Rosa's FloatVsDoubleBenchmark

Percentage Accurate: 70.1% → 99.5%

Time: 43.6s

Alternatives: 27

Speedup: 4.7×

• 47.4% 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: 70.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.5% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * x1) + 1.0)
	t_1 = fma(x1, Float64(x1 * 3.0), fma(2.0, x2, Float64(-x1)))
	t_2 = Float64(x1 * Float64(x1 * 3.0))
	t_3 = Float64(t_2 + Float64(2.0 * x2))
	t_4 = Float64(Float64(x1 - t_3) / t_0)
	tmp = 0.0
	if (Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_2 - Float64(2.0 * x2)) - x1) / t_0)) - Float64(Float64(Float64(Float64(t_2 * t_4) + Float64(t_0 * Float64(Float64(Float64(Float64(Float64(t_3 - x1) / t_0) - 3.0) * Float64(Float64(x1 * 2.0) * t_4)) + Float64(Float64(x1 * x1) * Float64(6.0 + Float64(4.0 * t_4)))))) - Float64(x1 * Float64(x1 * x1))) - x1))) <= Inf)
		tmp = Float64(x1 + fma(3.0, Float64(Float64(t_2 - fma(2.0, x2, x1)) / fma(x1, x1, 1.0)), fma(x1, Float64(x1 * Float64(t_1 / 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_1 / fma(x1, x1, 1.0)) * Float64(Float64(x1 * Float64(-6.0 + Float64(t_1 / 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))) + 9.0));
	end
	return tmp
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * 3.0), $MachinePrecision] + N[(2.0 * x2 + (-x1)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(x1 - t$95$3), $MachinePrecision] / t$95$0), $MachinePrecision]}, If[LessEqual[N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$2 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(N[(t$95$2 * t$95$4), $MachinePrecision] + N[(t$95$0 * N[(N[(N[(N[(N[(t$95$3 - x1), $MachinePrecision] / t$95$0), $MachinePrecision] - 3.0), $MachinePrecision] * N[(N[(x1 * 2.0), $MachinePrecision] * t$95$4), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 + N[(4.0 * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(x1 + N[(3.0 * N[(N[(t$95$2 - N[(2.0 * x2 + x1), $MachinePrecision]), $MachinePrecision] / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(x1 * N[(t$95$1 / 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$1 / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision] * N[(N[(x1 * N[(-6.0 + N[(t$95$1 / 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] + 9.0), $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 99.8%

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

   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 14.1%

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

      1. *-commutative 14.1%

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

   4. Simplified 14.1%

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

   5. Taylor expanded in x1 around inf 100.0%

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

4. Final simplification 99.9%

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

Alternative 2: 99.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := t_1 + 2 \cdot x2\\ t_3 := \frac{x1 - t_2}{t_0}\\ t_4 := t_0 \cdot \left(\left(\frac{t_2 - x1}{t_0} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot t_3\right) + \left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot t_3\right)\right)\\ t_5 := x1 \cdot \left(x1 \cdot x1\right)\\ \mathbf{if}\;x1 + \left(3 \cdot \frac{\left(t_1 - 2 \cdot x2\right) - x1}{t_0} - \left(\left(\left(t_1 \cdot t_3 + t_4\right) - t_5\right) - x1\right)\right) \leq \infty:\\ \;\;\;\;x1 + \left(\left(x1 + \left(t_5 + \left(x1 \cdot \left(x1 \cdot 9\right) - t_4\right)\right)\right) + \left(x1 \cdot -3 + x2 \cdot -6\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 + 6 \cdot {x1}^{4}\right) + 9\right)\\ \end{array} \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (+.f64 x1 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 (+.f64 (*.f64 (*.f64 (*.f64 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 98.9%

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

   3. Taylor expanded in x1 around 0 99.4%

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

   4. Taylor expanded in x1 around 0 99.4%

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

      1. unpow2 99.4%

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

      2. *-commutative 99.4%

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

      3. associate-*l* 99.4%

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

   6. Simplified 99.4%

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

   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 14.1%

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

      1. *-commutative 14.1%

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

   4. Simplified 14.1%

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

   5. Taylor expanded in x1 around inf 100.0%

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

4. Final simplification 99.6%

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

Alternative 3: 93.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 9\right)\\ t_1 := x1 \cdot x1 + 1\\ t_2 := x1 \cdot -3 + x2 \cdot -6\\ t_3 := x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\\ t_4 := x1 \cdot \left(x1 \cdot x1\right)\\ t_5 := \frac{x1 - t_3}{t_1}\\ \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(x2 \cdot \left(x1 \cdot -12 - 6\right) + \frac{x1 \cdot \left(x1 - x1 \cdot 9\right)}{x1 + x1 \cdot 3}\right)\\ \mathbf{elif}\;x1 \leq 6 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(t_4 + \left(t_0 - t_1 \cdot \left(\left(\frac{t_3 - x1}{t_1} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot t_5\right) + \left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot t_5\right)\right)\right)\right)\right) + t_2\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(t_2 - \left(\left(\left(\left(x1 \cdot \left(x1 \cdot 6\right)\right) \cdot \left(-1 - x1 \cdot x1\right) - t_0\right) - t_4\right) - x1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 9.0)))
        (t_1 (+ (* x1 x1) 1.0))
        (t_2 (+ (* x1 -3.0) (* x2 -6.0)))
        (t_3 (+ (* x1 (* x1 3.0)) (* 2.0 x2)))
        (t_4 (* x1 (* x1 x1)))
        (t_5 (/ (- x1 t_3) t_1)))
   (if (<= x1 -5.6e+102)
     (+
      x1
      (+
       (* x2 (- (* x1 -12.0) 6.0))
       (/ (* x1 (- x1 (* x1 9.0))) (+ x1 (* x1 3.0)))))
     (if (<= x1 6e+102)
       (+
        x1
        (+
         (+
          x1
          (+
           t_4
           (-
            t_0
            (*
             t_1
             (+
              (* (- (/ (- t_3 x1) t_1) 3.0) (* (* x1 2.0) t_5))
              (* (* x1 x1) (+ 6.0 (* 4.0 t_5))))))))
         t_2))
       (+
        x1
        (-
         t_2
         (- (- (- (* (* x1 (* x1 6.0)) (- -1.0 (* x1 x1))) t_0) t_4) x1)))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 9.0);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = (x1 * -3.0) + (x2 * -6.0);
	double t_3 = (x1 * (x1 * 3.0)) + (2.0 * x2);
	double t_4 = x1 * (x1 * x1);
	double t_5 = (x1 - t_3) / t_1;
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = x1 + ((x2 * ((x1 * -12.0) - 6.0)) + ((x1 * (x1 - (x1 * 9.0))) / (x1 + (x1 * 3.0))));
	} else if (x1 <= 6e+102) {
		tmp = x1 + ((x1 + (t_4 + (t_0 - (t_1 * (((((t_3 - x1) / t_1) - 3.0) * ((x1 * 2.0) * t_5)) + ((x1 * x1) * (6.0 + (4.0 * t_5)))))))) + t_2);
	} else {
		tmp = x1 + (t_2 - (((((x1 * (x1 * 6.0)) * (-1.0 - (x1 * x1))) - t_0) - t_4) - 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) :: 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 * 9.0d0)
    t_1 = (x1 * x1) + 1.0d0
    t_2 = (x1 * (-3.0d0)) + (x2 * (-6.0d0))
    t_3 = (x1 * (x1 * 3.0d0)) + (2.0d0 * x2)
    t_4 = x1 * (x1 * x1)
    t_5 = (x1 - t_3) / t_1
    if (x1 <= (-5.6d+102)) then
        tmp = x1 + ((x2 * ((x1 * (-12.0d0)) - 6.0d0)) + ((x1 * (x1 - (x1 * 9.0d0))) / (x1 + (x1 * 3.0d0))))
    else if (x1 <= 6d+102) then
        tmp = x1 + ((x1 + (t_4 + (t_0 - (t_1 * (((((t_3 - x1) / t_1) - 3.0d0) * ((x1 * 2.0d0) * t_5)) + ((x1 * x1) * (6.0d0 + (4.0d0 * t_5)))))))) + t_2)
    else
        tmp = x1 + (t_2 - (((((x1 * (x1 * 6.0d0)) * ((-1.0d0) - (x1 * x1))) - t_0) - t_4) - x1))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 9.0);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = (x1 * -3.0) + (x2 * -6.0);
	double t_3 = (x1 * (x1 * 3.0)) + (2.0 * x2);
	double t_4 = x1 * (x1 * x1);
	double t_5 = (x1 - t_3) / t_1;
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = x1 + ((x2 * ((x1 * -12.0) - 6.0)) + ((x1 * (x1 - (x1 * 9.0))) / (x1 + (x1 * 3.0))));
	} else if (x1 <= 6e+102) {
		tmp = x1 + ((x1 + (t_4 + (t_0 - (t_1 * (((((t_3 - x1) / t_1) - 3.0) * ((x1 * 2.0) * t_5)) + ((x1 * x1) * (6.0 + (4.0 * t_5)))))))) + t_2);
	} else {
		tmp = x1 + (t_2 - (((((x1 * (x1 * 6.0)) * (-1.0 - (x1 * x1))) - t_0) - t_4) - x1));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 9.0)
	t_1 = (x1 * x1) + 1.0
	t_2 = (x1 * -3.0) + (x2 * -6.0)
	t_3 = (x1 * (x1 * 3.0)) + (2.0 * x2)
	t_4 = x1 * (x1 * x1)
	t_5 = (x1 - t_3) / t_1
	tmp = 0
	if x1 <= -5.6e+102:
		tmp = x1 + ((x2 * ((x1 * -12.0) - 6.0)) + ((x1 * (x1 - (x1 * 9.0))) / (x1 + (x1 * 3.0))))
	elif x1 <= 6e+102:
		tmp = x1 + ((x1 + (t_4 + (t_0 - (t_1 * (((((t_3 - x1) / t_1) - 3.0) * ((x1 * 2.0) * t_5)) + ((x1 * x1) * (6.0 + (4.0 * t_5)))))))) + t_2)
	else:
		tmp = x1 + (t_2 - (((((x1 * (x1 * 6.0)) * (-1.0 - (x1 * x1))) - t_0) - t_4) - x1))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 9.0))
	t_1 = Float64(Float64(x1 * x1) + 1.0)
	t_2 = Float64(Float64(x1 * -3.0) + Float64(x2 * -6.0))
	t_3 = Float64(Float64(x1 * Float64(x1 * 3.0)) + Float64(2.0 * x2))
	t_4 = Float64(x1 * Float64(x1 * x1))
	t_5 = Float64(Float64(x1 - t_3) / t_1)
	tmp = 0.0
	if (x1 <= -5.6e+102)
		tmp = Float64(x1 + Float64(Float64(x2 * Float64(Float64(x1 * -12.0) - 6.0)) + Float64(Float64(x1 * Float64(x1 - Float64(x1 * 9.0))) / Float64(x1 + Float64(x1 * 3.0)))));
	elseif (x1 <= 6e+102)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(t_4 + Float64(t_0 - Float64(t_1 * Float64(Float64(Float64(Float64(Float64(t_3 - x1) / t_1) - 3.0) * Float64(Float64(x1 * 2.0) * t_5)) + Float64(Float64(x1 * x1) * Float64(6.0 + Float64(4.0 * t_5)))))))) + t_2));
	else
		tmp = Float64(x1 + Float64(t_2 - Float64(Float64(Float64(Float64(Float64(x1 * Float64(x1 * 6.0)) * Float64(-1.0 - Float64(x1 * x1))) - t_0) - t_4) - x1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * 9.0);
	t_1 = (x1 * x1) + 1.0;
	t_2 = (x1 * -3.0) + (x2 * -6.0);
	t_3 = (x1 * (x1 * 3.0)) + (2.0 * x2);
	t_4 = x1 * (x1 * x1);
	t_5 = (x1 - t_3) / t_1;
	tmp = 0.0;
	if (x1 <= -5.6e+102)
		tmp = x1 + ((x2 * ((x1 * -12.0) - 6.0)) + ((x1 * (x1 - (x1 * 9.0))) / (x1 + (x1 * 3.0))));
	elseif (x1 <= 6e+102)
		tmp = x1 + ((x1 + (t_4 + (t_0 - (t_1 * (((((t_3 - x1) / t_1) - 3.0) * ((x1 * 2.0) * t_5)) + ((x1 * x1) * (6.0 + (4.0 * t_5)))))))) + t_2);
	else
		tmp = x1 + (t_2 - (((((x1 * (x1 * 6.0)) * (-1.0 - (x1 * x1))) - t_0) - t_4) - x1));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x1 * -3.0), $MachinePrecision] + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision] + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(x1 - t$95$3), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[x1, -5.6e+102], N[(x1 + N[(N[(x2 * N[(N[(x1 * -12.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * N[(x1 - N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x1 + N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 6e+102], N[(x1 + N[(N[(x1 + N[(t$95$4 + N[(t$95$0 - N[(t$95$1 * N[(N[(N[(N[(N[(t$95$3 - x1), $MachinePrecision] / t$95$1), $MachinePrecision] - 3.0), $MachinePrecision] * N[(N[(x1 * 2.0), $MachinePrecision] * t$95$5), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 + N[(4.0 * t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(t$95$2 - N[(N[(N[(N[(N[(x1 * N[(x1 * 6.0), $MachinePrecision]), $MachinePrecision] * N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$0), $MachinePrecision] - t$95$4), $MachinePrecision] - x1), $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 0.1%

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

   3. Taylor expanded in x1 around 0 3.5%

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

      1. +-commutative 3.5%

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

      2. *-commutative 3.5%

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

      3. fma-def 3.5%

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

      4. *-commutative 3.5%

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

   5. Simplified 3.5%

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

   6. Taylor expanded in x2 around 0 20.3%

      \[\leadsto x1 + \color{blue}{\left(x2 \cdot \left(-12 \cdot x1 - 6\right) + \left(x1 + -3 \cdot x1\right)\right)} \]
   7. Step-by-step derivation

      1. flip-+ 5.4%

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

      2. *-commutative 5.4%

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

      3. *-commutative 5.4%

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

      4. *-commutative 5.4%

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

   8. Applied egg-rr 5.4%

      \[\leadsto x1 + \left(x2 \cdot \left(-12 \cdot x1 - 6\right) + \color{blue}{\frac{x1 \cdot x1 - \left(x1 \cdot -3\right) \cdot \left(x1 \cdot -3\right)}{x1 - x1 \cdot -3}}\right) \]
   9. Step-by-step derivation

      1. swap-sqr 5.4%

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

      2. metadata-eval 5.4%

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

      3. associate-*r* 5.4%

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

      4. distribute-lft-out-- 69.7%

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

      5. *-commutative 69.7%

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

      6. cancel-sign-sub-inv 69.7%

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

      7. metadata-eval 69.7%

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

      8. *-commutative 69.7%

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

   10. Simplified 69.7%

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

   if -5.60000000000000037e102 < x1 < 5.9999999999999996e102

   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 98.8%

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

   3. Taylor expanded in x1 around 0 99.4%

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

   4. Taylor expanded in x1 around 0 99.4%

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

      1. unpow2 99.4%

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

      2. *-commutative 99.4%

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

      3. associate-*l* 99.4%

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

   6. Simplified 99.4%

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

   if 5.9999999999999996e102 < x1

   1. Initial program 21.6%

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

   2. Taylor expanded in x1 around inf 21.6%

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

   3. Taylor expanded in x1 around 0 21.6%

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

   4. Taylor expanded in x1 around 0 21.6%

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

      1. unpow2 21.6%

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

      2. *-commutative 21.6%

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

      3. associate-*l* 21.6%

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

   6. Simplified 21.6%

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

   7. Taylor expanded in x1 around inf 100.0%

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

      1. *-commutative 100.0%

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

      2. unpow2 100.0%

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

      3. associate-*l* 100.0%

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

   9. Simplified 100.0%

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

4. Final simplification 94.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(x2 \cdot \left(x1 \cdot -12 - 6\right) + \frac{x1 \cdot \left(x1 - x1 \cdot 9\right)}{x1 + x1 \cdot 3}\right)\\ \mathbf{elif}\;x1 \leq 6 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(x1 \cdot \left(x1 \cdot 9\right) - \left(x1 \cdot x1 + 1\right) \cdot \left(\left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right)\right)\right)\right)\right) + \left(x1 \cdot -3 + x2 \cdot -6\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 \cdot -3 + x2 \cdot -6\right) - \left(\left(\left(\left(x1 \cdot \left(x1 \cdot 6\right)\right) \cdot \left(-1 - x1 \cdot x1\right) - x1 \cdot \left(x1 \cdot 9\right)\right) - x1 \cdot \left(x1 \cdot x1\right)\right) - x1\right)\right)\\ \end{array} \]

Alternative 4: 92.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := t_0 + 2 \cdot x2\\ t_2 := x1 \cdot \left(x1 \cdot x1\right)\\ t_3 := x1 \cdot \left(x1 \cdot 9\right)\\ t_4 := x1 \cdot x1 + 1\\ t_5 := \frac{x1 - t_1}{t_4}\\ t_6 := x1 \cdot -3 + x2 \cdot -6\\ t_7 := \left(x1 \cdot 2\right) \cdot t_5\\ \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(x2 \cdot \left(x1 \cdot -12 - 6\right) + \frac{x1 \cdot \left(x1 - x1 \cdot 9\right)}{x1 + x1 \cdot 3}\right)\\ \mathbf{elif}\;x1 \leq 0.6:\\ \;\;\;\;x1 + \left(t_6 + \left(x1 + \left(t_2 + \left(t_3 + t_4 \cdot \left(t_7 \cdot \left(3 + t_5\right) + \left(x1 \cdot x1\right) \cdot 6\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(t_2 - \left(t_4 \cdot \left(\left(\frac{t_1 - x1}{t_4} - 3\right) \cdot t_7 + \left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot t_5\right)\right) - 3 \cdot t_0\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(t_6 - \left(\left(\left(\left(x1 \cdot \left(x1 \cdot 6\right)\right) \cdot \left(-1 - x1 \cdot x1\right) - t_3\right) - t_2\right) - x1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (+ t_0 (* 2.0 x2)))
        (t_2 (* x1 (* x1 x1)))
        (t_3 (* x1 (* x1 9.0)))
        (t_4 (+ (* x1 x1) 1.0))
        (t_5 (/ (- x1 t_1) t_4))
        (t_6 (+ (* x1 -3.0) (* x2 -6.0)))
        (t_7 (* (* x1 2.0) t_5)))
   (if (<= x1 -5.6e+102)
     (+
      x1
      (+
       (* x2 (- (* x1 -12.0) 6.0))
       (/ (* x1 (- x1 (* x1 9.0))) (+ x1 (* x1 3.0)))))
     (if (<= x1 0.6)
       (+
        x1
        (+
         t_6
         (+
          x1
          (+ t_2 (+ t_3 (* t_4 (+ (* t_7 (+ 3.0 t_5)) (* (* x1 x1) 6.0))))))))
       (if (<= x1 2e+102)
         (+
          x1
          (+
           9.0
           (+
            x1
            (-
             t_2
             (-
              (*
               t_4
               (+
                (* (- (/ (- t_1 x1) t_4) 3.0) t_7)
                (* (* x1 x1) (+ 6.0 (* 4.0 t_5)))))
              (* 3.0 t_0))))))
         (+
          x1
          (-
           t_6
           (-
            (- (- (* (* x1 (* x1 6.0)) (- -1.0 (* x1 x1))) t_3) t_2)
            x1))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = t_0 + (2.0 * x2);
	double t_2 = x1 * (x1 * x1);
	double t_3 = x1 * (x1 * 9.0);
	double t_4 = (x1 * x1) + 1.0;
	double t_5 = (x1 - t_1) / t_4;
	double t_6 = (x1 * -3.0) + (x2 * -6.0);
	double t_7 = (x1 * 2.0) * t_5;
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = x1 + ((x2 * ((x1 * -12.0) - 6.0)) + ((x1 * (x1 - (x1 * 9.0))) / (x1 + (x1 * 3.0))));
	} else if (x1 <= 0.6) {
		tmp = x1 + (t_6 + (x1 + (t_2 + (t_3 + (t_4 * ((t_7 * (3.0 + t_5)) + ((x1 * x1) * 6.0)))))));
	} else if (x1 <= 2e+102) {
		tmp = x1 + (9.0 + (x1 + (t_2 - ((t_4 * (((((t_1 - x1) / t_4) - 3.0) * t_7) + ((x1 * x1) * (6.0 + (4.0 * t_5))))) - (3.0 * t_0)))));
	} else {
		tmp = x1 + (t_6 - (((((x1 * (x1 * 6.0)) * (-1.0 - (x1 * x1))) - t_3) - t_2) - 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) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: tmp
    t_0 = x1 * (x1 * 3.0d0)
    t_1 = t_0 + (2.0d0 * x2)
    t_2 = x1 * (x1 * x1)
    t_3 = x1 * (x1 * 9.0d0)
    t_4 = (x1 * x1) + 1.0d0
    t_5 = (x1 - t_1) / t_4
    t_6 = (x1 * (-3.0d0)) + (x2 * (-6.0d0))
    t_7 = (x1 * 2.0d0) * t_5
    if (x1 <= (-5.6d+102)) then
        tmp = x1 + ((x2 * ((x1 * (-12.0d0)) - 6.0d0)) + ((x1 * (x1 - (x1 * 9.0d0))) / (x1 + (x1 * 3.0d0))))
    else if (x1 <= 0.6d0) then
        tmp = x1 + (t_6 + (x1 + (t_2 + (t_3 + (t_4 * ((t_7 * (3.0d0 + t_5)) + ((x1 * x1) * 6.0d0)))))))
    else if (x1 <= 2d+102) then
        tmp = x1 + (9.0d0 + (x1 + (t_2 - ((t_4 * (((((t_1 - x1) / t_4) - 3.0d0) * t_7) + ((x1 * x1) * (6.0d0 + (4.0d0 * t_5))))) - (3.0d0 * t_0)))))
    else
        tmp = x1 + (t_6 - (((((x1 * (x1 * 6.0d0)) * ((-1.0d0) - (x1 * x1))) - t_3) - t_2) - x1))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = t_0 + (2.0 * x2);
	double t_2 = x1 * (x1 * x1);
	double t_3 = x1 * (x1 * 9.0);
	double t_4 = (x1 * x1) + 1.0;
	double t_5 = (x1 - t_1) / t_4;
	double t_6 = (x1 * -3.0) + (x2 * -6.0);
	double t_7 = (x1 * 2.0) * t_5;
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = x1 + ((x2 * ((x1 * -12.0) - 6.0)) + ((x1 * (x1 - (x1 * 9.0))) / (x1 + (x1 * 3.0))));
	} else if (x1 <= 0.6) {
		tmp = x1 + (t_6 + (x1 + (t_2 + (t_3 + (t_4 * ((t_7 * (3.0 + t_5)) + ((x1 * x1) * 6.0)))))));
	} else if (x1 <= 2e+102) {
		tmp = x1 + (9.0 + (x1 + (t_2 - ((t_4 * (((((t_1 - x1) / t_4) - 3.0) * t_7) + ((x1 * x1) * (6.0 + (4.0 * t_5))))) - (3.0 * t_0)))));
	} else {
		tmp = x1 + (t_6 - (((((x1 * (x1 * 6.0)) * (-1.0 - (x1 * x1))) - t_3) - t_2) - x1));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = t_0 + (2.0 * x2)
	t_2 = x1 * (x1 * x1)
	t_3 = x1 * (x1 * 9.0)
	t_4 = (x1 * x1) + 1.0
	t_5 = (x1 - t_1) / t_4
	t_6 = (x1 * -3.0) + (x2 * -6.0)
	t_7 = (x1 * 2.0) * t_5
	tmp = 0
	if x1 <= -5.6e+102:
		tmp = x1 + ((x2 * ((x1 * -12.0) - 6.0)) + ((x1 * (x1 - (x1 * 9.0))) / (x1 + (x1 * 3.0))))
	elif x1 <= 0.6:
		tmp = x1 + (t_6 + (x1 + (t_2 + (t_3 + (t_4 * ((t_7 * (3.0 + t_5)) + ((x1 * x1) * 6.0)))))))
	elif x1 <= 2e+102:
		tmp = x1 + (9.0 + (x1 + (t_2 - ((t_4 * (((((t_1 - x1) / t_4) - 3.0) * t_7) + ((x1 * x1) * (6.0 + (4.0 * t_5))))) - (3.0 * t_0)))))
	else:
		tmp = x1 + (t_6 - (((((x1 * (x1 * 6.0)) * (-1.0 - (x1 * x1))) - t_3) - t_2) - x1))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(t_0 + Float64(2.0 * x2))
	t_2 = Float64(x1 * Float64(x1 * x1))
	t_3 = Float64(x1 * Float64(x1 * 9.0))
	t_4 = Float64(Float64(x1 * x1) + 1.0)
	t_5 = Float64(Float64(x1 - t_1) / t_4)
	t_6 = Float64(Float64(x1 * -3.0) + Float64(x2 * -6.0))
	t_7 = Float64(Float64(x1 * 2.0) * t_5)
	tmp = 0.0
	if (x1 <= -5.6e+102)
		tmp = Float64(x1 + Float64(Float64(x2 * Float64(Float64(x1 * -12.0) - 6.0)) + Float64(Float64(x1 * Float64(x1 - Float64(x1 * 9.0))) / Float64(x1 + Float64(x1 * 3.0)))));
	elseif (x1 <= 0.6)
		tmp = Float64(x1 + Float64(t_6 + Float64(x1 + Float64(t_2 + Float64(t_3 + Float64(t_4 * Float64(Float64(t_7 * Float64(3.0 + t_5)) + Float64(Float64(x1 * x1) * 6.0))))))));
	elseif (x1 <= 2e+102)
		tmp = Float64(x1 + Float64(9.0 + Float64(x1 + Float64(t_2 - Float64(Float64(t_4 * Float64(Float64(Float64(Float64(Float64(t_1 - x1) / t_4) - 3.0) * t_7) + Float64(Float64(x1 * x1) * Float64(6.0 + Float64(4.0 * t_5))))) - Float64(3.0 * t_0))))));
	else
		tmp = Float64(x1 + Float64(t_6 - Float64(Float64(Float64(Float64(Float64(x1 * Float64(x1 * 6.0)) * Float64(-1.0 - Float64(x1 * x1))) - t_3) - t_2) - x1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * 3.0);
	t_1 = t_0 + (2.0 * x2);
	t_2 = x1 * (x1 * x1);
	t_3 = x1 * (x1 * 9.0);
	t_4 = (x1 * x1) + 1.0;
	t_5 = (x1 - t_1) / t_4;
	t_6 = (x1 * -3.0) + (x2 * -6.0);
	t_7 = (x1 * 2.0) * t_5;
	tmp = 0.0;
	if (x1 <= -5.6e+102)
		tmp = x1 + ((x2 * ((x1 * -12.0) - 6.0)) + ((x1 * (x1 - (x1 * 9.0))) / (x1 + (x1 * 3.0))));
	elseif (x1 <= 0.6)
		tmp = x1 + (t_6 + (x1 + (t_2 + (t_3 + (t_4 * ((t_7 * (3.0 + t_5)) + ((x1 * x1) * 6.0)))))));
	elseif (x1 <= 2e+102)
		tmp = x1 + (9.0 + (x1 + (t_2 - ((t_4 * (((((t_1 - x1) / t_4) - 3.0) * t_7) + ((x1 * x1) * (6.0 + (4.0 * t_5))))) - (3.0 * t_0)))));
	else
		tmp = x1 + (t_6 - (((((x1 * (x1 * 6.0)) * (-1.0 - (x1 * x1))) - t_3) - t_2) - x1));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x1 * N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$5 = N[(N[(x1 - t$95$1), $MachinePrecision] / t$95$4), $MachinePrecision]}, Block[{t$95$6 = N[(N[(x1 * -3.0), $MachinePrecision] + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(N[(x1 * 2.0), $MachinePrecision] * t$95$5), $MachinePrecision]}, If[LessEqual[x1, -5.6e+102], N[(x1 + N[(N[(x2 * N[(N[(x1 * -12.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * N[(x1 - N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x1 + N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 0.6], N[(x1 + N[(t$95$6 + N[(x1 + N[(t$95$2 + N[(t$95$3 + N[(t$95$4 * N[(N[(t$95$7 * N[(3.0 + t$95$5), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 2e+102], N[(x1 + N[(9.0 + N[(x1 + N[(t$95$2 - N[(N[(t$95$4 * N[(N[(N[(N[(N[(t$95$1 - x1), $MachinePrecision] / t$95$4), $MachinePrecision] - 3.0), $MachinePrecision] * t$95$7), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 + N[(4.0 * t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(3.0 * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(t$95$6 - N[(N[(N[(N[(N[(x1 * N[(x1 * 6.0), $MachinePrecision]), $MachinePrecision] * N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$3), $MachinePrecision] - t$95$2), $MachinePrecision] - x1), $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 0.1%

