3.0)))))))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = t_0 * (x1 + (x1 * ((x1 * 6.0) - 4.0)));
	double t_2 = x1 * ((x1 * 9.0) - 3.0);
	double tmp;
	if (x1 <= -40000.0) {
		tmp = ((x1 + (x2 * -6.0)) + t_2) + t_1;
	} else if (x1 <= 400000.0) {
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / t_0)) + (x1 + (4.0 * ((x1 * x2) * ((2.0 * x2) + -3.0)))));
	} else {
		tmp = t_1 + (t_2 + (x1 + ((x2 * -6.0) + (x1 * -3.0))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = (x1 * x1) + 1.0d0
    t_1 = t_0 * (x1 + (x1 * ((x1 * 6.0d0) - 4.0d0)))
    t_2 = x1 * ((x1 * 9.0d0) - 3.0d0)
    if (x1 <= (-40000.0d0)) then
        tmp = ((x1 + (x2 * (-6.0d0))) + t_2) + t_1
    else if (x1 <= 400000.0d0) then
        tmp = x1 + ((3.0d0 * ((((x1 * (x1 * 3.0d0)) - (2.0d0 * x2)) - x1) / t_0)) + (x1 + (4.0d0 * ((x1 * x2) * ((2.0d0 * x2) + (-3.0d0))))))
    else
        tmp = t_1 + (t_2 + (x1 + ((x2 * (-6.0d0)) + (x1 * (-3.0d0)))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = t_0 * (x1 + (x1 * ((x1 * 6.0) - 4.0)));
	double t_2 = x1 * ((x1 * 9.0) - 3.0);
	double tmp;
	if (x1 <= -40000.0) {
		tmp = ((x1 + (x2 * -6.0)) + t_2) + t_1;
	} else if (x1 <= 400000.0) {
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / t_0)) + (x1 + (4.0 * ((x1 * x2) * ((2.0 * x2) + -3.0)))));
	} else {
		tmp = t_1 + (t_2 + (x1 + ((x2 * -6.0) + (x1 * -3.0))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x1 * x1) + 1.0
	t_1 = t_0 * (x1 + (x1 * ((x1 * 6.0) - 4.0)))
	t_2 = x1 * ((x1 * 9.0) - 3.0)
	tmp = 0
	if x1 <= -40000.0:
		tmp = ((x1 + (x2 * -6.0)) + t_2) + t_1
	elif x1 <= 400000.0:
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / t_0)) + (x1 + (4.0 * ((x1 * x2) * ((2.0 * x2) + -3.0)))))
	else:
		tmp = t_1 + (t_2 + (x1 + ((x2 * -6.0) + (x1 * -3.0))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * x1) + 1.0)
	t_1 = Float64(t_0 * Float64(x1 + Float64(x1 * Float64(Float64(x1 * 6.0) - 4.0))))
	t_2 = Float64(x1 * Float64(Float64(x1 * 9.0) - 3.0))
	tmp = 0.0
	if (x1 <= -40000.0)
		tmp = Float64(Float64(Float64(x1 + Float64(x2 * -6.0)) + t_2) + t_1);
	elseif (x1 <= 400000.0)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(Float64(x1 * Float64(x1 * 3.0)) - Float64(2.0 * x2)) - x1) / t_0)) + Float64(x1 + Float64(4.0 * Float64(Float64(x1 * x2) * Float64(Float64(2.0 * x2) + -3.0))))));
	else
		tmp = Float64(t_1 + Float64(t_2 + Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * -3.0)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x1 * x1) + 1.0;
	t_1 = t_0 * (x1 + (x1 * ((x1 * 6.0) - 4.0)));
	t_2 = x1 * ((x1 * 9.0) - 3.0);
	tmp = 0.0;
	if (x1 <= -40000.0)
		tmp = ((x1 + (x2 * -6.0)) + t_2) + t_1;
	elseif (x1 <= 400000.0)
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / t_0)) + (x1 + (4.0 * ((x1 * x2) * ((2.0 * x2) + -3.0)))));
	else
		tmp = t_1 + (t_2 + (x1 + ((x2 * -6.0) + (x1 * -3.0))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$1 = N[(t$95$0 * N[(x1 + N[(x1 * N[(N[(x1 * 6.0), $MachinePrecision] - 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -40000.0], N[(N[(N[(x1 + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[x1, 400000.0], N[(x1 + N[(N[(3.0 * N[(N[(N[(N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision] - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(4.0 * N[(N[(x1 * x2), $MachinePrecision] * N[(N[(2.0 * x2), $MachinePrecision] + -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(t$95$2 + N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -4e4

