Rosa's FloatVsDoubleBenchmark

Percentage Accurate: 70.4% → 98.9%

Time: 39.3s

Alternatives: 20

Speedup: 4.7×

• 46.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 70.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.9% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 99.4%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x2 around 0 99.6%

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

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

   1. Initial program 0.0%

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

   3. Simplified 5.8%

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

   5. Taylor expanded in x1 around -inf 100.0%

      \[\leadsto \color{blue}{{x1}^{4} \cdot \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{15 + -1 \cdot \left(6 + -4 \cdot \left(2 \cdot x2 - 3\right)\right)}{x1}}{x1}\right)} \]

   6. Taylor expanded in x2 around -inf 49.3%

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

      1. mul-1-neg 49.3%

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

      2. distribute-rgt-neg-in 49.3%

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

      3. mul-1-neg 49.3%

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

      4. unsub-neg 49.3%

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

      5. *-commutative 49.3%

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

      6. associate-/l* 49.3%

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

   8. Simplified 49.3%

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

   9. Taylor expanded in x1 around inf 100.0%

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

       1. *-commutative 100.0%

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

   11. Simplified 100.0%

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

4. Final simplification 99.7%

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

Alternative 2: 99.4% accurate, 0.2× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 99.4%

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

      1. fma-define 99.4%

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

      2. *-commutative 99.4%

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

      3. fma-define 99.4%

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

      4. clear-num 99.4%

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

      5. inv-pow 99.4%

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

      6. *-commutative 99.4%

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

      7. fma-define 99.4%

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

      8. associate-*r* 99.4%

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

      9. fma-define 99.4%

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

      10. pow2 99.4%

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

   4. Applied egg-rr 99.4%

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

      1. unpow-1 99.4%

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

   6. Simplified 99.4%

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

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

   1. Initial program 0.0%

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

   3. Simplified 5.8%

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

   5. Taylor expanded in x1 around -inf 100.0%

      \[\leadsto \color{blue}{{x1}^{4} \cdot \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{15 + -1 \cdot \left(6 + -4 \cdot \left(2 \cdot x2 - 3\right)\right)}{x1}}{x1}\right)} \]

   6. Taylor expanded in x2 around -inf 49.3%

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

      1. mul-1-neg 49.3%

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

      2. distribute-rgt-neg-in 49.3%

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

      3. mul-1-neg 49.3%

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

      4. unsub-neg 49.3%

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

      5. *-commutative 49.3%

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

      6. associate-/l* 49.3%

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

   8. Simplified 49.3%

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

   9. Taylor expanded in x1 around inf 100.0%

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

       1. *-commutative 100.0%

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

   11. Simplified 100.0%

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

4. Final simplification 99.6%

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

Alternative 3: 99.4% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 99.4%

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

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

   1. Initial program 0.0%

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

   3. Simplified 5.8%

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

   5. Taylor expanded in x1 around -inf 100.0%

      \[\leadsto \color{blue}{{x1}^{4} \cdot \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{15 + -1 \cdot \left(6 + -4 \cdot \left(2 \cdot x2 - 3\right)\right)}{x1}}{x1}\right)} \]

   6. Taylor expanded in x2 around -inf 49.3%

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

      1. mul-1-neg 49.3%

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

      2. distribute-rgt-neg-in 49.3%

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

      3. mul-1-neg 49.3%

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

      4. unsub-neg 49.3%

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

      5. *-commutative 49.3%

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

      6. associate-/l* 49.3%

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

   8. Simplified 49.3%

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

   9. Taylor expanded in x1 around inf 100.0%

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

       1. *-commutative 100.0%

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

   11. Simplified 100.0%

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

4. Final simplification 99.6%

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

Alternative 4: 96.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := x1 \cdot x1 + 1\\ t_2 := \frac{\left(t\_0 + 2 \cdot x2\right) - x1}{t\_1}\\ \mathbf{if}\;x1 \leq -1.4 \cdot 10^{+58}:\\ \;\;\;\;6 \cdot {x1}^{4}\\ \mathbf{elif}\;x1 \leq 3.25 \cdot 10^{+49}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t\_0 - 2 \cdot x2\right) - x1}{t\_1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(t\_0 \cdot t\_2 + t\_1 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t\_2\right) \cdot \left(t\_2 - 3\right) + \left(x1 \cdot x1\right) \cdot 6\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;{x1}^{2} \cdot \left(x1 \cdot \left(x1 \cdot 6 - 3\right) + x2 \cdot \left(8 + 3 \cdot \frac{-1}{x2}\right)\right)\\ \end{array} \end{array} \]

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)))
   (if (<= x1 -1.4e+58)
     (* 6.0 (pow x1 4.0))
     (if (<= x1 3.25e+49)
       (+
        x1
        (+
         (* 3.0 (/ (- (- t_0 (* 2.0 x2)) x1) t_1))
         (+
          x1
          (+
           (* x1 (* x1 x1))
           (+
            (* t_0 t_2)
            (*
             t_1
             (+ (* (* (* x1 2.0) t_2) (- t_2 3.0)) (* (* x1 x1) 6.0))))))))
       (*
        (pow x1 2.0)
        (+ (* x1 (- (* x1 6.0) 3.0)) (* x2 (+ 8.0 (* 3.0 (/ -1.0 x2))))))))))

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 tmp;
	if (x1 <= -1.4e+58) {
		tmp = 6.0 * pow(x1, 4.0);
	} else if (x1 <= 3.25e+49) {
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * t_2) + (t_1 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * 6.0)))))));
	} else {
		tmp = pow(x1, 2.0) * ((x1 * ((x1 * 6.0) - 3.0)) + (x2 * (8.0 + (3.0 * (-1.0 / x2)))));
	}
	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 * 3.0d0)
    t_1 = (x1 * x1) + 1.0d0
    t_2 = ((t_0 + (2.0d0 * x2)) - x1) / t_1
    if (x1 <= (-1.4d+58)) then
        tmp = 6.0d0 * (x1 ** 4.0d0)
    else if (x1 <= 3.25d+49) then
        tmp = x1 + ((3.0d0 * (((t_0 - (2.0d0 * x2)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * t_2) + (t_1 * ((((x1 * 2.0d0) * t_2) * (t_2 - 3.0d0)) + ((x1 * x1) * 6.0d0)))))))
    else
        tmp = (x1 ** 2.0d0) * ((x1 * ((x1 * 6.0d0) - 3.0d0)) + (x2 * (8.0d0 + (3.0d0 * ((-1.0d0) / x2)))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = ((t_0 + (2.0 * x2)) - x1) / t_1;
	double tmp;
	if (x1 <= -1.4e+58) {
		tmp = 6.0 * Math.pow(x1, 4.0);
	} else if (x1 <= 3.25e+49) {
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * t_2) + (t_1 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * 6.0)))))));
	} else {
		tmp = Math.pow(x1, 2.0) * ((x1 * ((x1 * 6.0) - 3.0)) + (x2 * (8.0 + (3.0 * (-1.0 / x2)))));
	}
	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
	tmp = 0
	if x1 <= -1.4e+58:
		tmp = 6.0 * math.pow(x1, 4.0)
	elif x1 <= 3.25e+49:
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * t_2) + (t_1 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * 6.0)))))))
	else:
		tmp = math.pow(x1, 2.0) * ((x1 * ((x1 * 6.0) - 3.0)) + (x2 * (8.0 + (3.0 * (-1.0 / x2)))))
	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)
	tmp = 0.0
	if (x1 <= -1.4e+58)
		tmp = Float64(6.0 * (x1 ^ 4.0));
	elseif (x1 <= 3.25e+49)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_0 - Float64(2.0 * x2)) - x1) / t_1)) + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(t_0 * t_2) + Float64(t_1 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_2) * Float64(t_2 - 3.0)) + Float64(Float64(x1 * x1) * 6.0))))))));
	else
		tmp = Float64((x1 ^ 2.0) * Float64(Float64(x1 * Float64(Float64(x1 * 6.0) - 3.0)) + Float64(x2 * Float64(8.0 + Float64(3.0 * Float64(-1.0 / x2))))));
	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;
	tmp = 0.0;
	if (x1 <= -1.4e+58)
		tmp = 6.0 * (x1 ^ 4.0);
	elseif (x1 <= 3.25e+49)
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * t_2) + (t_1 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * 6.0)))))));
	else
		tmp = (x1 ^ 2.0) * ((x1 * ((x1 * 6.0) - 3.0)) + (x2 * (8.0 + (3.0 * (-1.0 / x2)))));
	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]}, If[LessEqual[x1, -1.4e+58], N[(6.0 * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 3.25e+49], N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$0 * t$95$2), $MachinePrecision] + 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] * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Power[x1, 2.0], $MachinePrecision] * N[(N[(x1 * N[(N[(x1 * 6.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision] + N[(x2 * N[(8.0 + N[(3.0 * N[(-1.0 / x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -1.3999999999999999e58

   1. Initial program 13.6%

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

   3. Simplified 22.7%

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

   5. Taylor expanded in x1 around -inf 100.0%

      \[\leadsto \color{blue}{{x1}^{4} \cdot \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{15 + -1 \cdot \left(6 + -4 \cdot \left(2 \cdot x2 - 3\right)\right)}{x1}}{x1}\right)} \]

   6. Taylor expanded in x2 around -inf 59.2%

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

      1. mul-1-neg 59.2%

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

      2. distribute-rgt-neg-in 59.2%

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

      3. mul-1-neg 59.2%

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

      4. unsub-neg 59.2%

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

      5. *-commutative 59.2%

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

      6. associate-/l* 59.2%

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

   8. Simplified 59.2%

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

   9. Taylor expanded in x1 around inf 100.0%

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

       1. *-commutative 100.0%

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

   11. Simplified 100.0%

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

   if -1.3999999999999999e58 < x1 < 3.25000000000000025e49

   1. Initial program 99.3%

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

      1. fma-define 99.3%

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

      2. *-commutative 99.3%

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

      3. fma-define 99.3%

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

      4. clear-num 99.3%

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

      5. inv-pow 99.3%

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

      6. *-commutative 99.3%

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

      7. fma-define 99.3%

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

      8. associate-*r* 99.4%

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

      9. fma-define 99.4%

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

      10. pow2 99.4%

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

   4. Applied egg-rr 99.4%

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

      1. unpow-1 99.4%

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

   6. Simplified 99.4%

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

   7. Taylor expanded in x1 around inf 94.3%

      \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(\color{blue}{12} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   if 3.25000000000000025e49 < x1

   1. Initial program 43.5%

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

   3. Simplified 43.5%

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

   5. Taylor expanded in x1 around -inf 100.0%

      \[\leadsto \color{blue}{{x1}^{4} \cdot \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{15 + -1 \cdot \left(6 + -4 \cdot \left(2 \cdot x2 - 3\right)\right)}{x1}}{x1}\right)} \]

   6. Taylor expanded in x2 around -inf 60.6%

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

      1. mul-1-neg 60.6%

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

      2. distribute-rgt-neg-in 60.6%

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

      3. mul-1-neg 60.6%

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

      4. unsub-neg 60.6%

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

      5. *-commutative 60.6%

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

      6. associate-/l* 60.5%

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

   8. Simplified 60.5%

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

   9. Taylor expanded in x1 around 0 99.9%

      \[\leadsto \color{blue}{{x1}^{2} \cdot \left(x1 \cdot \left(6 \cdot x1 - 3\right) + x2 \cdot \left(8 - 3 \cdot \frac{1}{x2}\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 96.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.4 \cdot 10^{+58}:\\ \;\;\;\;6 \cdot {x1}^{4}\\ \mathbf{elif}\;x1 \leq 3.25 \cdot 10^{+49}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot 6\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;{x1}^{2} \cdot \left(x1 \cdot \left(x1 \cdot 6 - 3\right) + x2 \cdot \left(8 + 3 \cdot \frac{-1}{x2}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 96.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := x1 \cdot x1 + 1\\ t_2 := \frac{\left(t\_0 + 2 \cdot x2\right) - x1}{t\_1}\\ \mathbf{if}\;x1 \leq -1.4 \cdot 10^{+58} \lor \neg \left(x1 \leq 4.4 \cdot 10^{+49}\right):\\ \;\;\;\;6 \cdot {x1}^{4}\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t\_0 - 2 \cdot x2\right) - x1}{t\_1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(t\_0 \cdot t\_2 + t\_1 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t\_2\right) \cdot \left(t\_2 - 3\right) + \left(x1 \cdot x1\right) \cdot 6\right)\right)\right)\right)\right)\\ \end{array} \end{array} \]

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)))
   (if (or (<= x1 -1.4e+58) (not (<= x1 4.4e+49)))
     (* 6.0 (pow x1 4.0))
     (+
      x1
      (+
       (* 3.0 (/ (- (- t_0 (* 2.0 x2)) x1) t_1))
       (+
        x1
        (+
         (* x1 (* x1 x1))
         (+
          (* t_0 t_2)
          (*
           t_1
           (+ (* (* (* x1 2.0) t_2) (- t_2 3.0)) (* (* x1 x1) 6.0)))))))))))

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 tmp;
	if ((x1 <= -1.4e+58) || !(x1 <= 4.4e+49)) {
		tmp = 6.0 * pow(x1, 4.0);
	} else {
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * t_2) + (t_1 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * 6.0)))))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = x1 * (x1 * 3.0d0)
    t_1 = (x1 * x1) + 1.0d0
    t_2 = ((t_0 + (2.0d0 * x2)) - x1) / t_1
    if ((x1 <= (-1.4d+58)) .or. (.not. (x1 <= 4.4d+49))) then
        tmp = 6.0d0 * (x1 ** 4.0d0)
    else
        tmp = x1 + ((3.0d0 * (((t_0 - (2.0d0 * x2)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * t_2) + (t_1 * ((((x1 * 2.0d0) * t_2) * (t_2 - 3.0d0)) + ((x1 * x1) * 6.0d0)))))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = ((t_0 + (2.0 * x2)) - x1) / t_1;
	double tmp;
	if ((x1 <= -1.4e+58) || !(x1 <= 4.4e+49)) {
		tmp = 6.0 * Math.pow(x1, 4.0);
	} else {
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * t_2) + (t_1 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * 6.0)))))));
	}
	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
	tmp = 0
	if (x1 <= -1.4e+58) or not (x1 <= 4.4e+49):
		tmp = 6.0 * math.pow(x1, 4.0)
	else:
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * t_2) + (t_1 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * 6.0)))))))
	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)
	tmp = 0.0
	if ((x1 <= -1.4e+58) || !(x1 <= 4.4e+49))
		tmp = Float64(6.0 * (x1 ^ 4.0));
	else
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_0 - Float64(2.0 * x2)) - x1) / t_1)) + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(t_0 * t_2) + Float64(t_1 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_2) * Float64(t_2 - 3.0)) + Float64(Float64(x1 * x1) * 6.0))))))));
	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;
	tmp = 0.0;
	if ((x1 <= -1.4e+58) || ~((x1 <= 4.4e+49)))
		tmp = 6.0 * (x1 ^ 4.0);
	else
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * t_2) + (t_1 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * 6.0)))))));
	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]}, If[Or[LessEqual[x1, -1.4e+58], N[Not[LessEqual[x1, 4.4e+49]], $MachinePrecision]], N[(6.0 * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$0 * t$95$2), $MachinePrecision] + 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] * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 2 regimes

