Rosa's FloatVsDoubleBenchmark

Percentage Accurate: 70.4% → 99.5%

Time: 49.6s

Alternatives: 22

Speedup: 5.5×

• 46.4% 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: 99.5% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 99.4%

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

   3. Simplified 99.7%

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

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

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around inf 0.0%

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

   3. Taylor expanded in x1 around 0 0.0%

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

      1. +-commutative 0.0%

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

      2. neg-mul-1 0.0%

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

      3. unsub-neg 0.0%

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

      4. *-commutative 0.0%

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

   5. Simplified 0.0%

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

   6. Taylor expanded in x1 around inf 100.0%

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

      1. *-commutative 100.0%

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

   8. Simplified 100.0%

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

4. Final simplification 99.8%

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

Alternative 2: 99.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot x1\right)\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := x1 \cdot x1 + 1\\ t_3 := \frac{\left(t_1 + 2 \cdot x2\right) - x1}{t_2}\\ t_4 := t_2 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t_3\right) \cdot \left(t_3 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(t_3 \cdot 4 - 6\right)\right)\\ t_5 := 3 \cdot \left(x2 \cdot -2 - x1\right)\\ \mathbf{if}\;x1 + \left(\left(x1 + \left(\left(t_4 + t_1 \cdot t_3\right) + t_0\right)\right) + 3 \cdot \frac{\left(t_1 - 2 \cdot x2\right) - x1}{t_2}\right) \leq \infty:\\ \;\;\;\;x1 + \left(t_5 + \left(x1 + \left(t_0 + \left(t_4 + 3 \cdot t_1\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 + 6 \cdot {x1}^{4}\right) + t_5\right)\\ \end{array} \end{array} \]

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_2
          (+
           (* (* (* x1 2.0) t_3) (- t_3 3.0))
           (* (* x1 x1) (- (* t_3 4.0) 6.0)))))
        (t_5 (* 3.0 (- (* x2 -2.0) x1))))
   (if (<=
        (+
         x1
         (+
          (+ x1 (+ (+ t_4 (* t_1 t_3)) t_0))
          (* 3.0 (/ (- (- t_1 (* 2.0 x2)) x1) t_2))))
        INFINITY)
     (+ x1 (+ t_5 (+ x1 (+ t_0 (+ t_4 (* 3.0 t_1))))))
     (+ x1 (+ (+ x1 (* 6.0 (pow x1 4.0))) t_5)))))

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_2 * ((((x1 * 2.0) * t_3) * (t_3 - 3.0)) + ((x1 * x1) * ((t_3 * 4.0) - 6.0)));
	double t_5 = 3.0 * ((x2 * -2.0) - x1);
	double tmp;
	if ((x1 + ((x1 + ((t_4 + (t_1 * t_3)) + t_0)) + (3.0 * (((t_1 - (2.0 * x2)) - x1) / t_2)))) <= ((double) INFINITY)) {
		tmp = x1 + (t_5 + (x1 + (t_0 + (t_4 + (3.0 * t_1)))));
	} else {
		tmp = x1 + ((x1 + (6.0 * pow(x1, 4.0))) + t_5);
	}
	return tmp;
}

Java

public static 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_2 * ((((x1 * 2.0) * t_3) * (t_3 - 3.0)) + ((x1 * x1) * ((t_3 * 4.0) - 6.0)));
	double t_5 = 3.0 * ((x2 * -2.0) - x1);
	double tmp;
	if ((x1 + ((x1 + ((t_4 + (t_1 * t_3)) + t_0)) + (3.0 * (((t_1 - (2.0 * x2)) - x1) / t_2)))) <= Double.POSITIVE_INFINITY) {
		tmp = x1 + (t_5 + (x1 + (t_0 + (t_4 + (3.0 * t_1)))));
	} else {
		tmp = x1 + ((x1 + (6.0 * Math.pow(x1, 4.0))) + t_5);
	}
	return tmp;
}

Python

def code(x1, x2):
	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_2 * ((((x1 * 2.0) * t_3) * (t_3 - 3.0)) + ((x1 * x1) * ((t_3 * 4.0) - 6.0)))
	t_5 = 3.0 * ((x2 * -2.0) - x1)
	tmp = 0
	if (x1 + ((x1 + ((t_4 + (t_1 * t_3)) + t_0)) + (3.0 * (((t_1 - (2.0 * x2)) - x1) / t_2)))) <= math.inf:
		tmp = x1 + (t_5 + (x1 + (t_0 + (t_4 + (3.0 * t_1)))))
	else:
		tmp = x1 + ((x1 + (6.0 * math.pow(x1, 4.0))) + t_5)
	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_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))))
	t_5 = Float64(3.0 * Float64(Float64(x2 * -2.0) - x1))
	tmp = 0.0
	if (Float64(x1 + Float64(Float64(x1 + Float64(Float64(t_4 + Float64(t_1 * t_3)) + t_0)) + Float64(3.0 * Float64(Float64(Float64(t_1 - Float64(2.0 * x2)) - x1) / t_2)))) <= Inf)
		tmp = Float64(x1 + Float64(t_5 + Float64(x1 + Float64(t_0 + Float64(t_4 + Float64(3.0 * t_1))))));
	else
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(6.0 * (x1 ^ 4.0))) + t_5));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	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_2 * ((((x1 * 2.0) * t_3) * (t_3 - 3.0)) + ((x1 * x1) * ((t_3 * 4.0) - 6.0)));
	t_5 = 3.0 * ((x2 * -2.0) - x1);
	tmp = 0.0;
	if ((x1 + ((x1 + ((t_4 + (t_1 * t_3)) + t_0)) + (3.0 * (((t_1 - (2.0 * x2)) - x1) / t_2)))) <= Inf)
		tmp = x1 + (t_5 + (x1 + (t_0 + (t_4 + (3.0 * t_1)))));
	else
		tmp = x1 + ((x1 + (6.0 * (x1 ^ 4.0))) + t_5);
	end
	tmp_2 = tmp;
end

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 99.4%

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

   2. Taylor expanded in x1 around inf 98.5%

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

   3. Taylor expanded in x1 around 0 99.4%

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

      1. +-commutative 99.4%

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

      2. neg-mul-1 99.4%

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

      3. unsub-neg 99.4%

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

      4. *-commutative 99.4%

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

   5. Simplified 99.4%

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

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

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around inf 0.0%

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

   3. Taylor expanded in x1 around 0 0.0%

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

      1. +-commutative 0.0%

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

      2. neg-mul-1 0.0%

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

      3. unsub-neg 0.0%

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

      4. *-commutative 0.0%

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

   5. Simplified 0.0%

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

   6. Taylor expanded in x1 around inf 100.0%

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

      1. *-commutative 100.0%

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

   8. Simplified 100.0%

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

4. Final simplification 99.6%

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

Alternative 3: 95.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 3 \cdot \left(x2 \cdot -2 - x1\right)\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := x1 \cdot \left(x1 \cdot x1\right)\\ t_3 := x1 \cdot x1 + 1\\ t_4 := \frac{\left(t_1 + 2 \cdot x2\right) - x1}{t_3}\\ t_5 := 3 \cdot t_1\\ \mathbf{if}\;x1 \leq -2.25 \cdot 10^{+104}:\\ \;\;\;\;x1 + \mathsf{fma}\left(x1, -2, x1 \cdot \left(x1 \cdot 9\right)\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+78}:\\ \;\;\;\;x1 + \left(t_0 + \left(x1 + \left(t_2 + \left(t_3 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t_4\right) \cdot \left(t_4 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(t_4 \cdot 4 - 6\right)\right) + t_5\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(t_0 + \left(x1 + \left(t_2 + \left(t_5 + t_3 \cdot \left(x1 \cdot \left(x1 \cdot 6\right)\right)\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* 3.0 (- (* x2 -2.0) x1)))
        (t_1 (* x1 (* x1 3.0)))
        (t_2 (* x1 (* x1 x1)))
        (t_3 (+ (* x1 x1) 1.0))
        (t_4 (/ (- (+ t_1 (* 2.0 x2)) x1) t_3))
        (t_5 (* 3.0 t_1)))
   (if (<= x1 -2.25e+104)
     (+ x1 (fma x1 -2.0 (* x1 (* x1 9.0))))
     (if (<= x1 5e+78)
       (+
        x1
        (+
         t_0
         (+
          x1
          (+
           t_2
           (+
            (*
             t_3
             (+
              (* (* (* x1 2.0) t_4) (- t_4 3.0))
              (* (* x1 x1) (- (* t_4 4.0) 6.0))))
            t_5)))))
       (+ x1 (+ t_0 (+ x1 (+ t_2 (+ t_5 (* t_3 (* x1 (* x1 6.0))))))))))))

C

double code(double x1, double x2) {
	double t_0 = 3.0 * ((x2 * -2.0) - x1);
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = x1 * (x1 * x1);
	double t_3 = (x1 * x1) + 1.0;
	double t_4 = ((t_1 + (2.0 * x2)) - x1) / t_3;
	double t_5 = 3.0 * t_1;
	double tmp;
	if (x1 <= -2.25e+104) {
		tmp = x1 + fma(x1, -2.0, (x1 * (x1 * 9.0)));
	} else if (x1 <= 5e+78) {
		tmp = x1 + (t_0 + (x1 + (t_2 + ((t_3 * ((((x1 * 2.0) * t_4) * (t_4 - 3.0)) + ((x1 * x1) * ((t_4 * 4.0) - 6.0)))) + t_5))));
	} else {
		tmp = x1 + (t_0 + (x1 + (t_2 + (t_5 + (t_3 * (x1 * (x1 * 6.0)))))));
	}
	return tmp;
}

Julia

function code(x1, x2)
	t_0 = Float64(3.0 * Float64(Float64(x2 * -2.0) - x1))
	t_1 = Float64(x1 * Float64(x1 * 3.0))
	t_2 = Float64(x1 * Float64(x1 * x1))
	t_3 = Float64(Float64(x1 * x1) + 1.0)
	t_4 = Float64(Float64(Float64(t_1 + Float64(2.0 * x2)) - x1) / t_3)
	t_5 = Float64(3.0 * t_1)
	tmp = 0.0
	if (x1 <= -2.25e+104)
		tmp = Float64(x1 + fma(x1, -2.0, Float64(x1 * Float64(x1 * 9.0))));
	elseif (x1 <= 5e+78)
		tmp = Float64(x1 + Float64(t_0 + Float64(x1 + Float64(t_2 + Float64(Float64(t_3 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_4) * Float64(t_4 - 3.0)) + Float64(Float64(x1 * x1) * Float64(Float64(t_4 * 4.0) - 6.0)))) + t_5)))));
	else
		tmp = Float64(x1 + Float64(t_0 + Float64(x1 + Float64(t_2 + Float64(t_5 + Float64(t_3 * Float64(x1 * Float64(x1 * 6.0))))))));
	end
	return tmp
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(t$95$1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$3), $MachinePrecision]}, Block[{t$95$5 = N[(3.0 * t$95$1), $MachinePrecision]}, If[LessEqual[x1, -2.25e+104], N[(x1 + N[(x1 * -2.0 + N[(x1 * N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 5e+78], N[(x1 + N[(t$95$0 + N[(x1 + N[(t$95$2 + N[(N[(t$95$3 * N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$4), $MachinePrecision] * N[(t$95$4 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$4 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(t$95$0 + N[(x1 + N[(t$95$2 + N[(t$95$5 + N[(t$95$3 * N[(x1 * N[(x1 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -2.2499999999999999e104

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around 0 0.0%

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

   3. Taylor expanded in x1 around 0 44.8%

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

      1. +-commutative 44.8%

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

      2. neg-mul-1 44.8%

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

      3. unsub-neg 44.8%

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

      4. +-commutative 44.8%

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

      5. *-commutative 44.8%

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

      6. fma-def 44.8%

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

      7. unpow2 44.8%

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

      8. cancel-sign-sub-inv 44.8%

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

      9. metadata-eval 44.8%

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

      10. *-commutative 44.8%

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

   5. Simplified 44.8%

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

   6. Taylor expanded in x1 around inf 44.8%

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

   7. Taylor expanded in x2 around 0 82.2%

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

      1. +-commutative 82.2%

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

      2. *-commutative 82.2%

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

      3. fma-def 82.2%

         \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(x1, -2, 9 \cdot {x1}^{2}\right)} \]

      4. *-commutative 82.2%

         \[\leadsto x1 + \mathsf{fma}\left(x1, -2, \color{blue}{{x1}^{2} \cdot 9}\right) \]

      5. unpow2 82.2%

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

      6. associate-*l* 82.2%

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

   9. Simplified 82.2%

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

   if -2.2499999999999999e104 < x1 < 4.99999999999999984e78

   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. Taylor expanded in x1 around inf 98.4%

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

   3. Taylor expanded in x1 around 0 99.4%

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

      1. +-commutative 99.4%

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

      2. neg-mul-1 99.4%

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

      3. unsub-neg 99.4%

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

      4. *-commutative 99.4%

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

   5. Simplified 99.4%

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

   if 4.99999999999999984e78 < x1

   1. Initial program 31.7%

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

   2. Taylor expanded in x1 around inf 31.7%

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

   3. Taylor expanded in x1 around 0 31.7%

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

      1. +-commutative 31.7%

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

      2. neg-mul-1 31.7%

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

      3. unsub-neg 31.7%

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

      4. *-commutative 31.7%

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

   5. Simplified 31.7%

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

   6. Taylor expanded in x1 around inf 100.0%

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

      1. *-commutative 100.0%

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

      2. unpow2 100.0%

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

      3. associate-*l* 100.0%

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

   8. Simplified 100.0%

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

4. Final simplification 96.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -2.25 \cdot 10^{+104}:\\ \;\;\;\;x1 + \mathsf{fma}\left(x1, -2, x1 \cdot \left(x1 \cdot 9\right)\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+78}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2 - x1\right) + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right)\right) + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2 - x1\right) + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(x1 \cdot \left(x1 \cdot 6\right)\right)\right)\right)\right)\right)\\ \end{array} \]

Alternative 4: 93.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 3 \cdot \left(x2 \cdot -2 - x1\right)\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := x1 \cdot \left(x1 \cdot x1\right)\\ t_3 := x1 \cdot x1 + 1\\ t_4 := \frac{\left(t_1 + 2 \cdot x2\right) - x1}{t_3}\\ t_5 := 3 \cdot t_1\\ \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 + 3 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(3 - x2 \cdot -2\right)\right)\\ \mathbf{elif}\;x1 \leq 10^{+79}:\\ \;\;\;\;x1 + \left(t_0 + \left(x1 + \left(t_2 + \left(t_3 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t_4\right) \cdot \left(t_4 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(t_4 \cdot 4 - 6\right)\right) + t_5\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(t_0 + \left(x1 + \left(t_2 + \left(t_5 + t_3 \cdot \left(x1 \cdot \left(x1 \cdot 6\right)\right)\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* 3.0 (- (* x2 -2.0) x1)))
        (t_1 (* x1 (* x1 3.0)))
        (t_2 (* x1 (* x1 x1)))
        (t_3 (+ (* x1 x1) 1.0))
        (t_4 (/ (- (+ t_1 (* 2.0 x2)) x1) t_3))
        (t_5 (* 3.0 t_1)))
   (if (<= x1 -5.6e+102)
     (+ x1 (* 3.0 (* (* x1 x1) (- 3.0 (* x2 -2.0)))))
     (if (<= x1 1e+79)
       (+
        x1
        (+
         t_0
         (+
          x1
          (+
           t_2
           (+
            (*
             t_3
             (+
              (* (* (* x1 2.0) t_4) (- t_4 3.0))
              (* (* x1 x1) (- (* t_4 4.0) 6.0))))
            t_5)))))
       (+ x1 (+ t_0 (+ x1 (+ t_2 (+ t_5 (* t_3 (* x1 (* x1 6.0))))))))))))

C

double code(double x1, double x2) {
	double t_0 = 3.0 * ((x2 * -2.0) - x1);
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = x1 * (x1 * x1);
	double t_3 = (x1 * x1) + 1.0;
	double t_4 = ((t_1 + (2.0 * x2)) - x1) / t_3;
	double t_5 = 3.0 * t_1;
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = x1 + (3.0 * ((x1 * x1) * (3.0 - (x2 * -2.0))));
	} else if (x1 <= 1e+79) {
		tmp = x1 + (t_0 + (x1 + (t_2 + ((t_3 * ((((x1 * 2.0) * t_4) * (t_4 - 3.0)) + ((x1 * x1) * ((t_4 * 4.0) - 6.0)))) + t_5))));
	} else {
		tmp = x1 + (t_0 + (x1 + (t_2 + (t_5 + (t_3 * (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) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_0 = 3.0d0 * ((x2 * (-2.0d0)) - x1)
    t_1 = x1 * (x1 * 3.0d0)
    t_2 = x1 * (x1 * x1)
    t_3 = (x1 * x1) + 1.0d0
    t_4 = ((t_1 + (2.0d0 * x2)) - x1) / t_3
    t_5 = 3.0d0 * t_1
    if (x1 <= (-5.6d+102)) then
        tmp = x1 + (3.0d0 * ((x1 * x1) * (3.0d0 - (x2 * (-2.0d0)))))
    else if (x1 <= 1d+79) then
        tmp = x1 + (t_0 + (x1 + (t_2 + ((t_3 * ((((x1 * 2.0d0) * t_4) * (t_4 - 3.0d0)) + ((x1 * x1) * ((t_4 * 4.0d0) - 6.0d0)))) + t_5))))
    else
        tmp = x1 + (t_0 + (x1 + (t_2 + (t_5 + (t_3 * (x1 * (x1 * 6.0d0)))))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = 3.0 * ((x2 * -2.0) - x1);
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = x1 * (x1 * x1);
	double t_3 = (x1 * x1) + 1.0;
	double t_4 = ((t_1 + (2.0 * x2)) - x1) / t_3;
	double t_5 = 3.0 * t_1;
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = x1 + (3.0 * ((x1 * x1) * (3.0 - (x2 * -2.0))));
	} else if (x1 <= 1e+79) {
		tmp = x1 + (t_0 + (x1 + (t_2 + ((t_3 * ((((x1 * 2.0) * t_4) * (t_4 - 3.0)) + ((x1 * x1) * ((t_4 * 4.0) - 6.0)))) + t_5))));
	} else {
		tmp = x1 + (t_0 + (x1 + (t_2 + (t_5 + (t_3 * (x1 * (x1 * 6.0)))))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = 3.0 * ((x2 * -2.0) - x1)
	t_1 = x1 * (x1 * 3.0)
	t_2 = x1 * (x1 * x1)
	t_3 = (x1 * x1) + 1.0
	t_4 = ((t_1 + (2.0 * x2)) - x1) / t_3
	t_5 = 3.0 * t_1
	tmp = 0
	if x1 <= -5.6e+102:
		tmp = x1 + (3.0 * ((x1 * x1) * (3.0 - (x2 * -2.0))))
	elif x1 <= 1e+79:
		tmp = x1 + (t_0 + (x1 + (t_2 + ((t_3 * ((((x1 * 2.0) * t_4) * (t_4 - 3.0)) + ((x1 * x1) * ((t_4 * 4.0) - 6.0)))) + t_5))))
	else:
		tmp = x1 + (t_0 + (x1 + (t_2 + (t_5 + (t_3 * (x1 * (x1 * 6.0)))))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(3.0 * Float64(Float64(x2 * -2.0) - x1))
	t_1 = Float64(x1 * Float64(x1 * 3.0))
	t_2 = Float64(x1 * Float64(x1 * x1))
	t_3 = Float64(Float64(x1 * x1) + 1.0)
	t_4 = Float64(Float64(Float64(t_1 + Float64(2.0 * x2)) - x1) / t_3)
	t_5 = Float64(3.0 * t_1)
	tmp = 0.0
	if (x1 <= -5.6e+102)
		tmp = Float64(x1 + Float64(3.0 * Float64(Float64(x1 * x1) * Float64(3.0 - Float64(x2 * -2.0)))));
	elseif (x1 <= 1e+79)
		tmp = Float64(x1 + Float64(t_0 + Float64(x1 + Float64(t_2 + Float64(Float64(t_3 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_4) * Float64(t_4 - 3.0)) + Float64(Float64(x1 * x1) * Float64(Float64(t_4 * 4.0) - 6.0)))) + t_5)))));
	else
		tmp = Float64(x1 + Float64(t_0 + Float64(x1 + Float64(t_2 + Float64(t_5 + Float64(t_3 * Float64(x1 * Float64(x1 * 6.0))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = 3.0 * ((x2 * -2.0) - x1);
	t_1 = x1 * (x1 * 3.0);
	t_2 = x1 * (x1 * x1);
	t_3 = (x1 * x1) + 1.0;
	t_4 = ((t_1 + (2.0 * x2)) - x1) / t_3;
	t_5 = 3.0 * t_1;
	tmp = 0.0;
	if (x1 <= -5.6e+102)
		tmp = x1 + (3.0 * ((x1 * x1) * (3.0 - (x2 * -2.0))));
	elseif (x1 <= 1e+79)
		tmp = x1 + (t_0 + (x1 + (t_2 + ((t_3 * ((((x1 * 2.0) * t_4) * (t_4 - 3.0)) + ((x1 * x1) * ((t_4 * 4.0) - 6.0)))) + t_5))));
	else
		tmp = x1 + (t_0 + (x1 + (t_2 + (t_5 + (t_3 * (x1 * (x1 * 6.0)))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(t$95$1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$3), $MachinePrecision]}, Block[{t$95$5 = N[(3.0 * t$95$1), $MachinePrecision]}, If[LessEqual[x1, -5.6e+102], N[(x1 + N[(3.0 * N[(N[(x1 * x1), $MachinePrecision] * N[(3.0 - N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1e+79], N[(x1 + N[(t$95$0 + N[(x1 + N[(t$95$2 + N[(N[(t$95$3 * N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$4), $MachinePrecision] * N[(t$95$4 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$4 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(t$95$0 + N[(x1 + N[(t$95$2 + N[(t$95$5 + N[(t$95$3 * N[(x1 * N[(x1 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -5.60000000000000037e102

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around 0 0.0%

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

   3. Taylor expanded in x1 around 0 44.8%

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

      1. +-commutative 44.8%

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

      2. neg-mul-1 44.8%

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

      3. unsub-neg 44.8%

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

      4. +-commutative 44.8%

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

      5. *-commutative 44.8%

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

      6. fma-def 44.8%

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

      7. unpow2 44.8%

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

      8. cancel-sign-sub-inv 44.8%

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

      9. metadata-eval 44.8%

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

      10. *-commutative 44.8%

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

   5. Simplified 44.8%

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

   6. Taylor expanded in x1 around inf 44.8%

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

   7. Taylor expanded in x1 around inf 71.7%

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

      1. unpow2 71.7%

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

      2. metadata-eval 71.7%

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

      3. cancel-sign-sub-inv 71.7%

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

      4. *-commutative 71.7%

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

   9. Simplified 71.7%

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

   if -5.60000000000000037e102 < x1 < 9.99999999999999967e78

   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. Taylor expanded in x1 around inf 98.4%