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

   3. Taylor expanded in x1 around 0 3.5%

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

      1. +-commutative 3.5%

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

      2. *-commutative 3.5%

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

      3. fma-def 3.5%

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

      4. *-commutative 3.5%

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

   5. Simplified 3.5%

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

   6. Taylor expanded in x2 around 0 20.3%

      \[\leadsto x1 + \color{blue}{\left(x2 \cdot \left(-12 \cdot x1 - 6\right) + \left(x1 + -3 \cdot x1\right)\right)} \]
   7. Step-by-step derivation

      1. flip-+ 5.4%

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

      2. *-commutative 5.4%

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

      3. *-commutative 5.4%

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

      4. *-commutative 5.4%

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

   8. Applied egg-rr 5.4%

      \[\leadsto x1 + \left(x2 \cdot \left(-12 \cdot x1 - 6\right) + \color{blue}{\frac{x1 \cdot x1 - \left(x1 \cdot -3\right) \cdot \left(x1 \cdot -3\right)}{x1 - x1 \cdot -3}}\right) \]
   9. Step-by-step derivation

      1. swap-sqr 5.4%

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

      2. metadata-eval 5.4%

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

      3. associate-*r* 5.4%

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

      4. distribute-lft-out-- 69.7%

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

      5. *-commutative 69.7%

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

      6. cancel-sign-sub-inv 69.7%

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

      7. metadata-eval 69.7%

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

      8. *-commutative 69.7%

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

   10. Simplified 69.7%

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

   if -5.60000000000000037e102 < x1 < 0.599999999999999978

   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 99.0%

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

   3. Taylor expanded in x1 around 0 99.4%

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

   4. Taylor expanded in x1 around 0 99.4%

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

      1. unpow2 99.4%

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

      2. *-commutative 99.4%

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

      3. associate-*l* 99.4%

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

   6. Simplified 99.4%

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

   7. Taylor expanded in x1 around inf 99.0%

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

      1. *-commutative 99.0%

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

      2. unpow2 99.0%

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

   9. Simplified 99.0%

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

   if 0.599999999999999978 < x1 < 1.99999999999999995e102

   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 98.0%

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

   3. Taylor expanded in x1 around inf 98.0%

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

   if 1.99999999999999995e102 < x1

   1. Initial program 21.6%

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

   2. Taylor expanded in x1 around inf 21.6%

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

   3. Taylor expanded in x1 around 0 21.6%

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

   4. Taylor expanded in x1 around 0 21.6%

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

      1. unpow2 21.6%

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

      2. *-commutative 21.6%

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

      3. associate-*l* 21.6%

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

   6. Simplified 21.6%

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

   7. Taylor expanded in x1 around inf 100.0%

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

      1. *-commutative 100.0%

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

      2. unpow2 100.0%

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

      3. associate-*l* 100.0%

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

   9. Simplified 100.0%

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

4. Final simplification 94.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(x2 \cdot \left(x1 \cdot -12 - 6\right) + \frac{x1 \cdot \left(x1 - x1 \cdot 9\right)}{x1 + x1 \cdot 3}\right)\\ \mathbf{elif}\;x1 \leq 0.6:\\ \;\;\;\;x1 + \left(\left(x1 \cdot -3 + x2 \cdot -6\right) + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(x1 \cdot \left(x1 \cdot 9\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right) \cdot \left(3 + \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot 6\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) - \left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right)\right) - 3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 \cdot -3 + x2 \cdot -6\right) - \left(\left(\left(\left(x1 \cdot \left(x1 \cdot 6\right)\right) \cdot \left(-1 - x1 \cdot x1\right) - x1 \cdot \left(x1 \cdot 9\right)\right) - x1 \cdot \left(x1 \cdot x1\right)\right) - x1\right)\right)\\ \end{array} \]

Alternative 5: 91.0% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot x1\right)\\ t_1 := x1 \cdot \left(x1 \cdot 9\right)\\ t_2 := x1 \cdot x1 + 1\\ t_3 := x1 \cdot -3 + x2 \cdot -6\\ t_4 := \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{t_2}\\ \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(x2 \cdot \left(x1 \cdot -12 - 6\right) + \frac{x1 \cdot \left(x1 - x1 \cdot 9\right)}{x1 + x1 \cdot 3}\right)\\ \mathbf{elif}\;x1 \leq 5.8 \cdot 10^{+49}:\\ \;\;\;\;x1 + \left(t_3 + \left(x1 + \left(t_0 + \left(t_1 + t_2 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t_4\right) \cdot \left(3 + t_4\right) + \left(x1 \cdot x1\right) \cdot 6\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(t_3 - \left(\left(\left(\left(x1 \cdot \left(x1 \cdot 6\right)\right) \cdot \left(-1 - x1 \cdot x1\right) - t_1\right) - t_0\right) - x1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 x1)))
        (t_1 (* x1 (* x1 9.0)))
        (t_2 (+ (* x1 x1) 1.0))
        (t_3 (+ (* x1 -3.0) (* x2 -6.0)))
        (t_4 (/ (- x1 (+ (* x1 (* x1 3.0)) (* 2.0 x2))) t_2)))
   (if (<= x1 -5.6e+102)
     (+
      x1
      (+
       (* x2 (- (* x1 -12.0) 6.0))
       (/ (* x1 (- x1 (* x1 9.0))) (+ x1 (* x1 3.0)))))
     (if (<= x1 5.8e+49)
       (+
        x1
        (+
         t_3
         (+
          x1
          (+
           t_0
           (+
            t_1
            (*
             t_2
             (+ (* (* (* x1 2.0) t_4) (+ 3.0 t_4)) (* (* x1 x1) 6.0))))))))
       (+
        x1
        (-
         t_3
         (- (- (- (* (* x1 (* x1 6.0)) (- -1.0 (* x1 x1))) t_1) t_0) x1)))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * x1);
	double t_1 = x1 * (x1 * 9.0);
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = (x1 * -3.0) + (x2 * -6.0);
	double t_4 = (x1 - ((x1 * (x1 * 3.0)) + (2.0 * x2))) / t_2;
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = x1 + ((x2 * ((x1 * -12.0) - 6.0)) + ((x1 * (x1 - (x1 * 9.0))) / (x1 + (x1 * 3.0))));
	} else if (x1 <= 5.8e+49) {
		tmp = x1 + (t_3 + (x1 + (t_0 + (t_1 + (t_2 * ((((x1 * 2.0) * t_4) * (3.0 + t_4)) + ((x1 * x1) * 6.0)))))));
	} else {
		tmp = x1 + (t_3 - (((((x1 * (x1 * 6.0)) * (-1.0 - (x1 * x1))) - t_1) - t_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) :: 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 * 9.0d0)
    t_2 = (x1 * x1) + 1.0d0
    t_3 = (x1 * (-3.0d0)) + (x2 * (-6.0d0))
    t_4 = (x1 - ((x1 * (x1 * 3.0d0)) + (2.0d0 * x2))) / t_2
    if (x1 <= (-5.6d+102)) then
        tmp = x1 + ((x2 * ((x1 * (-12.0d0)) - 6.0d0)) + ((x1 * (x1 - (x1 * 9.0d0))) / (x1 + (x1 * 3.0d0))))
    else if (x1 <= 5.8d+49) then
        tmp = x1 + (t_3 + (x1 + (t_0 + (t_1 + (t_2 * ((((x1 * 2.0d0) * t_4) * (3.0d0 + t_4)) + ((x1 * x1) * 6.0d0)))))))
    else
        tmp = x1 + (t_3 - (((((x1 * (x1 * 6.0d0)) * ((-1.0d0) - (x1 * x1))) - t_1) - t_0) - x1))
    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 * 9.0);
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = (x1 * -3.0) + (x2 * -6.0);
	double t_4 = (x1 - ((x1 * (x1 * 3.0)) + (2.0 * x2))) / t_2;
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = x1 + ((x2 * ((x1 * -12.0) - 6.0)) + ((x1 * (x1 - (x1 * 9.0))) / (x1 + (x1 * 3.0))));
	} else if (x1 <= 5.8e+49) {
		tmp = x1 + (t_3 + (x1 + (t_0 + (t_1 + (t_2 * ((((x1 * 2.0) * t_4) * (3.0 + t_4)) + ((x1 * x1) * 6.0)))))));
	} else {
		tmp = x1 + (t_3 - (((((x1 * (x1 * 6.0)) * (-1.0 - (x1 * x1))) - t_1) - t_0) - x1));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * x1)
	t_1 = x1 * (x1 * 9.0)
	t_2 = (x1 * x1) + 1.0
	t_3 = (x1 * -3.0) + (x2 * -6.0)
	t_4 = (x1 - ((x1 * (x1 * 3.0)) + (2.0 * x2))) / t_2
	tmp = 0
	if x1 <= -5.6e+102:
		tmp = x1 + ((x2 * ((x1 * -12.0) - 6.0)) + ((x1 * (x1 - (x1 * 9.0))) / (x1 + (x1 * 3.0))))
	elif x1 <= 5.8e+49:
		tmp = x1 + (t_3 + (x1 + (t_0 + (t_1 + (t_2 * ((((x1 * 2.0) * t_4) * (3.0 + t_4)) + ((x1 * x1) * 6.0)))))))
	else:
		tmp = x1 + (t_3 - (((((x1 * (x1 * 6.0)) * (-1.0 - (x1 * x1))) - t_1) - t_0) - x1))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * x1))
	t_1 = Float64(x1 * Float64(x1 * 9.0))
	t_2 = Float64(Float64(x1 * x1) + 1.0)
	t_3 = Float64(Float64(x1 * -3.0) + Float64(x2 * -6.0))
	t_4 = Float64(Float64(x1 - Float64(Float64(x1 * Float64(x1 * 3.0)) + Float64(2.0 * x2))) / t_2)
	tmp = 0.0
	if (x1 <= -5.6e+102)
		tmp = Float64(x1 + Float64(Float64(x2 * Float64(Float64(x1 * -12.0) - 6.0)) + Float64(Float64(x1 * Float64(x1 - Float64(x1 * 9.0))) / Float64(x1 + Float64(x1 * 3.0)))));
	elseif (x1 <= 5.8e+49)
		tmp = Float64(x1 + Float64(t_3 + Float64(x1 + Float64(t_0 + Float64(t_1 + Float64(t_2 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_4) * Float64(3.0 + t_4)) + Float64(Float64(x1 * x1) * 6.0))))))));
	else
		tmp = Float64(x1 + Float64(t_3 - Float64(Float64(Float64(Float64(Float64(x1 * Float64(x1 * 6.0)) * Float64(-1.0 - Float64(x1 * x1))) - t_1) - t_0) - x1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * x1);
	t_1 = x1 * (x1 * 9.0);
	t_2 = (x1 * x1) + 1.0;
	t_3 = (x1 * -3.0) + (x2 * -6.0);
	t_4 = (x1 - ((x1 * (x1 * 3.0)) + (2.0 * x2))) / t_2;
	tmp = 0.0;
	if (x1 <= -5.6e+102)
		tmp = x1 + ((x2 * ((x1 * -12.0) - 6.0)) + ((x1 * (x1 - (x1 * 9.0))) / (x1 + (x1 * 3.0))));
	elseif (x1 <= 5.8e+49)
		tmp = x1 + (t_3 + (x1 + (t_0 + (t_1 + (t_2 * ((((x1 * 2.0) * t_4) * (3.0 + t_4)) + ((x1 * x1) * 6.0)))))));
	else
		tmp = x1 + (t_3 - (((((x1 * (x1 * 6.0)) * (-1.0 - (x1 * x1))) - t_1) - t_0) - x1));
	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 * 9.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x1 * -3.0), $MachinePrecision] + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(x1 - N[(N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision] + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]}, If[LessEqual[x1, -5.6e+102], N[(x1 + N[(N[(x2 * N[(N[(x1 * -12.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * N[(x1 - N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x1 + N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 5.8e+49], N[(x1 + N[(t$95$3 + N[(x1 + N[(t$95$0 + N[(t$95$1 + N[(t$95$2 * N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$4), $MachinePrecision] * N[(3.0 + t$95$4), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(t$95$3 - N[(N[(N[(N[(N[(x1 * N[(x1 * 6.0), $MachinePrecision]), $MachinePrecision] * N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision] - t$95$0), $MachinePrecision] - x1), $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 0.1%

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

   3. Taylor expanded in x1 around 0 3.5%

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

      1. +-commutative 3.5%

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

      2. *-commutative 3.5%

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

      3. fma-def 3.5%

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

      4. *-commutative 3.5%

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

   5. Simplified 3.5%

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

   6. Taylor expanded in x2 around 0 20.3%

      \[\leadsto x1 + \color{blue}{\left(x2 \cdot \left(-12 \cdot x1 - 6\right) + \left(x1 + -3 \cdot x1\right)\right)} \]
   7. Step-by-step derivation

      1. flip-+ 5.4%

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

      2. *-commutative 5.4%

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

      3. *-commutative 5.4%

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

      4. *-commutative 5.4%

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

   8. Applied egg-rr 5.4%

      \[\leadsto x1 + \left(x2 \cdot \left(-12 \cdot x1 - 6\right) + \color{blue}{\frac{x1 \cdot x1 - \left(x1 \cdot -3\right) \cdot \left(x1 \cdot -3\right)}{x1 - x1 \cdot -3}}\right) \]
   9. Step-by-step derivation

      1. swap-sqr 5.4%

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

      2. metadata-eval 5.4%

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

      3. associate-*r* 5.4%

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

      4. distribute-lft-out-- 69.7%

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

      5. *-commutative 69.7%

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

      6. cancel-sign-sub-inv 69.7%

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

      7. metadata-eval 69.7%

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

      8. *-commutative 69.7%

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

   10. Simplified 69.7%

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

   if -5.60000000000000037e102 < x1 < 5.8e49

   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 98.8%

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

   3. Taylor expanded in x1 around 0 99.4%

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

   4. Taylor expanded in x1 around 0 99.4%

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

      1. unpow2 99.4%

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

      2. *-commutative 99.4%

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

      3. associate-*l* 99.4%

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

   6. Simplified 99.4%

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

   7. Taylor expanded in x1 around inf 97.4%

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

      1. *-commutative 97.4%

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

      2. unpow2 97.4%

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

   9. Simplified 97.4%

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

   if 5.8e49 < x1

   1. Initial program 41.9%

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

   2. Taylor expanded in x1 around inf 41.9%

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

   3. Taylor expanded in x1 around 0 41.9%

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

   4. Taylor expanded in x1 around 0 41.9%

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

      1. unpow2 41.9%

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

      2. *-commutative 41.9%

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

      3. associate-*l* 41.9%

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

   6. Simplified 41.9%

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

   7. Taylor expanded in x1 around inf 95.9%

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

      1. *-commutative 95.9%

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

      2. unpow2 95.9%

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

      3. associate-*l* 96.0%

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

   9. Simplified 96.0%

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

4. Final simplification 92.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(x2 \cdot \left(x1 \cdot -12 - 6\right) + \frac{x1 \cdot \left(x1 - x1 \cdot 9\right)}{x1 + x1 \cdot 3}\right)\\ \mathbf{elif}\;x1 \leq 5.8 \cdot 10^{+49}:\\ \;\;\;\;x1 + \left(\left(x1 \cdot -3 + x2 \cdot -6\right) + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(x1 \cdot \left(x1 \cdot 9\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right) \cdot \left(3 + \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot 6\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 \cdot -3 + x2 \cdot -6\right) - \left(\left(\left(\left(x1 \cdot \left(x1 \cdot 6\right)\right) \cdot \left(-1 - x1 \cdot x1\right) - x1 \cdot \left(x1 \cdot 9\right)\right) - x1 \cdot \left(x1 \cdot x1\right)\right) - x1\right)\right)\\ \end{array} \]