2. if x1 < -1.3999999999999999e58 or 4.4000000000000001e49 < x1

   1. Initial program 30.2%

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

   3. Simplified 34.2%

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

   5. Taylor expanded in x1 around -inf 100.0%

      \[\leadsto \color{blue}{{x1}^{4} \cdot \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{15 + -1 \cdot \left(6 + -4 \cdot \left(2 \cdot x2 - 3\right)\right)}{x1}}{x1}\right)} \]

   6. Taylor expanded in x2 around -inf 60.0%

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

      1. mul-1-neg 60.0%

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

      2. distribute-rgt-neg-in 60.0%

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

      3. mul-1-neg 60.0%

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

      4. unsub-neg 60.0%

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

      5. *-commutative 60.0%

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

      6. associate-/l* 60.0%

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

   8. Simplified 60.0%

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

   9. Taylor expanded in x1 around inf 98.9%

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

       1. *-commutative 98.9%

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

   11. Simplified 98.9%

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

   if -1.3999999999999999e58 < x1 < 4.4000000000000001e49

   1. Initial program 99.3%

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

      1. fma-define 99.3%

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

      2. *-commutative 99.3%

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

      3. fma-define 99.3%

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

      4. clear-num 99.3%

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

      5. inv-pow 99.3%

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

      6. *-commutative 99.3%

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

      7. fma-define 99.3%

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

      8. associate-*r* 99.4%

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

      9. fma-define 99.4%

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

      10. pow2 99.4%

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

   4. Applied egg-rr 99.4%

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

      1. unpow-1 99.4%

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

   6. Simplified 99.4%

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

   7. Taylor expanded in x1 around inf 94.3%

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

4. Final simplification 96.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.4 \cdot 10^{+58} \lor \neg \left(x1 \leq 4.4 \cdot 10^{+49}\right):\\ \;\;\;\;6 \cdot {x1}^{4}\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot 6\right)\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 88.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := x1 \cdot x1 + 1\\ t_2 := \frac{\left(t\_0 + 2 \cdot x2\right) - x1}{t\_1}\\ \mathbf{if}\;x1 \leq -2.45 \cdot 10^{+57} \lor \neg \left(x1 \leq 1.3 \cdot 10^{+39}\right):\\ \;\;\;\;6 \cdot {x1}^{4}\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t\_0 - 2 \cdot x2\right) - x1}{t\_1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(t\_0 \cdot t\_2 + t\_1 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(t\_2 \cdot 4 - 6\right) + 4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right)\right)\right)\right)\right)\\ \end{array} \end{array} \]

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)))
   (if (or (<= x1 -2.45e+57) (not (<= x1 1.3e+39)))
     (* 6.0 (pow x1 4.0))
     (+
      x1
      (+
       (* 3.0 (/ (- (- t_0 (* 2.0 x2)) x1) t_1))
       (+
        x1
        (+
         (* x1 (* x1 x1))
         (+
          (* t_0 t_2)
          (*
           t_1
           (+
            (* (* x1 x1) (- (* t_2 4.0) 6.0))
            (* 4.0 (* x1 (* x2 (- (* 2.0 x2) 3.0))))))))))))))

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 tmp;
	if ((x1 <= -2.45e+57) || !(x1 <= 1.3e+39)) {
		tmp = 6.0 * pow(x1, 4.0);
	} else {
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * t_2) + (t_1 * (((x1 * x1) * ((t_2 * 4.0) - 6.0)) + (4.0 * (x1 * (x2 * ((2.0 * x2) - 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 * 3.0d0)
    t_1 = (x1 * x1) + 1.0d0
    t_2 = ((t_0 + (2.0d0 * x2)) - x1) / t_1
    if ((x1 <= (-2.45d+57)) .or. (.not. (x1 <= 1.3d+39))) then
        tmp = 6.0d0 * (x1 ** 4.0d0)
    else
        tmp = x1 + ((3.0d0 * (((t_0 - (2.0d0 * x2)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * t_2) + (t_1 * (((x1 * x1) * ((t_2 * 4.0d0) - 6.0d0)) + (4.0d0 * (x1 * (x2 * ((2.0d0 * x2) - 3.0d0))))))))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = ((t_0 + (2.0 * x2)) - x1) / t_1;
	double tmp;
	if ((x1 <= -2.45e+57) || !(x1 <= 1.3e+39)) {
		tmp = 6.0 * Math.pow(x1, 4.0);
	} else {
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * t_2) + (t_1 * (((x1 * x1) * ((t_2 * 4.0) - 6.0)) + (4.0 * (x1 * (x2 * ((2.0 * x2) - 3.0))))))))));
	}
	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
	tmp = 0
	if (x1 <= -2.45e+57) or not (x1 <= 1.3e+39):
		tmp = 6.0 * math.pow(x1, 4.0)
	else:
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * t_2) + (t_1 * (((x1 * x1) * ((t_2 * 4.0) - 6.0)) + (4.0 * (x1 * (x2 * ((2.0 * x2) - 3.0))))))))))
	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)
	tmp = 0.0
	if ((x1 <= -2.45e+57) || !(x1 <= 1.3e+39))
		tmp = Float64(6.0 * (x1 ^ 4.0));
	else
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_0 - Float64(2.0 * x2)) - x1) / t_1)) + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(t_0 * t_2) + Float64(t_1 * Float64(Float64(Float64(x1 * x1) * Float64(Float64(t_2 * 4.0) - 6.0)) + Float64(4.0 * Float64(x1 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0)))))))))));
	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;
	tmp = 0.0;
	if ((x1 <= -2.45e+57) || ~((x1 <= 1.3e+39)))
		tmp = 6.0 * (x1 ^ 4.0);
	else
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * t_2) + (t_1 * (((x1 * x1) * ((t_2 * 4.0) - 6.0)) + (4.0 * (x1 * (x2 * ((2.0 * x2) - 3.0))))))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(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]}, If[Or[LessEqual[x1, -2.45e+57], N[Not[LessEqual[x1, 1.3e+39]], $MachinePrecision]], N[(6.0 * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$0 * t$95$2), $MachinePrecision] + N[(t$95$1 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$2 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] + N[(4.0 * N[(x1 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 2 regimes

2. if x1 < -2.45e57 or 1.3e39 < x1

   1. Initial program 32.9%

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

   3. Simplified 36.8%

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

   5. Taylor expanded in x1 around -inf 99.1%

      \[\leadsto \color{blue}{{x1}^{4} \cdot \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{15 + -1 \cdot \left(6 + -4 \cdot \left(2 \cdot x2 - 3\right)\right)}{x1}}{x1}\right)} \]