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

   3. Taylor expanded in x1 around 0 99.4%

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

      1. +-commutative 99.4%

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

      2. neg-mul-1 99.4%

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

      3. unsub-neg 99.4%

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

      4. *-commutative 99.4%

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

   5. Simplified 99.4%

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

   if 9.99999999999999967e78 < x1

   1. Initial program 31.7%

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

   2. Taylor expanded in x1 around inf 31.7%

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

   3. Taylor expanded in x1 around 0 31.7%

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

      1. +-commutative 31.7%

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

      2. neg-mul-1 31.7%

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

      3. unsub-neg 31.7%

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

      4. *-commutative 31.7%

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

   5. Simplified 31.7%

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

   6. Taylor expanded in x1 around inf 100.0%

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

      1. *-commutative 100.0%

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

      2. unpow2 100.0%

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

      3. associate-*l* 100.0%

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

   8. Simplified 100.0%

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

4. Final simplification 93.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 + 3 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(3 - x2 \cdot -2\right)\right)\\ \mathbf{elif}\;x1 \leq 10^{+79}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2 - x1\right) + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right)\right) + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2 - x1\right) + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(x1 \cdot \left(x1 \cdot 6\right)\right)\right)\right)\right)\right)\\ \end{array} \]

Alternative 5: 90.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot x1\right)\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := 3 \cdot t_1\\ t_3 := x1 \cdot x1 + 1\\ t_4 := \frac{\left(t_1 + 2 \cdot x2\right) - x1}{t_3}\\ t_5 := x1 + \left(\left(x1 + \left(t_0 + \left(t_2 + t_3 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t_4\right) \cdot \left(t_4 - 3\right) + \left(x1 \cdot x1\right) \cdot 6\right)\right)\right)\right) + 3 \cdot \left(x2 \cdot -2\right)\right)\\ \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 + 3 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(3 - x2 \cdot -2\right)\right)\\ \mathbf{elif}\;x1 \leq -0.05:\\ \;\;\;\;t_5\\ \mathbf{elif}\;x1 \leq 0.048:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t_1 - 2 \cdot x2\right) - x1}{t_3} + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{+76}:\\ \;\;\;\;t_5\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2 - x1\right) + \left(x1 + \left(t_0 + \left(t_2 + t_3 \cdot \left(x1 \cdot \left(x1 \cdot 6\right)\right)\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 x1)))
        (t_1 (* x1 (* x1 3.0)))
        (t_2 (* 3.0 t_1))
        (t_3 (+ (* x1 x1) 1.0))
        (t_4 (/ (- (+ t_1 (* 2.0 x2)) x1) t_3))
        (t_5
         (+
          x1
          (+
           (+
            x1
            (+
             t_0
             (+
              t_2
              (*
               t_3
               (+ (* (* (* x1 2.0) t_4) (- t_4 3.0)) (* (* x1 x1) 6.0))))))
           (* 3.0 (* x2 -2.0))))))
   (if (<= x1 -5.6e+102)
     (+ x1 (* 3.0 (* (* x1 x1) (- 3.0 (* x2 -2.0)))))
     (if (<= x1 -0.05)
       t_5
       (if (<= x1 0.048)
         (+
          x1
          (+
           (* 3.0 (/ (- (- t_1 (* 2.0 x2)) x1) t_3))
           (+ x1 (* 4.0 (* x2 (* x1 (- (* 2.0 x2) 3.0)))))))
         (if (<= x1 2e+76)
           t_5
           (+
            x1
            (+
             (* 3.0 (- (* x2 -2.0) x1))
             (+ x1 (+ t_0 (+ t_2 (* t_3 (* x1 (* x1 6.0))))))))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * x1);
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = 3.0 * t_1;
	double t_3 = (x1 * x1) + 1.0;
	double t_4 = ((t_1 + (2.0 * x2)) - x1) / t_3;
	double t_5 = x1 + ((x1 + (t_0 + (t_2 + (t_3 * ((((x1 * 2.0) * t_4) * (t_4 - 3.0)) + ((x1 * x1) * 6.0)))))) + (3.0 * (x2 * -2.0)));
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = x1 + (3.0 * ((x1 * x1) * (3.0 - (x2 * -2.0))));
	} else if (x1 <= -0.05) {
		tmp = t_5;
	} else if (x1 <= 0.048) {
		tmp = x1 + ((3.0 * (((t_1 - (2.0 * x2)) - x1) / t_3)) + (x1 + (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0))))));
	} else if (x1 <= 2e+76) {
		tmp = t_5;
	} else {
		tmp = x1 + ((3.0 * ((x2 * -2.0) - x1)) + (x1 + (t_0 + (t_2 + (t_3 * (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) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_0 = x1 * (x1 * x1)
    t_1 = x1 * (x1 * 3.0d0)
    t_2 = 3.0d0 * t_1
    t_3 = (x1 * x1) + 1.0d0
    t_4 = ((t_1 + (2.0d0 * x2)) - x1) / t_3
    t_5 = x1 + ((x1 + (t_0 + (t_2 + (t_3 * ((((x1 * 2.0d0) * t_4) * (t_4 - 3.0d0)) + ((x1 * x1) * 6.0d0)))))) + (3.0d0 * (x2 * (-2.0d0))))
    if (x1 <= (-5.6d+102)) then
        tmp = x1 + (3.0d0 * ((x1 * x1) * (3.0d0 - (x2 * (-2.0d0)))))
    else if (x1 <= (-0.05d0)) then
        tmp = t_5
    else if (x1 <= 0.048d0) then
        tmp = x1 + ((3.0d0 * (((t_1 - (2.0d0 * x2)) - x1) / t_3)) + (x1 + (4.0d0 * (x2 * (x1 * ((2.0d0 * x2) - 3.0d0))))))
    else if (x1 <= 2d+76) then
        tmp = t_5
    else
        tmp = x1 + ((3.0d0 * ((x2 * (-2.0d0)) - x1)) + (x1 + (t_0 + (t_2 + (t_3 * (x1 * (x1 * 6.0d0)))))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * x1);
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = 3.0 * t_1;
	double t_3 = (x1 * x1) + 1.0;
	double t_4 = ((t_1 + (2.0 * x2)) - x1) / t_3;
	double t_5 = x1 + ((x1 + (t_0 + (t_2 + (t_3 * ((((x1 * 2.0) * t_4) * (t_4 - 3.0)) + ((x1 * x1) * 6.0)))))) + (3.0 * (x2 * -2.0)));
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = x1 + (3.0 * ((x1 * x1) * (3.0 - (x2 * -2.0))));
	} else if (x1 <= -0.05) {
		tmp = t_5;
	} else if (x1 <= 0.048) {
		tmp = x1 + ((3.0 * (((t_1 - (2.0 * x2)) - x1) / t_3)) + (x1 + (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0))))));
	} else if (x1 <= 2e+76) {
		tmp = t_5;
	} else {
		tmp = x1 + ((3.0 * ((x2 * -2.0) - x1)) + (x1 + (t_0 + (t_2 + (t_3 * (x1 * (x1 * 6.0)))))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * x1)
	t_1 = x1 * (x1 * 3.0)
	t_2 = 3.0 * t_1
	t_3 = (x1 * x1) + 1.0
	t_4 = ((t_1 + (2.0 * x2)) - x1) / t_3
	t_5 = x1 + ((x1 + (t_0 + (t_2 + (t_3 * ((((x1 * 2.0) * t_4) * (t_4 - 3.0)) + ((x1 * x1) * 6.0)))))) + (3.0 * (x2 * -2.0)))
	tmp = 0
	if x1 <= -5.6e+102:
		tmp = x1 + (3.0 * ((x1 * x1) * (3.0 - (x2 * -2.0))))
	elif x1 <= -0.05:
		tmp = t_5
	elif x1 <= 0.048:
		tmp = x1 + ((3.0 * (((t_1 - (2.0 * x2)) - x1) / t_3)) + (x1 + (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0))))))
	elif x1 <= 2e+76:
		tmp = t_5
	else:
		tmp = x1 + ((3.0 * ((x2 * -2.0) - x1)) + (x1 + (t_0 + (t_2 + (t_3 * (x1 * (x1 * 6.0)))))))
	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(3.0 * t_1)
	t_3 = Float64(Float64(x1 * x1) + 1.0)
	t_4 = Float64(Float64(Float64(t_1 + Float64(2.0 * x2)) - x1) / t_3)
	t_5 = Float64(x1 + Float64(Float64(x1 + Float64(t_0 + Float64(t_2 + Float64(t_3 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_4) * Float64(t_4 - 3.0)) + Float64(Float64(x1 * x1) * 6.0)))))) + Float64(3.0 * Float64(x2 * -2.0))))
	tmp = 0.0
	if (x1 <= -5.6e+102)
		tmp = Float64(x1 + Float64(3.0 * Float64(Float64(x1 * x1) * Float64(3.0 - Float64(x2 * -2.0)))));
	elseif (x1 <= -0.05)
		tmp = t_5;
	elseif (x1 <= 0.048)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_1 - Float64(2.0 * x2)) - x1) / t_3)) + Float64(x1 + Float64(4.0 * Float64(x2 * Float64(x1 * Float64(Float64(2.0 * x2) - 3.0)))))));
	elseif (x1 <= 2e+76)
		tmp = t_5;
	else
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(x2 * -2.0) - x1)) + Float64(x1 + Float64(t_0 + Float64(t_2 + Float64(t_3 * Float64(x1 * Float64(x1 * 6.0))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * x1);
	t_1 = x1 * (x1 * 3.0);
	t_2 = 3.0 * t_1;
	t_3 = (x1 * x1) + 1.0;
	t_4 = ((t_1 + (2.0 * x2)) - x1) / t_3;
	t_5 = x1 + ((x1 + (t_0 + (t_2 + (t_3 * ((((x1 * 2.0) * t_4) * (t_4 - 3.0)) + ((x1 * x1) * 6.0)))))) + (3.0 * (x2 * -2.0)));
	tmp = 0.0;
	if (x1 <= -5.6e+102)
		tmp = x1 + (3.0 * ((x1 * x1) * (3.0 - (x2 * -2.0))));
	elseif (x1 <= -0.05)
		tmp = t_5;
	elseif (x1 <= 0.048)
		tmp = x1 + ((3.0 * (((t_1 - (2.0 * x2)) - x1) / t_3)) + (x1 + (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0))))));
	elseif (x1 <= 2e+76)
		tmp = t_5;
	else
		tmp = x1 + ((3.0 * ((x2 * -2.0) - x1)) + (x1 + (t_0 + (t_2 + (t_3 * (x1 * (x1 * 6.0)))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(3.0 * t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(t$95$1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$3), $MachinePrecision]}, Block[{t$95$5 = N[(x1 + N[(N[(x1 + N[(t$95$0 + N[(t$95$2 + N[(t$95$3 * N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$4), $MachinePrecision] * N[(t$95$4 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -5.6e+102], N[(x1 + N[(3.0 * N[(N[(x1 * x1), $MachinePrecision] * N[(3.0 - N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -0.05], t$95$5, If[LessEqual[x1, 0.048], N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$1 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$3), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(4.0 * N[(x2 * N[(x1 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 2e+76], t$95$5, N[(x1 + N[(N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(t$95$0 + N[(t$95$2 + N[(t$95$3 * N[(x1 * N[(x1 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -5.60000000000000037e102

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around 0 0.0%

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

   3. Taylor expanded in x1 around 0 44.8%

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

      1. +-commutative 44.8%

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

      2. neg-mul-1 44.8%

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

      3. unsub-neg 44.8%

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

      4. +-commutative 44.8%

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

      5. *-commutative 44.8%

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

      6. fma-def 44.8%

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

      7. unpow2 44.8%

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

      8. cancel-sign-sub-inv 44.8%

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

      9. metadata-eval 44.8%

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

      10. *-commutative 44.8%

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

   5. Simplified 44.8%

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

   6. Taylor expanded in x1 around inf 44.8%

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

   7. Taylor expanded in x1 around inf 71.7%

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

      1. unpow2 71.7%

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

      2. metadata-eval 71.7%

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

      3. cancel-sign-sub-inv 71.7%

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

      4. *-commutative 71.7%

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

   9. Simplified 71.7%

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

   if -5.60000000000000037e102 < x1 < -0.050000000000000003 or 0.048000000000000001 < x1 < 2.0000000000000001e76

   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. Taylor expanded in x1 around inf 99.1%

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

   3. Taylor expanded in x1 around inf 92.4%

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

   4. Taylor expanded in x1 around 0 92.4%

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

      1. *-commutative 30.0%

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

   6. Simplified 92.4%

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

   if -0.050000000000000003 < x1 < 0.048000000000000001

   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. Taylor expanded in x1 around 0 98.6%

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

   if 2.0000000000000001e76 < x1

   1. Initial program 31.7%

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

   2. Taylor expanded in x1 around inf 31.7%

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

   3. Taylor expanded in x1 around 0 31.7%

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

      1. +-commutative 31.7%

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

      2. neg-mul-1 31.7%

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

      3. unsub-neg 31.7%

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

      4. *-commutative 31.7%

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

   5. Simplified 31.7%

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

   6. Taylor expanded in x1 around inf 100.0%

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

      1. *-commutative 100.0%

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

      2. unpow2 100.0%

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

      3. associate-*l* 100.0%

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

   8. Simplified 100.0%

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

4. Final simplification 92.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 + 3 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(3 - x2 \cdot -2\right)\right)\\ \mathbf{elif}\;x1 \leq -0.05:\\ \;\;\;\;x1 + \left(\left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot 6\right)\right)\right)\right) + 3 \cdot \left(x2 \cdot -2\right)\right)\\ \mathbf{elif}\;x1 \leq 0.048:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{+76}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot 6\right)\right)\right)\right) + 3 \cdot \left(x2 \cdot -2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2 - x1\right) + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(x1 \cdot \left(x1 \cdot 6\right)\right)\right)\right)\right)\right)\\ \end{array} \]

Alternative 6: 90.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 3 \cdot \left(x2 \cdot -2 - x1\right)\\ t_1 := x1 \cdot \left(x1 \cdot x1\right)\\ t_2 := x1 \cdot \left(x1 \cdot 3\right)\\ t_3 := 3 \cdot t_2\\ t_4 := x1 \cdot x1 + 1\\ t_5 := \frac{\left(t_2 + 2 \cdot x2\right) - x1}{t_4}\\ \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 + 3 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(3 - x2 \cdot -2\right)\right)\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{+76}:\\ \;\;\;\;x1 + \left(t_0 + \left(x1 + \left(t_1 + \left(t_3 + t_4 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t_5\right) \cdot \left(t_5 - 3\right) + \left(x1 \cdot x1\right) \cdot 6\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(t_0 + \left(x1 + \left(t_1 + \left(t_3 + t_4 \cdot \left(x1 \cdot \left(x1 \cdot 6\right)\right)\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* 3.0 (- (* x2 -2.0) x1)))
        (t_1 (* x1 (* x1 x1)))
        (t_2 (* x1 (* x1 3.0)))
        (t_3 (* 3.0 t_2))
        (t_4 (+ (* x1 x1) 1.0))
        (t_5 (/ (- (+ t_2 (* 2.0 x2)) x1) t_4)))
   (if (<= x1 -5.6e+102)
     (+ x1 (* 3.0 (* (* x1 x1) (- 3.0 (* x2 -2.0)))))
     (if (<= x1 2e+76)
       (+
        x1
        (+
         t_0
         (+
          x1
          (+
           t_1
           (+
            t_3
            (*
             t_4
             (+ (* (* (* x1 2.0) t_5) (- t_5 3.0)) (* (* x1 x1) 6.0))))))))
       (+ x1 (+ t_0 (+ x1 (+ t_1 (+ t_3 (* t_4 (* x1 (* x1 6.0))))))))))))

C

double code(double x1, double x2) {
	double t_0 = 3.0 * ((x2 * -2.0) - x1);
	double t_1 = x1 * (x1 * x1);
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = 3.0 * t_2;
	double t_4 = (x1 * x1) + 1.0;
	double t_5 = ((t_2 + (2.0 * x2)) - x1) / t_4;
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = x1 + (3.0 * ((x1 * x1) * (3.0 - (x2 * -2.0))));
	} else if (x1 <= 2e+76) {
		tmp = x1 + (t_0 + (x1 + (t_1 + (t_3 + (t_4 * ((((x1 * 2.0) * t_5) * (t_5 - 3.0)) + ((x1 * x1) * 6.0)))))));
	} else {
		tmp = x1 + (t_0 + (x1 + (t_1 + (t_3 + (t_4 * (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) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_0 = 3.0d0 * ((x2 * (-2.0d0)) - x1)
    t_1 = x1 * (x1 * x1)
    t_2 = x1 * (x1 * 3.0d0)
    t_3 = 3.0d0 * t_2
    t_4 = (x1 * x1) + 1.0d0
    t_5 = ((t_2 + (2.0d0 * x2)) - x1) / t_4
    if (x1 <= (-5.6d+102)) then
        tmp = x1 + (3.0d0 * ((x1 * x1) * (3.0d0 - (x2 * (-2.0d0)))))
    else if (x1 <= 2d+76) then
        tmp = x1 + (t_0 + (x1 + (t_1 + (t_3 + (t_4 * ((((x1 * 2.0d0) * t_5) * (t_5 - 3.0d0)) + ((x1 * x1) * 6.0d0)))))))
    else
        tmp = x1 + (t_0 + (x1 + (t_1 + (t_3 + (t_4 * (x1 * (x1 * 6.0d0)))))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = 3.0 * ((x2 * -2.0) - x1);
	double t_1 = x1 * (x1 * x1);
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = 3.0 * t_2;
	double t_4 = (x1 * x1) + 1.0;
	double t_5 = ((t_2 + (2.0 * x2)) - x1) / t_4;
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = x1 + (3.0 * ((x1 * x1) * (3.0 - (x2 * -2.0))));
	} else if (x1 <= 2e+76) {
		tmp = x1 + (t_0 + (x1 + (t_1 + (t_3 + (t_4 * ((((x1 * 2.0) * t_5) * (t_5 - 3.0)) + ((x1 * x1) * 6.0)))))));
	} else {
		tmp = x1 + (t_0 + (x1 + (t_1 + (t_3 + (t_4 * (x1 * (x1 * 6.0)))))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = 3.0 * ((x2 * -2.0) - x1)
	t_1 = x1 * (x1 * x1)
	t_2 = x1 * (x1 * 3.0)
	t_3 = 3.0 * t_2
	t_4 = (x1 * x1) + 1.0
	t_5 = ((t_2 + (2.0 * x2)) - x1) / t_4
	tmp = 0
	if x1 <= -5.6e+102:
		tmp = x1 + (3.0 * ((x1 * x1) * (3.0 - (x2 * -2.0))))
	elif x1 <= 2e+76:
		tmp = x1 + (t_0 + (x1 + (t_1 + (t_3 + (t_4 * ((((x1 * 2.0) * t_5) * (t_5 - 3.0)) + ((x1 * x1) * 6.0)))))))
	else:
		tmp = x1 + (t_0 + (x1 + (t_1 + (t_3 + (t_4 * (x1 * (x1 * 6.0)))))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(3.0 * Float64(Float64(x2 * -2.0) - x1))
	t_1 = Float64(x1 * Float64(x1 * x1))
	t_2 = Float64(x1 * Float64(x1 * 3.0))
	t_3 = Float64(3.0 * t_2)
	t_4 = Float64(Float64(x1 * x1) + 1.0)
	t_5 = Float64(Float64(Float64(t_2 + Float64(2.0 * x2)) - x1) / t_4)
	tmp = 0.0
	if (x1 <= -5.6e+102)
		tmp = Float64(x1 + Float64(3.0 * Float64(Float64(x1 * x1) * Float64(3.0 - Float64(x2 * -2.0)))));
	elseif (x1 <= 2e+76)
		tmp = Float64(x1 + Float64(t_0 + Float64(x1 + Float64(t_1 + Float64(t_3 + Float64(t_4 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_5) * Float64(t_5 - 3.0)) + Float64(Float64(x1 * x1) * 6.0))))))));
	else
		tmp = Float64(x1 + Float64(t_0 + Float64(x1 + Float64(t_1 + Float64(t_3 + Float64(t_4 * Float64(x1 * Float64(x1 * 6.0))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = 3.0 * ((x2 * -2.0) - x1);
	t_1 = x1 * (x1 * x1);
	t_2 = x1 * (x1 * 3.0);
	t_3 = 3.0 * t_2;
	t_4 = (x1 * x1) + 1.0;
	t_5 = ((t_2 + (2.0 * x2)) - x1) / t_4;
	tmp = 0.0;
	if (x1 <= -5.6e+102)
		tmp = x1 + (3.0 * ((x1 * x1) * (3.0 - (x2 * -2.0))));
	elseif (x1 <= 2e+76)
		tmp = x1 + (t_0 + (x1 + (t_1 + (t_3 + (t_4 * ((((x1 * 2.0) * t_5) * (t_5 - 3.0)) + ((x1 * x1) * 6.0)))))));
	else
		tmp = x1 + (t_0 + (x1 + (t_1 + (t_3 + (t_4 * (x1 * (x1 * 6.0)))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - x1), $MachinePrecision]), $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 * t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$5 = N[(N[(N[(t$95$2 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$4), $MachinePrecision]}, If[LessEqual[x1, -5.6e+102], N[(x1 + N[(3.0 * N[(N[(x1 * x1), $MachinePrecision] * N[(3.0 - N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 2e+76], N[(x1 + N[(t$95$0 + N[(x1 + N[(t$95$1 + N[(t$95$3 + N[(t$95$4 * N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$5), $MachinePrecision] * N[(t$95$5 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(t$95$0 + N[(x1 + N[(t$95$1 + N[(t$95$3 + N[(t$95$4 * N[(x1 * N[(x1 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -5.60000000000000037e102