   1. Initial program 27.5%

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

   3. Simplified 47.5%

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

   5. Taylor expanded in x1 around inf 49.0%

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

   6. Taylor expanded in x1 around inf 41.2%

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

   7. Taylor expanded in x1 around 0 92.1%

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

      1. *-commutative 92.1%

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

   9. Simplified 92.1%

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

   if -4e4 < x1 < 4e5

   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 87.9%

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

      1. associate-*r* 98.5%

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

      2. *-commutative 98.5%

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

      3. sub-neg 98.5%

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

      4. metadata-eval 98.5%

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

   5. Simplified 98.5%

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

   if 4e5 < x1

   1. Initial program 46.4%

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

   3. Simplified 44.7%

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

   5. Taylor expanded in x1 around inf 46.4%

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

   6. Taylor expanded in x1 around inf 36.8%

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

   7. Taylor expanded in x1 around 0 90.1%

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

      1. +-commutative 90.1%

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

      2. *-commutative 90.1%

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

      3. *-commutative 90.1%

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

   9. Simplified 90.1%

      \[\leadsto \left(\left(x1 + \color{blue}{\left(x1 \cdot -3 + x2 \cdot -6\right)}\right) + x1 \cdot \left(9 \cdot x1 - 3\right)\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(x1 \cdot \left(6 \cdot x1 - 4\right) + x1\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 95.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -40000:\\ \;\;\;\;\left(\left(x1 + x2 \cdot -6\right) + x1 \cdot \left(x1 \cdot 9 - 3\right)\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(x1 + x1 \cdot \left(x1 \cdot 6 - 4\right)\right)\\ \mathbf{elif}\;x1 \leq 400000:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + 4 \cdot \left(\left(x1 \cdot x2\right) \cdot \left(2 \cdot x2 + -3\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x1 \cdot x1 + 1\right) \cdot \left(x1 + x1 \cdot \left(x1 \cdot 6 - 4\right)\right) + \left(x1 \cdot \left(x1 \cdot 9 - 3\right) + \left(x1 + \left(x2 \cdot -6 + x1 \cdot -3\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 93.6% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(x1 \cdot x1 + 1\right) \cdot \left(x1 + x1 \cdot \left(x1 \cdot 6 - 4\right)\right)\\ t_1 := x2 \cdot -6 + x1 \cdot -3\\ t_2 := x1 \cdot \left(x1 \cdot 9 - 3\right)\\ \mathbf{if}\;x1 \leq -3600:\\ \;\;\;\;\left(\left(x1 + x2 \cdot -6\right) + t\_2\right) + t\_0\\ \mathbf{elif}\;x1 \leq 490000:\\ \;\;\;\;x1 + \left(\left(x1 + 4 \cdot \left(\left(x1 \cdot x2\right) \cdot \left(2 \cdot x2 + -3\right)\right)\right) + t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0 + \left(t\_2 + \left(x1 + t\_1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* (+ (* x1 x1) 1.0) (+ x1 (* x1 (- (* x1 6.0) 4.0)))))
        (t_1 (+ (* x2 -6.0) (* x1 -3.0)))
        (t_2 (* x1 (- (* x1 9.0) 3.0))))
   (if (<= x1 -3600.0)
     (+ (+ (+ x1 (* x2 -6.0)) t_2) t_0)
     (if (<= x1 490000.0)
       (+ x1 (+ (+ x1 (* 4.0 (* (* x1 x2) (+ (* 2.0 x2) -3.0)))) t_1))
       (+ t_0 (+ t_2 (+ x1 t_1)))))))

C

double code(double x1, double x2) {
	double t_0 = ((x1 * x1) + 1.0) * (x1 + (x1 * ((x1 * 6.0) - 4.0)));
	double t_1 = (x2 * -6.0) + (x1 * -3.0);
	double t_2 = x1 * ((x1 * 9.0) - 3.0);
	double tmp;
	if (x1 <= -3600.0) {
		tmp = ((x1 + (x2 * -6.0)) + t_2) + t_0;
	} else if (x1 <= 490000.0) {
		tmp = x1 + ((x1 + (4.0 * ((x1 * x2) * ((2.0 * x2) + -3.0)))) + t_1);
	} else {
		tmp = t_0 + (t_2 + (x1 + 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) :: tmp
    t_0 = ((x1 * x1) + 1.0d0) * (x1 + (x1 * ((x1 * 6.0d0) - 4.0d0)))
    t_1 = (x2 * (-6.0d0)) + (x1 * (-3.0d0))
    t_2 = x1 * ((x1 * 9.0d0) - 3.0d0)
    if (x1 <= (-3600.0d0)) then
        tmp = ((x1 + (x2 * (-6.0d0))) + t_2) + t_0
    else if (x1 <= 490000.0d0) then
        tmp = x1 + ((x1 + (4.0d0 * ((x1 * x2) * ((2.0d0 * x2) + (-3.0d0))))) + t_1)
    else
        tmp = t_0 + (t_2 + (x1 + t_1))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = ((x1 * x1) + 1.0) * (x1 + (x1 * ((x1 * 6.0) - 4.0)));
	double t_1 = (x2 * -6.0) + (x1 * -3.0);
	double t_2 = x1 * ((x1 * 9.0) - 3.0);
	double tmp;
	if (x1 <= -3600.0) {
		tmp = ((x1 + (x2 * -6.0)) + t_2) + t_0;
	} else if (x1 <= 490000.0) {
		tmp = x1 + ((x1 + (4.0 * ((x1 * x2) * ((2.0 * x2) + -3.0)))) + t_1);
	} else {
		tmp = t_0 + (t_2 + (x1 + t_1));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = ((x1 * x1) + 1.0) * (x1 + (x1 * ((x1 * 6.0) - 4.0)))
	t_1 = (x2 * -6.0) + (x1 * -3.0)
	t_2 = x1 * ((x1 * 9.0) - 3.0)
	tmp = 0
	if x1 <= -3600.0:
		tmp = ((x1 + (x2 * -6.0)) + t_2) + t_0
	elif x1 <= 490000.0:
		tmp = x1 + ((x1 + (4.0 * ((x1 * x2) * ((2.0 * x2) + -3.0)))) + t_1)
	else:
		tmp = t_0 + (t_2 + (x1 + t_1))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(Float64(x1 * x1) + 1.0) * Float64(x1 + Float64(x1 * Float64(Float64(x1 * 6.0) - 4.0))))
	t_1 = Float64(Float64(x2 * -6.0) + Float64(x1 * -3.0))
	t_2 = Float64(x1 * Float64(Float64(x1 * 9.0) - 3.0))
	tmp = 0.0
	if (x1 <= -3600.0)
		tmp = Float64(Float64(Float64(x1 + Float64(x2 * -6.0)) + t_2) + t_0);
	elseif (x1 <= 490000.0)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(4.0 * Float64(Float64(x1 * x2) * Float64(Float64(2.0 * x2) + -3.0)))) + t_1));
	else
		tmp = Float64(t_0 + Float64(t_2 + Float64(x1 + t_1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = ((x1 * x1) + 1.0) * (x1 + (x1 * ((x1 * 6.0) - 4.0)));
	t_1 = (x2 * -6.0) + (x1 * -3.0);
	t_2 = x1 * ((x1 * 9.0) - 3.0);
	tmp = 0.0;
	if (x1 <= -3600.0)
		tmp = ((x1 + (x2 * -6.0)) + t_2) + t_0;
	elseif (x1 <= 490000.0)
		tmp = x1 + ((x1 + (4.0 * ((x1 * x2) * ((2.0 * x2) + -3.0)))) + t_1);
	else
		tmp = t_0 + (t_2 + (x1 + t_1));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision] * N[(x1 + N[(x1 * N[(N[(x1 * 6.0), $MachinePrecision] - 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * -3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -3600.0], N[(N[(N[(x1 + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision] + t$95$0), $MachinePrecision], If[LessEqual[x1, 490000.0], N[(x1 + N[(N[(x1 + N[(4.0 * N[(N[(x1 * x2), $MachinePrecision] * N[(N[(2.0 * x2), $MachinePrecision] + -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], N[(t$95$0 + N[(t$95$2 + N[(x1 + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -3600