   6. Taylor expanded in x2 around -inf 59.7%

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

      1. mul-1-neg 59.7%

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

      2. distribute-rgt-neg-in 59.7%

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

      3. mul-1-neg 59.7%

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

      4. unsub-neg 59.7%

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

      5. *-commutative 59.7%

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

      6. associate-/l* 59.7%

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

   8. Simplified 59.7%

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

   9. Taylor expanded in x1 around inf 97.1%

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

       1. *-commutative 97.1%

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

   11. Simplified 97.1%

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

   if -2.45e57 < x1 < 1.3e39

   1. Initial program 99.3%

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

   3. Taylor expanded in x1 around 0 93.7%

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

      1. +-commutative 93.7%

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

      2. mul-1-neg 93.7%

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

      3. unsub-neg 93.7%

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

   5. Simplified 93.7%

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

   6. Taylor expanded in x1 around 0 80.2%

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

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -2.45 \cdot 10^{+57} \lor \neg \left(x1 \leq 1.3 \cdot 10^{+39}\right):\\ \;\;\;\;6 \cdot {x1}^{4}\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right) + 4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right)\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 88.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := x1 \cdot \left(x1 \cdot x1\right)\\ t_2 := x1 \cdot \left(x1 \cdot 3\right)\\ t_3 := \frac{\left(t\_2 + 2 \cdot x2\right) - x1}{t\_0}\\ t_4 := \left(x1 \cdot x1\right) \cdot \left(t\_3 \cdot 4 - 6\right)\\ t_5 := t\_2 \cdot t\_3\\ \mathbf{if}\;x1 \leq -6.5 \cdot 10^{+85}:\\ \;\;\;\;x1 + x2 \cdot \left(\frac{x1 \cdot \left(x1 \cdot \left(9 + x1 \cdot -19\right) - 2\right)}{x2} - 6\right)\\ \mathbf{elif}\;x1 \leq -0.7:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(t\_1 + \left(t\_5 + t\_0 \cdot \left(t\_4 + \left(t\_3 - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(2 \cdot x2 - x1\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 26000:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(\left(-4 \cdot \left(x2 \cdot \left(3 + x2 \cdot -2\right)\right) + x1 \cdot \left(\left(2 \cdot \left(3 + x2 \cdot -4\right) + \left(3 \cdot \left(3 - x2 \cdot -2\right) + \left(x2 \cdot 6 + \left(x1 \cdot -19 + x2 \cdot 8\right)\right)\right)\right) - 6\right)\right) - 2\right)\right)\\ \mathbf{elif}\;x1 \leq 10^{+153}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t\_2 - 2 \cdot x2\right) - x1}{t\_0} + \left(x1 + \left(t\_1 + \left(t\_5 + t\_0 \cdot \left(x1 \cdot 2 + t\_4\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ (* x1 x1) 1.0))
        (t_1 (* x1 (* x1 x1)))
        (t_2 (* x1 (* x1 3.0)))
        (t_3 (/ (- (+ t_2 (* 2.0 x2)) x1) t_0))
        (t_4 (* (* x1 x1) (- (* t_3 4.0) 6.0)))
        (t_5 (* t_2 t_3)))
   (if (<= x1 -6.5e+85)
     (+ x1 (* x2 (- (/ (* x1 (- (* x1 (+ 9.0 (* x1 -19.0))) 2.0)) x2) 6.0)))
     (if (<= x1 -0.7)
       (+
        x1
        (+
         9.0
         (+
          x1
          (+
           t_1
           (+
            t_5
            (*
             t_0
             (+ t_4 (* (- t_3 3.0) (* (* x1 2.0) (- (* 2.0 x2) x1))))))))))
       (if (<= x1 26000.0)
         (+
          x1
          (+
           (* x2 -6.0)
           (*
            x1
            (-
             (+
              (* -4.0 (* x2 (+ 3.0 (* x2 -2.0))))
              (*
               x1
               (-
                (+
                 (* 2.0 (+ 3.0 (* x2 -4.0)))
                 (+
                  (* 3.0 (- 3.0 (* x2 -2.0)))
                  (+ (* x2 6.0) (+ (* x1 -19.0) (* x2 8.0)))))
                6.0)))
             2.0))))
         (if (<= x1 1e+153)
           (+
            x1
            (+
             (* 3.0 (/ (- (- t_2 (* 2.0 x2)) x1) t_0))
             (+ x1 (+ t_1 (+ t_5 (* t_0 (+ (* x1 2.0) t_4)))))))
           (+ (* x2 -6.0) (* x1 (+ (* x1 9.0) -1.0)))))))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = x1 * (x1 * x1);
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = ((t_2 + (2.0 * x2)) - x1) / t_0;
	double t_4 = (x1 * x1) * ((t_3 * 4.0) - 6.0);
	double t_5 = t_2 * t_3;
	double tmp;
	if (x1 <= -6.5e+85) {
		tmp = x1 + (x2 * (((x1 * ((x1 * (9.0 + (x1 * -19.0))) - 2.0)) / x2) - 6.0));
	} else if (x1 <= -0.7) {
		tmp = x1 + (9.0 + (x1 + (t_1 + (t_5 + (t_0 * (t_4 + ((t_3 - 3.0) * ((x1 * 2.0) * ((2.0 * x2) - x1)))))))));
	} else if (x1 <= 26000.0) {
		tmp = x1 + ((x2 * -6.0) + (x1 * (((-4.0 * (x2 * (3.0 + (x2 * -2.0)))) + (x1 * (((2.0 * (3.0 + (x2 * -4.0))) + ((3.0 * (3.0 - (x2 * -2.0))) + ((x2 * 6.0) + ((x1 * -19.0) + (x2 * 8.0))))) - 6.0))) - 2.0)));
	} else if (x1 <= 1e+153) {
		tmp = x1 + ((3.0 * (((t_2 - (2.0 * x2)) - x1) / t_0)) + (x1 + (t_1 + (t_5 + (t_0 * ((x1 * 2.0) + t_4))))));
	} else {
		tmp = (x2 * -6.0) + (x1 * ((x1 * 9.0) + -1.0));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_0 = (x1 * x1) + 1.0d0
    t_1 = x1 * (x1 * x1)
    t_2 = x1 * (x1 * 3.0d0)
    t_3 = ((t_2 + (2.0d0 * x2)) - x1) / t_0
    t_4 = (x1 * x1) * ((t_3 * 4.0d0) - 6.0d0)
    t_5 = t_2 * t_3
    if (x1 <= (-6.5d+85)) then
        tmp = x1 + (x2 * (((x1 * ((x1 * (9.0d0 + (x1 * (-19.0d0)))) - 2.0d0)) / x2) - 6.0d0))
    else if (x1 <= (-0.7d0)) then
        tmp = x1 + (9.0d0 + (x1 + (t_1 + (t_5 + (t_0 * (t_4 + ((t_3 - 3.0d0) * ((x1 * 2.0d0) * ((2.0d0 * x2) - x1)))))))))
    else if (x1 <= 26000.0d0) then
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * ((((-4.0d0) * (x2 * (3.0d0 + (x2 * (-2.0d0))))) + (x1 * (((2.0d0 * (3.0d0 + (x2 * (-4.0d0)))) + ((3.0d0 * (3.0d0 - (x2 * (-2.0d0)))) + ((x2 * 6.0d0) + ((x1 * (-19.0d0)) + (x2 * 8.0d0))))) - 6.0d0))) - 2.0d0)))
    else if (x1 <= 1d+153) then
        tmp = x1 + ((3.0d0 * (((t_2 - (2.0d0 * x2)) - x1) / t_0)) + (x1 + (t_1 + (t_5 + (t_0 * ((x1 * 2.0d0) + t_4))))))
    else
        tmp = (x2 * (-6.0d0)) + (x1 * ((x1 * 9.0d0) + (-1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = x1 * (x1 * x1);
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = ((t_2 + (2.0 * x2)) - x1) / t_0;
	double t_4 = (x1 * x1) * ((t_3 * 4.0) - 6.0);
	double t_5 = t_2 * t_3;
	double tmp;
	if (x1 <= -6.5e+85) {
		tmp = x1 + (x2 * (((x1 * ((x1 * (9.0 + (x1 * -19.0))) - 2.0)) / x2) - 6.0));
	} else if (x1 <= -0.7) {
		tmp = x1 + (9.0 + (x1 + (t_1 + (t_5 + (t_0 * (t_4 + ((t_3 - 3.0) * ((x1 * 2.0) * ((2.0 * x2) - x1)))))))));
	} else if (x1 <= 26000.0) {
		tmp = x1 + ((x2 * -6.0) + (x1 * (((-4.0 * (x2 * (3.0 + (x2 * -2.0)))) + (x1 * (((2.0 * (3.0 + (x2 * -4.0))) + ((3.0 * (3.0 - (x2 * -2.0))) + ((x2 * 6.0) + ((x1 * -19.0) + (x2 * 8.0))))) - 6.0))) - 2.0)));
	} else if (x1 <= 1e+153) {
		tmp = x1 + ((3.0 * (((t_2 - (2.0 * x2)) - x1) / t_0)) + (x1 + (t_1 + (t_5 + (t_0 * ((x1 * 2.0) + t_4))))));
	} else {
		tmp = (x2 * -6.0) + (x1 * ((x1 * 9.0) + -1.0));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x1 * x1) + 1.0
	t_1 = x1 * (x1 * x1)
	t_2 = x1 * (x1 * 3.0)
	t_3 = ((t_2 + (2.0 * x2)) - x1) / t_0
	t_4 = (x1 * x1) * ((t_3 * 4.0) - 6.0)
	t_5 = t_2 * t_3
	tmp = 0
	if x1 <= -6.5e+85:
		tmp = x1 + (x2 * (((x1 * ((x1 * (9.0 + (x1 * -19.0))) - 2.0)) / x2) - 6.0))
	elif x1 <= -0.7:
		tmp = x1 + (9.0 + (x1 + (t_1 + (t_5 + (t_0 * (t_4 + ((t_3 - 3.0) * ((x1 * 2.0) * ((2.0 * x2) - x1)))))))))
	elif x1 <= 26000.0:
		tmp = x1 + ((x2 * -6.0) + (x1 * (((-4.0 * (x2 * (3.0 + (x2 * -2.0)))) + (x1 * (((2.0 * (3.0 + (x2 * -4.0))) + ((3.0 * (3.0 - (x2 * -2.0))) + ((x2 * 6.0) + ((x1 * -19.0) + (x2 * 8.0))))) - 6.0))) - 2.0)))
	elif x1 <= 1e+153:
		tmp = x1 + ((3.0 * (((t_2 - (2.0 * x2)) - x1) / t_0)) + (x1 + (t_1 + (t_5 + (t_0 * ((x1 * 2.0) + t_4))))))
	else:
		tmp = (x2 * -6.0) + (x1 * ((x1 * 9.0) + -1.0))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * x1) + 1.0)
	t_1 = Float64(x1 * Float64(x1 * x1))
	t_2 = Float64(x1 * Float64(x1 * 3.0))
	t_3 = Float64(Float64(Float64(t_2 + Float64(2.0 * x2)) - x1) / t_0)
	t_4 = Float64(Float64(x1 * x1) * Float64(Float64(t_3 * 4.0) - 6.0))
	t_5 = Float64(t_2 * t_3)
	tmp = 0.0
	if (x1 <= -6.5e+85)
		tmp = Float64(x1 + Float64(x2 * Float64(Float64(Float64(x1 * Float64(Float64(x1 * Float64(9.0 + Float64(x1 * -19.0))) - 2.0)) / x2) - 6.0)));
	elseif (x1 <= -0.7)
		tmp = Float64(x1 + Float64(9.0 + Float64(x1 + Float64(t_1 + Float64(t_5 + Float64(t_0 * Float64(t_4 + Float64(Float64(t_3 - 3.0) * Float64(Float64(x1 * 2.0) * Float64(Float64(2.0 * x2) - x1))))))))));
	elseif (x1 <= 26000.0)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(Float64(-4.0 * Float64(x2 * Float64(3.0 + Float64(x2 * -2.0)))) + Float64(x1 * Float64(Float64(Float64(2.0 * Float64(3.0 + Float64(x2 * -4.0))) + Float64(Float64(3.0 * Float64(3.0 - Float64(x2 * -2.0))) + Float64(Float64(x2 * 6.0) + Float64(Float64(x1 * -19.0) + Float64(x2 * 8.0))))) - 6.0))) - 2.0))));
	elseif (x1 <= 1e+153)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_2 - Float64(2.0 * x2)) - x1) / t_0)) + Float64(x1 + Float64(t_1 + Float64(t_5 + Float64(t_0 * Float64(Float64(x1 * 2.0) + t_4)))))));
	else
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(x1 * 9.0) + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x1 * x1) + 1.0;
	t_1 = x1 * (x1 * x1);
	t_2 = x1 * (x1 * 3.0);
	t_3 = ((t_2 + (2.0 * x2)) - x1) / t_0;
	t_4 = (x1 * x1) * ((t_3 * 4.0) - 6.0);
	t_5 = t_2 * t_3;
	tmp = 0.0;
	if (x1 <= -6.5e+85)
		tmp = x1 + (x2 * (((x1 * ((x1 * (9.0 + (x1 * -19.0))) - 2.0)) / x2) - 6.0));
	elseif (x1 <= -0.7)
		tmp = x1 + (9.0 + (x1 + (t_1 + (t_5 + (t_0 * (t_4 + ((t_3 - 3.0) * ((x1 * 2.0) * ((2.0 * x2) - x1)))))))));
	elseif (x1 <= 26000.0)
		tmp = x1 + ((x2 * -6.0) + (x1 * (((-4.0 * (x2 * (3.0 + (x2 * -2.0)))) + (x1 * (((2.0 * (3.0 + (x2 * -4.0))) + ((3.0 * (3.0 - (x2 * -2.0))) + ((x2 * 6.0) + ((x1 * -19.0) + (x2 * 8.0))))) - 6.0))) - 2.0)));
	elseif (x1 <= 1e+153)
		tmp = x1 + ((3.0 * (((t_2 - (2.0 * x2)) - x1) / t_0)) + (x1 + (t_1 + (t_5 + (t_0 * ((x1 * 2.0) + t_4))))));
	else
		tmp = (x2 * -6.0) + (x1 * ((x1 * 9.0) + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(t$95$2 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]}, Block[{t$95$4 = N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$3 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(t$95$2 * t$95$3), $MachinePrecision]}, If[LessEqual[x1, -6.5e+85], N[(x1 + N[(x2 * N[(N[(N[(x1 * N[(N[(x1 * N[(9.0 + N[(x1 * -19.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision] / x2), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -0.7], N[(x1 + N[(9.0 + N[(x1 + N[(t$95$1 + N[(t$95$5 + N[(t$95$0 * N[(t$95$4 + N[(N[(t$95$3 - 3.0), $MachinePrecision] * N[(N[(x1 * 2.0), $MachinePrecision] * N[(N[(2.0 * x2), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 26000.0], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(N[(-4.0 * N[(x2 * N[(3.0 + N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(N[(N[(2.0 * N[(3.0 + N[(x2 * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(3.0 * N[(3.0 - N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x2 * 6.0), $MachinePrecision] + N[(N[(x1 * -19.0), $MachinePrecision] + N[(x2 * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1e+153], N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$2 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(t$95$1 + N[(t$95$5 + N[(t$95$0 * N[(N[(x1 * 2.0), $MachinePrecision] + t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x1 < -6.4999999999999994e85

   1. Initial program 7.3%

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

   3. Simplified 17.1%

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

   5. Taylor expanded in x1 around 0 61.5%

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

   6. Taylor expanded in x2 around 0 93.4%

      \[\leadsto x1 + \left(-6 \cdot x2 + x1 \cdot \left(\color{blue}{x1 \cdot \left(9 + -19 \cdot x1\right)} - 2\right)\right) \]
   7. Step-by-step derivation

      1. *-commutative 93.4%

         \[\leadsto x1 + \left(-6 \cdot x2 + x1 \cdot \left(x1 \cdot \left(9 + \color{blue}{x1 \cdot -19}\right) - 2\right)\right) \]

   8. Simplified 93.4%

      \[\leadsto x1 + \left(-6 \cdot x2 + x1 \cdot \left(\color{blue}{x1 \cdot \left(9 + x1 \cdot -19\right)} - 2\right)\right) \]

   9. Taylor expanded in x2 around inf 97.7%

      \[\leadsto x1 + \color{blue}{x2 \cdot \left(\frac{x1 \cdot \left(x1 \cdot \left(9 + -19 \cdot x1\right) - 2\right)}{x2} - 6\right)} \]

   if -6.4999999999999994e85 < x1 < -0.69999999999999996

   1. Initial program 98.8%

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

   3. Taylor expanded in x1 around 0 80.8%

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

      1. +-commutative 80.8%

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

      2. mul-1-neg 80.8%

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

      3. unsub-neg 80.8%

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

   5. Simplified 80.8%

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

   6. Taylor expanded in x1 around inf 80.8%

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

   if -0.69999999999999996 < x1 < 26000

   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 85.8%

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

   5. Taylor expanded in x1 around 0 71.2%

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

   6. Taylor expanded in x2 around 0 85.0%

      \[\leadsto x1 + \left(-6 \cdot x2 + x1 \cdot \left(\left(-4 \cdot \left(x2 \cdot \left(3 + -2 \cdot x2\right)\right) + x1 \cdot \left(\left(2 \cdot \left(3 + -4 \cdot x2\right) + \left(3 \cdot \left(3 - -2 \cdot x2\right) + \left(6 \cdot x2 + \left(8 \cdot x2 + \color{blue}{-19 \cdot x1}\right)\right)\right)\right) - 6\right)\right) - 2\right)\right) \]
   7. Step-by-step derivation

      1. *-commutative 85.0%

         \[\leadsto x1 + \left(-6 \cdot x2 + x1 \cdot \left(\left(-4 \cdot \left(x2 \cdot \left(3 + -2 \cdot x2\right)\right) + x1 \cdot \left(\left(2 \cdot \left(3 + -4 \cdot x2\right) + \left(3 \cdot \left(3 - -2 \cdot x2\right) + \left(6 \cdot x2 + \left(8 \cdot x2 + \color{blue}{x1 \cdot -19}\right)\right)\right)\right) - 6\right)\right) - 2\right)\right) \]

   8. Simplified 85.0%

      \[\leadsto x1 + \left(-6 \cdot x2 + x1 \cdot \left(\left(-4 \cdot \left(x2 \cdot \left(3 + -2 \cdot x2\right)\right) + x1 \cdot \left(\left(2 \cdot \left(3 + -4 \cdot x2\right) + \left(3 \cdot \left(3 - -2 \cdot x2\right) + \left(6 \cdot x2 + \left(8 \cdot x2 + \color{blue}{x1 \cdot -19}\right)\right)\right)\right) - 6\right)\right) - 2\right)\right) \]

   if 26000 < x1 < 1e153

   1. Initial program 99.5%

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

   3. Taylor expanded in x1 around 0 83.8%

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

      1. +-commutative 83.8%

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

      2. mul-1-neg 83.8%

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

      3. unsub-neg 83.8%

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

   5. Simplified 83.8%

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

   6. Taylor expanded in x1 around inf 86.9%

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

      1. *-commutative 86.9%

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

   8. Simplified 86.9%

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

   if 1e153 < x1

   1. Initial program 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in x1 around 0 0.0%

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

   6. Taylor expanded in x2 around 0 0.0%

      \[\leadsto x1 + \left(-6 \cdot x2 + x1 \cdot \left(\color{blue}{x1 \cdot \left(9 + -19 \cdot x1\right)} - 2\right)\right) \]
   7. Step-by-step derivation

      1. *-commutative 0.0%

         \[\leadsto x1 + \left(-6 \cdot x2 + x1 \cdot \left(x1 \cdot \left(9 + \color{blue}{x1 \cdot -19}\right) - 2\right)\right) \]

   8. Simplified 0.0%

      \[\leadsto x1 + \left(-6 \cdot x2 + x1 \cdot \left(\color{blue}{x1 \cdot \left(9 + x1 \cdot -19\right)} - 2\right)\right) \]

   9. Taylor expanded in x1 around 0 100.0%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -6.5 \cdot 10^{+85}:\\ \;\;\;\;x1 + x2 \cdot \left(\frac{x1 \cdot \left(x1 \cdot \left(9 + x1 \cdot -19\right) - 2\right)}{x2} - 6\right)\\ \mathbf{elif}\;x1 \leq -0.7:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right) + \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(2 \cdot x2 - x1\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 26000:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(\left(-4 \cdot \left(x2 \cdot \left(3 + x2 \cdot -2\right)\right) + x1 \cdot \left(\left(2 \cdot \left(3 + x2 \cdot -4\right) + \left(3 \cdot \left(3 - x2 \cdot -2\right) + \left(x2 \cdot 6 + \left(x1 \cdot -19 + x2 \cdot 8\right)\right)\right)\right) - 6\right)\right) - 2\right)\right)\\ \mathbf{elif}\;x1 \leq 10^{+153}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 \cdot x1 + 1\right) \cdot \left(x1 \cdot 2 + \left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 + -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 89.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := x1 \cdot x1 + 1\\ t_2 := \frac{\left(t\_0 + 2 \cdot x2\right) - x1}{t\_1}\\ t_3 := x1 + \left(3 \cdot \frac{\left(t\_0 - 2 \cdot x2\right) - x1}{t\_1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(t\_0 \cdot t\_2 + t\_1 \cdot \left(x1 \cdot 2 + \left(x1 \cdot x1\right) \cdot \left(t\_2 \cdot 4 - 6\right)\right)\right)\right)\right)\right)\\ \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 + x1 \cdot \left(x1 \cdot \left(9 + x1 \cdot -19\right) - 2\right)\\ \mathbf{elif}\;x1 \leq -3700000000:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x1 \leq 5500:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(\left(-4 \cdot \left(x2 \cdot \left(3 + x2 \cdot -2\right)\right) + x1 \cdot \left(\left(2 \cdot \left(3 + x2 \cdot -4\right) + \left(3 \cdot \left(3 - x2 \cdot -2\right) + \left(x2 \cdot 6 + \left(x1 \cdot -19 + x2 \cdot 8\right)\right)\right)\right) - 6\right)\right) - 2\right)\right)\\ \mathbf{elif}\;x1 \leq 10^{+153}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 + -1\right)\\ \end{array} \end{array} \]