Alternative 6: 88.8% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := x1 \cdot \left(x1 \cdot x1\right)\\ t_2 := x1 \cdot -3 + x2 \cdot -6\\ t_3 := x1 \cdot x1 + 1\\ \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(x2 \cdot \left(x1 \cdot -12 - 6\right) + \frac{x1 \cdot \left(x1 - x1 \cdot 9\right)}{x1 + x1 \cdot 3}\right)\\ \mathbf{elif}\;x1 \leq -1200:\\ \;\;\;\;x1 - \left(\left(\left(\left(t_3 \cdot \left(\frac{1}{x1} \cdot \left(\left(x1 \cdot 2\right) \cdot \left(3 + \frac{-1}{x1}\right)\right) + \left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{x1 - \left(t_0 + 2 \cdot x2\right)}{t_3}\right)\right) - 3 \cdot t_0\right) - t_1\right) - x1\right) - t_2\right)\\ \mathbf{elif}\;x1 \leq 260:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t_0 - 2 \cdot x2\right) - x1}{t_3} - \left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(3 - 2 \cdot x2\right)\right)\right) - x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(t_2 - \left(\left(\left(\left(x1 \cdot \left(x1 \cdot 6\right)\right) \cdot \left(-1 - x1 \cdot x1\right) - x1 \cdot \left(x1 \cdot 9\right)\right) - t_1\right) - x1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (* x1 (* x1 x1)))
        (t_2 (+ (* x1 -3.0) (* x2 -6.0)))
        (t_3 (+ (* x1 x1) 1.0)))
   (if (<= x1 -5.6e+102)
     (+
      x1
      (+
       (* x2 (- (* x1 -12.0) 6.0))
       (/ (* x1 (- x1 (* x1 9.0))) (+ x1 (* x1 3.0)))))
     (if (<= x1 -1200.0)
       (-
        x1
        (-
         (-
          (-
           (-
            (*
             t_3
             (+
              (* (/ 1.0 x1) (* (* x1 2.0) (+ 3.0 (/ -1.0 x1))))
              (* (* x1 x1) (+ 6.0 (* 4.0 (/ (- x1 (+ t_0 (* 2.0 x2))) t_3))))))
            (* 3.0 t_0))
           t_1)
          x1)
         t_2))
       (if (<= x1 260.0)
         (+
          x1
          (-
           (* 3.0 (/ (- (- t_0 (* 2.0 x2)) x1) t_3))
           (- (* 4.0 (* x2 (* x1 (- 3.0 (* 2.0 x2))))) x1)))
         (+
          x1
          (-
           t_2
           (-
            (-
             (- (* (* x1 (* x1 6.0)) (- -1.0 (* x1 x1))) (* x1 (* x1 9.0)))
             t_1)
            x1))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = x1 * (x1 * x1);
	double t_2 = (x1 * -3.0) + (x2 * -6.0);
	double t_3 = (x1 * x1) + 1.0;
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = x1 + ((x2 * ((x1 * -12.0) - 6.0)) + ((x1 * (x1 - (x1 * 9.0))) / (x1 + (x1 * 3.0))));
	} else if (x1 <= -1200.0) {
		tmp = x1 - (((((t_3 * (((1.0 / x1) * ((x1 * 2.0) * (3.0 + (-1.0 / x1)))) + ((x1 * x1) * (6.0 + (4.0 * ((x1 - (t_0 + (2.0 * x2))) / t_3)))))) - (3.0 * t_0)) - t_1) - x1) - t_2);
	} else if (x1 <= 260.0) {
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_3)) - ((4.0 * (x2 * (x1 * (3.0 - (2.0 * x2))))) - x1));
	} else {
		tmp = x1 + (t_2 - (((((x1 * (x1 * 6.0)) * (-1.0 - (x1 * x1))) - (x1 * (x1 * 9.0))) - t_1) - 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) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_0 = x1 * (x1 * 3.0d0)
    t_1 = x1 * (x1 * x1)
    t_2 = (x1 * (-3.0d0)) + (x2 * (-6.0d0))
    t_3 = (x1 * x1) + 1.0d0
    if (x1 <= (-5.6d+102)) then
        tmp = x1 + ((x2 * ((x1 * (-12.0d0)) - 6.0d0)) + ((x1 * (x1 - (x1 * 9.0d0))) / (x1 + (x1 * 3.0d0))))
    else if (x1 <= (-1200.0d0)) then
        tmp = x1 - (((((t_3 * (((1.0d0 / x1) * ((x1 * 2.0d0) * (3.0d0 + ((-1.0d0) / x1)))) + ((x1 * x1) * (6.0d0 + (4.0d0 * ((x1 - (t_0 + (2.0d0 * x2))) / t_3)))))) - (3.0d0 * t_0)) - t_1) - x1) - t_2)
    else if (x1 <= 260.0d0) then
        tmp = x1 + ((3.0d0 * (((t_0 - (2.0d0 * x2)) - x1) / t_3)) - ((4.0d0 * (x2 * (x1 * (3.0d0 - (2.0d0 * x2))))) - x1))
    else
        tmp = x1 + (t_2 - (((((x1 * (x1 * 6.0d0)) * ((-1.0d0) - (x1 * x1))) - (x1 * (x1 * 9.0d0))) - t_1) - x1))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = x1 * (x1 * x1);
	double t_2 = (x1 * -3.0) + (x2 * -6.0);
	double t_3 = (x1 * x1) + 1.0;
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = x1 + ((x2 * ((x1 * -12.0) - 6.0)) + ((x1 * (x1 - (x1 * 9.0))) / (x1 + (x1 * 3.0))));
	} else if (x1 <= -1200.0) {
		tmp = x1 - (((((t_3 * (((1.0 / x1) * ((x1 * 2.0) * (3.0 + (-1.0 / x1)))) + ((x1 * x1) * (6.0 + (4.0 * ((x1 - (t_0 + (2.0 * x2))) / t_3)))))) - (3.0 * t_0)) - t_1) - x1) - t_2);
	} else if (x1 <= 260.0) {
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_3)) - ((4.0 * (x2 * (x1 * (3.0 - (2.0 * x2))))) - x1));
	} else {
		tmp = x1 + (t_2 - (((((x1 * (x1 * 6.0)) * (-1.0 - (x1 * x1))) - (x1 * (x1 * 9.0))) - t_1) - x1));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = x1 * (x1 * x1)
	t_2 = (x1 * -3.0) + (x2 * -6.0)
	t_3 = (x1 * x1) + 1.0
	tmp = 0
	if x1 <= -5.6e+102:
		tmp = x1 + ((x2 * ((x1 * -12.0) - 6.0)) + ((x1 * (x1 - (x1 * 9.0))) / (x1 + (x1 * 3.0))))
	elif x1 <= -1200.0:
		tmp = x1 - (((((t_3 * (((1.0 / x1) * ((x1 * 2.0) * (3.0 + (-1.0 / x1)))) + ((x1 * x1) * (6.0 + (4.0 * ((x1 - (t_0 + (2.0 * x2))) / t_3)))))) - (3.0 * t_0)) - t_1) - x1) - t_2)
	elif x1 <= 260.0:
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_3)) - ((4.0 * (x2 * (x1 * (3.0 - (2.0 * x2))))) - x1))
	else:
		tmp = x1 + (t_2 - (((((x1 * (x1 * 6.0)) * (-1.0 - (x1 * x1))) - (x1 * (x1 * 9.0))) - t_1) - x1))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(x1 * Float64(x1 * x1))
	t_2 = Float64(Float64(x1 * -3.0) + Float64(x2 * -6.0))
	t_3 = Float64(Float64(x1 * x1) + 1.0)
	tmp = 0.0
	if (x1 <= -5.6e+102)
		tmp = Float64(x1 + Float64(Float64(x2 * Float64(Float64(x1 * -12.0) - 6.0)) + Float64(Float64(x1 * Float64(x1 - Float64(x1 * 9.0))) / Float64(x1 + Float64(x1 * 3.0)))));
	elseif (x1 <= -1200.0)
		tmp = Float64(x1 - Float64(Float64(Float64(Float64(Float64(t_3 * Float64(Float64(Float64(1.0 / x1) * Float64(Float64(x1 * 2.0) * Float64(3.0 + Float64(-1.0 / x1)))) + Float64(Float64(x1 * x1) * Float64(6.0 + Float64(4.0 * Float64(Float64(x1 - Float64(t_0 + Float64(2.0 * x2))) / t_3)))))) - Float64(3.0 * t_0)) - t_1) - x1) - t_2));
	elseif (x1 <= 260.0)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_0 - Float64(2.0 * x2)) - x1) / t_3)) - Float64(Float64(4.0 * Float64(x2 * Float64(x1 * Float64(3.0 - Float64(2.0 * x2))))) - x1)));
	else
		tmp = Float64(x1 + Float64(t_2 - Float64(Float64(Float64(Float64(Float64(x1 * Float64(x1 * 6.0)) * Float64(-1.0 - Float64(x1 * x1))) - Float64(x1 * Float64(x1 * 9.0))) - t_1) - x1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * 3.0);
	t_1 = x1 * (x1 * x1);
	t_2 = (x1 * -3.0) + (x2 * -6.0);
	t_3 = (x1 * x1) + 1.0;
	tmp = 0.0;
	if (x1 <= -5.6e+102)
		tmp = x1 + ((x2 * ((x1 * -12.0) - 6.0)) + ((x1 * (x1 - (x1 * 9.0))) / (x1 + (x1 * 3.0))));
	elseif (x1 <= -1200.0)
		tmp = x1 - (((((t_3 * (((1.0 / x1) * ((x1 * 2.0) * (3.0 + (-1.0 / x1)))) + ((x1 * x1) * (6.0 + (4.0 * ((x1 - (t_0 + (2.0 * x2))) / t_3)))))) - (3.0 * t_0)) - t_1) - x1) - t_2);
	elseif (x1 <= 260.0)
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_3)) - ((4.0 * (x2 * (x1 * (3.0 - (2.0 * x2))))) - x1));
	else
		tmp = x1 + (t_2 - (((((x1 * (x1 * 6.0)) * (-1.0 - (x1 * x1))) - (x1 * (x1 * 9.0))) - t_1) - x1));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x1 * -3.0), $MachinePrecision] + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, If[LessEqual[x1, -5.6e+102], N[(x1 + N[(N[(x2 * N[(N[(x1 * -12.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * N[(x1 - N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x1 + N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -1200.0], N[(x1 - N[(N[(N[(N[(N[(t$95$3 * N[(N[(N[(1.0 / x1), $MachinePrecision] * N[(N[(x1 * 2.0), $MachinePrecision] * N[(3.0 + N[(-1.0 / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 + N[(4.0 * N[(N[(x1 - N[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(3.0 * t$95$0), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision] - x1), $MachinePrecision] - t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 260.0], N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$3), $MachinePrecision]), $MachinePrecision] - N[(N[(4.0 * N[(x2 * N[(x1 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(t$95$2 - N[(N[(N[(N[(N[(x1 * N[(x1 * 6.0), $MachinePrecision]), $MachinePrecision] * N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x1 * N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision] - x1), $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 0.1%

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

   3. Taylor expanded in x1 around 0 3.5%

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

      1. +-commutative 3.5%

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

      2. *-commutative 3.5%

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

      3. fma-def 3.5%

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

      4. *-commutative 3.5%

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

   5. Simplified 3.5%

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

   6. Taylor expanded in x2 around 0 20.3%

      \[\leadsto x1 + \color{blue}{\left(x2 \cdot \left(-12 \cdot x1 - 6\right) + \left(x1 + -3 \cdot x1\right)\right)} \]
   7. Step-by-step derivation

      1. flip-+ 5.4%

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

      2. *-commutative 5.4%

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

      3. *-commutative 5.4%

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

      4. *-commutative 5.4%

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

   8. Applied egg-rr 5.4%

      \[\leadsto x1 + \left(x2 \cdot \left(-12 \cdot x1 - 6\right) + \color{blue}{\frac{x1 \cdot x1 - \left(x1 \cdot -3\right) \cdot \left(x1 \cdot -3\right)}{x1 - x1 \cdot -3}}\right) \]
   9. Step-by-step derivation

      1. swap-sqr 5.4%

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

      2. metadata-eval 5.4%

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

      3. associate-*r* 5.4%

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

      4. distribute-lft-out-- 69.7%

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

      5. *-commutative 69.7%

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

      6. cancel-sign-sub-inv 69.7%

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

      7. metadata-eval 69.7%

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

      8. *-commutative 69.7%

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

   10. Simplified 69.7%

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

   if -5.60000000000000037e102 < x1 < -1200

   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 99.5%

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

   3. Taylor expanded in x1 around 0 99.5%

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

   4. Taylor expanded in x1 around inf 94.8%

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

   5. Taylor expanded in x1 around inf 94.8%

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

   if -1200 < x1 < 260

   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 99.1%

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

   if 260 < x1

   1. Initial program 55.8%

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

   2. Taylor expanded in x1 around inf 55.2%

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

   3. Taylor expanded in x1 around 0 55.8%

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

   4. Taylor expanded in x1 around 0 55.8%

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

      1. unpow2 55.8%

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

      2. *-commutative 55.8%

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

      3. associate-*l* 55.8%

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

   6. Simplified 55.8%

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

   7. Taylor expanded in x1 around inf 85.5%

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

      1. *-commutative 85.5%

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

      2. unpow2 85.5%

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

      3. associate-*l* 85.5%

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

   9. Simplified 85.5%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(x2 \cdot \left(x1 \cdot -12 - 6\right) + \frac{x1 \cdot \left(x1 - x1 \cdot 9\right)}{x1 + x1 \cdot 3}\right)\\ \mathbf{elif}\;x1 \leq -1200:\\ \;\;\;\;x1 - \left(\left(\left(\left(\left(x1 \cdot x1 + 1\right) \cdot \left(\frac{1}{x1} \cdot \left(\left(x1 \cdot 2\right) \cdot \left(3 + \frac{-1}{x1}\right)\right) + \left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right)\right) - 3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right)\right) - x1 \cdot \left(x1 \cdot x1\right)\right) - x1\right) - \left(x1 \cdot -3 + x2 \cdot -6\right)\right)\\ \mathbf{elif}\;x1 \leq 260:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - \left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(3 - 2 \cdot x2\right)\right)\right) - x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 \cdot -3 + x2 \cdot -6\right) - \left(\left(\left(\left(x1 \cdot \left(x1 \cdot 6\right)\right) \cdot \left(-1 - x1 \cdot x1\right) - x1 \cdot \left(x1 \cdot 9\right)\right) - x1 \cdot \left(x1 \cdot x1\right)\right) - x1\right)\right)\\ \end{array} \]

Alternative 7: 87.7% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := x1 \cdot \left(x1 \cdot 6\right)\\ t_2 := x1 \cdot \left(x1 \cdot 3\right)\\ t_3 := x1 \cdot \left(x1 \cdot x1\right)\\ \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(x2 \cdot \left(x1 \cdot -12 - 6\right) + \frac{x1 \cdot \left(x1 - x1 \cdot 9\right)}{x1 + x1 \cdot 3}\right)\\ \mathbf{elif}\;x1 \leq -128000:\\ \;\;\;\;x1 + \left(\left(x1 + \left(t_3 + \left(t_0 \cdot t_1 - t_2 \cdot \frac{x1 - \left(t_2 + 2 \cdot x2\right)}{t_0}\right)\right)\right) + 3 \cdot \left(x2 \cdot -2\right)\right)\\ \mathbf{elif}\;x1 \leq 260:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t_2 - 2 \cdot x2\right) - x1}{t_0} - \left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(3 - 2 \cdot x2\right)\right)\right) - x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 \cdot -3 + x2 \cdot -6\right) - \left(\left(\left(t_1 \cdot \left(-1 - x1 \cdot x1\right) - x1 \cdot \left(x1 \cdot 9\right)\right) - t_3\right) - x1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ (* x1 x1) 1.0))
        (t_1 (* x1 (* x1 6.0)))
        (t_2 (* x1 (* x1 3.0)))
        (t_3 (* x1 (* x1 x1))))
   (if (<= x1 -5.6e+102)
     (+
      x1
      (+
       (* x2 (- (* x1 -12.0) 6.0))
       (/ (* x1 (- x1 (* x1 9.0))) (+ x1 (* x1 3.0)))))
     (if (<= x1 -128000.0)
       (+
        x1
        (+
         (+
          x1
          (+ t_3 (- (* t_0 t_1) (* t_2 (/ (- x1 (+ t_2 (* 2.0 x2))) t_0)))))
         (* 3.0 (* x2 -2.0))))
       (if (<= x1 260.0)
         (+
          x1
          (-
           (* 3.0 (/ (- (- t_2 (* 2.0 x2)) x1) t_0))
           (- (* 4.0 (* x2 (* x1 (- 3.0 (* 2.0 x2))))) x1)))
         (+
          x1
          (-
           (+ (* x1 -3.0) (* x2 -6.0))
           (-
            (- (- (* t_1 (- -1.0 (* x1 x1))) (* x1 (* x1 9.0))) t_3)
            x1))))))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = x1 * (x1 * 6.0);
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = x1 * (x1 * x1);
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = x1 + ((x2 * ((x1 * -12.0) - 6.0)) + ((x1 * (x1 - (x1 * 9.0))) / (x1 + (x1 * 3.0))));
	} else if (x1 <= -128000.0) {
		tmp = x1 + ((x1 + (t_3 + ((t_0 * t_1) - (t_2 * ((x1 - (t_2 + (2.0 * x2))) / t_0))))) + (3.0 * (x2 * -2.0)));
	} else if (x1 <= 260.0) {
		tmp = x1 + ((3.0 * (((t_2 - (2.0 * x2)) - x1) / t_0)) - ((4.0 * (x2 * (x1 * (3.0 - (2.0 * x2))))) - x1));
	} else {
		tmp = x1 + (((x1 * -3.0) + (x2 * -6.0)) - ((((t_1 * (-1.0 - (x1 * x1))) - (x1 * (x1 * 9.0))) - t_3) - 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) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_0 = (x1 * x1) + 1.0d0
    t_1 = x1 * (x1 * 6.0d0)
    t_2 = x1 * (x1 * 3.0d0)
    t_3 = x1 * (x1 * x1)
    if (x1 <= (-5.6d+102)) then
        tmp = x1 + ((x2 * ((x1 * (-12.0d0)) - 6.0d0)) + ((x1 * (x1 - (x1 * 9.0d0))) / (x1 + (x1 * 3.0d0))))
    else if (x1 <= (-128000.0d0)) then
        tmp = x1 + ((x1 + (t_3 + ((t_0 * t_1) - (t_2 * ((x1 - (t_2 + (2.0d0 * x2))) / t_0))))) + (3.0d0 * (x2 * (-2.0d0))))
    else if (x1 <= 260.0d0) then
        tmp = x1 + ((3.0d0 * (((t_2 - (2.0d0 * x2)) - x1) / t_0)) - ((4.0d0 * (x2 * (x1 * (3.0d0 - (2.0d0 * x2))))) - x1))
    else
        tmp = x1 + (((x1 * (-3.0d0)) + (x2 * (-6.0d0))) - ((((t_1 * ((-1.0d0) - (x1 * x1))) - (x1 * (x1 * 9.0d0))) - t_3) - x1))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = x1 * (x1 * 6.0);
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = x1 * (x1 * x1);
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = x1 + ((x2 * ((x1 * -12.0) - 6.0)) + ((x1 * (x1 - (x1 * 9.0))) / (x1 + (x1 * 3.0))));
	} else if (x1 <= -128000.0) {
		tmp = x1 + ((x1 + (t_3 + ((t_0 * t_1) - (t_2 * ((x1 - (t_2 + (2.0 * x2))) / t_0))))) + (3.0 * (x2 * -2.0)));
	} else if (x1 <= 260.0) {
		tmp = x1 + ((3.0 * (((t_2 - (2.0 * x2)) - x1) / t_0)) - ((4.0 * (x2 * (x1 * (3.0 - (2.0 * x2))))) - x1));
	} else {
		tmp = x1 + (((x1 * -3.0) + (x2 * -6.0)) - ((((t_1 * (-1.0 - (x1 * x1))) - (x1 * (x1 * 9.0))) - t_3) - x1));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x1 * x1) + 1.0
	t_1 = x1 * (x1 * 6.0)
	t_2 = x1 * (x1 * 3.0)
	t_3 = x1 * (x1 * x1)
	tmp = 0
	if x1 <= -5.6e+102:
		tmp = x1 + ((x2 * ((x1 * -12.0) - 6.0)) + ((x1 * (x1 - (x1 * 9.0))) / (x1 + (x1 * 3.0))))
	elif x1 <= -128000.0:
		tmp = x1 + ((x1 + (t_3 + ((t_0 * t_1) - (t_2 * ((x1 - (t_2 + (2.0 * x2))) / t_0))))) + (3.0 * (x2 * -2.0)))
	elif x1 <= 260.0:
		tmp = x1 + ((3.0 * (((t_2 - (2.0 * x2)) - x1) / t_0)) - ((4.0 * (x2 * (x1 * (3.0 - (2.0 * x2))))) - x1))
	else:
		tmp = x1 + (((x1 * -3.0) + (x2 * -6.0)) - ((((t_1 * (-1.0 - (x1 * x1))) - (x1 * (x1 * 9.0))) - t_3) - x1))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * x1) + 1.0)
	t_1 = Float64(x1 * Float64(x1 * 6.0))
	t_2 = Float64(x1 * Float64(x1 * 3.0))
	t_3 = Float64(x1 * Float64(x1 * x1))
	tmp = 0.0
	if (x1 <= -5.6e+102)
		tmp = Float64(x1 + Float64(Float64(x2 * Float64(Float64(x1 * -12.0) - 6.0)) + Float64(Float64(x1 * Float64(x1 - Float64(x1 * 9.0))) / Float64(x1 + Float64(x1 * 3.0)))));
	elseif (x1 <= -128000.0)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(t_3 + Float64(Float64(t_0 * t_1) - Float64(t_2 * Float64(Float64(x1 - Float64(t_2 + Float64(2.0 * x2))) / t_0))))) + Float64(3.0 * Float64(x2 * -2.0))));
	elseif (x1 <= 260.0)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_2 - Float64(2.0 * x2)) - x1) / t_0)) - Float64(Float64(4.0 * Float64(x2 * Float64(x1 * Float64(3.0 - Float64(2.0 * x2))))) - x1)));
	else
		tmp = Float64(x1 + Float64(Float64(Float64(x1 * -3.0) + Float64(x2 * -6.0)) - Float64(Float64(Float64(Float64(t_1 * Float64(-1.0 - Float64(x1 * x1))) - Float64(x1 * Float64(x1 * 9.0))) - t_3) - x1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x1 * x1) + 1.0;
	t_1 = x1 * (x1 * 6.0);
	t_2 = x1 * (x1 * 3.0);
	t_3 = x1 * (x1 * x1);
	tmp = 0.0;
	if (x1 <= -5.6e+102)
		tmp = x1 + ((x2 * ((x1 * -12.0) - 6.0)) + ((x1 * (x1 - (x1 * 9.0))) / (x1 + (x1 * 3.0))));
	elseif (x1 <= -128000.0)
		tmp = x1 + ((x1 + (t_3 + ((t_0 * t_1) - (t_2 * ((x1 - (t_2 + (2.0 * x2))) / t_0))))) + (3.0 * (x2 * -2.0)));
	elseif (x1 <= 260.0)
		tmp = x1 + ((3.0 * (((t_2 - (2.0 * x2)) - x1) / t_0)) - ((4.0 * (x2 * (x1 * (3.0 - (2.0 * x2))))) - x1));
	else
		tmp = x1 + (((x1 * -3.0) + (x2 * -6.0)) - ((((t_1 * (-1.0 - (x1 * x1))) - (x1 * (x1 * 9.0))) - t_3) - x1));
	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 * 6.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -5.6e+102], N[(x1 + N[(N[(x2 * N[(N[(x1 * -12.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * N[(x1 - N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x1 + N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -128000.0], N[(x1 + N[(N[(x1 + N[(t$95$3 + N[(N[(t$95$0 * t$95$1), $MachinePrecision] - N[(t$95$2 * N[(N[(x1 - N[(t$95$2 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 260.0], N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$2 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision] - N[(N[(4.0 * N[(x2 * N[(x1 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(N[(x1 * -3.0), $MachinePrecision] + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(N[(t$95$1 * N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x1 * N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$3), $MachinePrecision] - x1), $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 0.1%

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

   3. Taylor expanded in x1 around 0 3.5%

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

      1. +-commutative 3.5%

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

      2. *-commutative 3.5%

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

      3. fma-def 3.5%

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

      4. *-commutative 3.5%

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

   5. Simplified 3.5%

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

   6. Taylor expanded in x2 around 0 20.3%

      \[\leadsto x1 + \color{blue}{\left(x2 \cdot \left(-12 \cdot x1 - 6\right) + \left(x1 + -3 \cdot x1\right)\right)} \]
   7. Step-by-step derivation