   1. Initial program 27.5%

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

   3. Simplified 47.5%

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

   5. Taylor expanded in x1 around inf 49.0%

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

   6. Taylor expanded in x1 around inf 41.2%

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

   7. Taylor expanded in x1 around 0 92.1%

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

      1. *-commutative 92.1%

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

   9. Simplified 92.1%

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

   if -3600 < x1 < 4.9e5

   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 87.9%

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

      1. associate-*r* 98.5%

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

      2. *-commutative 98.5%

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

      3. sub-neg 98.5%

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

      4. metadata-eval 98.5%

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

   5. Simplified 98.5%

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

   6. Taylor expanded in x1 around 0 98.0%

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

      1. *-commutative 98.0%

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

      2. *-commutative 98.0%

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

   8. Simplified 98.0%

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

   if 4.9e5 < x1

   1. Initial program 46.4%

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

   3. Simplified 44.7%

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

   5. Taylor expanded in x1 around inf 46.4%

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

   6. Taylor expanded in x1 around inf 36.8%

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

   7. Taylor expanded in x1 around 0 90.1%

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

      1. +-commutative 90.1%

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

      2. *-commutative 90.1%

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

      3. *-commutative 90.1%

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

   9. Simplified 90.1%

      \[\leadsto \left(\left(x1 + \color{blue}{\left(x1 \cdot -3 + x2 \cdot -6\right)}\right) + x1 \cdot \left(9 \cdot x1 - 3\right)\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(x1 \cdot \left(6 \cdot x1 - 4\right) + x1\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 94.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -3600:\\ \;\;\;\;\left(\left(x1 + x2 \cdot -6\right) + x1 \cdot \left(x1 \cdot 9 - 3\right)\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(x1 + x1 \cdot \left(x1 \cdot 6 - 4\right)\right)\\ \mathbf{elif}\;x1 \leq 490000:\\ \;\;\;\;x1 + \left(\left(x1 + 4 \cdot \left(\left(x1 \cdot x2\right) \cdot \left(2 \cdot x2 + -3\right)\right)\right) + \left(x2 \cdot -6 + x1 \cdot -3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x1 \cdot x1 + 1\right) \cdot \left(x1 + x1 \cdot \left(x1 \cdot 6 - 4\right)\right) + \left(x1 \cdot \left(x1 \cdot 9 - 3\right) + \left(x1 + \left(x2 \cdot -6 + x1 \cdot -3\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 93.6% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -32000000 \lor \neg \left(x1 \leq 400000\right):\\ \;\;\;\;\left(\left(x1 + x2 \cdot -6\right) + x1 \cdot \left(x1 \cdot 9 - 3\right)\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(x1 + x1 \cdot \left(x1 \cdot 6 - 4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 + 4 \cdot \left(\left(x1 \cdot x2\right) \cdot \left(2 \cdot x2 + -3\right)\right)\right) + \left(x2 \cdot -6 + x1 \cdot -3\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x1 -32000000.0) (not (<= x1 400000.0)))
   (+
    (+ (+ x1 (* x2 -6.0)) (* x1 (- (* x1 9.0) 3.0)))
    (* (+ (* x1 x1) 1.0) (+ x1 (* x1 (- (* x1 6.0) 4.0)))))
   (+
    x1
    (+
     (+ x1 (* 4.0 (* (* x1 x2) (+ (* 2.0 x2) -3.0))))
     (+ (* x2 -6.0) (* x1 -3.0))))))

C

double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -32000000.0) || !(x1 <= 400000.0)) {
		tmp = ((x1 + (x2 * -6.0)) + (x1 * ((x1 * 9.0) - 3.0))) + (((x1 * x1) + 1.0) * (x1 + (x1 * ((x1 * 6.0) - 4.0))));
	} else {
		tmp = x1 + ((x1 + (4.0 * ((x1 * x2) * ((2.0 * x2) + -3.0)))) + ((x2 * -6.0) + (x1 * -3.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if ((x1 <= (-32000000.0d0)) .or. (.not. (x1 <= 400000.0d0))) then
        tmp = ((x1 + (x2 * (-6.0d0))) + (x1 * ((x1 * 9.0d0) - 3.0d0))) + (((x1 * x1) + 1.0d0) * (x1 + (x1 * ((x1 * 6.0d0) - 4.0d0))))
    else
        tmp = x1 + ((x1 + (4.0d0 * ((x1 * x2) * ((2.0d0 * x2) + (-3.0d0))))) + ((x2 * (-6.0d0)) + (x1 * (-3.0d0))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -32000000.0) || !(x1 <= 400000.0)) {
		tmp = ((x1 + (x2 * -6.0)) + (x1 * ((x1 * 9.0) - 3.0))) + (((x1 * x1) + 1.0) * (x1 + (x1 * ((x1 * 6.0) - 4.0))));
	} else {
		tmp = x1 + ((x1 + (4.0 * ((x1 * x2) * ((2.0 * x2) + -3.0)))) + ((x2 * -6.0) + (x1 * -3.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x1 <= -32000000.0) or not (x1 <= 400000.0):
		tmp = ((x1 + (x2 * -6.0)) + (x1 * ((x1 * 9.0) - 3.0))) + (((x1 * x1) + 1.0) * (x1 + (x1 * ((x1 * 6.0) - 4.0))))
	else:
		tmp = x1 + ((x1 + (4.0 * ((x1 * x2) * ((2.0 * x2) + -3.0)))) + ((x2 * -6.0) + (x1 * -3.0)))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x1 <= -32000000.0) || !(x1 <= 400000.0))
		tmp = Float64(Float64(Float64(x1 + Float64(x2 * -6.0)) + Float64(x1 * Float64(Float64(x1 * 9.0) - 3.0))) + Float64(Float64(Float64(x1 * x1) + 1.0) * Float64(x1 + Float64(x1 * Float64(Float64(x1 * 6.0) - 4.0)))));
	else
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(4.0 * Float64(Float64(x1 * x2) * Float64(Float64(2.0 * x2) + -3.0)))) + Float64(Float64(x2 * -6.0) + Float64(x1 * -3.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x1 <= -32000000.0) || ~((x1 <= 400000.0)))
		tmp = ((x1 + (x2 * -6.0)) + (x1 * ((x1 * 9.0) - 3.0))) + (((x1 * x1) + 1.0) * (x1 + (x1 * ((x1 * 6.0) - 4.0))));
	else
		tmp = x1 + ((x1 + (4.0 * ((x1 * x2) * ((2.0 * x2) + -3.0)))) + ((x2 * -6.0) + (x1 * -3.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x1, -32000000.0], N[Not[LessEqual[x1, 400000.0]], $MachinePrecision]], N[(N[(N[(x1 + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision] * N[(x1 + N[(x1 * N[(N[(x1 * 6.0), $MachinePrecision] - 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x1 + N[(4.0 * N[(N[(x1 * x2), $MachinePrecision] * N[(N[(2.0 * x2), $MachinePrecision] + -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x1 < -3.2e7 or 4e5 < x1