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
          (+
           (* 3.0 (/ (- (- t_0 (* 2.0 x2)) x1) t_1))
           (+
            x1
            (+
             (* x1 (* x1 x1))
             (+
              (* t_0 t_2)
              (* t_1 (+ (* x1 2.0) (* (* x1 x1) (- (* t_2 4.0) 6.0)))))))))))
   (if (<= x1 -5.6e+102)
     (+ x1 (* x1 (- (* x1 (+ 9.0 (* x1 -19.0))) 2.0)))
     (if (<= x1 -3700000000.0)
       t_3
       (if (<= x1 5500.0)
         (+
          x1
          (+
           (* x2 -6.0)
           (*
            x1
            (-
             (+
              (* -4.0 (* x2 (+ 3.0 (* x2 -2.0))))
              (*
               x1
               (-
                (+
                 (* 2.0 (+ 3.0 (* x2 -4.0)))
                 (+
                  (* 3.0 (- 3.0 (* x2 -2.0)))
                  (+ (* x2 6.0) (+ (* x1 -19.0) (* x2 8.0)))))
                6.0)))
             2.0))))
         (if (<= x1 1e+153)
           t_3
           (+ (* x2 -6.0) (* x1 (+ (* x1 9.0) -1.0)))))))))

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 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * t_2) + (t_1 * ((x1 * 2.0) + ((x1 * x1) * ((t_2 * 4.0) - 6.0))))))));
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = x1 + (x1 * ((x1 * (9.0 + (x1 * -19.0))) - 2.0));
	} else if (x1 <= -3700000000.0) {
		tmp = t_3;
	} else if (x1 <= 5500.0) {
		tmp = x1 + ((x2 * -6.0) + (x1 * (((-4.0 * (x2 * (3.0 + (x2 * -2.0)))) + (x1 * (((2.0 * (3.0 + (x2 * -4.0))) + ((3.0 * (3.0 - (x2 * -2.0))) + ((x2 * 6.0) + ((x1 * -19.0) + (x2 * 8.0))))) - 6.0))) - 2.0)));
	} else if (x1 <= 1e+153) {
		tmp = t_3;
	} else {
		tmp = (x2 * -6.0) + (x1 * ((x1 * 9.0) + -1.0));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_0 = x1 * (x1 * 3.0d0)
    t_1 = (x1 * x1) + 1.0d0
    t_2 = ((t_0 + (2.0d0 * x2)) - x1) / t_1
    t_3 = x1 + ((3.0d0 * (((t_0 - (2.0d0 * x2)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * t_2) + (t_1 * ((x1 * 2.0d0) + ((x1 * x1) * ((t_2 * 4.0d0) - 6.0d0))))))))
    if (x1 <= (-5.6d+102)) then
        tmp = x1 + (x1 * ((x1 * (9.0d0 + (x1 * (-19.0d0)))) - 2.0d0))
    else if (x1 <= (-3700000000.0d0)) then
        tmp = t_3
    else if (x1 <= 5500.0d0) then
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * ((((-4.0d0) * (x2 * (3.0d0 + (x2 * (-2.0d0))))) + (x1 * (((2.0d0 * (3.0d0 + (x2 * (-4.0d0)))) + ((3.0d0 * (3.0d0 - (x2 * (-2.0d0)))) + ((x2 * 6.0d0) + ((x1 * (-19.0d0)) + (x2 * 8.0d0))))) - 6.0d0))) - 2.0d0)))
    else if (x1 <= 1d+153) then
        tmp = t_3
    else
        tmp = (x2 * (-6.0d0)) + (x1 * ((x1 * 9.0d0) + (-1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = ((t_0 + (2.0 * x2)) - x1) / t_1;
	double t_3 = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * t_2) + (t_1 * ((x1 * 2.0) + ((x1 * x1) * ((t_2 * 4.0) - 6.0))))))));
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = x1 + (x1 * ((x1 * (9.0 + (x1 * -19.0))) - 2.0));
	} else if (x1 <= -3700000000.0) {
		tmp = t_3;
	} else if (x1 <= 5500.0) {
		tmp = x1 + ((x2 * -6.0) + (x1 * (((-4.0 * (x2 * (3.0 + (x2 * -2.0)))) + (x1 * (((2.0 * (3.0 + (x2 * -4.0))) + ((3.0 * (3.0 - (x2 * -2.0))) + ((x2 * 6.0) + ((x1 * -19.0) + (x2 * 8.0))))) - 6.0))) - 2.0)));
	} else if (x1 <= 1e+153) {
		tmp = t_3;
	} else {
		tmp = (x2 * -6.0) + (x1 * ((x1 * 9.0) + -1.0));
	}
	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 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * t_2) + (t_1 * ((x1 * 2.0) + ((x1 * x1) * ((t_2 * 4.0) - 6.0))))))))
	tmp = 0
	if x1 <= -5.6e+102:
		tmp = x1 + (x1 * ((x1 * (9.0 + (x1 * -19.0))) - 2.0))
	elif x1 <= -3700000000.0:
		tmp = t_3
	elif x1 <= 5500.0:
		tmp = x1 + ((x2 * -6.0) + (x1 * (((-4.0 * (x2 * (3.0 + (x2 * -2.0)))) + (x1 * (((2.0 * (3.0 + (x2 * -4.0))) + ((3.0 * (3.0 - (x2 * -2.0))) + ((x2 * 6.0) + ((x1 * -19.0) + (x2 * 8.0))))) - 6.0))) - 2.0)))
	elif x1 <= 1e+153:
		tmp = t_3
	else:
		tmp = (x2 * -6.0) + (x1 * ((x1 * 9.0) + -1.0))
	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(3.0 * Float64(Float64(Float64(t_0 - Float64(2.0 * x2)) - x1) / t_1)) + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(t_0 * t_2) + Float64(t_1 * Float64(Float64(x1 * 2.0) + Float64(Float64(x1 * x1) * Float64(Float64(t_2 * 4.0) - 6.0)))))))))
	tmp = 0.0
	if (x1 <= -5.6e+102)
		tmp = Float64(x1 + Float64(x1 * Float64(Float64(x1 * Float64(9.0 + Float64(x1 * -19.0))) - 2.0)));
	elseif (x1 <= -3700000000.0)
		tmp = t_3;
	elseif (x1 <= 5500.0)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(Float64(-4.0 * Float64(x2 * Float64(3.0 + Float64(x2 * -2.0)))) + Float64(x1 * Float64(Float64(Float64(2.0 * Float64(3.0 + Float64(x2 * -4.0))) + Float64(Float64(3.0 * Float64(3.0 - Float64(x2 * -2.0))) + Float64(Float64(x2 * 6.0) + Float64(Float64(x1 * -19.0) + Float64(x2 * 8.0))))) - 6.0))) - 2.0))));
	elseif (x1 <= 1e+153)
		tmp = t_3;
	else
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(x1 * 9.0) + -1.0)));
	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 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * t_2) + (t_1 * ((x1 * 2.0) + ((x1 * x1) * ((t_2 * 4.0) - 6.0))))))));
	tmp = 0.0;
	if (x1 <= -5.6e+102)
		tmp = x1 + (x1 * ((x1 * (9.0 + (x1 * -19.0))) - 2.0));
	elseif (x1 <= -3700000000.0)
		tmp = t_3;
	elseif (x1 <= 5500.0)
		tmp = x1 + ((x2 * -6.0) + (x1 * (((-4.0 * (x2 * (3.0 + (x2 * -2.0)))) + (x1 * (((2.0 * (3.0 + (x2 * -4.0))) + ((3.0 * (3.0 - (x2 * -2.0))) + ((x2 * 6.0) + ((x1 * -19.0) + (x2 * 8.0))))) - 6.0))) - 2.0)));
	elseif (x1 <= 1e+153)
		tmp = t_3;
	else
		tmp = (x2 * -6.0) + (x1 * ((x1 * 9.0) + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(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[(3.0 * N[(N[(N[(t$95$0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$0 * t$95$2), $MachinePrecision] + N[(t$95$1 * N[(N[(x1 * 2.0), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$2 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -5.6e+102], N[(x1 + N[(x1 * N[(N[(x1 * N[(9.0 + N[(x1 * -19.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -3700000000.0], t$95$3, If[LessEqual[x1, 5500.0], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(N[(-4.0 * N[(x2 * N[(3.0 + N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(N[(N[(2.0 * N[(3.0 + N[(x2 * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(3.0 * N[(3.0 - N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x2 * 6.0), $MachinePrecision] + N[(N[(x1 * -19.0), $MachinePrecision] + N[(x2 * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1e+153], t$95$3, N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -5.60000000000000037e102

   1. Initial program 0.0%

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

   3. Simplified 10.5%

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

   5. Taylor expanded in x1 around 0 65.8%

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

   6. Taylor expanded in x2 around 0 100.0%

      \[\leadsto x1 + \left(-6 \cdot x2 + x1 \cdot \left(\color{blue}{x1 \cdot \left(9 + -19 \cdot x1\right)} - 2\right)\right) \]
   7. Step-by-step derivation

      1. *-commutative 100.0%

         \[\leadsto x1 + \left(-6 \cdot x2 + x1 \cdot \left(x1 \cdot \left(9 + \color{blue}{x1 \cdot -19}\right) - 2\right)\right) \]

   8. Simplified 100.0%

      \[\leadsto x1 + \left(-6 \cdot x2 + x1 \cdot \left(\color{blue}{x1 \cdot \left(9 + x1 \cdot -19\right)} - 2\right)\right) \]

   9. Taylor expanded in x2 around 0 100.0%

      \[\leadsto \color{blue}{x1 + x1 \cdot \left(x1 \cdot \left(9 + -19 \cdot x1\right) - 2\right)} \]

   if -5.60000000000000037e102 < x1 < -3.7e9 or 5500 < x1 < 1e153

   1. Initial program 99.3%

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

   3. Taylor expanded in x1 around 0 84.7%

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

      1. +-commutative 84.7%

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

      2. mul-1-neg 84.7%

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

      3. unsub-neg 84.7%

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

   5. Simplified 84.7%

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

   6. Taylor expanded in x1 around inf 86.1%

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

      1. *-commutative 86.1%

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

   8. Simplified 86.1%

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

   if -3.7e9 < x1 < 5500

   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 86.2%

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

   5. Taylor expanded in x1 around 0 69.3%

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

   6. Taylor expanded in x2 around 0 83.5%

      \[\leadsto x1 + \left(-6 \cdot x2 + x1 \cdot \left(\left(-4 \cdot \left(x2 \cdot \left(3 + -2 \cdot x2\right)\right) + x1 \cdot \left(\left(2 \cdot \left(3 + -4 \cdot x2\right) + \left(3 \cdot \left(3 - -2 \cdot x2\right) + \left(6 \cdot x2 + \left(8 \cdot x2 + \color{blue}{-19 \cdot x1}\right)\right)\right)\right) - 6\right)\right) - 2\right)\right) \]
   7. Step-by-step derivation

      1. *-commutative 83.5%

         \[\leadsto x1 + \left(-6 \cdot x2 + x1 \cdot \left(\left(-4 \cdot \left(x2 \cdot \left(3 + -2 \cdot x2\right)\right) + x1 \cdot \left(\left(2 \cdot \left(3 + -4 \cdot x2\right) + \left(3 \cdot \left(3 - -2 \cdot x2\right) + \left(6 \cdot x2 + \left(8 \cdot x2 + \color{blue}{x1 \cdot -19}\right)\right)\right)\right) - 6\right)\right) - 2\right)\right) \]

   8. Simplified 83.5%

      \[\leadsto x1 + \left(-6 \cdot x2 + x1 \cdot \left(\left(-4 \cdot \left(x2 \cdot \left(3 + -2 \cdot x2\right)\right) + x1 \cdot \left(\left(2 \cdot \left(3 + -4 \cdot x2\right) + \left(3 \cdot \left(3 - -2 \cdot x2\right) + \left(6 \cdot x2 + \left(8 \cdot x2 + \color{blue}{x1 \cdot -19}\right)\right)\right)\right) - 6\right)\right) - 2\right)\right) \]

   if 1e153 < x1

   1. Initial program 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in x1 around 0 0.0%

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

   6. Taylor expanded in x2 around 0 0.0%

      \[\leadsto x1 + \left(-6 \cdot x2 + x1 \cdot \left(\color{blue}{x1 \cdot \left(9 + -19 \cdot x1\right)} - 2\right)\right) \]
   7. Step-by-step derivation

      1. *-commutative 0.0%

         \[\leadsto x1 + \left(-6 \cdot x2 + x1 \cdot \left(x1 \cdot \left(9 + \color{blue}{x1 \cdot -19}\right) - 2\right)\right) \]

   8. Simplified 0.0%

      \[\leadsto x1 + \left(-6 \cdot x2 + x1 \cdot \left(\color{blue}{x1 \cdot \left(9 + x1 \cdot -19\right)} - 2\right)\right) \]