      1. flip-+ 5.4%

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

      2. *-commutative 5.4%

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

      3. *-commutative 5.4%

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

      4. *-commutative 5.4%

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

   8. Applied egg-rr 5.4%

      \[\leadsto x1 + \left(x2 \cdot \left(-12 \cdot x1 - 6\right) + \color{blue}{\frac{x1 \cdot x1 - \left(x1 \cdot -3\right) \cdot \left(x1 \cdot -3\right)}{x1 - x1 \cdot -3}}\right) \]
   9. Step-by-step derivation

      1. swap-sqr 5.4%

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

      2. metadata-eval 5.4%

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

      3. associate-*r* 5.4%

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

      4. distribute-lft-out-- 69.7%

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

      5. *-commutative 69.7%

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

      6. cancel-sign-sub-inv 69.7%

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

      7. metadata-eval 69.7%

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

      8. *-commutative 69.7%

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

   10. Simplified 69.7%

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

   if -5.60000000000000037e102 < x1 < -128000

   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 0 99.5%

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

      1. *-commutative 10.5%

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

   4. Simplified 99.5%

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

   5. Taylor expanded in x1 around inf 85.5%

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

      1. *-commutative 85.3%

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

      2. unpow2 85.3%

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

      3. associate-*l* 85.6%

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

   7. Simplified 85.8%

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

   if -128000 < x1 < 260

   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 99.1%

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

   if 260 < x1

   1. Initial program 55.8%

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

   2. Taylor expanded in x1 around inf 55.2%

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

   3. Taylor expanded in x1 around 0 55.8%

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

   4. Taylor expanded in x1 around 0 55.8%

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

      1. unpow2 55.8%

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

      2. *-commutative 55.8%

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

      3. associate-*l* 55.8%

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

   6. Simplified 55.8%

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

   7. Taylor expanded in x1 around inf 85.5%

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

      1. *-commutative 85.5%

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

      2. unpow2 85.5%

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

      3. associate-*l* 85.5%

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

   9. Simplified 85.5%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(x2 \cdot \left(x1 \cdot -12 - 6\right) + \frac{x1 \cdot \left(x1 - x1 \cdot 9\right)}{x1 + x1 \cdot 3}\right)\\ \mathbf{elif}\;x1 \leq -128000:\\ \;\;\;\;x1 + \left(\left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(x1 \cdot \left(x1 \cdot 6\right)\right) - \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right)\right)\right) + 3 \cdot \left(x2 \cdot -2\right)\right)\\ \mathbf{elif}\;x1 \leq 260:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - \left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(3 - 2 \cdot x2\right)\right)\right) - x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 \cdot -3 + x2 \cdot -6\right) - \left(\left(\left(\left(x1 \cdot \left(x1 \cdot 6\right)\right) \cdot \left(-1 - x1 \cdot x1\right) - x1 \cdot \left(x1 \cdot 9\right)\right) - x1 \cdot \left(x1 \cdot x1\right)\right) - x1\right)\right)\\ \end{array} \]

Alternative 8: 87.7% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(x2 \cdot \left(x1 \cdot -12 - 6\right) + \frac{x1 \cdot \left(x1 - x1 \cdot 9\right)}{x1 + x1 \cdot 3}\right)\\ \mathbf{elif}\;x1 \leq -48000 \lor \neg \left(x1 \leq 260\right):\\ \;\;\;\;x1 + \left(\left(x1 \cdot -3 + x2 \cdot -6\right) - \left(\left(\left(\left(x1 \cdot \left(x1 \cdot 6\right)\right) \cdot \left(-1 - x1 \cdot x1\right) - x1 \cdot \left(x1 \cdot 9\right)\right) - x1 \cdot \left(x1 \cdot x1\right)\right) - x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - \left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(3 - 2 \cdot x2\right)\right)\right) - x1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -5.6e+102)
   (+
    x1
    (+
     (* x2 (- (* x1 -12.0) 6.0))
     (/ (* x1 (- x1 (* x1 9.0))) (+ x1 (* x1 3.0)))))
   (if (or (<= x1 -48000.0) (not (<= x1 260.0)))
     (+
      x1
      (-
       (+ (* x1 -3.0) (* x2 -6.0))
       (-
        (-
         (- (* (* x1 (* x1 6.0)) (- -1.0 (* x1 x1))) (* x1 (* x1 9.0)))
         (* x1 (* x1 x1)))
        x1)))
     (+
      x1
      (-
       (* 3.0 (/ (- (- (* x1 (* x1 3.0)) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0)))
       (- (* 4.0 (* x2 (* x1 (- 3.0 (* 2.0 x2))))) x1))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = x1 + ((x2 * ((x1 * -12.0) - 6.0)) + ((x1 * (x1 - (x1 * 9.0))) / (x1 + (x1 * 3.0))));
	} else if ((x1 <= -48000.0) || !(x1 <= 260.0)) {
		tmp = x1 + (((x1 * -3.0) + (x2 * -6.0)) - (((((x1 * (x1 * 6.0)) * (-1.0 - (x1 * x1))) - (x1 * (x1 * 9.0))) - (x1 * (x1 * x1))) - x1));
	} else {
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / ((x1 * x1) + 1.0))) - ((4.0 * (x2 * (x1 * (3.0 - (2.0 * x2))))) - 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 <= (-5.6d+102)) then
        tmp = x1 + ((x2 * ((x1 * (-12.0d0)) - 6.0d0)) + ((x1 * (x1 - (x1 * 9.0d0))) / (x1 + (x1 * 3.0d0))))
    else if ((x1 <= (-48000.0d0)) .or. (.not. (x1 <= 260.0d0))) then
        tmp = x1 + (((x1 * (-3.0d0)) + (x2 * (-6.0d0))) - (((((x1 * (x1 * 6.0d0)) * ((-1.0d0) - (x1 * x1))) - (x1 * (x1 * 9.0d0))) - (x1 * (x1 * x1))) - x1))
    else
        tmp = x1 + ((3.0d0 * ((((x1 * (x1 * 3.0d0)) - (2.0d0 * x2)) - x1) / ((x1 * x1) + 1.0d0))) - ((4.0d0 * (x2 * (x1 * (3.0d0 - (2.0d0 * x2))))) - x1))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = x1 + ((x2 * ((x1 * -12.0) - 6.0)) + ((x1 * (x1 - (x1 * 9.0))) / (x1 + (x1 * 3.0))));
	} else if ((x1 <= -48000.0) || !(x1 <= 260.0)) {
		tmp = x1 + (((x1 * -3.0) + (x2 * -6.0)) - (((((x1 * (x1 * 6.0)) * (-1.0 - (x1 * x1))) - (x1 * (x1 * 9.0))) - (x1 * (x1 * x1))) - x1));
	} else {
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / ((x1 * x1) + 1.0))) - ((4.0 * (x2 * (x1 * (3.0 - (2.0 * x2))))) - x1));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -5.6e+102:
		tmp = x1 + ((x2 * ((x1 * -12.0) - 6.0)) + ((x1 * (x1 - (x1 * 9.0))) / (x1 + (x1 * 3.0))))
	elif (x1 <= -48000.0) or not (x1 <= 260.0):
		tmp = x1 + (((x1 * -3.0) + (x2 * -6.0)) - (((((x1 * (x1 * 6.0)) * (-1.0 - (x1 * x1))) - (x1 * (x1 * 9.0))) - (x1 * (x1 * x1))) - x1))
	else:
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / ((x1 * x1) + 1.0))) - ((4.0 * (x2 * (x1 * (3.0 - (2.0 * x2))))) - x1))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -5.6e+102)
		tmp = Float64(x1 + Float64(Float64(x2 * Float64(Float64(x1 * -12.0) - 6.0)) + Float64(Float64(x1 * Float64(x1 - Float64(x1 * 9.0))) / Float64(x1 + Float64(x1 * 3.0)))));
	elseif ((x1 <= -48000.0) || !(x1 <= 260.0))
		tmp = Float64(x1 + Float64(Float64(Float64(x1 * -3.0) + Float64(x2 * -6.0)) - Float64(Float64(Float64(Float64(Float64(x1 * Float64(x1 * 6.0)) * Float64(-1.0 - Float64(x1 * x1))) - Float64(x1 * Float64(x1 * 9.0))) - Float64(x1 * Float64(x1 * x1))) - x1)));
	else
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(Float64(x1 * Float64(x1 * 3.0)) - Float64(2.0 * x2)) - x1) / Float64(Float64(x1 * x1) + 1.0))) - Float64(Float64(4.0 * Float64(x2 * Float64(x1 * Float64(3.0 - Float64(2.0 * x2))))) - x1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -5.6e+102)
		tmp = x1 + ((x2 * ((x1 * -12.0) - 6.0)) + ((x1 * (x1 - (x1 * 9.0))) / (x1 + (x1 * 3.0))));
	elseif ((x1 <= -48000.0) || ~((x1 <= 260.0)))
		tmp = x1 + (((x1 * -3.0) + (x2 * -6.0)) - (((((x1 * (x1 * 6.0)) * (-1.0 - (x1 * x1))) - (x1 * (x1 * 9.0))) - (x1 * (x1 * x1))) - x1));
	else
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / ((x1 * x1) + 1.0))) - ((4.0 * (x2 * (x1 * (3.0 - (2.0 * x2))))) - x1));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -5.6e+102], N[(x1 + N[(N[(x2 * N[(N[(x1 * -12.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * N[(x1 - N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x1 + N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x1, -48000.0], N[Not[LessEqual[x1, 260.0]], $MachinePrecision]], N[(x1 + N[(N[(N[(x1 * -3.0), $MachinePrecision] + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(N[(N[(x1 * N[(x1 * 6.0), $MachinePrecision]), $MachinePrecision] * N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x1 * N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(3.0 * N[(N[(N[(N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision] - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(4.0 * N[(x2 * N[(x1 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x1), $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 0.1%

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

   3. Taylor expanded in x1 around 0 3.5%

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

      1. +-commutative 3.5%

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

      2. *-commutative 3.5%

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

      3. fma-def 3.5%

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

      4. *-commutative 3.5%

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

   5. Simplified 3.5%

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

   6. Taylor expanded in x2 around 0 20.3%

      \[\leadsto x1 + \color{blue}{\left(x2 \cdot \left(-12 \cdot x1 - 6\right) + \left(x1 + -3 \cdot x1\right)\right)} \]
   7. Step-by-step derivation

      1. flip-+ 5.4%

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

      2. *-commutative 5.4%

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

      3. *-commutative 5.4%

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

      4. *-commutative 5.4%

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

   8. Applied egg-rr 5.4%

      \[\leadsto x1 + \left(x2 \cdot \left(-12 \cdot x1 - 6\right) + \color{blue}{\frac{x1 \cdot x1 - \left(x1 \cdot -3\right) \cdot \left(x1 \cdot -3\right)}{x1 - x1 \cdot -3}}\right) \]
   9. Step-by-step derivation

      1. swap-sqr 5.4%

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

      2. metadata-eval 5.4%

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

      3. associate-*r* 5.4%

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

      4. distribute-lft-out-- 69.7%

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

      5. *-commutative 69.7%

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

      6. cancel-sign-sub-inv 69.7%

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

      7. metadata-eval 69.7%

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

      8. *-commutative 69.7%

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

   10. Simplified 69.7%

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

   if -5.60000000000000037e102 < x1 < -48000 or 260 < x1

   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 inf 65.9%

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

   3. Taylor expanded in x1 around 0 66.3%

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

   4. Taylor expanded in x1 around 0 66.3%

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

      1. unpow2 66.3%

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

      2. *-commutative 66.3%

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

      3. associate-*l* 66.3%

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

   6. Simplified 66.3%

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

   7. Taylor expanded in x1 around inf 85.4%

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

      1. *-commutative 85.4%

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

      2. unpow2 85.4%

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

      3. associate-*l* 85.5%

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

   9. Simplified 85.5%

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

   if -48000 < x1 < 260

   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 99.1%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(x2 \cdot \left(x1 \cdot -12 - 6\right) + \frac{x1 \cdot \left(x1 - x1 \cdot 9\right)}{x1 + x1 \cdot 3}\right)\\ \mathbf{elif}\;x1 \leq -48000 \lor \neg \left(x1 \leq 260\right):\\ \;\;\;\;x1 + \left(\left(x1 \cdot -3 + x2 \cdot -6\right) - \left(\left(\left(\left(x1 \cdot \left(x1 \cdot 6\right)\right) \cdot \left(-1 - x1 \cdot x1\right) - x1 \cdot \left(x1 \cdot 9\right)\right) - x1 \cdot \left(x1 \cdot x1\right)\right) - x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - \left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(3 - 2 \cdot x2\right)\right)\right) - x1\right)\right)\\ \end{array} \]

Alternative 9: 74.2% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\\ \mathbf{if}\;x1 \leq -9.5 \cdot 10^{+62}:\\ \;\;\;\;x1 + \left(x2 \cdot \left(x1 \cdot -12 - 6\right) + \frac{x1 \cdot \left(x1 - x1 \cdot 9\right)}{x1 + x1 \cdot 3}\right)\\ \mathbf{elif}\;x1 \leq 5.8 \cdot 10^{+100}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{t_1 - x1}{t_0} - \left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(3 - 2 \cdot x2\right)\right)\right) - x1\right)\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(x1 \cdot x1\right) \cdot \left(x1 + 15\right)\right) - 3 \cdot \frac{x1 - t_1}{t_0}\right)\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{+283}:\\ \;\;\;\;x1 \cdot \left(2 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - x2 \cdot -6}\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ (* x1 x1) 1.0)) (t_1 (- (* x1 (* x1 3.0)) (* 2.0 x2))))
   (if (<= x1 -9.5e+62)
     (+
      x1
      (+
       (* x2 (- (* x1 -12.0) 6.0))
       (/ (* x1 (- x1 (* x1 9.0))) (+ x1 (* x1 3.0)))))
     (if (<= x1 5.8e+100)
       (+
        x1
        (-
         (* 3.0 (/ (- t_1 x1) t_0))
         (- (* 4.0 (* x2 (* x1 (- 3.0 (* 2.0 x2))))) x1)))
       (if (<= x1 1.35e+154)
         (+ x1 (- (+ x1 (* (* x1 x1) (+ x1 15.0))) (* 3.0 (/ (- x1 t_1) t_0))))
         (if (<= x1 2e+283)
           (* x1 (+ 2.0 (* 4.0 (* x2 (- (* 2.0 x2) 3.0)))))
           (/ (- (* x1 x1) (* (* x2 x2) 36.0)) (- x1 (* x2 -6.0)))))))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = (x1 * (x1 * 3.0)) - (2.0 * x2);
	double tmp;
	if (x1 <= -9.5e+62) {
		tmp = x1 + ((x2 * ((x1 * -12.0) - 6.0)) + ((x1 * (x1 - (x1 * 9.0))) / (x1 + (x1 * 3.0))));
	} else if (x1 <= 5.8e+100) {
		tmp = x1 + ((3.0 * ((t_1 - x1) / t_0)) - ((4.0 * (x2 * (x1 * (3.0 - (2.0 * x2))))) - x1));
	} else if (x1 <= 1.35e+154) {
		tmp = x1 + ((x1 + ((x1 * x1) * (x1 + 15.0))) - (3.0 * ((x1 - t_1) / t_0)));
	} else if (x1 <= 2e+283) {
		tmp = x1 * (2.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0))));
	} else {
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (x1 * x1) + 1.0d0
    t_1 = (x1 * (x1 * 3.0d0)) - (2.0d0 * x2)
    if (x1 <= (-9.5d+62)) then
        tmp = x1 + ((x2 * ((x1 * (-12.0d0)) - 6.0d0)) + ((x1 * (x1 - (x1 * 9.0d0))) / (x1 + (x1 * 3.0d0))))
    else if (x1 <= 5.8d+100) then
        tmp = x1 + ((3.0d0 * ((t_1 - x1) / t_0)) - ((4.0d0 * (x2 * (x1 * (3.0d0 - (2.0d0 * x2))))) - x1))
    else if (x1 <= 1.35d+154) then
        tmp = x1 + ((x1 + ((x1 * x1) * (x1 + 15.0d0))) - (3.0d0 * ((x1 - t_1) / t_0)))
    else if (x1 <= 2d+283) then
        tmp = x1 * (2.0d0 + (4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0))))
    else
        tmp = ((x1 * x1) - ((x2 * x2) * 36.0d0)) / (x1 - (x2 * (-6.0d0)))
    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)) - (2.0 * x2);
	double tmp;
	if (x1 <= -9.5e+62) {
		tmp = x1 + ((x2 * ((x1 * -12.0) - 6.0)) + ((x1 * (x1 - (x1 * 9.0))) / (x1 + (x1 * 3.0))));
	} else if (x1 <= 5.8e+100) {
		tmp = x1 + ((3.0 * ((t_1 - x1) / t_0)) - ((4.0 * (x2 * (x1 * (3.0 - (2.0 * x2))))) - x1));
	} else if (x1 <= 1.35e+154) {
		tmp = x1 + ((x1 + ((x1 * x1) * (x1 + 15.0))) - (3.0 * ((x1 - t_1) / t_0)));
	} else if (x1 <= 2e+283) {
		tmp = x1 * (2.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0))));
	} else {
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x1 * x1) + 1.0
	t_1 = (x1 * (x1 * 3.0)) - (2.0 * x2)
	tmp = 0
	if x1 <= -9.5e+62:
		tmp = x1 + ((x2 * ((x1 * -12.0) - 6.0)) + ((x1 * (x1 - (x1 * 9.0))) / (x1 + (x1 * 3.0))))
	elif x1 <= 5.8e+100:
		tmp = x1 + ((3.0 * ((t_1 - x1) / t_0)) - ((4.0 * (x2 * (x1 * (3.0 - (2.0 * x2))))) - x1))
	elif x1 <= 1.35e+154:
		tmp = x1 + ((x1 + ((x1 * x1) * (x1 + 15.0))) - (3.0 * ((x1 - t_1) / t_0)))
	elif x1 <= 2e+283:
		tmp = x1 * (2.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0))))
	else:
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * x1) + 1.0)
	t_1 = Float64(Float64(x1 * Float64(x1 * 3.0)) - Float64(2.0 * x2))
	tmp = 0.0
	if (x1 <= -9.5e+62)
		tmp = Float64(x1 + Float64(Float64(x2 * Float64(Float64(x1 * -12.0) - 6.0)) + Float64(Float64(x1 * Float64(x1 - Float64(x1 * 9.0))) / Float64(x1 + Float64(x1 * 3.0)))));
	elseif (x1 <= 5.8e+100)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(t_1 - x1) / t_0)) - Float64(Float64(4.0 * Float64(x2 * Float64(x1 * Float64(3.0 - Float64(2.0 * x2))))) - x1)));
	elseif (x1 <= 1.35e+154)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(Float64(x1 * x1) * Float64(x1 + 15.0))) - Float64(3.0 * Float64(Float64(x1 - t_1) / t_0))));
	elseif (x1 <= 2e+283)
		tmp = Float64(x1 * Float64(2.0 + Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0)))));
	else
		tmp = Float64(Float64(Float64(x1 * x1) - Float64(Float64(x2 * x2) * 36.0)) / Float64(x1 - Float64(x2 * -6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x1 * x1) + 1.0;
	t_1 = (x1 * (x1 * 3.0)) - (2.0 * x2);
	tmp = 0.0;
	if (x1 <= -9.5e+62)
		tmp = x1 + ((x2 * ((x1 * -12.0) - 6.0)) + ((x1 * (x1 - (x1 * 9.0))) / (x1 + (x1 * 3.0))));
	elseif (x1 <= 5.8e+100)
		tmp = x1 + ((3.0 * ((t_1 - x1) / t_0)) - ((4.0 * (x2 * (x1 * (3.0 - (2.0 * x2))))) - x1));
	elseif (x1 <= 1.35e+154)
		tmp = x1 + ((x1 + ((x1 * x1) * (x1 + 15.0))) - (3.0 * ((x1 - t_1) / t_0)));
	elseif (x1 <= 2e+283)
		tmp = x1 * (2.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0))));
	else
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0));
	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[(N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision] - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -9.5e+62], N[(x1 + N[(N[(x2 * N[(N[(x1 * -12.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * N[(x1 - N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x1 + N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 5.8e+100], N[(x1 + N[(N[(3.0 * N[(N[(t$95$1 - x1), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision] - N[(N[(4.0 * N[(x2 * N[(x1 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.35e+154], N[(x1 + N[(N[(x1 + N[(N[(x1 * x1), $MachinePrecision] * N[(x1 + 15.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(3.0 * N[(N[(x1 - t$95$1), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 2e+283], N[(x1 * N[(2.0 + N[(4.0 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x1 * x1), $MachinePrecision] - N[(N[(x2 * x2), $MachinePrecision] * 36.0), $MachinePrecision]), $MachinePrecision] / N[(x1 - N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x1 < -9.5000000000000003e62

   1. Initial program 22.1%

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

   2. Taylor expanded in x1 around 0 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 3.3%

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

      1. +-commutative 3.3%

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

      2. *-commutative 3.3%

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

      3. fma-def 3.3%

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

      4. *-commutative 3.3%

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

   5. Simplified 3.3%

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

   6. Taylor expanded in x2 around 0 16.6%

      \[\leadsto x1 + \color{blue}{\left(x2 \cdot \left(-12 \cdot x1 - 6\right) + \left(x1 + -3 \cdot x1\right)\right)} \]
   7. Step-by-step derivation

      1. flip-+ 5.0%

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

      2. *-commutative 5.0%

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

      3. *-commutative 5.0%

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

      4. *-commutative 5.0%

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

   8. Applied egg-rr 5.0%

      \[\leadsto x1 + \left(x2 \cdot \left(-12 \cdot x1 - 6\right) + \color{blue}{\frac{x1 \cdot x1 - \left(x1 \cdot -3\right) \cdot \left(x1 \cdot -3\right)}{x1 - x1 \cdot -3}}\right) \]
   9. Step-by-step derivation

      1. swap-sqr 5.0%

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

      2. metadata-eval 5.0%

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

      3. associate-*r* 5.0%

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

      4. distribute-lft-out-- 55.0%

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

      5. *-commutative 55.0%

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

      6. cancel-sign-sub-inv 55.0%

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

      7. metadata-eval 55.0%

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

      8. *-commutative 55.0%

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

   10. Simplified 55.0%

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

   if -9.5000000000000003e62 < x1 < 5.8000000000000001e100

   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 80.2%

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

   if 5.8000000000000001e100 < x1 < 1.35000000000000003e154

   1. Initial program 100.0%

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

   2. Taylor expanded in x1 around inf 100.0%

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

   3. Taylor expanded in x1 around inf 88.9%

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

      1. *-commutative 88.9%

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

      2. unpow2 88.9%

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

   5. Simplified 88.9%

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

   6. Taylor expanded in x1 around 0 88.9%

      \[\leadsto x1 + \left(\left(\color{blue}{\left({x1}^{3} + 15 \cdot {x1}^{2}\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   7. Step-by-step derivation

      1. +-commutative 88.9%

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

      2. unpow2 88.9%

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

      3. cube-mult 88.9%

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

      4. distribute-rgt-out 88.9%

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

   8. Simplified 88.9%

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

   if 1.35000000000000003e154 < x1 < 1.99999999999999991e283

   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 75.6%

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

      1. *-commutative 75.6%

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

   5. Simplified 75.6%

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

   6. Taylor expanded in x1 around inf 75.6%

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

   if 1.99999999999999991e283 < x1

   1. Initial program 0.0%

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

   2. 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 10.5%

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

      1. *-commutative 10.5%

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

   5. Simplified 10.5%

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

      1. flip-+ 100.0%

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

   7. Applied egg-rr 100.0%

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

      1. swap-sqr 100.0%

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

      2. metadata-eval 100.0%

         \[\leadsto \frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot \color{blue}{36}}{x1 - x2 \cdot -6} \]