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around 0 0.0%

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

   3. Taylor expanded in x1 around 0 44.8%

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

      1. +-commutative 44.8%

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

      2. neg-mul-1 44.8%

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

      3. unsub-neg 44.8%

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

      4. +-commutative 44.8%

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

      5. *-commutative 44.8%

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

      6. fma-def 44.8%

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

      7. unpow2 44.8%

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

      8. cancel-sign-sub-inv 44.8%

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

      9. metadata-eval 44.8%

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

      10. *-commutative 44.8%

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

   5. Simplified 44.8%

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

   6. Taylor expanded in x1 around inf 44.8%

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

   7. Taylor expanded in x1 around inf 71.7%

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

      1. unpow2 71.7%

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

      2. metadata-eval 71.7%

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

      3. cancel-sign-sub-inv 71.7%

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

      4. *-commutative 71.7%

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

   9. Simplified 71.7%

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

   if -5.60000000000000037e102 < x1 < 2.0000000000000001e76

   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. Taylor expanded in x1 around inf 98.4%

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

   3. Taylor expanded in x1 around inf 96.9%

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

   4. Taylor expanded in x1 around 0 96.9%

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

      1. +-commutative 99.4%

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

      2. neg-mul-1 99.4%

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

      3. unsub-neg 99.4%

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

      4. *-commutative 99.4%

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

   6. Simplified 96.9%

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

   if 2.0000000000000001e76 < x1

   1. Initial program 31.7%

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

   2. Taylor expanded in x1 around inf 31.7%

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

   3. Taylor expanded in x1 around 0 31.7%

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

      1. +-commutative 31.7%

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

      2. neg-mul-1 31.7%

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

      3. unsub-neg 31.7%

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

      4. *-commutative 31.7%

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

   5. Simplified 31.7%

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

   6. Taylor expanded in x1 around inf 100.0%

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

      1. *-commutative 100.0%

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

      2. unpow2 100.0%

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

      3. associate-*l* 100.0%

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

   8. Simplified 100.0%

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

4. Final simplification 92.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 + 3 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(3 - x2 \cdot -2\right)\right)\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{+76}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2 - x1\right) + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot 6\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2 - x1\right) + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(x1 \cdot \left(x1 \cdot 6\right)\right)\right)\right)\right)\right)\\ \end{array} \]

Alternative 7: 87.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot x1\right)\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := 3 \cdot t_1\\ t_3 := x1 \cdot x1 + 1\\ t_4 := 3 \cdot \frac{\left(t_1 - 2 \cdot x2\right) - x1}{t_3}\\ \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 + 3 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(3 - x2 \cdot -2\right)\right)\\ \mathbf{elif}\;x1 \leq -2.05 \cdot 10^{+17}:\\ \;\;\;\;x1 + \left(t_4 + \left(x1 + \left(t_0 + \left(t_2 + t_3 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(\frac{\left(t_1 + 2 \cdot x2\right) - x1}{t_3} \cdot 4 - 6\right) + \left(x1 + x1\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 12800:\\ \;\;\;\;x1 + \left(t_4 + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2 - x1\right) + \left(x1 + \left(t_0 + \left(t_2 + t_3 \cdot \left(\left(x1 \cdot x1\right) \cdot 6\right)\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 x1)))
        (t_1 (* x1 (* x1 3.0)))
        (t_2 (* 3.0 t_1))
        (t_3 (+ (* x1 x1) 1.0))
        (t_4 (* 3.0 (/ (- (- t_1 (* 2.0 x2)) x1) t_3))))
   (if (<= x1 -5.6e+102)
     (+ x1 (* 3.0 (* (* x1 x1) (- 3.0 (* x2 -2.0)))))
     (if (<= x1 -2.05e+17)
       (+
        x1
        (+
         t_4
         (+
          x1
          (+
           t_0
           (+
            t_2
            (*
             t_3
             (+
              (* (* x1 x1) (- (* (/ (- (+ t_1 (* 2.0 x2)) x1) t_3) 4.0) 6.0))
              (+ x1 x1))))))))
       (if (<= x1 12800.0)
         (+ x1 (+ t_4 (+ x1 (* 4.0 (* x2 (* x1 (- (* 2.0 x2) 3.0)))))))
         (+
          x1
          (+
           (* 3.0 (- (* x2 -2.0) x1))
           (+ x1 (+ t_0 (+ t_2 (* t_3 (* (* x1 x1) 6.0))))))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * x1);
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = 3.0 * t_1;
	double t_3 = (x1 * x1) + 1.0;
	double t_4 = 3.0 * (((t_1 - (2.0 * x2)) - x1) / t_3);
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = x1 + (3.0 * ((x1 * x1) * (3.0 - (x2 * -2.0))));
	} else if (x1 <= -2.05e+17) {
		tmp = x1 + (t_4 + (x1 + (t_0 + (t_2 + (t_3 * (((x1 * x1) * (((((t_1 + (2.0 * x2)) - x1) / t_3) * 4.0) - 6.0)) + (x1 + x1)))))));
	} else if (x1 <= 12800.0) {
		tmp = x1 + (t_4 + (x1 + (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0))))));
	} else {
		tmp = x1 + ((3.0 * ((x2 * -2.0) - x1)) + (x1 + (t_0 + (t_2 + (t_3 * ((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) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_0 = x1 * (x1 * x1)
    t_1 = x1 * (x1 * 3.0d0)
    t_2 = 3.0d0 * t_1
    t_3 = (x1 * x1) + 1.0d0
    t_4 = 3.0d0 * (((t_1 - (2.0d0 * x2)) - x1) / t_3)
    if (x1 <= (-5.6d+102)) then
        tmp = x1 + (3.0d0 * ((x1 * x1) * (3.0d0 - (x2 * (-2.0d0)))))
    else if (x1 <= (-2.05d+17)) then
        tmp = x1 + (t_4 + (x1 + (t_0 + (t_2 + (t_3 * (((x1 * x1) * (((((t_1 + (2.0d0 * x2)) - x1) / t_3) * 4.0d0) - 6.0d0)) + (x1 + x1)))))))
    else if (x1 <= 12800.0d0) then
        tmp = x1 + (t_4 + (x1 + (4.0d0 * (x2 * (x1 * ((2.0d0 * x2) - 3.0d0))))))
    else
        tmp = x1 + ((3.0d0 * ((x2 * (-2.0d0)) - x1)) + (x1 + (t_0 + (t_2 + (t_3 * ((x1 * x1) * 6.0d0))))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * x1);
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = 3.0 * t_1;
	double t_3 = (x1 * x1) + 1.0;
	double t_4 = 3.0 * (((t_1 - (2.0 * x2)) - x1) / t_3);
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = x1 + (3.0 * ((x1 * x1) * (3.0 - (x2 * -2.0))));
	} else if (x1 <= -2.05e+17) {
		tmp = x1 + (t_4 + (x1 + (t_0 + (t_2 + (t_3 * (((x1 * x1) * (((((t_1 + (2.0 * x2)) - x1) / t_3) * 4.0) - 6.0)) + (x1 + x1)))))));
	} else if (x1 <= 12800.0) {
		tmp = x1 + (t_4 + (x1 + (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0))))));
	} else {
		tmp = x1 + ((3.0 * ((x2 * -2.0) - x1)) + (x1 + (t_0 + (t_2 + (t_3 * ((x1 * x1) * 6.0))))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * x1)
	t_1 = x1 * (x1 * 3.0)
	t_2 = 3.0 * t_1
	t_3 = (x1 * x1) + 1.0
	t_4 = 3.0 * (((t_1 - (2.0 * x2)) - x1) / t_3)
	tmp = 0
	if x1 <= -5.6e+102:
		tmp = x1 + (3.0 * ((x1 * x1) * (3.0 - (x2 * -2.0))))
	elif x1 <= -2.05e+17:
		tmp = x1 + (t_4 + (x1 + (t_0 + (t_2 + (t_3 * (((x1 * x1) * (((((t_1 + (2.0 * x2)) - x1) / t_3) * 4.0) - 6.0)) + (x1 + x1)))))))
	elif x1 <= 12800.0:
		tmp = x1 + (t_4 + (x1 + (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0))))))
	else:
		tmp = x1 + ((3.0 * ((x2 * -2.0) - x1)) + (x1 + (t_0 + (t_2 + (t_3 * ((x1 * x1) * 6.0))))))
	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(3.0 * t_1)
	t_3 = Float64(Float64(x1 * x1) + 1.0)
	t_4 = Float64(3.0 * Float64(Float64(Float64(t_1 - Float64(2.0 * x2)) - x1) / t_3))
	tmp = 0.0
	if (x1 <= -5.6e+102)
		tmp = Float64(x1 + Float64(3.0 * Float64(Float64(x1 * x1) * Float64(3.0 - Float64(x2 * -2.0)))));
	elseif (x1 <= -2.05e+17)
		tmp = Float64(x1 + Float64(t_4 + Float64(x1 + Float64(t_0 + Float64(t_2 + Float64(t_3 * Float64(Float64(Float64(x1 * x1) * Float64(Float64(Float64(Float64(Float64(t_1 + Float64(2.0 * x2)) - x1) / t_3) * 4.0) - 6.0)) + Float64(x1 + x1))))))));
	elseif (x1 <= 12800.0)
		tmp = Float64(x1 + Float64(t_4 + Float64(x1 + Float64(4.0 * Float64(x2 * Float64(x1 * Float64(Float64(2.0 * x2) - 3.0)))))));
	else
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(x2 * -2.0) - x1)) + Float64(x1 + Float64(t_0 + Float64(t_2 + Float64(t_3 * Float64(Float64(x1 * x1) * 6.0)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * x1);
	t_1 = x1 * (x1 * 3.0);
	t_2 = 3.0 * t_1;
	t_3 = (x1 * x1) + 1.0;
	t_4 = 3.0 * (((t_1 - (2.0 * x2)) - x1) / t_3);
	tmp = 0.0;
	if (x1 <= -5.6e+102)
		tmp = x1 + (3.0 * ((x1 * x1) * (3.0 - (x2 * -2.0))));
	elseif (x1 <= -2.05e+17)
		tmp = x1 + (t_4 + (x1 + (t_0 + (t_2 + (t_3 * (((x1 * x1) * (((((t_1 + (2.0 * x2)) - x1) / t_3) * 4.0) - 6.0)) + (x1 + x1)))))));
	elseif (x1 <= 12800.0)
		tmp = x1 + (t_4 + (x1 + (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0))))));
	else
		tmp = x1 + ((3.0 * ((x2 * -2.0) - x1)) + (x1 + (t_0 + (t_2 + (t_3 * ((x1 * x1) * 6.0))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(3.0 * t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$4 = N[(3.0 * N[(N[(N[(t$95$1 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$3), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -5.6e+102], N[(x1 + N[(3.0 * N[(N[(x1 * x1), $MachinePrecision] * N[(3.0 - N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -2.05e+17], N[(x1 + N[(t$95$4 + N[(x1 + N[(t$95$0 + N[(t$95$2 + N[(t$95$3 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(N[(N[(N[(N[(t$95$1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$3), $MachinePrecision] * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] + N[(x1 + x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 12800.0], N[(x1 + N[(t$95$4 + N[(x1 + N[(4.0 * N[(x2 * N[(x1 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(t$95$0 + N[(t$95$2 + N[(t$95$3 * N[(N[(x1 * x1), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -5.60000000000000037e102

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around 0 0.0%

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

   3. Taylor expanded in x1 around 0 44.8%

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

      1. +-commutative 44.8%

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

      2. neg-mul-1 44.8%

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

      3. unsub-neg 44.8%

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

      4. +-commutative 44.8%

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

      5. *-commutative 44.8%

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

      6. fma-def 44.8%

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

      7. unpow2 44.8%

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

      8. cancel-sign-sub-inv 44.8%

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

      9. metadata-eval 44.8%

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

      10. *-commutative 44.8%

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

   5. Simplified 44.8%

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

   6. Taylor expanded in x1 around inf 44.8%

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

   7. Taylor expanded in x1 around inf 71.7%

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

      1. unpow2 71.7%

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

      2. metadata-eval 71.7%

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

      3. cancel-sign-sub-inv 71.7%

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

      4. *-commutative 71.7%

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

   9. Simplified 71.7%

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

   if -5.60000000000000037e102 < x1 < -2.05e17

   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. Taylor expanded in x1 around 0 78.2%

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

   3. Taylor expanded in x1 around inf 92.2%

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

      1. rem-log-exp 21.5%

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

      2. *-commutative 21.5%

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

      3. exp-lft-sqr 21.5%

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

      4. log-prod 21.5%

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

      5. rem-log-exp 21.5%

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

      6. rem-log-exp 92.2%

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

   5. Simplified 92.2%

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

   6. Taylor expanded in x1 around inf 92.2%

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

   if -2.05e17 < x1 < 12800

   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. Taylor expanded in x1 around 0 96.6%

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

   if 12800 < x1

   1. Initial program 52.4%

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

   2. Taylor expanded in x1 around inf 52.1%

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

   3. Taylor expanded in x1 around 0 52.4%

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

      1. +-commutative 52.4%

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

      2. neg-mul-1 52.4%

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

      3. unsub-neg 52.4%

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

      4. *-commutative 52.4%

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

   5. Simplified 52.4%

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

   6. Taylor expanded in x1 around inf 87.9%

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

      1. *-commutative 87.9%

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

      2. unpow2 87.9%

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

   8. Simplified 87.9%

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

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 + 3 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(3 - x2 \cdot -2\right)\right)\\ \mathbf{elif}\;x1 \leq -2.05 \cdot 10^{+17}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right) + \left(x1 + x1\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 12800:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2 - x1\right) + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot 6\right)\right)\right)\right)\right)\\ \end{array} \]

Alternative 8: 86.2% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 + 3 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(3 - x2 \cdot -2\right)\right)\\ \mathbf{elif}\;x1 \leq -8 \cdot 10^{+34} \lor \neg \left(x1 \leq 11000\right):\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2 - x1\right) + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot t_1 + t_0 \cdot \left(x1 \cdot \left(x1 \cdot 6\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t_1 - 2 \cdot x2\right) - x1}{t_0} + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ (* x1 x1) 1.0)) (t_1 (* x1 (* x1 3.0))))
   (if (<= x1 -5.6e+102)
     (+ x1 (* 3.0 (* (* x1 x1) (- 3.0 (* x2 -2.0)))))
     (if (or (<= x1 -8e+34) (not (<= x1 11000.0)))
       (+
        x1
        (+
         (* 3.0 (- (* x2 -2.0) x1))
         (+
          x1
          (+ (* x1 (* x1 x1)) (+ (* 3.0 t_1) (* t_0 (* x1 (* x1 6.0))))))))
       (+
        x1
        (+
         (* 3.0 (/ (- (- t_1 (* 2.0 x2)) x1) t_0))
         (+ x1 (* 4.0 (* x2 (* x1 (- (* 2.0 x2) 3.0)))))))))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = x1 * (x1 * 3.0);
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = x1 + (3.0 * ((x1 * x1) * (3.0 - (x2 * -2.0))));
	} else if ((x1 <= -8e+34) || !(x1 <= 11000.0)) {
		tmp = x1 + ((3.0 * ((x2 * -2.0) - x1)) + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_1) + (t_0 * (x1 * (x1 * 6.0)))))));
	} else {
		tmp = x1 + ((3.0 * (((t_1 - (2.0 * x2)) - x1) / t_0)) + (x1 + (4.0 * (x2 * (x1 * ((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) :: tmp
    t_0 = (x1 * x1) + 1.0d0
    t_1 = x1 * (x1 * 3.0d0)
    if (x1 <= (-5.6d+102)) then
        tmp = x1 + (3.0d0 * ((x1 * x1) * (3.0d0 - (x2 * (-2.0d0)))))
    else if ((x1 <= (-8d+34)) .or. (.not. (x1 <= 11000.0d0))) then
        tmp = x1 + ((3.0d0 * ((x2 * (-2.0d0)) - x1)) + (x1 + ((x1 * (x1 * x1)) + ((3.0d0 * t_1) + (t_0 * (x1 * (x1 * 6.0d0)))))))
    else
        tmp = x1 + ((3.0d0 * (((t_1 - (2.0d0 * x2)) - x1) / t_0)) + (x1 + (4.0d0 * (x2 * (x1 * ((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) + 1.0;
	double t_1 = x1 * (x1 * 3.0);
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = x1 + (3.0 * ((x1 * x1) * (3.0 - (x2 * -2.0))));
	} else if ((x1 <= -8e+34) || !(x1 <= 11000.0)) {
		tmp = x1 + ((3.0 * ((x2 * -2.0) - x1)) + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_1) + (t_0 * (x1 * (x1 * 6.0)))))));
	} else {
		tmp = x1 + ((3.0 * (((t_1 - (2.0 * x2)) - x1) / t_0)) + (x1 + (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0))))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x1 * x1) + 1.0
	t_1 = x1 * (x1 * 3.0)
	tmp = 0
	if x1 <= -5.6e+102:
		tmp = x1 + (3.0 * ((x1 * x1) * (3.0 - (x2 * -2.0))))
	elif (x1 <= -8e+34) or not (x1 <= 11000.0):
		tmp = x1 + ((3.0 * ((x2 * -2.0) - x1)) + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_1) + (t_0 * (x1 * (x1 * 6.0)))))))
	else:
		tmp = x1 + ((3.0 * (((t_1 - (2.0 * x2)) - x1) / t_0)) + (x1 + (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0))))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * x1) + 1.0)
	t_1 = Float64(x1 * Float64(x1 * 3.0))
	tmp = 0.0
	if (x1 <= -5.6e+102)
		tmp = Float64(x1 + Float64(3.0 * Float64(Float64(x1 * x1) * Float64(3.0 - Float64(x2 * -2.0)))));
	elseif ((x1 <= -8e+34) || !(x1 <= 11000.0))
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(x2 * -2.0) - x1)) + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(3.0 * t_1) + Float64(t_0 * Float64(x1 * Float64(x1 * 6.0))))))));
	else
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_1 - Float64(2.0 * x2)) - x1) / t_0)) + Float64(x1 + Float64(4.0 * Float64(x2 * Float64(x1 * Float64(Float64(2.0 * x2) - 3.0)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x1 * x1) + 1.0;
	t_1 = x1 * (x1 * 3.0);
	tmp = 0.0;
	if (x1 <= -5.6e+102)
		tmp = x1 + (3.0 * ((x1 * x1) * (3.0 - (x2 * -2.0))));
	elseif ((x1 <= -8e+34) || ~((x1 <= 11000.0)))
		tmp = x1 + ((3.0 * ((x2 * -2.0) - x1)) + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_1) + (t_0 * (x1 * (x1 * 6.0)))))));
	else
		tmp = x1 + ((3.0 * (((t_1 - (2.0 * x2)) - x1) / t_0)) + (x1 + (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -5.6e+102], N[(x1 + N[(3.0 * N[(N[(x1 * x1), $MachinePrecision] * N[(3.0 - N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x1, -8e+34], N[Not[LessEqual[x1, 11000.0]], $MachinePrecision]], N[(x1 + N[(N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(3.0 * t$95$1), $MachinePrecision] + N[(t$95$0 * N[(x1 * N[(x1 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$1 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(4.0 * N[(x2 * N[(x1 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -5.60000000000000037e102

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around 0 0.0%

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

   3. Taylor expanded in x1 around 0 44.8%

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

      1. +-commutative 44.8%

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

      2. neg-mul-1 44.8%

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

      3. unsub-neg 44.8%

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

      4. +-commutative 44.8%

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

      5. *-commutative 44.8%

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

      6. fma-def 44.8%

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

      7. unpow2 44.8%

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

      8. cancel-sign-sub-inv 44.8%

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

      9. metadata-eval 44.8%

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

      10. *-commutative 44.8%

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

   5. Simplified 44.8%

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

   6. Taylor expanded in x1 around inf 44.8%

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

   7. Taylor expanded in x1 around inf 71.7%

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

      1. unpow2 71.7%

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

      2. metadata-eval 71.7%

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

      3. cancel-sign-sub-inv 71.7%

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

      4. *-commutative 71.7%

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

   9. Simplified 71.7%

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

   if -5.60000000000000037e102 < x1 < -7.99999999999999956e34 or 11000 < x1

   1. Initial program 60.3%

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

   2. Taylor expanded in x1 around inf 60.1%

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

   3. Taylor expanded in x1 around 0 60.3%

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

      1. +-commutative 60.3%

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

      2. neg-mul-1 60.3%

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

      3. unsub-neg 60.3%

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

      4. *-commutative 60.3%

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

   5. Simplified 60.3%

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

   6. Taylor expanded in x1 around inf 87.1%

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

      1. *-commutative 87.1%

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

      2. unpow2 87.1%

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

      3. associate-*l* 87.2%

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

   8. Simplified 87.2%

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

   if -7.99999999999999956e34 < x1 < 11000

   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. Taylor expanded in x1 around 0 95.9%

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

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 + 3 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(3 - x2 \cdot -2\right)\right)\\ \mathbf{elif}\;x1 \leq -8 \cdot 10^{+34} \lor \neg \left(x1 \leq 11000\right):\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2 - x1\right) + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(x1 \cdot \left(x1 \cdot 6\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right)\right)\\ \end{array} \]

Alternative 9: 86.2% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 3 \cdot \left(x2 \cdot -2 - x1\right)\\ t_1 := x1 \cdot \left(x1 \cdot x1\right)\\ t_2 := x1 \cdot \left(x1 \cdot 3\right)\\ t_3 := 3 \cdot t_2\\ t_4 := x1 \cdot x1 + 1\\ \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 + 3 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(3 - x2 \cdot -2\right)\right)\\ \mathbf{elif}\;x1 \leq -3.5 \cdot 10^{+34}:\\ \;\;\;\;x1 + \left(t_0 + \left(x1 + \left(t_1 + \left(t_3 + t_4 \cdot \left(x1 \cdot \left(x1 \cdot 6\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 2000:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t_2 - 2 \cdot x2\right) - x1}{t_4} + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(t_0 + \left(x1 + \left(t_1 + \left(t_3 + t_4 \cdot \left(\left(x1 \cdot x1\right) \cdot 6\right)\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* 3.0 (- (* x2 -2.0) x1)))
        (t_1 (* x1 (* x1 x1)))
        (t_2 (* x1 (* x1 3.0)))
        (t_3 (* 3.0 t_2))
        (t_4 (+ (* x1 x1) 1.0)))
   (if (<= x1 -5.6e+102)
     (+ x1 (* 3.0 (* (* x1 x1) (- 3.0 (* x2 -2.0)))))
     (if (<= x1 -3.5e+34)
       (+ x1 (+ t_0 (+ x1 (+ t_1 (+ t_3 (* t_4 (* x1 (* x1 6.0))))))))
       (if (<= x1 2000.0)
         (+
          x1
          (+
           (* 3.0 (/ (- (- t_2 (* 2.0 x2)) x1) t_4))
           (+ x1 (* 4.0 (* x2 (* x1 (- (* 2.0 x2) 3.0)))))))
         (+ x1 (+ t_0 (+ x1 (+ t_1 (+ t_3 (* t_4 (* (* x1 x1) 6.0))))))))))))