   9. Taylor expanded in x1 around 0 100.0%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 + x1 \cdot \left(x1 \cdot \left(9 + x1 \cdot -19\right) - 2\right)\\ \mathbf{elif}\;x1 \leq -3700000000:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 \cdot x1 + 1\right) \cdot \left(x1 \cdot 2 + \left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 5500:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(\left(-4 \cdot \left(x2 \cdot \left(3 + x2 \cdot -2\right)\right) + x1 \cdot \left(\left(2 \cdot \left(3 + x2 \cdot -4\right) + \left(3 \cdot \left(3 - x2 \cdot -2\right) + \left(x2 \cdot 6 + \left(x1 \cdot -19 + x2 \cdot 8\right)\right)\right)\right) - 6\right)\right) - 2\right)\right)\\ \mathbf{elif}\;x1 \leq 10^{+153}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 \cdot x1 + 1\right) \cdot \left(x1 \cdot 2 + \left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 + -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 88.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := x1 \cdot \left(x1 \cdot x1\right)\\ t_2 := x1 \cdot \left(x1 \cdot 3\right)\\ t_3 := 3 \cdot \frac{\left(t\_2 - 2 \cdot x2\right) - x1}{t\_0}\\ t_4 := \frac{\left(t\_2 + 2 \cdot x2\right) - x1}{t\_0}\\ t_5 := t\_2 \cdot t\_4\\ t_6 := \left(x1 \cdot x1\right) \cdot \left(t\_4 \cdot 4 - 6\right)\\ \mathbf{if}\;x1 \leq -6.5 \cdot 10^{+85}:\\ \;\;\;\;x1 + x2 \cdot \left(\frac{x1 \cdot \left(x1 \cdot \left(9 + x1 \cdot -19\right) - 2\right)}{x2} - 6\right)\\ \mathbf{elif}\;x1 \leq 8600000000000:\\ \;\;\;\;x1 + \left(t\_3 + \left(x1 + \left(t\_1 + \left(t\_5 + t\_0 \cdot \left(t\_6 + 4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 10^{+153}:\\ \;\;\;\;x1 + \left(t\_3 + \left(x1 + \left(t\_1 + \left(t\_5 + t\_0 \cdot \left(x1 \cdot 2 + t\_6\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ (* x1 x1) 1.0))
        (t_1 (* x1 (* x1 x1)))
        (t_2 (* x1 (* x1 3.0)))
        (t_3 (* 3.0 (/ (- (- t_2 (* 2.0 x2)) x1) t_0)))
        (t_4 (/ (- (+ t_2 (* 2.0 x2)) x1) t_0))
        (t_5 (* t_2 t_4))
        (t_6 (* (* x1 x1) (- (* t_4 4.0) 6.0))))
   (if (<= x1 -6.5e+85)
     (+ x1 (* x2 (- (/ (* x1 (- (* x1 (+ 9.0 (* x1 -19.0))) 2.0)) x2) 6.0)))
     (if (<= x1 8600000000000.0)
       (+
        x1
        (+
         t_3
         (+
          x1
          (+
           t_1
           (+ t_5 (* t_0 (+ t_6 (* 4.0 (* x1 (* x2 (- (* 2.0 x2) 3.0)))))))))))
       (if (<= x1 1e+153)
         (+ x1 (+ t_3 (+ x1 (+ t_1 (+ t_5 (* t_0 (+ (* x1 2.0) t_6)))))))
         (+ (* x2 -6.0) (* x1 (+ (* x1 9.0) -1.0))))))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = x1 * (x1 * x1);
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = 3.0 * (((t_2 - (2.0 * x2)) - x1) / t_0);
	double t_4 = ((t_2 + (2.0 * x2)) - x1) / t_0;
	double t_5 = t_2 * t_4;
	double t_6 = (x1 * x1) * ((t_4 * 4.0) - 6.0);
	double tmp;
	if (x1 <= -6.5e+85) {
		tmp = x1 + (x2 * (((x1 * ((x1 * (9.0 + (x1 * -19.0))) - 2.0)) / x2) - 6.0));
	} else if (x1 <= 8600000000000.0) {
		tmp = x1 + (t_3 + (x1 + (t_1 + (t_5 + (t_0 * (t_6 + (4.0 * (x1 * (x2 * ((2.0 * x2) - 3.0))))))))));
	} else if (x1 <= 1e+153) {
		tmp = x1 + (t_3 + (x1 + (t_1 + (t_5 + (t_0 * ((x1 * 2.0) + t_6))))));
	} else {
		tmp = (x2 * -6.0) + (x1 * ((x1 * 9.0) + -1.0));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: tmp
    t_0 = (x1 * x1) + 1.0d0
    t_1 = x1 * (x1 * x1)
    t_2 = x1 * (x1 * 3.0d0)
    t_3 = 3.0d0 * (((t_2 - (2.0d0 * x2)) - x1) / t_0)
    t_4 = ((t_2 + (2.0d0 * x2)) - x1) / t_0
    t_5 = t_2 * t_4
    t_6 = (x1 * x1) * ((t_4 * 4.0d0) - 6.0d0)
    if (x1 <= (-6.5d+85)) then
        tmp = x1 + (x2 * (((x1 * ((x1 * (9.0d0 + (x1 * (-19.0d0)))) - 2.0d0)) / x2) - 6.0d0))
    else if (x1 <= 8600000000000.0d0) then
        tmp = x1 + (t_3 + (x1 + (t_1 + (t_5 + (t_0 * (t_6 + (4.0d0 * (x1 * (x2 * ((2.0d0 * x2) - 3.0d0))))))))))
    else if (x1 <= 1d+153) then
        tmp = x1 + (t_3 + (x1 + (t_1 + (t_5 + (t_0 * ((x1 * 2.0d0) + t_6))))))
    else
        tmp = (x2 * (-6.0d0)) + (x1 * ((x1 * 9.0d0) + (-1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = x1 * (x1 * x1);
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = 3.0 * (((t_2 - (2.0 * x2)) - x1) / t_0);
	double t_4 = ((t_2 + (2.0 * x2)) - x1) / t_0;
	double t_5 = t_2 * t_4;
	double t_6 = (x1 * x1) * ((t_4 * 4.0) - 6.0);
	double tmp;
	if (x1 <= -6.5e+85) {
		tmp = x1 + (x2 * (((x1 * ((x1 * (9.0 + (x1 * -19.0))) - 2.0)) / x2) - 6.0));
	} else if (x1 <= 8600000000000.0) {
		tmp = x1 + (t_3 + (x1 + (t_1 + (t_5 + (t_0 * (t_6 + (4.0 * (x1 * (x2 * ((2.0 * x2) - 3.0))))))))));
	} else if (x1 <= 1e+153) {
		tmp = x1 + (t_3 + (x1 + (t_1 + (t_5 + (t_0 * ((x1 * 2.0) + t_6))))));
	} else {
		tmp = (x2 * -6.0) + (x1 * ((x1 * 9.0) + -1.0));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x1 * x1) + 1.0
	t_1 = x1 * (x1 * x1)
	t_2 = x1 * (x1 * 3.0)
	t_3 = 3.0 * (((t_2 - (2.0 * x2)) - x1) / t_0)
	t_4 = ((t_2 + (2.0 * x2)) - x1) / t_0
	t_5 = t_2 * t_4
	t_6 = (x1 * x1) * ((t_4 * 4.0) - 6.0)
	tmp = 0
	if x1 <= -6.5e+85:
		tmp = x1 + (x2 * (((x1 * ((x1 * (9.0 + (x1 * -19.0))) - 2.0)) / x2) - 6.0))
	elif x1 <= 8600000000000.0:
		tmp = x1 + (t_3 + (x1 + (t_1 + (t_5 + (t_0 * (t_6 + (4.0 * (x1 * (x2 * ((2.0 * x2) - 3.0))))))))))
	elif x1 <= 1e+153:
		tmp = x1 + (t_3 + (x1 + (t_1 + (t_5 + (t_0 * ((x1 * 2.0) + t_6))))))
	else:
		tmp = (x2 * -6.0) + (x1 * ((x1 * 9.0) + -1.0))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * x1) + 1.0)
	t_1 = Float64(x1 * Float64(x1 * x1))
	t_2 = Float64(x1 * Float64(x1 * 3.0))
	t_3 = Float64(3.0 * Float64(Float64(Float64(t_2 - Float64(2.0 * x2)) - x1) / t_0))
	t_4 = Float64(Float64(Float64(t_2 + Float64(2.0 * x2)) - x1) / t_0)
	t_5 = Float64(t_2 * t_4)
	t_6 = Float64(Float64(x1 * x1) * Float64(Float64(t_4 * 4.0) - 6.0))
	tmp = 0.0
	if (x1 <= -6.5e+85)
		tmp = Float64(x1 + Float64(x2 * Float64(Float64(Float64(x1 * Float64(Float64(x1 * Float64(9.0 + Float64(x1 * -19.0))) - 2.0)) / x2) - 6.0)));
	elseif (x1 <= 8600000000000.0)
		tmp = Float64(x1 + Float64(t_3 + Float64(x1 + Float64(t_1 + Float64(t_5 + Float64(t_0 * Float64(t_6 + Float64(4.0 * Float64(x1 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0)))))))))));
	elseif (x1 <= 1e+153)
		tmp = Float64(x1 + Float64(t_3 + Float64(x1 + Float64(t_1 + Float64(t_5 + Float64(t_0 * Float64(Float64(x1 * 2.0) + t_6)))))));
	else
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(x1 * 9.0) + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x1 * x1) + 1.0;
	t_1 = x1 * (x1 * x1);
	t_2 = x1 * (x1 * 3.0);
	t_3 = 3.0 * (((t_2 - (2.0 * x2)) - x1) / t_0);
	t_4 = ((t_2 + (2.0 * x2)) - x1) / t_0;
	t_5 = t_2 * t_4;
	t_6 = (x1 * x1) * ((t_4 * 4.0) - 6.0);
	tmp = 0.0;
	if (x1 <= -6.5e+85)
		tmp = x1 + (x2 * (((x1 * ((x1 * (9.0 + (x1 * -19.0))) - 2.0)) / x2) - 6.0));
	elseif (x1 <= 8600000000000.0)
		tmp = x1 + (t_3 + (x1 + (t_1 + (t_5 + (t_0 * (t_6 + (4.0 * (x1 * (x2 * ((2.0 * x2) - 3.0))))))))));
	elseif (x1 <= 1e+153)
		tmp = x1 + (t_3 + (x1 + (t_1 + (t_5 + (t_0 * ((x1 * 2.0) + t_6))))));
	else
		tmp = (x2 * -6.0) + (x1 * ((x1 * 9.0) + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(3.0 * N[(N[(N[(t$95$2 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(t$95$2 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]}, Block[{t$95$5 = N[(t$95$2 * t$95$4), $MachinePrecision]}, Block[{t$95$6 = N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$4 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -6.5e+85], N[(x1 + N[(x2 * N[(N[(N[(x1 * N[(N[(x1 * N[(9.0 + N[(x1 * -19.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision] / x2), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 8600000000000.0], N[(x1 + N[(t$95$3 + N[(x1 + N[(t$95$1 + N[(t$95$5 + N[(t$95$0 * N[(t$95$6 + N[(4.0 * N[(x1 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1e+153], N[(x1 + N[(t$95$3 + N[(x1 + N[(t$95$1 + N[(t$95$5 + N[(t$95$0 * N[(N[(x1 * 2.0), $MachinePrecision] + t$95$6), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -6.4999999999999994e85

   1. Initial program 7.3%

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

   3. Simplified 17.1%

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

   5. Taylor expanded in x1 around 0 61.5%

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

   6. Taylor expanded in x2 around 0 93.4%

      \[\leadsto x1 + \left(-6 \cdot x2 + x1 \cdot \left(\color{blue}{x1 \cdot \left(9 + -19 \cdot x1\right)} - 2\right)\right) \]
   7. Step-by-step derivation

      1. *-commutative 93.4%

         \[\leadsto x1 + \left(-6 \cdot x2 + x1 \cdot \left(x1 \cdot \left(9 + \color{blue}{x1 \cdot -19}\right) - 2\right)\right) \]

   8. Simplified 93.4%

      \[\leadsto x1 + \left(-6 \cdot x2 + x1 \cdot \left(\color{blue}{x1 \cdot \left(9 + x1 \cdot -19\right)} - 2\right)\right) \]

   9. Taylor expanded in x2 around inf 97.7%

      \[\leadsto x1 + \color{blue}{x2 \cdot \left(\frac{x1 \cdot \left(x1 \cdot \left(9 + -19 \cdot x1\right) - 2\right)}{x2} - 6\right)} \]

   if -6.4999999999999994e85 < x1 < 8.6e12

   1. Initial program 99.3%

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

   3. Taylor expanded in x1 around 0 95.5%

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

      1. +-commutative 95.5%

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

      2. mul-1-neg 95.5%

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

      3. unsub-neg 95.5%

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

   5. Simplified 95.5%

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

   6. Taylor expanded in x1 around 0 81.5%

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

   if 8.6e12 < x1 < 1e153

   1. Initial program 99.5%

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

   3. Taylor expanded in x1 around 0 83.8%

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

      1. +-commutative 83.8%

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

      2. mul-1-neg 83.8%

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

      3. unsub-neg 83.8%

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

   5. Simplified 83.8%

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

   6. Taylor expanded in x1 around inf 86.9%

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

      1. *-commutative 86.9%

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

   8. Simplified 86.9%

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

   if 1e153 < x1

   1. Initial program 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in x1 around 0 0.0%

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

   6. Taylor expanded in x2 around 0 0.0%

      \[\leadsto x1 + \left(-6 \cdot x2 + x1 \cdot \left(\color{blue}{x1 \cdot \left(9 + -19 \cdot x1\right)} - 2\right)\right) \]
   7. Step-by-step derivation

      1. *-commutative 0.0%

         \[\leadsto x1 + \left(-6 \cdot x2 + x1 \cdot \left(x1 \cdot \left(9 + \color{blue}{x1 \cdot -19}\right) - 2\right)\right) \]

   8. Simplified 0.0%

      \[\leadsto x1 + \left(-6 \cdot x2 + x1 \cdot \left(\color{blue}{x1 \cdot \left(9 + x1 \cdot -19\right)} - 2\right)\right) \]