      3. *-commutative 100.0%

         \[\leadsto \frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - \color{blue}{-6 \cdot x2}} \]

   9. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - -6 \cdot x2}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -9.5 \cdot 10^{+62}:\\ \;\;\;\;x1 + \left(x2 \cdot \left(x1 \cdot -12 - 6\right) + \frac{x1 \cdot \left(x1 - x1 \cdot 9\right)}{x1 + x1 \cdot 3}\right)\\ \mathbf{elif}\;x1 \leq 5.8 \cdot 10^{+100}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - \left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(3 - 2 \cdot x2\right)\right)\right) - x1\right)\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(x1 \cdot x1\right) \cdot \left(x1 + 15\right)\right) - 3 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right)\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{+283}:\\ \;\;\;\;x1 \cdot \left(2 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - x2 \cdot -6}\\ \end{array} \]

Alternative 10: 73.9% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -5.5 \cdot 10^{+70}:\\ \;\;\;\;x1 + \left(x2 \cdot \left(x1 \cdot -12 - 6\right) + \frac{x1 \cdot \left(x1 - x1 \cdot 9\right)}{x1 + x1 \cdot 3}\right)\\ \mathbf{elif}\;x1 \leq 5.8 \cdot 10^{+100}:\\ \;\;\;\;x1 + \left(\left(x1 \cdot -3 + x2 \cdot -6\right) - \left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(3 - 2 \cdot x2\right)\right)\right) - x1\right)\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(x1 \cdot x1\right) \cdot \left(x1 + 15\right)\right) - 3 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right)\\ \mathbf{elif}\;x1 \leq 2.1 \cdot 10^{+283}:\\ \;\;\;\;x1 \cdot \left(2 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - x2 \cdot -6}\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -5.5e+70)
   (+
    x1
    (+
     (* x2 (- (* x1 -12.0) 6.0))
     (/ (* x1 (- x1 (* x1 9.0))) (+ x1 (* x1 3.0)))))
   (if (<= x1 5.8e+100)
     (+
      x1
      (-
       (+ (* x1 -3.0) (* x2 -6.0))
       (- (* 4.0 (* x2 (* x1 (- 3.0 (* 2.0 x2))))) x1)))
     (if (<= x1 1.35e+154)
       (+
        x1
        (-
         (+ x1 (* (* x1 x1) (+ x1 15.0)))
         (*
          3.0
          (/ (- x1 (- (* x1 (* x1 3.0)) (* 2.0 x2))) (+ (* x1 x1) 1.0)))))
       (if (<= x1 2.1e+283)
         (* x1 (+ 2.0 (* 4.0 (* x2 (- (* 2.0 x2) 3.0)))))
         (/ (- (* x1 x1) (* (* x2 x2) 36.0)) (- x1 (* x2 -6.0))))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -5.5e+70) {
		tmp = x1 + ((x2 * ((x1 * -12.0) - 6.0)) + ((x1 * (x1 - (x1 * 9.0))) / (x1 + (x1 * 3.0))));
	} else if (x1 <= 5.8e+100) {
		tmp = x1 + (((x1 * -3.0) + (x2 * -6.0)) - ((4.0 * (x2 * (x1 * (3.0 - (2.0 * x2))))) - x1));
	} else if (x1 <= 1.35e+154) {
		tmp = x1 + ((x1 + ((x1 * x1) * (x1 + 15.0))) - (3.0 * ((x1 - ((x1 * (x1 * 3.0)) - (2.0 * x2))) / ((x1 * x1) + 1.0))));
	} else if (x1 <= 2.1e+283) {
		tmp = x1 * (2.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0))));
	} else {
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x1 <= (-5.5d+70)) then
        tmp = x1 + ((x2 * ((x1 * (-12.0d0)) - 6.0d0)) + ((x1 * (x1 - (x1 * 9.0d0))) / (x1 + (x1 * 3.0d0))))
    else if (x1 <= 5.8d+100) then
        tmp = x1 + (((x1 * (-3.0d0)) + (x2 * (-6.0d0))) - ((4.0d0 * (x2 * (x1 * (3.0d0 - (2.0d0 * x2))))) - x1))
    else if (x1 <= 1.35d+154) then
        tmp = x1 + ((x1 + ((x1 * x1) * (x1 + 15.0d0))) - (3.0d0 * ((x1 - ((x1 * (x1 * 3.0d0)) - (2.0d0 * x2))) / ((x1 * x1) + 1.0d0))))
    else if (x1 <= 2.1d+283) then
        tmp = x1 * (2.0d0 + (4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0))))
    else
        tmp = ((x1 * x1) - ((x2 * x2) * 36.0d0)) / (x1 - (x2 * (-6.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= -5.5e+70) {
		tmp = x1 + ((x2 * ((x1 * -12.0) - 6.0)) + ((x1 * (x1 - (x1 * 9.0))) / (x1 + (x1 * 3.0))));
	} else if (x1 <= 5.8e+100) {
		tmp = x1 + (((x1 * -3.0) + (x2 * -6.0)) - ((4.0 * (x2 * (x1 * (3.0 - (2.0 * x2))))) - x1));
	} else if (x1 <= 1.35e+154) {
		tmp = x1 + ((x1 + ((x1 * x1) * (x1 + 15.0))) - (3.0 * ((x1 - ((x1 * (x1 * 3.0)) - (2.0 * x2))) / ((x1 * x1) + 1.0))));
	} else if (x1 <= 2.1e+283) {
		tmp = x1 * (2.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0))));
	} else {
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -5.5e+70:
		tmp = x1 + ((x2 * ((x1 * -12.0) - 6.0)) + ((x1 * (x1 - (x1 * 9.0))) / (x1 + (x1 * 3.0))))
	elif x1 <= 5.8e+100:
		tmp = x1 + (((x1 * -3.0) + (x2 * -6.0)) - ((4.0 * (x2 * (x1 * (3.0 - (2.0 * x2))))) - x1))
	elif x1 <= 1.35e+154:
		tmp = x1 + ((x1 + ((x1 * x1) * (x1 + 15.0))) - (3.0 * ((x1 - ((x1 * (x1 * 3.0)) - (2.0 * x2))) / ((x1 * x1) + 1.0))))
	elif x1 <= 2.1e+283:
		tmp = x1 * (2.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0))))
	else:
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -5.5e+70)
		tmp = Float64(x1 + Float64(Float64(x2 * Float64(Float64(x1 * -12.0) - 6.0)) + Float64(Float64(x1 * Float64(x1 - Float64(x1 * 9.0))) / Float64(x1 + Float64(x1 * 3.0)))));
	elseif (x1 <= 5.8e+100)
		tmp = Float64(x1 + Float64(Float64(Float64(x1 * -3.0) + Float64(x2 * -6.0)) - Float64(Float64(4.0 * Float64(x2 * Float64(x1 * Float64(3.0 - Float64(2.0 * x2))))) - x1)));
	elseif (x1 <= 1.35e+154)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(Float64(x1 * x1) * Float64(x1 + 15.0))) - Float64(3.0 * Float64(Float64(x1 - Float64(Float64(x1 * Float64(x1 * 3.0)) - Float64(2.0 * x2))) / Float64(Float64(x1 * x1) + 1.0)))));
	elseif (x1 <= 2.1e+283)
		tmp = Float64(x1 * Float64(2.0 + Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0)))));
	else
		tmp = Float64(Float64(Float64(x1 * x1) - Float64(Float64(x2 * x2) * 36.0)) / Float64(x1 - Float64(x2 * -6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -5.5e+70)
		tmp = x1 + ((x2 * ((x1 * -12.0) - 6.0)) + ((x1 * (x1 - (x1 * 9.0))) / (x1 + (x1 * 3.0))));
	elseif (x1 <= 5.8e+100)
		tmp = x1 + (((x1 * -3.0) + (x2 * -6.0)) - ((4.0 * (x2 * (x1 * (3.0 - (2.0 * x2))))) - x1));
	elseif (x1 <= 1.35e+154)
		tmp = x1 + ((x1 + ((x1 * x1) * (x1 + 15.0))) - (3.0 * ((x1 - ((x1 * (x1 * 3.0)) - (2.0 * x2))) / ((x1 * x1) + 1.0))));
	elseif (x1 <= 2.1e+283)
		tmp = x1 * (2.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0))));
	else
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -5.5e+70], N[(x1 + N[(N[(x2 * N[(N[(x1 * -12.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * N[(x1 - N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x1 + N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 5.8e+100], N[(x1 + N[(N[(N[(x1 * -3.0), $MachinePrecision] + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision] - N[(N[(4.0 * N[(x2 * N[(x1 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.35e+154], N[(x1 + N[(N[(x1 + N[(N[(x1 * x1), $MachinePrecision] * N[(x1 + 15.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(3.0 * N[(N[(x1 - N[(N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision] - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 2.1e+283], N[(x1 * N[(2.0 + N[(4.0 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x1 * x1), $MachinePrecision] - N[(N[(x2 * x2), $MachinePrecision] * 36.0), $MachinePrecision]), $MachinePrecision] / N[(x1 - N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if x1 < -5.49999999999999986e70

   1. Initial program 20.7%

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

   2. Taylor expanded in x1 around 0 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 3.3%

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

      1. +-commutative 3.3%

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

      2. *-commutative 3.3%

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

      3. fma-def 3.3%

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

      4. *-commutative 3.3%

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

   5. Simplified 3.3%

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

   6. Taylor expanded in x2 around 0 16.8%

      \[\leadsto x1 + \color{blue}{\left(x2 \cdot \left(-12 \cdot x1 - 6\right) + \left(x1 + -3 \cdot x1\right)\right)} \]
   7. Step-by-step derivation

      1. flip-+ 5.1%

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

      2. *-commutative 5.1%

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

      3. *-commutative 5.1%

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

      4. *-commutative 5.1%

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

   8. Applied egg-rr 5.1%

      \[\leadsto x1 + \left(x2 \cdot \left(-12 \cdot x1 - 6\right) + \color{blue}{\frac{x1 \cdot x1 - \left(x1 \cdot -3\right) \cdot \left(x1 \cdot -3\right)}{x1 - x1 \cdot -3}}\right) \]
   9. Step-by-step derivation

      1. swap-sqr 5.1%

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

      2. metadata-eval 5.1%

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

      3. associate-*r* 5.1%

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

      4. distribute-lft-out-- 56.0%

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

      5. *-commutative 56.0%

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

      6. cancel-sign-sub-inv 56.0%

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

      7. metadata-eval 56.0%

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

      8. *-commutative 56.0%

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

   10. Simplified 56.0%

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

   if -5.49999999999999986e70 < x1 < 5.8000000000000001e100

   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 79.7%

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

   3. Taylor expanded in x1 around 0 79.4%

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

   if 5.8000000000000001e100 < x1 < 1.35000000000000003e154

   1. Initial program 100.0%

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

   2. Taylor expanded in x1 around inf 100.0%

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

   3. Taylor expanded in x1 around inf 88.9%

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

      1. *-commutative 88.9%

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

      2. unpow2 88.9%

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

   5. Simplified 88.9%

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

   6. Taylor expanded in x1 around 0 88.9%

      \[\leadsto x1 + \left(\left(\color{blue}{\left({x1}^{3} + 15 \cdot {x1}^{2}\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   7. Step-by-step derivation

      1. +-commutative 88.9%

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

      2. unpow2 88.9%

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

      3. cube-mult 88.9%

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

      4. distribute-rgt-out 88.9%

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

   8. Simplified 88.9%

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

   if 1.35000000000000003e154 < x1 < 2.10000000000000013e283

   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 75.6%

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

      1. *-commutative 75.6%

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

   5. Simplified 75.6%

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

   6. Taylor expanded in x1 around inf 75.6%

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

   if 2.10000000000000013e283 < x1

   1. Initial program 0.0%

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

   2. 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 10.5%

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

      1. *-commutative 10.5%

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

   5. Simplified 10.5%

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

      1. flip-+ 100.0%

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

   7. Applied egg-rr 100.0%

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

      1. swap-sqr 100.0%

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

      2. metadata-eval 100.0%

         \[\leadsto \frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot \color{blue}{36}}{x1 - x2 \cdot -6} \]

      3. *-commutative 100.0%

         \[\leadsto \frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - \color{blue}{-6 \cdot x2}} \]

   9. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - -6 \cdot x2}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.5 \cdot 10^{+70}:\\ \;\;\;\;x1 + \left(x2 \cdot \left(x1 \cdot -12 - 6\right) + \frac{x1 \cdot \left(x1 - x1 \cdot 9\right)}{x1 + x1 \cdot 3}\right)\\ \mathbf{elif}\;x1 \leq 5.8 \cdot 10^{+100}:\\ \;\;\;\;x1 + \left(\left(x1 \cdot -3 + x2 \cdot -6\right) - \left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(3 - 2 \cdot x2\right)\right)\right) - x1\right)\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(x1 \cdot x1\right) \cdot \left(x1 + 15\right)\right) - 3 \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right)}{x1 \cdot x1 + 1}\right)\\ \mathbf{elif}\;x1 \leq 2.1 \cdot 10^{+283}:\\ \;\;\;\;x1 \cdot \left(2 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - x2 \cdot -6}\\ \end{array} \]

Alternative 11: 59.9% accurate, 4.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 + \left(x2 \cdot -6 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)\\ \mathbf{if}\;x1 \leq -3.4 \cdot 10^{+70}:\\ \;\;\;\;x1 \cdot \left(-1 + x2 \cdot -12\right)\\ \mathbf{elif}\;x1 \leq -6 \cdot 10^{-231}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x1 \leq 6.8 \cdot 10^{-196}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + \left(x1 + x1 \cdot -3\right)\right)\\ \mathbf{elif}\;x1 \leq 7.6 \cdot 10^{+283}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - x2 \cdot -6}\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0
         (+
          x1
          (+ (* x2 -6.0) (* x1 (- (* 4.0 (* x2 (- (* 2.0 x2) 3.0))) 2.0))))))
   (if (<= x1 -3.4e+70)
     (* x1 (+ -1.0 (* x2 -12.0)))
     (if (<= x1 -6e-231)
       t_0
       (if (<= x1 6.8e-196)
         (+ x1 (+ (* x2 -6.0) (+ x1 (* x1 -3.0))))
         (if (<= x1 7.6e+283)
           t_0
           (/ (- (* x1 x1) (* (* x2 x2) 36.0)) (- x1 (* x2 -6.0)))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)));
	double tmp;
	if (x1 <= -3.4e+70) {
		tmp = x1 * (-1.0 + (x2 * -12.0));
	} else if (x1 <= -6e-231) {
		tmp = t_0;
	} else if (x1 <= 6.8e-196) {
		tmp = x1 + ((x2 * -6.0) + (x1 + (x1 * -3.0)));
	} else if (x1 <= 7.6e+283) {
		tmp = t_0;
	} else {
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x1 + ((x2 * (-6.0d0)) + (x1 * ((4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0))) - 2.0d0)))
    if (x1 <= (-3.4d+70)) then
        tmp = x1 * ((-1.0d0) + (x2 * (-12.0d0)))
    else if (x1 <= (-6d-231)) then
        tmp = t_0
    else if (x1 <= 6.8d-196) then
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 + (x1 * (-3.0d0))))
    else if (x1 <= 7.6d+283) then
        tmp = t_0
    else
        tmp = ((x1 * x1) - ((x2 * x2) * 36.0d0)) / (x1 - (x2 * (-6.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)));
	double tmp;
	if (x1 <= -3.4e+70) {
		tmp = x1 * (-1.0 + (x2 * -12.0));
	} else if (x1 <= -6e-231) {
		tmp = t_0;
	} else if (x1 <= 6.8e-196) {
		tmp = x1 + ((x2 * -6.0) + (x1 + (x1 * -3.0)));
	} else if (x1 <= 7.6e+283) {
		tmp = t_0;
	} else {
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)))
	tmp = 0
	if x1 <= -3.4e+70:
		tmp = x1 * (-1.0 + (x2 * -12.0))
	elif x1 <= -6e-231:
		tmp = t_0
	elif x1 <= 6.8e-196:
		tmp = x1 + ((x2 * -6.0) + (x1 + (x1 * -3.0)))
	elif x1 <= 7.6e+283:
		tmp = t_0
	else:
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0))) - 2.0))))
	tmp = 0.0
	if (x1 <= -3.4e+70)
		tmp = Float64(x1 * Float64(-1.0 + Float64(x2 * -12.0)));
	elseif (x1 <= -6e-231)
		tmp = t_0;
	elseif (x1 <= 6.8e-196)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 + Float64(x1 * -3.0))));
	elseif (x1 <= 7.6e+283)
		tmp = t_0;
	else
		tmp = Float64(Float64(Float64(x1 * x1) - Float64(Float64(x2 * x2) * 36.0)) / Float64(x1 - Float64(x2 * -6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)));
	tmp = 0.0;
	if (x1 <= -3.4e+70)
		tmp = x1 * (-1.0 + (x2 * -12.0));
	elseif (x1 <= -6e-231)
		tmp = t_0;
	elseif (x1 <= 6.8e-196)
		tmp = x1 + ((x2 * -6.0) + (x1 + (x1 * -3.0)));
	elseif (x1 <= 7.6e+283)
		tmp = t_0;
	else
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(4.0 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -3.4e+70], N[(x1 * N[(-1.0 + N[(x2 * -12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -6e-231], t$95$0, If[LessEqual[x1, 6.8e-196], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 + N[(x1 * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 7.6e+283], t$95$0, N[(N[(N[(x1 * x1), $MachinePrecision] - N[(N[(x2 * x2), $MachinePrecision] * 36.0), $MachinePrecision]), $MachinePrecision] / N[(x1 - N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -3.4000000000000001e70

   1. Initial program 20.7%

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

   2. Taylor expanded in x1 around 0 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 3.3%

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

      1. +-commutative 3.3%

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

      2. *-commutative 3.3%

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

      3. fma-def 3.3%

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

      4. *-commutative 3.3%

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

   5. Simplified 3.3%

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

   6. Taylor expanded in x2 around 0 16.8%

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

   7. Taylor expanded in x1 around inf 16.8%

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

   if -3.4000000000000001e70 < x1 < -6.0000000000000005e-231 or 6.8e-196 < x1 < 7.6000000000000004e283

   1. Initial program 84.5%

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

   2. Taylor expanded in x1 around 0 58.5%

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

   3. Taylor expanded in x1 around 0 64.7%

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

   if -6.0000000000000005e-231 < x1 < 6.8e-196

   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 99.6%

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

      1. +-commutative 99.6%

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

      2. *-commutative 99.6%

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

      3. fma-def 99.7%

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

      4. *-commutative 99.7%

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

   5. Simplified 99.7%

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

   6. Taylor expanded in x2 around 0 95.2%

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

   7. Taylor expanded in x1 around 0 95.2%

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

      1. *-commutative 95.2%

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

   9. Simplified 95.2%

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

   if 7.6000000000000004e283 < x1

   1. Initial program 0.0%

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

   2. 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 10.5%

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

      1. *-commutative 10.5%

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

   5. Simplified 10.5%

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

      1. flip-+ 100.0%

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

   7. Applied egg-rr 100.0%

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

      1. swap-sqr 100.0%

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

      2. metadata-eval 100.0%

         \[\leadsto \frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot \color{blue}{36}}{x1 - x2 \cdot -6} \]

      3. *-commutative 100.0%

         \[\leadsto \frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - \color{blue}{-6 \cdot x2}} \]

   9. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - -6 \cdot x2}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 60.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -3.4 \cdot 10^{+70}:\\ \;\;\;\;x1 \cdot \left(-1 + x2 \cdot -12\right)\\ \mathbf{elif}\;x1 \leq -6 \cdot 10^{-231}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)\\ \mathbf{elif}\;x1 \leq 6.8 \cdot 10^{-196}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + \left(x1 + x1 \cdot -3\right)\right)\\ \mathbf{elif}\;x1 \leq 7.6 \cdot 10^{+283}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - x2 \cdot -6}\\ \end{array} \]