   1. Initial program 36.4%

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

   3. Simplified 46.2%

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

   5. Taylor expanded in x1 around inf 47.8%

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

   6. Taylor expanded in x1 around inf 39.1%

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

   7. Taylor expanded in x1 around 0 91.2%

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

      1. *-commutative 91.2%

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

   9. Simplified 91.2%

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

   if -3.2e7 < x1 < 4e5

   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 87.9%

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

      1. associate-*r* 98.5%

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

      2. *-commutative 98.5%

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

      3. sub-neg 98.5%

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

      4. metadata-eval 98.5%

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

   5. Simplified 98.5%

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

   6. Taylor expanded in x1 around 0 98.0%

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

      1. *-commutative 98.0%

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

      2. *-commutative 98.0%

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

   8. Simplified 98.0%

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

4. Final simplification 94.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -32000000 \lor \neg \left(x1 \leq 400000\right):\\ \;\;\;\;\left(\left(x1 + x2 \cdot -6\right) + x1 \cdot \left(x1 \cdot 9 - 3\right)\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(x1 + x1 \cdot \left(x1 \cdot 6 - 4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 + 4 \cdot \left(\left(x1 \cdot x2\right) \cdot \left(2 \cdot x2 + -3\right)\right)\right) + \left(x2 \cdot -6 + x1 \cdot -3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 43.0% accurate, 4.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -5.2 \cdot 10^{+91}:\\ \;\;\;\;x1 + \left(9 + \left(x1 + x2 \cdot \left(x1 \cdot -12\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -7.4 \cdot 10^{-119} \lor \neg \left(x1 \leq 1.6 \cdot 10^{-68}\right):\\ \;\;\;\;x1 \cdot \left(2 + \left(2 \cdot x2 + -3\right) \cdot \left(x2 \cdot 4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -5.2e+91)
   (+ x1 (+ 9.0 (+ x1 (* x2 (* x1 -12.0)))))
   (if (or (<= x1 -7.4e-119) (not (<= x1 1.6e-68)))
     (* x1 (+ 2.0 (* (+ (* 2.0 x2) -3.0) (* x2 4.0))))
     (* x2 -6.0))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -5.2e+91) {
		tmp = x1 + (9.0 + (x1 + (x2 * (x1 * -12.0))));
	} else if ((x1 <= -7.4e-119) || !(x1 <= 1.6e-68)) {
		tmp = x1 * (2.0 + (((2.0 * x2) + -3.0) * (x2 * 4.0)));
	} else {
		tmp = x2 * -6.0;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x1 <= (-5.2d+91)) then
        tmp = x1 + (9.0d0 + (x1 + (x2 * (x1 * (-12.0d0)))))
    else if ((x1 <= (-7.4d-119)) .or. (.not. (x1 <= 1.6d-68))) then
        tmp = x1 * (2.0d0 + (((2.0d0 * x2) + (-3.0d0)) * (x2 * 4.0d0)))
    else
        tmp = x2 * (-6.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= -5.2e+91) {
		tmp = x1 + (9.0 + (x1 + (x2 * (x1 * -12.0))));
	} else if ((x1 <= -7.4e-119) || !(x1 <= 1.6e-68)) {
		tmp = x1 * (2.0 + (((2.0 * x2) + -3.0) * (x2 * 4.0)));
	} else {
		tmp = x2 * -6.0;
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -5.2e+91:
		tmp = x1 + (9.0 + (x1 + (x2 * (x1 * -12.0))))
	elif (x1 <= -7.4e-119) or not (x1 <= 1.6e-68):
		tmp = x1 * (2.0 + (((2.0 * x2) + -3.0) * (x2 * 4.0)))
	else:
		tmp = x2 * -6.0
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -5.2e+91)
		tmp = Float64(x1 + Float64(9.0 + Float64(x1 + Float64(x2 * Float64(x1 * -12.0)))));
	elseif ((x1 <= -7.4e-119) || !(x1 <= 1.6e-68))
		tmp = Float64(x1 * Float64(2.0 + Float64(Float64(Float64(2.0 * x2) + -3.0) * Float64(x2 * 4.0))));
	else
		tmp = Float64(x2 * -6.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -5.2e+91)
		tmp = x1 + (9.0 + (x1 + (x2 * (x1 * -12.0))));
	elseif ((x1 <= -7.4e-119) || ~((x1 <= 1.6e-68)))
		tmp = x1 * (2.0 + (((2.0 * x2) + -3.0) * (x2 * 4.0)));
	else
		tmp = x2 * -6.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -5.2e+91], N[(x1 + N[(9.0 + N[(x1 + N[(x2 * N[(x1 * -12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x1, -7.4e-119], N[Not[LessEqual[x1, 1.6e-68]], $MachinePrecision]], N[(x1 * N[(2.0 + N[(N[(N[(2.0 * x2), $MachinePrecision] + -3.0), $MachinePrecision] * N[(x2 * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x2 * -6.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -5.2000000000000001e91

   1. Initial program 4.1%

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

   3. Taylor expanded in x1 around 0 0.1%

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

      1. associate-*r* 0.1%

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

      2. *-commutative 0.1%

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

      3. sub-neg 0.1%

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

      4. metadata-eval 0.1%

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

   5. Simplified 0.1%

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

   6. Taylor expanded in x1 around inf 0.1%

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

   7. Taylor expanded in x2 around 0 15.7%

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

      1. *-commutative 15.7%

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

      2. *-commutative 15.7%

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

      3. associate-*l* 15.7%

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

   9. Simplified 15.7%

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

   if -5.2000000000000001e91 < x1 < -7.4000000000000003e-119 or 1.5999999999999999e-68 < x1