   9. Taylor expanded in x1 around 0 100.0%

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

4. Final simplification 87.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -6.5 \cdot 10^{+85}:\\ \;\;\;\;x1 + x2 \cdot \left(\frac{x1 \cdot \left(x1 \cdot \left(9 + x1 \cdot -19\right) - 2\right)}{x2} - 6\right)\\ \mathbf{elif}\;x1 \leq 8600000000000:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right) + 4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 10^{+153}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 \cdot x1 + 1\right) \cdot \left(x1 \cdot 2 + \left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 + -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 78.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -4 \cdot 10^{+76}:\\ \;\;\;\;x1 + x2 \cdot \left(\frac{x1 \cdot \left(x1 \cdot \left(9 + x1 \cdot -19\right) - 2\right)}{x2} - 6\right)\\ \mathbf{elif}\;x1 \leq 4.5 \cdot 10^{+150}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(\left(-4 \cdot \left(x2 \cdot \left(3 + x2 \cdot -2\right)\right) + x1 \cdot \left(\left(2 \cdot \left(3 + x2 \cdot -4\right) + \left(3 \cdot \left(3 - x2 \cdot -2\right) + \left(x2 \cdot 6 + \left(x2 \cdot 8 + x1 \cdot \left(\left(x2 \cdot \left(x2 \cdot 8 + 24\right) - 16\right) - 3\right)\right)\right)\right)\right) - 6\right)\right) - 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -4e+76)
   (+ x1 (* x2 (- (/ (* x1 (- (* x1 (+ 9.0 (* x1 -19.0))) 2.0)) x2) 6.0)))
   (if (<= x1 4.5e+150)
     (+
      x1
      (+
       (* x2 -6.0)
       (*
        x1
        (-
         (+
          (* -4.0 (* x2 (+ 3.0 (* x2 -2.0))))
          (*
           x1
           (-
            (+
             (* 2.0 (+ 3.0 (* x2 -4.0)))
             (+
              (* 3.0 (- 3.0 (* x2 -2.0)))
              (+
               (* x2 6.0)
               (+
                (* x2 8.0)
                (* x1 (- (- (* x2 (+ (* x2 8.0) 24.0)) 16.0) 3.0))))))
            6.0)))
         2.0))))
     (+ (* x2 -6.0) (* x1 (+ (* x1 9.0) -1.0))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -4e+76) {
		tmp = x1 + (x2 * (((x1 * ((x1 * (9.0 + (x1 * -19.0))) - 2.0)) / x2) - 6.0));
	} else if (x1 <= 4.5e+150) {
		tmp = x1 + ((x2 * -6.0) + (x1 * (((-4.0 * (x2 * (3.0 + (x2 * -2.0)))) + (x1 * (((2.0 * (3.0 + (x2 * -4.0))) + ((3.0 * (3.0 - (x2 * -2.0))) + ((x2 * 6.0) + ((x2 * 8.0) + (x1 * (((x2 * ((x2 * 8.0) + 24.0)) - 16.0) - 3.0)))))) - 6.0))) - 2.0)));
	} else {
		tmp = (x2 * -6.0) + (x1 * ((x1 * 9.0) + -1.0));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x1 <= (-4d+76)) then
        tmp = x1 + (x2 * (((x1 * ((x1 * (9.0d0 + (x1 * (-19.0d0)))) - 2.0d0)) / x2) - 6.0d0))
    else if (x1 <= 4.5d+150) then
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * ((((-4.0d0) * (x2 * (3.0d0 + (x2 * (-2.0d0))))) + (x1 * (((2.0d0 * (3.0d0 + (x2 * (-4.0d0)))) + ((3.0d0 * (3.0d0 - (x2 * (-2.0d0)))) + ((x2 * 6.0d0) + ((x2 * 8.0d0) + (x1 * (((x2 * ((x2 * 8.0d0) + 24.0d0)) - 16.0d0) - 3.0d0)))))) - 6.0d0))) - 2.0d0)))
    else
        tmp = (x2 * (-6.0d0)) + (x1 * ((x1 * 9.0d0) + (-1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= -4e+76) {
		tmp = x1 + (x2 * (((x1 * ((x1 * (9.0 + (x1 * -19.0))) - 2.0)) / x2) - 6.0));
	} else if (x1 <= 4.5e+150) {
		tmp = x1 + ((x2 * -6.0) + (x1 * (((-4.0 * (x2 * (3.0 + (x2 * -2.0)))) + (x1 * (((2.0 * (3.0 + (x2 * -4.0))) + ((3.0 * (3.0 - (x2 * -2.0))) + ((x2 * 6.0) + ((x2 * 8.0) + (x1 * (((x2 * ((x2 * 8.0) + 24.0)) - 16.0) - 3.0)))))) - 6.0))) - 2.0)));
	} else {
		tmp = (x2 * -6.0) + (x1 * ((x1 * 9.0) + -1.0));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -4e+76:
		tmp = x1 + (x2 * (((x1 * ((x1 * (9.0 + (x1 * -19.0))) - 2.0)) / x2) - 6.0))
	elif x1 <= 4.5e+150:
		tmp = x1 + ((x2 * -6.0) + (x1 * (((-4.0 * (x2 * (3.0 + (x2 * -2.0)))) + (x1 * (((2.0 * (3.0 + (x2 * -4.0))) + ((3.0 * (3.0 - (x2 * -2.0))) + ((x2 * 6.0) + ((x2 * 8.0) + (x1 * (((x2 * ((x2 * 8.0) + 24.0)) - 16.0) - 3.0)))))) - 6.0))) - 2.0)))
	else:
		tmp = (x2 * -6.0) + (x1 * ((x1 * 9.0) + -1.0))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -4e+76)
		tmp = Float64(x1 + Float64(x2 * Float64(Float64(Float64(x1 * Float64(Float64(x1 * Float64(9.0 + Float64(x1 * -19.0))) - 2.0)) / x2) - 6.0)));
	elseif (x1 <= 4.5e+150)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(Float64(-4.0 * Float64(x2 * Float64(3.0 + Float64(x2 * -2.0)))) + Float64(x1 * Float64(Float64(Float64(2.0 * Float64(3.0 + Float64(x2 * -4.0))) + Float64(Float64(3.0 * Float64(3.0 - Float64(x2 * -2.0))) + Float64(Float64(x2 * 6.0) + Float64(Float64(x2 * 8.0) + Float64(x1 * Float64(Float64(Float64(x2 * Float64(Float64(x2 * 8.0) + 24.0)) - 16.0) - 3.0)))))) - 6.0))) - 2.0))));
	else
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(x1 * 9.0) + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -4e+76)
		tmp = x1 + (x2 * (((x1 * ((x1 * (9.0 + (x1 * -19.0))) - 2.0)) / x2) - 6.0));
	elseif (x1 <= 4.5e+150)
		tmp = x1 + ((x2 * -6.0) + (x1 * (((-4.0 * (x2 * (3.0 + (x2 * -2.0)))) + (x1 * (((2.0 * (3.0 + (x2 * -4.0))) + ((3.0 * (3.0 - (x2 * -2.0))) + ((x2 * 6.0) + ((x2 * 8.0) + (x1 * (((x2 * ((x2 * 8.0) + 24.0)) - 16.0) - 3.0)))))) - 6.0))) - 2.0)));
	else
		tmp = (x2 * -6.0) + (x1 * ((x1 * 9.0) + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -4e+76], N[(x1 + N[(x2 * N[(N[(N[(x1 * N[(N[(x1 * N[(9.0 + N[(x1 * -19.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision] / x2), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 4.5e+150], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(N[(-4.0 * N[(x2 * N[(3.0 + N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(N[(N[(2.0 * N[(3.0 + N[(x2 * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(3.0 * N[(3.0 - N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x2 * 6.0), $MachinePrecision] + N[(N[(x2 * 8.0), $MachinePrecision] + N[(x1 * N[(N[(N[(x2 * N[(N[(x2 * 8.0), $MachinePrecision] + 24.0), $MachinePrecision]), $MachinePrecision] - 16.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -4.0000000000000002e76

   1. Initial program 11.6%

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

   3. Simplified 20.9%

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

   5. Taylor expanded in x1 around 0 61.1%

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

   6. Taylor expanded in x2 around 0 89.3%

      \[\leadsto x1 + \left(-6 \cdot x2 + x1 \cdot \left(\color{blue}{x1 \cdot \left(9 + -19 \cdot x1\right)} - 2\right)\right) \]
   7. Step-by-step derivation

      1. *-commutative 89.3%

         \[\leadsto x1 + \left(-6 \cdot x2 + x1 \cdot \left(x1 \cdot \left(9 + \color{blue}{x1 \cdot -19}\right) - 2\right)\right) \]

   8. Simplified 89.3%

      \[\leadsto x1 + \left(-6 \cdot x2 + x1 \cdot \left(\color{blue}{x1 \cdot \left(9 + x1 \cdot -19\right)} - 2\right)\right) \]

   9. Taylor expanded in x2 around inf 93.5%

      \[\leadsto x1 + \color{blue}{x2 \cdot \left(\frac{x1 \cdot \left(x1 \cdot \left(9 + -19 \cdot x1\right) - 2\right)}{x2} - 6\right)} \]

   if -4.0000000000000002e76 < x1 < 4.5e150

   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 88.8%

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

   5. Taylor expanded in x1 around 0 50.4%

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

   6. Taylor expanded in x2 around 0 68.0%

      \[\leadsto x1 + \left(-6 \cdot x2 + x1 \cdot \left(\left(-4 \cdot \left(x2 \cdot \left(3 + -2 \cdot x2\right)\right) + x1 \cdot \left(\left(2 \cdot \left(3 + -4 \cdot x2\right) + \left(3 \cdot \left(3 - -2 \cdot x2\right) + \left(6 \cdot x2 + \left(8 \cdot x2 + x1 \cdot \left(\left(-4 \cdot \left(x2 \cdot \left(3 + -2 \cdot x2\right)\right) + \color{blue}{\left(36 \cdot x2 - 16\right)}\right) - 3\right)\right)\right)\right)\right) - 6\right)\right) - 2\right)\right) \]

   7. Taylor expanded in x2 around 0 68.6%

      \[\leadsto x1 + \left(-6 \cdot x2 + x1 \cdot \left(\left(-4 \cdot \left(x2 \cdot \left(3 + -2 \cdot x2\right)\right) + x1 \cdot \left(\left(2 \cdot \left(3 + -4 \cdot x2\right) + \left(3 \cdot \left(3 - -2 \cdot x2\right) + \left(6 \cdot x2 + \left(8 \cdot x2 + x1 \cdot \left(\color{blue}{\left(x2 \cdot \left(24 + 8 \cdot x2\right) - 16\right)} - 3\right)\right)\right)\right)\right) - 6\right)\right) - 2\right)\right) \]

   if 4.5e150 < x1

   1. Initial program 3.1%

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

   3. Simplified 3.1%

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

   5. Taylor expanded in x1 around 0 0.0%

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

   6. Taylor expanded in x2 around 0 0.0%

      \[\leadsto x1 + \left(-6 \cdot x2 + x1 \cdot \left(\color{blue}{x1 \cdot \left(9 + -19 \cdot x1\right)} - 2\right)\right) \]
   7. Step-by-step derivation

      1. *-commutative 0.0%

         \[\leadsto x1 + \left(-6 \cdot x2 + x1 \cdot \left(x1 \cdot \left(9 + \color{blue}{x1 \cdot -19}\right) - 2\right)\right) \]

   8. Simplified 0.0%

      \[\leadsto x1 + \left(-6 \cdot x2 + x1 \cdot \left(\color{blue}{x1 \cdot \left(9 + x1 \cdot -19\right)} - 2\right)\right) \]

   9. Taylor expanded in x1 around 0 97.3%

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

4. Final simplification 76.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4 \cdot 10^{+76}:\\ \;\;\;\;x1 + x2 \cdot \left(\frac{x1 \cdot \left(x1 \cdot \left(9 + x1 \cdot -19\right) - 2\right)}{x2} - 6\right)\\ \mathbf{elif}\;x1 \leq 4.5 \cdot 10^{+150}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(\left(-4 \cdot \left(x2 \cdot \left(3 + x2 \cdot -2\right)\right) + x1 \cdot \left(\left(2 \cdot \left(3 + x2 \cdot -4\right) + \left(3 \cdot \left(3 - x2 \cdot -2\right) + \left(x2 \cdot 6 + \left(x2 \cdot 8 + x1 \cdot \left(\left(x2 \cdot \left(x2 \cdot 8 + 24\right) - 16\right) - 3\right)\right)\right)\right)\right) - 6\right)\right) - 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 + -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 77.5% accurate, 4.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -1.4 \cdot 10^{+58}:\\ \;\;\;\;x1 + x2 \cdot \left(\frac{x1 \cdot \left(x1 \cdot \left(9 + x1 \cdot -19\right) - 2\right)}{x2} - 6\right)\\ \mathbf{elif}\;x1 \leq 4.5 \cdot 10^{+150}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -1.4e+58)
   (+ x1 (* x2 (- (/ (* x1 (- (* x1 (+ 9.0 (* x1 -19.0))) 2.0)) x2) 6.0)))
   (if (<= x1 4.5e+150)
     (+ x1 (+ (* x2 -6.0) (* x1 (- (* 4.0 (* x2 (- (* 2.0 x2) 3.0))) 2.0))))
     (+ (* x2 -6.0) (* x1 (+ (* x1 9.0) -1.0))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -1.4e+58) {
		tmp = x1 + (x2 * (((x1 * ((x1 * (9.0 + (x1 * -19.0))) - 2.0)) / x2) - 6.0));
	} else if (x1 <= 4.5e+150) {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)));
	} else {
		tmp = (x2 * -6.0) + (x1 * ((x1 * 9.0) + -1.0));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x1 <= (-1.4d+58)) then
        tmp = x1 + (x2 * (((x1 * ((x1 * (9.0d0 + (x1 * (-19.0d0)))) - 2.0d0)) / x2) - 6.0d0))
    else if (x1 <= 4.5d+150) then
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * ((4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0))) - 2.0d0)))
    else
        tmp = (x2 * (-6.0d0)) + (x1 * ((x1 * 9.0d0) + (-1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= -1.4e+58) {
		tmp = x1 + (x2 * (((x1 * ((x1 * (9.0 + (x1 * -19.0))) - 2.0)) / x2) - 6.0));
	} else if (x1 <= 4.5e+150) {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)));
	} else {
		tmp = (x2 * -6.0) + (x1 * ((x1 * 9.0) + -1.0));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -1.4e+58:
		tmp = x1 + (x2 * (((x1 * ((x1 * (9.0 + (x1 * -19.0))) - 2.0)) / x2) - 6.0))
	elif x1 <= 4.5e+150:
		tmp = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)))
	else:
		tmp = (x2 * -6.0) + (x1 * ((x1 * 9.0) + -1.0))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -1.4e+58)
		tmp = Float64(x1 + Float64(x2 * Float64(Float64(Float64(x1 * Float64(Float64(x1 * Float64(9.0 + Float64(x1 * -19.0))) - 2.0)) / x2) - 6.0)));
	elseif (x1 <= 4.5e+150)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0))) - 2.0))));
	else
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(x1 * 9.0) + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -1.4e+58)
		tmp = x1 + (x2 * (((x1 * ((x1 * (9.0 + (x1 * -19.0))) - 2.0)) / x2) - 6.0));
	elseif (x1 <= 4.5e+150)
		tmp = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)));
	else
		tmp = (x2 * -6.0) + (x1 * ((x1 * 9.0) + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -1.4e+58], N[(x1 + N[(x2 * N[(N[(N[(x1 * N[(N[(x1 * N[(9.0 + N[(x1 * -19.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision] / x2), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 4.5e+150], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(4.0 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -1.3999999999999999e58