Alternative 12: 67.2% accurate, 4.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 + \left(x2 \cdot -6 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)\\ \mathbf{if}\;x1 \leq -6.4 \cdot 10^{+68}:\\ \;\;\;\;x1 + \left(x2 \cdot \left(x1 \cdot -12 - 6\right) + \frac{x1 \cdot \left(x1 - x1 \cdot 9\right)}{x1 + x1 \cdot 3}\right)\\ \mathbf{elif}\;x1 \leq -1.9 \cdot 10^{-205}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x1 \leq 1.55 \cdot 10^{-196}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2\right) + \left(x1 + 4 \cdot \left(x2 \cdot \left(\left(x1 \cdot 2\right) \cdot x2\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 5.5 \cdot 10^{+283}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - x2 \cdot -6}\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0
         (+
          x1
          (+ (* x2 -6.0) (* x1 (- (* 4.0 (* x2 (- (* 2.0 x2) 3.0))) 2.0))))))
   (if (<= x1 -6.4e+68)
     (+
      x1
      (+
       (* x2 (- (* x1 -12.0) 6.0))
       (/ (* x1 (- x1 (* x1 9.0))) (+ x1 (* x1 3.0)))))
     (if (<= x1 -1.9e-205)
       t_0
       (if (<= x1 1.55e-196)
         (+ x1 (+ (* 3.0 (* x2 -2.0)) (+ x1 (* 4.0 (* x2 (* (* x1 2.0) x2))))))
         (if (<= x1 5.5e+283)
           t_0
           (/ (- (* x1 x1) (* (* x2 x2) 36.0)) (- x1 (* x2 -6.0)))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)));
	double tmp;
	if (x1 <= -6.4e+68) {
		tmp = x1 + ((x2 * ((x1 * -12.0) - 6.0)) + ((x1 * (x1 - (x1 * 9.0))) / (x1 + (x1 * 3.0))));
	} else if (x1 <= -1.9e-205) {
		tmp = t_0;
	} else if (x1 <= 1.55e-196) {
		tmp = x1 + ((3.0 * (x2 * -2.0)) + (x1 + (4.0 * (x2 * ((x1 * 2.0) * x2)))));
	} else if (x1 <= 5.5e+283) {
		tmp = t_0;
	} else {
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x1 + ((x2 * (-6.0d0)) + (x1 * ((4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0))) - 2.0d0)))
    if (x1 <= (-6.4d+68)) then
        tmp = x1 + ((x2 * ((x1 * (-12.0d0)) - 6.0d0)) + ((x1 * (x1 - (x1 * 9.0d0))) / (x1 + (x1 * 3.0d0))))
    else if (x1 <= (-1.9d-205)) then
        tmp = t_0
    else if (x1 <= 1.55d-196) then
        tmp = x1 + ((3.0d0 * (x2 * (-2.0d0))) + (x1 + (4.0d0 * (x2 * ((x1 * 2.0d0) * x2)))))
    else if (x1 <= 5.5d+283) then
        tmp = t_0
    else
        tmp = ((x1 * x1) - ((x2 * x2) * 36.0d0)) / (x1 - (x2 * (-6.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)));
	double tmp;
	if (x1 <= -6.4e+68) {
		tmp = x1 + ((x2 * ((x1 * -12.0) - 6.0)) + ((x1 * (x1 - (x1 * 9.0))) / (x1 + (x1 * 3.0))));
	} else if (x1 <= -1.9e-205) {
		tmp = t_0;
	} else if (x1 <= 1.55e-196) {
		tmp = x1 + ((3.0 * (x2 * -2.0)) + (x1 + (4.0 * (x2 * ((x1 * 2.0) * x2)))));
	} else if (x1 <= 5.5e+283) {
		tmp = t_0;
	} else {
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)))
	tmp = 0
	if x1 <= -6.4e+68:
		tmp = x1 + ((x2 * ((x1 * -12.0) - 6.0)) + ((x1 * (x1 - (x1 * 9.0))) / (x1 + (x1 * 3.0))))
	elif x1 <= -1.9e-205:
		tmp = t_0
	elif x1 <= 1.55e-196:
		tmp = x1 + ((3.0 * (x2 * -2.0)) + (x1 + (4.0 * (x2 * ((x1 * 2.0) * x2)))))
	elif x1 <= 5.5e+283:
		tmp = t_0
	else:
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0))) - 2.0))))
	tmp = 0.0
	if (x1 <= -6.4e+68)
		tmp = Float64(x1 + Float64(Float64(x2 * Float64(Float64(x1 * -12.0) - 6.0)) + Float64(Float64(x1 * Float64(x1 - Float64(x1 * 9.0))) / Float64(x1 + Float64(x1 * 3.0)))));
	elseif (x1 <= -1.9e-205)
		tmp = t_0;
	elseif (x1 <= 1.55e-196)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(x2 * -2.0)) + Float64(x1 + Float64(4.0 * Float64(x2 * Float64(Float64(x1 * 2.0) * x2))))));
	elseif (x1 <= 5.5e+283)
		tmp = t_0;
	else
		tmp = Float64(Float64(Float64(x1 * x1) - Float64(Float64(x2 * x2) * 36.0)) / Float64(x1 - Float64(x2 * -6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)));
	tmp = 0.0;
	if (x1 <= -6.4e+68)
		tmp = x1 + ((x2 * ((x1 * -12.0) - 6.0)) + ((x1 * (x1 - (x1 * 9.0))) / (x1 + (x1 * 3.0))));
	elseif (x1 <= -1.9e-205)
		tmp = t_0;
	elseif (x1 <= 1.55e-196)
		tmp = x1 + ((3.0 * (x2 * -2.0)) + (x1 + (4.0 * (x2 * ((x1 * 2.0) * x2)))));
	elseif (x1 <= 5.5e+283)
		tmp = t_0;
	else
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(4.0 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -6.4e+68], N[(x1 + N[(N[(x2 * N[(N[(x1 * -12.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * N[(x1 - N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x1 + N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -1.9e-205], t$95$0, If[LessEqual[x1, 1.55e-196], N[(x1 + N[(N[(3.0 * N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(4.0 * N[(x2 * N[(N[(x1 * 2.0), $MachinePrecision] * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 5.5e+283], t$95$0, N[(N[(N[(x1 * x1), $MachinePrecision] - N[(N[(x2 * x2), $MachinePrecision] * 36.0), $MachinePrecision]), $MachinePrecision] / N[(x1 - N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -6.39999999999999989e68

   1. Initial program 20.7%

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

   2. Taylor expanded in x1 around 0 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 3.3%

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

      1. +-commutative 3.3%

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

      2. *-commutative 3.3%

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

      3. fma-def 3.3%

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

      4. *-commutative 3.3%

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

   5. Simplified 3.3%

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

   6. Taylor expanded in x2 around 0 16.8%

      \[\leadsto x1 + \color{blue}{\left(x2 \cdot \left(-12 \cdot x1 - 6\right) + \left(x1 + -3 \cdot x1\right)\right)} \]
   7. Step-by-step derivation

      1. flip-+ 5.1%

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

      2. *-commutative 5.1%

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

      3. *-commutative 5.1%

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

      4. *-commutative 5.1%

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

   8. Applied egg-rr 5.1%

      \[\leadsto x1 + \left(x2 \cdot \left(-12 \cdot x1 - 6\right) + \color{blue}{\frac{x1 \cdot x1 - \left(x1 \cdot -3\right) \cdot \left(x1 \cdot -3\right)}{x1 - x1 \cdot -3}}\right) \]
   9. Step-by-step derivation

      1. swap-sqr 5.1%

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

      2. metadata-eval 5.1%

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

      3. associate-*r* 5.1%

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

      4. distribute-lft-out-- 56.0%

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

      5. *-commutative 56.0%

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

      6. cancel-sign-sub-inv 56.0%

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

      7. metadata-eval 56.0%

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

      8. *-commutative 56.0%

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

   10. Simplified 56.0%

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

   if -6.39999999999999989e68 < x1 < -1.89999999999999996e-205 or 1.54999999999999996e-196 < x1 < 5.49999999999999986e283

   1. Initial program 84.1%

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

   2. Taylor expanded in x1 around 0 57.4%

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

   3. Taylor expanded in x1 around 0 64.9%

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

   if -1.89999999999999996e-205 < x1 < 1.54999999999999996e-196

   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 93.7%

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

      1. *-commutative 93.7%

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

   5. Simplified 93.7%

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

   6. Taylor expanded in x2 around inf 93.7%

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

      1. *-commutative 93.7%

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

      2. associate-*l* 93.7%

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

   8. Simplified 93.7%

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

   if 5.49999999999999986e283 < x1

   1. Initial program 0.0%

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

   2. 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 10.5%

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

      1. *-commutative 10.5%

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

   5. Simplified 10.5%

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

      1. flip-+ 100.0%

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

   7. Applied egg-rr 100.0%

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

      1. swap-sqr 100.0%

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

      2. metadata-eval 100.0%

         \[\leadsto \frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot \color{blue}{36}}{x1 - x2 \cdot -6} \]

      3. *-commutative 100.0%

         \[\leadsto \frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - \color{blue}{-6 \cdot x2}} \]

   9. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - -6 \cdot x2}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -6.4 \cdot 10^{+68}:\\ \;\;\;\;x1 + \left(x2 \cdot \left(x1 \cdot -12 - 6\right) + \frac{x1 \cdot \left(x1 - x1 \cdot 9\right)}{x1 + x1 \cdot 3}\right)\\ \mathbf{elif}\;x1 \leq -1.9 \cdot 10^{-205}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)\\ \mathbf{elif}\;x1 \leq 1.55 \cdot 10^{-196}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2\right) + \left(x1 + 4 \cdot \left(x2 \cdot \left(\left(x1 \cdot 2\right) \cdot x2\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 5.5 \cdot 10^{+283}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - x2 \cdot -6}\\ \end{array} \]

Alternative 13: 70.7% accurate, 4.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -5.8 \cdot 10^{+70}:\\ \;\;\;\;x1 + \left(x2 \cdot \left(x1 \cdot -12 - 6\right) + \frac{x1 \cdot \left(x1 - x1 \cdot 9\right)}{x1 + x1 \cdot 3}\right)\\ \mathbf{elif}\;x1 \leq 2.4 \cdot 10^{+283}:\\ \;\;\;\;x1 + \left(\left(x1 \cdot -3 + x2 \cdot -6\right) - \left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(3 - 2 \cdot x2\right)\right)\right) - x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - x2 \cdot -6}\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -5.8e+70)
   (+
    x1
    (+
     (* x2 (- (* x1 -12.0) 6.0))
     (/ (* x1 (- x1 (* x1 9.0))) (+ x1 (* x1 3.0)))))
   (if (<= x1 2.4e+283)
     (+
      x1
      (-
       (+ (* x1 -3.0) (* x2 -6.0))
       (- (* 4.0 (* x2 (* x1 (- 3.0 (* 2.0 x2))))) x1)))
     (/ (- (* x1 x1) (* (* x2 x2) 36.0)) (- x1 (* x2 -6.0))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -5.8e+70) {
		tmp = x1 + ((x2 * ((x1 * -12.0) - 6.0)) + ((x1 * (x1 - (x1 * 9.0))) / (x1 + (x1 * 3.0))));
	} else if (x1 <= 2.4e+283) {
		tmp = x1 + (((x1 * -3.0) + (x2 * -6.0)) - ((4.0 * (x2 * (x1 * (3.0 - (2.0 * x2))))) - x1));
	} else {
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x1 <= (-5.8d+70)) then
        tmp = x1 + ((x2 * ((x1 * (-12.0d0)) - 6.0d0)) + ((x1 * (x1 - (x1 * 9.0d0))) / (x1 + (x1 * 3.0d0))))
    else if (x1 <= 2.4d+283) then
        tmp = x1 + (((x1 * (-3.0d0)) + (x2 * (-6.0d0))) - ((4.0d0 * (x2 * (x1 * (3.0d0 - (2.0d0 * x2))))) - x1))
    else
        tmp = ((x1 * x1) - ((x2 * x2) * 36.0d0)) / (x1 - (x2 * (-6.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= -5.8e+70) {
		tmp = x1 + ((x2 * ((x1 * -12.0) - 6.0)) + ((x1 * (x1 - (x1 * 9.0))) / (x1 + (x1 * 3.0))));
	} else if (x1 <= 2.4e+283) {
		tmp = x1 + (((x1 * -3.0) + (x2 * -6.0)) - ((4.0 * (x2 * (x1 * (3.0 - (2.0 * x2))))) - x1));
	} else {
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -5.8e+70:
		tmp = x1 + ((x2 * ((x1 * -12.0) - 6.0)) + ((x1 * (x1 - (x1 * 9.0))) / (x1 + (x1 * 3.0))))
	elif x1 <= 2.4e+283:
		tmp = x1 + (((x1 * -3.0) + (x2 * -6.0)) - ((4.0 * (x2 * (x1 * (3.0 - (2.0 * x2))))) - x1))
	else:
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -5.8e+70)
		tmp = Float64(x1 + Float64(Float64(x2 * Float64(Float64(x1 * -12.0) - 6.0)) + Float64(Float64(x1 * Float64(x1 - Float64(x1 * 9.0))) / Float64(x1 + Float64(x1 * 3.0)))));
	elseif (x1 <= 2.4e+283)
		tmp = Float64(x1 + Float64(Float64(Float64(x1 * -3.0) + Float64(x2 * -6.0)) - Float64(Float64(4.0 * Float64(x2 * Float64(x1 * Float64(3.0 - Float64(2.0 * x2))))) - x1)));
	else
		tmp = Float64(Float64(Float64(x1 * x1) - Float64(Float64(x2 * x2) * 36.0)) / Float64(x1 - Float64(x2 * -6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -5.8e+70)
		tmp = x1 + ((x2 * ((x1 * -12.0) - 6.0)) + ((x1 * (x1 - (x1 * 9.0))) / (x1 + (x1 * 3.0))));
	elseif (x1 <= 2.4e+283)
		tmp = x1 + (((x1 * -3.0) + (x2 * -6.0)) - ((4.0 * (x2 * (x1 * (3.0 - (2.0 * x2))))) - x1));
	else
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -5.8e+70], N[(x1 + N[(N[(x2 * N[(N[(x1 * -12.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * N[(x1 - N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x1 + N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 2.4e+283], N[(x1 + N[(N[(N[(x1 * -3.0), $MachinePrecision] + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision] - N[(N[(4.0 * N[(x2 * N[(x1 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x1 * x1), $MachinePrecision] - N[(N[(x2 * x2), $MachinePrecision] * 36.0), $MachinePrecision]), $MachinePrecision] / N[(x1 - N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -5.7999999999999997e70

   1. Initial program 20.7%

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

   2. Taylor expanded in x1 around 0 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 3.3%

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

      1. +-commutative 3.3%

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

      2. *-commutative 3.3%

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

      3. fma-def 3.3%

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

      4. *-commutative 3.3%

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

   5. Simplified 3.3%

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

   6. Taylor expanded in x2 around 0 16.8%

      \[\leadsto x1 + \color{blue}{\left(x2 \cdot \left(-12 \cdot x1 - 6\right) + \left(x1 + -3 \cdot x1\right)\right)} \]
   7. Step-by-step derivation

      1. flip-+ 5.1%

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

      2. *-commutative 5.1%

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

      3. *-commutative 5.1%

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

      4. *-commutative 5.1%

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

   8. Applied egg-rr 5.1%

      \[\leadsto x1 + \left(x2 \cdot \left(-12 \cdot x1 - 6\right) + \color{blue}{\frac{x1 \cdot x1 - \left(x1 \cdot -3\right) \cdot \left(x1 \cdot -3\right)}{x1 - x1 \cdot -3}}\right) \]
   9. Step-by-step derivation

      1. swap-sqr 5.1%

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

      2. metadata-eval 5.1%

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

      3. associate-*r* 5.1%

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

      4. distribute-lft-out-- 56.0%

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

      5. *-commutative 56.0%

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

      6. cancel-sign-sub-inv 56.0%

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

      7. metadata-eval 56.0%

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

      8. *-commutative 56.0%

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

   10. Simplified 56.0%

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

   if -5.7999999999999997e70 < x1 < 2.39999999999999998e283

   1. Initial program 87.8%

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

   2. Taylor expanded in x1 around 0 67.5%

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

   3. Taylor expanded in x1 around 0 75.8%

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

   if 2.39999999999999998e283 < x1

   1. Initial program 0.0%

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

   2. 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 10.5%

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

      1. *-commutative 10.5%

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

   5. Simplified 10.5%

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

      1. flip-+ 100.0%

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

   7. Applied egg-rr 100.0%

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

      1. swap-sqr 100.0%

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

      2. metadata-eval 100.0%

         \[\leadsto \frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot \color{blue}{36}}{x1 - x2 \cdot -6} \]

      3. *-commutative 100.0%

         \[\leadsto \frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - \color{blue}{-6 \cdot x2}} \]

   9. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - -6 \cdot x2}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 72.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.8 \cdot 10^{+70}:\\ \;\;\;\;x1 + \left(x2 \cdot \left(x1 \cdot -12 - 6\right) + \frac{x1 \cdot \left(x1 - x1 \cdot 9\right)}{x1 + x1 \cdot 3}\right)\\ \mathbf{elif}\;x1 \leq 2.4 \cdot 10^{+283}:\\ \;\;\;\;x1 + \left(\left(x1 \cdot -3 + x2 \cdot -6\right) - \left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(3 - 2 \cdot x2\right)\right)\right) - x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - x2 \cdot -6}\\ \end{array} \]

Alternative 14: 60.2% accurate, 5.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x2 \leq -8.2 \cdot 10^{-26} \lor \neg \left(x2 \leq 2 \cdot 10^{-15}\right):\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2\right) + \left(x1 + 4 \cdot \left(x2 \cdot \left(\left(x1 \cdot 2\right) \cdot x2\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x2 -8.2e-26) (not (<= x2 2e-15)))
   (+ x1 (+ (* 3.0 (* x2 -2.0)) (+ x1 (* 4.0 (* x2 (* (* x1 2.0) x2))))))
   (+ x1 (+ (* x2 -6.0) (* x1 (- (* 4.0 (* x2 (- (* 2.0 x2) 3.0))) 2.0))))))

C

double code(double x1, double x2) {
	double tmp;
	if ((x2 <= -8.2e-26) || !(x2 <= 2e-15)) {
		tmp = x1 + ((3.0 * (x2 * -2.0)) + (x1 + (4.0 * (x2 * ((x1 * 2.0) * x2)))));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if ((x2 <= (-8.2d-26)) .or. (.not. (x2 <= 2d-15))) then
        tmp = x1 + ((3.0d0 * (x2 * (-2.0d0))) + (x1 + (4.0d0 * (x2 * ((x1 * 2.0d0) * x2)))))
    else
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * ((4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0))) - 2.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x2 <= -8.2e-26) || !(x2 <= 2e-15)) {
		tmp = x1 + ((3.0 * (x2 * -2.0)) + (x1 + (4.0 * (x2 * ((x1 * 2.0) * x2)))));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x2 <= -8.2e-26) or not (x2 <= 2e-15):
		tmp = x1 + ((3.0 * (x2 * -2.0)) + (x1 + (4.0 * (x2 * ((x1 * 2.0) * x2)))))
	else:
		tmp = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x2 <= -8.2e-26) || !(x2 <= 2e-15))
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(x2 * -2.0)) + Float64(x1 + Float64(4.0 * Float64(x2 * Float64(Float64(x1 * 2.0) * x2))))));
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0))) - 2.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x2 <= -8.2e-26) || ~((x2 <= 2e-15)))
		tmp = x1 + ((3.0 * (x2 * -2.0)) + (x1 + (4.0 * (x2 * ((x1 * 2.0) * x2)))));
	else
		tmp = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x2, -8.2e-26], N[Not[LessEqual[x2, 2e-15]], $MachinePrecision]], N[(x1 + N[(N[(3.0 * N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(4.0 * N[(x2 * N[(N[(x1 * 2.0), $MachinePrecision] * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(4.0 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x2 < -8.1999999999999997e-26 or 2.0000000000000002e-15 < x2

   1. Initial program 71.3%

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

   2. Taylor expanded in x1 around 0 54.5%

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

   3. Taylor expanded in x1 around 0 66.4%

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

      1. *-commutative 66.4%

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

   5. Simplified 66.4%

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

   6. Taylor expanded in x2 around inf 66.4%

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

      1. *-commutative 66.4%

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

      2. associate-*l* 66.4%

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

   8. Simplified 66.4%

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

   if -8.1999999999999997e-26 < x2 < 2.0000000000000002e-15

   1. Initial program 72.6%

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

   2. Taylor expanded in x1 around 0 48.5%

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

   3. Taylor expanded in x1 around 0 49.9%

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

4. Final simplification 59.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq -8.2 \cdot 10^{-26} \lor \neg \left(x2 \leq 2 \cdot 10^{-15}\right):\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2\right) + \left(x1 + 4 \cdot \left(x2 \cdot \left(\left(x1 \cdot 2\right) \cdot x2\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)\\ \end{array} \]

Alternative 15: 60.2% accurate, 5.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 3 \cdot \left(x2 \cdot -2\right)\\ \mathbf{if}\;x2 \leq -1.04 \cdot 10^{-25}:\\ \;\;\;\;x1 + \left(t_0 - \left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(3 - 2 \cdot x2\right)\right)\right) - x1\right)\right)\\ \mathbf{elif}\;x2 \leq 3.6 \cdot 10^{-21}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(t_0 + \left(x1 + 4 \cdot \left(x2 \cdot \left(\left(x1 \cdot 2\right) \cdot x2\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* 3.0 (* x2 -2.0))))
   (if (<= x2 -1.04e-25)
     (+ x1 (- t_0 (- (* 4.0 (* x2 (* x1 (- 3.0 (* 2.0 x2))))) x1)))
     (if (<= x2 3.6e-21)
       (+ x1 (+ (* x2 -6.0) (* x1 (- (* 4.0 (* x2 (- (* 2.0 x2) 3.0))) 2.0))))
       (+ x1 (+ t_0 (+ x1 (* 4.0 (* x2 (* (* x1 2.0) x2))))))))))

C

double code(double x1, double x2) {
	double t_0 = 3.0 * (x2 * -2.0);
	double tmp;
	if (x2 <= -1.04e-25) {
		tmp = x1 + (t_0 - ((4.0 * (x2 * (x1 * (3.0 - (2.0 * x2))))) - x1));
	} else if (x2 <= 3.6e-21) {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)));
	} else {
		tmp = x1 + (t_0 + (x1 + (4.0 * (x2 * ((x1 * 2.0) * x2)))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 3.0d0 * (x2 * (-2.0d0))
    if (x2 <= (-1.04d-25)) then
        tmp = x1 + (t_0 - ((4.0d0 * (x2 * (x1 * (3.0d0 - (2.0d0 * x2))))) - x1))
    else if (x2 <= 3.6d-21) then
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * ((4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0))) - 2.0d0)))
    else
        tmp = x1 + (t_0 + (x1 + (4.0d0 * (x2 * ((x1 * 2.0d0) * x2)))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = 3.0 * (x2 * -2.0);
	double tmp;
	if (x2 <= -1.04e-25) {
		tmp = x1 + (t_0 - ((4.0 * (x2 * (x1 * (3.0 - (2.0 * x2))))) - x1));
	} else if (x2 <= 3.6e-21) {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)));
	} else {
		tmp = x1 + (t_0 + (x1 + (4.0 * (x2 * ((x1 * 2.0) * x2)))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = 3.0 * (x2 * -2.0)
	tmp = 0
	if x2 <= -1.04e-25:
		tmp = x1 + (t_0 - ((4.0 * (x2 * (x1 * (3.0 - (2.0 * x2))))) - x1))
	elif x2 <= 3.6e-21:
		tmp = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)))
	else:
		tmp = x1 + (t_0 + (x1 + (4.0 * (x2 * ((x1 * 2.0) * x2)))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(3.0 * Float64(x2 * -2.0))
	tmp = 0.0
	if (x2 <= -1.04e-25)
		tmp = Float64(x1 + Float64(t_0 - Float64(Float64(4.0 * Float64(x2 * Float64(x1 * Float64(3.0 - Float64(2.0 * x2))))) - x1)));
	elseif (x2 <= 3.6e-21)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0))) - 2.0))));
	else
		tmp = Float64(x1 + Float64(t_0 + Float64(x1 + Float64(4.0 * Float64(x2 * Float64(Float64(x1 * 2.0) * x2))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = 3.0 * (x2 * -2.0);
	tmp = 0.0;
	if (x2 <= -1.04e-25)
		tmp = x1 + (t_0 - ((4.0 * (x2 * (x1 * (3.0 - (2.0 * x2))))) - x1));
	elseif (x2 <= 3.6e-21)
		tmp = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)));
	else
		tmp = x1 + (t_0 + (x1 + (4.0 * (x2 * ((x1 * 2.0) * x2)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(3.0 * N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x2, -1.04e-25], N[(x1 + N[(t$95$0 - N[(N[(4.0 * N[(x2 * N[(x1 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x2, 3.6e-21], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(4.0 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(t$95$0 + N[(x1 + N[(4.0 * N[(x2 * N[(N[(x1 * 2.0), $MachinePrecision] * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x2 < -1.04000000000000004e-25

   1. Initial program 74.9%

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

   2. Taylor expanded in x1 around 0 56.0%

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

   3. Taylor expanded in x1 around 0 64.1%

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

      1. *-commutative 64.1%

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

   5. Simplified 64.1%

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

   if -1.04000000000000004e-25 < x2 < 3.59999999999999989e-21

   1. Initial program 72.6%

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

   2. Taylor expanded in x1 around 0 48.5%

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

   3. Taylor expanded in x1 around 0 49.9%

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

   if 3.59999999999999989e-21 < x2

   1. Initial program 67.4%

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

   2. Taylor expanded in x1 around 0 53.0%

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

   3. Taylor expanded in x1 around 0 68.7%

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

      1. *-commutative 68.7%

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

   5. Simplified 68.7%

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

   6. Taylor expanded in x2 around inf 68.7%

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

      1. *-commutative 68.7%

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

      2. associate-*l* 68.7%

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

   8. Simplified 68.7%

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

4. Final simplification 59.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq -1.04 \cdot 10^{-25}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2\right) - \left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(3 - 2 \cdot x2\right)\right)\right) - x1\right)\right)\\ \mathbf{elif}\;x2 \leq 3.6 \cdot 10^{-21}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2\right) + \left(x1 + 4 \cdot \left(x2 \cdot \left(\left(x1 \cdot 2\right) \cdot x2\right)\right)\right)\right)\\ \end{array} \]