   1. Initial program 71.6%

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

   3. Taylor expanded in x1 around 0 46.4%

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

      1. associate-*r* 46.3%

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

      2. *-commutative 46.3%

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

      3. sub-neg 46.3%

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

      4. metadata-eval 46.3%

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

   5. Simplified 46.3%

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

   6. Taylor expanded in x1 around inf 45.7%

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

   7. Taylor expanded in x1 around inf 44.5%

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

      1. associate-*r* 44.5%

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

      2. sub-neg 44.5%

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

      3. *-commutative 44.5%

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

      4. metadata-eval 44.5%

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

   9. Simplified 44.5%

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

   if -7.4000000000000003e-119 < x1 < 1.5999999999999999e-68

   1. Initial program 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x1 around 0 71.0%

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

      1. *-commutative 71.0%

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

   7. Simplified 71.0%

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

   8. Taylor expanded in x1 around 0 71.5%

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

      1. *-commutative 71.5%

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

   10. Simplified 71.5%

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

4. Final simplification 49.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.2 \cdot 10^{+91}:\\ \;\;\;\;x1 + \left(9 + \left(x1 + x2 \cdot \left(x1 \cdot -12\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -7.4 \cdot 10^{-119} \lor \neg \left(x1 \leq 1.6 \cdot 10^{-68}\right):\\ \;\;\;\;x1 \cdot \left(2 + \left(2 \cdot x2 + -3\right) \cdot \left(x2 \cdot 4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 43.3% accurate, 4.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -4.4 \cdot 10^{+89}:\\ \;\;\;\;x1 + \left(9 + \left(x1 + x2 \cdot \left(x1 \cdot -12\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -6.8 \cdot 10^{-119}:\\ \;\;\;\;x1 + \left(9 + x1 \cdot \left(1 + x2 \cdot \left(-12 - x2 \cdot -8\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 8.4 \cdot 10^{-69}:\\ \;\;\;\;x2 \cdot -6\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot \left(2 + \left(2 \cdot x2 + -3\right) \cdot \left(x2 \cdot 4\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -4.4e+89)
   (+ x1 (+ 9.0 (+ x1 (* x2 (* x1 -12.0)))))
   (if (<= x1 -6.8e-119)
     (+ x1 (+ 9.0 (* x1 (+ 1.0 (* x2 (- -12.0 (* x2 -8.0)))))))
     (if (<= x1 8.4e-69)
       (* x2 -6.0)
       (* x1 (+ 2.0 (* (+ (* 2.0 x2) -3.0) (* x2 4.0))))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -4.4e+89) {
		tmp = x1 + (9.0 + (x1 + (x2 * (x1 * -12.0))));
	} else if (x1 <= -6.8e-119) {
		tmp = x1 + (9.0 + (x1 * (1.0 + (x2 * (-12.0 - (x2 * -8.0))))));
	} else if (x1 <= 8.4e-69) {
		tmp = x2 * -6.0;
	} else {
		tmp = x1 * (2.0 + (((2.0 * x2) + -3.0) * (x2 * 4.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x1 <= (-4.4d+89)) then
        tmp = x1 + (9.0d0 + (x1 + (x2 * (x1 * (-12.0d0)))))
    else if (x1 <= (-6.8d-119)) then
        tmp = x1 + (9.0d0 + (x1 * (1.0d0 + (x2 * ((-12.0d0) - (x2 * (-8.0d0)))))))
    else if (x1 <= 8.4d-69) then
        tmp = x2 * (-6.0d0)
    else
        tmp = x1 * (2.0d0 + (((2.0d0 * x2) + (-3.0d0)) * (x2 * 4.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= -4.4e+89) {
		tmp = x1 + (9.0 + (x1 + (x2 * (x1 * -12.0))));
	} else if (x1 <= -6.8e-119) {
		tmp = x1 + (9.0 + (x1 * (1.0 + (x2 * (-12.0 - (x2 * -8.0))))));
	} else if (x1 <= 8.4e-69) {
		tmp = x2 * -6.0;
	} else {
		tmp = x1 * (2.0 + (((2.0 * x2) + -3.0) * (x2 * 4.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -4.4e+89:
		tmp = x1 + (9.0 + (x1 + (x2 * (x1 * -12.0))))
	elif x1 <= -6.8e-119:
		tmp = x1 + (9.0 + (x1 * (1.0 + (x2 * (-12.0 - (x2 * -8.0))))))
	elif x1 <= 8.4e-69:
		tmp = x2 * -6.0
	else:
		tmp = x1 * (2.0 + (((2.0 * x2) + -3.0) * (x2 * 4.0)))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -4.4e+89)
		tmp = Float64(x1 + Float64(9.0 + Float64(x1 + Float64(x2 * Float64(x1 * -12.0)))));
	elseif (x1 <= -6.8e-119)
		tmp = Float64(x1 + Float64(9.0 + Float64(x1 * Float64(1.0 + Float64(x2 * Float64(-12.0 - Float64(x2 * -8.0)))))));
	elseif (x1 <= 8.4e-69)
		tmp = Float64(x2 * -6.0);
	else
		tmp = Float64(x1 * Float64(2.0 + Float64(Float64(Float64(2.0 * x2) + -3.0) * Float64(x2 * 4.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -4.4e+89)
		tmp = x1 + (9.0 + (x1 + (x2 * (x1 * -12.0))));
	elseif (x1 <= -6.8e-119)
		tmp = x1 + (9.0 + (x1 * (1.0 + (x2 * (-12.0 - (x2 * -8.0))))));
	elseif (x1 <= 8.4e-69)
		tmp = x2 * -6.0;
	else
		tmp = x1 * (2.0 + (((2.0 * x2) + -3.0) * (x2 * 4.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -4.4e+89], N[(x1 + N[(9.0 + N[(x1 + N[(x2 * N[(x1 * -12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -6.8e-119], N[(x1 + N[(9.0 + N[(x1 * N[(1.0 + N[(x2 * N[(-12.0 - N[(x2 * -8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 8.4e-69], N[(x2 * -6.0), $MachinePrecision], N[(x1 * N[(2.0 + N[(N[(N[(2.0 * x2), $MachinePrecision] + -3.0), $MachinePrecision] * N[(x2 * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -4.4e89

   1. Initial program 4.1%

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

   3. Taylor expanded in x1 around 0 0.1%

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

      1. associate-*r* 0.1%

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

      2. *-commutative 0.1%

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

      3. sub-neg 0.1%

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

      4. metadata-eval 0.1%

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

   5. Simplified 0.1%

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

   6. Taylor expanded in x1 around inf 0.1%

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

   7. Taylor expanded in x2 around 0 15.7%

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

      1. *-commutative 15.7%

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

      2. *-commutative 15.7%

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

      3. associate-*l* 15.7%

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

   9. Simplified 15.7%

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

   if -4.4e89 < x1 < -6.80000000000000047e-119

   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 66.5%

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

      1. associate-*r* 66.5%

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

      2. *-commutative 66.5%

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

      3. sub-neg 66.5%

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

      4. metadata-eval 66.5%

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

   5. Simplified 66.5%

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

   6. Taylor expanded in x1 around inf 38.3%

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

      1. +-commutative 38.3%

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

   8. Simplified 38.3%

      \[\leadsto x1 + \color{blue}{\left(x1 \cdot \left(1 + x2 \cdot \left(-12 + \left(-x2 \cdot -8\right)\right)\right) + 9\right)} \]