C

double code(double x1, double x2) {
	double t_0 = 3.0 * ((x2 * -2.0) - x1);
	double t_1 = x1 * (x1 * x1);
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = 3.0 * t_2;
	double t_4 = (x1 * x1) + 1.0;
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = x1 + (3.0 * ((x1 * x1) * (3.0 - (x2 * -2.0))));
	} else if (x1 <= -3.5e+34) {
		tmp = x1 + (t_0 + (x1 + (t_1 + (t_3 + (t_4 * (x1 * (x1 * 6.0)))))));
	} else if (x1 <= 2000.0) {
		tmp = x1 + ((3.0 * (((t_2 - (2.0 * x2)) - x1) / t_4)) + (x1 + (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0))))));
	} else {
		tmp = x1 + (t_0 + (x1 + (t_1 + (t_3 + (t_4 * ((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) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_0 = 3.0d0 * ((x2 * (-2.0d0)) - x1)
    t_1 = x1 * (x1 * x1)
    t_2 = x1 * (x1 * 3.0d0)
    t_3 = 3.0d0 * t_2
    t_4 = (x1 * x1) + 1.0d0
    if (x1 <= (-5.6d+102)) then
        tmp = x1 + (3.0d0 * ((x1 * x1) * (3.0d0 - (x2 * (-2.0d0)))))
    else if (x1 <= (-3.5d+34)) then
        tmp = x1 + (t_0 + (x1 + (t_1 + (t_3 + (t_4 * (x1 * (x1 * 6.0d0)))))))
    else if (x1 <= 2000.0d0) then
        tmp = x1 + ((3.0d0 * (((t_2 - (2.0d0 * x2)) - x1) / t_4)) + (x1 + (4.0d0 * (x2 * (x1 * ((2.0d0 * x2) - 3.0d0))))))
    else
        tmp = x1 + (t_0 + (x1 + (t_1 + (t_3 + (t_4 * ((x1 * x1) * 6.0d0))))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = 3.0 * ((x2 * -2.0) - x1);
	double t_1 = x1 * (x1 * x1);
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = 3.0 * t_2;
	double t_4 = (x1 * x1) + 1.0;
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = x1 + (3.0 * ((x1 * x1) * (3.0 - (x2 * -2.0))));
	} else if (x1 <= -3.5e+34) {
		tmp = x1 + (t_0 + (x1 + (t_1 + (t_3 + (t_4 * (x1 * (x1 * 6.0)))))));
	} else if (x1 <= 2000.0) {
		tmp = x1 + ((3.0 * (((t_2 - (2.0 * x2)) - x1) / t_4)) + (x1 + (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0))))));
	} else {
		tmp = x1 + (t_0 + (x1 + (t_1 + (t_3 + (t_4 * ((x1 * x1) * 6.0))))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = 3.0 * ((x2 * -2.0) - x1)
	t_1 = x1 * (x1 * x1)
	t_2 = x1 * (x1 * 3.0)
	t_3 = 3.0 * t_2
	t_4 = (x1 * x1) + 1.0
	tmp = 0
	if x1 <= -5.6e+102:
		tmp = x1 + (3.0 * ((x1 * x1) * (3.0 - (x2 * -2.0))))
	elif x1 <= -3.5e+34:
		tmp = x1 + (t_0 + (x1 + (t_1 + (t_3 + (t_4 * (x1 * (x1 * 6.0)))))))
	elif x1 <= 2000.0:
		tmp = x1 + ((3.0 * (((t_2 - (2.0 * x2)) - x1) / t_4)) + (x1 + (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0))))))
	else:
		tmp = x1 + (t_0 + (x1 + (t_1 + (t_3 + (t_4 * ((x1 * x1) * 6.0))))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(3.0 * Float64(Float64(x2 * -2.0) - x1))
	t_1 = Float64(x1 * Float64(x1 * x1))
	t_2 = Float64(x1 * Float64(x1 * 3.0))
	t_3 = Float64(3.0 * t_2)
	t_4 = Float64(Float64(x1 * x1) + 1.0)
	tmp = 0.0
	if (x1 <= -5.6e+102)
		tmp = Float64(x1 + Float64(3.0 * Float64(Float64(x1 * x1) * Float64(3.0 - Float64(x2 * -2.0)))));
	elseif (x1 <= -3.5e+34)
		tmp = Float64(x1 + Float64(t_0 + Float64(x1 + Float64(t_1 + Float64(t_3 + Float64(t_4 * Float64(x1 * Float64(x1 * 6.0))))))));
	elseif (x1 <= 2000.0)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_2 - Float64(2.0 * x2)) - x1) / t_4)) + Float64(x1 + Float64(4.0 * Float64(x2 * Float64(x1 * Float64(Float64(2.0 * x2) - 3.0)))))));
	else
		tmp = Float64(x1 + Float64(t_0 + Float64(x1 + Float64(t_1 + Float64(t_3 + Float64(t_4 * Float64(Float64(x1 * x1) * 6.0)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = 3.0 * ((x2 * -2.0) - x1);
	t_1 = x1 * (x1 * x1);
	t_2 = x1 * (x1 * 3.0);
	t_3 = 3.0 * t_2;
	t_4 = (x1 * x1) + 1.0;
	tmp = 0.0;
	if (x1 <= -5.6e+102)
		tmp = x1 + (3.0 * ((x1 * x1) * (3.0 - (x2 * -2.0))));
	elseif (x1 <= -3.5e+34)
		tmp = x1 + (t_0 + (x1 + (t_1 + (t_3 + (t_4 * (x1 * (x1 * 6.0)))))));
	elseif (x1 <= 2000.0)
		tmp = x1 + ((3.0 * (((t_2 - (2.0 * x2)) - x1) / t_4)) + (x1 + (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0))))));
	else
		tmp = x1 + (t_0 + (x1 + (t_1 + (t_3 + (t_4 * ((x1 * x1) * 6.0))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - x1), $MachinePrecision]), $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 * t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, If[LessEqual[x1, -5.6e+102], N[(x1 + N[(3.0 * N[(N[(x1 * x1), $MachinePrecision] * N[(3.0 - N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -3.5e+34], N[(x1 + N[(t$95$0 + N[(x1 + N[(t$95$1 + N[(t$95$3 + N[(t$95$4 * N[(x1 * N[(x1 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 2000.0], N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$2 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$4), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(4.0 * N[(x2 * N[(x1 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(t$95$0 + N[(x1 + N[(t$95$1 + N[(t$95$3 + N[(t$95$4 * N[(N[(x1 * x1), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -5.60000000000000037e102

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around 0 0.0%

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

   3. Taylor expanded in x1 around 0 44.8%

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

      1. +-commutative 44.8%

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

      2. neg-mul-1 44.8%

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

      3. unsub-neg 44.8%

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

      4. +-commutative 44.8%

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

      5. *-commutative 44.8%

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

      6. fma-def 44.8%

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

      7. unpow2 44.8%

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

      8. cancel-sign-sub-inv 44.8%

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

      9. metadata-eval 44.8%

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

      10. *-commutative 44.8%

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

   5. Simplified 44.8%

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

   6. Taylor expanded in x1 around inf 44.8%

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

   7. Taylor expanded in x1 around inf 71.7%

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

      1. unpow2 71.7%

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

      2. metadata-eval 71.7%

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

      3. cancel-sign-sub-inv 71.7%

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

      4. *-commutative 71.7%

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

   9. Simplified 71.7%

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

   if -5.60000000000000037e102 < x1 < -3.49999999999999998e34

   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. Taylor expanded in x1 around inf 99.3%

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

   3. Taylor expanded in x1 around 0 99.3%

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

      1. +-commutative 99.3%

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

      2. neg-mul-1 99.3%

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

      3. unsub-neg 99.3%

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

      4. *-commutative 99.3%

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

   5. Simplified 99.3%

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

   6. Taylor expanded in x1 around inf 83.2%

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

      1. *-commutative 83.2%

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

      2. unpow2 83.2%

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

      3. associate-*l* 83.5%

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

   8. Simplified 83.5%

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

   if -3.49999999999999998e34 < x1 < 2e3

   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. Taylor expanded in x1 around 0 95.9%

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

   if 2e3 < x1

   1. Initial program 52.4%

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

   2. Taylor expanded in x1 around inf 52.1%

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

   3. Taylor expanded in x1 around 0 52.4%

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

      1. +-commutative 52.4%

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

      2. neg-mul-1 52.4%

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

      3. unsub-neg 52.4%

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

      4. *-commutative 52.4%

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

   5. Simplified 52.4%

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

   6. Taylor expanded in x1 around inf 87.9%

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

      1. *-commutative 87.9%

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

      2. unpow2 87.9%

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

   8. Simplified 87.9%

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

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 + 3 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(3 - x2 \cdot -2\right)\right)\\ \mathbf{elif}\;x1 \leq -3.5 \cdot 10^{+34}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2 - x1\right) + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(x1 \cdot \left(x1 \cdot 6\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 2000:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2 - x1\right) + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot 6\right)\right)\right)\right)\right)\\ \end{array} \]

Alternative 10: 80.1% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ \mathbf{if}\;x1 \leq -4.8 \cdot 10^{+64}:\\ \;\;\;\;x1 + 3 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(3 - x2 \cdot -2\right)\right)\\ \mathbf{elif}\;x1 \leq 1.8:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + t_0\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(t_0 + 3 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x1 + 3\right) - x1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ x1 (* 4.0 (* x2 (* x1 (- (* 2.0 x2) 3.0)))))))
   (if (<= x1 -4.8e+64)
     (+ x1 (* 3.0 (* (* x1 x1) (- 3.0 (* x2 -2.0)))))
     (if (<= x1 1.8)
       (+
        x1
        (+
         (* 3.0 (/ (- (- (* x1 (* x1 3.0)) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0)))
         t_0))
       (+ x1 (+ t_0 (* 3.0 (- (* (* x1 x1) (+ x1 3.0)) x1))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 + (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0))));
	double tmp;
	if (x1 <= -4.8e+64) {
		tmp = x1 + (3.0 * ((x1 * x1) * (3.0 - (x2 * -2.0))));
	} else if (x1 <= 1.8) {
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / ((x1 * x1) + 1.0))) + t_0);
	} else {
		tmp = x1 + (t_0 + (3.0 * (((x1 * x1) * (x1 + 3.0)) - x1)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x1 + (4.0d0 * (x2 * (x1 * ((2.0d0 * x2) - 3.0d0))))
    if (x1 <= (-4.8d+64)) then
        tmp = x1 + (3.0d0 * ((x1 * x1) * (3.0d0 - (x2 * (-2.0d0)))))
    else if (x1 <= 1.8d0) then
        tmp = x1 + ((3.0d0 * ((((x1 * (x1 * 3.0d0)) - (2.0d0 * x2)) - x1) / ((x1 * x1) + 1.0d0))) + t_0)
    else
        tmp = x1 + (t_0 + (3.0d0 * (((x1 * x1) * (x1 + 3.0d0)) - x1)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 + (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0))));
	double tmp;
	if (x1 <= -4.8e+64) {
		tmp = x1 + (3.0 * ((x1 * x1) * (3.0 - (x2 * -2.0))));
	} else if (x1 <= 1.8) {
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / ((x1 * x1) + 1.0))) + t_0);
	} else {
		tmp = x1 + (t_0 + (3.0 * (((x1 * x1) * (x1 + 3.0)) - x1)));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 + (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0))))
	tmp = 0
	if x1 <= -4.8e+64:
		tmp = x1 + (3.0 * ((x1 * x1) * (3.0 - (x2 * -2.0))))
	elif x1 <= 1.8:
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / ((x1 * x1) + 1.0))) + t_0)
	else:
		tmp = x1 + (t_0 + (3.0 * (((x1 * x1) * (x1 + 3.0)) - x1)))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 + Float64(4.0 * Float64(x2 * Float64(x1 * Float64(Float64(2.0 * x2) - 3.0)))))
	tmp = 0.0
	if (x1 <= -4.8e+64)
		tmp = Float64(x1 + Float64(3.0 * Float64(Float64(x1 * x1) * Float64(3.0 - Float64(x2 * -2.0)))));
	elseif (x1 <= 1.8)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(Float64(x1 * Float64(x1 * 3.0)) - Float64(2.0 * x2)) - x1) / Float64(Float64(x1 * x1) + 1.0))) + t_0));
	else
		tmp = Float64(x1 + Float64(t_0 + Float64(3.0 * Float64(Float64(Float64(x1 * x1) * Float64(x1 + 3.0)) - x1))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 + (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0))));
	tmp = 0.0;
	if (x1 <= -4.8e+64)
		tmp = x1 + (3.0 * ((x1 * x1) * (3.0 - (x2 * -2.0))));
	elseif (x1 <= 1.8)
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / ((x1 * x1) + 1.0))) + t_0);
	else
		tmp = x1 + (t_0 + (3.0 * (((x1 * x1) * (x1 + 3.0)) - x1)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 + N[(4.0 * N[(x2 * N[(x1 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -4.8e+64], N[(x1 + N[(3.0 * N[(N[(x1 * x1), $MachinePrecision] * N[(3.0 - N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.8], N[(x1 + N[(N[(3.0 * N[(N[(N[(N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision] - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$0), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(t$95$0 + N[(3.0 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(x1 + 3.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -4.79999999999999999e64

   1. Initial program 11.8%

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

   2. Taylor expanded in x1 around 0 0.1%

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

   3. Taylor expanded in x1 around 0 39.7%

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

      1. +-commutative 39.7%

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

      2. neg-mul-1 39.7%

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

      3. unsub-neg 39.7%

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

      4. +-commutative 39.7%

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

      5. *-commutative 39.7%

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

      6. fma-def 39.7%

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

      7. unpow2 39.7%

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

      8. cancel-sign-sub-inv 39.7%

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

      9. metadata-eval 39.7%

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

      10. *-commutative 39.7%

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

   5. Simplified 39.7%

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

   6. Taylor expanded in x1 around inf 39.7%

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

   7. Taylor expanded in x1 around inf 65.2%

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

      1. unpow2 65.2%

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

      2. metadata-eval 65.2%

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

      3. cancel-sign-sub-inv 65.2%

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

      4. *-commutative 65.2%

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

   9. Simplified 65.2%

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

   if -4.79999999999999999e64 < x1 < 1.80000000000000004

   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. Taylor expanded in x1 around 0 94.5%

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

   if 1.80000000000000004 < x1

   1. Initial program 53.1%

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

   2. Taylor expanded in x1 around 0 18.8%

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

   3. Taylor expanded in x1 around 0 55.7%

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

      1. +-commutative 55.7%

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

      2. neg-mul-1 55.7%

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

      3. unsub-neg 55.7%

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

      4. *-commutative 55.7%

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

      5. fma-def 55.7%

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

      6. +-commutative 55.7%

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

      7. cube-mult 55.7%

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

      8. unpow2 55.7%

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

      9. distribute-rgt-out 62.4%

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

      10. unpow2 62.4%

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

      11. cancel-sign-sub-inv 62.4%

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

      12. metadata-eval 62.4%

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

   5. Simplified 62.4%

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

   6. Taylor expanded in x2 around 0 74.1%

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

      1. +-commutative 74.1%

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

      2. unpow2 74.1%

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

   8. Simplified 74.1%

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

4. Final simplification 82.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4.8 \cdot 10^{+64}:\\ \;\;\;\;x1 + 3 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(3 - x2 \cdot -2\right)\right)\\ \mathbf{elif}\;x1 \leq 1.8:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right) + 3 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x1 + 3\right) - x1\right)\right)\\ \end{array} \]

Alternative 11: 79.9% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ \mathbf{if}\;x1 \leq -8.1 \cdot 10^{+62}:\\ \;\;\;\;x1 + 3 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(3 - x2 \cdot -2\right)\right)\\ \mathbf{elif}\;x1 \leq 1.36 \cdot 10^{-34}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2 - x1\right) + t_0\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(t_0 + 3 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x1 + 3\right) - x1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ x1 (* 4.0 (* x2 (* x1 (- (* 2.0 x2) 3.0)))))))
   (if (<= x1 -8.1e+62)
     (+ x1 (* 3.0 (* (* x1 x1) (- 3.0 (* x2 -2.0)))))
     (if (<= x1 1.36e-34)
       (+ x1 (+ (* 3.0 (- (* x2 -2.0) x1)) t_0))
       (+ x1 (+ t_0 (* 3.0 (- (* (* x1 x1) (+ x1 3.0)) x1))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 + (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0))));
	double tmp;
	if (x1 <= -8.1e+62) {
		tmp = x1 + (3.0 * ((x1 * x1) * (3.0 - (x2 * -2.0))));
	} else if (x1 <= 1.36e-34) {
		tmp = x1 + ((3.0 * ((x2 * -2.0) - x1)) + t_0);
	} else {
		tmp = x1 + (t_0 + (3.0 * (((x1 * x1) * (x1 + 3.0)) - x1)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x1 + (4.0d0 * (x2 * (x1 * ((2.0d0 * x2) - 3.0d0))))
    if (x1 <= (-8.1d+62)) then
        tmp = x1 + (3.0d0 * ((x1 * x1) * (3.0d0 - (x2 * (-2.0d0)))))
    else if (x1 <= 1.36d-34) then
        tmp = x1 + ((3.0d0 * ((x2 * (-2.0d0)) - x1)) + t_0)
    else
        tmp = x1 + (t_0 + (3.0d0 * (((x1 * x1) * (x1 + 3.0d0)) - x1)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 + (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0))));
	double tmp;
	if (x1 <= -8.1e+62) {
		tmp = x1 + (3.0 * ((x1 * x1) * (3.0 - (x2 * -2.0))));
	} else if (x1 <= 1.36e-34) {
		tmp = x1 + ((3.0 * ((x2 * -2.0) - x1)) + t_0);
	} else {
		tmp = x1 + (t_0 + (3.0 * (((x1 * x1) * (x1 + 3.0)) - x1)));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 + (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0))))
	tmp = 0
	if x1 <= -8.1e+62:
		tmp = x1 + (3.0 * ((x1 * x1) * (3.0 - (x2 * -2.0))))
	elif x1 <= 1.36e-34:
		tmp = x1 + ((3.0 * ((x2 * -2.0) - x1)) + t_0)
	else:
		tmp = x1 + (t_0 + (3.0 * (((x1 * x1) * (x1 + 3.0)) - x1)))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 + Float64(4.0 * Float64(x2 * Float64(x1 * Float64(Float64(2.0 * x2) - 3.0)))))
	tmp = 0.0
	if (x1 <= -8.1e+62)
		tmp = Float64(x1 + Float64(3.0 * Float64(Float64(x1 * x1) * Float64(3.0 - Float64(x2 * -2.0)))));
	elseif (x1 <= 1.36e-34)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(x2 * -2.0) - x1)) + t_0));
	else
		tmp = Float64(x1 + Float64(t_0 + Float64(3.0 * Float64(Float64(Float64(x1 * x1) * Float64(x1 + 3.0)) - x1))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 + (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0))));
	tmp = 0.0;
	if (x1 <= -8.1e+62)
		tmp = x1 + (3.0 * ((x1 * x1) * (3.0 - (x2 * -2.0))));
	elseif (x1 <= 1.36e-34)
		tmp = x1 + ((3.0 * ((x2 * -2.0) - x1)) + t_0);
	else
		tmp = x1 + (t_0 + (3.0 * (((x1 * x1) * (x1 + 3.0)) - x1)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 + N[(4.0 * N[(x2 * N[(x1 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -8.1e+62], N[(x1 + N[(3.0 * N[(N[(x1 * x1), $MachinePrecision] * N[(3.0 - N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.36e-34], N[(x1 + N[(N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision] + t$95$0), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(t$95$0 + N[(3.0 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(x1 + 3.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -8.09999999999999998e62

   1. Initial program 11.8%

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

   2. Taylor expanded in x1 around 0 0.1%

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

   3. Taylor expanded in x1 around 0 39.7%

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

      1. +-commutative 39.7%

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

      2. neg-mul-1 39.7%

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

      3. unsub-neg 39.7%

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

      4. +-commutative 39.7%

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

      5. *-commutative 39.7%

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

      6. fma-def 39.7%

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

      7. unpow2 39.7%

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

      8. cancel-sign-sub-inv 39.7%

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

      9. metadata-eval 39.7%

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

      10. *-commutative 39.7%

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

   5. Simplified 39.7%

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

   6. Taylor expanded in x1 around inf 39.7%

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

   7. Taylor expanded in x1 around inf 65.2%

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

      1. unpow2 65.2%

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

      2. metadata-eval 65.2%

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

      3. cancel-sign-sub-inv 65.2%

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

      4. *-commutative 65.2%

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

   9. Simplified 65.2%

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

   if -8.09999999999999998e62 < x1 < 1.3600000000000001e-34

   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. Taylor expanded in x1 around 0 94.7%

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

   3. Taylor expanded in x1 around 0 94.7%

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

      1. +-commutative 99.4%

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

      2. neg-mul-1 99.4%

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

      3. unsub-neg 99.4%

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

      4. *-commutative 99.4%

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

   5. Simplified 94.7%

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

   if 1.3600000000000001e-34 < x1

   1. Initial program 59.7%

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

   2. Taylor expanded in x1 around 0 29.1%

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

   3. Taylor expanded in x1 around 0 60.7%

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

      1. +-commutative 60.7%

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

      2. neg-mul-1 60.7%

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

      3. unsub-neg 60.7%

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

      4. *-commutative 60.7%

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

      5. fma-def 60.7%

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

      6. +-commutative 60.7%

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

      7. cube-mult 60.7%

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

      8. unpow2 60.7%

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

      9. distribute-rgt-out 66.5%

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

      10. unpow2 66.5%

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

      11. cancel-sign-sub-inv 66.5%

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

      12. metadata-eval 66.5%

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

   5. Simplified 66.5%

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

   6. Taylor expanded in x2 around 0 76.5%

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

      1. +-commutative 76.5%

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

      2. unpow2 76.5%

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

   8. Simplified 76.5%

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

4. Final simplification 82.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -8.1 \cdot 10^{+62}:\\ \;\;\;\;x1 + 3 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(3 - x2 \cdot -2\right)\right)\\ \mathbf{elif}\;x1 \leq 1.36 \cdot 10^{-34}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2 - x1\right) + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right) + 3 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x1 + 3\right) - x1\right)\right)\\ \end{array} \]