Alternative 16: 52.2% accurate, 6.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x2 \leq -1.9 \cdot 10^{+187} \lor \neg \left(x2 \leq 3.6 \cdot 10^{+127}\right):\\ \;\;\;\;x1 + \left(9 + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 - \left(x2 \cdot \left(6 - x1 \cdot -12\right) - \left(x1 + x1 \cdot -3\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x2 -1.9e+187) (not (<= x2 3.6e+127)))
   (+ x1 (+ 9.0 (+ x1 (* 4.0 (* x2 (* x1 (- (* 2.0 x2) 3.0)))))))
   (- x1 (- (* x2 (- 6.0 (* x1 -12.0))) (+ x1 (* x1 -3.0))))))

C

double code(double x1, double x2) {
	double tmp;
	if ((x2 <= -1.9e+187) || !(x2 <= 3.6e+127)) {
		tmp = x1 + (9.0 + (x1 + (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0))))));
	} else {
		tmp = x1 - ((x2 * (6.0 - (x1 * -12.0))) - (x1 + (x1 * -3.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if ((x2 <= (-1.9d+187)) .or. (.not. (x2 <= 3.6d+127))) then
        tmp = x1 + (9.0d0 + (x1 + (4.0d0 * (x2 * (x1 * ((2.0d0 * x2) - 3.0d0))))))
    else
        tmp = x1 - ((x2 * (6.0d0 - (x1 * (-12.0d0)))) - (x1 + (x1 * (-3.0d0))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x2 <= -1.9e+187) || !(x2 <= 3.6e+127)) {
		tmp = x1 + (9.0 + (x1 + (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0))))));
	} else {
		tmp = x1 - ((x2 * (6.0 - (x1 * -12.0))) - (x1 + (x1 * -3.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x2 <= -1.9e+187) or not (x2 <= 3.6e+127):
		tmp = x1 + (9.0 + (x1 + (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0))))))
	else:
		tmp = x1 - ((x2 * (6.0 - (x1 * -12.0))) - (x1 + (x1 * -3.0)))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x2 <= -1.9e+187) || !(x2 <= 3.6e+127))
		tmp = Float64(x1 + Float64(9.0 + Float64(x1 + Float64(4.0 * Float64(x2 * Float64(x1 * Float64(Float64(2.0 * x2) - 3.0)))))));
	else
		tmp = Float64(x1 - Float64(Float64(x2 * Float64(6.0 - Float64(x1 * -12.0))) - Float64(x1 + Float64(x1 * -3.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x2 <= -1.9e+187) || ~((x2 <= 3.6e+127)))
		tmp = x1 + (9.0 + (x1 + (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0))))));
	else
		tmp = x1 - ((x2 * (6.0 - (x1 * -12.0))) - (x1 + (x1 * -3.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x2, -1.9e+187], N[Not[LessEqual[x2, 3.6e+127]], $MachinePrecision]], N[(x1 + N[(9.0 + 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[(x2 * N[(6.0 - N[(x1 * -12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x1 + N[(x1 * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x2 < -1.9e187 or 3.59999999999999979e127 < x2

   1. Initial program 64.9%

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

   2. Taylor expanded in x1 around 0 57.1%

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

   3. Taylor expanded in x1 around inf 72.0%

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

   if -1.9e187 < x2 < 3.59999999999999979e127

   1. Initial program 74.0%

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

   2. Taylor expanded in x1 around 0 50.4%

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

   3. Taylor expanded in x1 around 0 53.0%

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

      1. +-commutative 53.0%

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

      2. *-commutative 53.0%

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

      3. fma-def 53.0%

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

      4. *-commutative 53.0%

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

   5. Simplified 53.0%

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

   6. Taylor expanded in x2 around 0 49.4%

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

4. Final simplification 54.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq -1.9 \cdot 10^{+187} \lor \neg \left(x2 \leq 3.6 \cdot 10^{+127}\right):\\ \;\;\;\;x1 + \left(9 + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 - \left(x2 \cdot \left(6 - x1 \cdot -12\right) - \left(x1 + x1 \cdot -3\right)\right)\\ \end{array} \]

Alternative 17: 53.2% accurate, 6.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x2 \leq -3.2 \cdot 10^{+187}:\\ \;\;\;\;x1 + \left(9 + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x2 \leq 9.8 \cdot 10^{-20}:\\ \;\;\;\;x1 - \left(x2 \cdot \left(6 - x1 \cdot -12\right) - \left(x1 + x1 \cdot -3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 - x1 \cdot \left(4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right) - 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x2 -3.2e+187)
   (+ x1 (+ 9.0 (+ x1 (* 4.0 (* x2 (* x1 (- (* 2.0 x2) 3.0)))))))
   (if (<= x2 9.8e-20)
     (- x1 (- (* x2 (- 6.0 (* x1 -12.0))) (+ x1 (* x1 -3.0))))
     (- (* x2 -6.0) (* x1 (- (* 4.0 (* x2 (- 3.0 (* 2.0 x2)))) 2.0))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x2 <= -3.2e+187) {
		tmp = x1 + (9.0 + (x1 + (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0))))));
	} else if (x2 <= 9.8e-20) {
		tmp = x1 - ((x2 * (6.0 - (x1 * -12.0))) - (x1 + (x1 * -3.0)));
	} else {
		tmp = (x2 * -6.0) - (x1 * ((4.0 * (x2 * (3.0 - (2.0 * x2)))) - 2.0));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x2 <= (-3.2d+187)) then
        tmp = x1 + (9.0d0 + (x1 + (4.0d0 * (x2 * (x1 * ((2.0d0 * x2) - 3.0d0))))))
    else if (x2 <= 9.8d-20) then
        tmp = x1 - ((x2 * (6.0d0 - (x1 * (-12.0d0)))) - (x1 + (x1 * (-3.0d0))))
    else
        tmp = (x2 * (-6.0d0)) - (x1 * ((4.0d0 * (x2 * (3.0d0 - (2.0d0 * x2)))) - 2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x2 <= -3.2e+187) {
		tmp = x1 + (9.0 + (x1 + (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0))))));
	} else if (x2 <= 9.8e-20) {
		tmp = x1 - ((x2 * (6.0 - (x1 * -12.0))) - (x1 + (x1 * -3.0)));
	} else {
		tmp = (x2 * -6.0) - (x1 * ((4.0 * (x2 * (3.0 - (2.0 * x2)))) - 2.0));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x2 <= -3.2e+187:
		tmp = x1 + (9.0 + (x1 + (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0))))))
	elif x2 <= 9.8e-20:
		tmp = x1 - ((x2 * (6.0 - (x1 * -12.0))) - (x1 + (x1 * -3.0)))
	else:
		tmp = (x2 * -6.0) - (x1 * ((4.0 * (x2 * (3.0 - (2.0 * x2)))) - 2.0))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x2 <= -3.2e+187)
		tmp = Float64(x1 + Float64(9.0 + Float64(x1 + Float64(4.0 * Float64(x2 * Float64(x1 * Float64(Float64(2.0 * x2) - 3.0)))))));
	elseif (x2 <= 9.8e-20)
		tmp = Float64(x1 - Float64(Float64(x2 * Float64(6.0 - Float64(x1 * -12.0))) - Float64(x1 + Float64(x1 * -3.0))));
	else
		tmp = Float64(Float64(x2 * -6.0) - Float64(x1 * Float64(Float64(4.0 * Float64(x2 * Float64(3.0 - Float64(2.0 * x2)))) - 2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x2 <= -3.2e+187)
		tmp = x1 + (9.0 + (x1 + (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0))))));
	elseif (x2 <= 9.8e-20)
		tmp = x1 - ((x2 * (6.0 - (x1 * -12.0))) - (x1 + (x1 * -3.0)));
	else
		tmp = (x2 * -6.0) - (x1 * ((4.0 * (x2 * (3.0 - (2.0 * x2)))) - 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x2, -3.2e+187], N[(x1 + N[(9.0 + 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[x2, 9.8e-20], N[(x1 - N[(N[(x2 * N[(6.0 - N[(x1 * -12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x1 + N[(x1 * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x2 * -6.0), $MachinePrecision] - N[(x1 * N[(N[(4.0 * N[(x2 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x2 < -3.19999999999999993e187

   1. Initial program 68.0%

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

   2. Taylor expanded in x1 around 0 64.0%

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

   3. Taylor expanded in x1 around inf 75.7%

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

   if -3.19999999999999993e187 < x2 < 9.8000000000000003e-20

   1. Initial program 74.4%

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

   2. Taylor expanded in x1 around 0 49.6%

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

   3. Taylor expanded in x1 around 0 51.4%

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

      1. +-commutative 51.4%

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

      2. *-commutative 51.4%

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

      3. fma-def 51.5%

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

      4. *-commutative 51.5%

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

   5. Simplified 51.5%

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

   6. Taylor expanded in x2 around 0 49.3%

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

   if 9.8000000000000003e-20 < x2

   1. Initial program 67.4%

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

   2. Taylor expanded in x1 around 0 53.0%

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

   3. Taylor expanded in x1 around 0 68.7%

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

      1. *-commutative 68.7%

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

   5. Simplified 68.7%

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

   6. Taylor expanded in x1 around 0 60.7%

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

4. Final simplification 55.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq -3.2 \cdot 10^{+187}:\\ \;\;\;\;x1 + \left(9 + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x2 \leq 9.8 \cdot 10^{-20}:\\ \;\;\;\;x1 - \left(x2 \cdot \left(6 - x1 \cdot -12\right) - \left(x1 + x1 \cdot -3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 - x1 \cdot \left(4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right) - 2\right)\\ \end{array} \]

Alternative 18: 51.6% accurate, 6.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -9.5 \cdot 10^{+62}:\\ \;\;\;\;x1 \cdot \left(-1 + x2 \cdot -12\right)\\ \mathbf{elif}\;x1 \leq -2.5 \cdot 10^{-30}:\\ \;\;\;\;x1 + x1 \cdot \left(x2 \cdot \left(x2 \cdot 8\right)\right)\\ \mathbf{elif}\;x1 \leq 1.7 \cdot 10^{-5}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + \left(x1 + x1 \cdot -3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot \left(2 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -9.5e+62)
   (* x1 (+ -1.0 (* x2 -12.0)))
   (if (<= x1 -2.5e-30)
     (+ x1 (* x1 (* x2 (* x2 8.0))))
     (if (<= x1 1.7e-5)
       (+ x1 (+ (* x2 -6.0) (+ x1 (* x1 -3.0))))
       (* x1 (+ 2.0 (* 4.0 (* x2 (- (* 2.0 x2) 3.0)))))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -9.5e+62) {
		tmp = x1 * (-1.0 + (x2 * -12.0));
	} else if (x1 <= -2.5e-30) {
		tmp = x1 + (x1 * (x2 * (x2 * 8.0)));
	} else if (x1 <= 1.7e-5) {
		tmp = x1 + ((x2 * -6.0) + (x1 + (x1 * -3.0)));
	} else {
		tmp = x1 * (2.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x1 <= (-9.5d+62)) then
        tmp = x1 * ((-1.0d0) + (x2 * (-12.0d0)))
    else if (x1 <= (-2.5d-30)) then
        tmp = x1 + (x1 * (x2 * (x2 * 8.0d0)))
    else if (x1 <= 1.7d-5) then
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 + (x1 * (-3.0d0))))
    else
        tmp = x1 * (2.0d0 + (4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= -9.5e+62) {
		tmp = x1 * (-1.0 + (x2 * -12.0));
	} else if (x1 <= -2.5e-30) {
		tmp = x1 + (x1 * (x2 * (x2 * 8.0)));
	} else if (x1 <= 1.7e-5) {
		tmp = x1 + ((x2 * -6.0) + (x1 + (x1 * -3.0)));
	} else {
		tmp = x1 * (2.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0))));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -9.5e+62:
		tmp = x1 * (-1.0 + (x2 * -12.0))
	elif x1 <= -2.5e-30:
		tmp = x1 + (x1 * (x2 * (x2 * 8.0)))
	elif x1 <= 1.7e-5:
		tmp = x1 + ((x2 * -6.0) + (x1 + (x1 * -3.0)))
	else:
		tmp = x1 * (2.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0))))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -9.5e+62)
		tmp = Float64(x1 * Float64(-1.0 + Float64(x2 * -12.0)));
	elseif (x1 <= -2.5e-30)
		tmp = Float64(x1 + Float64(x1 * Float64(x2 * Float64(x2 * 8.0))));
	elseif (x1 <= 1.7e-5)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 + Float64(x1 * -3.0))));
	else
		tmp = Float64(x1 * Float64(2.0 + Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -9.5e+62)
		tmp = x1 * (-1.0 + (x2 * -12.0));
	elseif (x1 <= -2.5e-30)
		tmp = x1 + (x1 * (x2 * (x2 * 8.0)));
	elseif (x1 <= 1.7e-5)
		tmp = x1 + ((x2 * -6.0) + (x1 + (x1 * -3.0)));
	else
		tmp = x1 * (2.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -9.5e+62], N[(x1 * N[(-1.0 + N[(x2 * -12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -2.5e-30], N[(x1 + N[(x1 * N[(x2 * N[(x2 * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.7e-5], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 + N[(x1 * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 * N[(2.0 + N[(4.0 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -9.5000000000000003e62

   1. Initial program 22.1%

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

   2. Taylor expanded in x1 around 0 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 3.3%

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

      1. +-commutative 3.3%

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

      2. *-commutative 3.3%

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

      3. fma-def 3.3%

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

      4. *-commutative 3.3%

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

   5. Simplified 3.3%

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

   6. Taylor expanded in x2 around 0 16.6%

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

   7. Taylor expanded in x1 around inf 16.6%

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

   if -9.5000000000000003e62 < x1 < -2.49999999999999986e-30

   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 0 59.7%

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

   3. Taylor expanded in x2 around inf 47.9%

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

      1. associate-*r* 47.9%

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

      2. *-commutative 47.9%

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

      3. unpow2 47.9%

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

      4. associate-*r* 47.9%

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

      5. *-commutative 47.9%

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

   5. Simplified 47.9%

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

   if -2.49999999999999986e-30 < x1 < 1.7e-5

   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 99.1%

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

   3. Taylor expanded in x1 around 0 98.9%

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

      1. +-commutative 98.9%

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

      2. *-commutative 98.9%

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

      3. fma-def 98.9%

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

      4. *-commutative 98.9%

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

   5. Simplified 98.9%

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

   6. Taylor expanded in x2 around 0 78.4%

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

   7. Taylor expanded in x1 around 0 78.4%

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

      1. *-commutative 78.4%

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

   9. Simplified 78.4%

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

   if 1.7e-5 < x1

   1. Initial program 55.8%

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

   2. Taylor expanded in x1 around 0 7.4%

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

   3. Taylor expanded in x1 around 0 34.7%

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

      1. *-commutative 34.7%

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

   5. Simplified 34.7%

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

   6. Taylor expanded in x1 around inf 34.7%

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

4. Final simplification 52.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -9.5 \cdot 10^{+62}:\\ \;\;\;\;x1 \cdot \left(-1 + x2 \cdot -12\right)\\ \mathbf{elif}\;x1 \leq -2.5 \cdot 10^{-30}:\\ \;\;\;\;x1 + x1 \cdot \left(x2 \cdot \left(x2 \cdot 8\right)\right)\\ \mathbf{elif}\;x1 \leq 1.7 \cdot 10^{-5}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + \left(x1 + x1 \cdot -3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot \left(2 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ \end{array} \]

Alternative 19: 50.2% accurate, 6.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x2 \leq -1.16 \cdot 10^{+191} \lor \neg \left(x2 \leq 7.5 \cdot 10^{+127}\right):\\ \;\;\;\;x1 + x1 \cdot \left(x2 \cdot \left(x2 \cdot 8\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 - \left(x2 \cdot \left(6 - x1 \cdot -12\right) - \left(x1 + x1 \cdot -3\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x2 -1.16e+191) (not (<= x2 7.5e+127)))
   (+ x1 (* x1 (* x2 (* x2 8.0))))
   (- x1 (- (* x2 (- 6.0 (* x1 -12.0))) (+ x1 (* x1 -3.0))))))

C

double code(double x1, double x2) {
	double tmp;
	if ((x2 <= -1.16e+191) || !(x2 <= 7.5e+127)) {
		tmp = x1 + (x1 * (x2 * (x2 * 8.0)));
	} else {
		tmp = x1 - ((x2 * (6.0 - (x1 * -12.0))) - (x1 + (x1 * -3.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if ((x2 <= (-1.16d+191)) .or. (.not. (x2 <= 7.5d+127))) then
        tmp = x1 + (x1 * (x2 * (x2 * 8.0d0)))
    else
        tmp = x1 - ((x2 * (6.0d0 - (x1 * (-12.0d0)))) - (x1 + (x1 * (-3.0d0))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x2 <= -1.16e+191) || !(x2 <= 7.5e+127)) {
		tmp = x1 + (x1 * (x2 * (x2 * 8.0)));
	} else {
		tmp = x1 - ((x2 * (6.0 - (x1 * -12.0))) - (x1 + (x1 * -3.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x2 <= -1.16e+191) or not (x2 <= 7.5e+127):
		tmp = x1 + (x1 * (x2 * (x2 * 8.0)))
	else:
		tmp = x1 - ((x2 * (6.0 - (x1 * -12.0))) - (x1 + (x1 * -3.0)))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x2 <= -1.16e+191) || !(x2 <= 7.5e+127))
		tmp = Float64(x1 + Float64(x1 * Float64(x2 * Float64(x2 * 8.0))));
	else
		tmp = Float64(x1 - Float64(Float64(x2 * Float64(6.0 - Float64(x1 * -12.0))) - Float64(x1 + Float64(x1 * -3.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x2 <= -1.16e+191) || ~((x2 <= 7.5e+127)))
		tmp = x1 + (x1 * (x2 * (x2 * 8.0)));
	else
		tmp = x1 - ((x2 * (6.0 - (x1 * -12.0))) - (x1 + (x1 * -3.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x2, -1.16e+191], N[Not[LessEqual[x2, 7.5e+127]], $MachinePrecision]], N[(x1 + N[(x1 * N[(x2 * N[(x2 * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 - N[(N[(x2 * N[(6.0 - N[(x1 * -12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x1 + N[(x1 * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x2 < -1.15999999999999996e191 or 7.4999999999999996e127 < x2

   1. Initial program 64.3%

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

   2. Taylor expanded in x1 around 0 56.3%

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

   3. Taylor expanded in x2 around inf 62.2%

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

      1. associate-*r* 62.2%

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

      2. *-commutative 62.2%

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

      3. unpow2 62.2%

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

      4. associate-*r* 62.2%

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

      5. *-commutative 62.2%

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

   5. Simplified 62.2%

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

   if -1.15999999999999996e191 < x2 < 7.4999999999999996e127

   1. Initial program 74.1%

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

   2. Taylor expanded in x1 around 0 50.6%

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

   3. Taylor expanded in x1 around 0 53.2%

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

      1. +-commutative 53.2%

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

      2. *-commutative 53.2%

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

      3. fma-def 53.3%

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

      4. *-commutative 53.3%

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

   5. Simplified 53.3%

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

   6. Taylor expanded in x2 around 0 49.2%

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

4. Final simplification 52.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq -1.16 \cdot 10^{+191} \lor \neg \left(x2 \leq 7.5 \cdot 10^{+127}\right):\\ \;\;\;\;x1 + x1 \cdot \left(x2 \cdot \left(x2 \cdot 8\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 - \left(x2 \cdot \left(6 - x1 \cdot -12\right) - \left(x1 + x1 \cdot -3\right)\right)\\ \end{array} \]

Alternative 20: 42.6% accurate, 7.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 + x1 \cdot \left(x2 \cdot \left(x2 \cdot 8\right)\right)\\ t_1 := x2 \cdot \left(x1 \cdot -12 - 6\right)\\ \mathbf{if}\;x2 \leq -1.6 \cdot 10^{+189}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x2 \leq -7 \cdot 10^{-68}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x2 \leq 5 \cdot 10^{-92}:\\ \;\;\;\;x1 \cdot \left(-1 + x2 \cdot -12\right)\\ \mathbf{elif}\;x2 \leq 1.85 \cdot 10^{+127}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ x1 (* x1 (* x2 (* x2 8.0)))))
        (t_1 (* x2 (- (* x1 -12.0) 6.0))))
   (if (<= x2 -1.6e+189)
     t_0
     (if (<= x2 -7e-68)
       t_1
       (if (<= x2 5e-92)
         (* x1 (+ -1.0 (* x2 -12.0)))
         (if (<= x2 1.85e+127) t_1 t_0))))))

C

double code(double x1, double x2) {
	double t_0 = x1 + (x1 * (x2 * (x2 * 8.0)));
	double t_1 = x2 * ((x1 * -12.0) - 6.0);
	double tmp;
	if (x2 <= -1.6e+189) {
		tmp = t_0;
	} else if (x2 <= -7e-68) {
		tmp = t_1;
	} else if (x2 <= 5e-92) {
		tmp = x1 * (-1.0 + (x2 * -12.0));
	} else if (x2 <= 1.85e+127) {
		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 + (x1 * (x2 * (x2 * 8.0d0)))
    t_1 = x2 * ((x1 * (-12.0d0)) - 6.0d0)
    if (x2 <= (-1.6d+189)) then
        tmp = t_0
    else if (x2 <= (-7d-68)) then
        tmp = t_1
    else if (x2 <= 5d-92) then
        tmp = x1 * ((-1.0d0) + (x2 * (-12.0d0)))
    else if (x2 <= 1.85d+127) 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 + (x1 * (x2 * (x2 * 8.0)));
	double t_1 = x2 * ((x1 * -12.0) - 6.0);
	double tmp;
	if (x2 <= -1.6e+189) {
		tmp = t_0;
	} else if (x2 <= -7e-68) {
		tmp = t_1;
	} else if (x2 <= 5e-92) {
		tmp = x1 * (-1.0 + (x2 * -12.0));
	} else if (x2 <= 1.85e+127) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 + (x1 * (x2 * (x2 * 8.0)))
	t_1 = x2 * ((x1 * -12.0) - 6.0)
	tmp = 0
	if x2 <= -1.6e+189:
		tmp = t_0
	elif x2 <= -7e-68:
		tmp = t_1
	elif x2 <= 5e-92:
		tmp = x1 * (-1.0 + (x2 * -12.0))
	elif x2 <= 1.85e+127:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 + Float64(x1 * Float64(x2 * Float64(x2 * 8.0))))
	t_1 = Float64(x2 * Float64(Float64(x1 * -12.0) - 6.0))
	tmp = 0.0
	if (x2 <= -1.6e+189)
		tmp = t_0;
	elseif (x2 <= -7e-68)
		tmp = t_1;
	elseif (x2 <= 5e-92)
		tmp = Float64(x1 * Float64(-1.0 + Float64(x2 * -12.0)));
	elseif (x2 <= 1.85e+127)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 + (x1 * (x2 * (x2 * 8.0)));
	t_1 = x2 * ((x1 * -12.0) - 6.0);
	tmp = 0.0;
	if (x2 <= -1.6e+189)
		tmp = t_0;
	elseif (x2 <= -7e-68)
		tmp = t_1;
	elseif (x2 <= 5e-92)
		tmp = x1 * (-1.0 + (x2 * -12.0));
	elseif (x2 <= 1.85e+127)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 + N[(x1 * N[(x2 * N[(x2 * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x2 * N[(N[(x1 * -12.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x2, -1.6e+189], t$95$0, If[LessEqual[x2, -7e-68], t$95$1, If[LessEqual[x2, 5e-92], N[(x1 * N[(-1.0 + N[(x2 * -12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x2, 1.85e+127], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if x2 < -1.6e189 or 1.8499999999999999e127 < x2