   if -6.80000000000000047e-119 < x1 < 8.3999999999999999e-69

   1. Initial program 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x1 around 0 71.0%

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

      1. *-commutative 71.0%

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

   7. Simplified 71.0%

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

   8. Taylor expanded in x1 around 0 71.5%

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

      1. *-commutative 71.5%

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

   10. Simplified 71.5%

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

   if 8.3999999999999999e-69 < x1

   1. Initial program 58.3%

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

   3. Taylor expanded in x1 around 0 36.7%

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

      1. associate-*r* 36.7%

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

      2. *-commutative 36.7%

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

      3. sub-neg 36.7%

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

      4. metadata-eval 36.7%

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

   5. Simplified 36.7%

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

   6. Taylor expanded in x1 around inf 48.0%

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

   7. Taylor expanded in x1 around inf 48.0%

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

      1. associate-*r* 48.0%

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

      2. sub-neg 48.0%

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

      3. *-commutative 48.0%

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

      4. metadata-eval 48.0%

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

   9. Simplified 48.0%

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

4. Final simplification 49.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4.4 \cdot 10^{+89}:\\ \;\;\;\;x1 + \left(9 + \left(x1 + x2 \cdot \left(x1 \cdot -12\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -6.8 \cdot 10^{-119}:\\ \;\;\;\;x1 + \left(9 + x1 \cdot \left(1 + x2 \cdot \left(-12 - x2 \cdot -8\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 8.4 \cdot 10^{-69}:\\ \;\;\;\;x2 \cdot -6\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot \left(2 + \left(2 \cdot x2 + -3\right) \cdot \left(x2 \cdot 4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 63.2% accurate, 4.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -2.5 \cdot 10^{+90}:\\ \;\;\;\;x1 + \left(9 + \left(x1 + x2 \cdot \left(x1 \cdot -12\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 + 4 \cdot \left(\left(x1 \cdot x2\right) \cdot \left(2 \cdot x2 + -3\right)\right)\right) + \left(x2 \cdot -6 + x1 \cdot -3\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -2.5e+90)
   (+ x1 (+ 9.0 (+ x1 (* x2 (* x1 -12.0)))))
   (+
    x1
    (+
     (+ x1 (* 4.0 (* (* x1 x2) (+ (* 2.0 x2) -3.0))))
     (+ (* x2 -6.0) (* x1 -3.0))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -2.5e+90) {
		tmp = x1 + (9.0 + (x1 + (x2 * (x1 * -12.0))));
	} else {
		tmp = x1 + ((x1 + (4.0 * ((x1 * x2) * ((2.0 * x2) + -3.0)))) + ((x2 * -6.0) + (x1 * -3.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x1 <= (-2.5d+90)) then
        tmp = x1 + (9.0d0 + (x1 + (x2 * (x1 * (-12.0d0)))))
    else
        tmp = x1 + ((x1 + (4.0d0 * ((x1 * x2) * ((2.0d0 * x2) + (-3.0d0))))) + ((x2 * (-6.0d0)) + (x1 * (-3.0d0))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= -2.5e+90) {
		tmp = x1 + (9.0 + (x1 + (x2 * (x1 * -12.0))));
	} else {
		tmp = x1 + ((x1 + (4.0 * ((x1 * x2) * ((2.0 * x2) + -3.0)))) + ((x2 * -6.0) + (x1 * -3.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -2.5e+90:
		tmp = x1 + (9.0 + (x1 + (x2 * (x1 * -12.0))))
	else:
		tmp = x1 + ((x1 + (4.0 * ((x1 * x2) * ((2.0 * x2) + -3.0)))) + ((x2 * -6.0) + (x1 * -3.0)))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -2.5e+90)
		tmp = Float64(x1 + Float64(9.0 + Float64(x1 + Float64(x2 * Float64(x1 * -12.0)))));
	else
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(4.0 * Float64(Float64(x1 * x2) * Float64(Float64(2.0 * x2) + -3.0)))) + Float64(Float64(x2 * -6.0) + Float64(x1 * -3.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -2.5e+90)
		tmp = x1 + (9.0 + (x1 + (x2 * (x1 * -12.0))));
	else
		tmp = x1 + ((x1 + (4.0 * ((x1 * x2) * ((2.0 * x2) + -3.0)))) + ((x2 * -6.0) + (x1 * -3.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -2.5e+90], N[(x1 + N[(9.0 + N[(x1 + N[(x2 * N[(x1 * -12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x1 + N[(4.0 * N[(N[(x1 * x2), $MachinePrecision] * N[(N[(2.0 * x2), $MachinePrecision] + -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x1 < -2.5000000000000002e90