   1. Initial program 13.6%

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

   3. Simplified 22.7%

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

   5. Taylor expanded in x1 around 0 59.9%

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

   6. Taylor expanded in x2 around 0 87.5%

      \[\leadsto x1 + \left(-6 \cdot x2 + x1 \cdot \left(\color{blue}{x1 \cdot \left(9 + -19 \cdot x1\right)} - 2\right)\right) \]
   7. Step-by-step derivation

      1. *-commutative 87.5%

         \[\leadsto x1 + \left(-6 \cdot x2 + x1 \cdot \left(x1 \cdot \left(9 + \color{blue}{x1 \cdot -19}\right) - 2\right)\right) \]

   8. Simplified 87.5%

      \[\leadsto x1 + \left(-6 \cdot x2 + x1 \cdot \left(\color{blue}{x1 \cdot \left(9 + x1 \cdot -19\right)} - 2\right)\right) \]

   9. Taylor expanded in x2 around inf 91.5%

      \[\leadsto x1 + \color{blue}{x2 \cdot \left(\frac{x1 \cdot \left(x1 \cdot \left(9 + -19 \cdot x1\right) - 2\right)}{x2} - 6\right)} \]

   if -1.3999999999999999e58 < x1 < 4.5e150

   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%

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

   5. Taylor expanded in x1 around 0 66.2%

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

   if 4.5e150 < x1

   1. Initial program 3.1%

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

   3. Simplified 3.1%

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

   5. Taylor expanded in x1 around 0 0.0%

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

   6. Taylor expanded in x2 around 0 0.0%

      \[\leadsto x1 + \left(-6 \cdot x2 + x1 \cdot \left(\color{blue}{x1 \cdot \left(9 + -19 \cdot x1\right)} - 2\right)\right) \]
   7. Step-by-step derivation

      1. *-commutative 0.0%

         \[\leadsto x1 + \left(-6 \cdot x2 + x1 \cdot \left(x1 \cdot \left(9 + \color{blue}{x1 \cdot -19}\right) - 2\right)\right) \]

   8. Simplified 0.0%

      \[\leadsto x1 + \left(-6 \cdot x2 + x1 \cdot \left(\color{blue}{x1 \cdot \left(9 + x1 \cdot -19\right)} - 2\right)\right) \]

   9. Taylor expanded in x1 around 0 97.3%

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

4. Final simplification 74.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.4 \cdot 10^{+58}:\\ \;\;\;\;x1 + x2 \cdot \left(\frac{x1 \cdot \left(x1 \cdot \left(9 + x1 \cdot -19\right) - 2\right)}{x2} - 6\right)\\ \mathbf{elif}\;x1 \leq 4.5 \cdot 10^{+150}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 + -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 77.5% accurate, 4.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -1.18 \cdot 10^{+58}:\\ \;\;\;\;x1 + x2 \cdot \left(\frac{x1 \cdot \left(x1 \cdot \left(9 + x1 \cdot -19\right) - 2\right)}{x2} - 6\right)\\ \mathbf{elif}\;x1 \leq 4.5 \cdot 10^{+150}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -1.18e+58)
   (+ x1 (* x2 (- (/ (* x1 (- (* x1 (+ 9.0 (* x1 -19.0))) 2.0)) x2) 6.0)))
   (if (<= x1 4.5e+150)
     (+ (* x2 -6.0) (* x1 (+ (* 4.0 (* x2 (- (* 2.0 x2) 3.0))) -1.0)))
     (+ (* x2 -6.0) (* x1 (+ (* x1 9.0) -1.0))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -1.18e+58) {
		tmp = x1 + (x2 * (((x1 * ((x1 * (9.0 + (x1 * -19.0))) - 2.0)) / x2) - 6.0));
	} else if (x1 <= 4.5e+150) {
		tmp = (x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) + -1.0));
	} else {
		tmp = (x2 * -6.0) + (x1 * ((x1 * 9.0) + -1.0));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x1 <= (-1.18d+58)) then
        tmp = x1 + (x2 * (((x1 * ((x1 * (9.0d0 + (x1 * (-19.0d0)))) - 2.0d0)) / x2) - 6.0d0))
    else if (x1 <= 4.5d+150) then
        tmp = (x2 * (-6.0d0)) + (x1 * ((4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0))) + (-1.0d0)))
    else
        tmp = (x2 * (-6.0d0)) + (x1 * ((x1 * 9.0d0) + (-1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= -1.18e+58) {
		tmp = x1 + (x2 * (((x1 * ((x1 * (9.0 + (x1 * -19.0))) - 2.0)) / x2) - 6.0));
	} else if (x1 <= 4.5e+150) {
		tmp = (x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) + -1.0));
	} else {
		tmp = (x2 * -6.0) + (x1 * ((x1 * 9.0) + -1.0));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -1.18e+58:
		tmp = x1 + (x2 * (((x1 * ((x1 * (9.0 + (x1 * -19.0))) - 2.0)) / x2) - 6.0))
	elif x1 <= 4.5e+150:
		tmp = (x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) + -1.0))
	else:
		tmp = (x2 * -6.0) + (x1 * ((x1 * 9.0) + -1.0))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -1.18e+58)
		tmp = Float64(x1 + Float64(x2 * Float64(Float64(Float64(x1 * Float64(Float64(x1 * Float64(9.0 + Float64(x1 * -19.0))) - 2.0)) / x2) - 6.0)));
	elseif (x1 <= 4.5e+150)
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0))) + -1.0)));
	else
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(x1 * 9.0) + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -1.18e+58)
		tmp = x1 + (x2 * (((x1 * ((x1 * (9.0 + (x1 * -19.0))) - 2.0)) / x2) - 6.0));
	elseif (x1 <= 4.5e+150)
		tmp = (x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) + -1.0));
	else
		tmp = (x2 * -6.0) + (x1 * ((x1 * 9.0) + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -1.18e+58], N[(x1 + N[(x2 * N[(N[(N[(x1 * N[(N[(x1 * N[(9.0 + N[(x1 * -19.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision] / x2), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 4.5e+150], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(4.0 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -1.18000000000000003e58

   1. Initial program 13.6%

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

   3. Simplified 22.7%

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

   5. Taylor expanded in x1 around 0 59.9%

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

   6. Taylor expanded in x2 around 0 87.5%

      \[\leadsto x1 + \left(-6 \cdot x2 + x1 \cdot \left(\color{blue}{x1 \cdot \left(9 + -19 \cdot x1\right)} - 2\right)\right) \]
   7. Step-by-step derivation

      1. *-commutative 87.5%

         \[\leadsto x1 + \left(-6 \cdot x2 + x1 \cdot \left(x1 \cdot \left(9 + \color{blue}{x1 \cdot -19}\right) - 2\right)\right) \]

   8. Simplified 87.5%

      \[\leadsto x1 + \left(-6 \cdot x2 + x1 \cdot \left(\color{blue}{x1 \cdot \left(9 + x1 \cdot -19\right)} - 2\right)\right) \]

   9. Taylor expanded in x2 around inf 91.5%

      \[\leadsto x1 + \color{blue}{x2 \cdot \left(\frac{x1 \cdot \left(x1 \cdot \left(9 + -19 \cdot x1\right) - 2\right)}{x2} - 6\right)} \]

   if -1.18000000000000003e58 < x1 < 4.5e150

   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%

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

   5. Taylor expanded in x1 around 0 66.2%

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

   if 4.5e150 < x1

   1. Initial program 3.1%

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

   3. Simplified 3.1%

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

   5. Taylor expanded in x1 around 0 0.0%

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

   6. Taylor expanded in x2 around 0 0.0%

      \[\leadsto x1 + \left(-6 \cdot x2 + x1 \cdot \left(\color{blue}{x1 \cdot \left(9 + -19 \cdot x1\right)} - 2\right)\right) \]
   7. Step-by-step derivation

      1. *-commutative 0.0%

         \[\leadsto x1 + \left(-6 \cdot x2 + x1 \cdot \left(x1 \cdot \left(9 + \color{blue}{x1 \cdot -19}\right) - 2\right)\right) \]

   8. Simplified 0.0%

      \[\leadsto x1 + \left(-6 \cdot x2 + x1 \cdot \left(\color{blue}{x1 \cdot \left(9 + x1 \cdot -19\right)} - 2\right)\right) \]

   9. Taylor expanded in x1 around 0 97.3%

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

4. Final simplification 74.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.18 \cdot 10^{+58}:\\ \;\;\;\;x1 + x2 \cdot \left(\frac{x1 \cdot \left(x1 \cdot \left(9 + x1 \cdot -19\right) - 2\right)}{x2} - 6\right)\\ \mathbf{elif}\;x1 \leq 4.5 \cdot 10^{+150}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 + -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 76.8% accurate, 4.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -1.36 \cdot 10^{+58}:\\ \;\;\;\;x1 + x1 \cdot \left(x1 \cdot \left(9 + x1 \cdot -19\right) - 2\right)\\ \mathbf{elif}\;x1 \leq 4.5 \cdot 10^{+150}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -1.36e+58)
   (+ x1 (* x1 (- (* x1 (+ 9.0 (* x1 -19.0))) 2.0)))
   (if (<= x1 4.5e+150)
     (+ (* x2 -6.0) (* x1 (+ (* 4.0 (* x2 (- (* 2.0 x2) 3.0))) -1.0)))
     (+ (* x2 -6.0) (* x1 (+ (* x1 9.0) -1.0))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -1.36e+58) {
		tmp = x1 + (x1 * ((x1 * (9.0 + (x1 * -19.0))) - 2.0));
	} else if (x1 <= 4.5e+150) {
		tmp = (x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) + -1.0));
	} else {
		tmp = (x2 * -6.0) + (x1 * ((x1 * 9.0) + -1.0));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x1 <= (-1.36d+58)) then
        tmp = x1 + (x1 * ((x1 * (9.0d0 + (x1 * (-19.0d0)))) - 2.0d0))
    else if (x1 <= 4.5d+150) then
        tmp = (x2 * (-6.0d0)) + (x1 * ((4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0))) + (-1.0d0)))
    else
        tmp = (x2 * (-6.0d0)) + (x1 * ((x1 * 9.0d0) + (-1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= -1.36e+58) {
		tmp = x1 + (x1 * ((x1 * (9.0 + (x1 * -19.0))) - 2.0));
	} else if (x1 <= 4.5e+150) {
		tmp = (x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) + -1.0));
	} else {
		tmp = (x2 * -6.0) + (x1 * ((x1 * 9.0) + -1.0));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -1.36e+58:
		tmp = x1 + (x1 * ((x1 * (9.0 + (x1 * -19.0))) - 2.0))
	elif x1 <= 4.5e+150:
		tmp = (x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) + -1.0))
	else:
		tmp = (x2 * -6.0) + (x1 * ((x1 * 9.0) + -1.0))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -1.36e+58)
		tmp = Float64(x1 + Float64(x1 * Float64(Float64(x1 * Float64(9.0 + Float64(x1 * -19.0))) - 2.0)));
	elseif (x1 <= 4.5e+150)
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0))) + -1.0)));
	else
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(x1 * 9.0) + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -1.36e+58)
		tmp = x1 + (x1 * ((x1 * (9.0 + (x1 * -19.0))) - 2.0));
	elseif (x1 <= 4.5e+150)
		tmp = (x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) + -1.0));
	else
		tmp = (x2 * -6.0) + (x1 * ((x1 * 9.0) + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -1.36e+58], N[(x1 + N[(x1 * N[(N[(x1 * N[(9.0 + N[(x1 * -19.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 4.5e+150], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(4.0 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -1.35999999999999997e58

   1. Initial program 13.6%

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

   3. Simplified 22.7%

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

   5. Taylor expanded in x1 around 0 59.9%

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

   6. Taylor expanded in x2 around 0 87.5%

      \[\leadsto x1 + \left(-6 \cdot x2 + x1 \cdot \left(\color{blue}{x1 \cdot \left(9 + -19 \cdot x1\right)} - 2\right)\right) \]
   7. Step-by-step derivation

      1. *-commutative 87.5%

         \[\leadsto x1 + \left(-6 \cdot x2 + x1 \cdot \left(x1 \cdot \left(9 + \color{blue}{x1 \cdot -19}\right) - 2\right)\right) \]

   8. Simplified 87.5%

      \[\leadsto x1 + \left(-6 \cdot x2 + x1 \cdot \left(\color{blue}{x1 \cdot \left(9 + x1 \cdot -19\right)} - 2\right)\right) \]

   9. Taylor expanded in x2 around 0 87.5%

      \[\leadsto \color{blue}{x1 + x1 \cdot \left(x1 \cdot \left(9 + -19 \cdot x1\right) - 2\right)} \]

   if -1.35999999999999997e58 < x1 < 4.5e150

   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%

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

   5. Taylor expanded in x1 around 0 66.2%

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

   if 4.5e150 < x1

   1. Initial program 3.1%

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

   3. Simplified 3.1%

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

   5. Taylor expanded in x1 around 0 0.0%

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

   6. Taylor expanded in x2 around 0 0.0%

      \[\leadsto x1 + \left(-6 \cdot x2 + x1 \cdot \left(\color{blue}{x1 \cdot \left(9 + -19 \cdot x1\right)} - 2\right)\right) \]
   7. Step-by-step derivation

      1. *-commutative 0.0%

         \[\leadsto x1 + \left(-6 \cdot x2 + x1 \cdot \left(x1 \cdot \left(9 + \color{blue}{x1 \cdot -19}\right) - 2\right)\right) \]

   8. Simplified 0.0%

      \[\leadsto x1 + \left(-6 \cdot x2 + x1 \cdot \left(\color{blue}{x1 \cdot \left(9 + x1 \cdot -19\right)} - 2\right)\right) \]

   9. Taylor expanded in x1 around 0 97.3%

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

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.36 \cdot 10^{+58}:\\ \;\;\;\;x1 + x1 \cdot \left(x1 \cdot \left(9 + x1 \cdot -19\right) - 2\right)\\ \mathbf{elif}\;x1 \leq 4.5 \cdot 10^{+150}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 + -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 54.2% accurate, 6.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -4.8 \cdot 10^{+54} \lor \neg \left(x1 \leq 1.35\right):\\ \;\;\;\;8 \cdot \left(x2 \cdot \left(x1 \cdot x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot -2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x1 -4.8e+54) (not (<= x1 1.35)))
   (* 8.0 (* x2 (* x1 x1)))
   (+ x1 (+ (* x2 -6.0) (* x1 -2.0)))))