Alternative 12: 75.4% accurate, 4.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 + \left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right) + x2 \cdot -6\right)\\ \mathbf{if}\;x1 \leq -2.15 \cdot 10^{+63}:\\ \;\;\;\;x1 + 3 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(3 - x2 \cdot -2\right)\right)\\ \mathbf{elif}\;x1 \leq -1.9 \cdot 10^{-178}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x1 \leq 3.5 \cdot 10^{-229}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2\right) + \left(x1 + 4 \cdot \left(x2 \cdot \left(x2 \cdot \left(x1 + x1\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 3.8 \cdot 10^{+102}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x1 + 3\right) - x1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0
         (+
          x1
          (+ (* x1 (- (* 4.0 (* x2 (- (* 2.0 x2) 3.0))) 2.0)) (* x2 -6.0)))))
   (if (<= x1 -2.15e+63)
     (+ x1 (* 3.0 (* (* x1 x1) (- 3.0 (* x2 -2.0)))))
     (if (<= x1 -1.9e-178)
       t_0
       (if (<= x1 3.5e-229)
         (+ x1 (+ (* 3.0 (* x2 -2.0)) (+ x1 (* 4.0 (* x2 (* x2 (+ x1 x1)))))))
         (if (<= x1 3.8e+102)
           t_0
           (+ x1 (+ x1 (* 3.0 (- (* (* x1 x1) (+ x1 3.0)) x1))))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 + ((x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)) + (x2 * -6.0));
	double tmp;
	if (x1 <= -2.15e+63) {
		tmp = x1 + (3.0 * ((x1 * x1) * (3.0 - (x2 * -2.0))));
	} else if (x1 <= -1.9e-178) {
		tmp = t_0;
	} else if (x1 <= 3.5e-229) {
		tmp = x1 + ((3.0 * (x2 * -2.0)) + (x1 + (4.0 * (x2 * (x2 * (x1 + x1))))));
	} else if (x1 <= 3.8e+102) {
		tmp = t_0;
	} else {
		tmp = x1 + (x1 + (3.0 * (((x1 * x1) * (x1 + 3.0)) - x1)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x1 + ((x1 * ((4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0))) - 2.0d0)) + (x2 * (-6.0d0)))
    if (x1 <= (-2.15d+63)) then
        tmp = x1 + (3.0d0 * ((x1 * x1) * (3.0d0 - (x2 * (-2.0d0)))))
    else if (x1 <= (-1.9d-178)) then
        tmp = t_0
    else if (x1 <= 3.5d-229) then
        tmp = x1 + ((3.0d0 * (x2 * (-2.0d0))) + (x1 + (4.0d0 * (x2 * (x2 * (x1 + x1))))))
    else if (x1 <= 3.8d+102) then
        tmp = t_0
    else
        tmp = x1 + (x1 + (3.0d0 * (((x1 * x1) * (x1 + 3.0d0)) - x1)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 + ((x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)) + (x2 * -6.0));
	double tmp;
	if (x1 <= -2.15e+63) {
		tmp = x1 + (3.0 * ((x1 * x1) * (3.0 - (x2 * -2.0))));
	} else if (x1 <= -1.9e-178) {
		tmp = t_0;
	} else if (x1 <= 3.5e-229) {
		tmp = x1 + ((3.0 * (x2 * -2.0)) + (x1 + (4.0 * (x2 * (x2 * (x1 + x1))))));
	} else if (x1 <= 3.8e+102) {
		tmp = t_0;
	} else {
		tmp = x1 + (x1 + (3.0 * (((x1 * x1) * (x1 + 3.0)) - x1)));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 + ((x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)) + (x2 * -6.0))
	tmp = 0
	if x1 <= -2.15e+63:
		tmp = x1 + (3.0 * ((x1 * x1) * (3.0 - (x2 * -2.0))))
	elif x1 <= -1.9e-178:
		tmp = t_0
	elif x1 <= 3.5e-229:
		tmp = x1 + ((3.0 * (x2 * -2.0)) + (x1 + (4.0 * (x2 * (x2 * (x1 + x1))))))
	elif x1 <= 3.8e+102:
		tmp = t_0
	else:
		tmp = x1 + (x1 + (3.0 * (((x1 * x1) * (x1 + 3.0)) - x1)))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 + Float64(Float64(x1 * Float64(Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0))) - 2.0)) + Float64(x2 * -6.0)))
	tmp = 0.0
	if (x1 <= -2.15e+63)
		tmp = Float64(x1 + Float64(3.0 * Float64(Float64(x1 * x1) * Float64(3.0 - Float64(x2 * -2.0)))));
	elseif (x1 <= -1.9e-178)
		tmp = t_0;
	elseif (x1 <= 3.5e-229)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(x2 * -2.0)) + Float64(x1 + Float64(4.0 * Float64(x2 * Float64(x2 * Float64(x1 + x1)))))));
	elseif (x1 <= 3.8e+102)
		tmp = t_0;
	else
		tmp = Float64(x1 + Float64(x1 + Float64(3.0 * Float64(Float64(Float64(x1 * x1) * Float64(x1 + 3.0)) - x1))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 + ((x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)) + (x2 * -6.0));
	tmp = 0.0;
	if (x1 <= -2.15e+63)
		tmp = x1 + (3.0 * ((x1 * x1) * (3.0 - (x2 * -2.0))));
	elseif (x1 <= -1.9e-178)
		tmp = t_0;
	elseif (x1 <= 3.5e-229)
		tmp = x1 + ((3.0 * (x2 * -2.0)) + (x1 + (4.0 * (x2 * (x2 * (x1 + x1))))));
	elseif (x1 <= 3.8e+102)
		tmp = t_0;
	else
		tmp = x1 + (x1 + (3.0 * (((x1 * x1) * (x1 + 3.0)) - x1)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 + N[(N[(x1 * N[(N[(4.0 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision] + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -2.15e+63], N[(x1 + N[(3.0 * N[(N[(x1 * x1), $MachinePrecision] * N[(3.0 - N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -1.9e-178], t$95$0, If[LessEqual[x1, 3.5e-229], N[(x1 + N[(N[(3.0 * N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(4.0 * N[(x2 * N[(x2 * N[(x1 + x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 3.8e+102], t$95$0, N[(x1 + N[(x1 + N[(3.0 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(x1 + 3.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -2.15e63

   1. Initial program 11.8%

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

   2. Taylor expanded in x1 around 0 0.1%

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

   3. Taylor expanded in x1 around 0 39.7%

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

      1. +-commutative 39.7%

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

      2. neg-mul-1 39.7%

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

      3. unsub-neg 39.7%

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

      4. +-commutative 39.7%

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

      5. *-commutative 39.7%

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

      6. fma-def 39.7%

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

      7. unpow2 39.7%

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

      8. cancel-sign-sub-inv 39.7%

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

      9. metadata-eval 39.7%

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

      10. *-commutative 39.7%

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

   5. Simplified 39.7%

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

   6. Taylor expanded in x1 around inf 39.7%

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

   7. Taylor expanded in x1 around inf 65.2%

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

      1. unpow2 65.2%

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

      2. metadata-eval 65.2%

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

      3. cancel-sign-sub-inv 65.2%

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

      4. *-commutative 65.2%

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

   9. Simplified 65.2%

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

   if -2.15e63 < x1 < -1.90000000000000007e-178 or 3.5000000000000003e-229 < x1 < 3.79999999999999979e102

   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. Taylor expanded in x1 around 0 80.8%

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

   3. Taylor expanded in x1 around 0 76.9%

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

      1. +-commutative 76.9%

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

      2. neg-mul-1 76.9%

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

      3. unsub-neg 76.9%

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

      4. +-commutative 76.9%

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

      5. *-commutative 76.9%

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

      6. fma-def 76.9%

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

      7. unpow2 76.9%

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

      8. cancel-sign-sub-inv 76.9%

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

      9. metadata-eval 76.9%

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

      10. *-commutative 76.9%

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

   5. Simplified 76.9%

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

   6. Taylor expanded in x1 around 0 78.1%

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

   if -1.90000000000000007e-178 < x1 < 3.5000000000000003e-229

   1. Initial program 99.6%

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

   2. Taylor expanded in x1 around 0 99.6%

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

   3. Taylor expanded in x1 around 0 92.4%

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

      1. *-commutative 92.4%

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

   5. Simplified 92.4%

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

   6. Taylor expanded in x2 around inf 92.4%

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

      1. associate-*r* 92.4%

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

      2. *-commutative 92.4%

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

      3. associate-*l* 92.4%

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

      4. rem-log-exp 69.0%

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

      5. *-commutative 69.0%

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

      6. exp-lft-sqr 69.0%

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

      7. log-prod 69.0%

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

      8. rem-log-exp 76.4%

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

      9. rem-log-exp 92.4%

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

   8. Simplified 92.4%

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

   if 3.79999999999999979e102 < x1

   1. Initial program 20.0%

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

   2. Taylor expanded in x1 around 0 6.4%

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

   3. Taylor expanded in x1 around 0 80.0%

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

      1. +-commutative 80.0%

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

      2. neg-mul-1 80.0%

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

      3. unsub-neg 80.0%

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

      4. *-commutative 80.0%

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

      5. fma-def 80.0%

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

      6. +-commutative 80.0%

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

      7. cube-mult 80.0%

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

      8. unpow2 80.0%

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

      9. distribute-rgt-out 91.4%

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

      10. unpow2 91.4%

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

      11. cancel-sign-sub-inv 91.4%

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

      12. metadata-eval 91.4%

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

   5. Simplified 91.4%

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

   6. Taylor expanded in x2 around 0 100.0%

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

      1. +-commutative 100.0%

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

      2. unpow2 100.0%

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

   8. Simplified 100.0%

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

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -2.15 \cdot 10^{+63}:\\ \;\;\;\;x1 + 3 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(3 - x2 \cdot -2\right)\right)\\ \mathbf{elif}\;x1 \leq -1.9 \cdot 10^{-178}:\\ \;\;\;\;x1 + \left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right) + x2 \cdot -6\right)\\ \mathbf{elif}\;x1 \leq 3.5 \cdot 10^{-229}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2\right) + \left(x1 + 4 \cdot \left(x2 \cdot \left(x2 \cdot \left(x1 + x1\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 3.8 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right) + x2 \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x1 + 3\right) - x1\right)\right)\\ \end{array} \]

Alternative 13: 79.7% accurate, 4.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -1.55 \cdot 10^{+66}:\\ \;\;\;\;x1 + 3 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(3 - x2 \cdot -2\right)\right)\\ \mathbf{elif}\;x1 \leq 3.8 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2 - x1\right) + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x1 + 3\right) - x1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -1.55e+66)
   (+ x1 (* 3.0 (* (* x1 x1) (- 3.0 (* x2 -2.0)))))
   (if (<= x1 3.8e+102)
     (+
      x1
      (+
       (* 3.0 (- (* x2 -2.0) x1))
       (+ x1 (* 4.0 (* x2 (* x1 (- (* 2.0 x2) 3.0)))))))
     (+ x1 (+ x1 (* 3.0 (- (* (* x1 x1) (+ x1 3.0)) x1)))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -1.55e+66) {
		tmp = x1 + (3.0 * ((x1 * x1) * (3.0 - (x2 * -2.0))));
	} else if (x1 <= 3.8e+102) {
		tmp = x1 + ((3.0 * ((x2 * -2.0) - x1)) + (x1 + (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0))))));
	} else {
		tmp = x1 + (x1 + (3.0 * (((x1 * x1) * (x1 + 3.0)) - 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 <= (-1.55d+66)) then
        tmp = x1 + (3.0d0 * ((x1 * x1) * (3.0d0 - (x2 * (-2.0d0)))))
    else if (x1 <= 3.8d+102) then
        tmp = x1 + ((3.0d0 * ((x2 * (-2.0d0)) - x1)) + (x1 + (4.0d0 * (x2 * (x1 * ((2.0d0 * x2) - 3.0d0))))))
    else
        tmp = x1 + (x1 + (3.0d0 * (((x1 * x1) * (x1 + 3.0d0)) - x1)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= -1.55e+66) {
		tmp = x1 + (3.0 * ((x1 * x1) * (3.0 - (x2 * -2.0))));
	} else if (x1 <= 3.8e+102) {
		tmp = x1 + ((3.0 * ((x2 * -2.0) - x1)) + (x1 + (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0))))));
	} else {
		tmp = x1 + (x1 + (3.0 * (((x1 * x1) * (x1 + 3.0)) - x1)));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -1.55e+66:
		tmp = x1 + (3.0 * ((x1 * x1) * (3.0 - (x2 * -2.0))))
	elif x1 <= 3.8e+102:
		tmp = x1 + ((3.0 * ((x2 * -2.0) - x1)) + (x1 + (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0))))))
	else:
		tmp = x1 + (x1 + (3.0 * (((x1 * x1) * (x1 + 3.0)) - x1)))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -1.55e+66)
		tmp = Float64(x1 + Float64(3.0 * Float64(Float64(x1 * x1) * Float64(3.0 - Float64(x2 * -2.0)))));
	elseif (x1 <= 3.8e+102)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(x2 * -2.0) - x1)) + Float64(x1 + Float64(4.0 * Float64(x2 * Float64(x1 * Float64(Float64(2.0 * x2) - 3.0)))))));
	else
		tmp = Float64(x1 + Float64(x1 + Float64(3.0 * Float64(Float64(Float64(x1 * x1) * Float64(x1 + 3.0)) - x1))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -1.55e+66)
		tmp = x1 + (3.0 * ((x1 * x1) * (3.0 - (x2 * -2.0))));
	elseif (x1 <= 3.8e+102)
		tmp = x1 + ((3.0 * ((x2 * -2.0) - x1)) + (x1 + (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0))))));
	else
		tmp = x1 + (x1 + (3.0 * (((x1 * x1) * (x1 + 3.0)) - x1)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -1.55e+66], N[(x1 + N[(3.0 * N[(N[(x1 * x1), $MachinePrecision] * N[(3.0 - N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 3.8e+102], N[(x1 + N[(N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(4.0 * N[(x2 * N[(x1 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(x1 + N[(3.0 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(x1 + 3.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -1.55000000000000009e66

   1. Initial program 11.8%

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

   2. Taylor expanded in x1 around 0 0.1%

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

   3. Taylor expanded in x1 around 0 39.7%

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

      1. +-commutative 39.7%

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

      2. neg-mul-1 39.7%

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

      3. unsub-neg 39.7%

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

      4. +-commutative 39.7%

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

      5. *-commutative 39.7%

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

      6. fma-def 39.7%

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

      7. unpow2 39.7%

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

      8. cancel-sign-sub-inv 39.7%

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

      9. metadata-eval 39.7%

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

      10. *-commutative 39.7%

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

   5. Simplified 39.7%

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

   6. Taylor expanded in x1 around inf 39.7%

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

   7. Taylor expanded in x1 around inf 65.2%

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

      1. unpow2 65.2%

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

      2. metadata-eval 65.2%

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

      3. cancel-sign-sub-inv 65.2%

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

      4. *-commutative 65.2%

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

   9. Simplified 65.2%

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

   if -1.55000000000000009e66 < x1 < 3.79999999999999979e102

   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. Taylor expanded in x1 around 0 85.5%

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

   3. Taylor expanded in x1 around 0 84.9%

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

      1. +-commutative 99.4%

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

      2. neg-mul-1 99.4%

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

      3. unsub-neg 99.4%

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

      4. *-commutative 99.4%

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

   5. Simplified 84.9%

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

   if 3.79999999999999979e102 < x1

   1. Initial program 20.0%

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

   2. Taylor expanded in x1 around 0 6.4%

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

   3. Taylor expanded in x1 around 0 80.0%

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

      1. +-commutative 80.0%

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

      2. neg-mul-1 80.0%

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

      3. unsub-neg 80.0%

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

      4. *-commutative 80.0%

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

      5. fma-def 80.0%

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

      6. +-commutative 80.0%

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

      7. cube-mult 80.0%

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

      8. unpow2 80.0%

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

      9. distribute-rgt-out 91.4%

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

      10. unpow2 91.4%

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

      11. cancel-sign-sub-inv 91.4%

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

      12. metadata-eval 91.4%

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

   5. Simplified 91.4%

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

   6. Taylor expanded in x2 around 0 100.0%

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

      1. +-commutative 100.0%

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

      2. unpow2 100.0%

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

   8. Simplified 100.0%

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

4. Final simplification 82.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.55 \cdot 10^{+66}:\\ \;\;\;\;x1 + 3 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(3 - x2 \cdot -2\right)\right)\\ \mathbf{elif}\;x1 \leq 3.8 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2 - x1\right) + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x1 + 3\right) - x1\right)\right)\\ \end{array} \]

Alternative 14: 67.5% accurate, 5.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -9 \cdot 10^{+61}:\\ \;\;\;\;x1 + 3 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(3 - x2 \cdot -2\right)\right)\\ \mathbf{elif}\;x1 \leq -5.2 \cdot 10^{-120}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(8 \cdot \left(x2 \cdot x2\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 3.05 \cdot 10^{-12}:\\ \;\;\;\;x2 \cdot \left(x1 \cdot -12 - 6\right) + \left(x1 + x1 \cdot -2\right)\\ \mathbf{elif}\;x1 \leq 3.3 \cdot 10^{+102}:\\ \;\;\;\;x1 \cdot \left(2 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x1 + 3\right) - x1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -9e+61)
   (+ x1 (* 3.0 (* (* x1 x1) (- 3.0 (* x2 -2.0)))))
   (if (<= x1 -5.2e-120)
     (+ x1 (+ (* x2 -6.0) (* x1 (* 8.0 (* x2 x2)))))
     (if (<= x1 3.05e-12)
       (+ (* x2 (- (* x1 -12.0) 6.0)) (+ x1 (* x1 -2.0)))
       (if (<= x1 3.3e+102)
         (* x1 (+ 2.0 (* 4.0 (* x2 (- (* 2.0 x2) 3.0)))))
         (+ x1 (+ x1 (* 3.0 (- (* (* x1 x1) (+ x1 3.0)) x1)))))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -9e+61) {
		tmp = x1 + (3.0 * ((x1 * x1) * (3.0 - (x2 * -2.0))));
	} else if (x1 <= -5.2e-120) {
		tmp = x1 + ((x2 * -6.0) + (x1 * (8.0 * (x2 * x2))));
	} else if (x1 <= 3.05e-12) {
		tmp = (x2 * ((x1 * -12.0) - 6.0)) + (x1 + (x1 * -2.0));
	} else if (x1 <= 3.3e+102) {
		tmp = x1 * (2.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0))));
	} else {
		tmp = x1 + (x1 + (3.0 * (((x1 * x1) * (x1 + 3.0)) - 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 <= (-9d+61)) then
        tmp = x1 + (3.0d0 * ((x1 * x1) * (3.0d0 - (x2 * (-2.0d0)))))
    else if (x1 <= (-5.2d-120)) then
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * (8.0d0 * (x2 * x2))))
    else if (x1 <= 3.05d-12) then
        tmp = (x2 * ((x1 * (-12.0d0)) - 6.0d0)) + (x1 + (x1 * (-2.0d0)))
    else if (x1 <= 3.3d+102) then
        tmp = x1 * (2.0d0 + (4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0))))
    else
        tmp = x1 + (x1 + (3.0d0 * (((x1 * x1) * (x1 + 3.0d0)) - x1)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= -9e+61) {
		tmp = x1 + (3.0 * ((x1 * x1) * (3.0 - (x2 * -2.0))));
	} else if (x1 <= -5.2e-120) {
		tmp = x1 + ((x2 * -6.0) + (x1 * (8.0 * (x2 * x2))));
	} else if (x1 <= 3.05e-12) {
		tmp = (x2 * ((x1 * -12.0) - 6.0)) + (x1 + (x1 * -2.0));
	} else if (x1 <= 3.3e+102) {
		tmp = x1 * (2.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0))));
	} else {
		tmp = x1 + (x1 + (3.0 * (((x1 * x1) * (x1 + 3.0)) - x1)));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -9e+61:
		tmp = x1 + (3.0 * ((x1 * x1) * (3.0 - (x2 * -2.0))))
	elif x1 <= -5.2e-120:
		tmp = x1 + ((x2 * -6.0) + (x1 * (8.0 * (x2 * x2))))
	elif x1 <= 3.05e-12:
		tmp = (x2 * ((x1 * -12.0) - 6.0)) + (x1 + (x1 * -2.0))
	elif x1 <= 3.3e+102:
		tmp = x1 * (2.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0))))
	else:
		tmp = x1 + (x1 + (3.0 * (((x1 * x1) * (x1 + 3.0)) - x1)))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -9e+61)
		tmp = Float64(x1 + Float64(3.0 * Float64(Float64(x1 * x1) * Float64(3.0 - Float64(x2 * -2.0)))));
	elseif (x1 <= -5.2e-120)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(8.0 * Float64(x2 * x2)))));
	elseif (x1 <= 3.05e-12)
		tmp = Float64(Float64(x2 * Float64(Float64(x1 * -12.0) - 6.0)) + Float64(x1 + Float64(x1 * -2.0)));
	elseif (x1 <= 3.3e+102)
		tmp = Float64(x1 * Float64(2.0 + Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0)))));
	else
		tmp = Float64(x1 + Float64(x1 + Float64(3.0 * Float64(Float64(Float64(x1 * x1) * Float64(x1 + 3.0)) - x1))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -9e+61)
		tmp = x1 + (3.0 * ((x1 * x1) * (3.0 - (x2 * -2.0))));
	elseif (x1 <= -5.2e-120)
		tmp = x1 + ((x2 * -6.0) + (x1 * (8.0 * (x2 * x2))));
	elseif (x1 <= 3.05e-12)
		tmp = (x2 * ((x1 * -12.0) - 6.0)) + (x1 + (x1 * -2.0));
	elseif (x1 <= 3.3e+102)
		tmp = x1 * (2.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0))));
	else
		tmp = x1 + (x1 + (3.0 * (((x1 * x1) * (x1 + 3.0)) - x1)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -9e+61], N[(x1 + N[(3.0 * N[(N[(x1 * x1), $MachinePrecision] * N[(3.0 - N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -5.2e-120], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(8.0 * N[(x2 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 3.05e-12], N[(N[(x2 * N[(N[(x1 * -12.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(x1 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 3.3e+102], N[(x1 * N[(2.0 + N[(4.0 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(x1 + N[(3.0 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(x1 + 3.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if x1 < -9e61