   1. Initial program 4.1%

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

   3. Taylor expanded in x1 around 0 0.1%

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

      1. associate-*r* 0.1%

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

      2. *-commutative 0.1%

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

      3. sub-neg 0.1%

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

      4. metadata-eval 0.1%

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

   5. Simplified 0.1%

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

   6. Taylor expanded in x1 around inf 0.1%

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

   7. Taylor expanded in x2 around 0 15.7%

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

      1. *-commutative 15.7%

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

      2. *-commutative 15.7%

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

      3. associate-*l* 15.7%

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

   9. Simplified 15.7%

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

   if -2.5000000000000002e90 < x1

   1. Initial program 84.5%

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

   3. Taylor expanded in x1 around 0 64.1%

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

      1. associate-*r* 71.0%

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

      2. *-commutative 71.0%

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

      3. sub-neg 71.0%

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

      4. metadata-eval 71.0%

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

   5. Simplified 71.0%

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

   6. Taylor expanded in x1 around 0 77.5%

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

      1. *-commutative 77.5%

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

      2. *-commutative 77.5%

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

   8. Simplified 77.5%

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

4. Final simplification 65.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -2.5 \cdot 10^{+90}:\\ \;\;\;\;x1 + \left(9 + \left(x1 + x2 \cdot \left(x1 \cdot -12\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 + 4 \cdot \left(\left(x1 \cdot x2\right) \cdot \left(2 \cdot x2 + -3\right)\right)\right) + \left(x2 \cdot -6 + x1 \cdot -3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 57.7% accurate, 4.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x2 \leq -2.5 \cdot 10^{-23}:\\ \;\;\;\;x1 + \left(\left(x1 + 4 \cdot \left(\left(x1 \cdot x2\right) \cdot \left(2 \cdot x2 + -3\right)\right)\right) + 3 \cdot \left(x2 \cdot -2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(-2 + x2 \cdot \left(-12 + x2 \cdot 8\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x2 -2.5e-23)
   (+
    x1
    (+ (+ x1 (* 4.0 (* (* x1 x2) (+ (* 2.0 x2) -3.0)))) (* 3.0 (* x2 -2.0))))
   (+ x1 (+ (* x2 -6.0) (* x1 (+ -2.0 (* x2 (+ -12.0 (* x2 8.0)))))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x2 <= -2.5e-23) {
		tmp = x1 + ((x1 + (4.0 * ((x1 * x2) * ((2.0 * x2) + -3.0)))) + (3.0 * (x2 * -2.0)));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * (-2.0 + (x2 * (-12.0 + (x2 * 8.0))))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x2 <= (-2.5d-23)) then
        tmp = x1 + ((x1 + (4.0d0 * ((x1 * x2) * ((2.0d0 * x2) + (-3.0d0))))) + (3.0d0 * (x2 * (-2.0d0))))
    else
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * ((-2.0d0) + (x2 * ((-12.0d0) + (x2 * 8.0d0))))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x2 <= -2.5e-23) {
		tmp = x1 + ((x1 + (4.0 * ((x1 * x2) * ((2.0 * x2) + -3.0)))) + (3.0 * (x2 * -2.0)));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * (-2.0 + (x2 * (-12.0 + (x2 * 8.0))))));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x2 <= -2.5e-23:
		tmp = x1 + ((x1 + (4.0 * ((x1 * x2) * ((2.0 * x2) + -3.0)))) + (3.0 * (x2 * -2.0)))
	else:
		tmp = x1 + ((x2 * -6.0) + (x1 * (-2.0 + (x2 * (-12.0 + (x2 * 8.0))))))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x2 <= -2.5e-23)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(4.0 * Float64(Float64(x1 * x2) * Float64(Float64(2.0 * x2) + -3.0)))) + Float64(3.0 * Float64(x2 * -2.0))));
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(-2.0 + Float64(x2 * Float64(-12.0 + Float64(x2 * 8.0)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x2 <= -2.5e-23)
		tmp = x1 + ((x1 + (4.0 * ((x1 * x2) * ((2.0 * x2) + -3.0)))) + (3.0 * (x2 * -2.0)));
	else
		tmp = x1 + ((x2 * -6.0) + (x1 * (-2.0 + (x2 * (-12.0 + (x2 * 8.0))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x2, -2.5e-23], N[(x1 + N[(N[(x1 + N[(4.0 * N[(N[(x1 * x2), $MachinePrecision] * N[(N[(2.0 * x2), $MachinePrecision] + -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(-2.0 + N[(x2 * N[(-12.0 + N[(x2 * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x2 < -2.5000000000000001e-23

   1. Initial program 70.4%

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

   3. Taylor expanded in x1 around 0 49.4%

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

      1. associate-*r* 64.7%

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

      2. *-commutative 64.7%

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

      3. sub-neg 64.7%

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

      4. metadata-eval 64.7%

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

   5. Simplified 64.7%

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

   6. Taylor expanded in x1 around 0 75.4%

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

      1. *-commutative 75.4%

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

   8. Simplified 75.4%

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

   if -2.5000000000000001e-23 < x2

   1. Initial program 68.7%

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

   3. Simplified 68.7%

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

   5. Taylor expanded in x1 around 0 75.5%

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

   7. Simplified 75.5%

      \[\leadsto x1 + \color{blue}{\left(x1 \cdot \left(-2 + x2 \cdot \left(\left(2 \cdot x2\right) \cdot 4 + -12\right)\right) + \left(x2 \cdot -6 + {x1}^{2} \cdot \left(-6 + \left(\left(9 + \left(2 \cdot x2\right) \cdot 3\right) + \left(x2 \cdot -4 + \left(\left(6 + x2 \cdot -4\right) + x2 \cdot 14\right)\right)\right)\right)\right)\right)} \]

   8. Taylor expanded in x1 around 0 57.1%

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

      1. *-commutative 57.1%

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

      2. sub-neg 57.1%

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

      3. sub-neg 57.1%

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

      4. *-commutative 57.1%

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

      5. metadata-eval 57.1%

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

      6. metadata-eval 57.1%

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

   10. Simplified 57.1%

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

4. Final simplification 62.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq -2.5 \cdot 10^{-23}:\\ \;\;\;\;x1 + \left(\left(x1 + 4 \cdot \left(\left(x1 \cdot x2\right) \cdot \left(2 \cdot x2 + -3\right)\right)\right) + 3 \cdot \left(x2 \cdot -2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(-2 + x2 \cdot \left(-12 + x2 \cdot 8\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 57.2% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -3.7 \cdot 10^{+95}:\\ \;\;\;\;x1 + \left(9 + \left(x1 + x2 \cdot \left(x1 \cdot -12\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(-2 + x2 \cdot \left(-12 + x2 \cdot 8\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -3.7e+95)
   (+ x1 (+ 9.0 (+ x1 (* x2 (* x1 -12.0)))))
   (+ x1 (+ (* x2 -6.0) (* x1 (+ -2.0 (* x2 (+ -12.0 (* x2 8.0)))))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -3.7e+95) {
		tmp = x1 + (9.0 + (x1 + (x2 * (x1 * -12.0))));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * (-2.0 + (x2 * (-12.0 + (x2 * 8.0))))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x1 <= (-3.7d+95)) then
        tmp = x1 + (9.0d0 + (x1 + (x2 * (x1 * (-12.0d0)))))
    else
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * ((-2.0d0) + (x2 * ((-12.0d0) + (x2 * 8.0d0))))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= -3.7e+95) {
		tmp = x1 + (9.0 + (x1 + (x2 * (x1 * -12.0))));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * (-2.0 + (x2 * (-12.0 + (x2 * 8.0))))));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -3.7e+95:
		tmp = x1 + (9.0 + (x1 + (x2 * (x1 * -12.0))))
	else:
		tmp = x1 + ((x2 * -6.0) + (x1 * (-2.0 + (x2 * (-12.0 + (x2 * 8.0))))))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -3.7e+95)
		tmp = Float64(x1 + Float64(9.0 + Float64(x1 + Float64(x2 * Float64(x1 * -12.0)))));
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(-2.0 + Float64(x2 * Float64(-12.0 + Float64(x2 * 8.0)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -3.7e+95)
		tmp = x1 + (9.0 + (x1 + (x2 * (x1 * -12.0))));
	else
		tmp = x1 + ((x2 * -6.0) + (x1 * (-2.0 + (x2 * (-12.0 + (x2 * 8.0))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -3.7e+95], N[(x1 + N[(9.0 + N[(x1 + N[(x2 * N[(x1 * -12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(-2.0 + N[(x2 * N[(-12.0 + N[(x2 * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x1 < -3.7000000000000001e95