   1. Initial program 64.3%

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

   2. Taylor expanded in x1 around 0 56.3%

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

   3. Taylor expanded in x2 around inf 62.2%

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

      1. associate-*r* 62.2%

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

      2. *-commutative 62.2%

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

      3. unpow2 62.2%

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

      4. associate-*r* 62.2%

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

      5. *-commutative 62.2%

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

   5. Simplified 62.2%

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

   if -1.6e189 < x2 < -7.00000000000000026e-68 or 5.00000000000000011e-92 < x2 < 1.8499999999999999e127

   1. Initial program 76.3%

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

   2. Taylor expanded in x1 around 0 53.7%

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

   3. Taylor expanded in x1 around 0 57.4%

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

      1. +-commutative 57.4%

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

      2. *-commutative 57.4%

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

      3. fma-def 57.4%

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

      4. *-commutative 57.4%

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

   5. Simplified 57.4%

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

   6. Taylor expanded in x2 around 0 50.2%

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

   7. Taylor expanded in x2 around inf 49.2%

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

   if -7.00000000000000026e-68 < x2 < 5.00000000000000011e-92

   1. Initial program 71.3%

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

   2. Taylor expanded in x1 around 0 46.6%

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

   3. Taylor expanded in x1 around 0 47.9%

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

      1. +-commutative 47.9%

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

      2. *-commutative 47.9%

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

      3. fma-def 47.9%

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

      4. *-commutative 47.9%

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

   5. Simplified 47.9%

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

   6. Taylor expanded in x2 around 0 47.9%

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

   7. Taylor expanded in x1 around inf 34.3%

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

4. Final simplification 47.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq -1.6 \cdot 10^{+189}:\\ \;\;\;\;x1 + x1 \cdot \left(x2 \cdot \left(x2 \cdot 8\right)\right)\\ \mathbf{elif}\;x2 \leq -7 \cdot 10^{-68}:\\ \;\;\;\;x2 \cdot \left(x1 \cdot -12 - 6\right)\\ \mathbf{elif}\;x2 \leq 5 \cdot 10^{-92}:\\ \;\;\;\;x1 \cdot \left(-1 + x2 \cdot -12\right)\\ \mathbf{elif}\;x2 \leq 1.85 \cdot 10^{+127}:\\ \;\;\;\;x2 \cdot \left(x1 \cdot -12 - 6\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot \left(x2 \cdot \left(x2 \cdot 8\right)\right)\\ \end{array} \]

Alternative 21: 51.6% accurate, 7.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -8.8 \cdot 10^{+62}:\\ \;\;\;\;x1 \cdot \left(-1 + x2 \cdot -12\right)\\ \mathbf{elif}\;x1 \leq -3.4 \cdot 10^{-30} \lor \neg \left(x1 \leq 1.7 \cdot 10^{-5}\right):\\ \;\;\;\;x1 + x1 \cdot \left(x2 \cdot \left(x2 \cdot 8\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + \left(x1 + x1 \cdot -3\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -8.8e+62)
   (* x1 (+ -1.0 (* x2 -12.0)))
   (if (or (<= x1 -3.4e-30) (not (<= x1 1.7e-5)))
     (+ x1 (* x1 (* x2 (* x2 8.0))))
     (+ x1 (+ (* x2 -6.0) (+ x1 (* x1 -3.0)))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -8.8e+62) {
		tmp = x1 * (-1.0 + (x2 * -12.0));
	} else if ((x1 <= -3.4e-30) || !(x1 <= 1.7e-5)) {
		tmp = x1 + (x1 * (x2 * (x2 * 8.0)));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 + (x1 * -3.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x1 <= (-8.8d+62)) then
        tmp = x1 * ((-1.0d0) + (x2 * (-12.0d0)))
    else if ((x1 <= (-3.4d-30)) .or. (.not. (x1 <= 1.7d-5))) then
        tmp = x1 + (x1 * (x2 * (x2 * 8.0d0)))
    else
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 + (x1 * (-3.0d0))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= -8.8e+62) {
		tmp = x1 * (-1.0 + (x2 * -12.0));
	} else if ((x1 <= -3.4e-30) || !(x1 <= 1.7e-5)) {
		tmp = x1 + (x1 * (x2 * (x2 * 8.0)));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 + (x1 * -3.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -8.8e+62:
		tmp = x1 * (-1.0 + (x2 * -12.0))
	elif (x1 <= -3.4e-30) or not (x1 <= 1.7e-5):
		tmp = x1 + (x1 * (x2 * (x2 * 8.0)))
	else:
		tmp = x1 + ((x2 * -6.0) + (x1 + (x1 * -3.0)))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -8.8e+62)
		tmp = Float64(x1 * Float64(-1.0 + Float64(x2 * -12.0)));
	elseif ((x1 <= -3.4e-30) || !(x1 <= 1.7e-5))
		tmp = Float64(x1 + Float64(x1 * Float64(x2 * Float64(x2 * 8.0))));
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 + Float64(x1 * -3.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -8.8e+62)
		tmp = x1 * (-1.0 + (x2 * -12.0));
	elseif ((x1 <= -3.4e-30) || ~((x1 <= 1.7e-5)))
		tmp = x1 + (x1 * (x2 * (x2 * 8.0)));
	else
		tmp = x1 + ((x2 * -6.0) + (x1 + (x1 * -3.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -8.8e+62], N[(x1 * N[(-1.0 + N[(x2 * -12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x1, -3.4e-30], N[Not[LessEqual[x1, 1.7e-5]], $MachinePrecision]], N[(x1 + N[(x1 * N[(x2 * N[(x2 * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 + N[(x1 * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -8.80000000000000058e62

   1. Initial program 22.1%

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

   2. Taylor expanded in x1 around 0 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 3.3%

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

      1. +-commutative 3.3%

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

      2. *-commutative 3.3%

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

      3. fma-def 3.3%

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

      4. *-commutative 3.3%

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

   5. Simplified 3.3%

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

   6. Taylor expanded in x2 around 0 16.6%

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

   7. Taylor expanded in x1 around inf 16.6%

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

   if -8.80000000000000058e62 < x1 < -3.4000000000000003e-30 or 1.7e-5 < x1

   1. Initial program 64.7%

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

   2. Taylor expanded in x1 around 0 18.1%

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

   3. Taylor expanded in x2 around inf 37.4%

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

      1. associate-*r* 37.4%

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

      2. *-commutative 37.4%

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

      3. unpow2 37.4%

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

      4. associate-*r* 37.4%

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

      5. *-commutative 37.4%

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

   5. Simplified 37.4%

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

   if -3.4000000000000003e-30 < x1 < 1.7e-5

   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 99.1%

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

   3. Taylor expanded in x1 around 0 98.9%

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

      1. +-commutative 98.9%

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

      2. *-commutative 98.9%

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

      3. fma-def 98.9%

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

      4. *-commutative 98.9%

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

   5. Simplified 98.9%

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

   6. Taylor expanded in x2 around 0 78.4%

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

   7. Taylor expanded in x1 around 0 78.4%

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

      1. *-commutative 78.4%

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

   9. Simplified 78.4%

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

4. Final simplification 52.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -8.8 \cdot 10^{+62}:\\ \;\;\;\;x1 \cdot \left(-1 + x2 \cdot -12\right)\\ \mathbf{elif}\;x1 \leq -3.4 \cdot 10^{-30} \lor \neg \left(x1 \leq 1.7 \cdot 10^{-5}\right):\\ \;\;\;\;x1 + x1 \cdot \left(x2 \cdot \left(x2 \cdot 8\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + \left(x1 + x1 \cdot -3\right)\right)\\ \end{array} \]

Alternative 22: 36.2% accurate, 11.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -7.2 \cdot 10^{-84} \lor \neg \left(x1 \leq 1.15 \cdot 10^{-97}\right):\\ \;\;\;\;x1 \cdot \left(-1 + x2 \cdot -12\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x1 -7.2e-84) (not (<= x1 1.15e-97)))
   (* x1 (+ -1.0 (* x2 -12.0)))
   (* x2 -6.0)))

C

double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -7.2e-84) || !(x1 <= 1.15e-97)) {
		tmp = x1 * (-1.0 + (x2 * -12.0));
	} else {
		tmp = x2 * -6.0;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if ((x1 <= (-7.2d-84)) .or. (.not. (x1 <= 1.15d-97))) then
        tmp = x1 * ((-1.0d0) + (x2 * (-12.0d0)))
    else
        tmp = x2 * (-6.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -7.2e-84) || !(x1 <= 1.15e-97)) {
		tmp = x1 * (-1.0 + (x2 * -12.0));
	} else {
		tmp = x2 * -6.0;
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x1 <= -7.2e-84) or not (x1 <= 1.15e-97):
		tmp = x1 * (-1.0 + (x2 * -12.0))
	else:
		tmp = x2 * -6.0
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x1 <= -7.2e-84) || !(x1 <= 1.15e-97))
		tmp = Float64(x1 * Float64(-1.0 + Float64(x2 * -12.0)));
	else
		tmp = Float64(x2 * -6.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x1 <= -7.2e-84) || ~((x1 <= 1.15e-97)))
		tmp = x1 * (-1.0 + (x2 * -12.0));
	else
		tmp = x2 * -6.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x1, -7.2e-84], N[Not[LessEqual[x1, 1.15e-97]], $MachinePrecision]], N[(x1 * N[(-1.0 + N[(x2 * -12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x2 * -6.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x1 < -7.20000000000000007e-84 or 1.14999999999999997e-97 < x1

   1. Initial program 57.6%

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

   2. Taylor expanded in x1 around 0 27.5%

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

   3. Taylor expanded in x1 around 0 38.2%

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

      1. +-commutative 38.2%

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

      2. *-commutative 38.2%

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

      3. fma-def 38.2%

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

      4. *-commutative 38.2%

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

   5. Simplified 38.2%

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

   6. Taylor expanded in x2 around 0 22.2%

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

   7. Taylor expanded in x1 around inf 19.6%

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

   if -7.20000000000000007e-84 < x1 < 1.14999999999999997e-97

   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 0 99.5%

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

   3. Taylor expanded in x1 around 0 70.7%

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

      1. *-commutative 70.7%

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

   5. Simplified 70.7%

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

   6. Taylor expanded in x1 around 0 71.1%

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

4. Final simplification 37.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -7.2 \cdot 10^{-84} \lor \neg \left(x1 \leq 1.15 \cdot 10^{-97}\right):\\ \;\;\;\;x1 \cdot \left(-1 + x2 \cdot -12\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6\\ \end{array} \]

Alternative 23: 36.4% accurate, 11.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x2 \leq -1.44 \cdot 10^{-67} \lor \neg \left(x2 \leq 4.2 \cdot 10^{-92}\right):\\ \;\;\;\;x2 \cdot \left(x1 \cdot -12 - 6\right)\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot \left(-1 + x2 \cdot -12\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x2 -1.44e-67) (not (<= x2 4.2e-92)))
   (* x2 (- (* x1 -12.0) 6.0))
   (* x1 (+ -1.0 (* x2 -12.0)))))

C

double code(double x1, double x2) {
	double tmp;
	if ((x2 <= -1.44e-67) || !(x2 <= 4.2e-92)) {
		tmp = x2 * ((x1 * -12.0) - 6.0);
	} else {
		tmp = x1 * (-1.0 + (x2 * -12.0));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if ((x2 <= (-1.44d-67)) .or. (.not. (x2 <= 4.2d-92))) then
        tmp = x2 * ((x1 * (-12.0d0)) - 6.0d0)
    else
        tmp = x1 * ((-1.0d0) + (x2 * (-12.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x2 <= -1.44e-67) || !(x2 <= 4.2e-92)) {
		tmp = x2 * ((x1 * -12.0) - 6.0);
	} else {
		tmp = x1 * (-1.0 + (x2 * -12.0));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x2 <= -1.44e-67) or not (x2 <= 4.2e-92):
		tmp = x2 * ((x1 * -12.0) - 6.0)
	else:
		tmp = x1 * (-1.0 + (x2 * -12.0))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x2 <= -1.44e-67) || !(x2 <= 4.2e-92))
		tmp = Float64(x2 * Float64(Float64(x1 * -12.0) - 6.0));
	else
		tmp = Float64(x1 * Float64(-1.0 + Float64(x2 * -12.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x2 <= -1.44e-67) || ~((x2 <= 4.2e-92)))
		tmp = x2 * ((x1 * -12.0) - 6.0);
	else
		tmp = x1 * (-1.0 + (x2 * -12.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x2, -1.44e-67], N[Not[LessEqual[x2, 4.2e-92]], $MachinePrecision]], N[(x2 * N[(N[(x1 * -12.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision], N[(x1 * N[(-1.0 + N[(x2 * -12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x2 < -1.44000000000000003e-67 or 4.2e-92 < x2

   1. Initial program 72.1%

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

   2. Taylor expanded in x1 around 0 54.6%

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

   3. Taylor expanded in x1 around 0 64.7%

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

      1. +-commutative 64.7%

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

      2. *-commutative 64.7%

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

      3. fma-def 64.7%

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

      4. *-commutative 64.7%

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

   5. Simplified 64.7%

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

   6. Taylor expanded in x2 around 0 41.2%

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

   7. Taylor expanded in x2 around inf 40.6%

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

   if -1.44000000000000003e-67 < x2 < 4.2e-92

   1. Initial program 71.3%

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

   2. Taylor expanded in x1 around 0 46.6%

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

   3. Taylor expanded in x1 around 0 47.9%

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

      1. +-commutative 47.9%

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

      2. *-commutative 47.9%

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

      3. fma-def 47.9%

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

      4. *-commutative 47.9%

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

   5. Simplified 47.9%

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

   6. Taylor expanded in x2 around 0 47.9%

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

   7. Taylor expanded in x1 around inf 34.3%

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

4. Final simplification 38.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq -1.44 \cdot 10^{-67} \lor \neg \left(x2 \leq 4.2 \cdot 10^{-92}\right):\\ \;\;\;\;x2 \cdot \left(x1 \cdot -12 - 6\right)\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot \left(-1 + x2 \cdot -12\right)\\ \end{array} \]

Alternative 24: 30.3% accurate, 13.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x2 \leq -6 \cdot 10^{-68}:\\ \;\;\;\;x2 \cdot -6\\ \mathbf{elif}\;x2 \leq 2.5 \cdot 10^{-85}:\\ \;\;\;\;-x1\\ \mathbf{else}:\\ \;\;\;\;x1 + x2 \cdot -6\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x2 -6e-68)
   (* x2 -6.0)
   (if (<= x2 2.5e-85) (- x1) (+ x1 (* x2 -6.0)))))

C

double code(double x1, double x2) {
	double tmp;
	if (x2 <= -6e-68) {
		tmp = x2 * -6.0;
	} else if (x2 <= 2.5e-85) {
		tmp = -x1;
	} else {
		tmp = x1 + (x2 * -6.0);
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x2 <= (-6d-68)) then
        tmp = x2 * (-6.0d0)
    else if (x2 <= 2.5d-85) then
        tmp = -x1
    else
        tmp = x1 + (x2 * (-6.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x2 <= -6e-68) {
		tmp = x2 * -6.0;
	} else if (x2 <= 2.5e-85) {
		tmp = -x1;
	} else {
		tmp = x1 + (x2 * -6.0);
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x2 <= -6e-68:
		tmp = x2 * -6.0
	elif x2 <= 2.5e-85:
		tmp = -x1
	else:
		tmp = x1 + (x2 * -6.0)
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x2 <= -6e-68)
		tmp = Float64(x2 * -6.0);
	elseif (x2 <= 2.5e-85)
		tmp = Float64(-x1);
	else
		tmp = Float64(x1 + Float64(x2 * -6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x2 <= -6e-68)
		tmp = x2 * -6.0;
	elseif (x2 <= 2.5e-85)
		tmp = -x1;
	else
		tmp = x1 + (x2 * -6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x2, -6e-68], N[(x2 * -6.0), $MachinePrecision], If[LessEqual[x2, 2.5e-85], (-x1), N[(x1 + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x2 < -6e-68

   1. Initial program 75.1%

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

   2. Taylor expanded in x1 around 0 55.6%

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

   3. Taylor expanded in x1 around 0 35.1%

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

      1. *-commutative 35.1%

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

   5. Simplified 35.1%

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

   6. Taylor expanded in x1 around 0 35.2%

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

   if -6e-68 < x2 < 2.5000000000000001e-85

   1. Initial program 71.9%

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

   2. Taylor expanded in x1 around 0 47.8%

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

   3. Taylor expanded in x1 around 0 49.0%

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

      1. +-commutative 49.0%

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

      2. *-commutative 49.0%

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

      3. fma-def 49.0%

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

      4. *-commutative 49.0%

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

   5. Simplified 49.0%

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

   6. Taylor expanded in x2 around 0 49.0%

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

   7. Taylor expanded in x2 around 0 34.2%

      \[\leadsto \color{blue}{-3 \cdot x1 + 2 \cdot x1} \]
   8. Step-by-step derivation

      1. distribute-rgt-out 34.7%

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

      2. metadata-eval 34.7%

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

      3. *-commutative 34.7%

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

      4. neg-mul-1 34.7%

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

   9. Simplified 34.7%

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

   if 2.5000000000000001e-85 < x2

   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 52.6%

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

   3. Taylor expanded in x1 around 0 30.5%

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

      1. *-commutative 30.5%

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

   5. Simplified 30.5%

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

4. Final simplification 33.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq -6 \cdot 10^{-68}:\\ \;\;\;\;x2 \cdot -6\\ \mathbf{elif}\;x2 \leq 2.5 \cdot 10^{-85}:\\ \;\;\;\;-x1\\ \mathbf{else}:\\ \;\;\;\;x1 + x2 \cdot -6\\ \end{array} \]

Alternative 25: 30.1% accurate, 17.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x2 \leq -6 \cdot 10^{-68}:\\ \;\;\;\;x2 \cdot -6\\ \mathbf{elif}\;x2 \leq 4.2 \cdot 10^{-92}:\\ \;\;\;\;-x1\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x2 -6e-68) (* x2 -6.0) (if (<= x2 4.2e-92) (- x1) (* x2 -6.0))))

C

double code(double x1, double x2) {
	double tmp;
	if (x2 <= -6e-68) {
		tmp = x2 * -6.0;
	} else if (x2 <= 4.2e-92) {
		tmp = -x1;
	} else {
		tmp = x2 * -6.0;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x2 <= (-6d-68)) then
        tmp = x2 * (-6.0d0)
    else if (x2 <= 4.2d-92) then
        tmp = -x1
    else
        tmp = x2 * (-6.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x2 <= -6e-68) {
		tmp = x2 * -6.0;
	} else if (x2 <= 4.2e-92) {
		tmp = -x1;
	} else {
		tmp = x2 * -6.0;
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x2 <= -6e-68:
		tmp = x2 * -6.0
	elif x2 <= 4.2e-92:
		tmp = -x1
	else:
		tmp = x2 * -6.0
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x2 <= -6e-68)
		tmp = Float64(x2 * -6.0);
	elseif (x2 <= 4.2e-92)
		tmp = Float64(-x1);
	else
		tmp = Float64(x2 * -6.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x2 <= -6e-68)
		tmp = x2 * -6.0;
	elseif (x2 <= 4.2e-92)
		tmp = -x1;
	else
		tmp = x2 * -6.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x2, -6e-68], N[(x2 * -6.0), $MachinePrecision], If[LessEqual[x2, 4.2e-92], (-x1), N[(x2 * -6.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x2 < -6e-68 or 4.2e-92 < x2

   1. Initial program 72.1%

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

   2. Taylor expanded in x1 around 0 54.6%

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

   3. Taylor expanded in x1 around 0 33.0%

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

      1. *-commutative 33.0%

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

   5. Simplified 33.0%

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

   6. Taylor expanded in x1 around 0 32.7%

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

   if -6e-68 < x2 < 4.2e-92

   1. Initial program 71.3%

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

   2. Taylor expanded in x1 around 0 46.6%

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

   3. Taylor expanded in x1 around 0 47.9%

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

      1. +-commutative 47.9%

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

      2. *-commutative 47.9%

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

      3. fma-def 47.9%

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

      4. *-commutative 47.9%

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

   5. Simplified 47.9%

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

   6. Taylor expanded in x2 around 0 47.9%

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

   7. Taylor expanded in x2 around 0 33.8%

      \[\leadsto \color{blue}{-3 \cdot x1 + 2 \cdot x1} \]
   8. Step-by-step derivation

      1. distribute-rgt-out 34.3%

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

      2. metadata-eval 34.3%

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

      3. *-commutative 34.3%

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

      4. neg-mul-1 34.3%

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

   9. Simplified 34.3%

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

4. Final simplification 33.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq -6 \cdot 10^{-68}:\\ \;\;\;\;x2 \cdot -6\\ \mathbf{elif}\;x2 \leq 4.2 \cdot 10^{-92}:\\ \;\;\;\;-x1\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6\\ \end{array} \]

Alternative 26: 13.6% 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 71.8%

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

2. Taylor expanded in x1 around 0 51.9%

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

3. Taylor expanded in x1 around 0 59.0%

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

   1. +-commutative 59.0%

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

   2. *-commutative 59.0%

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

   3. fma-def 59.0%

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

   4. *-commutative 59.0%

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

5. Simplified 59.0%

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

6. Taylor expanded in x2 around 0 43.5%

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

7. Taylor expanded in x2 around 0 13.5%

   \[\leadsto \color{blue}{-3 \cdot x1 + 2 \cdot x1} \]
8. Step-by-step derivation

   1. distribute-rgt-out 13.7%

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

   2. metadata-eval 13.7%

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

   3. *-commutative 13.7%

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

   4. neg-mul-1 13.7%

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

9. Simplified 13.7%

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

10. Final simplification 13.7%

    \[\leadsto -x1 \]

Alternative 27: 3.3% accurate, 127.0× speedup

Math

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

FPCore

(FPCore (x1 x2) :precision binary64 x1)

C

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

Fortran

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

Java

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

Python

def code(x1, x2):
	return x1

Julia

function code(x1, x2)
	return x1
end

MATLAB

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

Wolfram

code[x1_, x2_] := x1

Derivation

1. Initial program 71.8%

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

2. Taylor expanded in x1 around 0 51.9%

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

3. Taylor expanded in x1 around 0 27.8%

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

   1. *-commutative 27.8%

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

5. Simplified 27.8%

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

6. Taylor expanded in x1 around inf 3.3%

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

7. Final simplification 3.3%

   \[\leadsto x1 \]

Reproduce

herbie shell --seed 2023200 
(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))))))