   1. Initial program 11.8%

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

   2. Taylor expanded in x1 around 0 0.1%

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

   3. Taylor expanded in x1 around 0 39.7%

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

      1. +-commutative 39.7%

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

      2. neg-mul-1 39.7%

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

      3. unsub-neg 39.7%

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

      4. +-commutative 39.7%

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

      5. *-commutative 39.7%

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

      6. fma-def 39.7%

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

      7. unpow2 39.7%

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

      8. cancel-sign-sub-inv 39.7%

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

      9. metadata-eval 39.7%

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

      10. *-commutative 39.7%

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

   5. Simplified 39.7%

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

   6. Taylor expanded in x1 around inf 39.7%

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

   7. Taylor expanded in x1 around inf 65.2%

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

      1. unpow2 65.2%

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

      2. metadata-eval 65.2%

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

      3. cancel-sign-sub-inv 65.2%

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

      4. *-commutative 65.2%

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

   9. Simplified 65.2%

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

   if -9e61 < x1 < -5.2000000000000002e-120

   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. Taylor expanded in x1 around 0 83.4%

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

   3. Taylor expanded in x1 around 0 81.5%

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

      1. +-commutative 81.5%

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

      2. neg-mul-1 81.5%

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

      3. unsub-neg 81.5%

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

      4. +-commutative 81.5%

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

      5. *-commutative 81.5%

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

      6. fma-def 81.5%

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

      7. unpow2 81.5%

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

      8. cancel-sign-sub-inv 81.5%

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

      9. metadata-eval 81.5%

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

      10. *-commutative 81.5%

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

   5. Simplified 81.5%

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

   6. Taylor expanded in x1 around 0 83.4%

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

   7. Taylor expanded in x2 around inf 63.2%

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

      1. associate-*r* 63.2%

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

      2. unpow2 63.2%

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

   9. Simplified 63.2%

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

   if -5.2000000000000002e-120 < x1 < 3.0500000000000001e-12

   1. Initial program 99.4%

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

   2. Taylor expanded in x1 around 0 99.4%

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

   3. Taylor expanded in x1 around 0 99.4%

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

      1. +-commutative 99.4%

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

      2. neg-mul-1 99.4%

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

      3. unsub-neg 99.4%

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

      4. +-commutative 99.4%

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

      5. *-commutative 99.4%

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

      6. fma-def 99.4%

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

      7. unpow2 99.4%

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

      8. cancel-sign-sub-inv 99.4%

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

      9. metadata-eval 99.4%

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

      10. *-commutative 99.4%

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

   5. Simplified 99.4%

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

   6. Taylor expanded in x1 around 0 86.2%

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

   7. Taylor expanded in x2 around 0 76.5%

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

   if 3.0500000000000001e-12 < x1 < 3.29999999999999999e102

   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. Taylor expanded in x1 around 0 37.9%

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

   3. Taylor expanded in x1 around 0 36.7%

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

      1. *-commutative 36.7%

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

   5. Simplified 36.7%

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

   6. Taylor expanded in x1 around inf 36.7%

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

   if 3.29999999999999999e102 < x1

   1. Initial program 20.0%

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

   2. Taylor expanded in x1 around 0 6.4%

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

   3. Taylor expanded in x1 around 0 80.0%

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

      1. +-commutative 80.0%

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

      2. neg-mul-1 80.0%

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

      3. unsub-neg 80.0%

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

      4. *-commutative 80.0%

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

      5. fma-def 80.0%

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

      6. +-commutative 80.0%

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

      7. cube-mult 80.0%

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

      8. unpow2 80.0%

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

      9. distribute-rgt-out 91.4%

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

      10. unpow2 91.4%

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

      11. cancel-sign-sub-inv 91.4%

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

      12. metadata-eval 91.4%

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

   5. Simplified 91.4%

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

   6. Taylor expanded in x2 around 0 100.0%

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

      1. +-commutative 100.0%

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

      2. unpow2 100.0%

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

   8. Simplified 100.0%

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

4. Final simplification 71.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -9 \cdot 10^{+61}:\\ \;\;\;\;x1 + 3 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(3 - x2 \cdot -2\right)\right)\\ \mathbf{elif}\;x1 \leq -5.2 \cdot 10^{-120}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(8 \cdot \left(x2 \cdot x2\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 3.05 \cdot 10^{-12}:\\ \;\;\;\;x2 \cdot \left(x1 \cdot -12 - 6\right) + \left(x1 + x1 \cdot -2\right)\\ \mathbf{elif}\;x1 \leq 3.3 \cdot 10^{+102}:\\ \;\;\;\;x1 \cdot \left(2 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x1 + 3\right) - x1\right)\right)\\ \end{array} \]

Alternative 15: 74.1% accurate, 5.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -1.8 \cdot 10^{+64}:\\ \;\;\;\;x1 + 3 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(3 - x2 \cdot -2\right)\right)\\ \mathbf{elif}\;x1 \leq 3.7 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right) + x2 \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x1 + 3\right) - x1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -1.8e+64)
   (+ x1 (* 3.0 (* (* x1 x1) (- 3.0 (* x2 -2.0)))))
   (if (<= x1 3.7e+102)
     (+ x1 (+ (* x1 (- (* 4.0 (* x2 (- (* 2.0 x2) 3.0))) 2.0)) (* x2 -6.0)))
     (+ x1 (+ x1 (* 3.0 (- (* (* x1 x1) (+ x1 3.0)) x1)))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -1.8e+64) {
		tmp = x1 + (3.0 * ((x1 * x1) * (3.0 - (x2 * -2.0))));
	} else if (x1 <= 3.7e+102) {
		tmp = x1 + ((x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)) + (x2 * -6.0));
	} else {
		tmp = x1 + (x1 + (3.0 * (((x1 * x1) * (x1 + 3.0)) - 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 <= (-1.8d+64)) then
        tmp = x1 + (3.0d0 * ((x1 * x1) * (3.0d0 - (x2 * (-2.0d0)))))
    else if (x1 <= 3.7d+102) then
        tmp = x1 + ((x1 * ((4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0))) - 2.0d0)) + (x2 * (-6.0d0)))
    else
        tmp = x1 + (x1 + (3.0d0 * (((x1 * x1) * (x1 + 3.0d0)) - x1)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= -1.8e+64) {
		tmp = x1 + (3.0 * ((x1 * x1) * (3.0 - (x2 * -2.0))));
	} else if (x1 <= 3.7e+102) {
		tmp = x1 + ((x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)) + (x2 * -6.0));
	} else {
		tmp = x1 + (x1 + (3.0 * (((x1 * x1) * (x1 + 3.0)) - x1)));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -1.8e+64:
		tmp = x1 + (3.0 * ((x1 * x1) * (3.0 - (x2 * -2.0))))
	elif x1 <= 3.7e+102:
		tmp = x1 + ((x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)) + (x2 * -6.0))
	else:
		tmp = x1 + (x1 + (3.0 * (((x1 * x1) * (x1 + 3.0)) - x1)))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -1.8e+64)
		tmp = Float64(x1 + Float64(3.0 * Float64(Float64(x1 * x1) * Float64(3.0 - Float64(x2 * -2.0)))));
	elseif (x1 <= 3.7e+102)
		tmp = Float64(x1 + Float64(Float64(x1 * Float64(Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0))) - 2.0)) + Float64(x2 * -6.0)));
	else
		tmp = Float64(x1 + Float64(x1 + Float64(3.0 * Float64(Float64(Float64(x1 * x1) * Float64(x1 + 3.0)) - x1))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -1.8e+64)
		tmp = x1 + (3.0 * ((x1 * x1) * (3.0 - (x2 * -2.0))));
	elseif (x1 <= 3.7e+102)
		tmp = x1 + ((x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)) + (x2 * -6.0));
	else
		tmp = x1 + (x1 + (3.0 * (((x1 * x1) * (x1 + 3.0)) - x1)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -1.8e+64], N[(x1 + N[(3.0 * N[(N[(x1 * x1), $MachinePrecision] * N[(3.0 - N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 3.7e+102], N[(x1 + N[(N[(x1 * N[(N[(4.0 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision] + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(x1 + N[(3.0 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(x1 + 3.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -1.80000000000000007e64

   1. Initial program 11.8%

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

   2. Taylor expanded in x1 around 0 0.1%

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

   3. Taylor expanded in x1 around 0 39.7%

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

      1. +-commutative 39.7%

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

      2. neg-mul-1 39.7%

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

      3. unsub-neg 39.7%

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

      4. +-commutative 39.7%

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

      5. *-commutative 39.7%

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

      6. fma-def 39.7%

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

      7. unpow2 39.7%

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

      8. cancel-sign-sub-inv 39.7%

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

      9. metadata-eval 39.7%

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

      10. *-commutative 39.7%

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

   5. Simplified 39.7%

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

   6. Taylor expanded in x1 around inf 39.7%

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

   7. Taylor expanded in x1 around inf 65.2%

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

      1. unpow2 65.2%

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

      2. metadata-eval 65.2%

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

      3. cancel-sign-sub-inv 65.2%

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

      4. *-commutative 65.2%

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

   9. Simplified 65.2%

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

   if -1.80000000000000007e64 < x1 < 3.70000000000000023e102

   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. Taylor expanded in x1 around 0 85.5%

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

   3. Taylor expanded in x1 around 0 82.5%

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

      1. +-commutative 82.5%

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

      2. neg-mul-1 82.5%

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

      3. unsub-neg 82.5%

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

      4. +-commutative 82.5%

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

      5. *-commutative 82.5%

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

      6. fma-def 82.5%

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

      7. unpow2 82.5%

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

      8. cancel-sign-sub-inv 82.5%

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

      9. metadata-eval 82.5%

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

      10. *-commutative 82.5%

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

   5. Simplified 82.5%

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

   6. Taylor expanded in x1 around 0 77.1%

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

   if 3.70000000000000023e102 < x1

   1. Initial program 20.0%

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

   2. Taylor expanded in x1 around 0 6.4%

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

   3. Taylor expanded in x1 around 0 80.0%

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

      1. +-commutative 80.0%

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

      2. neg-mul-1 80.0%

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

      3. unsub-neg 80.0%

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

      4. *-commutative 80.0%

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

      5. fma-def 80.0%

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

      6. +-commutative 80.0%

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

      7. cube-mult 80.0%

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

      8. unpow2 80.0%

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

      9. distribute-rgt-out 91.4%

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

      10. unpow2 91.4%

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

      11. cancel-sign-sub-inv 91.4%

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

      12. metadata-eval 91.4%

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

   5. Simplified 91.4%

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

   6. Taylor expanded in x2 around 0 100.0%

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

      1. +-commutative 100.0%

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

      2. unpow2 100.0%

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

   8. Simplified 100.0%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.8 \cdot 10^{+64}:\\ \;\;\;\;x1 + 3 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(3 - x2 \cdot -2\right)\right)\\ \mathbf{elif}\;x1 \leq 3.7 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right) + x2 \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x1 + 3 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x1 + 3\right) - x1\right)\right)\\ \end{array} \]

Alternative 16: 61.7% accurate, 6.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 + 3 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(3 - x2 \cdot -2\right)\right)\\ \mathbf{if}\;x1 \leq -1.65 \cdot 10^{+65}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x1 \leq -5.2 \cdot 10^{-120}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(8 \cdot \left(x2 \cdot x2\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 7.2 \cdot 10^{-13}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot -2\right)\\ \mathbf{elif}\;x1 \leq 3.3 \cdot 10^{+184}:\\ \;\;\;\;x1 \cdot \left(2 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ x1 (* 3.0 (* (* x1 x1) (- 3.0 (* x2 -2.0)))))))
   (if (<= x1 -1.65e+65)
     t_0
     (if (<= x1 -5.2e-120)
       (+ x1 (+ (* x2 -6.0) (* x1 (* 8.0 (* x2 x2)))))
       (if (<= x1 7.2e-13)
         (+ x1 (+ (* x2 -6.0) (* x1 -2.0)))
         (if (<= x1 3.3e+184)
           (* x1 (+ 2.0 (* 4.0 (* x2 (- (* 2.0 x2) 3.0)))))
           t_0))))))

C

double code(double x1, double x2) {
	double t_0 = x1 + (3.0 * ((x1 * x1) * (3.0 - (x2 * -2.0))));
	double tmp;
	if (x1 <= -1.65e+65) {
		tmp = t_0;
	} else if (x1 <= -5.2e-120) {
		tmp = x1 + ((x2 * -6.0) + (x1 * (8.0 * (x2 * x2))));
	} else if (x1 <= 7.2e-13) {
		tmp = x1 + ((x2 * -6.0) + (x1 * -2.0));
	} else if (x1 <= 3.3e+184) {
		tmp = x1 * (2.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0))));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x1 + (3.0d0 * ((x1 * x1) * (3.0d0 - (x2 * (-2.0d0)))))
    if (x1 <= (-1.65d+65)) then
        tmp = t_0
    else if (x1 <= (-5.2d-120)) then
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * (8.0d0 * (x2 * x2))))
    else if (x1 <= 7.2d-13) then
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * (-2.0d0)))
    else if (x1 <= 3.3d+184) then
        tmp = x1 * (2.0d0 + (4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0))))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 + (3.0 * ((x1 * x1) * (3.0 - (x2 * -2.0))));
	double tmp;
	if (x1 <= -1.65e+65) {
		tmp = t_0;
	} else if (x1 <= -5.2e-120) {
		tmp = x1 + ((x2 * -6.0) + (x1 * (8.0 * (x2 * x2))));
	} else if (x1 <= 7.2e-13) {
		tmp = x1 + ((x2 * -6.0) + (x1 * -2.0));
	} else if (x1 <= 3.3e+184) {
		tmp = x1 * (2.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0))));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 + (3.0 * ((x1 * x1) * (3.0 - (x2 * -2.0))))
	tmp = 0
	if x1 <= -1.65e+65:
		tmp = t_0
	elif x1 <= -5.2e-120:
		tmp = x1 + ((x2 * -6.0) + (x1 * (8.0 * (x2 * x2))))
	elif x1 <= 7.2e-13:
		tmp = x1 + ((x2 * -6.0) + (x1 * -2.0))
	elif x1 <= 3.3e+184:
		tmp = x1 * (2.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0))))
	else:
		tmp = t_0
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 + Float64(3.0 * Float64(Float64(x1 * x1) * Float64(3.0 - Float64(x2 * -2.0)))))
	tmp = 0.0
	if (x1 <= -1.65e+65)
		tmp = t_0;
	elseif (x1 <= -5.2e-120)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(8.0 * Float64(x2 * x2)))));
	elseif (x1 <= 7.2e-13)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * -2.0)));
	elseif (x1 <= 3.3e+184)
		tmp = Float64(x1 * Float64(2.0 + Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0)))));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 + (3.0 * ((x1 * x1) * (3.0 - (x2 * -2.0))));
	tmp = 0.0;
	if (x1 <= -1.65e+65)
		tmp = t_0;
	elseif (x1 <= -5.2e-120)
		tmp = x1 + ((x2 * -6.0) + (x1 * (8.0 * (x2 * x2))));
	elseif (x1 <= 7.2e-13)
		tmp = x1 + ((x2 * -6.0) + (x1 * -2.0));
	elseif (x1 <= 3.3e+184)
		tmp = x1 * (2.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0))));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 + N[(3.0 * N[(N[(x1 * x1), $MachinePrecision] * N[(3.0 - N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -1.65e+65], t$95$0, If[LessEqual[x1, -5.2e-120], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(8.0 * N[(x2 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 7.2e-13], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 3.3e+184], N[(x1 * N[(2.0 + N[(4.0 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -1.65000000000000012e65 or 3.2999999999999998e184 < x1

   1. Initial program 8.5%

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

   2. Taylor expanded in x1 around 0 0.0%

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

   3. Taylor expanded in x1 around 0 54.2%

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

      1. +-commutative 54.2%

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

      2. neg-mul-1 54.2%

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

      3. unsub-neg 54.2%

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

      4. +-commutative 54.2%

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

      5. *-commutative 54.2%

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

      6. fma-def 54.2%

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

      7. unpow2 54.2%

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

      8. cancel-sign-sub-inv 54.2%

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

      9. metadata-eval 54.2%

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

      10. *-commutative 54.2%

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

   5. Simplified 54.2%

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

   6. Taylor expanded in x1 around inf 54.2%

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

   7. Taylor expanded in x1 around inf 72.5%

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

      1. unpow2 72.5%

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

      2. metadata-eval 72.5%

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

      3. cancel-sign-sub-inv 72.5%

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

      4. *-commutative 72.5%

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

   9. Simplified 72.5%

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

   if -1.65000000000000012e65 < x1 < -5.2000000000000002e-120

   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. Taylor expanded in x1 around 0 83.4%

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

   3. Taylor expanded in x1 around 0 81.5%

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

      1. +-commutative 81.5%

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

      2. neg-mul-1 81.5%

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

      3. unsub-neg 81.5%

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

      4. +-commutative 81.5%

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

      5. *-commutative 81.5%

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

      6. fma-def 81.5%

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

      7. unpow2 81.5%

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

      8. cancel-sign-sub-inv 81.5%

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

      9. metadata-eval 81.5%

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

      10. *-commutative 81.5%

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

   5. Simplified 81.5%

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

   6. Taylor expanded in x1 around 0 83.4%

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

   7. Taylor expanded in x2 around inf 63.2%

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

      1. associate-*r* 63.2%

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

      2. unpow2 63.2%

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

   9. Simplified 63.2%

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

   if -5.2000000000000002e-120 < x1 < 7.1999999999999996e-13

   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. Taylor expanded in x1 around 0 99.4%

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

   3. Taylor expanded in x1 around 0 99.4%

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

      1. +-commutative 99.4%

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

      2. neg-mul-1 99.4%

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

      3. unsub-neg 99.4%

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

      4. +-commutative 99.4%

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

      5. *-commutative 99.4%

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

      6. fma-def 99.4%

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

      7. unpow2 99.4%

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

      8. cancel-sign-sub-inv 99.4%

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

      9. metadata-eval 99.4%

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

      10. *-commutative 99.4%

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

   5. Simplified 99.4%

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

   6. Taylor expanded in x1 around 0 86.2%

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

   7. Taylor expanded in x2 around 0 76.5%

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

      1. *-commutative 76.5%

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

   9. Simplified 76.5%

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

   if 7.1999999999999996e-13 < x1 < 3.2999999999999998e184

   1. Initial program 86.8%

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

   2. Taylor expanded in x1 around 0 31.9%

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

   3. Taylor expanded in x1 around 0 41.5%

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

      1. *-commutative 41.5%

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

   5. Simplified 41.5%

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

   6. Taylor expanded in x1 around inf 41.5%

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

4. Final simplification 68.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.65 \cdot 10^{+65}:\\ \;\;\;\;x1 + 3 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(3 - x2 \cdot -2\right)\right)\\ \mathbf{elif}\;x1 \leq -5.2 \cdot 10^{-120}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(8 \cdot \left(x2 \cdot x2\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 7.2 \cdot 10^{-13}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot -2\right)\\ \mathbf{elif}\;x1 \leq 3.3 \cdot 10^{+184}:\\ \;\;\;\;x1 \cdot \left(2 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + 3 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(3 - x2 \cdot -2\right)\right)\\ \end{array} \]

Alternative 17: 61.7% accurate, 6.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 + 3 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(3 - x2 \cdot -2\right)\right)\\ \mathbf{if}\;x1 \leq -6.2 \cdot 10^{+65}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x1 \leq -6.5 \cdot 10^{-120}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(8 \cdot \left(x2 \cdot x2\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 6.4 \cdot 10^{-10}:\\ \;\;\;\;x2 \cdot \left(x1 \cdot -12 - 6\right) + \left(x1 + x1 \cdot -2\right)\\ \mathbf{elif}\;x1 \leq 3.3 \cdot 10^{+184}:\\ \;\;\;\;x1 \cdot \left(2 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ x1 (* 3.0 (* (* x1 x1) (- 3.0 (* x2 -2.0)))))))
   (if (<= x1 -6.2e+65)
     t_0
     (if (<= x1 -6.5e-120)
       (+ x1 (+ (* x2 -6.0) (* x1 (* 8.0 (* x2 x2)))))
       (if (<= x1 6.4e-10)
         (+ (* x2 (- (* x1 -12.0) 6.0)) (+ x1 (* x1 -2.0)))
         (if (<= x1 3.3e+184)
           (* x1 (+ 2.0 (* 4.0 (* x2 (- (* 2.0 x2) 3.0)))))
           t_0))))))

C

double code(double x1, double x2) {
	double t_0 = x1 + (3.0 * ((x1 * x1) * (3.0 - (x2 * -2.0))));
	double tmp;
	if (x1 <= -6.2e+65) {
		tmp = t_0;
	} else if (x1 <= -6.5e-120) {
		tmp = x1 + ((x2 * -6.0) + (x1 * (8.0 * (x2 * x2))));
	} else if (x1 <= 6.4e-10) {
		tmp = (x2 * ((x1 * -12.0) - 6.0)) + (x1 + (x1 * -2.0));
	} else if (x1 <= 3.3e+184) {
		tmp = x1 * (2.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0))));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x1 + (3.0d0 * ((x1 * x1) * (3.0d0 - (x2 * (-2.0d0)))))
    if (x1 <= (-6.2d+65)) then
        tmp = t_0
    else if (x1 <= (-6.5d-120)) then
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * (8.0d0 * (x2 * x2))))
    else if (x1 <= 6.4d-10) then
        tmp = (x2 * ((x1 * (-12.0d0)) - 6.0d0)) + (x1 + (x1 * (-2.0d0)))
    else if (x1 <= 3.3d+184) then
        tmp = x1 * (2.0d0 + (4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0))))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 + (3.0 * ((x1 * x1) * (3.0 - (x2 * -2.0))));
	double tmp;
	if (x1 <= -6.2e+65) {
		tmp = t_0;
	} else if (x1 <= -6.5e-120) {
		tmp = x1 + ((x2 * -6.0) + (x1 * (8.0 * (x2 * x2))));
	} else if (x1 <= 6.4e-10) {
		tmp = (x2 * ((x1 * -12.0) - 6.0)) + (x1 + (x1 * -2.0));
	} else if (x1 <= 3.3e+184) {
		tmp = x1 * (2.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0))));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 + (3.0 * ((x1 * x1) * (3.0 - (x2 * -2.0))))
	tmp = 0
	if x1 <= -6.2e+65:
		tmp = t_0
	elif x1 <= -6.5e-120:
		tmp = x1 + ((x2 * -6.0) + (x1 * (8.0 * (x2 * x2))))
	elif x1 <= 6.4e-10:
		tmp = (x2 * ((x1 * -12.0) - 6.0)) + (x1 + (x1 * -2.0))
	elif x1 <= 3.3e+184:
		tmp = x1 * (2.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0))))
	else:
		tmp = t_0
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 + Float64(3.0 * Float64(Float64(x1 * x1) * Float64(3.0 - Float64(x2 * -2.0)))))
	tmp = 0.0
	if (x1 <= -6.2e+65)
		tmp = t_0;
	elseif (x1 <= -6.5e-120)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(8.0 * Float64(x2 * x2)))));
	elseif (x1 <= 6.4e-10)
		tmp = Float64(Float64(x2 * Float64(Float64(x1 * -12.0) - 6.0)) + Float64(x1 + Float64(x1 * -2.0)));
	elseif (x1 <= 3.3e+184)
		tmp = Float64(x1 * Float64(2.0 + Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0)))));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 + (3.0 * ((x1 * x1) * (3.0 - (x2 * -2.0))));
	tmp = 0.0;
	if (x1 <= -6.2e+65)
		tmp = t_0;
	elseif (x1 <= -6.5e-120)
		tmp = x1 + ((x2 * -6.0) + (x1 * (8.0 * (x2 * x2))));
	elseif (x1 <= 6.4e-10)
		tmp = (x2 * ((x1 * -12.0) - 6.0)) + (x1 + (x1 * -2.0));
	elseif (x1 <= 3.3e+184)
		tmp = x1 * (2.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0))));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 + N[(3.0 * N[(N[(x1 * x1), $MachinePrecision] * N[(3.0 - N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -6.2e+65], t$95$0, If[LessEqual[x1, -6.5e-120], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(8.0 * N[(x2 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 6.4e-10], N[(N[(x2 * N[(N[(x1 * -12.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(x1 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 3.3e+184], N[(x1 * N[(2.0 + N[(4.0 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -6.19999999999999981e65 or 3.2999999999999998e184 < x1