C

double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -4.8e+54) || !(x1 <= 1.35)) {
		tmp = 8.0 * (x2 * (x1 * x1));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * -2.0));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if ((x1 <= (-4.8d+54)) .or. (.not. (x1 <= 1.35d0))) then
        tmp = 8.0d0 * (x2 * (x1 * x1))
    else
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * (-2.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -4.8e+54) || !(x1 <= 1.35)) {
		tmp = 8.0 * (x2 * (x1 * x1));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * -2.0));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x1 <= -4.8e+54) or not (x1 <= 1.35):
		tmp = 8.0 * (x2 * (x1 * x1))
	else:
		tmp = x1 + ((x2 * -6.0) + (x1 * -2.0))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x1 <= -4.8e+54) || !(x1 <= 1.35))
		tmp = Float64(8.0 * Float64(x2 * Float64(x1 * x1)));
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * -2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x1 <= -4.8e+54) || ~((x1 <= 1.35)))
		tmp = 8.0 * (x2 * (x1 * x1));
	else
		tmp = x1 + ((x2 * -6.0) + (x1 * -2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x1, -4.8e+54], N[Not[LessEqual[x1, 1.35]], $MachinePrecision]], N[(8.0 * N[(x2 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x1 < -4.79999999999999997e54 or 1.3500000000000001 < x1

   1. Initial program 38.8%

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

   3. Simplified 41.5%

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

   5. Taylor expanded in x1 around -inf 95.0%

      \[\leadsto \color{blue}{{x1}^{4} \cdot \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{15 + -1 \cdot \left(6 + -4 \cdot \left(2 \cdot x2 - 3\right)\right)}{x1}}{x1}\right)} \]

   6. Taylor expanded in x2 around inf 35.2%

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

      1. pow2 35.2%

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

   8. Applied egg-rr 35.2%

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

   if -4.79999999999999997e54 < x1 < 1.3500000000000001

   1. Initial program 99.3%

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

   3. Simplified 86.7%

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

   5. Taylor expanded in x1 around 0 63.6%

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

   6. Taylor expanded in x2 around 0 66.4%

      \[\leadsto x1 + \left(-6 \cdot x2 + x1 \cdot \left(\color{blue}{x1 \cdot \left(9 + -19 \cdot x1\right)} - 2\right)\right) \]
   7. Step-by-step derivation

      1. *-commutative 66.4%

         \[\leadsto x1 + \left(-6 \cdot x2 + x1 \cdot \left(x1 \cdot \left(9 + \color{blue}{x1 \cdot -19}\right) - 2\right)\right) \]

   8. Simplified 66.4%

      \[\leadsto x1 + \left(-6 \cdot x2 + x1 \cdot \left(\color{blue}{x1 \cdot \left(9 + x1 \cdot -19\right)} - 2\right)\right) \]

   9. Taylor expanded in x1 around 0 64.9%

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

       1. *-commutative 64.9%

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

   11. Simplified 64.9%

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

4. Final simplification 51.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4.8 \cdot 10^{+54} \lor \neg \left(x1 \leq 1.35\right):\\ \;\;\;\;8 \cdot \left(x2 \cdot \left(x1 \cdot x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot -2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 54.2% accurate, 7.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -4.8 \cdot 10^{+54} \lor \neg \left(x1 \leq 1.35\right):\\ \;\;\;\;8 \cdot \left(x2 \cdot \left(x1 \cdot x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 - x1\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x1 -4.8e+54) (not (<= x1 1.35)))
   (* 8.0 (* x2 (* x1 x1)))
   (- (* x2 -6.0) x1)))

C

double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -4.8e+54) || !(x1 <= 1.35)) {
		tmp = 8.0 * (x2 * (x1 * x1));
	} else {
		tmp = (x2 * -6.0) - x1;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if ((x1 <= (-4.8d+54)) .or. (.not. (x1 <= 1.35d0))) then
        tmp = 8.0d0 * (x2 * (x1 * x1))
    else
        tmp = (x2 * (-6.0d0)) - x1
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -4.8e+54) || !(x1 <= 1.35)) {
		tmp = 8.0 * (x2 * (x1 * x1));
	} else {
		tmp = (x2 * -6.0) - x1;
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x1 <= -4.8e+54) or not (x1 <= 1.35):
		tmp = 8.0 * (x2 * (x1 * x1))
	else:
		tmp = (x2 * -6.0) - x1
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x1 <= -4.8e+54) || !(x1 <= 1.35))
		tmp = Float64(8.0 * Float64(x2 * Float64(x1 * x1)));
	else
		tmp = Float64(Float64(x2 * -6.0) - x1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x1 <= -4.8e+54) || ~((x1 <= 1.35)))
		tmp = 8.0 * (x2 * (x1 * x1));
	else
		tmp = (x2 * -6.0) - x1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x1, -4.8e+54], N[Not[LessEqual[x1, 1.35]], $MachinePrecision]], N[(8.0 * N[(x2 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x2 * -6.0), $MachinePrecision] - x1), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x1 < -4.79999999999999997e54 or 1.3500000000000001 < x1

   1. Initial program 38.8%

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

   3. Simplified 41.5%

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

   5. Taylor expanded in x1 around -inf 95.0%

      \[\leadsto \color{blue}{{x1}^{4} \cdot \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{15 + -1 \cdot \left(6 + -4 \cdot \left(2 \cdot x2 - 3\right)\right)}{x1}}{x1}\right)} \]

   6. Taylor expanded in x2 around inf 35.2%

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

      1. pow2 35.2%

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

   8. Applied egg-rr 35.2%

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

   if -4.79999999999999997e54 < x1 < 1.3500000000000001

   1. Initial program 99.3%

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

   3. Simplified 86.7%

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

   5. Taylor expanded in x1 around 0 63.6%

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

   6. Taylor expanded in x2 around 0 66.4%

      \[\leadsto x1 + \left(-6 \cdot x2 + x1 \cdot \left(\color{blue}{x1 \cdot \left(9 + -19 \cdot x1\right)} - 2\right)\right) \]
   7. Step-by-step derivation

      1. *-commutative 66.4%

         \[\leadsto x1 + \left(-6 \cdot x2 + x1 \cdot \left(x1 \cdot \left(9 + \color{blue}{x1 \cdot -19}\right) - 2\right)\right) \]

   8. Simplified 66.4%

      \[\leadsto x1 + \left(-6 \cdot x2 + x1 \cdot \left(\color{blue}{x1 \cdot \left(9 + x1 \cdot -19\right)} - 2\right)\right) \]

   9. Taylor expanded in x1 around 0 64.9%

      \[\leadsto \color{blue}{-6 \cdot x2 + -1 \cdot x1} \]
   10. Step-by-step derivation

       1. *-commutative 64.9%

          \[\leadsto \color{blue}{x2 \cdot -6} + -1 \cdot x1 \]

       2. neg-mul-1 64.9%

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

       3. unsub-neg 64.9%

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

   11. Simplified 64.9%

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

4. Final simplification 51.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4.8 \cdot 10^{+54} \lor \neg \left(x1 \leq 1.35\right):\\ \;\;\;\;8 \cdot \left(x2 \cdot \left(x1 \cdot x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 - x1\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 63.5% accurate, 7.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x2 \leq 1.7 \cdot 10^{+104}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 + -1\right)\\ \mathbf{else}:\\ \;\;\;\;8 \cdot \left(x2 \cdot \left(x1 \cdot x1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x2 1.7e+104)
   (+ (* x2 -6.0) (* x1 (+ (* x1 9.0) -1.0)))
   (* 8.0 (* x2 (* x1 x1)))))

C

double code(double x1, double x2) {
	double tmp;
	if (x2 <= 1.7e+104) {
		tmp = (x2 * -6.0) + (x1 * ((x1 * 9.0) + -1.0));
	} else {
		tmp = 8.0 * (x2 * (x1 * x1));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x2 <= 1.7d+104) then
        tmp = (x2 * (-6.0d0)) + (x1 * ((x1 * 9.0d0) + (-1.0d0)))
    else
        tmp = 8.0d0 * (x2 * (x1 * x1))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x2 <= 1.7e+104) {
		tmp = (x2 * -6.0) + (x1 * ((x1 * 9.0) + -1.0));
	} else {
		tmp = 8.0 * (x2 * (x1 * x1));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x2 <= 1.7e+104:
		tmp = (x2 * -6.0) + (x1 * ((x1 * 9.0) + -1.0))
	else:
		tmp = 8.0 * (x2 * (x1 * x1))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x2 <= 1.7e+104)
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(x1 * 9.0) + -1.0)));
	else
		tmp = Float64(8.0 * Float64(x2 * Float64(x1 * x1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x2 <= 1.7e+104)
		tmp = (x2 * -6.0) + (x1 * ((x1 * 9.0) + -1.0));
	else
		tmp = 8.0 * (x2 * (x1 * x1));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x2, 1.7e+104], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(8.0 * N[(x2 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x2 < 1.6999999999999998e104

   1. Initial program 73.2%

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

   3. Simplified 70.8%

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

   5. Taylor expanded in x1 around 0 54.3%

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

   6. Taylor expanded in x2 around 0 59.3%

      \[\leadsto x1 + \left(-6 \cdot x2 + x1 \cdot \left(\color{blue}{x1 \cdot \left(9 + -19 \cdot x1\right)} - 2\right)\right) \]
   7. Step-by-step derivation

      1. *-commutative 59.3%

         \[\leadsto x1 + \left(-6 \cdot x2 + x1 \cdot \left(x1 \cdot \left(9 + \color{blue}{x1 \cdot -19}\right) - 2\right)\right) \]

   8. Simplified 59.3%

      \[\leadsto x1 + \left(-6 \cdot x2 + x1 \cdot \left(\color{blue}{x1 \cdot \left(9 + x1 \cdot -19\right)} - 2\right)\right) \]

   9. Taylor expanded in x1 around 0 70.6%

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

   if 1.6999999999999998e104 < x2

   1. Initial program 70.1%

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

   3. Simplified 48.7%

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

   5. Taylor expanded in x1 around -inf 45.4%

      \[\leadsto \color{blue}{{x1}^{4} \cdot \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{15 + -1 \cdot \left(6 + -4 \cdot \left(2 \cdot x2 - 3\right)\right)}{x1}}{x1}\right)} \]

   6. Taylor expanded in x2 around inf 42.1%

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

      1. pow2 42.1%

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

   8. Applied egg-rr 42.1%

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

4. Final simplification 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq 1.7 \cdot 10^{+104}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 + -1\right)\\ \mathbf{else}:\\ \;\;\;\;8 \cdot \left(x2 \cdot \left(x1 \cdot x1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 38.5% accurate, 25.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 72.6%

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

3. Simplified 66.7%

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

5. Taylor expanded in x1 around 0 45.9%

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

6. Taylor expanded in x2 around 0 52.3%

   \[\leadsto x1 + \left(-6 \cdot x2 + x1 \cdot \left(\color{blue}{x1 \cdot \left(9 + -19 \cdot x1\right)} - 2\right)\right) \]
7. Step-by-step derivation

   1. *-commutative 52.3%

      \[\leadsto x1 + \left(-6 \cdot x2 + x1 \cdot \left(x1 \cdot \left(9 + \color{blue}{x1 \cdot -19}\right) - 2\right)\right) \]

8. Simplified 52.3%

   \[\leadsto x1 + \left(-6 \cdot x2 + x1 \cdot \left(\color{blue}{x1 \cdot \left(9 + x1 \cdot -19\right)} - 2\right)\right) \]

9. Taylor expanded in x1 around 0 37.6%

   \[\leadsto \color{blue}{-6 \cdot x2 + -1 \cdot x1} \]
10. Step-by-step derivation

    1. *-commutative 37.6%

       \[\leadsto \color{blue}{x2 \cdot -6} + -1 \cdot x1 \]

    2. neg-mul-1 37.6%

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

    3. unsub-neg 37.6%

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

11. Simplified 37.6%

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

Alternative 18: 27.1% accurate, 25.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 72.6%

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

3. Simplified 66.7%

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

5. Taylor expanded in x1 around 0 45.9%

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

6. Taylor expanded in x2 around 0 52.3%

   \[\leadsto x1 + \left(-6 \cdot x2 + x1 \cdot \left(\color{blue}{x1 \cdot \left(9 + -19 \cdot x1\right)} - 2\right)\right) \]
7. Step-by-step derivation

   1. *-commutative 52.3%

      \[\leadsto x1 + \left(-6 \cdot x2 + x1 \cdot \left(x1 \cdot \left(9 + \color{blue}{x1 \cdot -19}\right) - 2\right)\right) \]

8. Simplified 52.3%

   \[\leadsto x1 + \left(-6 \cdot x2 + x1 \cdot \left(\color{blue}{x1 \cdot \left(9 + x1 \cdot -19\right)} - 2\right)\right) \]

9. Taylor expanded in x2 around inf 27.0%

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

    1. *-commutative 27.0%

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

11. Simplified 27.0%

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

Alternative 19: 26.9% 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 72.6%

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

3. Simplified 72.6%

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

5. Taylor expanded in x1 around 0 26.8%

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

   1. *-commutative 26.8%

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

7. Simplified 26.8%

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

Alternative 20: 3.2% accurate, 127.0× speedup

Math

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

FPCore

(FPCore (x1 x2) :precision binary64 x1)

C

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

Fortran

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

Java

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

Python

def code(x1, x2):
	return x1

Julia

function code(x1, x2)
	return x1
end

MATLAB

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

Wolfram

code[x1_, x2_] := x1

Derivation

1. Initial program 72.6%

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

3. Simplified 66.7%

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

5. Taylor expanded in x1 around 0 45.9%

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

6. Taylor expanded in x2 around 0 52.3%

   \[\leadsto x1 + \left(-6 \cdot x2 + x1 \cdot \left(\color{blue}{x1 \cdot \left(9 + -19 \cdot x1\right)} - 2\right)\right) \]
7. Step-by-step derivation

   1. *-commutative 52.3%

      \[\leadsto x1 + \left(-6 \cdot x2 + x1 \cdot \left(x1 \cdot \left(9 + \color{blue}{x1 \cdot -19}\right) - 2\right)\right) \]

8. Simplified 52.3%

   \[\leadsto x1 + \left(-6 \cdot x2 + x1 \cdot \left(\color{blue}{x1 \cdot \left(9 + x1 \cdot -19\right)} - 2\right)\right) \]

9. Taylor expanded in x2 around inf 27.0%

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

    1. *-commutative 27.0%

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

11. Simplified 27.0%

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

12. Taylor expanded in x1 around inf 3.2%

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

Reproduce

herbie shell --seed 2024188 
(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))))))