   1. Initial program 4.1%

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

   3. Taylor expanded in x1 around 0 0.1%

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

      1. associate-*r* 0.1%

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

      2. *-commutative 0.1%

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

      3. sub-neg 0.1%

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

      4. metadata-eval 0.1%

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

   5. Simplified 0.1%

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

   6. Taylor expanded in x1 around inf 0.1%

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

   7. Taylor expanded in x2 around 0 15.7%

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

      1. *-commutative 15.7%

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

      2. *-commutative 15.7%

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

      3. associate-*l* 15.7%

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

   9. Simplified 15.7%

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

   if -3.7000000000000001e95 < x1

   1. Initial program 84.5%

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

   3. Simplified 84.5%

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

   5. Taylor expanded in x1 around 0 70.4%

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

   7. Simplified 70.9%

      \[\leadsto x1 + \color{blue}{\left(x1 \cdot \left(-2 + x2 \cdot \left(\left(2 \cdot x2\right) \cdot 4 + -12\right)\right) + \left(x2 \cdot -6 + {x1}^{2} \cdot \left(-6 + \left(\left(9 + \left(2 \cdot x2\right) \cdot 3\right) + \left(x2 \cdot -4 + \left(\left(6 + x2 \cdot -4\right) + x2 \cdot 14\right)\right)\right)\right)\right)\right)} \]

   8. Taylor expanded in x1 around 0 70.4%

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

      1. *-commutative 70.4%

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

      2. sub-neg 70.4%

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

      3. sub-neg 70.4%

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

      4. *-commutative 70.4%

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

      5. metadata-eval 70.4%

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

      6. metadata-eval 70.4%

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

   10. Simplified 70.4%

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

4. Final simplification 59.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -3.7 \cdot 10^{+95}:\\ \;\;\;\;x1 + \left(9 + \left(x1 + x2 \cdot \left(x1 \cdot -12\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(-2 + x2 \cdot \left(-12 + x2 \cdot 8\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 33.1% accurate, 6.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -4.2 \cdot 10^{+83} \lor \neg \left(x1 \leq 6 \cdot 10^{-8}\right):\\ \;\;\;\;x1 + \left(9 + \left(x1 + x2 \cdot \left(x1 \cdot -12\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x1 -4.2e+83) (not (<= x1 6e-8)))
   (+ x1 (+ 9.0 (+ x1 (* x2 (* x1 -12.0)))))
   (* x2 -6.0)))

C

double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -4.2e+83) || !(x1 <= 6e-8)) {
		tmp = x1 + (9.0 + (x1 + (x2 * (x1 * -12.0))));
	} else {
		tmp = x2 * -6.0;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if ((x1 <= (-4.2d+83)) .or. (.not. (x1 <= 6d-8))) then
        tmp = x1 + (9.0d0 + (x1 + (x2 * (x1 * (-12.0d0)))))
    else
        tmp = x2 * (-6.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -4.2e+83) || !(x1 <= 6e-8)) {
		tmp = x1 + (9.0 + (x1 + (x2 * (x1 * -12.0))));
	} else {
		tmp = x2 * -6.0;
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x1 <= -4.2e+83) or not (x1 <= 6e-8):
		tmp = x1 + (9.0 + (x1 + (x2 * (x1 * -12.0))))
	else:
		tmp = x2 * -6.0
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x1 <= -4.2e+83) || !(x1 <= 6e-8))
		tmp = Float64(x1 + Float64(9.0 + Float64(x1 + Float64(x2 * Float64(x1 * -12.0)))));
	else
		tmp = Float64(x2 * -6.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x1 <= -4.2e+83) || ~((x1 <= 6e-8)))
		tmp = x1 + (9.0 + (x1 + (x2 * (x1 * -12.0))));
	else
		tmp = x2 * -6.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x1, -4.2e+83], N[Not[LessEqual[x1, 6e-8]], $MachinePrecision]], N[(x1 + N[(9.0 + N[(x1 + N[(x2 * N[(x1 * -12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x2 * -6.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x1 < -4.20000000000000005e83 or 5.99999999999999946e-8 < x1

   1. Initial program 30.3%

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

   3. Taylor expanded in x1 around 0 14.0%

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

      1. associate-*r* 14.0%

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

      2. *-commutative 14.0%

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

      3. sub-neg 14.0%

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

      4. metadata-eval 14.0%

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

   5. Simplified 14.0%

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

   6. Taylor expanded in x1 around inf 28.6%

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

   7. Taylor expanded in x2 around 0 16.0%

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

      1. *-commutative 16.0%

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

      2. *-commutative 16.0%

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

      3. associate-*l* 16.0%

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

   9. Simplified 16.0%

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

   if -4.20000000000000005e83 < x1 < 5.99999999999999946e-8

   1. Initial program 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in x1 around 0 51.2%

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

      1. *-commutative 51.2%

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

   7. Simplified 51.2%

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

   8. Taylor expanded in x1 around 0 51.8%

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

      1. *-commutative 51.8%

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

   10. Simplified 51.8%

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

4. Final simplification 36.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4.2 \cdot 10^{+83} \lor \neg \left(x1 \leq 6 \cdot 10^{-8}\right):\\ \;\;\;\;x1 + \left(9 + \left(x1 + x2 \cdot \left(x1 \cdot -12\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 26.8% accurate, 25.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 69.1%

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

3. Simplified 69.1%

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

5. Taylor expanded in x1 around 0 30.1%

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

   1. *-commutative 30.1%

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

7. Simplified 30.1%

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

8. Final simplification 30.1%

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

Alternative 16: 26.6% accurate, 42.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 69.1%

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

3. Simplified 69.1%

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

5. Taylor expanded in x1 around 0 30.1%

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

   1. *-commutative 30.1%

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

7. Simplified 30.1%

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

8. Taylor expanded in x1 around 0 30.0%

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

   1. *-commutative 30.0%

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

10. Simplified 30.0%

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

11. Final simplification 30.0%

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

Alternative 17: 3.5% accurate, 127.0× speedup

Math

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

FPCore

(FPCore (x1 x2) :precision binary64 9.0)

C

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

Fortran

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

Java

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

Python

def code(x1, x2):
	return 9.0

Julia

function code(x1, x2)
	return 9.0
end

MATLAB

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

Wolfram

code[x1_, x2_] := 9.0

Derivation

1. Initial program 69.1%

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

3. Taylor expanded in x1 around 0 51.9%

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

   1. associate-*r* 57.4%

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

   2. *-commutative 57.4%

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

   3. sub-neg 57.4%

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

   4. metadata-eval 57.4%

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

5. Simplified 57.4%

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

6. Taylor expanded in x1 around inf 25.1%

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

7. Taylor expanded in x1 around 0 3.5%

   \[\leadsto \color{blue}{9} \]

8. Final simplification 3.5%

   \[\leadsto 9 \]
9. Add Preprocessing

Reproduce

herbie shell --seed 2024048 
(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))))))