   1. Initial program 8.5%

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

   2. Taylor expanded in x1 around 0 0.0%

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

   3. Taylor expanded in x1 around 0 54.2%

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

      1. +-commutative 54.2%

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

      2. neg-mul-1 54.2%

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

      3. unsub-neg 54.2%

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

      4. +-commutative 54.2%

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

      5. *-commutative 54.2%

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

      6. fma-def 54.2%

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

      7. unpow2 54.2%

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

      8. cancel-sign-sub-inv 54.2%

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

      9. metadata-eval 54.2%

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

      10. *-commutative 54.2%

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

   5. Simplified 54.2%

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

   6. Taylor expanded in x1 around inf 54.2%

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

   7. Taylor expanded in x1 around inf 72.5%

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

      1. unpow2 72.5%

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

      2. metadata-eval 72.5%

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

      3. cancel-sign-sub-inv 72.5%

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

      4. *-commutative 72.5%

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

   9. Simplified 72.5%

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

   if -6.19999999999999981e65 < x1 < -6.50000000000000029e-120

   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. Taylor expanded in x1 around 0 83.4%

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

   3. Taylor expanded in x1 around 0 81.5%

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

      1. +-commutative 81.5%

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

      2. neg-mul-1 81.5%

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

      3. unsub-neg 81.5%

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

      4. +-commutative 81.5%

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

      5. *-commutative 81.5%

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

      6. fma-def 81.5%

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

      7. unpow2 81.5%

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

      8. cancel-sign-sub-inv 81.5%

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

      9. metadata-eval 81.5%

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

      10. *-commutative 81.5%

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

   5. Simplified 81.5%

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

   6. Taylor expanded in x1 around 0 83.4%

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

   7. Taylor expanded in x2 around inf 63.2%

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

      1. associate-*r* 63.2%

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

      2. unpow2 63.2%

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

   9. Simplified 63.2%

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

   if -6.50000000000000029e-120 < x1 < 6.39999999999999961e-10

   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. Taylor expanded in x1 around 0 99.4%

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

   3. Taylor expanded in x1 around 0 99.4%

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

      1. +-commutative 99.4%

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

      2. neg-mul-1 99.4%

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

      3. unsub-neg 99.4%

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

      4. +-commutative 99.4%

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

      5. *-commutative 99.4%

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

      6. fma-def 99.4%

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

      7. unpow2 99.4%

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

      8. cancel-sign-sub-inv 99.4%

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

      9. metadata-eval 99.4%

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

      10. *-commutative 99.4%

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

   5. Simplified 99.4%

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

   6. Taylor expanded in x1 around 0 86.2%

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

   7. Taylor expanded in x2 around 0 76.5%

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

   if 6.39999999999999961e-10 < x1 < 3.2999999999999998e184

   1. Initial program 86.8%

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

   2. Taylor expanded in x1 around 0 31.9%

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

   3. Taylor expanded in x1 around 0 41.5%

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

      1. *-commutative 41.5%

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

   5. Simplified 41.5%

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

   6. Taylor expanded in x1 around inf 41.5%

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

4. Final simplification 68.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -6.2 \cdot 10^{+65}:\\ \;\;\;\;x1 + 3 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(3 - x2 \cdot -2\right)\right)\\ \mathbf{elif}\;x1 \leq -6.5 \cdot 10^{-120}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(8 \cdot \left(x2 \cdot x2\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 6.4 \cdot 10^{-10}:\\ \;\;\;\;x2 \cdot \left(x1 \cdot -12 - 6\right) + \left(x1 + x1 \cdot -2\right)\\ \mathbf{elif}\;x1 \leq 3.3 \cdot 10^{+184}:\\ \;\;\;\;x1 \cdot \left(2 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + 3 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(3 - x2 \cdot -2\right)\right)\\ \end{array} \]

Alternative 18: 61.1% accurate, 6.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 + 3 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(3 - x2 \cdot -2\right)\right)\\ \mathbf{if}\;x1 \leq -40000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x1 \leq 1.02 \cdot 10^{-12}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot -2\right)\\ \mathbf{elif}\;x1 \leq 3.3 \cdot 10^{+184}:\\ \;\;\;\;x1 \cdot \left(2 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ x1 (* 3.0 (* (* x1 x1) (- 3.0 (* x2 -2.0)))))))
   (if (<= x1 -40000.0)
     t_0
     (if (<= x1 1.02e-12)
       (+ x1 (+ (* x2 -6.0) (* x1 -2.0)))
       (if (<= x1 3.3e+184)
         (* x1 (+ 2.0 (* 4.0 (* x2 (- (* 2.0 x2) 3.0)))))
         t_0)))))

C

double code(double x1, double x2) {
	double t_0 = x1 + (3.0 * ((x1 * x1) * (3.0 - (x2 * -2.0))));
	double tmp;
	if (x1 <= -40000.0) {
		tmp = t_0;
	} else if (x1 <= 1.02e-12) {
		tmp = x1 + ((x2 * -6.0) + (x1 * -2.0));
	} else if (x1 <= 3.3e+184) {
		tmp = x1 * (2.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0))));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x1 + (3.0d0 * ((x1 * x1) * (3.0d0 - (x2 * (-2.0d0)))))
    if (x1 <= (-40000.0d0)) then
        tmp = t_0
    else if (x1 <= 1.02d-12) then
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * (-2.0d0)))
    else if (x1 <= 3.3d+184) then
        tmp = x1 * (2.0d0 + (4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0))))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 + (3.0 * ((x1 * x1) * (3.0 - (x2 * -2.0))));
	double tmp;
	if (x1 <= -40000.0) {
		tmp = t_0;
	} else if (x1 <= 1.02e-12) {
		tmp = x1 + ((x2 * -6.0) + (x1 * -2.0));
	} else if (x1 <= 3.3e+184) {
		tmp = x1 * (2.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0))));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 + (3.0 * ((x1 * x1) * (3.0 - (x2 * -2.0))))
	tmp = 0
	if x1 <= -40000.0:
		tmp = t_0
	elif x1 <= 1.02e-12:
		tmp = x1 + ((x2 * -6.0) + (x1 * -2.0))
	elif x1 <= 3.3e+184:
		tmp = x1 * (2.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0))))
	else:
		tmp = t_0
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 + Float64(3.0 * Float64(Float64(x1 * x1) * Float64(3.0 - Float64(x2 * -2.0)))))
	tmp = 0.0
	if (x1 <= -40000.0)
		tmp = t_0;
	elseif (x1 <= 1.02e-12)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * -2.0)));
	elseif (x1 <= 3.3e+184)
		tmp = Float64(x1 * Float64(2.0 + Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0)))));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 + (3.0 * ((x1 * x1) * (3.0 - (x2 * -2.0))));
	tmp = 0.0;
	if (x1 <= -40000.0)
		tmp = t_0;
	elseif (x1 <= 1.02e-12)
		tmp = x1 + ((x2 * -6.0) + (x1 * -2.0));
	elseif (x1 <= 3.3e+184)
		tmp = x1 * (2.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0))));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 + N[(3.0 * N[(N[(x1 * x1), $MachinePrecision] * N[(3.0 - N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -40000.0], t$95$0, If[LessEqual[x1, 1.02e-12], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 3.3e+184], N[(x1 * N[(2.0 + N[(4.0 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -4e4 or 3.2999999999999998e184 < x1

   1. Initial program 19.3%

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

   2. Taylor expanded in x1 around 0 5.6%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 52.6%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(-1 \cdot x1 + \left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right)\right)}\right) \]
   4. Step-by-step derivation

      1. +-commutative 52.6%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(\left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right) + -1 \cdot x1\right)}\right) \]

      2. neg-mul-1 52.6%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right) + \color{blue}{\left(-x1\right)}\right)\right) \]

      3. unsub-neg 52.6%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(\left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right) - x1\right)}\right) \]

      4. +-commutative 52.6%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\color{blue}{\left(\left(3 - -2 \cdot x2\right) \cdot {x1}^{2} + -2 \cdot x2\right)} - x1\right)\right) \]

      5. *-commutative 52.6%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\left(\color{blue}{{x1}^{2} \cdot \left(3 - -2 \cdot x2\right)} + -2 \cdot x2\right) - x1\right)\right) \]

      6. fma-def 52.6%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\color{blue}{\mathsf{fma}\left({x1}^{2}, 3 - -2 \cdot x2, -2 \cdot x2\right)} - x1\right)\right) \]

      7. unpow2 52.6%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(\color{blue}{x1 \cdot x1}, 3 - -2 \cdot x2, -2 \cdot x2\right) - x1\right)\right) \]

      8. cancel-sign-sub-inv 52.6%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, \color{blue}{3 + \left(--2\right) \cdot x2}, -2 \cdot x2\right) - x1\right)\right) \]

      9. metadata-eval 52.6%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, 3 + \color{blue}{2} \cdot x2, -2 \cdot x2\right) - x1\right)\right) \]

      10. *-commutative 52.6%

          \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, 3 + 2 \cdot x2, \color{blue}{x2 \cdot -2}\right) - x1\right)\right) \]

   5. Simplified 52.6%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(\mathsf{fma}\left(x1 \cdot x1, 3 + 2 \cdot x2, x2 \cdot -2\right) - x1\right)}\right) \]

   6. Taylor expanded in x1 around inf 52.6%

      \[\leadsto x1 + \color{blue}{\left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right) + 3 \cdot \left({x1}^{2} \cdot \left(3 + 2 \cdot x2\right)\right)\right)} \]

   7. Taylor expanded in x1 around inf 66.6%

      \[\leadsto x1 + \color{blue}{3 \cdot \left({x1}^{2} \cdot \left(3 + 2 \cdot x2\right)\right)} \]
   8. Step-by-step derivation

      1. unpow2 66.6%

         \[\leadsto x1 + 3 \cdot \left(\color{blue}{\left(x1 \cdot x1\right)} \cdot \left(3 + 2 \cdot x2\right)\right) \]

      2. metadata-eval 66.6%

         \[\leadsto x1 + 3 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(3 + \color{blue}{\left(--2\right)} \cdot x2\right)\right) \]

      3. cancel-sign-sub-inv 66.6%

         \[\leadsto x1 + 3 \cdot \left(\left(x1 \cdot x1\right) \cdot \color{blue}{\left(3 - -2 \cdot x2\right)}\right) \]

      4. *-commutative 66.6%

         \[\leadsto x1 + 3 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(3 - \color{blue}{x2 \cdot -2}\right)\right) \]

   9. Simplified 66.6%

      \[\leadsto x1 + \color{blue}{3 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(3 - x2 \cdot -2\right)\right)} \]

   if -4e4 < x1 < 1.02e-12

   1. Initial program 99.4%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 99.3%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 99.3%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(-1 \cdot x1 + \left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right)\right)}\right) \]
   4. Step-by-step derivation

      1. +-commutative 99.3%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(\left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right) + -1 \cdot x1\right)}\right) \]

      2. neg-mul-1 99.3%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right) + \color{blue}{\left(-x1\right)}\right)\right) \]

      3. unsub-neg 99.3%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(\left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right) - x1\right)}\right) \]

      4. +-commutative 99.3%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\color{blue}{\left(\left(3 - -2 \cdot x2\right) \cdot {x1}^{2} + -2 \cdot x2\right)} - x1\right)\right) \]

      5. *-commutative 99.3%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\left(\color{blue}{{x1}^{2} \cdot \left(3 - -2 \cdot x2\right)} + -2 \cdot x2\right) - x1\right)\right) \]

      6. fma-def 99.3%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\color{blue}{\mathsf{fma}\left({x1}^{2}, 3 - -2 \cdot x2, -2 \cdot x2\right)} - x1\right)\right) \]

      7. unpow2 99.3%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(\color{blue}{x1 \cdot x1}, 3 - -2 \cdot x2, -2 \cdot x2\right) - x1\right)\right) \]

      8. cancel-sign-sub-inv 99.3%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, \color{blue}{3 + \left(--2\right) \cdot x2}, -2 \cdot x2\right) - x1\right)\right) \]

      9. metadata-eval 99.3%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, 3 + \color{blue}{2} \cdot x2, -2 \cdot x2\right) - x1\right)\right) \]

      10. *-commutative 99.3%

          \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, 3 + 2 \cdot x2, \color{blue}{x2 \cdot -2}\right) - x1\right)\right) \]

   5. Simplified 99.3%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(\mathsf{fma}\left(x1 \cdot x1, 3 + 2 \cdot x2, x2 \cdot -2\right) - x1\right)}\right) \]

   6. Taylor expanded in x1 around 0 88.7%

      \[\leadsto x1 + \color{blue}{\left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right) + -6 \cdot x2\right)} \]

   7. Taylor expanded in x2 around 0 73.4%

      \[\leadsto x1 + \left(\color{blue}{-2 \cdot x1} + -6 \cdot x2\right) \]
   8. Step-by-step derivation

      1. *-commutative 73.4%

         \[\leadsto x1 + \left(\color{blue}{x1 \cdot -2} + -6 \cdot x2\right) \]

   9. Simplified 73.4%

      \[\leadsto x1 + \left(\color{blue}{x1 \cdot -2} + -6 \cdot x2\right) \]

   if 1.02e-12 < x1 < 3.2999999999999998e184

   1. Initial program 86.8%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 31.9%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 41.5%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(-2 \cdot x2\right)}\right) \]
   4. Step-by-step derivation

      1. *-commutative 41.5%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(x2 \cdot -2\right)}\right) \]

   5. Simplified 41.5%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(x2 \cdot -2\right)}\right) \]

   6. Taylor expanded in x1 around inf 41.5%

      \[\leadsto \color{blue}{x1 \cdot \left(2 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -40000:\\ \;\;\;\;x1 + 3 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(3 - x2 \cdot -2\right)\right)\\ \mathbf{elif}\;x1 \leq 1.02 \cdot 10^{-12}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot -2\right)\\ \mathbf{elif}\;x1 \leq 3.3 \cdot 10^{+184}:\\ \;\;\;\;x1 \cdot \left(2 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + 3 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(3 - x2 \cdot -2\right)\right)\\ \end{array} \]

Alternative 19: 42.5% accurate, 7.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 + \left(x2 \cdot x2\right) \cdot \left(x1 \cdot 8\right)\\ t_1 := x1 + x2 \cdot -6\\ \mathbf{if}\;x2 \leq -2.35 \cdot 10^{+116}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x2 \leq -2.9 \cdot 10^{-151}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x2 \leq 1.6 \cdot 10^{-98}:\\ \;\;\;\;-x1\\ \mathbf{elif}\;x2 \leq 5.5 \cdot 10^{+113}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ x1 (* (* x2 x2) (* x1 8.0)))) (t_1 (+ x1 (* x2 -6.0))))
   (if (<= x2 -2.35e+116)
     t_0
     (if (<= x2 -2.9e-151)
       t_1
       (if (<= x2 1.6e-98) (- x1) (if (<= x2 5.5e+113) t_1 t_0))))))

C

double code(double x1, double x2) {
	double t_0 = x1 + ((x2 * x2) * (x1 * 8.0));
	double t_1 = x1 + (x2 * -6.0);
	double tmp;
	if (x2 <= -2.35e+116) {
		tmp = t_0;
	} else if (x2 <= -2.9e-151) {
		tmp = t_1;
	} else if (x2 <= 1.6e-98) {
		tmp = -x1;
	} else if (x2 <= 5.5e+113) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x1 + ((x2 * x2) * (x1 * 8.0d0))
    t_1 = x1 + (x2 * (-6.0d0))
    if (x2 <= (-2.35d+116)) then
        tmp = t_0
    else if (x2 <= (-2.9d-151)) then
        tmp = t_1
    else if (x2 <= 1.6d-98) then
        tmp = -x1
    else if (x2 <= 5.5d+113) then
        tmp = t_1
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 + ((x2 * x2) * (x1 * 8.0));
	double t_1 = x1 + (x2 * -6.0);
	double tmp;
	if (x2 <= -2.35e+116) {
		tmp = t_0;
	} else if (x2 <= -2.9e-151) {
		tmp = t_1;
	} else if (x2 <= 1.6e-98) {
		tmp = -x1;
	} else if (x2 <= 5.5e+113) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 + ((x2 * x2) * (x1 * 8.0))
	t_1 = x1 + (x2 * -6.0)
	tmp = 0
	if x2 <= -2.35e+116:
		tmp = t_0
	elif x2 <= -2.9e-151:
		tmp = t_1
	elif x2 <= 1.6e-98:
		tmp = -x1
	elif x2 <= 5.5e+113:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 + Float64(Float64(x2 * x2) * Float64(x1 * 8.0)))
	t_1 = Float64(x1 + Float64(x2 * -6.0))
	tmp = 0.0
	if (x2 <= -2.35e+116)
		tmp = t_0;
	elseif (x2 <= -2.9e-151)
		tmp = t_1;
	elseif (x2 <= 1.6e-98)
		tmp = Float64(-x1);
	elseif (x2 <= 5.5e+113)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 + ((x2 * x2) * (x1 * 8.0));
	t_1 = x1 + (x2 * -6.0);
	tmp = 0.0;
	if (x2 <= -2.35e+116)
		tmp = t_0;
	elseif (x2 <= -2.9e-151)
		tmp = t_1;
	elseif (x2 <= 1.6e-98)
		tmp = -x1;
	elseif (x2 <= 5.5e+113)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 + N[(N[(x2 * x2), $MachinePrecision] * N[(x1 * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x2, -2.35e+116], t$95$0, If[LessEqual[x2, -2.9e-151], t$95$1, If[LessEqual[x2, 1.6e-98], (-x1), If[LessEqual[x2, 5.5e+113], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if x2 < -2.3500000000000002e116 or 5.5000000000000001e113 < x2

   1. Initial program 70.1%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 65.4%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 61.8%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(-1 \cdot x1 + \left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right)\right)}\right) \]
   4. Step-by-step derivation

      1. +-commutative 61.8%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(\left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right) + -1 \cdot x1\right)}\right) \]

      2. neg-mul-1 61.8%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right) + \color{blue}{\left(-x1\right)}\right)\right) \]

      3. unsub-neg 61.8%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(\left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right) - x1\right)}\right) \]

      4. +-commutative 61.8%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\color{blue}{\left(\left(3 - -2 \cdot x2\right) \cdot {x1}^{2} + -2 \cdot x2\right)} - x1\right)\right) \]

      5. *-commutative 61.8%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\left(\color{blue}{{x1}^{2} \cdot \left(3 - -2 \cdot x2\right)} + -2 \cdot x2\right) - x1\right)\right) \]

      6. fma-def 61.8%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\color{blue}{\mathsf{fma}\left({x1}^{2}, 3 - -2 \cdot x2, -2 \cdot x2\right)} - x1\right)\right) \]

      7. unpow2 61.8%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(\color{blue}{x1 \cdot x1}, 3 - -2 \cdot x2, -2 \cdot x2\right) - x1\right)\right) \]

      8. cancel-sign-sub-inv 61.8%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, \color{blue}{3 + \left(--2\right) \cdot x2}, -2 \cdot x2\right) - x1\right)\right) \]

      9. metadata-eval 61.8%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, 3 + \color{blue}{2} \cdot x2, -2 \cdot x2\right) - x1\right)\right) \]

      10. *-commutative 61.8%

          \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, 3 + 2 \cdot x2, \color{blue}{x2 \cdot -2}\right) - x1\right)\right) \]

   5. Simplified 61.8%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(\mathsf{fma}\left(x1 \cdot x1, 3 + 2 \cdot x2, x2 \cdot -2\right) - x1\right)}\right) \]

   6. Taylor expanded in x2 around inf 53.8%

      \[\leadsto x1 + \color{blue}{8 \cdot \left({x2}^{2} \cdot x1\right)} \]
   7. Step-by-step derivation

      1. *-commutative 53.8%

         \[\leadsto x1 + \color{blue}{\left({x2}^{2} \cdot x1\right) \cdot 8} \]

      2. associate-*l* 53.8%

         \[\leadsto x1 + \color{blue}{{x2}^{2} \cdot \left(x1 \cdot 8\right)} \]

      3. unpow2 53.8%

         \[\leadsto x1 + \color{blue}{\left(x2 \cdot x2\right)} \cdot \left(x1 \cdot 8\right) \]

   8. Simplified 53.8%

      \[\leadsto x1 + \color{blue}{\left(x2 \cdot x2\right) \cdot \left(x1 \cdot 8\right)} \]

   if -2.3500000000000002e116 < x2 < -2.90000000000000013e-151 or 1.6e-98 < x2 < 5.5000000000000001e113

   1. Initial program 68.7%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 52.3%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 68.8%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(-1 \cdot x1 + \left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right)\right)}\right) \]
   4. Step-by-step derivation

      1. +-commutative 68.8%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(\left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right) + -1 \cdot x1\right)}\right) \]

      2. neg-mul-1 68.8%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right) + \color{blue}{\left(-x1\right)}\right)\right) \]

      3. unsub-neg 68.8%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(\left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right) - x1\right)}\right) \]

      4. +-commutative 68.8%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\color{blue}{\left(\left(3 - -2 \cdot x2\right) \cdot {x1}^{2} + -2 \cdot x2\right)} - x1\right)\right) \]

      5. *-commutative 68.8%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\left(\color{blue}{{x1}^{2} \cdot \left(3 - -2 \cdot x2\right)} + -2 \cdot x2\right) - x1\right)\right) \]

      6. fma-def 68.8%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\color{blue}{\mathsf{fma}\left({x1}^{2}, 3 - -2 \cdot x2, -2 \cdot x2\right)} - x1\right)\right) \]

      7. unpow2 68.8%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(\color{blue}{x1 \cdot x1}, 3 - -2 \cdot x2, -2 \cdot x2\right) - x1\right)\right) \]

      8. cancel-sign-sub-inv 68.8%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, \color{blue}{3 + \left(--2\right) \cdot x2}, -2 \cdot x2\right) - x1\right)\right) \]

      9. metadata-eval 68.8%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, 3 + \color{blue}{2} \cdot x2, -2 \cdot x2\right) - x1\right)\right) \]

      10. *-commutative 68.8%

          \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, 3 + 2 \cdot x2, \color{blue}{x2 \cdot -2}\right) - x1\right)\right) \]

   5. Simplified 68.8%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(\mathsf{fma}\left(x1 \cdot x1, 3 + 2 \cdot x2, x2 \cdot -2\right) - x1\right)}\right) \]

   6. Taylor expanded in x1 around 0 43.4%

      \[\leadsto x1 + \color{blue}{-6 \cdot x2} \]
   7. Step-by-step derivation

      1. *-commutative 43.4%

         \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]

   8. Simplified 43.4%

      \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]

   if -2.90000000000000013e-151 < x2 < 1.6e-98

   1. Initial program 66.3%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 47.4%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 80.9%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(-1 \cdot x1 + \left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right)\right)}\right) \]
   4. Step-by-step derivation

      1. +-commutative 80.9%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(\left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right) + -1 \cdot x1\right)}\right) \]

      2. neg-mul-1 80.9%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right) + \color{blue}{\left(-x1\right)}\right)\right) \]

      3. unsub-neg 80.9%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(\left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right) - x1\right)}\right) \]

      4. +-commutative 80.9%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\color{blue}{\left(\left(3 - -2 \cdot x2\right) \cdot {x1}^{2} + -2 \cdot x2\right)} - x1\right)\right) \]

      5. *-commutative 80.9%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\left(\color{blue}{{x1}^{2} \cdot \left(3 - -2 \cdot x2\right)} + -2 \cdot x2\right) - x1\right)\right) \]

      6. fma-def 80.9%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\color{blue}{\mathsf{fma}\left({x1}^{2}, 3 - -2 \cdot x2, -2 \cdot x2\right)} - x1\right)\right) \]

      7. unpow2 80.9%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(\color{blue}{x1 \cdot x1}, 3 - -2 \cdot x2, -2 \cdot x2\right) - x1\right)\right) \]

      8. cancel-sign-sub-inv 80.9%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, \color{blue}{3 + \left(--2\right) \cdot x2}, -2 \cdot x2\right) - x1\right)\right) \]

      9. metadata-eval 80.9%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, 3 + \color{blue}{2} \cdot x2, -2 \cdot x2\right) - x1\right)\right) \]

      10. *-commutative 80.9%

          \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, 3 + 2 \cdot x2, \color{blue}{x2 \cdot -2}\right) - x1\right)\right) \]

   5. Simplified 80.9%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(\mathsf{fma}\left(x1 \cdot x1, 3 + 2 \cdot x2, x2 \cdot -2\right) - x1\right)}\right) \]

   6. Taylor expanded in x1 around 0 48.6%

      \[\leadsto x1 + \color{blue}{\left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right) + -6 \cdot x2\right)} \]

   7. Taylor expanded in x2 around 0 38.0%

      \[\leadsto \color{blue}{x1 + -2 \cdot x1} \]
   8. Step-by-step derivation

      1. distribute-rgt1-in 38.0%

         \[\leadsto \color{blue}{\left(-2 + 1\right) \cdot x1} \]

      2. metadata-eval 38.0%

         \[\leadsto \color{blue}{-1} \cdot x1 \]

      3. mul-1-neg 38.0%

         \[\leadsto \color{blue}{-x1} \]

   9. Simplified 38.0%

      \[\leadsto \color{blue}{-x1} \]
3. Recombined 3 regimes into one program.

4. Final simplification 45.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq -2.35 \cdot 10^{+116}:\\ \;\;\;\;x1 + \left(x2 \cdot x2\right) \cdot \left(x1 \cdot 8\right)\\ \mathbf{elif}\;x2 \leq -2.9 \cdot 10^{-151}:\\ \;\;\;\;x1 + x2 \cdot -6\\ \mathbf{elif}\;x2 \leq 1.6 \cdot 10^{-98}:\\ \;\;\;\;-x1\\ \mathbf{elif}\;x2 \leq 5.5 \cdot 10^{+113}:\\ \;\;\;\;x1 + x2 \cdot -6\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot x2\right) \cdot \left(x1 \cdot 8\right)\\ \end{array} \]

Alternative 20: 49.1% accurate, 9.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x2 \leq -4.7 \cdot 10^{+112} \lor \neg \left(x2 \leq 8.2 \cdot 10^{+100}\right):\\ \;\;\;\;x1 + \left(x2 \cdot x2\right) \cdot \left(x1 \cdot 8\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot -2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x2 -4.7e+112) (not (<= x2 8.2e+100)))
   (+ x1 (* (* x2 x2) (* x1 8.0)))
   (+ x1 (+ (* x2 -6.0) (* x1 -2.0)))))

C

double code(double x1, double x2) {
	double tmp;
	if ((x2 <= -4.7e+112) || !(x2 <= 8.2e+100)) {
		tmp = x1 + ((x2 * x2) * (x1 * 8.0));
	} 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 ((x2 <= (-4.7d+112)) .or. (.not. (x2 <= 8.2d+100))) then
        tmp = x1 + ((x2 * x2) * (x1 * 8.0d0))
    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 ((x2 <= -4.7e+112) || !(x2 <= 8.2e+100)) {
		tmp = x1 + ((x2 * x2) * (x1 * 8.0));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * -2.0));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x2 <= -4.7e+112) or not (x2 <= 8.2e+100):
		tmp = x1 + ((x2 * x2) * (x1 * 8.0))
	else:
		tmp = x1 + ((x2 * -6.0) + (x1 * -2.0))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x2 <= -4.7e+112) || !(x2 <= 8.2e+100))
		tmp = Float64(x1 + Float64(Float64(x2 * x2) * Float64(x1 * 8.0)));
	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 ((x2 <= -4.7e+112) || ~((x2 <= 8.2e+100)))
		tmp = x1 + ((x2 * x2) * (x1 * 8.0));
	else
		tmp = x1 + ((x2 * -6.0) + (x1 * -2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x2, -4.7e+112], N[Not[LessEqual[x2, 8.2e+100]], $MachinePrecision]], N[(x1 + N[(N[(x2 * x2), $MachinePrecision] * N[(x1 * 8.0), $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 x2 < -4.69999999999999997e112 or 8.2000000000000006e100 < x2

   1. Initial program 69.6%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 65.1%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 62.7%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(-1 \cdot x1 + \left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right)\right)}\right) \]
   4. Step-by-step derivation

      1. +-commutative 62.7%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(\left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right) + -1 \cdot x1\right)}\right) \]

      2. neg-mul-1 62.7%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right) + \color{blue}{\left(-x1\right)}\right)\right) \]

      3. unsub-neg 62.7%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(\left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right) - x1\right)}\right) \]

      4. +-commutative 62.7%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\color{blue}{\left(\left(3 - -2 \cdot x2\right) \cdot {x1}^{2} + -2 \cdot x2\right)} - x1\right)\right) \]

      5. *-commutative 62.7%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\left(\color{blue}{{x1}^{2} \cdot \left(3 - -2 \cdot x2\right)} + -2 \cdot x2\right) - x1\right)\right) \]

      6. fma-def 62.7%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\color{blue}{\mathsf{fma}\left({x1}^{2}, 3 - -2 \cdot x2, -2 \cdot x2\right)} - x1\right)\right) \]

      7. unpow2 62.7%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(\color{blue}{x1 \cdot x1}, 3 - -2 \cdot x2, -2 \cdot x2\right) - x1\right)\right) \]

      8. cancel-sign-sub-inv 62.7%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, \color{blue}{3 + \left(--2\right) \cdot x2}, -2 \cdot x2\right) - x1\right)\right) \]

      9. metadata-eval 62.7%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, 3 + \color{blue}{2} \cdot x2, -2 \cdot x2\right) - x1\right)\right) \]

      10. *-commutative 62.7%

          \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, 3 + 2 \cdot x2, \color{blue}{x2 \cdot -2}\right) - x1\right)\right) \]

   5. Simplified 62.7%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(\mathsf{fma}\left(x1 \cdot x1, 3 + 2 \cdot x2, x2 \cdot -2\right) - x1\right)}\right) \]

   6. Taylor expanded in x2 around inf 53.7%

      \[\leadsto x1 + \color{blue}{8 \cdot \left({x2}^{2} \cdot x1\right)} \]
   7. Step-by-step derivation

      1. *-commutative 53.7%

         \[\leadsto x1 + \color{blue}{\left({x2}^{2} \cdot x1\right) \cdot 8} \]

      2. associate-*l* 53.7%

         \[\leadsto x1 + \color{blue}{{x2}^{2} \cdot \left(x1 \cdot 8\right)} \]

      3. unpow2 53.7%

         \[\leadsto x1 + \color{blue}{\left(x2 \cdot x2\right)} \cdot \left(x1 \cdot 8\right) \]

   8. Simplified 53.7%

      \[\leadsto x1 + \color{blue}{\left(x2 \cdot x2\right) \cdot \left(x1 \cdot 8\right)} \]

   if -4.69999999999999997e112 < x2 < 8.2000000000000006e100

   1. Initial program 67.7%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 49.9%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 74.5%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(-1 \cdot x1 + \left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right)\right)}\right) \]
   4. Step-by-step derivation

      1. +-commutative 74.5%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(\left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right) + -1 \cdot x1\right)}\right) \]

      2. neg-mul-1 74.5%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right) + \color{blue}{\left(-x1\right)}\right)\right) \]

      3. unsub-neg 74.5%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(\left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right) - x1\right)}\right) \]

      4. +-commutative 74.5%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\color{blue}{\left(\left(3 - -2 \cdot x2\right) \cdot {x1}^{2} + -2 \cdot x2\right)} - x1\right)\right) \]

      5. *-commutative 74.5%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\left(\color{blue}{{x1}^{2} \cdot \left(3 - -2 \cdot x2\right)} + -2 \cdot x2\right) - x1\right)\right) \]

      6. fma-def 74.5%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\color{blue}{\mathsf{fma}\left({x1}^{2}, 3 - -2 \cdot x2, -2 \cdot x2\right)} - x1\right)\right) \]

      7. unpow2 74.5%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(\color{blue}{x1 \cdot x1}, 3 - -2 \cdot x2, -2 \cdot x2\right) - x1\right)\right) \]

      8. cancel-sign-sub-inv 74.5%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, \color{blue}{3 + \left(--2\right) \cdot x2}, -2 \cdot x2\right) - x1\right)\right) \]

      9. metadata-eval 74.5%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, 3 + \color{blue}{2} \cdot x2, -2 \cdot x2\right) - x1\right)\right) \]

      10. *-commutative 74.5%

          \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, 3 + 2 \cdot x2, \color{blue}{x2 \cdot -2}\right) - x1\right)\right) \]

   5. Simplified 74.5%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(\mathsf{fma}\left(x1 \cdot x1, 3 + 2 \cdot x2, x2 \cdot -2\right) - x1\right)}\right) \]

   6. Taylor expanded in x1 around 0 51.0%

      \[\leadsto x1 + \color{blue}{\left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right) + -6 \cdot x2\right)} \]

   7. Taylor expanded in x2 around 0 49.0%

      \[\leadsto x1 + \left(\color{blue}{-2 \cdot x1} + -6 \cdot x2\right) \]
   8. Step-by-step derivation

      1. *-commutative 49.0%

         \[\leadsto x1 + \left(\color{blue}{x1 \cdot -2} + -6 \cdot x2\right) \]

   9. Simplified 49.0%

      \[\leadsto x1 + \left(\color{blue}{x1 \cdot -2} + -6 \cdot x2\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 50.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq -4.7 \cdot 10^{+112} \lor \neg \left(x2 \leq 8.2 \cdot 10^{+100}\right):\\ \;\;\;\;x1 + \left(x2 \cdot x2\right) \cdot \left(x1 \cdot 8\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot -2\right)\\ \end{array} \]

Alternative 21: 31.4% accurate, 13.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x2 \leq -2.3 \cdot 10^{-149} \lor \neg \left(x2 \leq 8 \cdot 10^{-99}\right):\\ \;\;\;\;x1 + x2 \cdot -6\\ \mathbf{else}:\\ \;\;\;\;-x1\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x2 -2.3e-149) (not (<= x2 8e-99))) (+ x1 (* x2 -6.0)) (- x1)))

C

double code(double x1, double x2) {
	double tmp;
	if ((x2 <= -2.3e-149) || !(x2 <= 8e-99)) {
		tmp = x1 + (x2 * -6.0);
	} else {
		tmp = -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 <= (-2.3d-149)) .or. (.not. (x2 <= 8d-99))) then
        tmp = x1 + (x2 * (-6.0d0))
    else
        tmp = -x1
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x2 <= -2.3e-149) || !(x2 <= 8e-99)) {
		tmp = x1 + (x2 * -6.0);
	} else {
		tmp = -x1;
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x2 <= -2.3e-149) or not (x2 <= 8e-99):
		tmp = x1 + (x2 * -6.0)
	else:
		tmp = -x1
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x2 <= -2.3e-149) || !(x2 <= 8e-99))
		tmp = Float64(x1 + Float64(x2 * -6.0));
	else
		tmp = Float64(-x1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x2 <= -2.3e-149) || ~((x2 <= 8e-99)))
		tmp = x1 + (x2 * -6.0);
	else
		tmp = -x1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x2, -2.3e-149], N[Not[LessEqual[x2, 8e-99]], $MachinePrecision]], N[(x1 + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision], (-x1)]

Derivation

1. Split input into 2 regimes

2. if x2 < -2.3e-149 or 8.0000000000000002e-99 < x2

   1. Initial program 69.4%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 58.7%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 65.4%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(-1 \cdot x1 + \left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right)\right)}\right) \]
   4. Step-by-step derivation

      1. +-commutative 65.4%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(\left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right) + -1 \cdot x1\right)}\right) \]

      2. neg-mul-1 65.4%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right) + \color{blue}{\left(-x1\right)}\right)\right) \]

      3. unsub-neg 65.4%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(\left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right) - x1\right)}\right) \]

      4. +-commutative 65.4%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\color{blue}{\left(\left(3 - -2 \cdot x2\right) \cdot {x1}^{2} + -2 \cdot x2\right)} - x1\right)\right) \]

      5. *-commutative 65.4%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\left(\color{blue}{{x1}^{2} \cdot \left(3 - -2 \cdot x2\right)} + -2 \cdot x2\right) - x1\right)\right) \]

      6. fma-def 65.4%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\color{blue}{\mathsf{fma}\left({x1}^{2}, 3 - -2 \cdot x2, -2 \cdot x2\right)} - x1\right)\right) \]

      7. unpow2 65.4%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(\color{blue}{x1 \cdot x1}, 3 - -2 \cdot x2, -2 \cdot x2\right) - x1\right)\right) \]

      8. cancel-sign-sub-inv 65.4%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, \color{blue}{3 + \left(--2\right) \cdot x2}, -2 \cdot x2\right) - x1\right)\right) \]

      9. metadata-eval 65.4%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, 3 + \color{blue}{2} \cdot x2, -2 \cdot x2\right) - x1\right)\right) \]

      10. *-commutative 65.4%

          \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, 3 + 2 \cdot x2, \color{blue}{x2 \cdot -2}\right) - x1\right)\right) \]

   5. Simplified 65.4%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(\mathsf{fma}\left(x1 \cdot x1, 3 + 2 \cdot x2, x2 \cdot -2\right) - x1\right)}\right) \]

   6. Taylor expanded in x1 around 0 28.8%

      \[\leadsto x1 + \color{blue}{-6 \cdot x2} \]
   7. Step-by-step derivation

      1. *-commutative 28.8%

         \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]

   8. Simplified 28.8%

      \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]

   if -2.3e-149 < x2 < 8.0000000000000002e-99

   1. Initial program 66.3%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 47.4%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 80.9%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(-1 \cdot x1 + \left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right)\right)}\right) \]
   4. Step-by-step derivation

      1. +-commutative 80.9%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(\left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right) + -1 \cdot x1\right)}\right) \]

      2. neg-mul-1 80.9%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right) + \color{blue}{\left(-x1\right)}\right)\right) \]

      3. unsub-neg 80.9%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(\left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right) - x1\right)}\right) \]

      4. +-commutative 80.9%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\color{blue}{\left(\left(3 - -2 \cdot x2\right) \cdot {x1}^{2} + -2 \cdot x2\right)} - x1\right)\right) \]

      5. *-commutative 80.9%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\left(\color{blue}{{x1}^{2} \cdot \left(3 - -2 \cdot x2\right)} + -2 \cdot x2\right) - x1\right)\right) \]

      6. fma-def 80.9%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\color{blue}{\mathsf{fma}\left({x1}^{2}, 3 - -2 \cdot x2, -2 \cdot x2\right)} - x1\right)\right) \]

      7. unpow2 80.9%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(\color{blue}{x1 \cdot x1}, 3 - -2 \cdot x2, -2 \cdot x2\right) - x1\right)\right) \]

      8. cancel-sign-sub-inv 80.9%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, \color{blue}{3 + \left(--2\right) \cdot x2}, -2 \cdot x2\right) - x1\right)\right) \]

      9. metadata-eval 80.9%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, 3 + \color{blue}{2} \cdot x2, -2 \cdot x2\right) - x1\right)\right) \]

      10. *-commutative 80.9%

          \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, 3 + 2 \cdot x2, \color{blue}{x2 \cdot -2}\right) - x1\right)\right) \]

   5. Simplified 80.9%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(\mathsf{fma}\left(x1 \cdot x1, 3 + 2 \cdot x2, x2 \cdot -2\right) - x1\right)}\right) \]

   6. Taylor expanded in x1 around 0 48.6%

      \[\leadsto x1 + \color{blue}{\left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right) + -6 \cdot x2\right)} \]

   7. Taylor expanded in x2 around 0 38.0%

      \[\leadsto \color{blue}{x1 + -2 \cdot x1} \]
   8. Step-by-step derivation

      1. distribute-rgt1-in 38.0%

         \[\leadsto \color{blue}{\left(-2 + 1\right) \cdot x1} \]

      2. metadata-eval 38.0%

         \[\leadsto \color{blue}{-1} \cdot x1 \]

      3. mul-1-neg 38.0%

         \[\leadsto \color{blue}{-x1} \]

   9. Simplified 38.0%

      \[\leadsto \color{blue}{-x1} \]
3. Recombined 2 regimes into one program.

4. Final simplification 31.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq -2.3 \cdot 10^{-149} \lor \neg \left(x2 \leq 8 \cdot 10^{-99}\right):\\ \;\;\;\;x1 + x2 \cdot -6\\ \mathbf{else}:\\ \;\;\;\;-x1\\ \end{array} \]

Alternative 22: 14.1% accurate, 63.5× 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 Float64(-x1)
end

MATLAB

function tmp = code(x1, x2)
	tmp = -x1;
end

Wolfram

code[x1_, x2_] := (-x1)

Derivation

1. Initial program 68.4%

   \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

2. Taylor expanded in x1 around 0 55.0%

   \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

3. Taylor expanded in x1 around 0 70.6%

   \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(-1 \cdot x1 + \left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right)\right)}\right) \]
4. Step-by-step derivation

   1. +-commutative 70.6%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(\left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right) + -1 \cdot x1\right)}\right) \]

   2. neg-mul-1 70.6%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right) + \color{blue}{\left(-x1\right)}\right)\right) \]

   3. unsub-neg 70.6%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(\left(-2 \cdot x2 + \left(3 - -2 \cdot x2\right) \cdot {x1}^{2}\right) - x1\right)}\right) \]

   4. +-commutative 70.6%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\color{blue}{\left(\left(3 - -2 \cdot x2\right) \cdot {x1}^{2} + -2 \cdot x2\right)} - x1\right)\right) \]

   5. *-commutative 70.6%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\left(\color{blue}{{x1}^{2} \cdot \left(3 - -2 \cdot x2\right)} + -2 \cdot x2\right) - x1\right)\right) \]

   6. fma-def 70.6%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\color{blue}{\mathsf{fma}\left({x1}^{2}, 3 - -2 \cdot x2, -2 \cdot x2\right)} - x1\right)\right) \]

   7. unpow2 70.6%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(\color{blue}{x1 \cdot x1}, 3 - -2 \cdot x2, -2 \cdot x2\right) - x1\right)\right) \]

   8. cancel-sign-sub-inv 70.6%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, \color{blue}{3 + \left(--2\right) \cdot x2}, -2 \cdot x2\right) - x1\right)\right) \]

   9. metadata-eval 70.6%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, 3 + \color{blue}{2} \cdot x2, -2 \cdot x2\right) - x1\right)\right) \]

   10. *-commutative 70.6%

       \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\mathsf{fma}\left(x1 \cdot x1, 3 + 2 \cdot x2, \color{blue}{x2 \cdot -2}\right) - x1\right)\right) \]

5. Simplified 70.6%

   \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(\mathsf{fma}\left(x1 \cdot x1, 3 + 2 \cdot x2, x2 \cdot -2\right) - x1\right)}\right) \]

6. Taylor expanded in x1 around 0 54.2%

   \[\leadsto x1 + \color{blue}{\left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right) + -6 \cdot x2\right)} \]

7. Taylor expanded in x2 around 0 15.6%

   \[\leadsto \color{blue}{x1 + -2 \cdot x1} \]
8. Step-by-step derivation

   1. distribute-rgt1-in 15.6%

      \[\leadsto \color{blue}{\left(-2 + 1\right) \cdot x1} \]

   2. metadata-eval 15.6%

      \[\leadsto \color{blue}{-1} \cdot x1 \]

   3. mul-1-neg 15.6%

      \[\leadsto \color{blue}{-x1} \]

9. Simplified 15.6%

   \[\leadsto \color{blue}{-x1} \]

10. Final simplification 15.6%

    \[\leadsto -x1 \]

Reproduce

herbie shell --seed 2023224 
(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))))))